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 NA2521 
 
 Arch. lib. 
 
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 NA2i:21 
 S45 
 
 Arch. Lib. 
 
 129734 
 
 PERMANENT RESERVE 
 
i>^i 
 
S H AWS 
 
 CIVIL ARCHITECTURE; 
 
 BEING 
 
 A COMPLETE THEORETICAL AND PRACTICAL 
 
 SYSTEM OF BUILDING, 
 
 CONTAINING 
 
 THE FUNDAMENTAL PRINCIPLES OF THE ART, 
 
 ILLUSTRATED BY EIGHTY-TWO COPPERPLATE ENGRAVINGS. 
 
 By EDWARD SHAW, Architect. 
 
 SIXTH EDITION, REVISED AND IMPROVED. 
 
 TO WHICH AEE ADDED 
 
 TWENTY COPPERPLATE ENGRAVINGS, 
 
 ALSO, 
 
 A TREATISE ON GOTHIC ARCHITECTURE, WITH PLATES, &c 
 
 BY THOMAS W. SILLOWAY AND GEORGE M. HARDING, 
 
 AKCHITECTS. 
 
 BOSTON : 
 
 PUBLISHED BY JOHN P. JEWETT AND COMPANY 
 
 CLEVELAND, OHIO : JEWETT, PROCTOR, AND WORTHINGTON. 
 
 MDCCCLII. 
 
Entered according to act of Congress, in tlie year 1859, by 
 
 LUTHER STEVENS, 
 
 In the Clerk's Office of the District Court of the District of Massachusetts. 
 
ADYERTISEMENT 
 
 TO THE FIRST EDITION. 
 
 It is obvious that most writers on CivU Architecture have not entered into those mathematical 
 principles on which this noble art ultimately rests, and from which it derives its very existence. 
 They may rather be said to consider it merely as an art than as a science also, and are more cal- 
 culated to instruct the student in dra-\ving architectiu'al plans than to point out and elucidate 
 those imalterable rules and first principles which, however unperceived, (as Mr. Nicholson justly 
 observes,) must enter into the very essence of every plan that is correct and practicable. 
 
 The student, in the outset, should commence his inquiry by going back to the most simple 
 elements of mathematical knowledge, there to obtain the real clew to his future studies, and from 
 thence, gradually and scientifically, to proceed to more complex problems and more diversified 
 plans. On this principle is founded the superior skUl of the Grecian and Eoman artists, which 
 has, as yet, been mirivalled. 
 
 We should not content ourselves by merely drawing from their works, and then superadding 
 the invention of our ovm imagination ; but we should continually recur to the ground on which 
 they trod, and make that the criterion of all our attempts. It is principally to assist the practical 
 mechanic, as well as the student, that this work has been projected ; and, as will appear, much 
 pains have been taken to lay down the fundamental principles of architectiu'e m a clear, distinct, 
 and intelligible manner, and to apply the whole to practice by plain and obvious examples and 
 illustrations. I have endeavored to arrange the contents so as to be useful to the student, as well 
 as to all classes of operative builders. 
 
 Those workmen, therefore, Avho aspire to any degree of superiority and taste in either of these 
 branches, will be able from hence, by improving their leisure hours, in a short time to understand 
 the principles of theu- respective occupations, and to execute with taste and pleasure what they do 
 now but mechanically. 
 
 In this work is given whatever the experience of the most judicious professors has sanctioned 
 as the best mode of affecting their professional purposes, with the reasons on which that preference 
 is founded. To this are added examples both of Grecian and Roman antiquities, and remarks on 
 the beauties of each. Particular attention is paid to the theory of shadows, both from dhcct and 
 reflected light, and examples adduced of the relative degrees of light and shade on different sur- 
 faces, variously inclined to the luminary and the eye. Also, a select set of problems are di'awn 
 from Nicholson's writings, entirely new, and all ultimately connected with the subject in hand. 
 
 lJc9784 
 
4 ADVERTISEMENT. 
 
 They are disposed in methodical order, and are preceded by the necessary definitions. It is not 
 intended by this part wholly to set aside the study of Euclid and authors who have written on 
 Conic Sections. An attentive perusal of their works will always amply repay the student's 
 trouble. 
 
 When the vast importance and utility of Geometry are considered, the student will never regret 
 any pains he may take to make himself thoroughly master of every part of it. Particular atten- 
 tion has been paid to ellipses and curves — the problems relating to which will be found par- 
 ticularly useful in describing elliptical and Gothic arches, finding their joints, and describing 
 mouldings of every degree of cru'vature, under various circimistances, with Conic Sections ; also, 
 the Sections of Solids, a thorough acquaintance with them being absolutely necessary for under- 
 standing the theory and disposition of shadows, the explanation of which will be highly gratifying 
 to every scientific reader. 
 
 In view of the present taste for architectural knowledge, and the inadequacy of means to 
 
 obtain that science, arising from the costly and voluminous works on the subject, I have been 
 
 chiefly induced to compile a work of this kind. Being fully convinced of its utility, from very 
 
 arduous research into its constituent principles, from my early apprenticeship to the present 
 
 time, — having had more than twenty years' practice in the art of building, — I have brought 
 
 together the following system in a concise but intelligible manner, Avhich consists principally of 
 
 extracts from Vitruvius, Stuart, Chambers, Nicholson, and other authors of eminence. If I have 
 
 made a judicious arrangement of the several subjects, I have accomplished all I anticipated ; and 
 
 under these considerations, therefore, I submit this work to the public for their approbation and 
 
 patronage. 
 
 EDWARD SHAW. 
 
ADYEETISEMENT 
 
 TO THE SIXTH EDITION. 
 
 Being encouraged by the rapid and extensive sale of the five former editions of this work, and 
 the urgent calls made in consequence of its having been out of print for several years, I have been 
 induced by the advice of my friends to secure the valuable services of Messrs. SUloway and 
 Harding, architects of Boston, gentlemen well versed in the science they profess, to assist in 
 revising the fifth edition, and prepare additional di-awings for a sixth, which has resulted in the 
 exclusion of several of the old plates, and the substitution of twenty new ones of a character in 
 keeping with the improvements of the day, and of great practical use to the carpenter and 
 builder, among which are four plates of Gothic details selected from Pugin, one of the best of the 
 English authors on this subject. 
 
 The sixth edition, thus improved and enlarged, I now offer for the attention and patronage of 
 
 an enlightened public. 
 
 EDWARD SHAW. 
 Januaky 1, 1852. 
 
CONTENTS. 
 
 PAGE PLATE 
 
 INTRODUCTION. 9 
 
 Construction of Houses, 17 
 
 Doors and Windows, 18 
 
 Mouldings, 22 
 
 To draw Volutes, Columns, and Cornices, 22, 23 
 
 Construction of Bridges, 27 
 
 Wooden Bridges, 32 
 
 Iron Bridges, 33 
 
 Western Avenue, 34 
 
 Warren Bridge, 34 
 
 PRACTICAL GEOMETRY. 
 
 Definition of Lines and Points, 37 1 
 
 Circles, 38 2 
 
 Problems on Points and Lines 39 2, 3 
 
 Trapeziums, 43 4 
 
 CONIC SECTIONS. 
 
 Definitions, 45 5 
 
 Ellipses, 46 (i 
 
 Conjugates, 47 7 
 
 To describe Ellipses, 48 8 
 
 The Parabola, 49 9 
 
 Hyperbola 50 10 
 
 To describe a Conic Section, 51 11 
 
 Sections of Solids, 52 12 
 
 Sections of a Cone, 53 12, 13 
 
 Cycloid or Epicycloid, 56 13 
 
 Section of Planes, 56 14 
 
 Application of the Trihedral, 57 14 
 
 Principles of Projection, 59 15 
 
 Development of tlie Surfaces of Solids, 59 15 
 
 Projections of Prisms, 64 16 
 
 SHADOWS. 
 
 Efiect of Distance, 66 
 
 Seat of the Sun's Rays, 67 17 
 
 Upright Prisms, 68 18 
 
 Polygonal Ring, 69 19 
 
 Elevation of a Circular Ring, 70 19 
 
 Lines of Light and Shade on a Sphere, 71 20 
 
 PAGE PLATE 
 
 Lines of Light and Shade from the Abacus of a 
 
 Cylinder, 71 20 
 
 Light and Shade on a Prism, 72 21 
 
 ESect of do. on Mouldings, 73 22 
 
 Base and Capital, 77 23, 24 
 
 Of a Cylmdrical Recess, 78 25 
 
 A Hemisphere, 78 25 
 
 MOULDINGS. 
 
 Definitions, 79 
 
 Roman Mouldings, 80 26 
 
 Modem " 82 27 
 
 Grecian « 82 28,29 
 
 Architraves, 83 30 
 
 ORDERS. 
 
 Tuscan Order of Vitruvius, 84 31 
 
 Modern Tuscan Order, 84 32 
 
 ROMAN DORIC. 
 
 Example by Palladio, 85 33 
 
 Example from the Diocletian Baths, 86 34 
 
 Roman Doric, as approved by Chambers, 85 35 
 
 ROMAN CORINTHIAN. 
 
 Example from the Temple of Jupiter Stator, 87 36 
 
 Details of the same, 87 37 
 
 Example from the Pantheon, at Rome, 87 38 
 
 COMPOSITE ORDER. 
 
 Example from the Arch of Titus, at Rome, 87 39 
 
 Pilasters, 88 
 
 Arcades and Arches, 90 40 
 
 Pedestals, 90 41 
 
 Imposts and Bases, 92 42 
 
 Balusters and Balustrades, 93 43 
 
 GRECIAN ORDERS. 
 
 Definitions, 94 
 
 Grecian Doric, 95 
 
 Temple of Minerva, at Athens, 97 44 
 
8 
 
 CONTENTS. 
 
 PAGE PLATE 
 
 Details of the same, i^'' 45 
 
 Example from the Temple of Theseus, at Atliens,. . . 97 46 
 
 Example from the Portico of Philip, King of Macedon, 98 47 
 
 Choragic Monument of Thrasyllus, 98 48 
 
 GRECIAN IONIC. 
 
 Example from the River Hyssus 99 49 
 
 Details of the same 99 50, 51 
 
 « u 99 53 
 
 •• .. 100 53 
 
 <c « 100 54 
 
 Example from the Temple of Bacchus, 100 55 
 
 " " Miner\-a, 100 55 
 
 Polias at Athens 100 50 
 
 Grecian Architecture, 101 
 
 Choragic Monument of Lysicrates 102 57 
 
 To draw Flutes of Columns, 102 58 
 
 Bases 102 59 
 
 Entablatures 103 
 
 Designs for Cornices, 104 CO, 61 
 
 Chimney-pieces, 104 62, 63 
 
 Doors, 105 
 
 Modern Doors, 107 64 
 
 Outside Doors, 107 65 
 
 Ionic Front Door, 107 66 
 
 WINDOWS. 
 
 Plan of Windows, 110 67 
 
 Design for French Windows, 110 68 
 
 « Oriel " 110 69 
 
 Details of the same, 110 70 
 
 Elements of Foliage Ill 
 
 To draw Ornaments, Ill 71 
 
 Details from the Arch of Adrian, 112 72 
 
 Rose in the Arch of Titus, &c., 112 74, 75 
 
 Outline of Shaded Leaf, 112 76 
 
 Composition of Foliage, 112 77 
 
 Ornaments for Mouldings 112 78 
 
 Ornaments from the Arch of Titus, 113 79 
 
 Septimus Severus, 113 80 
 
 CARPENTIIY. 
 
 Floors, 113 
 
 Partitions 115 
 
 PAGE PLATK 
 
 Framing, 116 
 
 Trusses, 116 81 
 
 Plan of Floor Framing, 117 82 
 
 Roofs, 117 
 
 Method of ascertaining the Length and Backing of 
 
 Angle Rafters, 117 83 
 
 Designs for large Trussed Roofs, 118 84, 85 
 
 " Framing Domes, 118 86 
 
 STAIRS. 
 
 To find the Helinet, 122 87 
 
 Formation of the FaUing Mould, 122 88 
 
 Scrolls, 125 89, 90 
 
 Application of tlie Mould 126 91 
 
 Resting Points, 127 92 
 
 Formation of the String, 127 93 
 
 BRIDGES. 
 
 Town's Bridge 129 94 
 
 Waterloo " 133 95 
 
 Rural Villa, 134 96 
 
 Church Edifice, 134 97 
 
 GOTHIC ARCHITECTURE. 
 
 DetaUs, 129 98, 101 
 
 Dimensions of English Cathedrals, 139 
 
 BUILDING. 
 
 Mortar, 143 
 
 Masonry, 144 
 
 Stone Arches 146 102 
 
 Bricldaying, 147 
 
 Plastering, 149 
 
 Mastic Cement 151 
 
 Lathing and Plastering, 153 
 
 Slating, 157 
 
 Plumbing, 160 
 
 Painting, " 166 
 
 Tables showing Weight of different Materials, 
 
 Strength of Columns, &c., 1G8 
 
 Glossary of Architectural Terms 171 
 
 Glossary of Tcclmical Terms used by Carpenters 
 
 and Masons, 178 
 
 Rules of Work, &c., 1 84 
 
INTHODUCTION. 
 
 The term Architecture is originally derived from 
 the Greek language, in which it signifies the prin- 
 cipal handicraft, or mechanical operation ; an expres- 
 sion very applicable to the construction of habita- 
 tions for civilized men, without which few of the 
 other practical arts could be desirable, or, indeed, of 
 any value whatever. La the genial climates of the 
 interior of Asia, where human beings first appeared, 
 defence from the inclemency of the weather was 
 not an object of research. Shelter from the intense 
 rays of the sun and from the torrents of rain pecu- 
 liar to those climates ; protection from the wild beasts 
 of the field ; the necessity of privacy and complete 
 separation from then' fellow-creatm-es, — these and 
 other motives, which might easily be specified, would, 
 nevertheless, render architecture, however rude and 
 simple, one of the earliest arts of life. From the 
 Hebrew Scriptures, we learn that it had arrived at 
 considerable perfection, even under the second gen- 
 eration of manldnd ; for there we learn that Cain, 
 after the murder of his brother, withdrew from the 
 habitation of his parents, and built a city in a re- 
 mote quarter of the world. 
 
 The progress of architecture from rudeness to 
 refinement is thus related by Viti'uvius, whose cel- 
 ebrated treatise on architectm-e appeared in Italy in 
 the reign of Augustus Cfcsar, about the beginning 
 of the Christian era. His notions were formed on 
 tradition and conjecture ; for the vvTitings of Moses, 
 which contain the most ancient account of the origin 
 of the human race and of human society, were 
 either unknown, or generally disregarded, in his time 
 in Europe. 
 
 " In the fiirst times," says Vitruvius, " men lived in 
 woods and caves ; but at last, bon'owing hints from 
 the birds, which bruit their nests with equal ingenu- 
 ity and industry, they began to form huts for them- 
 selves. These huts were probably, at first, conical, 
 because that figure is of the most obvious construc- 
 
 tion, composed of trees or branches fixed in a circle 
 on the ground, and joined together in a point at the 
 top ; the whole covered with reeds, leaves, and clay. 
 Finding, however, in the course of time, this conical 
 figure inconvenient, on account of the slope of its 
 sides, the form of the hut was changed to that of a 
 cube, or of a paraUelopiped. Marking out the space 
 to be occupied by the intended structure, they fixed 
 in the ground upright trunks of trees to form the 
 sides, filling the intervals with branches, closely in- 
 terwoven, and covering the whole with clay. The 
 sides being thus completed, four long beams were 
 placed on the upright posts, which, being well joined 
 at the angles, kept the sides firm, and likewise served 
 to support the covering or roof of the building, com- 
 posed of other beams, on which were laid beds of 
 reeds, leaves, and clay. When the art of construct- 
 ing habitations was so far advanced, men bethought 
 themselves of methods of rendering their 
 not only commodious for present use, but 
 and durable. They stripped the bark and other in' 
 equalities from the trunks and branches employed in 
 the walls, raised them above the damp ground by 
 placing them on flat stones, and covered each post 
 with a flat stone, to throw oft' the rain. The spaces 
 bettt'cen the ends of the joists were closed with clay, 
 and the ends of the joists themselves were covered 
 with thin boards, cut in the form of what are called 
 triglijphs. The position of the roofs was also al- 
 tered. Being flat, they were ill calculated for throw- 
 ing off" the rain ; they were therefore raised up in 
 the middle, so as, with the horizontal beams con- 
 necting the uprights of the walls, to form a triangular 
 pediment or gable. From these simple elements, 
 architecture took its beginning ; for when wood was 
 found inconvenient for constructing dm'able dwell- 
 ings, and men set themselves to erect more solid and 
 extensive buildings of clay dried in the sun, or stone, 
 they still imitated the forms of those parts which 
 
 dwellings 
 elegant 
 
 0. H. HrLL LfBRARY 
 
 Ndf th Ciroiina State College 
 
10 
 
 INTRODUCTION. 
 
 necessity had originally introduced. The upright 
 posts, with the flat stones under and above them, 
 were converted into columns with their bases and 
 capitals ; the beams, rafters, and layers of materials 
 composing the roof were gradually improved into 
 architraves, friezes, triglyphs, cornices, and the other 
 ornamental parts of modern architecture." So far 
 Vitruvius. 
 
 It may be further remarked, that in many coun- 
 tries, among the rudest tribes of men, excavations 
 and fissures of rocks, hollows of trees, and caves of 
 the earth have served as habitations. Travellers in- 
 form us of a tree growing in Africa, the hollow of 
 which affords a habitation for thirty negro families, 
 which is said to be the largest tree in the world. 
 They also inform us of a subterraneous city or cave, 
 occupied by Moors, in which there are several hun- 
 dred inhabitants. Armstrong, in his "Journal of 
 Travels in the seat of war between Russia and Tur- 
 key," has the following observations : " The Geor- 
 gian or Tartar dwellings are seldom to be found 
 above ground. The tops are covered with beams of 
 wood, branches of trees, and, above all, with a coat 
 of earth, which make them level with the ground. 
 The natives are frequently disturbed, when sitting 
 around the fire, by the leg of some unfortunate cow 
 or camel making its appearance down the chimney ; 
 and it is not uncommon for the lambs to fall through, 
 and spoil whatever may happen to be cooking." 
 But among a civilized people, the desire of seeking 
 for more agreeable habitations must be soon felt. 
 The nature of the climate and the materials which it 
 more readily afforded regulated, in a great degree, 
 the construction of the first buildings in which men 
 sheltered themselves. According to Diodorus 8icu- 
 lus, the first buildings of Palestine were of reeds and 
 canes interwoven, and so compact as not to admit of 
 the rain and wind. Wood appears to be a material 
 so proper for building, and so easily wrought, that 
 men would, in all ages, employ it for these purposes, 
 in places where it could be easily procured. The 
 branches of trees, stuck in the ground and rudely 
 interwoven, formed a material for constructing them. 
 It is probable that this method of setting trees on 
 end, and bindhig them together at the top and bot- 
 tom, first gave rise to the idea of base and capital of 
 columns. When these branches were daubed with 
 clay, and covered over with leaves and turf, they 
 presented a model of those cabins, in which, accord- 
 ing to Vitruvius, the earliest tribes of men were 
 accustomed to dwell. At first, before men became 
 acquainted witli edge tools of iron, trees were felled 
 by means of fire, or by axes made of -sharp stones. 
 They undermined the trees by little at a time, by 
 continuing a fire at their roots ; and by the same 
 means they could divide a tree into the requisite 
 length. By degrees, however, tools for cutting 
 and smoothing wood were invented. The tools for 
 
 smoothing were at first nothing more than sharp 
 stones, sufficiently hard and free from brittleness. 
 Some of our North American Indians make use of 
 the same kind of tools at the present time. " The 
 use of bricks or masses of clay formed in moulds 
 and dried in the sun, or baked in stoves, as the 
 materials of buildings, is of very great antiquity, 
 and is a sufficiently obvious invention." According 
 to Moses, the tower of Babel was built of bricks : 
 " Go to, let us make bricks, and burn them thor- 
 oughly : and they had brick for stone, and slime had 
 they for mortar." (Gen. xi. 3.) Pliny informs us, 
 that in the most remote ages of the Egyptians they 
 made iise of bricks for building their houses, and 
 tiles for covering them. To employ stones for the 
 same purpose was very natiural, where they were 
 abundant, and found in masses sufficient to be 
 removed by manual dexterity. 
 
 Ai'chitccture is arranged in different orders and 
 styles, according to the nations by whom, or the 
 country in which, it was originally employed, such 
 as the Grecian, the Roman, the Saxon, the Norman, 
 the Saracenic or Arabian, the Gothic, (kc. The 
 Grecian architecture is divided into the Doric, the 
 Ionic, and the Corinthian, so named fjom the invent- 
 ors, or from those parts of Greece, or of the Grecian 
 colonies in Asia Minor, where each Idnd first ap- 
 peared. Roman or Italian architecture was divided 
 into the Tuscan and the Composite — the first being 
 employed, as it is said, by the ancient inhabitants of 
 Tuscany, and the last being a later improvement 
 adopted by the Romans, compounded of the two 
 Grecian orders, the Ionic and the Corinthian. 
 
 When architecture was in its glory in ancient 
 Greece, the Ionic was the favorite order, as being 
 the most graceful, light, and elegant. Of this order 
 were the temple of the Delphic oracle, the temple of 
 Apollo, at JNIiletus, and the temple of Diana, at 
 Ephesus. 
 
 " The Ionic, then, with decent matron grace 
 Her airy pillar heaved." 
 
 After the Ionic, the Corinthian was introduced, 
 in which in attempting greater perfection, they devi- 
 ated from the true simplicity of nature. It marked 
 age of luxury and magnificence, when pomp and 
 splendor had become the predominant passion, but 
 had not yet extinguished the taste for the sublime 
 and beautiful. Attempts were made to unite all 
 these characters ; but a corrupted taste, only, was 
 pleased, a chastened judgment was not satisfied. 
 
 " Luxuriant last, 
 The rich Corinthian spreads her wanton wreath." 
 
 In the Composite order, this deviation is more 
 remarkable. This was invented by the Italians; 
 and, although rich and profuse in its ornaments, dis- 
 covers an obvious want of correct taste and judg- 
 
INTRODUCTION. 
 
 11 
 
 mcnt, and shows that the Grecians had cxhausd-d all 
 the principles of grandeur and beauty in the original 
 orders. And in these they had arrived at the acme 
 of perfection, because the Composite could not pos- 
 sibly have been introduced without combining all the 
 rest; conse<iucntly, that simplicity is desti-oyed, which 
 is in conformity with nature, and the great concomi- 
 tant of beauty. It is said this order was fii-st used 
 by the Romans in their ti-iumphal arches, to show 
 their dominion over the people whom they con- 
 quered.* 
 
 An order in architecture consists of two principal 
 parts — the column and the entablature, or parts 
 supported by Ihe column. Of these two principal 
 parts, each consists of three subdivisions. Those of 
 the column are the base on which it rests, the shaft, 
 or tali tapering portion, and the capital, or ornament- 
 al part crowning the shaft. Those of the entabla- 
 ture are, first, the architrave, then the frieze, and 
 above all, the cornice. Each of the smaller parts is 
 again subdivided and distributed in various ways, 
 according to the orders to which they belong, as ex- 
 isting in antique monuments, but more frequently 
 according to the taste and fancy of the authors who 
 have ^^^:itten on the subject of architecture. 
 
 The principal character of the various kinds of 
 architecture depending on the column and its requi- 
 site accompaniments, the whole is commonly and 
 almost universally divided into five species or orders, 
 viz., the Tuscan, the Doric, the Ionic, the Corinthian, 
 
 * An anonjinous ■\\Titer on the history of architecture observes, 
 that the art is supposed to have arrived at its glory in the time of 
 Augustus Ceesar ; but was, as "vvell as other polite arts, neglected 
 under Tiberius. Nero, indeed, notwithstanding his vices, retained 
 an uncommon passion for architecture ; but luxury and dissoluteness 
 had a greater share in it than real magnificence. In the time of 
 Trajan, Apollodotus excelled in the art, by which he obtained the 
 favor of that prince, and erected that famous pUIav called " Tra- 
 jan's," which is remaining to this day. But after this time archi- 
 tecture began to decline, though it was for some time supported by 
 the care and munificence of Alexander Severus ; yet it fell with the 
 western empire, and sunk into corruption. All the most beautiful 
 monuments of antiquity were destroyed by the ravages of the Visi- 
 goths, and from that time architecture became so coarse and artless 
 that these professed arcliitects were totally ignorant of just design- 
 ing, ^^hcrein the whole beauty of architecture consists ; hence a new 
 manner of architecture, called Gothic, took its rise. Charlemagne 
 industriously labored for the restoration of architecture ; and the 
 French applied themselves to it with success, under the encourage- 
 ment of Hugh Capet. Ilis son Robert prosecuted the same design 
 of modern architecture, and, by degrees, ran into as great an excess 
 of delicacy as the Goths had before done of massivencss. To those 
 we may add the Arabesques and Moresque or Moorish architecture, 
 which were much of the same nature with the Gothic, except that 
 83 the former were brought from the north by the Goths and Van- 
 dals, the latter was brought from the south by the Moors and Sar- 
 acens. The architects of the thirteenth, fourteenth, fifteenth, and 
 sixteenth centuries, who liad some knowledge of sculpture, seemed 
 to make perfection consist wholly in the delicacy and multitude of 
 ornaments which they lavishly bc'stowed on their' buUdings, but fre- 
 quently without conduct or taste. In the two last centuries, the 
 architects of Italy and France assiduously endeavored to retrieve 
 the primitive simplicity and beauty of ancient architecture ; nor did 
 they fail of success, insomuch that now most churches, palaces, &c., 
 are built entirely after the antique. 
 
 and the Comjiosilc. This distribution and arrange- 
 ment would seem to have been founded on the pro- 
 gressive proportion, strength, and ornament of the 
 orders ; they arc, however, well calculated to mislead 
 the student and the architect, in tracing the origin 
 and gradual advancement of each order. Without 
 attempting to search for the commencement of either 
 of the above orders, it is sulficient for us to know 
 that the Grecians- employed only the Doric, ihc 
 Ionic, and the Corinthian ; and that the Tuscan and 
 Composite were only used in Italy — the one more 
 rude and the other more ornamented than the Gre- 
 cian orders, which occupied a middle rank. To 
 attain, therefore, a proper knowledge of the princi- 
 ples of architecture, the student ought to confine 
 himself to the three Grecian orders, not only because 
 in them these principles are most displayed, but 
 because of aU the monuments of antiquity which 
 have subsisted to modern times, few, perhaps none, 
 can be pointed out in Avhich the Roman or Italic 
 mode of construction is certainly to be traced. 
 
 In architecture, various terms are employed in a 
 peculiar sense, of which the following are the chief: 
 Column is a Latin word, signifying, in general, a 
 piUar or supporter of some superincumbent load; 
 but is now confined to a round pUlar, smaller above 
 than below, and thereby closely imitating the trunk 
 of a tree, from which it was originally drawn. When 
 the pillar is not round and tapering, but square, and 
 of equal dimensions above and below, it is called 
 an ante. The column consists of three principal 
 divisions : 1st, the base, from the Latin term basis, 
 the foundation on which any thing rests ; 2d, the 
 shaft, or circular tapering portion ; and 3d, the cap- 
 itaj, from the Latin term for the head, or the prin- 
 cipal member. 
 
 The base is subdivided into different small parts, 
 according to the order to which the column belongs ; 
 but all the lowermost part is the plinth, from the 
 Grecian term for a brick, because the ancient bricks 
 were in general about square, and comparatively 
 thin, resembling our paving bricks or tUes. Above 
 the plinth lay the torus, a round moulding resembling 
 a rope, so called in Greek, and imitating the band 
 tied round the bottom of the original tree, as the 
 plinth did the flat brick or stone on which it stood, 
 to keep it fi-om the ground. Between these two 
 members was sometimes introduced a hollow chan- 
 nel, called scotia, from the Greek word for darkness, 
 because little light could enter it. 
 
 The column was generally quite plain and smooth 
 in its whole length ; but in buildings where ornament 
 was particularly admitted, the shaft was cut into a 
 succession of small perpendicular channels, resem- 
 bling the inside of a pipe or flute cut lengthwise into 
 two parts ; hence the shaft is cTiWed fluted. In some 
 instances, one third part of the flutings from the bot- 
 tom was, as it were, filled up with the half of a 
 
12 
 
 INTRODUCTION. 
 
 round rod lying in the liollow. It is singular, that 
 the flutings may have been originally intended as 
 an imitation of the natural hollows of the bark 
 of a tree, and might therefore be expected in the 
 earliest productions of architecture, it is only in 
 the more improved works that fluted columns are to 
 be found. 
 
 The capital is variously subdivided and orna- 
 mented in the different orders — simple in the Doric, 
 more ornamented in the Ionic, and highly enriched 
 in the Corinthian. In all, however, a narrow mould- 
 ing runs through the shaft, near the upper end, called 
 the astragal, because it seemed to occupy the posi- 
 tion of the upper bone of the neck. Because the 
 word astragal also means, in the Greek, the heel, it 
 is, in some treatises on architecture, most ridiculously 
 called by that name. The uppermost member of 
 the capital is the abacus, so called, as being broad 
 and thin, LLlvc the board or tablet employed by the 
 ancients in arithmetical calculations. 
 
 Tlie volute is an ornament introduced in the Ionic 
 order, being, as its Latin word implies, a spii-al scroU, 
 imitating the ends of some flexible substance loosely 
 rolled up. 
 
 The capital of the Corinthian order is encircled by 
 rows of leaves of difierent sorts. The parts which 
 rest upon, and are supported by, the columns, are 
 comprehended under the general name of the entab- 
 lature, because, agreeably to the meaning of the term 
 tabula, in Latin, they consist of boards, planks, or 
 stone slabs, of difierent forms and magnitudes. The 
 entablatm-e is a compound of three principal parts, 
 first the architrave, next the frieze, and, uppermost, 
 the cornice. The architrave is so called, by a name 
 partly Greek and partly Latin, as being the principal 
 beam which, resting on the capitals of the columns, 
 supports the remaining parts of the entablature. In 
 some cases it is plain, in others it is broken in two or 
 three pieces, like so many separate beams lying on 
 each other. 
 
 The frieze consists of one piece, but commonly 
 enriched with sculptiu-e of different sorts. In the 
 Doric order, this ornament consists of two whole 
 channels, and two half channels, forming one, if 
 joined together, and therefore called by a Greek 
 name triglyphs, or three hollows. The square spaces 
 between the successive triglyphs are called metopes, 
 a term expressing the hollow open spaces between 
 the beams, the ends of which are represented by the 
 triglyphs. In those metopes are sometimes repre- 
 sented the head of some divinity, the skull of some 
 animal used in sacrifice, or other emblem of the pur- 
 pose to which was destined the building on which 
 the ornaments were introduced. 
 
 The cornice, from the French corniche, and the 
 Latin corona, is so called because, being the upper- 
 most part of 1hc cntablatm-e, it croirns the whole 
 architectm-al distribution of the columns ; and it is 
 
 divided and ornamented in different ways, according 
 to the order employed. 
 
 1. The first Grecian order in point of antiquity is 
 the Doric, so named from the Dores, a small tribe in 
 Greece, or, as some say, from Dorus, an Aehaian 
 chief, who first employed that order in erecting a 
 temple to Juno at Aigos. In all the most perfect 
 specimens of this order now remaining, the column 
 springs immediately from the foundation, having no 
 base properly so called, but only a small swelling 
 round the bottom, resembling what we see at the 
 root of a tree, and sufficient to show that we sec the 
 whole of the shaft. The base, we learn from "S^itTU- 
 vius, first appeared in the Ionic column. The Doric 
 column being short in proportion to its diameter, and 
 consequently strong, the entablature placed upon it, 
 is, of course, more massive than tliat of the other 
 orders, being in height one fourth part of the total 
 height of the column. 
 
 2. The Ionic order derives its name from the Tones, 
 a Greek people on the east coast of the Archipelago, 
 whose capital was Ephesus, celebrated on many 
 accounts, but particularly for the magnificent temple 
 of Diana. This admirable sti'ucture was in length 
 425 feet, and in breadth 220 feet. It was surrounded 
 on all sides by a double range of marble columns, 
 70 feet in height, and conseqiiently 7 feet 9^ inches 
 in diameter at the bottom. 
 
 The Ionic column is taller than the Doric, contain- 
 ing 9 diameters, or 18 modules ; and, although sim- 
 ple, is nevertheless gi-aceful and majestic. If the 
 Doric were meant to represent the manly, robust 
 figure of Hercules, the Ionic might properly be the 
 emblem of the dignified simplicity and elegance of 
 Diana. In this order, as has been already observed, 
 the base supporting the column was first introduced. 
 An ornament peculiar to the Ionic column is the 
 volute or spiral scroll already mentioned, which is 
 described by a succession of portions of circles, 
 drawn from different central points. The height of 
 the whole entablatm-e is | of that of tlie column, 
 being the medium between that of the Doric, which 
 is |, and that of the Corinthian, which is -j|. The 
 height of the base is one module, or half the diam- 
 eter of the shaft. 
 
 3. The Corinthian order took its rise in the flour- 
 ishing days of Corinth, a celebrated city, command- 
 ing the communication of the peninsula of Pelopon- 
 nesus with the continent of Cireece. The beautiful 
 foliage of the capital of this order is traced back, 
 according to Callimachus, to the following incident : 
 A young lady of Corinth dying, her nurse carried 
 her playthings in a basket, the day after her funeral, 
 and placed it on the grave. The basket, covered 
 with a flat tile, was placed accidentally on the stem 
 of the plant acanthus, which, sending out leaves, 
 soon enclosed the basket, having their ends turned 
 downwards when they reached the tile. This object 
 
INTRODUCTION. 
 
 13 
 
 struck the fancy of a celebrated sculptor of those 
 (lays — Callimachus, who immediately introduced a 
 figure of it on the top of an elegant column of his 
 invention. Thus the capital of the Corinthian col- 
 umn always resembles a deep narrow basket covered 
 with a tile, and completely surrounded by foliage. 
 Such is the account given by Vitruvius ; but later 
 writers on architecture have imagined they could dis- 
 cover this ornamented capital in the description given 
 of the temple erected by Solomon, in Jerusalem ; 
 with this difference, that there the foliage represented 
 branches of the palm, and not the leaves of the 
 acanthus. It is, however, to be observed, that the 
 foliage of the Corinthian capital is frequently an 
 imitation of the leaves, not of the acanthus, but of 
 the olive, and of other plants, according to the taste 
 of the architect. The Corinthian column is in height 
 10 diameters, or 20 modules, of which the base is 1 
 module and the capital 2^ modules; consequently, 
 the shaft measures 16| modules. The entablature 
 is ^ of the column. 
 
 1. The first Italic order is called the Tuscan, as 
 having been employed by that ancient people, once 
 very powerful in Italy. It is, however, remarkable 
 that no vestiges now exist of any building in which 
 the Tuscan column was employed to support an 
 entablature, or any other weight. Vitruvius, it is 
 true, gives instructions for erecting temples accord- 
 ing to this order ; biit it does not appear that such 
 edifices were actually erected. The only examples 
 of the use of the Tuscan column that have come 
 down to our times are the admirable monuments 
 still subsisting in their original perfection, the column 
 of Trajan and Antoninus in Rome, and the col- 
 umn of Theodosius in Constantinople. The column 
 erected to the honor of Trajan, (next to Julius Cassar 
 perhaps the most valuable of the Roman emperors,) 
 who flourished a century after Christ, is, in all, 118 
 feet high. The shaft of the column is in length 
 14i modules, or 7i diameters, each 11 feet 2 inches. 
 
 The pedestal supporting the column is a cube of 
 3 modules ; the base is 1 module, and the capital 
 I module. On the capital is another pedestal, on 
 which stood a colossal statue of Trajan ; but this 
 was removed, and one of St. Peter now occupies the 
 same place. The other column, commonly said to 
 have been erected to Antoninus, is of the same Icind, 
 but a little smaller. It now supports the statue of 
 St. Paid. The magnificent but unhappily situated 
 column or monument erected in London to com- 
 memorate the dreadful conflagration which, in 1666, 
 laid waste the greater part of that city, although 
 copied from those in Rome, and of considerably 
 larger dimensions, is not properly Tuscan, but a 
 fluted Doric. 
 
 2. The other Italic order is called the Composite, 
 because it seems to be a combination of the Ionic 
 and the Corinthian orders, to which last it bears the 
 
 greatest resemblance, imitating the former only in 
 the adoption of the complete volute in the capital, in 
 addition to the Corinthian foliage. A specimen of 
 the Composite order, richly ornamented, is to be seen 
 in the triumphal arch, of which are represented, in 
 Scripture, the golden candlestick of seven branches, 
 and other precious articles carried away from the last 
 temple of Jerusalem. 
 
 Besides columns, properly so called, which are al- 
 ways circular, another kind of pillar, caUed pilasters, 
 are frequently employed, especially where a great 
 weight is to be supported. The plan of a pilaster is 
 usually a square ; but those, the plan of which is a 
 parallelogram, are also inti'oduced. The chief use 
 of pilasters is to support arches. Thus the piers of 
 a bridge are in fact short pilasters. The arches sep- 
 arating the nave from the side aisle of St. Paul s 
 Chm-ch in London, and of St. Peter's in Rome, are 
 supported on pilasters. In some buildings, it is true, 
 we find ranges of arches supported on columns of 
 even the delicate Corinthian order ; but as columns 
 are of a tapering form, the upper diameter being less 
 than the lower, and as this diminution is increased 
 in the eyes of the spectator by the distance of the 
 upper part, the columns have a slender and even a 
 feeble appearance, and consequently are ill adapted 
 for supporting an arch. On the other hand, pilasters 
 being of equal dimensions all over their height, and 
 very short in proportion to then- diameter, possess 
 a solidity and strength capable of bearing arches of 
 the greatest weight and magnitude. By pilasters we 
 also mean an ornament applied to walls, internal and 
 external, resembling in parts and form a column, biit 
 flattened instead of round. Pilasters of this sort 
 have their base, shaft, and capital, and are plain or 
 fluted, according to the architectural order to which 
 they belong. It is a matter still unsettled whether 
 such a pilaster ought to diminish in breadth, like a 
 column, or to retain the same breadth above and 
 below, like a soM pier. Pilasters usually project 
 one fourth part of their breadth from the wall to 
 which they are applied. Both columns and pilasters 
 are frequently raised from the gi-ound, and on pedes- 
 tals — a construction not without its propriety in 
 certain cases, as in our churches, where the galleries 
 rest upon pilasters, and the front of the gallery coin- 
 cides with the pedestal of the column which rises to 
 the roof. Pedestals are by no means essential to 
 columns or pilasters ; but when employed, they must 
 be formed and ornamented conformably to the order 
 of the columns they support. 
 
 Columns are placed at different distances, accord- 
 ing to their destination, and the spaces between them 
 are termed intercolnmniations. This separation in 
 the Greek orders varies firom one diameter and a half 
 of the lower end of the column to four diameters ; 
 but if the Tuscan column were employed, the archi- 
 trave being supposed to consist of beams of timber, 
 
14 
 
 INTRODUCTION. 
 
 the intercolumniation may be much wider than if it 
 consisted of blocks of stone. That interval, how- 
 ever, between columns, which has received the sanc- 
 tion of the best monuments of antiquity, and of the 
 most judicious architects, is equal to two diameters 
 and a quarter of the column. Hence it is called 
 Euslijle, from two Greek terms expressing the proper 
 arrangement of columns. The latter term, stylos, a 
 column, enters into the composition of several other 
 architectiu-al terms, as pycnostyle, to express columns 
 placed close together ; prostyle, a number of columns 
 placed as in a jjortico before the entrance, front of a 
 building, of winch we have examples in London, 
 in the Churches of St. Martin-in-the-Fields, of St. 
 George, Hanover Square, of St. George, Blooms- 
 bury, in imitation of ancient edifices in Rome, &c. 
 When ranges of columns are carried quite round the 
 outside of a building, they form a peristyle. 
 
 Ai'ches may, perhaps, be considered less magnificent 
 than ranges of columns ; but they are very solid, and 
 liable to few accidents. The importance of arches 
 in afibrding a commodious passage over a river 
 needs no illustration. It has long been the practice 
 to construct bridges of arches, increasing in width, 
 and consequently in height, from each end to the 
 middle, so that the road formed the segment of a 
 large ckcle. The arches have also been generally 
 semicircles. The practice was first laid aside in 
 France, where many noble bridges are now to be 
 seen, consisting, like the ancient Greek and Roman, 
 of arches all of the same span or width, and the 
 same height ; so that the road is carried on a level 
 all the way along the bridge. In order to keep the 
 bridge low, the arches vary greatly from a semicircle, 
 being segments of circles of large diameter. Nay, 
 in some instances in France the arches are portions 
 of ellipses, and not circular, by which measure the 
 crown of the arch is kept very low. On this most 
 improved plan a bridge is eonstrttcted in London 
 over the Thames, between Blackfriars' and West- 
 minster Bridges, which, for excellence of materials 
 and structure, for magnificent simplicity and extent, 
 is perhaps without a parallel in Europe. It consists 
 indeed of only 9 equal elliptic arches ; but each is of 
 120 feet span. The extent of each pier between the 
 arches is 20 feet, and the length of the bridge 1280 
 feet, very nearly a quarter of a mile, on the same 
 level line from one end to the other. To enable the 
 reader to form some judgment of the properties of 
 this work, (called the Strand Bridge, because it leads 
 into that street, on the west side of Somerset Place,) 
 the following account of some other remarkable 
 bridges is given: Of the adjoining comnumications 
 over the Thames, London Bridge consists of 19 
 arches, and is in length 915 feet ; Blackfriars' Bridge 
 consists of 9 arches, and is 995 feet long ; and West- 
 minster Bridge, consisting of 15 arches, is in length 
 1223 feet. The celebrated bridge over the Loire at 
 
 Tours, in France, is horizontal, consisting of 15 ellip- 
 tic arches, and in length 1335 feet. The bridge ovei 
 the Moldaw at Prague, the capital of Bohemia, is in 
 length 1700 feet. But these are all far surpassed in 
 length by the antique bridge over the rapid Rhone, 
 at St. Esprit, in the south part of France, which, 
 constructed on a multitude of small arches, extends 
 to the length of 3000 feet, possessing this singu- 
 larity, that, instead of being straight, it consists of 
 two lines of direction, meeting in the river at a very 
 obtuse angle, pointed up against the stream, as if the 
 better to resist its violence. 
 
 In various edifices, ancient and modern, we find 
 columns and arches placed in ranges one above 
 another. In such works care must be taken that the 
 more massive are made to support the more slender, 
 placing first the Doric order, next the Ionic, and, 
 above all, the Corinthian or Composite. Li this 
 arrangement, the upper diameter of the superior col- 
 umn is usually made equal to the lower diameter of 
 the inferior column, giving the succession of columns 
 the an- of one tail, tapering tree cut into so many sep- 
 arate portions. 
 
 The most remarkable edifices of antiquity which 
 have subsisted with tolerable entirencss to our days 
 are temples of various sorts. The stntcture of these 
 temples is exti-emely simple, the building being a 
 parallelogi-am, seldom of great dimensions. Some 
 have a portico of columns at the entrance, and the 
 external walls plain or adorned with pilasters. Older 
 temples, however, are surrounded on all parts by a 
 single, and even by a double, range of columns, sup- 
 porting the architrave, frieze, and cornice, together 
 with the roof; so that the temple itself is in a man- 
 ner concealed from the view, and receives no light 
 but from the entrance. Such a construction is evi- 
 dently very ill adapted to the purposes of a Christian, 
 and especially of a Protestant, place of worship. It 
 has nevertheless been imitated in many magnificent 
 structures, Avith some alterations and the addition of 
 projections in each of the long sides, for the purpose 
 of resembling the cross, the emblem of the Christian 
 faith. According to the system of divine service 
 which for many centuries has prevailed in the Roman 
 Catholic worship, the sacred offices may be con- 
 ducted, without mutual interference, in sundry parts 
 of the church at the same time. In the Protestant 
 system, however, whether Lutheran, Calvinistic, or 
 Anglican, in which nothing is done as it were in 
 secret, and in which every member of the congrega- 
 tion is to hear and participate in every part of the 
 service, sacred edifices must, to be useful, be iimited 
 in magnitude and form. To be satisfied of the truth 
 of this observation, it will be qitite sufficient to enter 
 St. Paul's Church, in London, at a time when ser- 
 vice is performing. A comparatively small portion 
 of that grand structure is set apart for the congre- 
 gation, while the great body of the building pre- 
 
INTRODUCTION. 
 
 15 
 
 sents the appearance of a vast, useless void, neither 
 applied, nor indeed applicable, to any purpose of the 
 Protestant worship. The same observation belongs 
 to the most ancient Gothic cathedrals ; but these 
 were constructed with a very different view. 
 
 The columns of the portico and pilasters of the 
 body of St. Peter's, at Rome, reach at once from the 
 ground to the attic ; but in St. Paul's, at London, 
 the whole of the edifice is divided into two ranges 
 of columns and pilasters — an arrangement which, 
 by breaking the whole into a repetition of small 
 parts and members, counteracts the etTect which 
 would be produced by the great dimensions of the 
 edifice were it adorned with columns occupying the 
 whole height of the building. On the other hand, 
 the intervals between the grand columns of the por- 
 tico of St. Peter's having been built up into two 
 stories of arcades and balconies, to accommodate the 
 pope in certain ceremonies, the effect of the portico 
 is destroyed ; and, instead of one open range of lofty 
 pillars, the eye is offended to see them half sunk, as 
 it were, into a wall, the use of which is by no means 
 at first sight apparent. From this material defect, 
 the front of St. Paul's, although broken into two 
 ranges of pUlars, is fortunately free. 
 
 Columns grouped, or placed tw^o and two together, 
 have always a bad efl'ect ; for they suggest to the 
 observer the idea that single columns have been at 
 first employed, and, being found too weak for their 
 load, another set of columns had been placed beside 
 them to take off a part of the burden. Grouped or 
 double columns are ^vholly a modern invention, 
 nothing of the kind being found in any antique 
 work ; and although they were employed by the 
 first-rate architects who constructed the celebrated 
 colonnade of the palace of the Louvre, in Paris, the 
 front portico of St. Paul's, the entrance into Somer- 
 set Place, in London, &c., the grouping of columns 
 is, nevertheless, a departure from the genuine rules 
 of the art. 
 
 Instead of different ranges of columns, it is iisual 
 to throw the ground floor of an edifice into the form 
 of a basement, on which rise the columns or pilas- 
 ters to ornament the front. This basement ought 
 never to be less in height than half the length of the 
 order it supports. Basements are generally rusti- 
 cated ; that is, the stones are cut and placed so as to 
 resemble the rude blocks as they are supposed to rise 
 from the quarry. In the application of this rusti- 
 cation, however, the judgment and taste of the archi- 
 tect wili be displayed. In London, we have exam- 
 ples of the judicious employment of rusticated 
 walls, and of the very reverse. The huge, ponderous 
 masses apparently in all their native rudeness com- 
 posing the exterior of Newgate prison, admirably 
 indicate and characterize the nature of the edifice. 
 The less rude, it is true, but still rusticated, walls of 
 Carlton House are, on the contrary, equally incon- 
 
 gruous with tlie delicate and richly-ornamented por- 
 tico, and with the purposes to which that structure is 
 appropriated. 
 
 When a building is divided into different floors, or 
 stories, it seems proper that each story should have 
 its separate range of columns or pUastcrs which then 
 appear each to support the entablature and the pro- 
 jecting timbers of the superincumbent floors. When, 
 on the contrary, two, and even three, tiers of windows 
 are all included in the height of one range of col- 
 umns or pUasters, the want of use, and even of con- 
 nection, in columns of such a length, must strUie 
 every observer. 
 
 When a range of columns, surmounted with their 
 proper entablature, supports the end of a roof, a tri- 
 angular space is formed, called the pediment, the two 
 incLuied sides being finished agreeably to the cornice 
 below them, the enclosed ti'iangular space or tympa- 
 num is often fUled with historic or emblematic sciilp- 
 ture. Pediments on a small scale, triangular or as 
 arches of circles, are frequently placed alternately 
 over windows in modern buildings ; and instances 
 of the same intermixture are not wanting in vestiges 
 of ancient structures. The most proper proportion 
 of a pediment, whether triangular or circular, is to 
 make its perpendicular height from one fifth to one 
 fourth part of the base. 
 
 The preceding observations belong to the Grecian 
 and Roman systems of architecture ; but another 
 system, conducted on very different ideas, and of 
 which many specimens of admirable contrivance and 
 execiition stiU adorn the principal states of Europe, 
 namely, the Gothic, remains to be noticed. The 
 term is often improperly employed to express every 
 mode of construction not reducible to the ancient 
 Grecian. In this way, works erected by the Saxons 
 and the Normans in the northern and middle parts, 
 and by the Saracens or Moors from Africa in the 
 southern parts of Europe, are often confounded 
 under the general name of Gothic with those to 
 which that name properly belongs. This last species 
 of building is supposed to have first appeared in 
 England after the conquest, in the reign of Henry II., 
 who died in 1189 ; introduced, most probably, fi-om 
 Normandy and other parts of France, where splen- 
 did monuments of Gothic architecture are very com- 
 mon. 
 
 On the origin of the Gothic mode of building, in- 
 genious men have varied much in opinion, and even 
 on the origin of the name. The Goths were in 
 early times the inhabitants of Sweden; but in the 
 decay of the Roman empire, they with other north- 
 ern tribes invaded and even overrun aU the southern 
 parts of Europe, even to the Straits of Gibraltar. 
 Ignorant of every art but that of war, the science 
 and skill introduced into those parts by the Romans 
 were overwhelmed, and architecture gradually as- 
 sumed forms unknown to the Romans and the 
 
16 
 
 INTRODUCTION. 
 
 Greeks. Hence, buildings constructed on principles 
 different from those of antiquity came to be dis- 
 tingnit^hcd as Gothic, not because the Goths alone 
 were their founders, but because the Goths and their 
 neighbors the Vandals, having established a regular 
 succession of kings in Spain, their name became 
 more famous than that of any other northern race. 
 The Saxon, Norman, and Gotliic styles of architec- 
 ture, though nearly related in sundry particidars, 
 have still each its peculiar character. 
 
 The Saxon and Norman agree in this, that the 
 form of the building is in both the same. The pil- 
 lars are round, square, or polygonal, and very short, 
 massive, and strong ; but the arches and heads of the 
 doors and windows are semicircular. If, in these 
 particulars, any difference be found, it consists in the 
 superior massiveness and large dimensions of the 
 Norman architecture. The Saxon churches, of which 
 sundry examples, or parts at least, have remained to 
 our times, were often well constructed, and even 
 elegant, but generally of moderate size. Those 
 erected by the Normans, on the other hand, were 
 usually large and magnificent, can-ied up to a great 
 height, with two, and even three, ranges of pillars, 
 one above the other, of various dimensions, but con- 
 nected by circular arches. In the centi-e was a lofty 
 tower, with two others at the west end, where was 
 the principal entrance. In the course of time, how- 
 ever, the Normans introduced pillars of a much more 
 agreeable form, tall and slender. In England, the 
 Saxon and Norman styles are generally found mixed 
 in the same building — the latter, introduced in the 
 twelfth century, being ingrafted on the former, which 
 had been in use for centuries preceding. 
 
 The principal marks by which the true Gothic 
 architecture is distinguished are, its projecting but- 
 tresses around the exterior of the building, its pin- 
 nacles and spii-es, its large branching windows, its 
 niches, its canopies and sculptured angels, saints, 
 and kings, the fretted roof, the clustered pillar, but, 
 above all, the arch, always more or less acutely 
 pointed. As plainness and solidity constitute the 
 leading features of the Saxon and Norman build- 
 ings, so the Gothic architecture is distinguished by 
 the lightness of the work, the lofty boldness of its 
 elevation, the peculiar slenderness of its pillars, the 
 profuse and delicate richness of its ornaments, and, 
 we must add, the astonishing exceUence of the 
 masonry. 
 
 In inquh-ics into the origin of the proper Gothic 
 style of building, we meet with no less genius and 
 fancy than in similar inquiries concerning the Greek 
 orders, and much greater variety of sentiment. Some 
 writers imagine the Gothic style was brought into 
 England Ijy the crusaders on their return irom the 
 Holy Land and other parts of the East, and think 
 that lliis slylc should be called Saracenic. Others 
 would call it Moresque, as having been introduced 
 
 into Spain by the Moors. On the other hand, the 
 pointed arch which characterizes the Gothic is, by 
 some, traced to the intersection of two semicircles, 
 svich as is frequently seen in Saxon buildings — the 
 one arch being described from the end of the diam- 
 eter, and passing through the centre of the other. 
 Such an intersection would form an angle of 60°, 
 and lines from it to the other extremities of the 
 arches would, of course, form an eqirilateral triangle 
 — a form certainly not unfrcquent in Gothic build- 
 ings. The scheme, however, which has gained the 
 most general assent is, that the Gothic is derived 
 from the ancient practice of religious ceremonies 
 being performed in groves of lofty trees. The eye 
 being accustomed to contemplate the arches formed 
 by the branches of trees that shaded their altars and 
 sheltered their assemblies, it was natural, when cov- 
 ered buildings succeeded to the groxTJs as places of 
 worship, that men should endeavor to introduce some 
 similitude between them and those places in which 
 they had been accustomed so long to perform their 
 religious ceremonies. Accordingly, we find not only 
 the intersecting arches formed by the branches ex- 
 actly imitated by the pointed arch, but also the stems 
 of the trees as accurately represented by the slender 
 and clustering pillars of a Gothic cathedral. Indeed, 
 no attentive observer ever viewed a regular avenue 
 of well-gi-own trees intermixing their branches over 
 head but it presently put him in mind of the long 
 vista through a Gothic church, or ever entered one 
 of the laro;er and more elesrant edifices of this kind 
 but it presented to his imagination an avenue of 
 lofty trees intermingling their branches over his head. 
 Under this idea of so extraordinary a species of 
 architecture, all the irregular transgressions of art, all 
 the monstrous offences against nature, as some men 
 speak, disappear ; every thing has its reason, every 
 thing is in order, and an harmonious whole arises 
 from the studious application of means proper and 
 proportioned to the end. For, could the arches be 
 otherwise than pointed where the workmen were to 
 imitate the curve made by two opposite trees by 
 their mutual insertion into one another? Could the 
 columns be otherwise than split into distinct shafts, 
 when they were to represent the stems of a clump 
 of trees gi-owing close together ? On the same prin- 
 ciples they formed the spreading ramifications of the 
 stonework in the windows and the stained glass in the 
 open interstices, — the one to represent the branches, 
 and the other the leaves of an opening grove, — both 
 concurring to preserve that gloomy fight which, in 
 the gi-eater number of men, insph-es religious awe 
 and veneration. Hence we see the reason of theii 
 studied aversion to apparent solidity in these stu- 
 pendous masses of building, deemed so absurd by 
 men accustomed to the apparent as \vell as real 
 strength of Grecian architecture ; for the surprising 
 fightness of the Gothic building, united with real 
 
INTRODUCTION. 
 
 17 
 
 strength, was necessary to complete the execution of 
 their original idea of a sylvan temple. 
 
 The origin of Gothic architecture here pointed out 
 has been very happily illustrated and exemplified by 
 Sir James Hall, in a dissertation published in the 
 Transactions of the Royal Sociely of Edinburgh, 
 and in a subsequent separate publication on the same 
 curious subject, well worthy of attention. 
 
 In the architecture of the Greeks and Romans, the 
 columns were admired for the elegance of their pro- 
 portions ; but in the Gothic, the column h seldom, if 
 ever, diminished in diameter ; nor do we find any 
 fixed proportion between the diameter and the height 
 of the column ; nor is the intercolumniation or space 
 between any two pillars regulated by the diameter of 
 their height. Examples of the widest diflerence in 
 the intercolumniations are common. For instance, 
 in the nave of the Cathedral of York, and in the 
 aisles of the conventual Church of Newark-upon- 
 Trent, both edifices deservedly admired, but widely 
 differing in the proportions of their columns and the 
 intervals between them. 
 
 The Gothic column not being diminished above, 
 and having no entablature, is the better suited, in 
 point of stability, to support the arch springing 
 immediately from it, as only a continuation of one 
 half of the column. An arch sprLngmg from a 
 Greek or Roman column has always, as was before 
 observed, an unfavorable effect. The striking im- 
 pression of a Gothic structure is produced by taking 
 in the whole, in all its relations ; but in the Greek 
 architecture, our pleasure often arises from contem- 
 plating the elegance and fine proportions of its 
 several parts. 
 
 On viewing a Gothic building, we soon perceive 
 how admirably the parts are constructed for the eye 
 to embrace the whole. The column is generally an 
 assemblage of vertical mouldings, or a bundle of 
 rods, enclosing a tall slender post or trunk of a tree 
 acting as a conductor to the eye. The capitals pre- 
 sent nttle or no interruption to the sight, which 
 glides up along the pointed arch, and embraces the 
 whole upper portion of the edifice. One of the ver- 
 tical rods forming the column pierces through the 
 capital, and ascends to the roof, and firom it spring 
 the ribs of the vaulting. 
 
 The exterior of a Gothic edifice has an effect sim- 
 ilar to that of the interior. The vertical rods of the 
 columns run up to the top of the pediment and the 
 terminating pinnacle, and the pyramidal buttresses 
 on the outside produce similar etfects on the eye of 
 the beholder. 
 
 GENERAL OBSERVATIONS ON THE CONSTRUCTION OF 
 HOUSES. 
 
 In building, the situation is the first point to be 
 determined. For dwellings, the position ought to be 
 sufficiently elevated to be free from damps and 
 
 a 
 
 noxious vapors, but, at the same time, not ox])oscd 
 to the wintry blasts. The neighborhood of fens, 
 marshes, and stagnating waters should always be 
 avoided ; but water for domestic uses should always 
 be easily and plentifully attainable. When a full 
 southern aspect cannot be procured, the next best is 
 a western ; for the heat is always greater at ecjual 
 distances from noon in the afternoon than in the 
 morning. With respect to the gi-ound to be built 
 upon, it should be carefully examined by boring or 
 sinking pits. Stone or gravel afford the best foun- 
 dations ; but if these be not of considerable thick- 
 ness, dependence ought not, in all cases, to be placed 
 upon such soils. If, however, it becomes necessary 
 to found upon sandy, or upon marshy, boggy groiind, 
 the foundation must be secured by piling, planking, 
 laying large ledges, or other contrivances of the same 
 nature. 
 
 The situation being determined upon, the architect 
 or builder prepares plans of the intended edifice, gen- 
 eral and particular, with elevations of the fronts and 
 ends, not drawn as they would appear to the eye of 
 a spectator, agreeably to the rules of perspective, but 
 according to their general dimensions as measured on 
 a given scale. To the plans of each separate story 
 must be added sections in length and breadth of the 
 whole building, to show the elevation of the internal 
 parts. As, however, no building can ever appear to 
 the eye in the precise form of a geometrical eleva- 
 tion upon paper, and as it requires considerable skill 
 and practice to be able, from such an elevation, to 
 form a judgment of the appearance of the edifice 
 when actually erected, it is most satisfactory, and, 
 indeed, but just to the proprietor, to furnish him with 
 views of the intended structure from different points 
 of sight, accompanied by its attendant out-buUdings, 
 shrubbery, &c., such as they may be expected to be 
 when brought to perfection. From the want of such 
 general perspective representations, many a propri- 
 etor has beheld with disgust or mortification the 
 completion of a residence on which vast sums were 
 expended, and the arcliitect has very unjustly been 
 blamed ; nay, in some cases ruined in his business, in 
 consequence of such vexations and disappointments, 
 occasioned by his unscientific employer. In cases of 
 great public buildings, models of timber are often 
 constructed, which, when done upon a properly 
 adapted scale, convey a very perfect conception of 
 the intended structiures. 
 
 The external form, and the internal distribution of 
 houses, are necessarily susceptible of such variety, 
 that it is impossible to lay down any particular rules 
 on these heads. A country seat is, of late years, 
 usually arranged with a centre building for the fam-> 
 ily, and two wings, connected by covered passages 
 with the centre, for various other purposes. The 
 proportion that these wings should bear to the centre 
 has never yet been ascertained ; yet every passing 
 
18 
 
 INTRODUCTION. 
 
 spectator will exclaim against the architect when the 
 disproportion between the wings and the cenire 
 strikes him as extravagant. In some modern build- 
 ings of this nature we find the length of its wings 
 in front, each only one third part of that of the cen- 
 tre; in others, one half; but nothing has a worse 
 effect than disproportion between the body and the 
 wings in point of height. The connecting passage 
 or colonnade always looks best when it forms exactly 
 a quarter of a circle. 
 
 The groat difficulty in architecture is to combine 
 utility witli ornament and magnificence. This can, 
 indeed, be properly done in structures of a certain 
 extent alone ; but even space and expense have not 
 always been sufficient to insure these essential ends. 
 
 Excess of ornament is always misplaced in small 
 buildings, which have then more the air of models 
 of other great works than real places of abode. It 
 was observed of Chiswick House, on the banks of 
 the Thames, above London, (buUt in imitation, but 
 on a small scale, of a noted structure of Palladio, 
 near Vicenza, in the north of Italy,) that it was too 
 large to hang to one's watch chain, and too small for 
 a man to live in. 
 
 DOORS. 
 
 The size and proportion of doors must be regu- 
 lated by the purposes of the building to which they 
 belong. The door of a dwelling-house, correspond- 
 ing to the human size, is confined to seven or eight 
 feet in height, and three or four in breadth. In pri- 
 vate hovises, four feet may be the greatest breadth. 
 In small doors, the breadth or width may be to the 
 height as three to seven ; but in large doors, as one 
 to two. Doors intended to have but one leaf, or 
 close, should never exceed three feet six inches in 
 breadth, otherwise the door becomes too heavy for 
 convenient use. Doors of a wider aperture, especial- 
 ly in the outer wall, arc best formed with two fold- 
 ing leaves. 
 
 As to the modern fashion of opening a wide com- 
 munication between rooms on the same floor, by 
 means of broad folding doors, the practice sets all 
 rules of proportion completely at defiance. 
 
 The external lintels of doors and windows should 
 always be on the same level, and the doors should 
 never be narrower than the windows. When the 
 outward wall is ornamented with half columns and 
 arches, forming blank arcades, the doors and win- 
 dows should just rise up to the springing of the 
 arches. 
 
 The most common way of ornamenting the aper- 
 ture of a door is by an architrave on the top, and 
 also down the sides. Sometimes a cornice and even 
 a complete entablature may be placed above the lin- 
 tel. Pilasters and semicolumns have also a good 
 effect when applied to outer doors. Porticoes of four or 
 more columns are properly adapted to large buildings. 
 
 WINDOWS. 
 
 The ininiber and size of the windows of a build- 
 ing must be regulated by the nature and purposes of 
 that building. The climate, the aspect, the extent, 
 the elevation, even the thickness of the walls must 
 be taken into consideration. When the walls are 
 thick, which is commonly the case in detached stone 
 buildings, the windows may liave a considerable 
 opening inwardly, which will admit nearly as much 
 light as if the whole aperture in the wall were en- 
 larged. The proportions of windows depend on 
 their situation ; only their width ought to be the 
 same in every story — those in each, however, being 
 proportioned in height to that of the apartments in 
 each story. In the principal floor, the height of the 
 windows may be two and one eighth to two and one 
 thud of the width. In the ground story, where the 
 apartments are lower, the apertures of the windows 
 seldom exceed a double square ; that is, the height is 
 just double the breadth. When the basement is riis- 
 ticated, the height is generally much less. In the 
 second floor, the height of the windows may be from 
 one and a half to one and four fifths, or, rather, three 
 fourths of the width. The window in the attics and 
 mezzaninos or entresols may be a perfect square, or 
 even lower. 
 
 The windows of the principal floor are the most 
 enriched. The simplest ornament of such windows 
 is an architrave carried round the aperture, with a 
 frieze and cornice on the top. The windows of the 
 ground floor are sometimes entirely plain ; at other 
 times they are surrounded with rustics or a regular 
 architrave. Those of the second floor are generally 
 closed with an architrave, crowned at times with a 
 frieze and cornice ; but these last ornaments would 
 be improper in the attics. The breasts of aU the 
 windows on the same floor ought to be on the same 
 level, and raised from two feet six inches to three feet 
 above the floor. In warm climates, or in country 
 houses in our own climates, seated amid gardens and 
 pleasure grounds, the windows of the gi'ound story 
 being cut dowi: to the floor, render the apartments 
 pleasant and agreeable. In country houses, indeed, 
 in France, Italy, and other warm parts of Europe, 
 the principal apartments are aU on the gi'ound floor ; 
 and the other floors diminish in height as they rise 
 above it. The windows of the ground floor being 
 cut down even with the doors, .and thus affording a 
 ready communication with the garden or lawn, have 
 a peculiar propriety. How far the same practice in 
 the windows of the first and other floors, in the 
 streets of large cities, by which the damps and cold 
 of winter must inevitably penetrate into the apart- 
 ments, ought to be avoided, is a point to be decided 
 by those who prefer comfort and health to absurd- 
 ities, however fashionable. 
 
 Not contented with adopting usages suited to 
 
INTRODUCTION. 
 
 19 
 
 the genial temperature of the south of Europe, a 
 stranger on passing along the new quarters of Lon- 
 don might be tempted to imagine himself transported 
 to the burning climates of India, when he beholds 
 the fronts of the houses, whatever be their exposure, 
 adorned, or, rather, loaded and bloeked up, with vast 
 projecting galleries, intended, but very unnaturally, 
 lo imitate the light, airy, and refreshing verandas of 
 the East. 
 
 In so far as these galleries are on the outside of 
 ihe windows and walls, they are certainly of use to 
 intercept the immediate action of the sun's rays. 
 On the same account, what we call Venetian blinds 
 ought to be placed on the outside, and not on the 
 inside, of our windows. On the inside, they keep off 
 the glare of the sun's rays, but not the heat, which 
 communicates to the air of the room, warming it 
 just as much as if no blind intervened. On the out- 
 side, the blinds reflect and repel the heat as well as 
 the light, and the au* within the room preserves a 
 desirable coolness of temperature. 
 
 The intervals of walls between windows should 
 never be less than the aperture of the windows, nor 
 in dwelling-houses gi-eater than twice that aperture, 
 otherwise the light will be deficient. The usual rule 
 for proportioning the quantity of light to a room is, 
 to multiply the length of the room by the breadth, 
 and the product by the height. The square root of 
 the last product gives the number of square feet of 
 aperture requisite for properly lighting the room. 
 Thus, suppose a room to be in length 32 feet 6 
 inches, in breadth 24 feet, and in height 15 feet ; the 
 product of these quantities multiplied successively 
 into each other will be 1700 ; the square root of 
 which, in even numbers, — 108, — will be the number 
 of square feet of aperture required to lighten the room. 
 This quantity, distributed among three windows, 
 gives 36 square feet for each window ; the width of 
 each being 4 feet, the height must be twice and 
 one fourth, or 9 feet. Had it been proper to open 
 four windows in the same room, each must have 
 contained only 27 square feet ; and if the breadth of 
 each were 3 feet 6 inches, the height would be 7 
 feet 8i inches. It is, however, to be observed, that 
 both internal and external openings in houses, such 
 as windows, doors, &c., ought always to consist of 
 the uneven numbers, 1, 3, 5, 7, 9, &c., and never of 
 the even numbers, 2, 4, 6, 8, 10, &c. 
 
 This rule cannot always, it is true, be observed in 
 the confined spaces allotted to houses in towns ; but 
 in other situations, if the number of windows be 
 even, the door cannot be opened in the centre of the 
 building, and the want of an equal corresponding 
 extent and balance on each side must strike the 
 most careless spectator. The same rule is to be 
 observed in distributing the arches of a bridge or 
 an arcade, the intercolumniations of a portico or 
 colonnade. 
 
 The proportions of rooms, in length, breadlii, and 
 height, arc more the objects of taste and experience 
 than of geometrical regulation. A circle or a scjuare 
 is a more perfect figure than an oval or a parallel- 
 ogram ; and a globe, a cylinder, or a cube, than a 
 parallelopiped. A room, however, in the form of a 
 cylinder or a cube, would, in general, be neither useful 
 nor agreeable. The parallelopiped is, therefore, the 
 form universally adopted for rooms or chambers of 
 every sort, in which the greatest dimension is the 
 length, the next is the breadth, and the smallest is 
 the height. Some architects have made the breadth 
 one half more than the height, and the length one 
 half more than the breadth. Thus, for example, if 
 the height of the room be 16 feet, the breadth will 
 be 24 feet, and length 36 feet ; and on the other 
 hand, if the length be given, 22 feet 6 inches, the 
 breadth will be two thirds of it, or 15 feet, and the 
 height two thirds of the breadth, or 10 feet. Such a 
 rule, however, must evidently be subject to many 
 modifications. 
 
 The rooms on the gi-ound or the second floor may 
 be of the same length and breadth with those on the 
 principal floor ; but if they were of the same height, 
 the impropriety would immediately strike and offend 
 the eye. No defect in proportion, however, is more 
 offensive than that in the height, and none takes 
 more off from the appearance of a room. A low 
 apartment, whatever be its other dimensions, never 
 can possess either dignity or beauty. 
 
 It is the common remark of every one who, for the 
 first time, enters the matchless fabric of St. Peter's, 
 in Rome, that it by no means strikes the eye as so 
 vast as it is known to be. This effect arises from 
 the correct proportions of the whole edifice, in length, 
 breadth, and height, and of the various members of 
 which it consists. Had it been narrow, our attention 
 would have been attracted to its great length. Had 
 the ceiling been low, we should have been offended 
 by its disproportionate length and breadth. Such, 
 on the contrary, is the harmony of the several dimen- 
 sions of the building, that no excess or defect in 
 either of them leads us to institute a comparison be- 
 tween them. It is only by observing the time neces- 
 sary merely to walk round and give a cursory glance 
 to the interior of St. Peter's that the stranger can be 
 convinced of its prodigious extent in all directions. 
 Comparisons are seldom pleasing, and not always 
 just ; it would, therefore, be on many accounts unfair 
 to compare St. Paul's of London with St. Peter's 
 of Rome. It must, however, be acknowledged that 
 the first view of the former has an effect very differ- 
 ent from that produced by the latter, the chief cause 
 of which is, that the nave of St. Paul's is really 
 gloomy, and apparently narrow and low for its 
 length ; so that the spacious and lofty dome, instead 
 of being only accessory, becomes the principal part 
 of the edifice. 
 
20 
 
 INTRODUCTION. 
 
 The proportions and dimensions of rooms must be 
 reg^ated by their uses. A dining-room and a bed- 
 chamber require very different proportions. A gal- 
 lery for exercise in bad weather, especially if to be 
 adorned with paintings and statues, must be of a 
 length in proportion to its height and breadth, which 
 last must be governed by the necessity of possessing 
 light from windows on one side only, to exhibit with 
 due advantage the paintings and sculpture ranged 
 along the opposite side. A passage should be just 
 wide enough to give a convenient communication 
 betw^een the several parts of the house ; and if it be 
 wider, we are offended with the waste of space 
 which the architect ouglit to have turned to some 
 other use. 
 
 There is no part of a building in which the taste 
 of a builder can be better displayed than in the 
 position and distribution of stairs. Even in the 
 most spacious buildings, a step may be made too 
 broad, so as to require a sort of effort to move up or 
 down from one to another. In spacious stairs, the 
 steps should vary from 12 to 18 inches in breadth, 
 and from 4 to 7 inches in height ; the length, also, 
 varies fjom 6 to 15 feet. Even in small houses, a 
 step over 7 or 8 inches high would be inconvenient ; 
 and the breadth should never be less than 9 inches, 
 nor the length shorter than three feet. 
 
 We have thus given a pretty lengthy account of 
 the theory of Architecture ; and would now invite 
 the attention of the student to the subjoined remarks 
 on the practical branch of the science. 
 
 A competent knowledge of the methods of draw- 
 ing on paper, and of working in stone, timber, or 
 other materials, the several kinds or orders of col- 
 umns, &c., is absolutely indispensable to enable the 
 architect to discharge his duty to his employer, and 
 the artisan to execute his commission. 
 
 It has been already mentioned, that an order of 
 architecture consists of three principal parts, viz., the 
 column, its pedestal, and its entablature. Each of 
 these parts is again subdivided into three parts, thus : 
 the pedestal into its base or lowest member; the 
 cubical body, called from its figure the die or trunk ; 
 and the cornice above all. The column into the 
 base, the shaft, and the capital. The entablature 
 into the architrave, the frieze, and the cornice. 
 
 To give a minute, full, and perfect explanation of 
 the proportions and manner of constructing these 
 several members, with the various ornaments apper- 
 taining to each, would require an extent and a num- 
 ber of engravings totally incompatible with the de- 
 sign of Ihc present work. Nor is this particular 
 explaiialion deemed essential; for the number of 
 publications on this head is already so numerous, 
 that it is probable the student will find it more diffi- 
 cult to determine which to follow than to find a 
 guide. Our obser\'ations will, therefore, be general 
 and limited. 
 
 The simplest problem in mechanical architectiu-e 
 seems to be, to determine the best form for a column 
 The length and the weight (that is, the quantity of 
 materials in the column) being given, it is of impor- 
 tance to investigate the form wliich affords the great- 
 est possible strength ; but it is somewhat difficult to 
 ascertain the precise nature and direction of all the 
 forces to be resisted which act upon the column. If 
 a column were considered only as a beam fixed in 
 the ground, and acted upon by a force pressing trans- 
 versely, or on one side, it ought to be much tapered, 
 and reduced almost to a point at the upper end. 
 But it is seldom that any force of this kind can be 
 so powerful as to do more than overcome the weight 
 of the column. The only thing, therefore, to be con- 
 sidered, is the load which presses on it from above ; 
 hence, whether we regard the force as tending to 
 bend the column or to crush it, the forms commonly 
 employed appear sufficiently eligible. Some math- 
 ematicians have erroneously recommended the cyl- 
 inder as the strongest form to resist bending ; and in 
 this opinion, those who have not considered the sub- 
 ject are ready to join them, because a cylinder, 
 standing perpendicularly on one end, being of equal 
 thickness, seems also to be of equal strength through- 
 out. From the principles of mechanical philosophy, 
 however, it can be shown that the strongest form of 
 an upright column approaches, in fact, much more 
 nearly to that of an oblong spheroid or spindle of 
 which the outside is an arch of an ellipsis. But the 
 consideration of the flexure of a column is of the 
 less practical importance in architectvure, that, ixpon a 
 rough estimate of the properties of the materials 
 usually employed, a column of stone (in order to be 
 capable of being bent by any weight which will not 
 crush it) must be at least forty times as high as it is 
 thick, although a bar of wood or of iron may be 
 bent by a superincumbent load, if its length exceed 
 about twelve times its thickness. But as, even in the 
 Composite order, — the tallest and most delicate of 
 all, — the height of the column is only, at the most, 
 ten times the thickness at the base, the action of the 
 incumbent weight, in bending the column, ceases to 
 be an object of much consideration. It is only, then, 
 as a crushing force that the weight requires to be 
 estimated ; and since the lower parts of the column 
 itself have not only the weight above, but its own 
 upper parts, to support, the thickness below ought to 
 be somewhat increased. It appears, by experience 
 of the direction in which the fracture of a column is 
 made when crushed by too great a weight, that the 
 outline ought to be made a little convex, or to sweU 
 a little on the outside of a straight line, joining the 
 extremities of the shaft, and more curved above than 
 below. This is the usual, but not the universal, 
 practice. An elliptic arch is, perhaps, the most eli- 
 gible outline, or a curve formed by bending a rule^ 
 fixed at the summit of the column. It is very 
 
INTRODUCTION. 
 
 21 
 
 natural, in forming a column, to copy the working of 
 nature in forming the trunk of a tree, which may be 
 considered, in a general sense, as a portion of a 
 tapering cone, enclosed by straight lines joining the 
 top and the bottom. But, independent of other con- 
 siderations, it is to be remembered that the great 
 load of the boughs, branches, and leaves act upon 
 the trunk of the tree very differently from the load 
 usually to be borne by a column. A light-house 
 placed upon a rock in the sea may be considered as 
 a column erected, not to support a weight, but to 
 withstand the action of wind and water. If we cal- 
 culated what would be the best form for a wooden 
 pillar, intended to remain always immersed to a cer- 
 tain depth in water, we should find that a cone or a 
 pyramid would possess the greatest possible strength 
 for resisting the motion ,of water ; and a cone still 
 more acute than this would be equally capable 
 of resisting the force of the wind, supposing it to be 
 less powerful than that of the water. The part be- 
 low the surface of the water might, therefore, be 
 widened, so as to become a part of a more obtuse 
 cone, the upper part remaining more slender ; and 
 the agitation of the sea being greatest at its surface, 
 the basis of the pOlar might be a little contracted, so 
 as to have the outline of the lower part a little con- 
 vex outwards, if the depth of water were consider- 
 able. But in the case of a building of stone, the 
 strength often depends as much on the weight as on 
 the cohesion of the materials ; and the lateral adhe- 
 sion, which is materially influenced by the weight, 
 constitutes a very important part of the strength. 
 For resisting a force tending to overset the building, 
 the form in which the weight gives the greatest 
 strength is that of a conoid ; that is, a solid, of 
 which the outline is a parabola, (a section of a cone 
 parallel to its sides,) concave towards the axis, and 
 convex outwardly ; and for procuring, by means of 
 the weight, a lateral adhesion every where propor- 
 tional to the force, the form must be cylindrical. 
 Hence, in a building such as this pillar is supposed 
 to be, no reasons appear why cither portion of its 
 outline, taken separately, should be made convex 
 towards the axis, although the joining of the two 
 cones might very properly be rounded off. Of the 
 form adopted for a building exposed to the violence 
 of both water and wind, we have a remarkable ex- 
 ample in the light-house erected on the Eddystone 
 Rock, situated in the entrance of Plymouth Haven, 
 about fom-teen miles out from the land. The top of 
 the rock on which the light-house is founded is, it is 
 true, constantly above the surface of the water when 
 the sea is calm ; but in stormy weather, every part 
 of the building is exposed to the action of the waves, 
 the water being often thrown up to a height far 
 above that of the light-house ; so that it may be con- 
 sidered as exposed to the force of a fluid acting 
 more and more forcibly as it is nearer to the foun- 
 
 dation. On this account, the architect, the late in- 
 genious Mr. Smeaton, chose for the walls a slope 
 concave outwards, difl'ering in form but little from 
 that which the most accurate theory could have 
 pointed out. The building, however, is probably a 
 little weaker nearly as high as the middle of its 
 height than in any other part. The light-house is 
 wholly composed of cut stone, and about 16 feet in 
 diameter at the bottom. The height of the building 
 is 73 feet 6 inches from the rock to the top of the 
 cornice ; thence to the base of the lantern 7 feet 6 
 inches ; and thence to the summit of the ball on the 
 top 17 feet 6 inches ; making the whole height 98 
 feet 6 inches. 
 
 In diminishing their columns, various rules seem 
 to have been practised by the ancient architects. 
 Sometimes the diminution began at the base, the 
 shaft being formed by straight lines tending to a 
 junction at a point beyond the summit of the col- 
 umn, by which measure the shaft became a frustum, 
 or portion of a very acute cone. In other instances, 
 we find the column carried up perfectly cylindric, or 
 of the same diameter, for one fourth, or more com- 
 monly for one third of its height, at which points the 
 diminution begins, and extends to the capital. This 
 junction, however, of the cylinder and the cone, 
 although the angle formed by their outlines be al- 
 most imperceptible to the eye, appearing an imper- 
 fection, it was proposed and practised by eminent 
 architects to form the outline of the shaft, by a curve 
 running within the cylinder, but without the cone, 
 from the base to the capital, in such a way that the 
 diameter of the shaft was, in every part, less than 
 that at the base, but greater than that at the capital. 
 The observations made on this point by Vitruvius, 
 the great teacher of architectural mechanics, who 
 flourished about the beginning of the Christian era, 
 having in late times been misunderstood, it is no 
 uncommon thing, in different parts of Eiurope, (to 
 say nothing of our own country,) to meet with col- 
 umns, the outlines of which consist of a curve, 
 actually swelling outwards, so that at one third of 
 their height their diameter considerably exceeds that 
 at the base — a practice so offensive to the eye, as 
 weU as to reason, as to create wonder how it should 
 ever be adopted by men who had ever seen, or even 
 read, of the monuments remaining of ancient archi- 
 tecture. 
 
 The different methods of giving to columns the 
 proper diminution and most elegant sweeping out- 
 line are particularly described in the body of this 
 work. In this place, we must content ourselves with 
 giving the following plain instructions, by which 
 every practical artisan may form his model and plan 
 with accuracy sufficient for ordinary occasions : — 
 
 Take the lower and upper diameter of the shaft 
 of a column to be drawn. On the centre of the 
 lower diameter describe a semicircle, and erect a 
 
22 
 
 INTRODUCTION. 
 
 perpendicular to represent the axis of a column. 
 Through the extremity of the upper diameter draw 
 a line parallel to the axis of the column, cutting the 
 semicircle at the base. Now, divide the arc of the 
 semicircle made by the intersection of the last-men- 
 tioned line and the extremity of the base line into 
 any number of equal parts, the more the better, as 
 into 4, by points marked 1, 2, 3, &c. Li the same 
 way, divide the axis into the same number of equal 
 parts, through each of which draw indefinite right 
 lines, at right angles, to the axis. Through the 
 points of the arc, at the base, draw lines parallel to 
 the axis, producing them respectively until they meet 
 the transverse lines ckawn through on the axis, 
 which will thus become points in the surface of the 
 column. To assist in drawing these parallel perpen- 
 diculars, it will be convenient, through the points in 
 the arc at the base, to draw lines to the axis parallel 
 to the diameter, and setting off a distance equal to 
 one of these lines upon the transverse line passing 
 tlrrough the first line. Another, equal to that of the 
 second, the points of the axis will be obtained as 
 before. The setting on the transverses through the 
 first point, a distance equal to the extreme points : 
 in this manner, the points on the opposite side of the 
 axis may be obtained. K, now, nails or pegs be 
 fijced in the several points in the surface of the col- 
 umn thus ascertained, and along them and through 
 the two extreme points of the upper and lower diam- 
 eters a thin slip of timber, equally flexible in every 
 part, be applied, it will show the contour or section 
 of the exterior of the column. The curve thus 
 formed, being carefully transferred, will mark the 
 edge of the rule to be used in diminishing the shaft. 
 In this process, it is evident that the more numerous 
 the points of the surface ascertained, the more accu- 
 rately will the slip of timber assume the proper form, 
 and the diminishing scale be constructed. 
 
 MOULDINGS. 
 
 Although the shaft of a column may not admit of 
 any ornament on its body, yet, at each end, in the 
 base and the capital, various ornamental parts are 
 introduced, in the due disti-ibution and proportion of 
 which consists their principal beauty. These arc, in 
 general, called mouldings, because they are always of 
 the same shape, as if they all proceeded from the 
 same mould or form. Mouldings are, by some 
 writers, divided into Grecian and Roman, with a ref- 
 erence to the remains of the architecture of those 
 nations still in existence. The difference consists in 
 this — that the Romans generally employed circular 
 arches in their ornaments, while the Greeks often 
 introduced parts of an ellipsis, or of some other sec- 
 tion of a cone varying from the circle. The princi- 
 ple parts of mouldings are these : 1st. The flat part 
 under or above a moulding is 2i fillet, as resembling a 
 
 bandage or turban tied round the column. 2d. When 
 the moulding projects in the form of a quadrant or a 
 smaller portion of a circle, it becomes an echinus 
 or Romano ovolo, from its likeness to a portion of 
 the shell of a sea-hedgehog or of a common egg. 
 3d. But if the moulding, reversing that figure, be a 
 hollow of the same shape, it is, therefore, called a 
 cave/lo. 4th. A small ])rojecting semicircular mould- 
 ing is in general called a head, as particularly belong- 
 ing to the astragal, or neck ; but, 5th. K the moulding 
 be much larger, with a fillet above or below it, it 
 then becomes a torus, as imitating a rope or cable 
 applied to the column. 6th. If the section be a con- 
 cave semicircle, or scmielLipsis, it becomes a scotia, 
 because the interior is dark. 7th. When the projec- 
 tion is not properly a part of a circle, but rather of 
 an ellipsis, or of some other section of a cone, re- 
 turning in quickly at the upper part, it is called a 
 Grecian ovolo ; and the quick return in it is by 
 workmen called a quirk. 8th. A contour or section, 
 partly concave and partly convex, is a ci/matium, be- 
 cause it imitates the waves of the sea. 9th. If the 
 concave part be uppermost, it is a ci/ma recta ; but 
 if the convex part be uppermost, it is a ci/ma reversa, 
 or ogee. 
 
 VOLUTES. 
 
 A volute is a kind of spiral scroll, used in the 
 Ionic and Composite capitals, of which it makes the 
 principal characteristic and ornament. It has been 
 called the ram's horn, from its figure, which bears a 
 near resemblance to it. Most architects suppose that 
 the ancients intended the volute to represent the bark 
 of a tree, laid under the abacus, and twisted thus at 
 each extreme, where it is at liberty. Others regard 
 it as a sort of pillow or bolster laid between the 
 abacus and echinus, to prevent the latter from being 
 broken by the weight of the former and the entabla- 
 ture over it. Accordingly, they call it jnthdnus. 
 Others, after Vih'uvius, contend that it is designed to 
 represent the curls or tresses of a woman's hair. 
 
 The number of volutes in the Ionic order is four ; 
 in the Composite, eight. There are also eight angu- 
 lar volutes in the Corinthian capital, accompanied 
 with eight other smaller ones, called helices. There 
 are several diversities practised in the volute. In 
 some the list or edge, throughout all the circumvolu- 
 tions, is in the same line or plane. Such are the 
 antique Ionic volutes, and those of Vignola. In 
 others, the spires or circumvolutions fall back ; in 
 others, they project or stand out. Again : in some, 
 the circumvolutions are oval ; in others, the canal or 
 one circumvolution is detached from the list of 
 another by a vacuity or aperture. In others, the rind 
 is parallel to the abacus, and springs out from behind 
 the flowers of it. In others, it seems to spring out 
 of the vase from behind the ovum, and rises to the 
 abacus, as in most of the fine Composite capitals. 
 
INTKODUCTION. 
 
 23 
 
 The volute is a part of great importance to the 
 beauty of the column ; hence architects have invent- 
 ed divers ways of delineating it. The principal are 
 that of Vitruvius, which was long lost, and at last 
 restored by Goldman, and that of Palladio. 
 
 DRAWING A COLUMN. 
 
 In drawing a column of any particular order, the 
 several dimensions and members are measured by a 
 proportional scale, founded on the diameter of the 
 lower extremity of the shaft, immediately above the 
 projection of the base, where the shaft becomes rec- 
 tilineal. This diameter is divided into t^vo equal 
 parts, each being the radius of the transverse section 
 of the column, and it is termed a module. The 
 whole diameter is subdivided into sixty equal parts 
 or minutes, of which, consequently, thirty are con- 
 tained in a module. These proportional quantities 
 are easily converted into real when the lower diam- 
 eter of the column is given in measure. Thus, if the 
 lower diameter of a Doric column be 5 feet, or 60 
 inches, the module must be 2i feet, or 30 inches, and 
 each minute will be 1 inch ; and the Doric column 
 being in height 8 diameters, the height of the given 
 column will be 40 feet : hence the entablature, being 
 one fourth of the height of the column, its height in 
 this case will be 10 feet, and so on. 
 
 Li the Tuscan order, the height of the column is 7 
 times the lower diameter, or 14 modules ; the entab- 
 lature one fourth of the column, and pedestal one 
 fifth of the height of all the parts. Hence, let the 
 whole height of a Tuscan column, with its pedestal 
 and entablature, be fLxcd at 40 feet, the pedestal, 
 being one fifth of the whole, will be 8 feet high. 
 The remaining 32 feet, divided by 5, will give nearly 
 6 feet 5 inches for the entablature, and 25 feet 7 
 inches for the column, of which the lower diameter, 
 being one seventh, will be nearly 3 feet 8 inches. 
 Had the order been Ionic, the whole height, 40 feet, 
 divided as before by 5, (for, in all the orders, the ped- 
 estal is always one fifth of the entire height,) would 
 have given 8 feet for the pedestal, and the remaining 
 32 feet, divided by 6, would have given 5 feet 4 
 inches for the entablature, leaving 25 feet 8 inches 
 for the column, of which the ninth part, or 2 feet Hi 
 inches, is the lower diameter. But, in general, when 
 the whole height of the column, with its pedestal 
 and entablature, is given, the several portions are 
 thus found in all the orders. For the Tuscan, divide 
 the entire height by 5 ; the quotient is the pedestal, 
 and the remaining height, divided by 5, wiU give the 
 entablature. The remainder, divided by 7, gives the 
 lower diameter of the column. In the Doric, divide 
 the whole height by 5, for the pedestal ; one fifth of 
 the remainder is the entablature, the rest is the col- 
 umn, of which the eighth part is the diameter. Ionic 
 — deducting from the entire height one fifth for the 
 
 pedestal, one sixth of the remaining height is the 
 entablature, and one ninth of the remainder is the 
 diameter of the column. 
 
 CORINTHIAN. 
 
 After cutting off the pedestal, as before, the entab- 
 lature is one sixth of the remainder, as in the Ionic ; 
 and one tenth of the rest is the diameter of the col- 
 umn. For the Composite order, the same proportions 
 are employed. In laying down any order on paper, 
 draw a perpendicular right line to represent the axis 
 of the column. Near the bottom, draw another line 
 (horizontally) at right angles, on which, from the 
 perpendicular, set off on each side a distance equal 
 to a module, on one half the diameter. On a sep- 
 arate line equal to this diameter form a scale of sixty 
 equal parts or minutes, by which to measure all the 
 dimensions, reducing them to minutes from the num- 
 ber of feet and inches in which they are usually 
 given. The construction of such scale is, however, 
 generally unnecessary, from the variety to be found 
 on Gunter's and other scales of wood, brass, &c., 
 sold by the makers of mathematical instruments. 
 On the axis of the column produced below it, set off, 
 progressively downwards from the bottom of the col- 
 umn, the heights of the several members composing 
 the base and pedestal ; and through each of those 
 points draw pencil lines at right angles to the axis. 
 Again : from the same bottom line of the column 
 set up along the axis the several heights of the cap- 
 ital, architrave, frieze, and cornice, drawing, as be- 
 fore, lines at right angles through each point thus 
 ascertained. Then, from the axis, set off, on each 
 horizontal line, the proper projection of all the sev- 
 eral parts in order, by which means the true elevation 
 and projection of each \viU be obtained. The ex- 
 tremities of these horizontal lines are then connected 
 by the fillet, the ovolo, cyma recta, &c., according to 
 the kind of ornamental profile belonging to each par- 
 ticular order of architecture. 
 
 The relative proportions of the various parts of 
 the orders being accurately marked on the plates, 
 any account of them here might be regarded as a 
 work of supererogation. 
 
 A specimen of the Composite order, singularly 
 rich and beautiful, exists at Rome, in the triumphal 
 arch erected to commemorate the awful and pre- 
 dicted destruction brought upoia the city and temple 
 of Jerusalem by the Romans, in the year 70, under 
 Titus, during the reign of his father Vespasian.* 
 
 * The remains of this triumphal arch stand very near the south- 
 western limits of the ancient Forum. They are thus noticed by 
 Theodore Dwight, Esq., in the Journal of his Tour in Italy : " It 
 (the arch) is built with solidity, of large blocks of marble, in the 
 form of a simple gateway ; but the deep channels worn into its sur- 
 face by time, and the immediate historical connection it has with 
 the overthrow of Jerusalem, have imparted to it a moral grandeur 
 which even superior antiquity or magnitude alone could never 
 
24 
 
 INTRODUCTION. 
 
 Under the arch are sculptured the golden candela- 
 brum of seven branches, the tables of showbread, 
 and other spoils carried away from the temple. It is 
 the ingenious, and not improbable, fancy of some 
 eminent ^^Titers on architecture, that the general idea 
 of the Composite order, as it appears in the Arch of 
 Titus, was borrowed by some Roman artist in the 
 suite of that general from the structure of the Tem- 
 ple of Jerusalem itself, after the conquest of the city, 
 but before its final overtlirow. Josephus, it is trvie, 
 says the columns of the temple were Corinthian ; 
 but the dilTerences between that order and the Com- 
 posite might not attract his attention, nor would 
 they have been generally deserving of notice. At 
 any rate, the triumphal and tropheal Arch of Titus is 
 the most ancient monument in which the Composite 
 order is discovered. This arch possesses another 
 peculiarity, that it is supposed to be the first struc- 
 ture of the tropheal or triumphal kind erected by the 
 Romans — an example soon afterwards imitated by 
 the abject adulation of the people, or, rather, by 
 the insulting vanity of their princes, until at last 
 such trophies, being lavished without discrimination, 
 ceased to be marks of honorable distinction. 
 
 The feelings and duties of human beings in a 
 social state of existence natiurally spring from that 
 state. To a person brought up from infancy in abso- 
 lute solitude, such feelings would only produce mis- 
 ery, and such duties would be a nonentity. Let, 
 however, two persons be placed in mutual commu- 
 nication, and that instant feelings of kindness or 
 dislike, of affection or hatred, will arise. Let both 
 be hungry, and let an apple or an orange only be 
 procured ; this each will instinctively desire to appro- 
 priate to himself, for an equal distribution of the 
 object of their desires between them must be the 
 
 possess. Those who have read the Scriptures &om infancy, and been 
 taught to mourn with the saints and prophets of Israel over the des- 
 olation of the city of David and the house of God, can never ap- 
 proach, unaffected, and regard this monument of heathen triumph. 
 As we entered the shelter of the arch we trod the stones of the 
 old Sacred Way, which lay yet undisturbed under our feet — prob- 
 ably the same pavement that Titus passed over in his triimiphal 
 march to the Capitol, when they brought the spoils of the Holy 
 Temple and a largo company of Jewish captives. On the right are 
 seen, beautifully sculptured in relief, the seven golden candlesticks, 
 the silver trumpet, the table of showbread, and the book of the law, 
 all borne by priests marching in order ; and on the other side is the 
 emperor in his triumphal car, drawn by four horses harnessed 
 abreast, and represented with the highest skill of the sculptor. The 
 chariot is accompanied by the Genius of the Senate and Victory, 
 bearing a crown of a branch of palm from Palestine. This record 
 of history, containing more details than I have enumerated, still 
 speaks to the eye and to the mind in language as clear and impres- 
 sive as when it was first erected. But the unyielding spirit of the 
 captives retains, to tliis day, all its pride .ind sternness. There are 
 many Jews now in Home, the descendants of the prisoners of Titus ; 
 but it is said that not a son of Israel has ever passed this detested 
 Bpot, and trodden this part of tlic Sacred Way, since the day of his 
 triumph. They still delight to trace back their pedigree to those 
 whose humiliation they have inherited ; while, it is said, not a man 
 in being can establish a clear and undoubted claim to the blood of 
 any ancient Roman family." 
 
 result of posterior experience and reflection, and not 
 the spontaneous suggestion of the occasion. If the 
 one is a little stronger or more alert than the other, 
 he w'\\\ avail himself of these advantages over his 
 fellow-being to seize the object of his wishes. By 
 this sole appropriation, the other sustains not an 
 imaginary, but a real, loss. The natural desire for 
 necessary aliment will aggravate his feelings of dis- 
 appointment and defeat into aversion, resentment, 
 and revenge against his spoiler ; and should lie be 
 frequently thwarted in a similar way by his com- 
 panion, notliing short of the entire destruction of 
 that companion will appear sufficient to secure him- 
 self from future privations and sufferings. This 
 process will take place in the breast of the weaker 
 being, even although the stronger should not attempt 
 to assitme to himself still greater advantages, in 
 consequence of his acknowledged superiority. That 
 the latter will, however, be governed by sentiments 
 so moderate, is extremely improbable. Tlie self- 
 gratulation arising from consciousness of power 
 wiU yield a flower too delicious not to induce the 
 desire of again experiencing such delight. He will 
 thus naturally be disposed to exercise his superior 
 faculties, not when the calls of necessity only, but 
 when the suggestions of vanity or caprice, may fiu-- 
 nish opportunity. Hence, his feebler neighbor will, 
 by degrees, be reduced to absolute slavery, depend- 
 ent on the other for even the necessary means of 
 existence ; and of this existence itself, should he 
 long continue refractory, he will probably be at last 
 deprived. Thus may be traced the origin of the 
 worst feelings and actions by which human beings 
 are distinguished ; and by a similar, bttt opposite, 
 process, may the rise and progress of the best senti- 
 ments and conduct be explained. In absolute se- 
 questration and solitude, neither virtue nor vice can 
 exist ; but without virtue and vice in society, human 
 beings can have no existence. When this simple 
 and obvious theory of what is called the origin of 
 evil (a theory by far too simple and too obvious to 
 have fixed the attention of presumptuous philosophy 
 in any period of the world) is considered, it will ex- 
 cite no surprise that the history of mankind, imder 
 even the most favorable circumstances, sliould pre- 
 sent little else than an endless chain of deplorable 
 wickedness and WTctchedness, equally the natural 
 consequences of folly and vice. " We are a con- 
 temptible gang of plunderers, pests of society, mer- 
 iting, forsooth, punishment the most severe and dis- 
 graceful, because we appropriate to ourselves the 
 property of unoffending men, and even, on some 
 occasions, deprive the owners of life ; and all this we 
 do, few in number, more frequently by secret strat- 
 agem than by open force, and even in some measure 
 authorized by the sanction of necessity. Thou, on 
 the other hand, born to independence, to wealth, to 
 power, to supreme dominion, without even a rival to 
 
INTRODUCTION. 
 
 25 
 
 attempt to obstruct the gratification of thy desires, 
 without provocation, without invitation, without ne- 
 cessity, without any motive or reason which a man 
 of genuine coru'age and truth, a friend to human kind, 
 would avow ; thou destroyest cities, the abode of in- 
 dustry, knowledge, and patriotism ; thou layest waste 
 peaceable and flourishing countries, where thou hast 
 received no injury ; thou causest to flow torrents of 
 the blood of nations who never even heard of thy 
 name ; and all this thou dost at the head of armed 
 myriads, in open defiance of common justice and hu- 
 manity ; therefore art thou exalted to the rank of a 
 hero, a conqueror of worlds, a demigod." In such a 
 strain, we are told, was the mighty Alexander of 
 Macedon addressed by the chief of a petty band of 
 pirates who fell into his hands, and whom he con- 
 ceived himself autliorized to punish, in an exemplary 
 manner, for their outrages on society ; and the obser- 
 vations are fully warranted by the undeviating prac- 
 tice of aU people and of aU times. Hence, we find 
 in the most ancient records of human society ap- 
 plause and reward lavishly bestowed on the successful 
 warrior, whether just or unjust the cause in which 
 he was engaged. But, beside tliis and other marks 
 of the real or supposed admiration and gratitude of 
 their armies and people, conquerors were in the habit 
 of constructmg some more substantial evidence of 
 their victories on the scene of their exploits. 
 
 At one time a rude block of stone, at another a 
 mould or liillock of stones and earth, raised on the 
 field of battle, served at once to point out the spots 
 where the honors of the victor were achieved, and 
 where rested from their toils the human beings thus 
 cut off in the performance of the duties he imposed. 
 Of such monuments many examples still survive the 
 long lapse of ages, in Great Britain — in Cornwall, in 
 Wales, and in Scotland. These dumb memorials 
 came at last into disrepute ; they recorded, indeed, a 
 slaughter and a victory ; but succeeding generations, 
 when tradition grew feeble or entirely died away, 
 were left to conjecture the cause of their erection ; 
 and the mighty warrior was thus bereft of half his 
 glory. When the Romans began to establish them- 
 selves in the southern parts of Gaul, and to extend 
 the boundaries of their province, now Provence, Lan- 
 guedoc and Dauphiny, in France, they first constructed 
 durable memorials of the success usually accompany- 
 ing the exertions of united and well-disciplined bands, 
 although far firom numerous, against countless mul- 
 titudes of irregular, ungovernable barbarians. Two 
 Roman generals, Domitius ^nobarbus and Fabius 
 Maximus, erected on the banks of the Rhone, saxosw 
 turres, towers built of stone, supporting trophies, con- 
 sisting of arms offensive and defensive, standards, 
 instruments of martial music, and other pledges of 
 victory taken from the ancient CJauls. This conduct 
 on the part of their commanders was highly reproved 
 at Rome ; for untQ then the Romans had never al- 
 
 4 
 
 lowed themselves, even after their most signal success 
 in war, to erect, in the midst of a conquered people, 
 any monument whatever, by which they should be 
 reminded of their subjection, and, consequently, be ex- 
 cited to endeavor to regain their former independence. 
 " Never before this," says the historian, "did the Ro- 
 man people upbraid any conquered nation with their 
 own defeat." This happened about one hundred and 
 twenty years before England's era. Some time after- 
 wards, Pompey constructed, on the summit of the 
 Pyrenees, near their eastern extremity, a permanent 
 building, as a memorial of his successes, slight enough, 
 indeed, over the partial but patriotic attempt of the 
 Spaniards to throw off" the Romish yoke. This ac- 
 tion was severely reprobated at Rome. The same 
 magnanimous sentiment actuated not the free states 
 of Greece only, but even the despotic and military 
 kingdom of Macedon. " States and nations," said 
 those ancients, "like individuals and families, will 
 differ upon particidar points, where their interests, real 
 or supposed, are concerned. These differences will 
 lead to quan-els, and even to the most hostile proceed- 
 ings and opeir warfare. It is not unnatural that, in 
 these contests in arms, the victors should endeavor to 
 confirm the courage and ardor of their own people, 
 and to depress the spirit of their adversaries, by some 
 public testimony of their superiority. For such a pur- 
 pose, a few helmets, and breastplates, and shields, 
 and swords, taken from the vanquished and supported 
 against a spear, or suspended on a tree, on the scene 
 of victory, will be fidly sufficient : let not, however, 
 such emblems of superiority be of long duration. 
 The passions of men will cool, their views of interest 
 will change, and the parties which to-day meet with 
 deadly rancor in the field will be found in a short 
 time united in one common cause, and fighting, as 
 friends and brothers, against an ally of one of the 
 parties on a former occasion, but now become a com- 
 mon foe. It is, besides, to be considered that suc- 
 cess in war is not always attached to one side ; no 
 nation was ever always victorious, nor always dis- 
 comfited. Let us never, therefore, by permanent rec- 
 ords of our temporary superiority, labor to cherish and 
 foment among oiur neighbors that spirit of hostility 
 which, at no distant day, it may be equally our de- 
 sire and our interest entirely to extinguish. Lijuries 
 men often will, and do, forgive ; insults, perhaps, 
 never." Such were the wise and magnanimous sen- 
 timents and principles of the Greeks and Romans, the 
 two most enlightened nations of antiquity, in their 
 best days. In the degenerate days of Titus and Ves- 
 pasian, however, when Rome reigned paramount over 
 the greater portion of the civilized world, the feeling 
 of national importance and independence, the source 
 and support of every manly, generous, and patriotic 
 principle, was next to extmct in the nations of Eu- 
 rope. The example set in the case of Titus was 
 speedily followed ; and not only Rome itself, but 
 
 D. H. HILL LfBRARY 
 North Carolina Stafe College 
 
26 
 
 INTRODUCTION. 
 
 numbers of tlie principal cities over the empire, were 
 adorned with edifices, triumphal, tropheal, and com- 
 memoratory, many of which stiU remain, exhil)iting 
 admirable specimens of architecture and sculj)ture, 
 and, by the inscriptions and representations with which 
 they are charged, serving to illustrate and establish 
 the dates of laiany important historical facts. Wis- 
 dom, justice, and moderation arc immutable ; and, 
 as such, never (let weak, and consequently narrow- 
 minded, men say what they may) can be inexpedient 
 or out of season. Human nature is, at this day, what 
 it was twenty centuries ago. Let, then, the prudence 
 and humanity by which states were then governed, 
 and not the overbearing presumption and insolence 
 on the one hand, and tlie abject, interested adulation 
 on the other, by which later periods have often been 
 characterized, suggest the most commendable models 
 for modern imitation. 
 
 But to return to the jVixh of Titus. It may be just 
 to add, that the unfortunate branches of the Hebrew 
 nation established in Rome made an arrangement, 
 many years ago, with the government, agi-eeably to 
 which, for the payment of a certain sura of money, 
 they were permitted to open a naiTow passage by the 
 side of that arch, which, although not now connected 
 with the inhabited part of the town, is situated in the 
 heart of the old city, on a very public thoroughfare, 
 that then- minds might not be tortured unnecessarily 
 by the display of the emblems of the final dcsti-uction 
 and extinction of their religion and their state, of 
 their name and their nation. This digression the 
 reader will, it is trusted, without difficulty pardon. 
 It arose natm-ally from the subject, and may, per- 
 haps, suggest certain considerations not entncly un- 
 profitable. 
 
 With respect to the kind and degree of ornaments 
 to be introduced into a column and its appendages, 
 it is a maxim, founded in our natural sentiment of 
 what is decorous and beautiful, that if we are in 
 doubt concerning the proper medium, we should al- 
 ways stop short of the proposed point, and be careful 
 never to go beyond it. The pupU of an ancient 
 painter in Greece produced a Venus loaded with jew- 
 els. " Unable to make the goddess bcautifid," said 
 his master, " you have thought to atone for that de- 
 fect, by making her rich and fine." The dignified 
 sobriety and gravity becoming an edifice appropriat- 
 ed to religious purposes or to the senatorial and 
 legislative assemblies of a great and enlightened peo- 
 ple; the massive solidity and strength inherent in our 
 idea of a forh'css; the light, airy, exhilarating notion 
 attached to the name of a theatre or other places of 
 amusement, — all these qualifications of the edifices to 
 be conslrneted will, to an architect of genius, suggest 
 the species and (he measure of the ornament suitable 
 to each. A slender, delicate, and highly-enriched 
 Corinthian portico to Newgate prison could not be 
 more incongruous, nor indicate a greater want of 
 
 taste in the builder, than a massive, heavy, clumsy 
 Doric (if Doric it be) range of pUlars, and their pedi- 
 ments coiTcspontUng — apparently forbidding, but 
 doubtless meaning to invite, the passing sh-anger to 
 enter the theatre of Covcnt Garden. When we ex- 
 amine the monuments remaining from antiquity, we 
 find that the cyma, the cavetto, or other ornament, 
 formed by cutting into the substance of the work, 
 is employed as a finishing only, and never where 
 strength is required ; that the ovolo and talon are 
 employed to support the essential parts of the entab- 
 lature, such as the modillions, dentils, and corona ; 
 that the principal use of the torus and astiagal is to 
 secm-e and strengthen the extremities of the columns, 
 being also employed for the same purpose in pedes- 
 tals, carved so as to resemble a rope or cable, agree- 
 ably to the original signification of the term torus ; 
 that the scotia serves merely to separate the members 
 of the base, as does also the fillet, not only in the 
 base, but in profiles of all kinds. By the term pro- 
 file, is here meant the assemblage of parts, mouldings, 
 and ornaments of a cornice, &c., in which the eleva- 
 tion and projection of each member are exhibited. 
 The most perfect profiles are those consisting of the 
 fewest mouldings, adapted to the order of the column, 
 so disposed that the right lined and the cm-vcd mem- 
 bers succeed one another alternately. In every profile 
 one member should be predominant, to which all oth- 
 ers must appear subordinate : thus, in a cornice, the 
 corona is the chief member, the cyma of the cavetto 
 covers and defends it from the rain, while the modil- 
 lions, dentils, ovolo, and talon serve to support it. 
 In the arrangement of the exterior of a building, 
 whatever does not tend to characterize its destina- 
 tion, however beautiful in itself, is always misplaced. 
 Greatness of character in an edifice is principally 
 produced by largeness and simplicity of parts ; such 
 parts, not only by their own magnitude, but by the gi-eat 
 masses of light and shade tliey exhibit when fully 
 illuminated, excite the idea of grandeur. An object 
 may be gi'cat, and not be grand ; but gi-andeur and 
 smallness of parts are incompatible. One of the most 
 extensive edifices in Europe is the King of Spain's 
 palace, at the Escurial, not far from Madrid. It 
 covers a vast extent of gi'ound, enclosing a number 
 of courts, porticoes, chapels, &c., in its bosom. Hav- 
 ing, however, been constructed as a monastery rather 
 than as a palace, (for the royal apartments are con- 
 fined to a very small portion of the structure, the 
 building is divided into various floors, and conse- 
 quently, the exterior walls are pierced with various 
 ranges of comparatively small windows, adapted to 
 the cells and halls of monks. The consequence of 
 all this is, that the idea of grandeur and magnificence 
 raised in the mind of the spectator, while approach- 
 ing it from a distance and observing its prodigious 
 dimensions, entirely vanishes away, when, on a closer 
 view, the whole is discovered to be only an assemblage 
 
INTRODUCTION. 
 
 27 
 
 of small diminutive parts and members, such as 
 might be suitably introduced into a manufactory, a 
 barrack, a hospital, or a convent. Many objections 
 have been made to Blenheim Palace, in Oxfordshu'e, 
 England, as clumsy, ponderous, inelegant, and by no 
 means corresponding to the customary notion of a 
 country residence. That magnificent edifice was 
 erected, at the expense of the nation, to commemo- 
 rate the signal victory obtained in 1704, near Blen- 
 heim, a village on the north bank of the Danube, by 
 tlie allied army, under the Duke of Marlborough. 
 That distinguished and modest commander stands, 
 next to Julius Ctesar, unrivalled in history for perfect 
 coolness and possession of himself in action ; who, 
 so far from ever exposing himself to the possibility 
 of being svu-priscd, whatever might have been the 
 talents of his opponent, never rested until he was so 
 close upon the enemy as, in many cases, to discover 
 their measures, and prevent their forming any project 
 against himself for the greater part of the campaign. 
 Like Cirsar, also, in person a hero, he was scrupu- 
 lously tender of the lives of his men, and, to spare 
 them, would often forego the opportunity of a bril- 
 liant, but sanguinary and i;seless victory, for the more 
 slow, but more secure and difficult advantages to be 
 obtained by a sldlful occupation of ground. On a 
 due consideration of the destination of Blenheim, it 
 will be manifest that the architect, Sir John Vanburg, 
 intended, by throwing the structure into a variety of 
 large, projecting, and retmng masses of building, to 
 produce broad and powerful eflccts of light and 
 shade, and by that contrivance to fill the spectator 
 with the idea of the vast magnitude of the parts and 
 of the whole far beyond what their real magnitude, 
 considered as it is, could be expected to excite. 
 
 Besides regular columns and pilasters, we some- 
 times meet, in ancient and modern architecture, en- 
 tablatiu'cs supported by human figures. These are 
 termed Cari/atidcs, from the following circumstance : 
 Five hundred years before our era, Xerxes, the power- 
 ful monarch of Persia, led a prodigious army and 
 fleet against the free and independent republics of 
 Greece. Successful at first, more by treachery than 
 by valor, he was at last discomfited at every point, 
 and compelled to return in disgrace and ruin to his 
 own country. Carya, a town of Peloponnesus, had 
 basely formed a league with the invader ; and upon 
 his flight it was besieged by the other states, levelled 
 to the ground, the male inhabitants put to the sword, 
 and the unhappy, perhaps innocent, females reduced 
 to slavery of the severest land. To perpetuate to 
 future ages the infamy and punishment of the people 
 of Carya, in Athens, and in many other parts of 
 Greece, buildings were erected, in which were intro- 
 duced, in the place of columns and pilasters, figures 
 of Caryan women supporting the load of a cornice 
 and entablature. In general, these figiu-es are at- 
 tached, like pilasters, to the wall ; but in Athens they 
 
 arc also found detached, and performing the duty of 
 columns. Male figures are also employed in the 
 same way in some ancient buildings in Greece and 
 in Rome ; in Greece, they are evidently intended to 
 represent Persian prisoners taken from Xerxes. 
 From this account, it is evident that human figures, 
 in the place of columns or pilasters, ought, if at all, 
 to be introduced on very particular occasions indeed. 
 They nevertheless are often seen in the palaces of 
 princes, and even in private dweUmgs. Our churches 
 themselves, in which all adventitious distinctions 
 among mankind ought, if any where, to disappear, 
 are not free from this absurdity. These poor females, 
 humiliated, borne down with a heavy load, are meant, 
 we are to understand, for the Muses and the Graces, 
 the Vu-tues, and the Angels themselves. Could the 
 vices which corrupt, and the furies which torment, the 
 human race be thus chained down, and so rendered 
 in some sort subservient to our use, such an applica- 
 tion of Persians and Caryatides might easily be 
 reconciled to reason. 
 
 Not only entire human figures, but simple busts, 
 are also employed, occasionally, to support the entab- 
 latiues of monuments, chimney pieces, &c. The 
 head is placed on a stand, smaller below than above ; 
 and the whole is called a term, from terminus, a 
 boundary, the Roman name of the landmarks or 
 march stones erected on fields and possessions to 
 point out the boundaries between the lands of differ- 
 ent proprietors. The protecting charge of these land- 
 marks, as of every thing else connected with the affaks 
 of industry and commerce, being intrusted to Mer- 
 cury, by the Romans as well as the Greeks, the top 
 of the stone or post was carved in resemblance of his 
 head ; so that to destroy, or remove, or deface such 
 monuments was regarded not only as gross uijustice 
 to men, but as a voluntary and impiovis offence 
 against the powers above. 
 
 It now remains to give a few observations on the 
 constructions of bridges, one of the most important 
 and difficult applications of architectural skill. 
 
 CONSTRUCTION OF EraDGES. 
 
 By a bridge, we mean a structure of stone, brick, 
 timber, or iron, erected over a river, a canal, a vaUey, 
 or other depression in the ground ; and supported on 
 piers and arches, or on posts, for opening a communi- 
 cation for passengers, cattle, and carriages across 
 from the one side to the other. 
 
 The perfection of a bridge consists in its having a 
 good foundation, that it may be dm-able ; of an easy 
 ascent and descent, that it may be convenient ; and 
 of a just proportion in its several parts, that it may 
 be beautiful. Bridges should always be placed at 
 right angles to the course of the river, &:c., and the 
 piers should never be thicker than is just necessary 
 
28 
 
 INTRODUCTION. 
 
 to support the structure against the force of the 
 current. 
 
 The simplest theory of the arch supporting itself 
 in eqiiilihrio (that is, in such a state that the ten- 
 dency of every part to fall down or give way is per- 
 fectly equal) is that of Dr. Hookc, the greatest of all 
 philosophical mechanics, who flourished in tiie latter 
 part of the seventeenth century. The arch, when it 
 has only its own weight to bear, may be considered 
 as the reverse of a chain suspended freely at each 
 end ; for the chain hangs in such a form that the 
 weight in each link is held in equilibrio by the result 
 of the tsvo forces acting at its extremities. Two 
 forces, or tensions, are produced, the one by the weight 
 of the portion of the chain below any particular link, 
 the other by the same weight, increased by that of 
 the link, both of them acting originally in a vertical 
 direction. Now, supposing the chain inverted so as 
 to constitute an arch of the same form and weight, 
 the relative situation of all the lines indicating the 
 direction of the forces will remain the same, the 
 forces acting only in contrary directions ; so that they 
 are compounded in a similar manner, and balance 
 each other on the same conditions, but with this dif- 
 ference, that the equilibrium of the chain is stable, 
 and that of the arch is tottering. When the links are 
 supposed to be infinitely small, and the curvatiu-e of 
 the chain is greatest in the middle, the chain forms 
 what is called a catenarian curve, from catena, a chain. 
 In common cases, this form of an arch differs but 
 little from a circular arch of about one hundred and 
 twenty degrees, or one third of a whole cncle, rising 
 ftom the abutments, with an inclination of thirty 
 degrees to the perpendicular ; the arch, however, be- 
 comes more curved at some distance below the sum- 
 mit, and then again less curved. The supposition, 
 however, of an arch resisting a weight acting only in 
 a vertical dhection, is by no means perfectly applica- 
 ble to cases usually occurring in practice. The pres- 
 sure of loose stones and earth, moistened as they gen- 
 erally must be by rain, is exerted very nearly in the 
 same manner as the pressure of fluids, which act 
 equally in all directions; and even if the stones and 
 earth were united in a solid mass, they would consti- 
 tute a sort of wedge, and produce a pressure of a 
 similar nature. 
 
 A bridge must also be so calculated as to support 
 itself without being in danger of fallmg by the de- 
 fect of the lateral adhesion of its parts. Li order 
 that it may, in this respect, be of equal strength 
 throughout, the depth at each point must be propor- 
 tional to the weight of the parts beyond it. This 
 property belongs to the logarithmic curve alone, the 
 length being made to correspond with the logarithm 
 of the depth. But, in the construction of bridges, it 
 is necessary to inquire what is the best form for sup- 
 porting any weight which may occasionally be placed 
 on the bridge ; in particular, on its weakest part. 
 
 which is usually the middle of the arch. Supposing 
 the depth at the summit of the arch and at tiie abut- 
 ments to be given, it may be considerably reduced in 
 the intermediate parts, without impairing the strength; 
 and whether the road along the bridge be horizontal 
 or a little inclined, it is agreed that an elliptic arch, 
 not differing much from a circular, is the best calcu- 
 lated for complying, as much as possible, with all 
 necessary conditions. 
 
 The tier of bricks cut obliquely, which is placed 
 over a door or window, is a real arch, but so flat as 
 to allow the outline to appear horizontal. Little 
 dependence, however, can be placed on so flat an 
 arch, since it j^roduces a lateral thrust, that might 
 easily overpower the resistance of a side wall. For 
 the horizontal force required to support each end of 
 an arch is always equal to the weight of a quantity 
 of the materials supported by its summit, supposed 
 to be continued of their actual depth, to the length 
 of the radius of the circle, of which the summit of 
 the arch is a portion. This simple calculation will 
 enable an architect to avoid such accidents as but too 
 often happen to bridges for want of sufficient firm- 
 ness in the abutments. Very eminent modern arclu- 
 tects have sometimes been less successful in con- 
 structing arches of bridges and other edifices than 
 those of former times, whom it is but too common to 
 despise ; and, for want of attention to mechanical 
 principles, they have committed such errors in their 
 attempts to procure an equilibrium as have been 
 followed by the most mischievous consequences. 
 Examples of this mismanagement might be pointed 
 out in the bridges of our own country, and the 
 churches of others ; but if we are masters of the true 
 nature and action of pressure, we shall be able to 
 avoid similar errors, unless some defect in the mate- 
 rials, the foundation, &c., occur, Avhich could not be 
 foreseen. 
 
 It is desirable that the piers of bridges should be 
 so firm as to be able not only to support the weight 
 of half of each adjoining arch, but always to sustain 
 the side thrust of one of them, should the other give 
 way. The same condition is necessary for the sta- 
 bility of walls of any kind employed in supporting 
 an arched or vaulted roof; hence the utility of the 
 external buttresses, which strengthen and adorn 
 Gothic structures. There are two w^ays in which a 
 pier or a wall may give way ; it may either be over- 
 set, or caused to slide away horizontally. But since 
 the friction or adhesion ■which resists the side motion 
 is usually greater than one third of the pressure, it 
 seldom happens that the whole thrust of the arch is 
 so oblique as not to produce a sufficient vertical 
 pressure for secm'ing the stability in this respect', 
 and it is only necessary to make the pier heavy 
 enough to resist the force which tends to overset it 
 It is not, however, the weight of the pier only, but 
 that of half of the arch which rests on it, that resists 
 
INTRODUCTION. 
 
 29 
 
 every effort to overset it ; and, in order that the pier 
 may stand, the sum of these weights acting on the 
 end of a lever, equal to half the thickness of the pier, 
 must be more than equivalent to tlic horizontal 
 thrust acting on the whole height of the pier. The 
 pier may also be considered simply as forming a 
 continuation of the arch ; and the stability will be 
 preserved as long as the curve indicating the direc- 
 tion of the pressure remains within its substance. 
 The dimensions of the piers must depend on the 
 size and form of the arch, as also on the force of the 
 current to be opposed. In tide rivers, the current 
 acts twice a day in contrary directions, rising consid- 
 erably above the surface of the river itself, and re- 
 turning to that level. The pressure on the piers is, 
 therefore, very unequal ; and, from the circumstance 
 that the stones must be thus in a continual alteration 
 between wet and dry, the selection and placing of 
 the materials becomes a matter of the greatest im- 
 portance. Some persons are of opinion that blocks 
 of stone resist the action of water and sun, of 
 wet and dry weather, best, when placed exactly in 
 the same position as when they lay in the quarry. 
 Whether this circumstance, if real, was attended to 
 or not in the construction of Blackfriar's Bridge, in 
 London, or whether the stone was of an improper 
 kind, it is certain that such parts of the piers as are 
 exposed to be covered by the tide are now in a state 
 of manifest decay, while the corresponding parts of 
 Westminster Bridge are comparatively but little 
 affected, although it was founded in 1738, and the 
 former bridge not till 1760. The new Strand Bridge 
 is built of granite, the least svibject to decay of all 
 stone from external causes. The stone employed in 
 constructing the grand quay along the front of the 
 arsenal of Woolwich, in England, was drawn from 
 the vicinity of Dundee, in Scotland, and is found to 
 answer much better in such a situation, where it is 
 alternately, with short intervals, wet and dry, than 
 any formerly employed. It has been likewise used 
 in some of the great basins and docks in London, 
 and in constructing the piers to support the iron 
 bridge over the Thames, at Vauxhall. 
 
 In building a bridge, the most essential part of 
 the enterprise is to secure a good foundation. The 
 most simple method of doing this, and carrying up 
 the piers to the ordinary height of the water, is to 
 turn the river out of its course, above the position of 
 the bridge, into a new channel opened for it, near 
 the place where it makes an elbow or bend, or by 
 raising an enclosure round the spot where the pier is 
 to be buUt, to keep out the water, by driving a double 
 row of piles into the bed of the river, very near one 
 another, with their tops above the siurface of the 
 water. Hurdles are then put within this double 
 row of piles, the side of the row which is next the 
 intended pier is closed up, and the hollow between 
 the rows filled with rushes and mud, so closely 
 
 rammed down that water will not pass through. 
 The mud, sand, stones, &c., within this enclosure, 
 are dug out, until a solid foundation appears. When 
 such a foundation cannot be found, one of wooden 
 piles, having their lower ends well charred to prevent 
 rotting, and driven into the bottom of the river as 
 close together as possible, must be made. Some 
 architects have formed a continued foundation the 
 whole length of the bridge, and not merely under the 
 piers. In doing this, first one part of the river is 
 excluded, and then another, until the whole foun- 
 dation be laid. When a river is but of moderate 
 depth, having such a bed as may serve for a natural 
 foundation, capable of bearing, without subsidence, 
 in whole or in part, a heavy pier, then a strong frame 
 of oak is constructed, and kept upon the surface by 
 boats around it. On this frame is laid a thick stra- 
 tum or layer of stone, cramped together by iron bars, 
 and united by strong terras mortar, the whole of 
 which, being then specifically heavier than the water, 
 is suffered gently to sink down to the bottom, where 
 the pier is to stand. If it be required to construct a 
 bridge across a fordable river, or a canal, where the 
 covu'se of the water may be turned off, either by a 
 wooden fence placed obliquely across the river or by 
 a channel dug one side, then a dam must be formed 
 entirely across the stream, with pUes at a convenient 
 distance above the place of the intended bridge. 
 The ground is then dug out, until a proper solid 
 foundation presents itself, and all the piers may be 
 founded and raised up to the usual height of the 
 river at the same time ; after which, the river is per- 
 mitted to return to its original channel. When the 
 stream is by far too considerable to be tiu-ned aside, 
 coffer dams are formed, of a circular shape, to enclose 
 the spot where each pier is to be built. The dam is 
 made, as before said, by driving into the bed of the 
 river a double row of stout piles, either charred at 
 the lower end, when the bed is easily penetrable, or 
 shod for several feet with ii'on where it is hard. The 
 pUes are forced into the ground by repeated blows 
 from the pile engine ; the piles are covered with 
 boarding, without and within, so as to be tolerably 
 water tight ; and the water which does make its way 
 through the walls, or which springs out of the en- 
 closed bed, is drawn off by pumps and hand labor, 
 or, if the undertaking be considerable, by means of 
 a steam engine. 
 
 Besides bridges, other bodies of masoiu'y are also 
 requisite, if not completely to transverse, at least to 
 advance, a considerable way into the water. Such 
 are the moles and piers carried out from the land 
 into the sea, from opposite points of the shore, and 
 mutually bending round towards each other at their 
 extreme points, where they leave an interval suffi- 
 cient for the passage of ships out or in. In our seas, 
 where we have the advantage of the retreat of the 
 sea twice a day, at low water such structures can be 
 
30 
 
 INTRODUCTION. 
 
 founded and carried up, in general, without partic- 
 ular difficulty. In the Mediterranean, however, where 
 the rise and fall of the tide is either very unimpor- 
 tant or wholly insensible, — as along the coasts of 
 Spain, France, Italy, &:c., — the construction of a mole 
 becomes an enterprise of vast labor, difficulty, and 
 expense. 
 
 The work begins at the shore, by throwing into 
 the sea blocks of rock or stone, the larger the more 
 useful. These find thcii- place in the bottom, and, 
 by accumulating block upon block over them, they 
 at last rise above the surface of the water. The 
 work being so far advanced, advantage is taken of 
 the blocks above water to form a road, by which 
 other blocks arc carried out and rolled into the sea 
 beyond those akeady placed, and these again in their 
 turn serve, when they come to the surface, to convey 
 another succession of blocks, until the foundation of 
 the mole be earned out to the intended extent. When 
 we take into consideration the inequalities of the 
 bottom of the sea, where not covered with hard sand, 
 the incessant internal motion of the waters, produced 
 by currents, to say nothing of the superficial agita- 
 tion produced by the winds, that most rocks and 
 stones lose a great part of theu- weight when im- 
 mersed in salt water, — and are, consequently, more 
 easily moved about from place to place by the mo- 
 tion of the waters, — also the gi-cat extent in breadth 
 to which rude blocks of stone or rock will necessa- 
 rily roll before they find a bed, cither in the bottom 
 of the sea, or on one another, — when all these things 
 are considered, the structure of moles and piers in 
 such seas must appear to be an enterprise of extreme 
 difficulty and expense. In siich seas, however, no 
 other mode of consti-ucting an artificial harbor can 
 be devised. When the foundation is supposed to be 
 sufficiently consolidated, and is raised above the 
 aurface of the water, the mole is completed by a 
 structure of hewn stone, founded in the interstices of 
 the sunk blocks, adapted to the purposes of com- 
 mercial and maritime affairs. Of this constriiction 
 are the old and new models of Gibraltar, of Alicant, 
 Tarragona, and Barcelona, in Spain ; of Sette and 
 Toulon, in France ; of Genoa, Leghorn, Civita 
 -^ Vecchia, Naples, and Anchona, in Italy, (S:c. The 
 famous antique mole at Pozzuoli, in tlic Bay of 
 Naples, is constructed with piers and arches founded 
 in the sea, and is, fi-om its appearance, called Calig- 
 ula's Bridge, having been, as is supposed, erected by 
 that imperial monster. On the same principles with 
 the moles just described is consti-uctcd what is called 
 the Breakwater, in the enti-ancc of Plymouth Haven, 
 in England, in the view of abating "the violence of 
 the waves and currents which have, on many occa- 
 sions, proved most prejudicial to the fleets resorting 
 to that otherwise admirable station for shipping of 
 every sort. In the report laid before the British 
 Parliament concerning this prodigious enterprise, 
 
 which was earned on at the public expense, the en- 
 gineers, Messrs. Rennie and Whitby, (the former the 
 engineer for the Strand Bridge, in London,) state 
 that tliere are, properly spealdng, tliree entrances into 
 Plymouth Sound or Haven, viz., one on the west 
 side of the bay, bounded by a long cluster of small 
 rocks, called Scott's Ciround, and the depth is only 
 from 3 to 4 fathoms, (fi-om 18 to 24 feet,) at low 
 water ; and on the east by the Knap and Panther, 
 on which is about the same depth of water. This 
 channel is about 500 fathoms wide, and the general 
 depth is from 5J to 6 fathoms at low water. The 
 middle channel is bounded by the Knap and Panther 
 on the west, and by tlie Tinker and Shovel on the 
 cast ; about 300 fathoms wide, and the general depth 
 from 6i to 8 fathoms, at low water. 
 
 From this description, it appears that a large part 
 of the middle of Plymouth Sound is shut up by the 
 Shovel and St. Carlos's Rocks ; that is, as a channel 
 for large ships. Of com'sc, works erected on those 
 rocks would be no obstruction to a passage in or out 
 of the Sound. If a pier or breakwater were con- 
 structed on the Shovel Rocks, and extended west- 
 ward, so as to shut up in part the channel between 
 them and the Panther, and also to shut up or narrow 
 the spaces between St. Carlos's Rocks and Andurn 
 Point, the tide being then confined to a naiTow space, 
 the velocity of the current would be increased, and, 
 consequently, the channels where it passed. It 
 seemed, therefore, proper that a pier or breakwater 
 should be constructed in the Sound, having its east- 
 ern end about 60 fathoms east from St. Carlos's 
 Rocks, and its western end about 300 fathoms west 
 from the Shovel, forming, in the whole, a length of 
 850 fathoms. Of this pier, 500 fathoms in the mid- 
 dle should be straight, and 175 at each end inclined 
 at an angle of 120 degi-ccs. In addition to this 
 breakwater, another should be extended fi-om Andurn 
 Point, on tlie shore, towards the former, of about 400 
 fathoms in length, having also a part inclined at an 
 equal angle. These inclined parts were to repel the 
 waves in such a manner as to prevent them from 
 passing violently through the opening between the 
 piers, and to shelter tlie Sound within, so as to permit 
 fifty sail of line-of-battle ships to ride at anchor in 
 safety, in all winds and weather, and with ample 
 room to work thek way out to sea, by one or other 
 of the channels, as then- position and state of the 
 wind might render most convenient. 
 
 These great works were to be constructed by large 
 blocks of stone thrown at random into the sea, in the 
 line of the intended breakwater, to find their own 
 bed. Stones from a ton and a half to two tons in 
 weight would probably resist the swell of the Sound, 
 in stormy weather. Where the water is five fathoms 
 deep, the base of the breakwater should not be less 
 than seven times that depth, or seventy yards in 
 breadth, and ten yards broad, at a height of ten feet 
 
INTRODUCTION. 
 
 31 
 
 above the level at low water or ordinary spring tides. 
 The slope of this foundation on tlio outer side, next 
 to the sea, should be in tlic proportion of three yards 
 horizontal for one yard perpendicular ; but the slope 
 on the inside, next tlie Sound, would require an in- 
 clination of only half that quantity, or one and a 
 half yards horizontal for one yard perpendicular. To 
 the project here described (and now completed) 
 various objections were made, particularly by Mr. 
 Bentham, who had executed some works at Shecr- 
 ness, at the conflux of the Thames and the jNIedway, 
 somewhat of the same nature, but in circumstances 
 incomparably more easy to manage than in the open, 
 stormy entrance at Plymouth Sound. He observed 
 that such a work as that proposed by Messrs. Rennie 
 and Whitby, even supposing sufficient precaution to 
 have been taken to prevent any injury to the harbor 
 during its execution, and that the whole were com- 
 pleted in its gi'catcst perfection, would, nevertheless, 
 by opposing throughout its extent a complete inter- 
 ruption to the water, occasion such eddies in the 
 wake of the work, and such an increased action on 
 the bottom and sides of the parts left open, as could 
 not fail of forming shoals, more or less injurious, 
 according to the nature of the soil and other local 
 ch-cumstances. Mr. Bentham's plan was to sink in 
 the sea, but in a line of dkection difterent from that 
 of the other engmeers, a double row of cylincbical 
 masses of stone work, leaving an interval between 
 each two masses above equal to their diameter; 
 placing the masses in one row opposite to, and cover- 
 ing the intervals between, the masses in the other 
 row. By this an-angement, while the two rows in 
 conjunction formed a complete obstacle to the dii-ect 
 course of the waves, tlie tide or current would be 
 allowed to pass freely between the masses, through- 
 out the whole extent of the breakwater ; boats also, 
 and even small vessels, might, in moderate weather, 
 pass through the intervals without danger. Notwith- 
 standing these objections and proi>osals, the scheme 
 of Messrs. Rennie and Whitby, all circumstances 
 duly balanced, was adopted by government, and or- 
 dered to be earned into effect. On a plan much of 
 the kind proposed by Mr. Bcnham, was begun in 
 France, before the revolution, a project for forming 
 an artificial roadstead, or place of anchorage for ships 
 of war, in fi-ont of Cherbourg, on the north coast of 
 Normandy. This place, situated in the bottom of a 
 wide, open bay, on a part of the coast projecting 
 considerably into the British Channel, lies only about 
 sixty miles south from the Isle of Wight, and, tliere- 
 fore, offers a most advantageous position for watching 
 the motions of British fleets moving up and down 
 the channel, or proceeding from or into the great 
 place of rendezvous at Portsmouth or Spithead. 
 Cherbourg possesses no natural qualifications for a 
 shipping station, being merely a tide harbor formed 
 by a small river falling into the sea. Basins ha->'e 
 
 been excavated and locks constructed, in former 
 times, by means of which frigates and smaller vessels 
 could be conveniently protected ; all with uncommon 
 ingenuity, and at a very moderate expense. It was 
 not enough for an engineer in France to give proof 
 of his genius and skill in his profession, in producing 
 the best method of accomplishing any desired object ; 
 his great merit consisted in inventing how to accom- 
 plish that object in the most economical, as well as 
 the most iiig-enious, manner. By giving this turn to 
 the public mind, works of the highest importance to 
 the state and to individuals were carried on, in that 
 country, for sums which, in some other countries, 
 would be regarded as utterly inadequate to the pur- 
 pose. All persons charged with the execution of 
 public works, even those we call civil engineers, em- 
 ployed in the construction of harbors, bridges, canals, 
 roads, &c., were military men, regularly bred, and 
 under due but liberal control, enjoying rank and 
 emolument sufficient for their station in society. An 
 instance of a superior officer of the French corps of 
 Royal Engineers suspected, accused, tried, and con- 
 victed of recommending works which he well knew 
 to be unnecessary, not to say prejudicial, that he 
 might have an opportunity of enriching himself dur- 
 ing theu- execution ; or of conniving at, not to say 
 inventing, enormous abuses and extravagant expendi- 
 ture, in the management of the public moneys, in 
 order that he might be suffered, by the plunderers 
 under him, quietly to amass his ti'easures ; that a field 
 officer of engineers should be proved to have stooped 
 so low as even to make false returns of the quantity 
 of coals and candles necessary for his official busi- 
 ness, — an instance of such degrading delinquency is 
 unknown in the history of French military jurispru- 
 dence. How far the same remark can be applied to 
 another country, the constant rival, and often the en- 
 emy, of France, the records of the courts which take 
 cognizance of such offences against duty, honor, and 
 even common honesty, will bear ample Ijut humiliat- 
 ing testimony. As Cherbourg possessed no outer 
 harbor or road such as Portsmouth possesses at Spit- 
 head, it became necessary to enclose a portion of the 
 bay to answer that purpose. Piers or breakwaters 
 of continued construction were thought of; but at 
 last it was resolved to sink a long range of wooden 
 truncated cones into the sea at certain distances 
 asunder, which, being afterwards filled with massy 
 blocks of stone, would form a succession of solid, 
 immovable masses, sufficient to break the violence 
 of the external waves, and render the space within 
 incomparably more quiet and secure than it was 
 in its natural state. The cones were strongly com- 
 pacted of oak, narrower above than below, and re- 
 sembling a deep tub standing on its base, w^ithout a 
 bottom. By most ingenious contrivances, the cones 
 were floated out to their destined situations by means 
 of empty casks, made air tight, which were afterwards 
 
32 
 
 INTRODUCTION. 
 
 detached, and the frame allowed to sink to the bot- 
 tom. The sides were of sufficient height to be 
 always above water, and, when filled with stone, 
 withstood the action of the tide and waves. 
 
 This great enterprise, the only thing of the kind in 
 the world, was naturally interrupted by the disorders 
 of the revolution in France, but was afterguards re- 
 sumed with great activity, so that, in future wars with 
 France, Cherbourg may become a most troublesome 
 neighbor to Britain. 
 
 WOODEN BRIDGES. 
 
 Besides stone, timber is, on many occasions, em- 
 ployed to open a communication across a river ; and 
 in some cases it has greatly the advantage, as when 
 the current is particularly rapid ; for there the posts 
 or piles supporting the road, presenting, either indi- 
 vidually or collectively, but a small obstacle to the 
 stream, often effectually resist its violence, when a 
 stone pier, if it could easily be constructed in such a 
 position, would not long keep its ground. Hence it 
 is, that not only in England, but more particularly 
 on the continent, stone bridges over great rivers are 
 comparatively rare. Thus, on the Rhone, for in- 
 stance, which, rising in the highest Alps of Switzer- 
 land, makes its way to the sea through the southern 
 parts of France, bridges of stone have often been 
 constructed, and as often carried away by the stream, 
 so that at this day, perhaps, not more than two re- 
 main. The Rhone is, however, the most rapid river 
 of its size in Europe. On the Rhine, which, rising 
 not far from the source of the Rhone, takes an oppo- 
 site course through Germany and Holland into the 
 German Ocean, and is so much less rapid as its 
 course is longer, stone bridges are quite unknown. 
 But this is owing not only to the great body of water 
 it carries along, but also to the policy of the different 
 states along its banks, each unwilling that the oppo- 
 site state should, by a standing bridge of masonry, 
 possess means of making hostile attempts across the 
 river. At Strasbiu-g, for instance, a large and pros- 
 perous city of Alsace, in France, seated on the west 
 bank of the Rhine, commanding by its fortifications 
 a much frequented passage over the river into Ger- 
 many, the bridge is formed by ranges of pUes driven 
 into the river to form the piers, supporting rafters and 
 planks for the road, kept in their place by wooden bolts 
 or treenails, so that, with a few strokes of a hammer or 
 hatchet, the planks could be cast loose and removed, 
 and all passage along the bridge effectually cut off. 
 The German end of the bridge was also guarded by 
 works to prevent the French from penetrating by that 
 communication. This is the bridge of Kehl, cele- 
 brated in every history of hostilities between France 
 and Germany. 
 
 Various arc the methods employed in the construc- 
 tion of wooden bridges, governed principally by the 
 
 extent of water they are to cross. Even in the nar- 
 rowest it is improper to trust to the resistance of 
 beams reaching from bank to bank, for they ought to 
 be trussed ; that is, to be supported by pieces of tim- 
 ber reaching from each bank, near the water, obliquely 
 towards the middle of the bridge. This contrivance 
 will add greatly to its strength, and prevent its bend- 
 ing under passing loads. 
 
 One of the most important particulars to be con- 
 sidered, in wooden bridges, is the seasoning of the 
 timber. It is well known that the decay of fir timber 
 is generally owing to the moist, sappy nature of its 
 exterior surface. This moisture must be completely 
 removed before any paint or priming be applied, in 
 the view of securing it from the weather. K left in 
 this natural state, this sap would, by the action of 
 the wind and heat, be gradually carried off, and the 
 fir beam become internally dry and solid ; but if the 
 surface be covered with paint, oil, pitch, or other sub- 
 stances of this kind, the sap is confined, and will soon 
 corrupt the timber, which wUl give way before its 
 time, and without any external symptom of decay. 
 In order to dissipate the moisture or sap of the sur- 
 face, it is sometimes the practice to scorch the tim- 
 bers over a fire, turning it round regularly. The heat 
 will attract the moisture to the surface and evaporate 
 it, and the timber will acquire a hard crust, of great 
 service in resisting the weather. When this is done, 
 the parts that are to be under water shotild be care- 
 fully covered with pitch and tar, sprinkled with sand 
 and powdered shells. Those which are in sight 
 should, while the wood is still hot from the fire, be 
 rubbed over with linseed oil, mLxed with a little tar, 
 which will then strike deep into the wood, and soon 
 become so hard as to be fit to paint. Fii' timber, thus 
 prepared, is found to be nearly equal to oak in dura- 
 bility. At Schaffhausen, in the north part of Swit- 
 zerland, was once to be seen a wooden bridge over 
 the Rhine, there very rapid, so that no stone bridge 
 could resist it — admirable in its construction, and be- 
 ing the production of a plain country carpenter. The 
 builder was directed to avail himself of a part of one 
 of the piers of the stone bridge still remaining in its 
 place, to support the intended structure. With this 
 order he apparently complied, but so conti'ived mat- 
 ters that, in the opinion of the best judges, his bridge 
 actually consisted of but one immense arch, of near 
 four hvmdred feet, (the breadth of the river,) having a 
 part stooping down, as it were, to rest upon the pier 
 in the water, but not, as far as coiold be discovered, 
 actually resting on it. With very long fir beams, 
 prepared for the pvirpose, extended at an angle of mod- 
 erate elevation above the horizon from both sides of 
 the river, and in conjunction with intermediate tun- 
 bers, meeting over the water, two arches were formed, 
 being segments of large circles, and resembling the 
 circular frame of the centring of a stone bridge. 
 These arches were placed parallel to one another, 
 
INTRODUCTION. 
 
 33 
 
 at a distance sufficient for the breadtli of the road, 
 which was formed upon timbers suspended from the 
 arches on each side, so as to be quite horizontal from 
 end to end ; and, instead of going over the supporting 
 arches, was, in fact, let down between them. The 
 whole was roofed over, and enclosed at the sides, 
 with windows at convenient distances to defend the 
 timber from the weather. This most ingenious and 
 most useful piece of carpentry, which had gained the 
 applause of all men of genius and skill, completely 
 answered its destination from 1740, when it was 
 constructed, to 1799, when it was destroyed by the 
 French. 
 
 IRON BRIDGES. 
 
 Bridges of iron are the production of British inge- 
 nuity exclusively. Iron being the great staple metal 
 of the country, it has of late been employed in many 
 works where great strength is required in proportion 
 t6 the weight of the materials. Melted or cast iron 
 possesses several advantages over stone or wood ; and 
 these, in their turn, possess advantages over cast iron. 
 To stone, iron is superior in tenacity and elasticity, 
 and thence in strength, in facility of formation in any 
 desired shape, and in extent of the masses in which 
 it may be formed — qualities all conducing to its 
 superior lightness and cheapness. To wood, iron is 
 superior in the same particulars, together with dura- 
 bility ; but in this last respect, stone has greatly the 
 advantage over iroii equally exposed to the weather 
 or other natural agents. The greater durability of 
 stone arises from its being less liable to decomposi- 
 tion from the atmosphere, and from its being less 
 elastic, and consequently less subject to friction among 
 its component particles, in yielding to the load and 
 motion of carriages passing over it. Several ways 
 may, however, be adopted to remedy, in a great de- 
 gree, these defects of iron. Paint will prevent it from 
 oxidation, or rusting, for many years, and the appli- 
 cation may, when necessary, be repeated without 
 much expense. Cast-iron carriages of garrison guns 
 have, by various external applications, been perfectly 
 preserved for upwards of a century. The vibratory 
 motion of an iron bridge may also be considerably 
 diminished by the manner of placing and connecting 
 the bars of which it consists, so that each bar shall 
 act as nearly as possible at right angles against 
 another, and be at the same time so short as not to 
 be in danger of being bent or crushed by the pressure 
 against its length. The greatest objection in this 
 respect to cast iron is this — that, on account of the 
 imperceptible differences in the purityand other qual- 
 ities of the metal, it is impossible to cast two bars or 
 blocks even in the same mould, which shall shrink 
 perfectly and equally in cooling, and, consequently, be 
 of precisely the same dimensions when employed in 
 the work. When such pieces come to be joined to- 
 
 gether, therefore, some empty space must necessarily 
 exist among them, which in a large work, where uianv 
 pieces are employed, must produce a very sensible 
 play in the joinings, and, consequently, great vibration 
 or reciprocal motion in the whole structure. This 
 inaccuracy of the joinings may, it is true, be in some 
 measure corrected, by inserting pieces of sheet lead 
 in the joinings; but this metal possesses by far too 
 little cohesion of parts, and too little elasticity, to be 
 of use for any length of time. In order to prevent 
 the evils arising from these defects of cast iron, it has 
 been proposed to fill up the vacant spaces left be- 
 tween the iron framing with some compact, cheaj) 
 materials, such as brick united with the composition 
 called Roman or Parke's cement, or Pozzolano, or 
 terras, which would readily and intimately combine 
 with the iron, thus defending it from the action of 
 the atmosphere. The interstices between the bars 
 being thus also filled up by a consolidated substance, 
 the play, friction, and vibratory motion of the bridge 
 would be greatly diminished. Lightness being, how- 
 ever, a most desirable property, it has also been pro- 
 posed to form hollow bricks solely for this purpose, 
 which, being carefully and thoroughly baked, or even 
 semi-vitrified on the surface, would be proof against 
 the effects of the atmosphere. In many parts, bricks 
 are still seen in remains of Roman buildings, fifteen 
 or sixteen hundred years old in perfect preservation, 
 while the stones, with which the bricks are buOt up 
 in alternate layers, are often greatly decayed, unless 
 when enveloped in the admirably-constituted mortar 
 of those days. Iron may be used for bridges, either 
 on the principle of equilibration, as stone is employed, 
 or on that of connection by framing, as wood is some- 
 times employed in bridges, but generally in roofing 
 houses. For bridges of considerable dimensions the 
 former is, by many judges, esteemed the best mode ; 
 but for small bridges, the latter mode will probably 
 be found the cheapest. As iron bars, rods, or blocks 
 may be firmly connected together by bolts, or other 
 means, an iron arch may be constructed much flatter ; 
 that is, in the segment of a much greater circle than 
 if it were of stone — an advantage of very great im- 
 portance in certain positions, where arches of great 
 span are required. The first iron bridge of any note 
 constructed in England was that of Colebrookdale, 
 in Shropshire. It consists of five ribs, each of three 
 concentric arches, bound together by pieces in the 
 direction of radii of the circle. The interior arch 
 forms a semicircle, but the others reach only to sills 
 under the road way. These arcs pass through an up- 
 right frame of iron at each end, serving as a guide ; 
 and the small space in the haunches, between the 
 frames and outer arc, is filled up with a large iron 
 ring. On the ribs are laid cast-iron plates, to support 
 the road. The span, or opening of the arch, is 100 
 feet 6 inches, and the height from the base line to the 
 centre is 40 feet. The road along the bridge is 24 
 
34 
 
 INTRODUCTION. 
 
 feet broad, formed on a bed of clay and iron slag, 
 (the refuse from the furnace where iron ore is smelted,) 
 a foot in depth. 
 
 Another bridge of the same material was after- 
 wards erected over the mouth of the River Were, form- 
 ing the Harbor of Sunderland, a great coal port in the 
 county of Durham. The peculiar construction of 
 this bridge consisted in applying iron, or other metal- 
 lic substance or compound, to form arches on the 
 same principle with stone arches, by a subdivision 
 into blocks easily portable, answering to the key- 
 stones of a common arch, which, being made to bear 
 on one another, will have all the firmness of a stone 
 arch. At the same time, by the great open spaces 
 left between the blocks and their respective lateral 
 distances, the arch becomes materially lighter than 
 if it were of solid stone, and, by the tenacity of the 
 metal, the parts are so intimately connected that the 
 delicate but indispensable calculation of the size and 
 weight of the stones composing the arch becomes of 
 but little importance. This bridge is in span 236 
 feet, and as the stones from which the arch springs 
 on each side project 2 feet, the whole opening is 240 
 feet. The arch is a segment of a circle of 222 feet 
 radius, and the height from the chord to the top of 
 the arch is 34 feet ; but the whole height of the mid- 
 dle of the arch above the surface of the river, at low 
 water, is about 100 feet, so that ships can pass under 
 it. A series of 105 blocks form one rib, and six of 
 such ribs compose the width of the bridge. The va- 
 cant spaces between the arch and the road are filled 
 up by cast-iron circles, which touch the outer circum- 
 ference of the arch, and also support the road, grad- 
 ually diminishing from the abutments towards the 
 centre of the bridge. Diagonal iron bars are laid on 
 the top of the ribs, reaching to the abutments, to keep 
 the ribs from twisting. The supersti-ucture is a strong 
 frame of timber, planked over to support the carriage 
 road, composed of marble, limestone, and gravel, with 
 a cement of tar and chalk laid on the planks in order 
 to preserve them. The whole width of the bridge is 
 32 feet. The abutments are masses almost of solid 
 masonry, 24 feet in thickness, 42 in breadth at the 
 bottom, and 37 at the top. The weight of the iron 
 in the whole work is 260 tons, of which 214 are cast, 
 and 42 wrought iron. The expense of the whole, 
 forty years ago, was £27,000, or $119,880. The 
 Waterloo Bridge, over the Thames, will be illustrated 
 by a plate for that purpose. 
 
 BRIDGES IN BOSTON. 
 
 Some of the most striking objects which attract 
 the notice of strangers on visiting Boston, Massachu- 
 setts, are the bridges which lead from its various 
 points. Although wc cannot boast of so grand su- 
 perstructures as the ancient city of London, we, nev- 
 ertheless, have a greater number of those convenient 
 
 avenues. The Western Avenue is a splendid mill 
 dam, built of solid materials. Warren Bridge was 
 built in 1828. All these bridges are well lighted by 
 lamps when the evenings are dark ; and the lights, 
 placed at regular distances, have a splendid and 
 romantic appearance. 
 
 WESTERN AVENUE. 
 
 This splendid work was projected by Mr. Uriah 
 Cotting, who, with others associated, received an act 
 of incorporation, June, 1814, under the title of " The 
 Boston and Roxbury Mill Corporation." It was com- 
 menced in 1818, under Mr. Cotting's direction, but he 
 did not live to witness its completion. His place was 
 supplied by Colonel Loammi Baldwin, and the road 
 was opened for passengers July 2, 1821. This Avenue, 
 or Mill Dam, leads from Beacon Street, in Boston, to 
 Sewall's Point, in Brookline, and is composed of solid 
 materials, water-tight, with a gravelled siuface, raised 
 three or four feet above high-water mark. It is one 
 mile and a half in length, and a part of the way 100 
 feet in width. The water which is admitted is ren- 
 dered subservient and manageable. Very extensive 
 mill privileges are gained by the aid of a cross dam, 
 running from the principal one to a point of land in 
 Roxbury, which divides the reservoir or full basin on 
 the west from the running or empty basin on the 
 east. There are five pairs of floodgates in the long 
 dam, grooved in massy piers of hewn stone ; each 
 pair moves from their opposite pivots towards the 
 centre of the aperture on a horizontal platform of 
 stone, lentil they close in an obtuse angle, on a pro- 
 jected line cut on the platform, from the pivots in the 
 piers to the centre of the space, with thefr angular 
 points towards the open or iincnclosed part of the 
 bay, to shut against the flow of tide, and prevent the 
 passage of water into the empty basin. In this man- 
 ner, all the water is kept out from this basin, except 
 what is necessary to pass from the full basin through 
 the cross dam, to keep the mill works in operation. 
 The reservoir is kept full by means of similar flood- 
 gates opening into the full basin, (when the rising 
 of the tide gets ascendency over the water in the 
 reservoir,) and fills at every flow, and closes again on 
 the receding of the tide. In this way, at every high 
 tide, the reservoir is filled, and a continual supply of 
 water is made to pass through the sluice ways in the 
 cross dam, sufficient to keep in motion, at all times, 
 at least one hundred mills or factories. At low 
 water, the floodgates of the receiving basin open and 
 discharge the water received from the reservoir. 
 
 WARREN BRIDGE. 
 
 The construction of this bridge was commenced in 
 June, 1828, and was completed in November follow- 
 ing, under the superintendence of Joshua Burr, Esq., 
 
INTRODUCTION. 
 
 of Cliurlestown, Massachusotts. It is one of the most 
 pertect works of its kind in the Commonwealth. It is 
 certainly not exceeded by any other in point of dura- 
 bility and ease of travel. It opens on the Charles- 
 town side, about ten rods above (west) Charles River 
 Bridge, and, running in a southerly direction, termi- 
 nates on the westerly part of the Will Pond Land, so 
 called, in Boston, just east of the Middlesex Canal. 
 It is the most direct, and the shortest, communication 
 between Boston and Charlestown. 
 
 The bridge is supported by 75 piers, placed at 
 equal distances of 18 feet. It is 1390 feet in length, 
 and 44 in width, allowing 30 feet for the carriage 
 way, and 6^ on either side, handsomely railed, for 
 foot passengers. The floor of tlie bridge is composed 
 of hewn hemlock timber, about 14 inches deep, the 
 apertm-es between which arc well chinked with small 
 pieces of stone, the whole covered with 6 inches of 
 tempered clay. On this is spread 8 inches of coarse 
 gravel, covered with 8 inches of macadamized stone. 
 The sides of the carriage way are secured by edge 
 stones, 12 inches deep and 9 thick. The floor tim- 
 bers are placed lower than those of other bridges, in 
 order that they may be occasionally wet by the high 
 tides, which, it is thought, will tend to their preser- 
 vation. That teams pass over this bridge with great 
 ease is sufficiently demonstrated by the fact that a 
 single yoke of oxen has been known to convey 161 
 tons at one time, from the draw into Charlestown, 
 without any unusual effort. 
 
 The draw, in the centre of the bridge, is of suffi- 
 cient width to admit vessels of three hundred tons. 
 It has wharves on each side, built on piers which are 
 planked from the capsill to low-water mark, for the 
 more safe and easy passage of vessels. Its con- 
 veniences, in this particular, are in strict agreement 
 with the general excellence of the whole structure.* 
 
 * This bridge ■was considered, at the time it was built, to be a 
 yery durable and scientific structure ; but, in 1S40, it was found to 
 be in so decayed a state that imnacdiato repairs were necessary to 
 render it in any degree safe for travel ; a thorough examination was 
 made, -which resulted in a recommendation to remove the clay and 
 stones referred to, and make such other alterations as the case might 
 demand. 
 
 In the Bay State Democrat of October 8, 1842, we find the fol- 
 lowing description of the repairs made at that time : — 
 
 " Warren Bridge has recently been thoroughly repaired in all its 
 parts. All the old timbers have been removed, and new materials 
 substituted. This -work has been done under the direct superin- 
 tendence of Ebenezer Barker, Esq., the agent of Warren Bridge, 
 ■who has completed it in a manner highly creditable to himself, and 
 ■worthy of the magnitude of the enterprise. It is a fine specimen of 
 mechanical skQl, is somewhat novel in its style of execution, and 
 may be looked upon as one of the greatest ■works of its kind in the 
 country. We have thought that some statistics in connection ■with 
 this subject ■would not prove uninteresting to the general reader. 
 
 " Warren Bridge ■was incorporated March 12, 1828, and opened in 
 the subsequent December. It is now 1388 feet in length, of which 
 1318 feet are covered by hexagonal blocks of white pine. Its 
 whole width is 44 feet — the travel way being 30 feet, and the side 
 walks occupying 7 feet each. To begin at the foundation of the 
 work, and for the purpose of giving the pubUc accurate information 
 
 TOWN'S IMPROVED BRIDGES. 
 
 A minute and accurate description of Town's i.n- 
 provement in the construction of wooden and iron 
 bridges is given in a succeeding part of this work. 
 We commend the article to the learner, as being par- 
 ticularly worthy of his serious and attentive consid- 
 eration. 
 
 WHITE'S TUBULAR SUSPENSION BRIDGE. 
 [Patent Right secured.] 
 
 Ammi White, Esq., of Boston, has a model of a 
 bridge, which supersedes the necessity of piers in 
 crossing our largest rivers. He asserts that it can 
 with safety be extended, even for railroad purposes, 
 fifteen hundred feet. The mode of its construction 
 is as follows : — 
 
 " First, erect the towers on good and firm abut- 
 ments, or on a rocky bank ; then extend across the 
 stream two or more sets of stringers, according to the 
 number of road beds needed. The number of string- 
 ers in each set will depend upon the amount of 
 strength required in the bridge. Each stringer is 
 made by selecting a tree of proper size, which is 
 sawed square, and is tapered from the top to within 
 about five feet of the base. This serves as a start- 
 ing-point, on which are spliced good sound boards, 
 six or seven inches in width, on a curve of forty feet 
 in five hundred, till the required length and thickness 
 is obtained, the whole terminating in a corresponding 
 timber which forms the other extremity. Li securing 
 one board upon another, care is taken to fix keys of 
 wood or iron into mortises made half into one board, 
 and half into the other, to prevent the stringer from 
 elongating, which, with the additional bolts placed 
 near the dowels, is as incapable of divulsion as the 
 
 of its whole construction, we wiU say, first, that on the heads of the 
 pUes white pine caps, 14 inches square, are placed ; on these caps 
 rest stringers 6 by 14 inches, of the same material, in a longitudinal 
 direction, being on the outside 12 inches deep ; thus making in the 
 centre a crown of two inches elevation. On these stringers, trans- 
 versely or at right angles, rest yellow N. C. pine ribbons, or laths. 
 4 by 5 inches, and spiked to every other stringer by 8 uich spikes. 
 Upon the end of these ribbons, and over the outside stringer of the 
 road way, white pine edge timber, 10 by Oj inches, is laid so as to 
 project 2 inches each way beyond the stringer beneath it. This tim- 
 ber is bolted to the stringers once in every 4 feet, to secure more 
 firmly the ends of the ribbons in then- places ; and on the under side 
 of these timbers, and about one inch from each edge, grooves of 
 half an inch deep and wide are made. 
 
 " On such a foundation as this, the white pine blocks — which, by 
 the way, are of Maine pine, and have been alluded to — are laid. As 
 a matter of experiment, blocks of 10 and 11 inches size are put 
 down on the Boston side, and of 12 inch size on the Charlestown 
 side. These blocks are all tongued and grooved, or matched, which 
 serves to secure the ■(vhole firmly together, and to present an even 
 and uniform surface. On the surface of these blocks is put a liquid 
 preparation — first, a coat of turpentine mLxed with oil, then a coat 
 of tar and pitch poured on very hot. To this is added a coat of 
 gravel, rolled in by a machine, so as to fill the interstices and pores 
 of the blocks. The object of all this care is to preserve the material 
 
36 
 
 INTRODUCTION. 
 
 tree itself. This suspension cliain or stringer is run 
 across the stream by means of a wire cable and pul- 
 leys, and when locked and keyed fast in the towers, 
 with the two backstays, is allowed to take a catenary 
 curve. After a sufficient number has been extended 
 across, the suspension rods are bolted to them and to 
 the girders, which arc made slightly arching, and to 
 the floor joist. The rafter is connected with the 
 stringer and top of the suspension rod, to which is 
 bolted the roof, constructed of double diagonal 
 hoarding. The floor, if a turnpike bridge, made of 
 double diagonal planking, bolted together, is then 
 laid, and, in the capacity of cross bracing, serves to 
 render firm the whole structure. If a railroad bridge, 
 the cross bracing is fitted under the floor joist, in con- 
 nection with the girders. By loading either kind of 
 bridge with double the weight it is required to sus- 
 tain, the girders will be brought down to a level, and, 
 while the weight is on, the sides are covered with a 
 double-diagonal boarding, similar to that of the roof, 
 both of which must be firmly attached to the towers 
 and backstays to form a part of the strength of the 
 
 of the bridge, to make it water-tight, and to prevent horses from 
 slipping in travelling. 
 
 " We would say here, that about 40 feet of the bridge, and in differ- 
 ent sections of the same, are laid blocks of chestnut wood, from 
 New Hampshire. 
 
 " Under the sidewalks, the outside stringer is 12 inches wide, and 
 the inside 6 by 12. On these are placed floor joists, 3 by 5 inches, 
 covered by two inch plank. The railing is handsome and perma- 
 nent ; and near the draw is a wooden covering, with a 25 feet roof, 
 for the convenience of pedestrians in inclement weather. The num- 
 ber of lamps and lamp posts arc 22. The form of the bridge is a 
 regular ascending plain, rising from the respective abutments to the 
 draw, about 4 inches to every 100 feet." 
 
 The structure remained in the form in which it was thus repaired 
 until 1846, when it was found that the blocks -with which the sur- 
 face was covered had decayed so much that it was necessary to 
 remove them, and it was at length decided to cover the southern 
 pine timbers, before referred to, with common two inch pine planks, 
 and these again in the same manner. This is the form in which the 
 surface is now covered, and it is, without doubt, the best method 
 which has been made use of since the bridge was first built. 
 
 How long the blocks would have lasted under an ordinary amount 
 of travel, we are not prepared to state ; but it was foimd that the 
 blocks at the outer edge of the bridge were in a tolerable state 
 of preservation, while those in the centre were in a very decayed 
 state. 
 
 It may be well here to state, in order to give the reader some 
 idea of the trave over this bridge, that from an account kept by 
 order of Marshal Tukey, on Saturday, October 6, 1851, from half 
 
 bridge. The direct arches are formed by bolting to- 
 gether planks on the right curve. One springs from 
 the abutment, and connects with the stringer at the 
 top of the suspension rod ; the other starts from the 
 same point, and connects with the other girder, both 
 connecting in their course with the suspension rods. 
 The side guards, or braces, are formed by fitting a 
 fender rave to the floor joist, which extends over the 
 girder several feet, according to the length of the 
 bridge. Short rafters connect with the fender rave 
 and the suspension rod. These, together with the 
 projecting floor joists, are covered with double diag- 
 onal boarding. These braces prevent the bridge 
 from vibrating. The backstays connected with the 
 studs inserted in the sills of the towers extend back 
 on shore the required distance, and are firmly at- 
 tached to stone posts, deeply set in the ground at the 
 extremity of the sills." 
 
 [As regards the strength, economy, durability, 
 and safety of this bridge, we feel warranted in 
 saying it excels that of a great majority of bridges. 
 — Editors.] 
 
 past six, A. M., until half past seven, P. M., as published in the Com- 
 monwealth newspaper at the time, was 3158 vehicles, 6223 passen- 
 gers in the same, and 6095 passengers on foot. In consideration of 
 this immense amount of travel, and also that the principal part of 
 the vehicles consist of heavily-ladcd trucks and large freight wag- 
 ons, it is a matter of astonishment that the blocks lasted as long as 
 they did ; for, as may be supposed, hollows and channels were soon 
 formed in them, and the water standing in the same caused a con- 
 stant decay. 
 
 In reference to this kind of paving, we would state, for the benefit 
 of our readers, that it has been thoroughly tested in the streets of 
 Boston, in some eases using hemlock, and in some others spruce 
 but the same result as that with the pine on the bridge has followed 
 and that now rough granite blocks, twelve inches square, are found 
 to be the most serviceable as well as economical. 
 
 We ought perhaps to state in regard to the last repairs on Warren 
 Bridge that, at the Boston end about the Fitchburg Depot, the 
 timbers were lowered and covered with mud from the dock for 
 about two feet deep, and upon this, in the centre of the bridge, as 
 far as the draw, is placed granite blocks, as above described, and 
 that the sidewalks for the same distance are paved with bricks. 
 This method seems to work well, as yet, and it has been so highly 
 approved that a new bridge which is now being erected on a new 
 road leading from the Mill Dam Avenue to Brookline is constructed 
 for the entire length in the same manner. 
 
 To our respected friend, Ebenezer Barker, Esq., who is superin- 
 tending the new bridge, we tender our acknowledgments for his 
 gentlemanly and kind assistance in procuring the facts relative to 
 this importimt structure — the Warren Bridge. — Editors. 
 
ill 
 
 vV H 
 
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 //r.rifr/^i// . 
 
 f'r/rlf/f>» . 
 
CIVIL ARCHITECTURE. 
 
 PRACTICAL QEOMETEY, 
 
 The System of Geometry here introduced is as concise and sim- 
 ple as is compatible with a proper understanding of this interesting 
 branch of mechanical science. 
 
 Descriptive Geometry is employed to communicate a knowledge 
 of different objects. It furnishes the means of constructing ge- 
 ographical charts, plans of buildings and machines, architectural 
 designs, sun dials, &c. It is used, likewise, to describe the forms 
 and relative positions of objects. By it, stone cutters, carpenters, 
 shipbuilders, &c., find the dimensions of the works which they ex- 
 ecute, inasmuch as these dimensions admit of a rigorous definition. 
 
 That a knowledge of Geometry is essential to the greater part of 
 our practical mechanics, does not admit of a doubt ; yet they have 
 too generally regarded the subject with a degree of indifference, as 
 though the ends proposed to be accomplished by it could be as 
 accurately, and much more easily, attained by other means. This 
 erroneous notion, however, is fast giving way to the force of truth 
 and demonstration ; and perhaps more attention is paid to the sub- 
 ject at the present time, by operative mechanics, than at any pre- 
 vious period since the discovery of the science. Many attempts 
 have been made to simplify the study, and to render the acquisition 
 of it more easy to the learner. In many instances, these attempts 
 have been partially successful ; but the student will bear in mind 
 the memorable reply of Euclid — " Tliere is no royal road to geom- 
 etry." There is no turnpike, though there are some cross roads ; 
 but we doubt not that he who travels the old road, which has been 
 so often proved to be good, and over which so many have travelled 
 before him, will be as well pleased with his journey when it is 
 accomplished as he who arrives at the end by a shorter route. It 
 has been said, but we trust with more severity than truth, that the 
 generality of mechanics are displeased at the sight of a geometrical 
 theorem. If so, a very little attention to the subject will satisfy 
 them that no study can be better calculated to awaken the dormant 
 faculties of the mind and to force them into action. 
 
 DEFINITIONS. 
 Plate 1. 
 
 1. Geometry is that science which treats of the 
 descriptions and properties of magnitudes in general. 
 
 2. A point has neither parts nor magnitude, as A. 
 
 3. A line is length, without breadth or thickness, 
 asB. 
 
 4. Superficies has length and breadth only. 
 
 5. A solid is a figure of three dimensions, having 
 length, breadth, and thickness. Hence, surfaces are 
 the extremities of solids, and lines the extremities of 
 surfaces, and points the extremities of Unes. 
 
 6. Lines are either right, curved, or mixed, as E. 
 
 7. A right or straight line lies in the same direc- 
 tion between its extremities, and is the shortest dis- 
 tance between two points. 
 
 8. A curve continually changes its directions be- 
 tween its extreme points, as F. 
 
 9. Lines are either parallel, oblique, perpendicular, 
 or tangential. 
 
 10. Parallel lines are always at the same distance, 
 and will never meet, though ever so far produced, as 
 C and D. 
 
 11. Oblique right lines in the same plane change 
 their distance, and would meet, if produced, as I. 
 
 12. One line is perpendicular to another when it 
 inclines no more to one side than another, as H. 
 
 13. One line is tangent to another when it touches 
 it without cutting, when both are produced, as G. 
 
 14. An angle is the inclination of two lines to- 
 wards one another, meeting in a point, as J. 
 
 15. Angles are either right, acute, or oblique, as K. 
 
 16. A right angle is that which is made by one 
 line perpendicular to another, or when the angles on 
 each side are equal, as M. 
 
 17. An acute angle is less than a right angle, as 
 N,2. 
 
 18. An obtuse angle is greater than a right angle, 
 as N. 
 
38 
 
 PRACTICAL GEOMETRY. 
 
 19. Superficies are either plane or curved. 
 
 20. A plane, or plane surface, is that to which a 
 right line will every way coincide ; but if not, it is 
 curved. 
 
 21. Plane figures are bounded either by right lines 
 or curves. 
 
 22. Plane figures, bounded by right lines, haije 
 names according to the number of their sides or 
 angles, for they have as many sides as angles. The 
 least number is three. 
 
 23. An equilateral triangle is that whose three 
 sides are equal, as O. 
 
 24. An isosceles triangle has only two sides equal, 
 as P. 
 
 25. A scalene triangle has all its sides unequal, as 
 Qor U. 
 
 26. A right angled triangle has one right angle, as 
 R. 
 
 27. Other triangles are oblique angled, and are 
 either obtuse or acute. 
 
 28. An acute angled triangle has all its angles 
 acute, as S or T. 
 
 29. An obtuse angled triangle has one obtuse 
 angle, as U. 
 
 30. A figure of four sides and angles is called a 
 quadrangle, or quadrilateral, as V, W, X, Y, Z, &. 
 
 31. A. parallelogram is a quadi'Uateral, which has 
 both pairs of its opposite sides parallel, as V, W, X, 
 Y, and takes the following particular names : — 
 
 32. A rectangle is a parallelogram, having all its 
 mgles right ones, as V and W. 
 
 33. A square is an equilateral rectangle, having all 
 its sides equal, and aU its angles right ones, as W. 
 
 34. A rhombus is an equilateral parallelogram, 
 whose angles are oblique, as X. 
 
 35. A rhomboid is an oblique-angled parallelogram, 
 as Y 
 
 36. A trapezium is a quadrilateral, which has 
 neither pair of its sides parallel, as Z. 
 
 37. A trapezoid has only one pair of its opposite 
 sides parallel, as &. 
 
 38. Plane figures having more than four sides are, 
 in general, called polygons, and receive other partic- 
 ular names, according to the number of their sides 
 or angles. 
 
 39. A. pentagon is a polygon of five sides. A hex- 
 agon has six sides, a heptagon seven, an octagon 
 
 eight, a nonagon nine, a decagon ten, an undecagon 
 eleven, and a dodecagon twelve sides. 
 
 40. A regular polygon has all its sides and angles 
 equal ; and if they are not equal, the polygon is 
 irregular. 
 
 41. Aji equilateral triangle is also a regular figure 
 of three sides, and a square is one of four — the 
 former being called a trigon, and the latter a tetra- 
 gon. 
 
 Plate 2. 
 
 42. A circle is a plane figure bounded by a curve 
 line, called the circumference, which is every where 
 equidistant from a certain point within, called its 
 centre. 
 
 43. The radius of a circle is a right line drawn 
 from the centre to the circumference, a b, at A. 
 
 44. A diameter of a circle is a right line drawn 
 through the centre, terminating on both sides of the 
 circumference, as c d, at B. 
 
 45. An arc of a circle is any part of the circum- 
 ference, 
 
 46. A chord is a right line joining the extremities 
 of an arc, as a b, at C. 
 
 47. A segment is any part of a circle bounded by 
 an arc and its chord, as D. 
 
 48. A semicircle is half the circle, or a segment 
 cut off by the diameter, as E. 
 
 49. A sector is any part of a circle bounded by an 
 arc and two radii, drawn to its extremities, as F. 
 
 50. A quadrant, or quarter of a circle, is a sector, 
 having a quarter of the circumference for its arc, and 
 the two radii are perpendicular to each other, as G. 
 
 51. The height or altitude of any figure is a per- 
 pendicular let fall from an angle, or its vertex, to the 
 opposite side, called the base, as a b, at H. 
 
 52. When an angle is denoted by three letters, the 
 middle one is the place of the angle, and the other 
 two denote the sides containing that angle. Thus : 
 let a & c be the angle at I, then b will be the angular 
 point, and a b and b c will be the two sides contain- 
 ing that angle. 
 
 53. The measure of any right-lined angle is an 
 arc of any circle contained between the two lines 
 which form the angle, the angular point being in the 
 centre, as K. Thus, if the arc b c d he double of the 
 arc b c, then the angle bad will be double that of 
 b a c. 
 
-i. 
 
 \ 
 
 .0 /' 
 
 l'K<)JJJ,r-M s 
 
 II. 
 
 /■ 
 
 ?}yf. 1 . 
 
 
 . // 
 
 '■■ 
 
 < 
 
 
 HI. 
 
 
 '/ 
 
 1) 
 
 .V ■-■..„. 
 
 li 
 
 
 
 
 
PRACTICAL GEOMETRY. 
 
 39 
 
 PROBLEMS. 
 
 Plate 3. 
 
 PROBLEM :. 
 
 To bisect a given line, A B. 
 
 1. From the points A and B, as centres, with any 
 distance greater than half A B, describe arcs cutting 
 each other in c and d. 
 
 2. Draw the line c d, and the point E, where it cuts 
 A B, will be the middle of the line required. 
 
 PEOBLEM II. 
 
 From a given point, C, in a given right line, 
 A B, to erect a perpendicular. 
 
 Fig. 1. Wlien the point is near the middle of the line. 
 
 1. On each side of the point C take any two equal 
 distances, C d and C e. 
 
 2. From d and e, with any radius greater than C d, 
 or C e, describe two arcs cutting each other in /. 
 
 3. Through the points/ C , draw the line/ C, and 
 it will be the perpendicular required. 
 
 Fig. 2. When the point is at, or near, the end of the line. 
 
 1. Take any point d above the line, and with the 
 radius or distance, d C, describe the arc e C/, cutting 
 A B in e and C. 
 
 2. Through the centre d in the point e, draw the 
 line e df, cutting the arc e Cf, inf. 
 
 3. Through the points / C draw the line / C, and 
 it will be the perpendicular required. 
 
 PROBLEM III. 
 
 From a given point, C, out of a given right line, 
 A B, to let fall a perpendicular. 
 
 1. From the point C, with any radius, describe the 
 arc d e, cutting A B in e and d. 
 
 2. From the points e d with the same, or any other 
 radius, describe two arcs cutting each other in /. 
 
 3. Through the pomts C / di-aw the line CD/, 
 and C D will be the perpendicular required. 
 
 PROBLEM IV. 
 
 A t a given point, D, upon the right line, D E, to 
 make an angle equal to a given angle, a B J. 
 
 1. From the point B, with any radius, describe the 
 arc a b, cutting the legs B a, B 6, in the points a and b. 
 
 2. Draw the line D e, and from the point D, with 
 the same radius as before, describe the arc ef, cutting 
 DEin e. 
 
 3. Take the distance b a, and apply it to the arc 
 ef, from e to/. 
 
 4. Through the points D/draw the line D/, and 
 the angle e D/will be equal to the angle 6 B a, as 
 was required. 
 
 PROBLEM V. 
 
 To divide a given angle, ABC, into two equal 
 
 angles. 
 
 1. From the point B, with any radius, describe the 
 arc A C. 
 
 2. From A and C, with the same or any other ra- 
 dius, describe arcs cutting each other in d. 
 
 3. Draw the line B d, and it will bisect the angle 
 A B C, as was required. 
 
 PROBLEM VI. 
 
 To trisect or divide a right angle, ABC, into 
 three equal angles. 
 
 1. From the point B, with any radius B A, describe 
 the arc A C, cutting the legs B A and B C, in A 
 and C. 
 
 2. From the point A and C, with the radius A B, 
 or B C, cross the arc A C, in (? and e. 
 
 3. Through the points e d draw the lines B e, B rf, 
 and they will trisect the angle, as was required. 
 
 PROBLEM VII. 
 
 Through a given point, C, to draw a line par- 
 allel to a given line, A B. 
 
 1. Take any point rf, in A B, upon d and C, with 
 the distance C d, describe two arcs, e C and d f, cut- 
 ting the line A B, in e and d. 
 
 2. Make d f equal to e C ; through C and / draw 
 C/, which will be the line required. 
 
 Fig. 2. Wlien the parallel is to be at a given distance, 
 C D from A B. 
 
 1. From any two points c and d, in the line A B, 
 with a radius equal to C D, describe the arcs e and/. 
 
 2. Draw the line C B, to touch those arcs without 
 cutting them, and it will be parallel to A B, as was 
 required. 
 
40 
 
 PRACTICAL GEOMETRY. 
 
 PROBLEM VUI. 
 
 To divide a given line, A B, into any proposed 
 number of equal parts. 
 
 1. From A, one end of the line, draw A c, making 
 any angle with A B ; and from B, the other end, 
 draw B d, making the angle AB d equal to B A c. 
 
 2. In each of the lines A c, and B d, beginning at 
 A and B, set off as many equal parts, of any length, 
 as A B is to be divided into. 
 
 3. Join the points A 5, 1 4, 2 3, &c., and A B will 
 be divided as was required. 
 
 PROBLEM IX. 
 
 To find the centre of a given circle, or one al- 
 ready described. 
 
 1. Draw any chord A B, and bisect it with the 
 perpendicular C D. 
 
 2. Bisect C D with the diameter E /, and the inter- 
 section O will be the centre required. 
 
 PROBLEM X. 
 
 To draw a tangent to a given cii-cle, that shall 
 pass through a given point, A. 
 
 1. From the centre O, draw the radius O A. 
 
 2. Tluough the point A draw D E perpendicular 
 to O A, and it will be the tangent required. 
 
 PROBLEM XI. 
 
 To draw a tangent to a circle, or any segment 
 of a circle, ABC, through a given point, B, 
 without making use of the centre of the 
 circle. 
 
 1. Take any two equal divisions upon the circle ; 
 from the given point B, towards d and e, draw the 
 chord e B. 
 
 2. Upon B, as a centre, with the distance B d, de- 
 scribe the arc fd g, cutting the chord e B, in/. 
 
 3. Make d g equal to df, through g draw g B, and 
 it wU". be the tangent required. 
 
 PROBLEM XII. 
 
 A circle, A B C, being given, and a tangent, D 
 H, to that circle, to find the point of contact. 
 
 1. Take any point e, in the tangent D H ; from e, 
 to the centre of the circle G, draw e G. 
 
 2. Bisect e G, in/, and with the radius /e, or/ G, 
 describe the semicircle e C G, cutting the tangent 
 and the circle in C ; it will be the point required. 
 
 PROBLEM XIII. 
 
 Given three points, ABC, not in a straight 
 line, to find a number of points Ipng between 
 them, so that they shaU aU be in the circum- 
 ference of a circle, without drawing any part 
 of the circle, or finding the centre. 
 
 1. From A, through B and C, draw A B and A /. 
 
 2. On A, as a centre, with any radius A/, describe 
 an arc/e d, cutting A B in </, and A C mf. 
 
 3. Bisect arc df in e; through e draw A e h. 
 
 4. Join C B, bisect it in g, draw g h perpendicular, 
 cutting A e /t at A, then h will also be in the same 
 circumference with A C B. In the same manner 
 may a point be found between C A and h B. 
 
 PROBLEM XIV. 
 
 Given three points, ABC, not in a right line, 
 to find another point without these points, so 
 that the four points shall all be in the circum- 
 ference of a circle, without drawing any part 
 of the circle, or finding the centre. 
 
 1. Draw A e and A C, from A, through B and C. 
 
 2. On A, as a centre, with any radius A e, draw 
 the arc e/g-, cutting A B in e, and A C in/. 
 
 3. Make f g equal to / e, through A and g draw 
 A g indefinitely towards d. 
 
 4. Upon C, with the distance C B, cross the line 
 Ag &i d; it wiU be the point required. 
 
 If a fifth point, or any other number of points, are 
 required, the process will be the same. 
 
 Plate 3. 
 
 PROBLEM XV. 
 
 Given three points, ABC, not in a straight line, 
 to draw a circle through them. 
 
 1. Bisect the lines A B and B C by the perpen- 
 diculars, meeting at d. 
 
 2. Upon d, with the distance d A, dB, ox d C, de- 
 scribe A B C ; it will be the circle required. 
 
W II 
 
 AAlIl 
 
 .\X1\ . 
 
 XXV. 
 
 XXVI 
 
 J-'u/.:^. 
 
 I'u/.:j . 
 
 XXMl. 
 
 A h 
 
P U A C T 1 C A L G E O M E T 11 Y , 
 
 41 
 
 PROBLEM XVI. 
 
 To describe the segment of a circle to any 
 length, A B, and breadtli, C D. 
 
 1. Bisect A B, by (lie perpendicular D g; cutting 
 A B in C. 
 
 2. From r, make c D on the perpendicular equal 
 to C D. 
 
 3. Bisect A D, by a perpendicular e f, cutting D g 
 
 ill S'- 
 
 4. Upon g-, the centre, describe A D B ; it will be 
 the segment required. 
 
 PROBLEM XVII. 
 
 To describe the segment of a circle, by means 
 of two rules, to any length, A B, and per- 
 pendicular height, C D, in the middle of A 
 B, without making use of the centre. 
 
 It will be most convenient for practice to make the 
 rules C E and C F each equal to A B, as room is 
 sometimes wanted. 
 
 1. Place the rules to the height at C, bring the 
 edges close to A and B, tack them together at C, and 
 fix a rod across to keep them tight. 
 
 2. Put in pins at A and B, then move your rules 
 round these pins ; hold a pencil to the angular point 
 at C ; it will describe the segment required. 
 
 Fig. 2. Bi/ means of a triangle. 
 
 Let A B be the length of the segment, and C D 
 the perpendicular height in the middle. 
 
 1. Through the points D and B draw D B. 
 
 2. Draw D E parallel to A B for conveniency • 
 make D E equal to D B, and join E B. 
 
 3. Make a triangle E D B ; put in pins at the 
 points A D B ; then move your triangle round the 
 points D and B, and the angular point will describe 
 half the segment; the other half will be described in 
 the same manner, which will complete the whole 
 segment, as was required. 
 
 Fig. 3- Another method, by means of points. 
 
 Let A B be the length, and C D, bisecting A B, 
 the perpendicular height. 
 
 1. Through D, draw G H parallel to A B. 
 
 2. Draw D B, the half chord. 
 
 3. From B, make B H perpendicular to D B, cut- 
 ting G H in H, and make D G equal to D H. 
 
 6 
 
 4. Draw A F and B E, each perpendicular to A B, 
 cutting G H in F and E. 
 
 5. Divide D G, D H, C A, C B, and A F, B E, 
 each into a like number of equal parts, as five. 
 
 G. Draw the cross lines, 4 4, 3 3, 2 2, 11, &e. 
 
 7. From the division on A F, and B E, draw 
 lines to D, cutting the other cross lines at d, e, 
 /. §•) &c. 
 
 8. Put pins in these points, bend a sbp round them, 
 and draw the curve by it, which will be the segment 
 reqiiired. 
 
 Fig. 4. Another method, by points nearly true, when 
 the segment is very flat. 
 
 Let A B be the length, and C D, bisecting A B, 
 the perpendicular height. 
 
 1. Draw A E and B F, perpendicular to A B, each 
 equal to C D. 
 
 2. Divide C B and C A each into the same num- 
 ber of equal parts, as five. 
 
 3. From the points 4, 3, 2, 1, &c., on A B, draw 
 the perpendicular 4 4, 3 3, 2 2, 11, &c., to A B. 
 
 4. Divide A E and B F into five equal parts 
 each. 
 
 5. Draw lines from the points 1, 2, 3, 4, 5, at each 
 end, to D, and complete the segment in the same 
 manner as fig. 3. 
 
 PROBLEM XVIII. 
 
 To describe a circle within a given triangle, so 
 that ABC will be tangical. 
 
 1. Take equal distances on C A, also on C B, 
 from C ; intersect towards D. 
 
 2. Draw lines E D, from A and C, through the 
 intersection E and D ; from E let fall a perpendicu- 
 lar, which will be the radius of the circle required. 
 
 PROBLEM XIX. 
 
 In a given square, A B C D, to inscribe a reg- 
 ular octagon. 
 
 1. Draw the diagonals A C and B D, intersect- 
 ing at e. 
 
 2. Upon the points A B C D, as centres, with a 
 radius e C, describe arcs h e l,ke n, meg,fe i. 
 
 3. Jomfn,mh,ki,lg; it will be the octagon re- 
 quired. 
 
42 
 
 PRACTICAL GEOMETRY. 
 
 PROBLEM XX. 
 
 In a given circle to inscribe an equilateral tri- 
 angle, a hexagon, or a dodecagon. 
 
 For the Equilateral Triangle. 
 
 1. Upon any point A, in the circumference, with 
 the radius A G, describe the arc B G F. 
 
 2. Draw B F, make B D equal to B F. 
 
 3. Join D F, and B D F will be the equilateral 
 triangle required. 
 
 For the Hexagon. 
 Carry the radius A G sLx times round the circum- 
 ference ; the figure A B C D E F will be the hexagon. 
 
 For the Dodecagon. 
 
 Bisect the arc A B in //, and A h being carried 
 twelve times round the chrcumference, will also form 
 the dodecagon. 
 
 PROBLEM xxr. 
 
 In a given circle to inscribe a square or an 
 octagon. 
 
 1. Draw the diameters A C and B D at right 
 angles. 
 
 2. Join A B, B C, C D, D A, and A B C D will 
 be the square. 
 
 For the Octagon. 
 
 Bisect the arc A B in E, and A E being carried 
 eight times round, will also form the octagon. 
 
 PROBLEM XXII. 
 
 In a given circle to inscribe a pentagon or a 
 decagon. 
 
 For a Pentagon. 
 
 1. Draw the diameters A C and B D at right 
 angles. 
 
 2. Bisect B C in /, upon /; Avith the distance/ D 
 describe the arc D g upon D ; with the distance D g 
 describe the arc g H, cutting the circle in H. 
 
 3. Join D IT, and caiTy it round the circle five times, 
 which wUl form the pentagon. 
 
 For the Decagon. 
 
 Bisect the arc D II in i, and D i being carried ten 
 times round, will also form the decagon. 
 
 PROBLEM XXIII. 
 
 In a given circle to inscribe any regulai 
 polygon. 
 
 1. Draw tlic diameter A B, from E the centre ; erect 
 Ihc perpendicular E F C, cutting the circle at F. 
 
 2. Divide E F into fom- equal parts, and set three 
 parts from F to C. 
 
 3. Divide the diameter A B into as many equal 
 parts as the polygon is requu'ed to have sides. 
 
 4. From C, through the second division in the di- 
 ameter, draw C D. 
 
 5. Join A D ; it will be the side of the polygon 
 rcquu'ed. 
 
 PROBLEM XXIV. 
 
 Upon a given line, A B, to describe an equilat- 
 eral triangle. 
 
 1. Upon the points A and B, with a radius equal 
 to A B, describe arcs cutting each other at C. 
 
 2. Draw A C and B C; it will be the triangle 
 required. 
 
 PROBLEM XXY. 
 
 Upon a given line, A B, to describe a square. 
 
 1. Upon A and B, as centres, with a radius A B, 
 describe two arcs, A e C, B e D, cutting each other 
 at e. 
 
 2. Bisect A e at/; from e make e D and e C equal 
 to ef. 
 
 3. Join A D, D C, C B, and it will be the square 
 required. 
 
 PROBLEM XXVI. 
 
 Upon a given line, A B, to construct any regular 
 polygon. 
 
 1. Upon A and B, as centres, with a radius A B, 
 describe two arcs intersecting each other at F. 
 
 2. From B, draw B C perpendicular, and divide 
 the arc A C into as many equal parts as the polygon 
 is to have sides. 
 
 3. Through the second division D draw B G, make 
 F E equal to F D, and through E draw A G, meet- 
 ing B G at G ; then G will be the centre, and G A 
 the radius of a circle, that will contain A B to any 
 number of sides required. 
 
 PROBLEM XXVII. 
 
 To make a triangle, whose three sides shall be 
 
PI . I 
 
 .\.\\ 111 . 
 
 X \ 1 X 
 
 XXX. 
 
 I' I K I, n 
 
 leF^Ovtti-v Sc. 
 
PRACTICAL GEOMETRY. 
 
 43 
 
 equal to three given lines, D, E, F, if any 
 two are greater tlian the third. 
 
 1. Draw A B equal to the line D. 
 
 2. Upon B, with the length of E, describe an arc 
 at C. 
 
 2. Upon B, with the length F, describe another arc, 
 intersecting the former at C. 
 
 4. Draw A C and C B, and A B C will be the tri- 
 angle required. 
 
 Plate 4. 
 
 PROBLEM XXVIII. 
 
 To make a trapezium equal and similar to a 
 given trapezium, A B C D. 
 
 1. Divide the given trapezium A B C D into two 
 triangles, by a diagonal, A C. 
 
 2. ]Make E F equal to A B upon E F, construct 
 the triangle E F, whose three sides will be respec- 
 tively equal to the triangle ABC. 
 
 3. Upon E G, which is equal to A C, construct 
 the triangle E G H, w"hose two sides, E H and G H, 
 are respectively equal to A D and C D, then E F 
 G H wUl be the trapezium required. 
 
 Li the same manner may any irregular polygon be 
 made equal and similar to a given irregular polygon, 
 by dividing the given polygon into triangles, and con- 
 structing the triangles in the same manner in the re- 
 quired polygon, as is shown by figures. 
 
 PROBLEM XXIX. 
 
 To make a triangle equal to a given trapezium, 
 ABCD. 
 
 1. Draw the diagonal B D, make C E parallel to 
 to it, meeting the side A B, produced in E. 
 
 2. Join D E, and A D E will be the triangle. 
 
 PROBLEM XXX. 
 
 To make a triangle equal to a given right-lined 
 figure, ABODE.' 
 
 1. Produce the side A B both ways at pleasure. 
 
 2. Draw the diagonals A D and B D, and make 
 E F and G H parallel to them. 
 
 3. Join D F, D G, then D F G will be the triangle 
 required. 
 
 Much after the same manner may any other right- 
 lined figure be reduced to a triangle. 
 
 PROBLEM XXXI. 
 
 To reduce a triangle, A B C, to a rectangle. 
 
 1. Bisect the altitude C G, in D ; tlu'ough D draw 
 E F parallel to A B. 
 
 2. From B draw B F perpendicular to A B, through 
 A draw A E parallel to B F, then A B F E \vill be 
 the rectangle required. 
 
 PROBLEM XXXII. 
 
 To make a rectangle, having a side equal to a 
 given line, A B, and equal to a given rectan- 
 gle, C D E F. 
 
 1. Produce the sides of the rectangle C F, D E, 
 F E, and CD. 
 
 2. Make E G equal to A B, through G draw L H 
 parallel to F E, cutting C F produced at L. 
 
 3. Draw the diagonal L E, and produce it till it 
 cut C D at K. 
 
 4. Draw K H paraUel to E G, then wiU E I H G 
 be the rectangle required. 
 
 PROBLEM XXXIII. 
 
 To make a square equal to a given rectangle, 
 ABCD. 
 
 1. Produce the side A B, make B E equal to B C. 
 
 2. Bisect A E, in I ; on I, as the centre, with the 
 radius I E or I A, describe the semicircle A H E. 
 
 3. Produce the side of C B to cut the circle in H; 
 on B H describe the square B H G F ; it will be the 
 square required. 
 
 PROBLEM XXXIV. 
 
 To make a square equal to two given squares, 
 A and B. 
 
 1. Make D E equal to the side of the square A, 
 and D F perpendicular to D E, equal to the side of 
 the square B. 
 
 2. Draw the hypothenuse F E ; on it describe the 
 square E F G H ; it wiU be the square required. 
 
 PROBLEM XXXV. 
 
 To make a square equal to three given squares, 
 ABC. 
 
 1. Make D E equal to the side of the square A, 
 and D F perpendicular to D E, equal to the side of 
 the square B. 
 
 2. Join F E ; draw F G perpendicular to it. 
 
44 
 
 PRACTICAL GEOMETRY 
 
 3. Make F G equal to the side of the square C ; 
 join G E, then G E will be the side of the square 
 required. 
 
 PROBLEM XXXVI. 
 
 Two right lines, A B, and C D, being given, to 
 find a third proportional. 
 
 1. Make an angle H E I at pleasure, irom E, make 
 E F equal to A B, and E G equal to C B ; join F G. 
 
 2. Make E H equal to E G, and draw H I parallel 
 to E G, then E I will be the third proportional re- 
 quired, that is, E F : E G : : E H : E I, or A B : 
 C D : : C D : E I. 
 
 PROBLEM XXXVII. 
 
 Three right lines, A B, C D, E F, being given, 
 to find a fourth proportional. 
 
 1. ]\Iake the angle, H G I, at pleasure ; from G 
 make G H equal to A B ; G I equal to C D ; and 
 join H I. 
 
 2. Make G K equal to E F, draw K L through K 
 parallel to H I, then G L will be the fourth propor- 
 tional required ; that is, G H : G I : : G K : G L, or 
 A B : C D : : E F : G L. 
 
 PROBLEM XXXVIII. 
 
 To divide a given line, A B, in the same propor- 
 tion as another, C D, is divided. 
 
 1. Make any angle K H I, and make H I equal 
 to A B ; then apply the several divisions of C D from 
 H to K, and join K I. 
 
 2. Draw the lines h e, i f, k g, parallel to I K, and 
 the line H I will be divided in /;, i, k, as was required. 
 
 PROBLEM XXXIX. 
 
 Between two given right lines, A B, and C D, 
 to find a mean proportional. 
 
 1. Draw the right line E G, in which make E F 
 equal to A B, and F G equal to C D. 
 
 2. Bisect E G in H, and with H E or H G de- 
 scribe the semicircle E I G. 
 
 3. From F draw F I perpendicular to E G, cutting 
 the circle in I, and I F will be the mean proportional 
 required. 
 
 PROBLEM XL. 
 
 To find a line nearly equal to the circumference 
 of its circle, A BCD. 
 
 1. Draw the diameters A B and C D at right 
 angles. 
 
 2. Produce A B, lill the part A G without be three 
 quarters of the radius. 
 
 3. Draw E F through B, parallel to C D, through 
 G, and the points C and D ; draw G E and G F, cut- 
 ting the tangent in E and F ; then E and F will be 
 equal to half the circumference. 
 
 Much after the same manner may a straight line 
 be found equal to any part of a circle, as is shown at 
 Fig. 2, but the following method is much better for 
 small arcs, as it requires less room : — 
 
 Remark. — K any number of divisions E I, I K 
 K L, L B, are taken on E F, and from the points I, 
 K, L, lines are drawn to G, to cut the circumference 
 i, k, I, the divisions on the circle, viz., C i, i k, k I, I B, 
 will be respectively equal to their corresponding 
 divisions, E I, I K, K L, L B, on the tangent line 
 E F ; that is, to k i, and I E equal to i C. 
 
 PROBLEM XLI. 
 
 To find the length of any arc, A C B, of a 
 circle. 
 
 1. Draw the chord A B indefinitely towards E, and 
 bisect the arc A C B at C. 
 
 2. Make A D equal to twice the half chord 
 A C ; divide B D into three equal parts, and set one 
 towards E ; then will A E be the length of the arc 
 line A C B. 
 
Del iiiilii)iis 
 
 I'KOI! . I. 
 
 Ill ll„- l'.ll|,,M. 
 
 IV. 
 
 V. 
 
 W.F.Stnttti-v ,Si". 
 
PRACTICAL GEOMETRY, 
 
 45 
 
 CONIC SECTIONS. 
 
 C D bisecting the 
 and terminated by 
 
 OF THE ELLIPSIS. 
 
 DEFINITIONS. 
 
 Plate 5. 
 
 1. If two pins are fixed at the points E and F, 
 a string being put about them, and the ends tied 
 together at C, the point C being moved round, keep- 
 ing the string stretched, it will describe a cm-ve 
 called an Ellipsis. 
 
 2. Foci are the two points E and F, about which 
 tlie string is made to revolve. 
 
 3. Transverse axis is the line A B, passing through 
 the foci, and terminated by the curve at A and B. 
 
 4. Centre is the point G, bisecting the transverse 
 axis A B. 
 
 5. Conjugate axis is the line 
 transverse axis at right angles, 
 the curve. 
 
 6. Latiis rectum is a right line passing through the 
 focus F, at right angles to the transverse axis, ter- 
 minated by the curve. This is also called the Pa- 
 rameter, 
 
 7. Diameter is any line passing through the centre 
 G, terminated by the curve. 
 
 8. Conjugate diameter is a right line drawn through 
 the centre, parallel to a tangent at the extreme of the 
 other diameter, and terminated by the curve. 
 
 9. Double ordinate is a line drawn through any 
 diameter, parallel to a tangent at the extreme of that 
 diameter, terminated by the curve. 
 
 PROBLEMS. 
 
 PROBLEM I. 
 
 The transverse and conjugate axes, A B, and 
 C D, of an ellipsis being given, to find the 
 two foci, from thence to describe an ellipsis. 
 
 1. Take the semitransverse A E, or E B, and 
 from C, as a centre, describe an arc, cutting A B at 
 F and G, which are the foci. 
 
 2. Fix pins in these points, a string being stretched 
 about the points F C G ; then move the point C 
 round the fbced points F and G, keeping the string 
 
 tight. It wUl describe the ellipsis as in the first 
 definition. 
 
 PROBLEM II. 
 
 The same being given, as in the last problem, to 
 describe an ellipsis, by an instrument called a 
 trammel. 
 
 The trammel, as used by artificers, is two rules, 
 with a groove in each, fijced together so that the 
 grooves will be at right angles to each other. To 
 this there is a rod with two movable nuts, and 
 another fixed at the end, with a hole through it, 
 to hold a pencil. On the under side of the sliding 
 nuts are two round pins, made to fill the groove of 
 the trammel, and are used as follows : — 
 
 Operation. — Set the distance of the first pin at B, 
 from the pencil at A, to half the shortest axis, and 
 the distance of the second pin at C, from A, to half 
 the longest axis, the pins being put in the grooves, 
 as is shown by the figure ; then move the pencil at 
 A. It will describe the ellipsis required. 
 
 PROBLEM III. 
 
 A diameter, A B, and a double ordinate, C D, 
 to that diameter, being given, to find the 
 parameter. 
 
 1. Join A C, A D, and B C, B D ; bisect A B in 
 H, through H draw H I parallel to D C, cutting 
 B C in I. 
 
 2. From A, make A F equal to H I ; through F 
 draw G H parallel to C D, cutting A C in G, and 
 A D in H ; then G H is the parameter sought. 
 
 PROBLEM IV. 
 
 To describe an ellipsis by finding points in the 
 curve, having the two conjugate diameters, 
 A B and C D, given. 
 
 1. Find F G half the parameter ; through G draw 
 H H parallel to A B. 
 
 2. Draw E H parallel to C D, cutting H H at I. 
 
 3. Set off any number of equal divisions from H 
 towards G. Set the same parts from E towards C. 
 
46 
 
 PRACTICAL GEOMETRY 
 
 4. From the point B, through the points 1, 2, 3, in 
 E C, draw the lines B i, B k, B /. 
 
 5. From A, through the poijits in H G, draw the 
 lines A i, A k, A I, intersecting the former lines in 
 t, k, I. They will be in the periphery of the ellipsis. 
 
 PROBLEM V. 
 
 Having a diameter, and a double ordinate to 
 that diameter, to describe the ellipsis, by 
 finding points in the curve. 
 
 This problem will be completed in the same man- 
 ner as Problem IV., and as is plainly shown by the 
 figures 2 and 3. 
 
 Plate 6. 
 PROBLEM VI 
 
 To describe an ellipsis, or any segment of an 
 ellipsis, having a diameter and a double ordi- 
 nate, by means of points being found in the 
 curve, without finding the parameter. 
 
 Let A B be the diameter or double ordinate, let 
 C D be its conjugate, and let E D be the height of 
 the segment. 
 
 1. Through D draw F G parallel to A B ; also, 
 through the points A and B draw A F and B G, 
 parallel to D E, cutting F G in F and G. 
 
 2. Divide A E and E B into a lilvc number of 
 equal parts, as four ; likewise B G and A F into the 
 same number of equal parts. 
 
 3. From the point D, through the points 1, 2, 3, in 
 A F and B G, draw 1 D, 2 D, 3 D. 
 
 4. From the point C, through the points 1, 2, 3, in 
 A B, draw C a, C b, C c ; cutting the lines 1 D, 2 D, 
 3 D, in a, b, c, they will be in the periphery of the 
 ellipsis ; a curve being traced througli these points 
 will form the ellipsis required. 
 
 But if the ciirve is very large, as in practical 
 works, the best way is to put in nails or pins at the 
 points a, b, c, Sec, bend a slip round them, and draw 
 a curve by it ; it will appear quite regular. 
 
 PROBLEM VII. 
 
 To draw the representation of an ellipsis, with 
 a compass, to any length, A B, and width, 
 C D. 
 I. Draw B P parallel and equal to E C, and bisect 
 
 it at 1, then draw 1 C and P D, cutting each other 
 
 at K ; bisect K C by a perpendicular, meeting C D 
 at O ; and on O, with the radius O C, describe the 
 quadrant C G Q. 
 
 Througli Q, and A draw Q G, cutting the quad- 
 rant at G ; tlien ckaw G O, cutting A B at M ; make 
 E L equal to E M ; also E N equal to E O. From 
 O, through M and L, draw O G and O K ; likewise 
 from N, through M and L, draw N II and N I ; then 
 M, L, N, O, are the four centres ; by help of these, 
 the foiir opposite sectors will be described. 
 
 Fig. 2. To describe an ellipsis more accurately with 
 a compass than the foregoing, having the tivo axes 
 A B and C D given. 
 
 1. Draw A 3 parallel and equal to E C, divide it 
 into three equal parts, and draw 2 C and 1 C ; then 
 divide A E also into three equal parts, and from D, 
 through the points 1, 2, in A E, draw D Q and D P, 
 cutting the lines 1 C and 2 C, in Q, and P. 
 
 2. Bisect C P by a perpendicular, meeting C D 
 produced at S ; join P S, cutting A E at X ; then 
 make E W equal to E X, and E U equal to E S ; 
 and through X and W draw P S and O S ; also 
 through the same points, X and W, draw U K and 
 UL. 
 
 3. Bisect P Q by a perpendicular, meeting P S at 
 F ; draw Z F parallel to A B ; then with the radius 
 F Q, describe the arc Q Z, cutting F Z at Z ; through 
 Z and A draw Z y, cutting the arc Z Q at y ; and 
 join y F, cutting A B at V. On X, malvc X I equal 
 to X F; with the same radius on W make W H 
 and W G ; through V draw I R, make E T equal 
 to E V, through T draw 11 IM and G N ; then U, S, 
 G, H, I, F, T, V are the centres. 
 
 PROBLEM VIII. 
 
 Ha\'ing the two axes, or any other conjugate 
 diameters, A B and C D, given, to describe 
 an ellipsis through points, at the extremes of 
 any diameters taken at pleasure. 
 
 1. Through D draw P Q, parallel to A B from D ; 
 draw D F perpendicular to P Q, and make it equal 
 to E B, or E A; upon F, with llu- distance F D, de- 
 scribe the circle n D /■'. 
 
 2. Through tlie centre E draw the line PEN, 
 < E M, s E L, &c., at pleasure, cutting the tangent 
 P Q at P, t, s, &c. Join P F, < F, s F, &c., cutting 
 the circle n D k. at the points m n I, &c. ; likewise 
 
I'l. r, 
 
 nioi; . \i 
 
 /•'if/.-4- 
 
 //./.J. 
 
 />;/.•/. 
 
I'l 7 
 
 TKOn. XI. 
 
 Xll . 
 
 .\1\' 
 
 JCVl 
 
PRACTICAL GEOMETRY. 
 
 41 
 
 join E F, if necessary, and draw n N, vi M, / L, &c., 
 parallel to it, cutting the diameters N N, M M, L L, 
 &c., at N M L, &c. ; tlicn these points will be in the 
 periphery of the ellipsis. If the diameters arc pro- 
 duced to the opposite sides, at N M L, and the dis- 
 tances E N, E M, E L, &c., are made respectively to 
 their corresponding opposite distances, E N, E M, 
 and E L, &e., then the points N M L, on the under 
 5ide of the diameter A B, will also be in the curve. 
 
 PEOBLEM IX. 
 
 To draw an ellipsis by ordinates, having the 
 axes, or any other conjugate diameters, A B, 
 and C D, given. 
 
 1. From E, the cenh-e, cb-aw E F perpendicular to 
 C D. Upon E, with the radius E C, describe the 
 quadrant C F ; divide E F into any number of equal 
 parts, as four ; from these points draw 1 a, 2 b, 3 c, 
 parallel to E C, cutting the quadi-ant at a, b, and c. 
 
 2. Divide E A and E B each in the same number 
 of equal parts ; through the points 1, 2, 3, &c., draw 
 a a, b b, c c, &c., parallel to C D. 
 
 3. Make the distances 1 a, 2 b,3 c, See, equal to 
 then- coiTcsponding distances, 1 a, 2 b, on the quad- 
 rant ; then the points a, b, c, &c., will be all in the 
 periphery of the ellipsis. 
 
 PROBLEM X. 
 
 An ellipsis, A B C D, being given, to find the 
 transverse and conjugate axes. 
 
 1. Draw any two parallel lines A B, and C D, cut- 
 ting the ellipsis at the points A, B, C, D ; bisect them 
 in c and/. 
 
 2. Through e and/ draw G 11, cutting the ellipsis 
 at G and H; bisect G H at I; it will give the centre. 
 
 3. Upon I, with any radius, describe a circle, cut- 
 ting the ellipsis in the four points, k, I, m, n. 
 
 4. Join k I, and m n ; bisect k I, or vi n, at o or p. 
 
 5. Through the points o I, or Ip, draw Q, R, cut- 
 ting the ellipsis at Q and R ; then Q, R will be the 
 transverse axis. 
 
 6. Through I, draw T S parallel to k I, cutting the 
 ellipsis at T and S, and T S will be the conjugate 
 axis. 
 
 Plate 7. 
 
 PROBLEM XI. 
 
 Any diameter, A B, being given, and an ordi- 
 
 nate, C D, to find its conjugate, without draw- 
 ing any part of the ellipsis. 
 
 1. Draw C I perpendicular to A B ; bisect A B in 
 F, and draw F H parallel to C D. 
 
 2. On F, with the distance F A, or F B, describe 
 the semicircle A I B, cutting C I at I. 
 
 3. Make A E equal to C I ; cbaw E G parallel and 
 equal to C D ; through G and A draw A H, cutting 
 F H at H ; then F H is the semi-conjugate. 
 
 Much after the same manner, if two conjugate 
 diameters are given, an ordinate may be found with- 
 out drawing any part of the ellipsis. 
 
 PROBLEM XII. 
 
 Any two conjugate diameters, A B and C D, 
 being given, and a right line, G H, passing 
 through the centre, F, to find a diameter 
 which will be conjugate to G H, without 
 drawing any part of the ellipsis. 
 
 1. Through D draw E K parallel to A B, and pro- 
 duce the given line H G to cut the tangent in E. 
 
 2. From D, make D I perpendicular to E F, and 
 equal to F A, or F B. 
 
 3. Join E I; from I, di-aw I K perpendicular to 
 I E, cutting the tangent E K at K ; through the centre 
 F draw F K. 
 
 4. Through the points g- and m, where the lines 
 E I and I K cut the circle, draw g- G and vi M par- 
 allel to I F, cutting E F, and K F, at the points 
 G and M ; make F H equal to F G, and F L equal to 
 F M ; then M L and G H will be the two other 
 conjugate diameters. 
 
 PROBLEM XIII. 
 
 Any two conjugate diameters, A B and C D, 
 being given, to find the two axes, from thence 
 to describe the ellipsis. 
 
 1. Through D draw E F, parallel to A B ; draw 
 D I perpendicular to E F, and equal to M A, or M B. 
 
 2. Upon I, with the radius I D, describe the arc 
 g- D /. 
 
 3. Join I M, and bisect it by a perpendicular, meet- 
 ing the tangent E F at N. 
 
 4. On N, as a centre, with the distance N I, de- 
 scribe a semicircle E I F, cutting E F at the points 
 E and F. 
 
48 
 
 PRACTICAL GEOMETRY. 
 
 5. Through the centre M draw F K and E H. 
 
 6. Join I E and I F, cutting the arc g- D / at 
 g and /. 
 
 7. Draw I L and g G parallel to I M, cutting K F 
 and H E at G and L. Make M K equal to M L, 
 and P*I H equal to M G ; then E H and K L will be 
 the two axes required. 
 
 PROBLEM XIV. 
 
 An ellipsis being given, to draw a tangent 
 through a given point H, in the curve. 
 
 1. Find the foci F and G ; join F H and G H. 
 
 2. Produce C G H to I upon H, with any radius ; 
 describe the arc K L I, cutting G I and F H at 
 K and I. 
 
 3. Bisect the arc K L I at L ; through L and H 
 draw L H ; it will be the tangent required. 
 
 PROBLEM XV. 
 
 To draw two tangents to an ellipsis from a 
 given point, E, without it having any two 
 conjugate diameters, A B and C D, given, 
 without drawing any part of the ellipsis. 
 
 1. Let the point E be in the diameter D C, pro- 
 duced. 
 
 2. From the centre H make H I equal to H C, 
 and join I E. 
 
 3. Through C draw C K parallel to I E, cutting 
 H A in K. 
 
 4. Make H L equal to H K ; through L chraw F G 
 parallel to A B ; find the extreme points F and G of 
 the ordinate F G by Problem XI. From E, through 
 the points F and G, draw E F and E G. They 
 will be the tangents required. 
 
 If the point E is in neither of the given diameters 
 A B or C D, when produced, draw a line from the 
 given point E, through the centre ; by Problem XII., 
 find a conjugate to that Line, and the extremities of 
 both ; then the construction will be the same as in 
 this. 
 
 PROBLEM XVL 
 
 To describe an ellipsis similar to a given one, 
 A D B C, to any given length, I K, or to 
 a given width, M L. 
 
 1. Let A B and C D be the two axes of the given 
 ellipsis. 
 
 2. Through the points of contact, A, D, B, C, 
 complete the rectangle G E H F ; draw the diag- 
 onals E F and G H. They will pass through the 
 centre at R. 
 
 3. Through I and K draw P N and O Q parallel 
 to C D, cutting the diagonals E F and G II at P, 
 N, Q, O. 
 
 4. Join P O and N Q, cutting C D at L and M ; 
 then I K is the transverse, M L the conjugate axis 
 of an ellipsis that will be similar to the given one, 
 A D B C, which may be described by some of the 
 
 foregoing methods. 
 
 Plate 8. 
 
 PROBLEM XVII. 
 
 Given the rectangle A B C D, to circumscribe 
 an ellipsis which shall have its two axes in 
 the same ratio as the sides of the rectangle. 
 
 1. Draw the diagonals A C and B D, cutting each 
 other at S, the centre. 
 
 2. Through S draw E F and G H parallel to A B 
 and A D. 
 
 3. Upon S, with a radius, S I, equal to half A D or 
 B C, describe the quadrant I K L cutting E F at L. 
 
 4. Bisect the arc I K L at K ; through K draw 
 M N parallel to E F, cutting the diagonal B D at N. 
 
 5. Join I N ; through B draw B G parallel to it, 
 cutting G H at G, and make S H equal to S G. 
 
 6. Join N O ; through B draw B F parallel to it, 
 cutting E F at F ; make S E equal to S F ; then 
 E F and G H are the two axes which may be de- 
 scribed by some of the methods which are shown in 
 the foregoing problems. 
 
 PROBLEM XVIII. 
 
 Given the trapezium, A B C D, and a point E, 
 in one of the sides, to find a point in each of 
 the other sides, so that, if an ellipsis was to 
 be inscribed, it Avould touch the trapezium in 
 these points. 
 
 1. Produce the sides of the trapezium till they 
 meet at K and L. 
 
 2. Draw the diagonals A C and B D, cutting each 
 other at F ; produce B D till it cut K L at M. 
 
 3. Through F, and the given point E, draw E G, 
 cutting B C at G. 
 
I'l '! I'liOl'. . X\'l\ 
 
 c. 
 
 XX'lil. 
 
 XIX 
 
 \X 1 
 
I 'I 
 
 |)rl!llllliiiis. 
 
 Ill' llll' I'.i 1 .ilxil.i 
 
 ruoi'. . 1 . 
 
 V 
 
 11 ^v I 
 
 1' !•: f. 
 
 V. 
 
 •■ ii 
 
 /■W/. ?. 
 
 / or 111,- iiv|M-ii 
 
PRACTICAL GEOMETRY. 
 
 49 
 
 4. From M, through the points E and G, draw 
 M H and M G, cutting the other two sides in the 
 points I and H, then E, H, G, I, will be the four 
 points requii'cd. 
 
 PROBLEM XIX. 
 
 A trapezium, A B C D, being given, and a point 
 E, in one of the sides, to find the centre of 
 an ellipsis that may be described in the trape- 
 zium, and pass through the point of contact 
 E, without dramng any part of the ellipsis. 
 
 1. Find the points of contact H, G, I, E, as in the 
 last problem. 
 
 2. Join the points G and E by the right line G E, 
 bisect it in M, and from K, where the opposite sides 
 A D and B C meet, and through the point M, draw 
 K M indefinitely. 
 
 3. Also join any other t\.vo points of contact, as 
 H I ; bisect H I at N, from L, where the opposite 
 sides B A and C D meet ; di-aw L N, meeting K M 
 at P ; then P will be the centi'c of the ellipsis re- 
 quired. 
 
 And, in lilce manner, if the points G and H were 
 joined and bisected at Q, and a line being drawn 
 from B where the opposite sides A B and C D meet 
 through Q, it woidd also meet in P, the centre, &c. 
 
 PROBLEM XX. 
 
 Given a trapezium, A B C D, and a point E, in 
 one of the sides, to find the two axes of an 
 ellipsis that may be inscribed in the trape- 
 zium, and pass through the pomt E without 
 drawing any part of the ellipsis. 
 
 1. Find the opposite pomts of contact, H, E, F, G, 
 by Problem XVIII. 
 
 2. From thence, find the centre, P, by the last prob- 
 lem. 
 
 3. From E, and through the centre, P, draw E M, 
 making P M equal to P E. 
 
 4. Through H, or any other point of contact, draw 
 H K parallel to D C, cutting E M at K ; then K H 
 is an ordinate to the diameter E M. 
 
 5. Tlu-ough P, the centre, draw P E parallel to 
 H K. 
 
 6. Find the extremities R and S, of the diameter 
 R S, by Problem XL 
 
 7 
 
 7. The conjugate diameters E M and R S, being 
 now found, then find the two axes, V W and X Y, 
 by Problem XIII. 
 
 PROBLEM XXI. 
 
 To find the centre and transverse axis of an 
 ellipsis by means of a square and rule. 
 
 1. Apply the square A B, Problem XXI. 
 
 2. Place the ellipsis tangical to A B, at pleasure, 
 
 3. Draw lines C D, touching the opposite sides of 
 the ellipsis. 
 
 4. Draw lines E F, intersecting the ellipsis ; and 
 C is the centre, and E F the transverse axis required. 
 Also, E F is equal, added together, in whatever 
 direction the ellipsis may be appHed to the square 
 and rule. 
 
 OF THE PARABOLA. 
 
 DEFINITIONS. 
 Plate 9. 
 
 1. If a thread, equal in length to B C be fixed at C, 
 the end of a square, ABC, and the other end fixed 
 at F ; and if the side A B, of the square, be moved 
 along the right line, A D; and if the point E be 
 always kept close to the edge B C, of the square, 
 keeping the string tight, the point or pm E will de- 
 scribe a curve E G I H, called a parabola. 
 
 2. Focus is the fixed point F, about which the 
 string revolves. 
 
 3. Directrix is the line A D, which the side of the 
 square moves along. 
 
 4. Axis is the line L K, drawn tlu-ough the focus 
 F, perpendicular to the directi-is. 
 
 5. Vertex is the point I, where the line L K cuts 
 the curve. 
 
 6. Latus rectum, or parameter, is the line G H, 
 passing through the focus F, at right angles to the 
 axis I K, and terminated by the curve. 
 
 7. Diameter is any line M N, drawn parallel to the 
 axis I K. 
 
 8. Double ordinate is a right line R S, drawn par- 
 allel to a tangent at M, the exti-eme of the diameter 
 M N, terminated by the curve. 
 
 9. Abscissa is that part of a diameter contained 
 between the curve and its ordinate, as M N. 
 
6( 
 
 PRACTICAL GEOMETRY. 
 
 PROBLEMS. 
 
 PROBLEM I. 
 
 To describe a parabola by finding points in 
 the curve, tlic axis A B, or any diameter be- 
 ing given, and a double ordinate C D. 
 
 1. Through A draw E F parallel to C D. 
 
 2. Through C and D, di-aw D F and C E parallel 
 to A B, cutting E F at E and F. 
 
 3. Divide B C and B D each into any number of 
 equal parts, as four. 
 
 4. Likewise divide C E and D F into the same 
 number of equal parts, viz., four. 
 
 5. Through the points 1, 2, 3, &c., in C D, draw 
 the lines 1 a,2b,S c, &c., parallel to C D. 
 
 6. Also through the points 1, 2, 3, in C E and D 
 F, draw the lines 1 A, 2 A, 3 A, cutting the parallel 
 lines at the points a, b, c, then the points a, b, c are 
 in the curve of the parabola. 
 
 Fig. 2. Another method. 
 
 1. Join A C and A D ; from A make A E equal 
 to B C or B D. 
 
 2. Through A and E, draw H I and F G parallel 
 to C D, cutting A C and A D in the points F and G. 
 
 3. Through F and G, di-aw F H and G I parallel 
 to A B, cutting H I at the points H and L 
 
 4. From the points H and I, take any number of 
 equal divisions on the lines H F and I G ; from these 
 points draw lines to A. 
 
 5. From B, set the same divisions towards C and 
 D ; draw the parallel lines 1 a, 2 6, 3 c, &c., intersect- 
 ing the former at the points a, b, c ; they will be in 
 the curve of the parabola. 
 
 OF THE HYPERBOLA. 
 
 DEFINITIONS. 
 1. If B and Care two fixed points, and a rule A B 
 be made movable about the point B, a string ADC, 
 being tied to the other end of the rule, and to the 
 point C, and if the point A is moved round the cen- 
 tre B, towards E, the angle D, of the string ADC, 
 by keeping it always tight and close to the edge of 
 the rule, A B, will describe a curve, D F H G, called 
 an hyperbola. 
 
 2. If the end of the rule at B was made movable 
 about the point C, the string being tied from the end 
 of the rule A to B, and a cui-ve being described after 
 the same manner, it would be an opposite hyperbola. 
 
 3. Foci are the two points B and C, about which 
 the rule and string revolve. 
 
 4. Transverse axis is the line I II, terminated by 
 the two curves passing through the foci, if continued. 
 
 5. Centre is the point M, in the middle of the 
 transverse axis I H. 
 
 6. Conjugate axis is the line N O, passing through 
 the centre M, and terminated by a circle from H, 
 whose radius is M C, at N and O. 
 
 7. Diameter is any line V W, drawn through the 
 centre M, and terminated by the opposite curves. 
 
 8. Conjugate diameter to another is the line drawn 
 through the centre parallel to a tangent with either 
 of the curves, at the extreme of the other diameter, 
 terminated by the curves. 
 
 9. Abseissa is when any diameter is contained 
 within the curve, terminated by a double ordinate 
 and the cm-ve, then the part within is called the 
 abscissa. 
 
 10. Double ordinate is a line di'awn through any 
 diameter, parallel to its conjugate, and terminated 
 by the cm"ve. 
 
 11. Parameter, or latus rectum, is a line di-awn 
 through the focus, perpendicular to the transverse 
 axis, and terminated by the curve. 
 
 12. Asymptotes are two right lines drawn from the 
 centre M, and the points R S, which are parallel to 
 the conjugate axis N O, and drawn through the end 
 of the ti'ansverse axis I H; II R and H S being 
 equal to M N or M O, then M X and M Y are 
 asymptotes. 
 
 13. Equilateral or right-angled hyperbola is when 
 its transverse or conjugate axes are equal. 
 
 PROBLEMS. 
 Plate lO. 
 
 PROBLEM I. 
 
 To describe an hj^icrbola by finding points in 
 the curve having the diameter, or axis A B, 
 its abscissa B C, and double ordinate D E. 
 
 1. Through B, draw G F parallel to D E ; from D 
 and E, draAv D G and E F parallel to B C, cutting 
 G F in F and G. 
 
ruoi". . I 
 
 ir 
 
 I'l 
 
 A 
 
 5 
 
 I> J 2 J C 
 
 3 Z J 
 
 III 
 
 n^ ( 
 
 .-••'" 
 
 \X 
 
I'l II 
 
 \'ll 
 
 I'KOl'.. I 
 
 a!I(S^O®!iaS ®1? 3®[Lfl®g. 
 
 Ol'a CNlnnlir 
 
 ::X 
 
PRACTICAL GEOMETRY. 
 
 51 
 
 2. Divide C D and C E each into any number of 
 equal parts, as four ; through the points of division, 
 1, 2, 3, draw lines to A. 
 
 3. Likewise divide D G and E F into the same 
 number of equal parts, viz., four ; from the divisions 
 on D G and E F draw lines to B, and a curve being 
 drawn tlirough the intersections at B a ft c E, wUl be 
 the hyperbola required. 
 
 PROBLEM 11. 
 
 Given the asjinptotes A B, C D, and a point 
 E, in the curve, to describe the hyperbola. 
 
 1. Through the given point E, di-aw any right line 
 E F, cutting the asymptotes in the points i and I. 
 
 2. Malce i F equal to I E ; from F draw as many 
 lines as you please, cutting the asymptotes in the 
 points g-, h, i, k, &c., and G, H, I, K, &c. 
 
 3. Make G /, H /, K /, &c., respectively, equal to 
 g F, h F, k F, &c., through the points/,/,/, describe 
 a curve, and it is the hyperbola required. 
 
 In the same manner may the opposite hyperbola 
 be described. 
 
 PROBLEM IIL 
 
 Given the two conjugate diameters A B and C D, 
 to find any number of j)oints in the curve. 
 
 1. Through B draw F G parallel to C D, make 
 B F and B G equal to E C, or E D ftom E, tlirough 
 F and G di"aw E H, and E I, the asymptotes. 
 
 2. From A di-aw any lines A C, A D, A E, and 
 A F, cutting the asymptotes at the points a, a, a, &c., 
 and c, d, e, /, &c. Make the distances « C, « D, « E, 
 a F, &c., equal to A c, A d, A e, and A/, &c., then 
 the points C, D, E, F will be in the curve. 
 
 Fig. 2. Another method. 
 
 1. From the centre E, draw E I perpendicular and 
 equal to E A or E B. 
 
 2. Join B C, take any number of points, F, G, H, 
 in E B, and chaw F / G g-, H h parallel to B C, 
 cutting E C at/ g-, h. 
 
 3. Through/ g-, h, B C, di-aw/ A', g I, h m, i n, &c., 
 take the distance F I, and make//c equal to it; then 
 take G I, and make g I equal to it ; in the same 
 manner, find the points m n. And if E B and E C 
 are produced indefinitely beyond B and C, and lines 
 be drawn parallel to B E, as before, any number of 
 points beyond will be fomid in the same manner. 
 
 PROBLEM IV. 
 
 Given the asymptotes, and a point in the curve, 
 to find two conjugate diameters. 
 
 1. From the point B, draw B H D parallel to the 
 asymptote C G. Make H D equal to H B, draw 
 D C E, making C E equal to C D. Make C A equal 
 to C B, then D E is the conjugate to A B. 
 
 PROBLEM V. 
 
 To describe a conic section through five given 
 points, A, B, C, D, E, provided that all these 
 points are joined by right lines, and that 
 any exterior or angle, formed by these lines, 
 be less than two right angles. 
 
 1. Join any four points, A, B, C, E, forming the 
 quadrilateral A B C E. 
 
 2. Through the fifth point D, draw D / and D g 
 parallel to A E and B C, meeting A B, produced 
 both ways at the points / and g-, if necessary. 
 
 3. Also, tln:ough D, draw h i parallel to E C, 
 meetmg B C and A E, produced at the points h and i. 
 
 4. Divide D //, D i, and D/ T> g, into any number 
 of equal parts, as sLx ; likewise divide D F and D G 
 into the same, viz., sbc. 
 
 5. From the point b, and through the points 1, 2, 
 
 3, 4, 5, in D i, draw the lines 1 E, 2 E, 3 E, 4 E, 5 E, 
 cutting the lines B a, B ft, B f, B d', B f, and B/ at 
 the points a, ft, c, d, c, draw from B, through 1, 2, 3, 
 
 4, 5, in D F, which are all in the curve. 
 
 In the same manner, the points between B and D 
 wiU. be found, viz., by drawing Luies from the points 
 A and C, through the lines D g and D h. 
 
 And if the lines D i and D / are produced, and 
 
 the equal parts, 7, 8, 9, extended upon these lines, you 
 
 would obtain as many points, g^ h, i, &c., between A 
 
 and B. 
 
 Plate 11. 
 
 PROBLEM VI. 
 
 To describe a conic section to touch a right 
 line A B, in a given point C, to i^ass through 
 three other points, D, E, and F. 
 
 1. Join D C, E C, and D E ; through F draw F A 
 and F B parallel to E C and D C, cutting A B at 
 A and B. 
 
 2. Through F, draw G H parallel to D E, and pro- 
 duce the sides C D and C E, to cut it at G and H. 
 
52 
 
 PKACTICAL GEOMETRY. 
 
 3. Divide F G and F H, F A and F B, each into 
 any number of equal parts, as four. 
 
 4. From C, through 1, 2, 3, in F H, draw Ca,Cb, 
 C c, &c. 
 
 5. From E, through 1, 2, 3, in F H, draw 1 E, 2 E, 
 3 E, &c., cutting the former in the points a, b, c, which 
 are in the curve. 
 
 In the same manner may points be found in the 
 other side. 
 
 PROBLEM VII. 
 
 To describe a conic section to touch two right 
 lines, A B and B C, in the points A and 
 C, and to pass through a given point, D. 
 
 1. Join the points A and C; through D draw D E 
 and D F parallel to B A and B C. 
 
 2. Through D draw G H, parallel to A C, cutting 
 B A and B C in G and H, and divide D G and D H, 
 D E and D F, each into the same number of equal 
 parts. 
 
 3. From A, through the points 1, 2, 3, in D E, draw 
 the lines A c, A 6, A c. 
 
 4. From C, through the points 1, 2, 3, in D H, draw 
 1 C, 2 C, 3 C, cutting the former in a, h, c, which are 
 in the curve. 
 
 In the same manner may points be found between 
 A and D. 
 
 SECTIONS OF SOLIDS. 
 
 OF A CYLINDER. — DEFINITIONS. 
 
 1. A cylinder is a solid, generated by the revolution 
 of a right-angled parallelogram, or rectangle, about 
 one of its sides ; and, consequently, the ends of the 
 cylinder are equal circles. 
 
 2. Axis is a right line passing from the centres of 
 the two circles which form the ends of the cylinder. 
 
 3. If a cylinder is cut by a plane, parallel to a 
 plane passing through its axis, it will be cut in two 
 parts, which arc called segments of the cylinder. 
 
 4. A segment of a cylinder is comprehended under 
 three planes, and the curve surface of the cylinder ; 
 two of these are segments of circles : the other plane 
 is a parallelogram, which is here, for distinction's 
 sake, called the plane of the segment, and the circu- 
 lar segments are called the ends of the cylinder. 
 
 5. The two sides of the parallelogram, which is 
 parallel to the axis of the cylinder, are called the 
 sides of the segment of the cylinder, and the other 
 two sides of the parallelogram are chords to the ends 
 of the cylinder. 
 
 6. If a cylmder, or segment of a cylinder, stands 
 upon one of its ends, that end on wliich it stands is 
 called the base. 
 
 7. K the segment of a cylinder is cut obliquely by 
 a plane, the intersection of that plane with the plane 
 of the segment is called the chord of the section. 
 
 8. The section of a cylinder cut by any plane ui- 
 clined to its axis is an ellipsis. 
 
 This is proved by the writers of conic sections, 
 
 PROBLEMS. 
 
 Plate 12. 
 
 PROBLEM I. 
 
 To find the section of a semi-cylinder, cut by 
 a plane at right angles to the plane A B F E, 
 whicli passes through its axis, making a given 
 angle E F B, vnih. either of the sides B F. 
 
 1. Let A D B be the circle of the base, and C its 
 centre. 
 
 2. Through the centre of the circle C draw G D 
 parallel to F B, cutting the circle of the base in D, 
 and E F at G ; from G draw G H perpendicular to 
 E F ; make G H equal to C D ; then E F is the 
 transverse axis, and G H the semi-conjugate. 
 
 Or it may be described by ordinates, as in Fig. 2, 
 taken from the base and transferred to the section, as 
 the figm*es direct. 
 
 Li the same manner may any segment be found, 
 viz., by drawing lines parallel to the sides of the 
 plane of the segment till it cut the chords of the 
 section ; from these points, draw perpendiculars to 
 the chord ; make their several lengths from the chord 
 equal to those of the base corresponding to them ; a 
 curve line being drawn through these points, will be 
 the true section of the segment required, as is plamly 
 shown by Fig. 3. 
 
 PROBLEM II. 
 
 To find the tAVO axes of the section of a semi- 
 cylinder cut by a plane, making a given 
 angle A B C, with the plane E F G H, pass- 
 
11 1. 
 
 Si'l^A'S)^ 
 
 I'KOIi. I 
 
 _sL — q| 'V 'rj ii 
 
 II . 
 
PRACTICAL GEOMETRY. 
 
 53 
 
 ing through its axis; also in a given direc- 
 tion K I with the side K F. 
 
 1. Let E M F be the circle of the base, and L its 
 centre. 
 
 2. From the angular point B of the given angle 
 ABC, draw B D perpendicvdar to B A, and equal 
 to L E or L F, the radius of the base ; di-aw D C 
 parallel to B A, cutting B C at C. 
 
 3. Draw Q R, at the distance D C, parallel to I K ; 
 through the centre of the circle L draw O M par- 
 allel to K F, cutting the circle of the base at M, and 
 I K at O ; through the point O draw O P parallel 
 to E F, cutting Q. R at P; also through M draw 
 M N parallel to E F, from P draw P S perpendicular 
 to Q R, and P N parallel to O M, cutting M N at 
 N; join L N, cutting the circle at Z; make U S 
 equal to B C, and join O S upon O S ; from O, 
 make O V equal to L Z, then O V is the semi- 
 conjugate axis. 
 
 4. Through O draw W X perpendicular to O S ; 
 draw L T perpendicular to L N, cutting the circle 
 of the base at T ; from T, draw T Y parallel to 
 L N, cutting the base F E, produced at Y ; from Y, 
 draw Y a parallel to O JM, cutting K I, produced at 
 a; from a, draw a W parallel to O S, cutting W X 
 at W, making O X equal to O W ; then W X is 
 the transverse axis. 
 
 PROBLEM III. 
 
 To find the section of a segment of a cylinder, 
 by ordinates cut by a plane through a given 
 line I K, in the plane of a segment, making 
 a given angle A B C at I K, with the ^jlane 
 E F K I. 
 
 1. Draw the tangent Z IVI parallel to E F, and 
 draw O M parallel to K F, cutting the tangent at M, 
 and I K at O. 
 
 2. Take the distance L M, and make B D perpen- 
 dicular to the angular point B of the given angle 
 ABC equal to it ; proceed as in the last problem ; 
 Qnd O V and L Z. 
 
 3. Draw any number of lines a a, b b, c c, &c., 
 parallel to O L, cutting the lines I K and E F at the 
 points a, b, c, &c. 
 
 4. From the points a, b, c, &c., in I K, draw lines 
 a 1, 5 2, c 3, &c., parallel to O V. 
 
 5. Through the points a, &, c, in E F, draw lines 
 
 al,b2,c3, &c., parallel to L Z, cutting the arc line 
 of the base at 1, 2, 3, &c. 
 
 6. Make all the distances a 1, b 2, c 3, &c., from 
 I K, equal to all theur corresponding distances, a 1, 
 Z> 2, c 3, &c., on the base. 
 
 7. A curve line being traced through these points, 
 I W K will be the section required. 
 
 In the same manner the section of any irregular 
 figure may be found, as is plainly shown by Fig. 2. 
 
 Fig. 3 shows how to find the section when the 
 angle A B C is oblique. 
 
 OF A CONE. 
 
 DEFINITIONS. 
 
 1. A cone is a solid figure standing upon a circu- 
 lar base, diminishing to a point at the top, called its 
 vertex, in such a manner that, if a straight line be 
 applied from the vertex round the circle of the base, 
 it shall coincide every where with the curve surface 
 of the cone. 
 
 2. A right line passing through the cone, from the 
 vertex to the centre of the circle at the base, is called 
 the axis. 
 
 3. If a cone be cut by a plane not parallel to its 
 base, passing quite through the curve surface, the 
 figure is an ellipsis. 
 
 4. If a cone be cut by a plane, parallel to a plane 
 touching the curve surface, the section is a parabola. 
 
 5. If a cone be cut by a plane, parallel to any 
 plane within the cone that passes through its vertex, 
 then the figure is an hyperbola. 
 
 These three last definitions are proved by the 
 writers of conic sections. 
 
 Note. — The cone in the following problem is supposed to be an 
 upright one. 
 
 PROBLEM. 
 Plate 12. 
 
 PROBLEM I. 
 
 To describe the conic section from the cone. 
 
 Note. — A D N is a section of the plane, passing through its axia 
 at right angles with the sections of the ellipsis, parabola, or hyper- 
 bola. 
 
 For the Ellipsis. 
 1. Let G H be its transverse axis in the plane 
 A D N ; bisect it at K ; through K draw R Q, paral- 
 lel to A D. 
 
54 
 
 PRACTICAL GEOMETRY. 
 
 2. Bisect Q, R at M; vnth the radius M R or M Q, 
 describe the semicircle R P G. 
 
 3. From K, draw K H perpendicular to Q R, cut- 
 ting the cu-cle at H; then K H is the semi-conjugate 
 axis, from which the ellipsis may be described as at 
 No. 1. 
 
 For the Parabola. 
 
 1, Let S E be the axis of the parabola, parallel to 
 the other side, N D. 
 
 2. From E, draw E C at right angles to A D, the 
 base, cutting the semicu-cle at C ; then E C is an or- 
 dinate or half the base of the parabola, which may 
 be described at No. 2. 
 
 For the Hyperbola. 
 
 1. Let I F be the height of the hyperbola ; pro- 
 duce it till it cut the opposite side A N, produced at 
 L ; then F L is the transverse axis. 
 
 2. From I, draw I B at right angles to A D ; then 
 I B is half the base, which may be described as at 
 No. 3. 
 
 XoTE. — The letters arc made to eorrespond at No. 1, 2, and 3, 
 with, those of the cone from where they are taken. 
 
 OF A GLOBE. 
 
 DEFINITIONS. 
 
 A globe is a solid figure, and may be supposed to 
 be generated by the revolution of a semicircle about 
 its diameter, which becomes the axis of the globe, 
 and the centre of the semicu-cle is the centre of the 
 globe. 
 
 Corollarij 1. Hence all right lines drawn from the 
 centre to the circumference of a globe are equal to 
 one another, for the semicircle touches the surface of 
 the globe in every point as it revolves round. 
 
 Corollarij 2. The section of a globe by a plane 
 passing through its centre is a circle, whose diameter 
 is equal to the diameter of the generating semicfrcle. 
 
 Corollary 3. Every section of a globe cut by a 
 plane is a circle, for aU the lines drawn from the cen- 
 tre to its surface are equal ; consequently, the gen- 
 erating semicircle may revolve round any line, as an 
 axis ; therefore, every point in the semicircle will 
 generate a circle. 
 
 Corollary 4. If a semiglobe is cut at right angles 
 to the plane of its base, the section is a semicircle. 
 
 PROBLEMS. 
 Plate 12. 
 
 TROBLEM I. 
 
 To find the section of a semiglobe at right 
 angles to the plane A B D, thiough its cen 
 tre, and pass through the line A B in that 
 plane. 
 
 Bisect A B in D ; on D, as a centre, ■w^th the radius 
 D A, or D B, describe the semicircle A E B, and it 
 will be the section required. 
 
 PROBLEM II. 
 
 Given two segments of cu-cles, ABC and 
 D E F, equal or unequal, ha^dng their two 
 chords, A C and D F, equal to each other, 
 and the segment ABC being placed upon 
 D F, so that A C shall coincide with D F, 
 and the segment A B C at right angles to 
 D E F, to find the radius of a globe, so that 
 the arc Imcs ABC and D E F shall be in 
 its surface when the two segments are placed 
 in the above position. 
 
 1. Make a rectangle A D F C, so that the opposite 
 sides, A C and D F, will be the bases of *the segments 
 A B C and D E F. 
 
 2. Find the centres G and H of these segments. 
 
 3. Through H draw I K parallel to G F, and com- 
 plete the semicircle I D E F K. 
 
 4. Through G or H di-aw H L parallel to G F, 
 cutting A C and I K at L and H ; make H ]\I equal 
 to L G, join M K or M I, and it will be the radius 
 required. 
 
 If upon E, as a centre, with the distance M I, or 
 M K, a segment I N K is described, it will be part 
 of the greatest circle that can be drawn in the globe. 
 
 PROBLEM III. 
 
 A figure being generated by the revolution of a 
 plain figure, ha^ing two perpendicular legs, 
 and the other side being irregular, or straight, 
 or a curve Hue of any kind, the figure bemg 
 made to revoh"e about one of its perpendicu- 
 lar legs. To find the figure of the section, 
 cut any where across the base and right an- 
 
SE©ini®RlS (j&i? 3®ILaiDS. 
 
 i'l.l.t 
 
 ^•\ c^-liiuLfr aTi<l its Sections . F«j;e Ij. 
 
 A ( ' one and its Sectioius . Rige 47. 
 
 j\ Sphere or r.li:)be. 
 
 A Splieroid &'! 
 
PRACTICAL GEOMETRY. 
 
 55 
 
 gles to the plane of the base, havhig that sec- 
 tion which passes through the axis. given. 
 
 1. Let A F E G B be the cu-cle of the base, and 
 let the section required be cut across F G ; also let 
 A B C be a section of the soUd passing tlnough the 
 axis. 
 
 2. From the centre O, draw the concentric cncles 
 H //, It, K k,lj I, to cut A B, in the points H, I, K, L, 
 and F G, in the points h, i, k, I. 
 
 3. Erect perpendiculars to the lines A B and F G, 
 both ways from these points, to cut A C in H, I, 
 K, L. 
 
 4. Make the distances h Ji, i i, k k, 1 1, equal to their 
 corresponding distances H H, 1 1, K K, L L ; a cmve 
 being drawn through these points, it will be the sec- 
 tion reqvured. 
 
 If the given section is triangle, the section is an 
 upright hyperbola. 
 
 K the given section is a semicncle, the required 
 section will also be a semicircle ; these appear plain 
 by the figures, and m this case there is no tracing 
 required. 
 
 OF A SPHEEOID. 
 
 DEFINITIONS. 
 
 1. A spheroid is a soUd, generated by the rotation 
 of a semi-ellipsis about the transverse or conjugate 
 axis, and the centre of the ellipsis is the centre of 
 the spheroid. 
 
 2. The line about which the ellipsis revolves is 
 called the axis. 
 
 3. If the spheroid is generated about the conjugate 
 axis of the semi-eUipsis, then it is called a prolate 
 spheroid. 
 
 4. K the spheroid is generated by the semi-ellipsis 
 about the transverse axis, then it is called an oblate 
 spheroid. 
 
 Proposition 1.^ Every section of a spheroid is an 
 ellipsis, except when it is perpendicular to that axis 
 about which it is generated, in wliich case it is a 
 circle. 
 
 Proposition 2. — All sections of a spheroid parallel 
 to each other are similar figures. 
 
 Proposition 3. — If a semi-spheroid is cut by a plane 
 
 at right angles to the base,* then the section is a 
 semi-ellipsis, and tlic intersection with the base will 
 be one of its axes ; and if a line is drawn perpendic- 
 ular from the middle of that intersection to the base 
 of the spheroid, to cut its surface, that line will be 
 half the other axis, whether transverse or conjugate. 
 
 PROBLEMS. 
 
 Plate 13. 
 
 PROBLEM I. 
 
 Given the base A D B C, which is a section 
 through the longest axis of an oblong sphe- 
 roid, to find the foiTn of the section, by cut- 
 ting the base through the line E F, at light 
 angles to its plane. 
 
 1. Let A B be the transverse, and C D the conju- 
 gate axis of the base; through the centi-e G draw 
 H I parallel to the given direction E F, cutting the 
 ellipsis at the poiiits H and I. 
 
 2. Produce E F towards K ; make Q, K equal to 
 G H or G I ; and erect the perpendicular K M. 
 
 3. Make K M equal to C G or G D, and bisect 
 E F at Q, and draw M Q. Erect the perpendicular 
 F P, cutting M Q at the point P, through Q, ; draw 
 Q, R parallel and equal to K M ; then Q, R will be 
 the semi-conjugate, and E F the transverse axis of 
 the section requfred, from which the ellipsis may be 
 described by any of the foregoing methods. 
 
 PROBLEM II. 
 
 To find the length of any arc A B C, of a cir- 
 cle mechanically, very near ; or to transfer 
 the same on the circumference of another 
 cu-cle F G H, of a difierent radius, from a 
 given point F. 
 
 1. Take your compass at any small opening, be- 
 ginning at A, and take the equal parts, 1, 2, 3, 4, 5, 
 6, on the arc ABC. 
 
 2. From D, lay the same number of equal parts 
 on the right line D E, towards E, viz., 1, 2, 3, 4, 5, 6, 
 and from the arc ABC take the remaining part 
 B C, and place it on the right line D E, from 6 to E ; 
 
 * It is here meant that the base is a section made by a plane, 
 passing through the centre of the spheroid, at right angles to the 
 transverse or conjugate axis of the spheroid. 
 
56 
 
 PRACTICAL GEOMETRY 
 
 then will the length of the right line D E be nearly 
 equal to the arc A B C stretched out. 
 
 In the same manner may A B C be transferred to 
 the cncle F G H, viz., by taking the divisions, 1, 2, 
 3, 4, 5, 6, and beginning at F, with the same opening 
 of your compass, setting off the divisions, 1, 2, 3, 4, 
 5, 6, on the arc F G H, and transferring the part 6 C 
 to 6 H, as before ; then ^vtII the arc F G H be equal 
 to tlie arc ABC. 
 
 OF A CYCLOID OR EPICYCLOID. 
 
 DEFINITION. 
 
 A cycloid or epicyloid is a figure generated by a 
 circle rolling along the straight edge of a ruler, or 
 another circle at rest, while a point in the circumfer- 
 ence describes a figm'c on the plane called a cycloid 
 or epicycloid. 
 
 PROBLEMS. 
 Plate 13. 
 
 PROBLEM I. 
 
 To describe a cycloid. 
 
 1. Let B C be the edge of a sti-aight ruler; erect 
 A D perpendicular to B C, equal to tlie diameter of 
 the generating circle ; upon the diameter A D de- 
 scribe a circle ; tlurough the centre, at E, draw Q, E. 
 parallel to B C. 
 
 2. Divide the semi-circumference D 1 2 3, &c., to 
 A, into equal parts, and lay the same number of equal 
 parts upon the right line A B, from A towards B ; 
 from all the divisions on A C erect perpendiculars, 
 cutting Q R at tlie points F, G, H, &c. 
 
 3. With the radius E D or E A, on the points 
 F, G, H, &c., as centres, describe arcs 1 /, 2 g-, 3 h, 
 &c.; take the chords A 1, A 2, A3, &c., from the semi- 
 circle ; make tlie distance 1 /, 2 g-, 3 h, &c., respec- 
 tively to them, then these points will be in the ciuve 
 of the cycloid. 
 
 rROBLEM II. 
 
 To describe an epicycloid. 
 
 1. Let B A C be the edge of the circle round which 
 the other circle is to turn ; through the centre S and 
 the point A, in the circuraierencc, draw the right line 
 
 S D ; make A D equal to the diameter of the gen- 
 erating circle. 
 
 2. Divide the circumference D 1 2 3, &c., into 
 equal parts, and place them upon the arc A C, from 
 A to 1, 2, 3, &c., to 8. 
 
 3. With the radius S E, on the centre S, describe 
 the arc Q R ; through the centre S and the points 
 1, 2, 3, &c., draw lines, cuttmg Q R at F, G, H, &c., 
 and proceed in every other respect, as in the cycloid, 
 and you will get the curve. 
 
 SECTION OF PLANES. 
 
 Of the Positions of Lines and Planes, and the Prop' 
 erties arising from their Intersections. 
 
 DEFINITIONS. 
 
 1. A plane is a surface in which a straight line 
 may coincide in all dii-ections. 
 
 2. A straight line is in a plane when it has two 
 points in common with that plane. 
 
 3. Two sti-aight lines which cut each other in space, 
 or woidd intersect, if produced, are in the same plane ; 
 and two lines that are parallel are also in the same 
 plane. 
 
 4. Three points given in space, and not in a sti-aight 
 line, are necessary and sufficient for determining the 
 position of a plane. Hence two planes which have 
 tliree points common coincide with each other. 
 
 5. The intersection of two planes is a sti'aight line. 
 
 PROBLEM. 
 Plate 14. 
 
 ^Vlien two planes A B C D, A B F E, (Fig. 1,) 
 intersect, tlicy form between them a certain 
 angle, wliicli is called the inclination of the 
 two planes, and -n-hich is measured by the 
 angle contained by two lines ; one drawn in 
 each of the planes, perpendicular to their 
 line of common section. 
 
 1. Thus, if the line A F, in the plane A B E F, be 
 perpendicular to A B, and the line A D, in the plane 
 A B C D, be the perpendicular also to A B, then the 
 angle F A D is the measure of the inclination of 
 the planes A B E F, A B C D. When the angle 
 
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 / 
 
 f'lW. 1. 
 
 fYo. r;. 
 
 
 
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PRACTICAL GEOMETRY. 
 
 57 
 
 F A D is a right angle, the two planes are perpen- 
 dicular. 
 
 2. (Fig. 2.) A line, A B, is perpendicular to a plane 
 P Q, when the line A B is perpendicular to any line 
 B C, in the plane P Q, which passes through the 
 point B, where the line meets the plane. The point 
 B is called the foot of the perpendicular. 
 
 3. A line A B (Fig. 8) is parallel to a plane 
 P Q, when the line A B is parallel to another straight 
 line C B, in the plane P Q,. 
 
 4. If a straight line have one of its intermediate 
 points in common with a plane, the whole line will 
 be in the plane. 
 
 5. Two planes are parallel to one another when 
 they cannot intersect in any direction. 
 
 6. The intersections of two parallel planes with a 
 third are parallel. Thus, in Fig. 4, the lines A B, 
 C D, comprehended by the parallel plane P Q, R S, 
 are parallel. 
 
 7. Any number of parallel lines, comprised be- 
 tween two parallel planes, are equal. Thus, Fig. 5, 
 
 the parallel lines A a, B b, C c, , comprised 
 
 by the parallel planes P Q, R S, are all equal. 
 
 8. If two planes C D E F, G H I J, Fig. 6, are 
 perpendicular to a third plane, P Q, their intersection, 
 A B, will be perpendicular to the third plane P Q. 
 
 9. If two straight lines be cut by several parallel 
 planes, these straight lines will be divided in the 
 same proportion. 
 
 GENERAL APPLICATION OF THE TRE- 
 HEDRAL TO TANGENT PLANES. 
 
 PROBLEM. 
 
 Plate 14. 
 
 Given the inclination and seat of the axis of an 
 oblique cylinder or cylindroid, to find the 
 angle which a tangent makes at any point in 
 the circumference of the base, with the plane 
 of the base. 
 
 1. (Figs. 1, 3, Plate 14.) Let A E B O be the base 
 of the cylinder or cylindroid, C B the seat of the axis, 
 and let B C D be the angle of inclination, and let O 
 be the point where the tangent plane touches the 
 curved surface of the solid. 
 
 R 
 
 2. Draw O N a tangent line at the point O in the 
 base, and draw O P parallel to C B. Make the angle 
 P O R equal to B C D, and draw P R perpendicular 
 to P O. 
 
 3. Then if the triangle P O R be conceived to be 
 revolved round the line P O, as an axis, until its plane 
 becomes perpendicular to the plane of llic circle 
 A E B C, the straight line, O R, will, in this position, 
 coincide with the cylincWcal surface, and a plane 
 touching the cylinder or cylindroid at () will pass 
 through the lines O N and O R. Here will now be 
 given the two legs, P O R and P O N, of a right- 
 angled trehedral to find the angle which the hypothe- 
 nuse makes with the base. Draw P Q, perpendicular 
 to O N, intersecting it in 7n, and draw P S perpen- 
 dicular to P Q. Make P S equal to P R, and join 
 VI S ; then P m S is the angle required. 
 
 4. The hypothenuse will be easily constructed at the 
 same time, thus : make m Q, equal to tn S, and join 
 O Q, then N O Q will be the hypothenuse required. 
 
 5. In Fig. 1, the method of finding the angle which 
 the tangent plane makes with the base and the hypoth- 
 enuse is exhibited at four different points. In the first 
 two points, O from A, in the first quadrant, the tan- 
 gent planes make an acute angle at each point O ; 
 but in the second quadrant, they make an obtuse 
 angle at each point O. 
 
 6. Fig. 2 is the second position of the construction 
 from the point A, for finding the angle which the 
 tangent plane makes with the base, and for finding 
 the hypothenuse enlarged ; in order to show a more 
 convenient method by not only requu'ing less space, 
 but less labor, it may be thus described, the two given 
 legs P' Q' R' and P' O' N'. 
 
 7. Draw P' m' perpendicular to O' N', meeting 
 O N in m'. In P' O', make P' v' equal to P' m', and 
 draw the straight line v' R', then P' v' R' will be the 
 inclination of the tangent plane at the point O. 
 
 8. Again : in O' P' make O' t' equal to O' m', and 
 draw i' u' parallel to P' R'. From O', with the radius 
 O' R', describe an arc meeting i' u' in ti', and draw 
 the straight line O' u' ; then t' O' u' is the hypothenuse. 
 
 9. For since P' S' is equal to P' R', and P' v' equal 
 to P' ?«', and the angles m' P' S' and v' P' R' are 
 right angles ; therefore, the triangle v' P' R' is equal 
 to the triangle m' P' S', and the remaining angles of 
 the one equal to the remaining angles of the other, 
 each to each ; hence the angle P' v' R' is equal to the 
 angle P' m' S'. 
 
58 
 
 PRACTICAL GEOMETRY. 
 
 10. Again : because O' t' is equal to O' m', and O' 
 Q,' is equal to O' R', and O' u' is also equal to O' R', 
 therefore O' u' is equal to O' Q' ; and since the angles 
 O' t' u' and O' m' Q,' are each a right angle, therefore 
 the t\vo right-angled triangles have their hypothenuses 
 equal to each other, and have also one leg in each 
 equal to each other ; therefore the remaining side of 
 the one triangle is equal to the remaining side of the 
 other, and therefore, also, the angles which are oppo- 
 site to the equal sides are equal; hence the angle 
 P' O' w' is equal to N' O' Q'. 
 
 11. By considering this construction by the trans- 
 position of the triangles, the whole of the angles 
 which the tangent planes make at a series of points 
 O, in figures 1 and 3, their hypothenuses may be all 
 found in one diagram, as in Fig. 4. 
 
 12. Thus, in Fig. 4, if the angles A C O, A C O' 
 A C O", A C O'", be respectively equal to A C O, 
 A C O', A C O", A C O'", Fig. 1, and in Fig. 4, the 
 semicircle A O' B be described, and if C D be drawn 
 perpendicular to A B, and the angles CAD, C B D, 
 be made equal to BCD, Fig. 1, then each half 
 of Fig. 4, being constructed as in Fig. 2, the angles 
 at m m' m" m'" will be respectively equal to the 
 angles P m S, P' m' S', Q" m" S", Q" m'" S", in Fig. 1. 
 
 Also, in Fig. 4, the angles C A E, C Ag-, C A /(, 
 C B t, C B k, C B F will be the hypothenuses at the 
 points A, O, O', O", 0"\ B, in Fig. 1. 
 
 We may here observe. Fig. 1, that the angles 
 which the tangent planes make with the plane of the 
 base in the first quadrant are acute ; and those in the 
 second quadrant arc obtuse ; and those in the second 
 quadrant arc the supplements of the angles V m S ; 
 and, moreover, that all the angles which constitute 
 the hypothenuses of the trehedral are all acute, 
 whether in the first quadrant or the second quadrant 
 of the semicircle A O B. 
 
 SECTIONS 
 On the projection of a straight line bent vpon a cylin- 
 dric surface, and the method of draiving a tangent 
 to such a projection. 
 
 Plate 14. 
 
 PROBLEM I. 
 
 Given the development of the surface of the 
 semi-cylinder, and a straight line in the devel- 
 
 opment, to find the projection of the straight 
 line on a plane passing through the axis of 
 the cyliuder, supposing the development to 
 incase the semi-cylincbic surface. 
 
 Fig. 5. Let A B C be the development of the 
 cylindric surface, B C being the development of the 
 semi-circumference, and let A C be the straight line 
 given. 
 
 Produce C B to D, making B D equal to the diam- 
 eter of the cylinder. On B D, as a diameter, describe 
 the semicircle BED, and divide the semicircular arc 
 BED into any number of equal parts, at 1, 2, 3, 
 &c., and its development B C into the same number 
 of equal parts, at the points /, §•, h, &c. Draw the 
 straight lines / /.-, g I, h m, &c., parallel to B A, meet- 
 ing A C at the points k, I, m, &c. ; also parallel to 
 B A draw the straight lines 1 o, 2 p, S q, &c., and 
 draw ko, Ip, m q, &c., parallel to C D ; and the 
 points o,p, q, &c., are the projections or seats of the 
 points k, I, m, &c., in the development of the straight 
 line A C. 
 
 The projection of a screw is found by this method : 
 B D may be considered as the diameter of the cylin- 
 der from which the screw is formed ; and the angle 
 B A C the inclination of the thread, with a straight 
 line on the surface ; or B C A the inclination of the 
 thread with the end of the cylinder. The same prin- 
 ciple also appUes to the delineations of the hand rails 
 of stairs, and in the construction of bevel bridges, of 
 which we shall treat in a subsequent part of this 
 work. 
 
 PROBLEM II. 
 
 Given the entire projection of a helix or screw, 
 in the surface of a semi-cylinder, and the 
 projection of a circle in that surface perpen- 
 dicular to the axis, upon the plane passing 
 through the axis, to draw a tangent to the 
 curve at a given point. 
 
 Fig. 6. Let B P K be the projection of the helix 
 or screw, and B A the projection of the circumference 
 of a circle, and since this circle is in a plane perpen- 
 dicular to the plane of projection, it will be projected 
 into a straight line A B, equal to the diameter of the 
 cylinder. 
 
 On A B, as a diameter, describe the semicircle 
 
I'll:. 
 
 ri'<'. 1. 
 
 />'</. -i. 
 
 / 
 v^ — 
 
 V* 
 
 ■V 
 
 
 ^ 
 
 /'ti/.S. 
 
 \ 
 
 „ . 7 
 
 V 
 
 / 
 
 yjy.tf. 
 
 / -!J- 
 
 
 -/' / 
 
 7 
 
 / 
 
 -/ — *■ ■-.' 
 
 L.I.V. 
 
 ---.v 
 
 / 
 
 f^7i tJ/^ develffj/e7//''///s >'/ '/'//' si/nwrrs I'l' S,'//'i/s 
 
 jt-^ 
 
 /■ 
 
 
 
 IVfXo.i'ltmS': 
 
PRACTICAL GEOMETRY. 
 
 59 
 
 A. r B, and draw P r perpendicular to, and inter- 
 secting, A B in q, join tlio points e r, and produce 
 e r to /. 
 
 Produce A B to C, so that B C may be equal to 
 the semicircular arc B r A. Draw C D perpendic- 
 ular to B C, and make C D equal to A K, and draw 
 the straight line B D ; then B D will be the devel- 
 opment of the curve line B P K. 
 
 Dra\\- P ti parallel to A C, meeting B D in u, and 
 draw u t perpendicular to B C. Draw r g perpen- 
 dicular to e ;•, and make r g equal to B t. Draw g n 
 perpendicular to A C, meeting B C in n, and draw 
 the straight line n P ; then n P will touch the curve 
 at the point P. 
 
 Or the tangent may be drawn independent of 
 BCD, thus : Draw P r perpendicular to A B, and r g 
 a tangent at r. Make r g equal to the development 
 of r B, and draw g n perpendicular to B C, meet- 
 ing B C in n, and join n P, which is the tangent 
 required. 
 
 PEELIMINARY PRINCIPLES 
 OF PROJECTION. 
 
 PROBLEM. 
 Plate 15. 
 
 If from a point A', Fig. 1, in space, a perpendic- 
 ular A' a be let fall to any plane P Q whatever, the 
 foot a of this perpendicular is called the projection 
 of the point A' upon the plane P Q. 
 
 K, through different points A', B', C, D',....Figs. 
 2, 3, 4, of any line A', B', C, D', . . . . whatever in 
 space, perpendiculars A' o, B' b, C c,T>' d, . 
 be let fall upon any plane P Q, whatever, and if 
 
 tlu-ough a, b, c, d, the projections of the 
 
 points A', B', C, D', iji the plane P Q, a line be 
 drawn, the line thus drawn will be the projection of 
 the line A' B' C D' . . . . given in space. 
 
 If the line A' B' C D' . . . . Fig. 3, be straight, 
 the projection abed. . . . will also be a straight 
 line ; and if the line A' B' C D' . . . . Fig. 2, be a 
 curve not in plane perpendicular to the plane P Q, 
 the curve abed.... which is the projection of 
 the curve A' B' CD',.... in space, will be of the 
 same species with the original curve, of which it is 
 the projection. Hence, in this case, if the original 
 
 curve A' B' C D' . . . . be an ellipse, a parabola, an 
 hyperbola, &c., the projection abed.... will be 
 an ellipse, a parabola, an hyperbola, &c. The circle 
 and the ellipse being of the same species, the pro- 
 jected curve may be a circle or ellipse, whether the 
 original be a circle or ellipse, as in Fig. 4. 
 
 The plane in which the projection of any point, 
 line, or plane figure is situated is called the plane of 
 projection, and the point or line to be projected is 
 called the primitive. 
 
 The projection of a curve will be a straight line 
 when tlie curve to be projected is in a plane perpen- 
 dicular to the plane of projection. Hence the pro- 
 jection of a plane curve is a straight line. 
 
 If a curve be situated in a plane which is parallel 
 to the plane of projection, the projection of the curve 
 will be another curve equal and similar to the curve 
 of which it is the projection. 
 
 The projection upon a plane of any curve of double 
 curvature whatever is always a curve line. 
 
 In order to fi:x the position and form of any line 
 whatever in space, the position of the line is given to 
 each of two planes which are perpendicular to each 
 other ; the one is called the horizontal plane, and the 
 other the vertical plane ; the projection of the line in 
 question is made on each of these two planes, and 
 the two projections are called the two projections of 
 the line to be projected. 
 
 Thus we see, in Fig. 5, where the parallelogram 
 U V W X represents the horizontal plane, and the 
 parallelogram U V Y Z represents the vertical plane ; 
 the projection a b ot the line A' A' in space upon the 
 horizontal plane U V W X is called the horizontal 
 projeetion; and the projection A B, of the same line 
 upon the vertical plane U V Y Z, is called the verti- 
 eal projeetion. 
 
 The two planes upon which we project any line 
 whatever are called the planes of projection. 
 
 The intersection U V of the two planes of projec- 
 tion, is called the ground line. 
 
 When we have two projections a &, A B of any line 
 A B' in space, the line A' B' will be determined by- 
 erecting to the planes of projection the perpendiculars 
 a A, i B' . . . A A', B B' . . . through the projections 
 
 a,b, A, B, of the original points A', B'. 
 
 of the line in question. For the perpendiculars 
 
 a A', A A' erected from the projections a, A of the 
 same point A' will intersect each other in space in a 
 point A', which will be one of these in the line \v 
 
60 
 
 PRACTICAL GEOMETRY. 
 
 question. It is clear tiiat the other points must be 
 found in the same manner a.s this which has now 
 been done. 
 
 When we iiavc obtained the two projections of a 
 line in space, whether immediately from the line it- 
 self or by any other means whatever, we must aban- 
 don this line in order to consider its two projections 
 only, since, when we design a working drawing, we 
 operate only upon the two projections of this line 
 that we have brought together upon one plane, and 
 we no longer see any thing in space. 
 
 However, to conceive that which we design, it is 
 absolutely necessary to carry by thought the opera- 
 tions into space from their projections. This is the 
 most difficult part that a beginner has to surmount, 
 particularly when he has to consider at the same 
 time a great number of lines in various positions 
 in space. 
 
 The perpendicular A- a, Fig. 5, let fall from any 
 point A whatever in space upon the plane X V of 
 projection, is called the projectant of the point A' 
 upon this plane. Moreover, the perpendicular dis- 
 tance between the point A' and the horizontal plane 
 X V, is called the projectant upon the horizontal 
 plane, or simply the horizontal projectant; and the 
 perpendicular distance A' A between- the original 
 point A' and the vertical plane U Y, is called the pro- 
 jectant upon the vertical plane, or simply the vertical 
 projection. 
 
 We shall rcmarlc, so as to prevent any mistake, 
 that the horizontal projectant A' a is the perpendic- 
 ular let fall from the original point upon the horizon- 
 tal plane, and that the vertical projectant is the per- 
 dicular let fall from that point upon the vertical plane. 
 Hence the horizontal projectant is parallel to the ver- 
 tical plane, and is equal to the distance between the 
 original point and the horizontal plane; and the ver- 
 tical projectant is parallel to the horizontal plane, and 
 is equal to the distance between the original point 
 and the vertical plane. 
 
 We may remark, that if through a. Fig. G, the hori- 
 zontal projection of the point A', we draw a perpen- 
 dicular a to U V, the ground line, this perpendicular a 
 will be equal to the measure of the vertical project- 
 ant A' A; consequently, the distance of the point A' 
 to the vertical plane is equal to the distance between 
 a, its horizontal projection, and U V, the ground line 
 measured in a perpendicular to U V. In like man- 
 ner, if through A, the vertical projection of the point 
 
 A', wc draw a perpendicular A a to U V, the ground 
 line, this perpendicular A a will be equal to the 
 measure of the horizontal projectant A o; conse- 
 quently, the distance of this point A' to the horizon- 
 tal plane is equal to the distance between A, its ver- 
 tical projection, and U V, the ground line measured 
 in a perpendicular to U V. 
 
 To these very important remarks we shall add one 
 which is not less so. Two perpendiculars, a a, Fig. 
 6, A a, being let fall from the projections a, A to the 
 same point A' upon the ground line U V, will meet 
 each other in the same point a, of the said ground 
 line U V. 
 
 If we now wished the two projections of a point 
 A', Fig. 6, or of any line A' B' whatever, to be upon 
 one or the same plane, it is sufficient to imagine the 
 vertical plane U V Y Z to turn round the ground 
 line U V in such a manner as to be the prolongation 
 of the horizontal plane U V W X; for it is clear that 
 this plane will carry with it the vertical projection A 
 or A B of the point, or of the line in question. More- 
 over, we see, and it is very important, that the lines 
 A a, B b, perpendicular to the ground line U V, will 
 not cease to be so in the motion of the plane U V Y 
 Z ; and as the corresponding lines « a, i b, are also 
 perpendiculars to the ground line U V, it follows 
 that the lines a a', b b', will be the respective pro- 
 longation of the lines a a, i b. 
 
 Hence it results, when we consider objects upon a 
 single plane, the projections a A, of a point A' in 
 space, are necessarily upon the same perpendicular 
 A a to the ground line U Y. 
 
 It is necessary to call to mind that the distance 
 A a, measures the distance from the point in space to 
 the horizontal plane, (the point A being the vertical 
 projection of this point,) and that the line a a meas- 
 ures the distance from the same point in space to 
 the vertical plane. 
 
 It follows, that if the point in space be upon the 
 horizontal plane, its distance with regard to this last- 
 named plane will be zero or nothing, and the vertical 
 A a will be zero also. Moreover, the vertical projection 
 of this point will be upon the ground line at the foot 
 a, of the perpendicular a a, lot fall upon the ground 
 line, from the horizontal projection a of this point. 
 
 Again : if the point in space be upon the vertical 
 plane, its distance, in respect of this plane, will be 
 zero, the horizontal a a will be zero, and the hoiizon- 
 tal projection of the point in question will be the foot 
 
PRACTICAL GEOMETRY 
 
 61 
 
 a, of the perpendicular A a, let fall upon the ground 
 line from the vertical projection A, of this point. 
 
 In general, we suppose that the vertical projection 
 of a point is above the ground line, and that the 
 horizontal projection is below ; but from what has 
 been said, it is evident that, if the point in space be 
 situated below the horizontal line, its vertical projec- 
 tion will be below the ground line ; for the distance 
 from this point to the horizontal plane cannot be 
 taken from the base line to the top, but from the top 
 to the base with respect to its plane. 
 
 So if the point in space be situated behind the 
 vertical plane, its horizontal projection wUl be above 
 the ground line; from which we conclude, — 
 
 1. K the point in question be situated above the 
 horizontal plane, and before the vertical plane, its 
 vertical projection will be above, and its horizontal 
 projection below, the ground line. 
 
 2. If the point be situated before the vertical plane, 
 and below the horizontal plane, the tw'o projections 
 will be above the ground line. 
 
 3. K the point be situated above the horizontal 
 plane, but behind the vertical plane, the two projec- 
 tions wiU be above the ground line. 
 
 . 4. Lastly. If the point be situated above the hori- 
 zontal plane, and behind the vertical plane, the verti- 
 cal projection will be below, and the horizontal pro- 
 jection above, the ground line. 
 
 The reciprocals of these propositions are also true. 
 
 If a line be parallel to one of these planes of pro- 
 jection, its projection upon the other plane will be 
 parallel to the ground line. Thus, for example, if a 
 line be parallel to a horizontal plane, its vertical pro- 
 jection will be parallel to the ground line ; and if it is 
 parallel to the vertical plane, its horizontal projection 
 wiU be parallel to the ground line. 
 
 Reciprocally, if one of the projections of a line be 
 parallel to the ground line, this line will be parallel 
 to the plane of the other projection. Thus, for ex- 
 ample, if the vertical projection of a line be parallel 
 to the groimd line, this line will be parallel to the 
 horizontal plane, and vice versa. 
 
 If a line be at any time parallel to the two planes 
 of projection, the two projections of this line will be 
 parallel to the ground line ; and reciprocally, if the 
 two projections of a line be parallel to the ground 
 line, the line itself will be at the same time parallel 
 to the two planes' of projection. 
 
 K a line be perpendicular to one of the planes of 
 
 projection, its projection upon this plane will only be 
 a point, and its projection upon the other plane will 
 be perpendicular to the ground line. Thus, for ex- 
 ample, if the line in question be perpendicular to the 
 horizontal plane, its horizontal projection wiU be only 
 a point, and its vertical projection will be perpendic- 
 ular to the ground line. 
 
 Reciprocally, if one of the projections of a straight 
 line be a point, and the projection of the other per- 
 pendicular to the ground line, this line will be per- 
 pendicular to the plane of projection upon which its 
 projection is a point. Thus the line will be perpen- 
 dicular to the horizontal plane, if its projection be 
 the given point in the horizontal plane. 
 
 K a line be perpendicular to the ground line, the 
 two projections will also be perpendicular to this line. 
 The reciprocal is not true ; that is to say, that the 
 two projections of a line maybe perpendicular to the 
 ground line, without having the same line perpendic- 
 ular to the ground line. 
 
 K a line be situated in one of the planes of pro- 
 jection, its projection upon the other will be upon the 
 grovmd line. Thus, if a line be situated upon a hori- 
 zontal plane, its vertical projection will be upon the 
 ground line ; and if this line were given upon the 
 vertical plane, its horizontal projection would be upon 
 the ground line. 
 
 Reciprocally, if one of the projections of a line be 
 upon the ground line, this line will be upon the plane 
 of the other projection. Thus, for example, if it be 
 the vertical projection of the line in question, which 
 is upon the ground, this line will be upon the hori- 
 zontal plane ; if, on the contrary, it were upon the 
 horizontal projection of this line which was upon the 
 ground line, this line would be upon the vertical 
 plane. 
 
 If a line be at any time upon the two planes of 
 projcctioM, the tA.vo projections of this line would be 
 upon the ground line, and the line in question would 
 coincide with this ground line. Reciprocally, if the 
 t^vo projections of a line were upon the ground line, 
 the line itself would be upon the ground line. 
 
 If two lines in space are parallel, their projections 
 upon each plane of projection are also parallel. Re- 
 ciprocally, if the projections of two lines are parallel 
 on each plane of projection, the two lines will be 
 parallel to one another in space. 
 
 If any two lines whatever in space cut each other, 
 the projections of their point of intersection will be 
 
62 
 
 PRACTICAL GEOMETRY 
 
 upon the same perpendicular line to the ground line, 
 and upon the points of intersection of the projections 
 of these lines. Reciprocally, if the projections of 
 any two lines whatever cut each other in the two 
 planes of projection in such a manner that their 
 points of intersection are upon the same perpendic- 
 ular to tlie ground line, these two lines in question 
 will cut each other in space. 
 
 The position of a plane is determined in space 
 when we know the intersections of this plane with 
 the planes of projection. 
 
 The intersections A B, A C, of the plane in ques- 
 tion, witli the planes of projections, arc called the 
 traces of this plane. 
 
 The trace situated in the horizontal plane is called 
 the horizontal trace, and the trace situated in the ver- 
 tical piano is called the vertical trace. 
 
 A very important remark is, that the two traces of 
 a plane intersect each other upon the ground line. 
 
 If a plane be parallel to one of the planes of pro- 
 jection, this plane wiU have only one trace, which 
 will be paraDel to the ground line, and situated in 
 the other plane of projection. Reciprocally, if a 
 plane has a trace parallel to the ground line, this 
 plane will be parallel to the plane of projection, 
 which docs not contain this trace. Thus : — 
 
 1. If a plane be parallel to the horizontal plane, 
 this plane will not have a horizontal trace, and its 
 vertical trace will be parallel to the ground line. 
 Likewise, if a plane be parallel to the vertical plane, 
 this piano will not have a vertical trace, and its hori- 
 zontal trace will be parallel to the ground line. 
 
 2. If a plane has only one trace, and this ti-ace 
 parallel to the ground line, let it be in the vertical 
 plane ; then the plane will be parallel to the horizon- 
 tal plane. So if the trace of the plane be in the 
 horizontal plane, and parallel to the ground line, the 
 plane will be parallel to the vertical plane. . 
 
 If one of the traces of a plane be perpendicular to 
 the ground line, and the other trace in any position 
 whatever, this plane will be perpendicular to the 
 plane of projection in which the second trace is. 
 Thus, if it bo a horizontal trace which is perpendic- 
 ular to the ground line, the plane will be perpendic- 
 idar to the vertical plane of projection ; and if, on 
 the contrary, the vortical trace be that which is per- 
 pendicular to the ground line, tiien the plane will be 
 perpendicular to the horizontal plane. 
 
 Reciprocally, if a plane be perpendicular to one of 
 
 the planes of projection, without being parallel to the 
 other, its trace upon the plane of projection, to which 
 it is perpendicular, will be perpendicular to any posi- 
 tion whatever, and the other trace will be perpendic- 
 ular to the ground line. Thus, for example, if the 
 plane be perpendicular to the vertical plane, the ver- 
 tical trace will be perpendicular to the ground line. 
 The reverse will also be true, if the plane be perpen- 
 dicular to the horizontal plane. 
 
 If a plane be perpendicular to the two planes of 
 projection, its two traces will be perpendicular to the 
 ground line. Reciprocally, if the two traces of a 
 plane are in the same straight line perpendicular to 
 the ground line, this plane will be perpendicular to 
 both the planes of projection. 
 
 If the two traces of a plane are parallel to the 
 ground line, this plane will be also parallel to the 
 ground line. Reciprocally, if a plane be parallel to 
 the ground line, its two traces will be parallel to the 
 ground line. 
 
 When a plane is not parallel to either of the planes 
 of projection, and one of its traces is parallel to the 
 ground line, the other trace is also necessarily par- 
 allel to the ground line. 
 
 If two planes arc parallel, their traces in each of 
 the planes of projection will also be parallel. Recip- 
 rocally, if on each plane of projection the traces of 
 the two planes are parallel, the planes will also be 
 parallel. 
 
 If a line be perpendicular to a plane, the projec- 
 tions of this line will be in each plane of projection 
 perpendicular to the respective traces in this plane. 
 Reciprocally, if the projections of a line are respec- 
 tively perpendicular to the traces of a plane, the line 
 will be perpendicular to the plane. 
 
 If a line be situated in a given plane by its traces, 
 this line can only intersect the planes of projection 
 upon the traces of the plane which contains it. 
 Moreover, the line in question can only meet the 
 plane of projection in its own projection. Whence 
 it follows, that the points of meeting of the right 
 line, and the planes of projection, arc respectively 
 upon the intersections of this right line, and the 
 traces of the plane which contains it. 
 
 K a right line, situated in a given plane by its 
 ti-aces, is parallel to the horizontal plane, its horizon- 
 tal projection will be parallel to the horizontal trace 
 of the given plane, and its vertical projection will be 
 parallel to the ground line. Likewise, if the right 
 
PRACTICAL GEOMETRY. 
 
 63 
 
 line situated in a given plane by its traces is parallel 
 to the vertical plane, its vertical projection will be 
 parallel to the vertical line of the plane which con- 
 tains it, and its horizontal projection will be parallel 
 to the ground line. 
 
 Reciprocally, if a line be situated in a given plane 
 by its traces, and, for example, its horizontal pro- 
 jection be parallel to the horizontal trace of the 
 given plane, this line will be parallel to the horizon- 
 tal plane, and its vertical projection wiU be parallel 
 to the ground line. Liliewise, if the vertical projec- 
 tion of the line in question be parallel to the vertical 
 trace of the given plane, this line will be parallel to 
 the vertical plane, and its horizontal projection wiU 
 be parallel to the ground line. 
 
 SECTION 
 
 On the Developments of the Surfaces of Solids. 
 
 PROBLEMS. 
 Plate 15. 
 
 PROBLEM I. 
 
 To find tlie development of the surface of a 
 right semi-cylinder. 
 
 Fig. 1. Let A C D E be the plane passing through 
 the axis. On A C, as a diameter, describe the semi- 
 circular arc ABC. Produce C A to B, and make 
 A F equal to the development of the arc ABC. 
 Draw F G parallel to A E, and E G parallel to 
 A F ; then A F G E is the development required. 
 
 PROBLEM II. 
 
 To find the development of that part of a semi- 
 cylinder contained between two perpendicular 
 surfaces. 
 
 Figs. 2, 3, 4. Let A B C D E be a portion of a 
 plane passing through the axis of the cylinder, C D 
 and A E being sections of the surface, and let D E 
 and F G be the insisting lines of the perpendicular 
 sTirface ; also, let A C be perpendicular to A E and 
 C D. On A C, as a diameter, describe the semicir- 
 cular arc ABC. Produce C A to H, and make 
 A H equal to the development of the arc ABC. 
 Divide the arc ABC and its development each 
 
 into the same number of equal parts, at the points 
 1, 2, 3. 
 
 Though the points 1, 2, 3, &c., in the semicircular 
 arc, and in its development, draw straight lines par- 
 allel to A E, and let the parallel lines through 1, 2, 3, 
 in the arc ABC, meet F G in p, rj, r, Sec, and A C 
 in k, I, m, &c. Transfer the distances Icp, Iq, vir, &c., 
 to the development upon the lines 1 a,2 b,3 c, &c. 
 Through the points F, a, b, c, &c., draw the curve 
 line F c 1. In the same manner draw the curve line 
 E K ; then F E I K will be the development re- 
 quired. 
 
 PROBLEM III. 
 
 To find the development of the half surface of 
 a right cone, terminated by a plane passing 
 through the axis. 
 
 Fig. 5. Let A C E be the section of the cone pass- 
 ing along the axis A E, and C E the straight lines 
 which terminate the conic surface, or the two lines 
 which are common to the section C A E and the 
 conic surface ; and let A C be the line of common 
 section of the axal plane and the base of the cone. 
 
 On A C, as a diameter, describe a semicircle, 
 ABC. From E, with the radius E A, describe the 
 arc A F, and make the arc A F equal to the semi- 
 circular arc ABC, and join E F; then the sector 
 A E F is the development of the portion of the 
 conic surface required. 
 
 PROBLEM IV. 
 
 To find the development of that portion of a 
 conic surface contained by a plane passing 
 along the axes, and two surfaces perpendic- 
 ular to that plane. 
 
 Fig. 6. Let A C E be the section of the cone 
 along the axis, and let A C and G I be the insisting 
 lines of the perpendicular surfaces. Find the devel- 
 opment A E F, as in the preceding problem. Divide 
 the semicircular arc ABC, and the sectorial arc 
 A F, each into the same number of equal parts at 
 the points 1, 2, 3, &c. From the points 1, 2, 3, &c., 
 in the semicircular arc, draw straight Lines, 1 k, 2 /, 
 3 m, &c., perpendicular to A C. From the points 
 k, I, m, &c., draw straight lines, A; E, Z E, m E, Sec, 
 intersecting the curve A C in j?, q, r, &c. Draw the 
 straight lines pt, qu, rv, &cc, parallel to one side, E C 
 meeting A C in the points t, u, v, Sec Also from the 
 
64 
 
 PROJECTION OF PRISMS. 
 
 points 1, 2, 3, in the sectorial arc A F, draw the 
 straight lines 1 E, 2 E, 3 E, &c. Transfer the dis- 
 tances pt, qii, rv, &c., to 1 a, 2 b, 3 c, &cc. ; then, 
 through the points A, a, b, c, &c., draw the curve 
 A c F, and A c F is one of tlie edges of the develop- 
 ment, and by drawing the other edge, the entire de- 
 velopment, A G H, will be found. 
 
 Note. — This treatise on the subject of Geometry we have 
 thought best to insert in the form in which it was fiist written. It 
 
 is a system in a degree peculiar to its author, and it is, without 
 doubt, the production of a laborious research ; and although the 
 same conclusions would, in some cases, be arrived at by the more 
 direct process of demonstration used at the present day, yet, from its 
 extent and completeness, we have concluded, as a whole, that no 
 part could be materially changed for the better without seriously 
 intruding upon the theories of our venerable author, and that, too, 
 at the expense of interfering with liis style of writing, wliich will 
 at once be recognized as the original. We will state here, that we 
 have endeavored, as much as possible, to preserve every idea that 
 he has advanced, and that, toO; in his own language. — Editors. 
 
 PROJECTION or PRISMS. 
 
 In the annexed definitions and problems, the student will find 
 enough to give him a correct and sufficiently perfect idea of the 
 nature and importance of this useful branch of science ; and he 
 will also find occasion to apply the geometrical principles, a knowl- 
 edge of which he is presumed to have acquired from the preceding 
 pages of the present work. 
 
 DEFINITIONS. 
 
 1. When straight lines are drawn according to a 
 certain law from the several parts of any figure or 
 object cut by a plane, and by that cutting or inter- 
 section describe a figure on that plane, the figure so 
 described is called the projection of the other figure 
 or object. 
 
 2. The lines taken altogether, which produce the 
 projection of the figure, are called a syatem of rays. 
 
 3. When the system of rays are all parallel to 
 each other, and are cut by a plane perpendicular to 
 them, the projection on the plane is called the orlhog- 
 raphy of the figure proposed. 
 
 4. When the system of parallel rays is perpendic- 
 ular to the horizon, and projected on a plane parallel 
 to the horizon, the orthographical projection is then 
 called the ichnography, or plan of the figure proposed. 
 
 5. When the rays of the system are parallel to 
 each other and to the horizon, and if the projection 
 be made on a plane perpendicular to those rays and 
 to th(! horizon, it is called the elevation of the figure 
 proposed. 
 
 [In this kind of projections, the projection of any 
 particular point or line is sometimes called the seat 
 of that point or line, on the plane of projection.] 
 
 G. If a solid be cut by a plane passing quite 
 
 through it, the figure of that part of the solid which 
 is cut by the plane is called a section. 
 
 7. When any solid is projected orthographieally 
 upon a plane, the outline or boundary of the projec- 
 tion is called the contour or profile of the projection. 
 
 Note. — Although the term orthography signifies, in general, the 
 projection of any plane which is perpendicular to the projecting 
 rays, without regarding the position of the plane on which the ob- 
 ject is projected, yet writers on projection substitute it for elevation, 
 as already defined, by which means it will be impossible to know 
 when we mean that particular position of orthographical projection 
 which is made on a plane perpendicular to the hori/on. 
 
 Axiom. — K any point, line, or plane of any origi- 
 nal figure or object touch the plane on which it is 
 to be projected, the place where it touches the pro- 
 jecting plane is the projection of that point, line, or 
 plane of the original figure or object. 
 
 Proposition. — The orthographical projection of a 
 line which is parallel to the plane of projection is a 
 line equal and parallel to its original. 
 
 PROBLEMS. 
 
 Plate 16. 
 
 PROBLEM I. 
 
 To project the elevation of a prism standing on 
 
 a plane perpendicular to the projecting plane ; 
 
 giA'en, the base of the prism and its position 
 
 to the projecting plane. 
 
 Fig. 1. Let A B C D, No. 1, be the base of the 
 prism ; let H F be the intersection of the projecting 
 plane, with the plane on which the prism stands. 
 
 Draw lines from every angle of the base, cutting 
 
T K 
 
 fw /.]■■■/ 
 
PEOJECTION OF PRISMS. 
 
 65 
 
 H F at H, and F will be the projection of the points 
 A and C ; the angle D, touching H F at D, is its 
 projection. 
 
 From each of the points H, D, F, in No. 2, draw 
 the lines H I, D E, and F G, each perpendiciilar to 
 H F ; make D E eqnal to the height of the prism ; 
 through E di'aw I G, cutting H I and F G at I and 
 G, which will give the projection sought. 
 
 PROBLEM II. 
 
 To project the ichnograpliy and elevation of a 
 square prism, to rest upon one of its angles 
 upon a given point A, in the plane, on which 
 tlie ichnography is to be described ; given the 
 ichnograpliy A L, of an angle, wliich the two 
 under planes make with each other; the 
 angle ]\I a I, which the angle of the solid 
 makes with its ichnography A L ; the inter- 
 section A a of one of its ends with the plane 
 of the ichnography ; the angle D A «, which 
 one side of the end makes at A, with the in- 
 tersection A a of that end ; also given one of 
 the sides of the ends, and the length of the 
 prism. 
 
 Fig. 2. At the given point A, with the intersection 
 A a, make an angle a AT>, equal to the angle which 
 one of the sides of the end makes with A a; make 
 A D equal to one of the sides of the end; then on 
 A D consti-uct the square A B C D ; through the 
 angles of the square B, C, D, draw lines B H, C I, 
 and D M, parallel to A L ; then at the point a, in 
 the right line D M, make an angle M a 1, with a M, 
 equal to the angle of the solid, whose projection is 
 A L, with A L ; make a I equal to the length of the 
 
 9 
 
 solid ; through the points a and /, No. 1, draw the lines 
 a e and I i perpendicular to a I ; through the points 
 B and C, No. 2, draw B R and C S parallel to A a, 
 cutting D M, produced at E, and S ; on a, as a cen- 
 tre, with the distances a D, a R, and a S, describe 
 ares V g, R/, and S e, cutting a e, No. 1, at g-, /, e ; 
 through the points g, f, e, draw the lines g- k, f h, 
 and e i, parallel to a I, and No. 1 will be completed, 
 which will be the projection of tlie prism on a plane 
 parallel to A L. Through the points g, f, e, draw 
 the lines e E, / F, and g G, perpendicular to D M, 
 or A L, cutting D E, C I, and B H, respectively, at 
 G, E, F; also through the points I, k, h, i, cbaw the 
 lines I L, k K, h H, and i I, Hkewise parallel to A L, 
 cutting A L, G M, B H, and C I, respectively, at the 
 points L, K, H, and I ; join E F, E G, and H I, 
 I K, K L, L H, then will the planes E F H I, 
 E I K L, and H I K L represent the ichnogi-aphy 
 of the upper sides of the solid ; and if F A and A G 
 be joined, then will F A G E, F A L H, and G A 
 L K represent the sides of the solid next to the 
 plane of projection. Then to project the elevation 
 on a plane whose intersection is T U, from F, E, G, 
 A, H, I, K, and L, that is, from all the points in the 
 ichnography representing the solid angles, di-aw the 
 lines F /, E e, G^, A o, H h, I i, K k, and L I, per- 
 pendicular to the intersection T U, cutting T U at 
 P> 5') (^> §"> o, m, and k ; make p f^ q e, g g,n h, o i, 
 m I, and k k, at No. 3, respectively, equal to P/, Q e, 
 G g-, N A, O i, M I, and K k, at No. 1 ; then join 
 f a, a g, g e, e f; e i, i k, k g, k I, and la; and 
 fage, geik, gkla will be the elevations of the 
 outside planes of the solid; and by joining/ A, and 
 h i,fh i e,fh I a, and i h I k will be the elevations 
 of the planes of the solid next to the plane on which 
 the elevation is projected. 
 
66 
 
 SHADOWS 
 
 SHADOWS. 
 
 This' is one of the most interesting branches of architectural sci- 
 ence I or perhaps it may, with more propriety, be termed a branch 
 of geometry, for it is almost entirely dcpenilent on, and governed 
 by, geometrical principles. 
 
 From a knowledge of it the architect is enabled to draught his plans, 
 and to give them their true effect, or representation of light and 
 shade ; to construct his windows in order to receive light to the best 
 advantage, &c., &c. The art of keeping a proper gradation of light 
 and shade on objects, according to their several distances, colors, 
 and other circumstances, is of the utmost consequence to the artist. 
 
 THE EFFECT OF DISTANCE ON THE 
 ' COLOR OF OBJECTS. 
 
 The art of giving a due diminution or degradation 
 to the strength of the light and shade and colors of 
 objects, according to the different distances, the quan- 
 tity of light which falls on their surfaces, and the 
 medium through which they are seen, is called 
 keeping;. 
 
 1. When objects are removed to a gi-cat distance 
 from the eye, the rays- of light Avhicli they reflect 
 will be less vivid, and the color will become more 
 diluted, and tinged wiih a faint bluish cast, by rea- 
 son of the great body of air through which they are 
 seen. 
 
 2. In general, the shadows of objects, according as 
 they are more remote from Hie eye, will be lighter, 
 and the light parts will become darker ; and at a 
 certain distance the light and shadow are not distin- 
 guishable from each other, for both will seem to ter- 
 minate in a bluish lint of the color of the atmosphere, 
 and will appear entirely lost in that color. 
 
 3. If the rays of light fall upon any colored sub- 
 stance, the reflected rays will be tinged with the color 
 of that substance. 
 
 4. If the colored rays be reflected upon any object, 
 the color of that object will then be compounded 
 of the color of the reflected rays and the color 
 of the object ; so that the color of the object which 
 receives the reflection will be changed into another 
 color. 
 
 5. From the closeness or openness of tlie place 
 where the object is situated, the light, being much 
 
 more variously directed, as in objects which are sur- 
 romidcd by buildings, will be more deprived of re- 
 flection, and, consequently, will be darker than those 
 which have no other objects in their vicinity, except 
 the surrounding objects are so disposed as to reflect 
 the rays of light upon them. 
 
 6. In a room, the light being more variously di- 
 rected and reflected than abroad in the open air, (for 
 every apertm-e gives an inlet to a different stream,) 
 which direction is various, according to the place and 
 position of the apertm-e, whereby every diflcrent side 
 of the room, and even the same side in such a situa- 
 tion, will be variously afTected with respect to their 
 light, shade, and colors, from what they would in an 
 open place when exposed to rays coming in the same 
 direction. 
 
 Some original colors naturally reflect light in a 
 greater proportion than others, though equally ex- 
 posed to the same degrees of it, whereby their degra- 
 dation at different distances will be different from 
 that of other colors which reflect less light. 
 
 The art of keeping a degradation of light and shade 
 on objects, according to their several distances, colors, 
 and other circumstances, is of the utmost conse- 
 quence to the artist. 
 
 In orthographical projections, where equal and 
 similar objects stand in the same position to the 
 plane of projection, they will be represented similar, 
 and of an equal magnitude at every distance from 
 that plane ; and, consequently, planes wliich are par- 
 allel to each other would not appear to have any dis- 
 tance, so that the representation of any number of 
 objects, at different distances from each other, would 
 be entirely confused, and no particular object could 
 be distinguished from the others ; but, by a proper 
 attention to the art of kccpitig;, every object will be 
 distinct and separate, and their respective distances 
 and colors from each other will be preserved. But 
 though a proper degradation of light and shade ought 
 to be preserved, according to the respective distances 
 of objects from each other, artists in general take too 
 gi"cat liberties with nature : we frequently see in the 
 drawings of architects the art of keeping carried to 
 so great an extreme as to render their performances 
 ridiculous. 
 
SHADOWS. 
 
 67 
 
 DEFINITIONS. 
 
 1. A body which is continually emitting a stream 
 of matter from itself, and thereby rendering objects 
 visible to our sense of seeing, is called a luminary; 
 such as the sun, or any other body producing the 
 same effect. 
 
 2. The stream of matter which is emitted from the 
 luminary is called light. 
 
 3. A substance or body which light cannot pene- 
 trate is called an opaque hodij. 
 
 4. If a space be deprived of light by an opaque 
 body, it is called a shade. 
 
 5. The whole or part of any sm-face on which a 
 shade is projected is called a shadow. 
 
 6. A body which will admit of light to pass through 
 it is called a transparent substance. 
 
 7. A line of light emitted from the luminary is 
 called a ray. 
 
 Proposition 1. — The rays of light, after issuing 
 from the luminary, proceed in straight lines. 
 
 Proposition 2. — If the rays of light fall upon a re- 
 flectiiig plane, the angle made by any incident ray, 
 and a perpendicular to the reflecting plane, is called 
 the angle of incidence, and ■wHl be equal to the angle 
 that its reflected ray will make with the same per- 
 pendicular, called the angle of reflection ; these two 
 propositions are known lirom experiment. 
 
 Proposition 3. — If the rays of light fall upon any 
 curved surface, whether concave or convex, or mLxed 
 of the tvs^o, the angle of reflection will stiU be equal 
 to the angle of incidence. 
 
 Proposition 4. — Any uneven reflecting surface, 
 whose parts lie in various directions, will reflect the 
 rays of the sun in as many different directions. 
 
 Demonstration. — If any ray fall upon a part of 
 the surface which is perpendicular to that ray, it will 
 be reflected m the same line as the incident ray ; but 
 the more or less any part of the surface is inclmed to 
 a ray, falling upon that part of the surface, the greater 
 or less angle will the reflected ray make with the in- 
 cident ray. For imagine a perpendicular to be erected 
 to that part of the surface where any incident ray 
 impinges on the surface, it is evident that the meas- 
 ure of the angle of incidence is equal to the obtuse 
 angle made by the incident ray, and the reflecting 
 surface at the impinging point made less by a right 
 angle ; but the angle of reflection is equal to the an- 
 gle of incidence ; wherefore it follows that the whole 
 
 angle formed by the incident and reflected rays is 
 double of the angle of incidence ; and, consequently, 
 a reflecting surface, whose parts lie in various direc- 
 tions, wiU reflect the sun's rays in as many directions. 
 Corollary. — Hence appears the reason why objects 
 and their parts become visible to our sight when im- 
 mersed ui shade. 
 
 SEAT OF THE SUN'S RAYS. 
 
 DEFINITIONS. 
 
 1. If a given straight line pass through or cut a 
 given plane, and if an imaginary plane be supposed 
 to pass through any two points m the straight Ihie, 
 perpendicular to the other plane, the angle made by 
 the intersection of the two planes and the given 
 straight line is called the inclination or altitude of 
 the given line on the given plane. 
 
 2. The intersection of the planes is called the seat 
 of the given line on the given plane. 
 
 Corollary. — The angle made by a ray of light, 
 and the seat of that ray, is the angle of the sun's in 
 clination. 
 
 3. If on the surface of any solid there be any point 
 or points in the surface where the sun's rays fall per- 
 pendicular, this point or points which the sun's rays 
 fall perpendicular to are called points of light. 
 
 4. If on the sm-face of any solid there be any Ime 
 drawn upon that surface, and if the line so drawn 
 upon the surface be lighter than any other line that 
 can be drawn upon the said surface, then the line first 
 drawn is called the line of light. 
 
 5. K the sun's rays fall upon any solid, and if a 
 line or lines be drawn on the surface of the solid 
 where the sun's rays are a tangent, or upon the place 
 or places of the surface which divide the dark side 
 from the light side, then the line or lines so described 
 are caUed a line or lines of shade. 
 
 6. If the sun's rays be parallel to any plane, that 
 plane to which they are parallel is called a plane of 
 shade. 
 
 PROBLEiAIS. 
 
 PROBLEM I. 
 
 Given the ichnography aud elevation of a prism, 
 whose sides stand perpenchcular to the hori- 
 zon, and whose ichnography is a figure of 
 
68 
 
 SHADOWS. 
 
 an) kind, regular or irregular ; given the scat 
 of the sun on the ichnography, also on the 
 elevation, and the intersection of the plane 
 of the elevation with the plane of the ichnog- 
 raphy; the representation of the point being 
 likewise given on the elevation, and also on 
 the ichnography, to determine the representa- 
 tion of the shadow on the elevation. 
 
 Through the representation of the given point in 
 the plane of tlie ichnography ckaw a line parallel to 
 the scat of the sun's rays on that plane, and produce 
 it till it cut the intersection ; from that point on the 
 elevation draw a line perpendicular to the intersec- 
 tion ; then through the representation of the given 
 point on the elevation draw a line parallel to the sun's 
 seat on the elevation, cutting the line that was di-awn 
 perpendicular to the intersection, and that point will 
 be the representation of the shadow on the elevation. 
 
 Plate 17. 
 
 PROBLEM 11. 
 
 Given the altitude and seat of the sun on the 
 horizon and the intersection of a plane, mak- 
 ing a given angle with the horizon ; to find 
 the seat and altitude of the sun on the other 
 plane. 
 
 Fig. 1. Let D F be the seat of the sun on the 
 horizon, and D F G the angle of the sun's elevation, 
 E F the intersection of the plane with the horizon, 
 and ABC the angle which that plane is to make 
 with the horizon. 
 
 Produce D F till it meet E F in F ; through any 
 point D, in the seat D F, draw D G perpendicular to 
 D F, cutting F G in G ; also, through D draw D K 
 perpendicular to E F, cutting E F in E ; through D 
 draw D I perpendicular to D K; make the angle 
 D E 11 equal to the given angle ABC; make D I 
 equal to D G ; through I draw I H perpendicular to 
 E H, cutting it in II; make E K equal to E II; join 
 K F ; fi'om K make K L perpendicular to K F ; from 
 K make K L equal to H I ; join L F ; then will I K 
 be the scat of the sun on the other plane, and K F L 
 will be the angle of the altitude. 
 
 If the plane KEF stands perpendicular to the 
 horizon, as m Fig. 2, the operation will be more sim- 
 
 ple, as follows, the same letters standing for the same 
 things : — 
 
 Make E K equal to D G ; join K F ; draw K L, 
 as before, and make K L equal to D E ; join L F ; 
 then will K F be the seat of the sun on the horizon, 
 and K F L be the seat of the altitude. 
 
 Plate 18. 
 
 PROBLEM UI. 
 
 Given the ichnography A B C D E F G H I K, 
 and elevation L M N O, of an upright prism, 
 whose base or ichnography is a regular poly- 
 gon, and the seat of the sun's rays on the base, 
 to determine the various degrees of light and 
 shade on the different sides of the prism. 
 
 Fig. 1. Let P Q, in the ichnography, be the seat 
 of the sun ; and if it cut C D perpendicular, then will 
 C D be the lightest side of the prism ; the sides D E 
 and C B will be a small degree darker, as P Q is 
 more inclined to D E and C B ; and in general, ac- 
 cording as the sides recede on each side of C D, they 
 wiU be contintially darker untU they become wholly 
 deprived of light ; then suppose the sun's ray to touch 
 the side G H, then G H -will be the plane of shade, 
 or that side where the light wiU end. 
 
 Much in the same manner may the different de- 
 grees of shade be found on the surface of a cylinder, 
 as in Fig. 2, where A B C D is the ichnogi-aphy, and 
 G H I K the elevation ; that is, if B P be the direc- 
 tion of the sun's rays, cutting the ichnogi-aphy in B. 
 then will B be the lightest place ; and it will be con- 
 tinually darker and darker in each side of the pomt 
 B, until it arrives at the point C, where the ray 
 touches the side of the cylinder, and there the light 
 will end and the darkness begin. 
 
 PROBLEM IV. 
 
 To represent the boundaries of light and shade 
 on the ele^■ation of a cone illumined by the 
 sun, given the angle that any ray of light takes 
 with the base of the cone ; also to determine 
 the line of light, or that place on the surface 
 that will be the lightest. 
 
 Figs. 3 and 4. Let A E D be the elevation of the 
 cone, and let F I L G be the ichnography or base of 
 the cone ; let F L be the seat of any ray in a plane 
 
II 17 
 
,111 
 
 «!ll'J<?\'i.'i(:)'5 
 
 K M 
 
 O I 
 
 J^t^^sT IB 
 
ri.m 
 
 
SHADOWS, 
 
 69 
 
 passing through the axis, and let the angles M L F, 
 Fig. 3, and L F M, Fig. 4, be the angles which a ray 
 of light makes with the base of the cone, and let 
 F N L be a section of the cone passing through the 
 axis, and through F L; consequently, the rays M L 
 and F ]\I will be in that plane. 
 
 Produce the rays M L and F M, if necessary, until 
 they cut the sides of the section N F and N L; 
 Fig. 3 will be cut at the points M and L, and Fig. 4 
 at the points F and M : bisect each of the lines M L 
 and F M ; and through N, the vertex of the cone, 
 and the point of bisection, draw N K ; through K 
 draw I K G, at right angles to F L ; through the 
 points G and F di-aw the lines G C and F B per- 
 pendicular to A D, the representation of the base, 
 cutting A D at B, and C in the elevation, and join 
 B E and C E ; then will B E be the lightest line that 
 can be di-awn on the sm-face of the cone, and C E 
 will be the representation of a line which will divide 
 the light side of the cone from the dark side, and 
 B E C will be the representation of half the enlight- 
 ened side of the cone. 
 
 Plate 19. 
 
 PROBLEM V. 
 
 Given the iclinography and elevation of a polyg- 
 onal ring, or a ring made of cylinders of 
 equal lengths, and making equal angles with 
 each other, to determine the representation 
 of the boundaries of light and shade on the 
 ichnography and elevation ; the sun's altitude 
 and seat to the plane on which the ichnog- 
 raphy is described being given. 
 
 Let A C be the seat of the sun in the plane of the 
 ichnography, cutting the thickness of the ring at A 
 and B ; let A C D be the angle which the sun's rays 
 make with the plane of the ichnogi'aphy, or seat A C. 
 
 Bisect A B in c; with the radius c A or c B de- 
 scribe a circle ; and through the centre c draw c d 
 parallel to C D, cutting the circle at d; also through 
 c ch-aw the line a 6 at right angle to c d, cutting the 
 circles at a and b ; through the points d and b draw 
 lines parallel tc the sides A and B of the ring ; then 
 the dark line nearest to A will represent the line of 
 light ; and that which is nearest to B will represent 
 that line which separates the light side from the 
 dark side. 
 
 To find the lines of light and shade on the next 
 side of the ichnography: from the centre C draw 
 C E at right angles to the side E, cutting the sides 
 E and F at E and F ; through the point A draw 
 H A G at right angles to E C, cutting E C at G ; 
 from G make G II equal to A D, join H C, and 
 bisect E F at c ; then with the radius c E on c F 
 describe a circle, and through its centre e, draw c k 
 parallel to C H, cutting the circle at k; also through 
 c draw p f at right angles to c k ; through the points 
 k and/, draw lines parallel to the sides E and F ; 
 then will the line next to E, that cuts C F at ^, be 
 the line of light, and the line next to F the line of 
 sliade. 
 
 In like manner proceed with the side I and K; that 
 is, through C draw the line CI at right angles to the 
 side I, cutting the sides I and K at I and K ; bisect 
 I K at c ; with the radius c I or c K describe a circle ; 
 through the point A, as before, di-aw the line A L 
 perpendicular to C I, cutting C I at L ; from L, make 
 L M equal to A D ; join M C ; through c draw c m 
 parallel to C M, cutting the circle at m ; also through 
 c draw g h perpendicular to c m, cutting the circle at 
 g and h; then through the points m and h draw lines 
 parallel to the sides I and K ; then the line next to I, 
 which cuts I K at s, will give the line of light, and 
 the line next to K the line of shade. 
 
 In like manner, to find the common boundary of 
 light and shade upon that side of the ring next to 
 the ichnography, draw lines through the points a,p,g, 
 parallel to the sides A, E, I, as are shown by the 
 dotted lines, which will give lines of shade on the 
 imder side of each cylindrical part. The lines for 
 one quarter of the ring being found, the other quar- 
 ter, on the other side of the seat A C, may be found 
 from the last quarter, each being in the same order, 
 receding from the line A C, or drawing towards it. 
 One half being now found, the other half will be 
 found by observing that opposite sides of the ring 
 are parallel to each other ; and, consequently, if one is 
 found, the other will also be found ; for the light will 
 be at the same distance upon the same sides of that 
 which is to be found as that cylinder which is found. 
 Then to find the lightest lines on the elevation, Fig. 2, 
 and also those lines which will be the boundaries of 
 the light and shade, proceed as follows : — 
 
 Through the points n, o, p, q, draw the lines n N, 
 o O, /? P, (7 Q, perpendicular to the elevation, cutting 
 the line P K, which represents a plane passing 
 
70 
 
 SHADOWS. 
 
 through the axes of all the straight cylinders at the 
 points P, Q, N, O ; make P H equal top k; from Q, 
 make Q, E equal to q e ; from N, make N D equal to 
 II d; from O, make O A equal to o a; then through 
 (he points II, D, E, A, Fig. 2, draw lines parallel to 
 P K; tlien will the lines H and D represent the lines 
 of light, and E and A will represent the lines of 
 shade. Now, since the side D A, in the elevation, 
 Fig. 2, represents the cylindrical part A B on the 
 ichnography, and because that the lines of light and 
 shade arc in the same order on each side of A B, — 
 that is, the light and shade will be the same height 
 from the plane of ichnography, on each of the cylin- 
 drical parts that are equidistant from the cylindiical 
 part A B, on each side of it, and, consequently, will 
 be represented on each of the cylindrical parts, Fig. 2, 
 equidistant from A D, at the same altitude, — then 
 make P H and Q, E, the next cylindrical part to the 
 centre of the elevation, equal to P H and Q, E, on 
 the outside cylinth-ical part, which the side E F, on 
 the ichnography, represents ; make S M and R G, in 
 the elevation, equal to s m and r g- on the ichnog- 
 raphy ; the height of the lines on each side of the 
 elevation representing the light and shade being 
 taken from its corresponding place on the ichnog- 
 raphy, as is already shown, will complete the lines 
 of light and shade on the elevation. 
 
 OBSERVATIONS. 
 
 1. If the seat ot the sun's rays be drawn on any 
 plane, and if a cylinder lay on that plane with its 
 axis perpendicular to its seat, and parallel to the 
 plane, the lightest line on the cylinder will be nearer 
 the plane in this position than in any other. 2. But 
 if the axis of the cylinder make oblique angles, 
 then the line of light will be higher on the cylinder. 
 3. Again : if the axis of the cylinder be parallel to 
 the seat of the sun, the lightest line on the cylinder 
 in this case will be at its greatest distance from tlic 
 plane, because then the line of light will be wliere a 
 plane passing through the axis of the cylinder cuts 
 the upper surface perpendicular to the plane on 
 which the cylinder lies ; the line of light in the fii-st 
 position of the cylinder is brighter than the line of 
 light in the second position, and the line of light 
 in the second position of the cylinder is brighter 
 than the line of light in the tliird position ; the axis 
 of the cylinder in all these cases being parallel 
 
 and equidistant from the plane of the ichnogra- 
 phy ; consequently, the lines of light in the first 
 and third positions of the cylinder arc the extremes 
 of all the varieties which happen between these two 
 positions ; that is, the first is the lightest possible, and 
 the tliird is the darkest possible. The boundaries of 
 light and shade, called in this book the lines of shade, 
 or those lines which separate the light side from the 
 dark side, are always at a quadrant's distance from 
 each other ; and, consequently, that arc which is the 
 under line of darkness in the first position will be 
 higher in the second position, and still higher in the 
 third ; and if a plane be made to touch the cylin- 
 der upon that line, it will be perpendicular to the 
 plane on which the cylinder lies, and, therefore, its 
 ichnography will be represented by the edge of the 
 cylinder. Now, suppose that cylinder to be turned 
 round by moving continually the same way, until the 
 axis of the cylinder comes into that position in which 
 the axis would be perpendicular with its seat, then 
 the line of darkness would be in its highest position. 
 
 Plate 19. 
 
 PROBLEM VI. 
 
 To find tlie lightest line, also tlie line that 
 divides the lightest side from the dark side 
 on the ichnography and elevation of a cir- 
 cular ring. 
 
 Let A C be the seat of the sun, or any line parallel 
 to it, passing through the centre C of the ichnogra- 
 phy, (Fig. 1,) cutting the thickness of the ring at 
 B and H, and let B C D be the sun's altitude ; take 
 the point G, at one quarter of the circumference of 
 the ring, distant from the point B ; and take any 
 points E and F in the circumference bet^^een B and 
 G, and draw the lines E C, F C, and G C, cutting 
 the inside of the ring at I, K, and L; through the 
 point B draw the lines B M, B N, and B U, each re- 
 spectively perpendicular to E C, F C, and G C, cut- 
 ting E C, F C, and G C, at O and P ; make O M, 
 P N, and C U, on B II, E I, F K, and G L, as diam- 
 eters; describe circles whose centres are a, b,c,a; 
 through these centres draw the lines c, d, c, m, c, n, 
 and ?«', i(, parallel to C D, C M, C N, and C U, cut- 
 ting the circles at a, m, n, n, and c, c, c, w ; also, 
 through the centres a, b, c, v, draw lines i, q, p, s, k, y, 
 and L G, respectively perpendicular to C D, C M, 
 
ri.jii 
 
 ,7 
 
SHADOWS. 
 
 71 
 
 C N, and C U, cutting tlie circle at i, q, p, s, k, y, 
 L and C>. 
 
 Through the points (/, w, n, u, draw the lines d, g, 
 m, e, n, o, and v, v, perpendicular to the diameters 
 B H, E I, F K, and G L, cutting B H, E T, F K, and 
 G L, respectively at the points g; c, o, v ; draw a curve 
 which will be part of the line of light for one quarter ; 
 also through the points </, s, y, draw the lines q, r, s, t, 
 and y x, cutting the diameters at r, f, x; then through 
 the points r, t, x, and L, draw a curve line r t xIj, 
 which will be the upper line of shade for that quar- 
 ter, or that line which divides the dark side from the 
 light side, upon the upper side of the ring on that 
 half which is next to the luminary. 
 
 One quarter being now found of the line of light 
 and shade on the ichnography of the visible side of 
 the ring, the other three quarters will be found from 
 that quarter which is already found, in the same 
 manner as in the last problem, and the points D, M, 
 N, U, I, P, K, G, also in the elevation of the curves 
 D, I\I, N, U, and I, P, K, G, being drawn, then 
 D ai N U will be the line of light, and I P K G the 
 line of shade. 
 
 Plate 20. 
 
 PROBLEM VII. 
 
 To represent the lines of equal gradation on 
 the surface of a sphere given ; the seat of a 
 ray of light on the plane of projection, and 
 the elevation of the ray. 
 
 Let A B be the diameter of the sphere and seat of 
 the sun. Find the centre C, and describe a circle 
 with the radius C A or C B ; this cii'cle will represent 
 the contour of the sphere. Make the angle A C D 
 equal to the elevation of the ray above the seat C A; 
 and let C D be produced so as to cut the circumfer- 
 ence line in D and E. Draw the lines F G, H I, 
 K A, L jM, N O, P Q, perpendicular to D E, to cut 
 the cu-cle at the points F, G, H, I, K, A, L, M, N, O, 
 P, Q ; then will F G, H I, K A, L RI, N O, P Q, be 
 the diameters of circles which have equal intensities 
 of light around each circumference on the sphere. 
 Draw D R, G S, F T, H V, K C, L W, NX, P Y 
 perpendicular to B A; then E- will be the projected 
 point, representing the lightest point on the surface ; 
 T S is the shorter axis of the ellipsis, and F G the 
 greater. Describe the ellipsis aT b s, which will rep- 
 resent a circle of equal intensity of light in every part 
 
 of its circumference on the surface of the sphere. In 
 like manner, if the ellipsis c Y d e he drawn, it will 
 represent another circle of equal intensity. Proceed 
 in this manner, and represent all the intermediate cir- 
 cles of the sphere to that, the diameter of which is 
 P Q, where a ray of the sun would at any point be 
 a tangent, and the representation of this last circle, 
 K Y Z, will be the line of separation of light and 
 shade ; then every succeeding ellipsis towards the 
 lightest point R wiU represent graduating lines con- 
 tinually lighter. 
 
 PROBLEM VIII. 
 
 Given the ichnography and elevation of a cyl- 
 inder, havuig a square projecture or abacus, 
 and the seat of the sun on the ichnography, 
 also its seat on the elevation ; to find the 
 shadow of the abacus, also the line of light 
 and shade on the cylinder. 
 Let A H I K L ]\I N O B be the ichnography of 
 the cylinder ; D E F G that of the abacus ; V W the 
 elevation of the cylinder ; and E F the elevation of 
 the abacus ; let C F be the seat of one of the sun's 
 rays on the ichnogi-aphy, passing through the centime 
 C ; draw F o, maldng an angle with E F, equal to 
 the angle which the seat of any of the rays make 
 with E F ; through C draw C H perpendicular to 
 C O, cutting the ichnogi'aphy at H ; between the points 
 H and O, take any points I, K, L, M, and N; then 
 through the points H, I, K, L, M, N, draw lines B B, 
 I Q, K R, L S, M T, N U, paraUel to C F, cutting 
 H P at P, Q, R, S, T, U ; through the points P, Q, 
 R, S, T, U, di-aw lines parallel to F o ; also through 
 the points B, I, K, L, JM, N, O, draw lines H /*, I i, 
 K k; L /, M m, N w, O o, paraUel to the sides of the 
 cylinder, cutting P /;, Q i, R k, S /, T m, U n, F o, at 
 the points /;, i, k, I, m, n, o ; through these points draw 
 a curve, and it will be the shadow of the abacus ; H h 
 will be the line of shade, and O o the line of light. 
 
 PROBLEM IX. 
 
 Given the ichnography and elevation of a cylin- 
 der having a circular projection over it ; the 
 seat of the sun on the ichnography; also its 
 seat on the elevation being given ; to find the 
 shadow of the projecture on the cylinder; 
 also the line of light and shade. 
 Fig. 2. Let A D E F G H I B be the ichnography 
 
72 
 
 SHADOWS. 
 
 of the cylinder, R K L M N O P Q the ichnography 
 of the projection ; let U T be the elevation of the 
 cylinder, and V S that of the projecture; also, let 
 C O be the seat of the sun's rays, passing through 
 the centre C of the ichnography, and o h the scat of 
 the sun on the elevation. 
 
 Through C draw C D perpendicular, cutting the 
 circvimference of tiie inner circle at D; take any point 
 E, F, G, I, B, in the circumference ; ch-aw the lines 
 B K, E L, F M, G N, H O, I P, and B O, parallel 
 to C IT, cutting the outward circle at the points K, L, 
 M, N, O, P, Q ; from the points D, E, F, G, H, I, draw 
 the Imes D rf, E e, F/, Gg-, H h, I i; also, through 
 the points K, L, M, N, O, P, Q, draw the lines K k, 
 L /, M m, N n, O o, V p, Q q, cutting V S at the 
 points /••, /, m, n, o, p, q ; through the points k, I, m, n, 
 o, p, q, draw k d, I e, m f, n g, o h, p i, parallel to o h, 
 cutting the lines D d, E c, F/, Gg-, H h, I i, at the 
 points d, e,f, g,h,i; a ciurve being traced through 
 these points will be the representation of the shadow 
 upon the cylinder ; D d will be the line of shade, 
 and H the line of light. 
 
 Plate 21. 
 
 PROBLEM X. 
 
 The ichnography and elevation of the prism 
 standing upon a polygonal base, having the 
 projecture or cap of the same figure upon it, 
 projecting equally over its sides ; given the 
 seat of the sun's rays on the plane of the 
 ichnography, and also on the elevation ; to 
 project the shadow of the cap on the prism, 
 and also on a plain parallel to the axis of 
 the prism. 
 
 Let A B C D E F G be the ichnogi-aphy of the 
 prism, H IJ K L M N the ichnogi-aphy of the cap 
 W A and G P, parts of the ichnography of the plane 
 on each side of the prism, J W be the projection of a 
 ray on the ichnography, and j lu on the elevation. 
 From all the points H, I, J, K, L, M, N, in the ich- 
 nography of the angles of the cap, draw the lines 
 H /(, I i, J j, K k, L I, M «!, N n, perpendicular to 
 W P, to cut the under side of the cap at h, i,j, k, I, 
 m, n. Draw the lines A4 «, B 5 i», C 6 c, D 7 </, E 8 e, 
 F 9/, G 10 g-, perpendicular to W P, cutting the bot- 
 tom of the prism at 4, 5, 6, 7, 8, 9, 10, then the lines 
 4 o, 5 6, 6 c, 7 rf, 8 e, 9/, 10 g, represent the angles 
 
 on the elevation. Draw the lines H Z, I X, J 'W, 
 K Q, L R, M T, N U, parallel to J W, cutting the 
 ichnography of the plane at the points Z X W, and 
 the ichnography of the prism at Q, R, T, U. Through 
 the points h, i,j, k, I, in, n, the projection of the an- 
 gles of the cap on its mider edges, and parallel to 
 j «', draw the projections of the rays h z, i x,j u; k q, 
 I r, m t, n v. Draw the perpendiculars Z z, X.r, W iv, 
 Q (7, R r, T <, U u, then the points z, x, to, are the 
 projections of the angles of the cap on the plane, and 
 q, r, t, t(, the projection of the other angles on the 
 elevation of the prism. Draw C Y, to touch the 
 prism at C, and draw Y j/ perpendicular to W P, 
 then Y y will be the termination of the shadow of 
 tlie body of the prism on the wall. Then, because 
 that the point q is in the plane G c d7, the point r in 
 the plane 7 (Z e 8, and the points t and v, in the plane 
 9/g- 10, and the lines j, k, I, m, n, parallel to these 
 planes, the lines /, k, 1, m, n, will make parallel shad- 
 ows ; therefore, draw q c, r d, t v, parallel toy, k, I, ot 
 ■m n, to cut c 6 in c, k 7 in d, and G g- at n ; join d q; 
 then, to find the depth of the shadow of I m on the 
 elevation, draw Sf s on the ichnogi-aphy parallel to 
 J W ; draw Sf & perpendicular to W P, likewise Sf s, 
 parallel to the ray on the elevation, and S s parallel 
 to the axis of the prism ; then s is the depth of the 
 shadow; but as the projections of the exh-emities of 
 I VI fall upon the adjacent planes at ?• and t, draw 
 e f through s, cutting 8 e at e, and 9/ at f ; then join 
 e r, f t. Lastly : draw G V on the ichnogi-aphy par- 
 allel to W J, cutting the projection of the cap at V; 
 draw V v perpendicular, cutting the cap at v, and 
 draw V g parallel to the rays on the elevation, and 
 join u g; then c q d, r e { t tt g will be the shadow 
 of the cap on the elevation ; but as the shadow of the 
 parts of the abacus H I, I J, will be from the top of 
 tiie cap, make lu 1, x 2,z 3, parallel to the angles of 
 the prism on the elevation, and equal to the thick- 
 ness of the cap. Join 1, 2 ; 2; 2, 3 ; then will 3, 2, 
 1 10 7/ be the shadow of the abacus on the wall. 
 Tlirough g di-aw g m and k i in the same straight 
 line with g m, cutting 3 2 at k ; then i k 2, / w y, is 
 the complete shadow of the cap on the plane. 
 
 Much after the same manner rnay the shadow of 
 a cylinder be found, having a circular projection over 
 it, as is shown at Fig. 2, and also the shadow of the 
 cylinder projecture may be found on a plane parallel 
 to the axis of the cylinder, having the same tiling 
 given as before ; but for more easy inspection, letters 
 
I'l.J) 
 
 4L^/ 
 
 3 /A 
 
 T 
 
 \ ■.">'. 
 
 L* 
 
 \¥ 
 
 i 
 
 
 '' : i i 
 
 ... 
 
 ■' 
 
 '/ 
 
 \n\ ..- 
 
 ,<•' 
 
 ' 
 
 
 
 Fi)>. 1 . 
 
 % 
 
 
 
 
 1 
 
 N''\l. 
 
 y 
 
 
 ::■-». 
 
 
 i 
 
 '' 1 
 
 \K.V; -> 
 
 N> 
 
 
 ■ : \ 
 
 
 ] 
 
 
 V: 
 
 : :■■ \ 
 
 
 
 
 
 II 
 
 
 
 
 
 3Jv' 
 
 : '• I'.'T 
 
 
 Si^. i /&. 
 
 / 
 
 
I'l 
 
 SMAiD.SWS 
 
 D^z 
 
 
 lllllllllllllllllllIlllllllllllllllllllllllllllllllllllllllllllllllllJllllllllllllllll^lP^ 
 
SHADOWS. 
 
 78 
 
 are placed on the ichnography and elevation, repre- 
 senting the correspondiiig parts of each other ; that 
 is, capital letters are placed on the ichnography, and 
 small letters of the same name on the elevation, 
 representing those of the same name on the ichnog- 
 raphy. 
 
 PROBLEM XI. 
 
 Given the seat and altitude of the sun on any 
 plane, also the seat and altitude of a Ime to 
 the same plane ; to determine the shadow of 
 the line upon that plane. 
 
 Let K L be the seat of the line upon the plane, 
 and G H, Fig. 3, the angle wliich the line makes 
 with its seat ; make the angle M K L, Fig. 2, equal 
 to the angle H G I ; through L draw L M, perpen- 
 dicular to K L, cutting K M at M ; also, through L 
 draw L O parallel to the seat of the sun. Again : 
 through L draw L N perpendicular to L O, and 
 make L N equal to L M ; then upon the right line 
 L N, and from the point N, make the angle L N O 
 equal to the complement of the angle of the sun's 
 inclination to a right angle ; produce N O, cutting 
 L O at O; then join the points K and O, and the 
 line K O will be the shadow required. 
 
 Tliis problem will be found of great use in finding 
 the shadows upon inclined planes. 
 
 XoTE. If the seat and altitude of the 8>in be given on any other 
 plane, making a given angle ■with the plane on which the shadow 
 is to be projected, the sun's altitude and seat may be found by 
 Problem II. 
 
 PROBLEM XII. 
 
 Given the seat and angle of inclination of the 
 sun on the horizon, and the intersection of 
 a plane perpendicular to the horizon ; to de- 
 termine the angles which a plane of shade, 
 made by a right line, parallel both to the 
 horizontal and perpendicular planes, will 
 make with each of the planes. 
 
 Let A B be the seat of the sun on the horizon, and 
 A A D, as Fig. 1, the angle of inclination to the seat 
 A B, and let C B be the intersection of a plane per- 
 pendicular to the horizon ; take any point C in C B, 
 and from C draw C A perpendicular to C B, cutting 
 A B at A ; from A, draw A E perpendicular to A C, 
 
 10 
 
 and A D perpendicular to A B, cutting D B at D ; 
 make A E equal to A D, and join C E ; then will 
 the angle B C E be the angle which the plane of 
 shade makes with the perpendicular plane, and the 
 angle ACE the angle which the plane of shade 
 makes with the horizon. 
 
 This problem will be very useful in shading mould- 
 iiigs which project from planes that stand perpendic- 
 ular to the horizon, the sun's altitude and seat beinc 
 given to the horizon, as will be shown in the next 
 problem. 
 
 Plate 32. 
 
 PROBLEM XIII. 
 
 A moulding of any kind being given, and the 
 angle which a plane of shade makes with a 
 perpendicular part of the moulding, either 
 being given or found by the last problem, 
 ha^ing the sun's altitude and seat on the 
 horizon; to deteimine the shadow on the 
 moulding. 
 
 Let the ovolo, fillets, and hollow. Fig. 1, be the 
 given moulding ; draw C D parallel to the inclination 
 which the plane of shade makes with the vertical 
 part of the moulding, touching the ovolo at C, and 
 cutting the vertical part below D ; then a line drawn 
 through D perpendicular to the fillet will give the 
 lower edge of the shadow, and an imaginary line, 
 supposed to be drawn through C, will give the line of 
 shade ; and if a line is drawn through A, the lower 
 edge of the fillet above the ovolo parallel to C D, 
 cutting the ovolo at G, then a line being drawn 
 through B, parallel to the fillet, will give the edge of 
 the shadow from the fillet. 
 
 Much in the same manner, may the shadow upon 
 the cima reversa and cima recta be found, as shown 
 by the dotted lines. 
 
 ON MOULDINGS 
 
 Plate 22. 
 
 The form or shape of mouldings, in most cases, 
 may be ascertained from the various degrees 
 of light and shade upon them, without ob- 
 
74 
 
 SHADOWS. 
 
 serving the profiles; which will appear evi- 
 dent from the following observations: — 
 
 Observations on Surfaces, and their Poiver to reflect 
 Light. 
 
 It has already been observed in the second propo- 
 sition, that if the sun's rays fall upon a reflecting 
 plane, the angles made by the reflected rays, with 
 perpendiculars at the impinging points, will be equal 
 to the angles made by their corresponding incident 
 rays with the said perpendiculars ; so that the rays 
 in this case will have only one direction after reflec- 
 tion : but by experiment wc are shown that there is 
 no such thing as a perfect plane ; for, if a sm-face is 
 even polished to the greatest degree, yet this polished 
 surface will be but rough and uneven ; for, if viewed 
 through a microscope having a great magnifying 
 power, the surface will appear quite irregular, and 
 the different parts of the surface will be inclined to 
 any fixed plane, in all manner of directions; and, 
 consequently, if the sun's rays fall upon such a sur- 
 face, the rays will not be enthrely reflected in the same 
 direction, but a great part of them will be reflected 
 in all manner of directions by the different positions 
 of the surface, by Proposition IV. It may be ob- 
 served, that the higher any surface can be polished, 
 the nearer it approximates to a plain, and, conse- 
 quently, the rays wUl be more and more reflected in 
 the same direction ; but there is no surface which 
 will reflect the sun's rays entirely in the same direc- 
 tion ; that is, parallel to each other ; but a great part 
 of them will be reflected in all manner of directions : 
 it will be also necessary to observe, that the power 
 of reflection will depend very much on the lightness 
 of the color of materials ; for the darker any sub- 
 stance iS; the more will the rays of light be absorbed 
 in that substance, and, consequently, will have a less 
 power to reflect. 
 
 White, being the lightest of all colors, will reflect 
 the most rays ; and the more any substance inclines 
 to a white, the greater power wiU that surface have 
 to reflect the rays of light. 
 
 CASE I. 
 
 Observations on Mouldings in Shade. 
 
 If the sun's rays fall upon any building, also upon 
 
 the ground or horizon below the building, and if 
 
 there are any projectures from the building, such as 
 
 mouldings or other ornaments, and if any of the 
 
 parts of those mouldings or ornaments are entirely 
 in shadow by the projecture of somethmg else which 
 prevents the rays of the sun from falling upon them, 
 those parts of the mouldings which are in shade will 
 become visible; for, besides a reflection from the 
 ground, there will be a strong reflection from the 
 surface of the Iniilding, immediately under the 
 mouldings or ornaments. It has already been ob- 
 served, that these rays will be reflected in all direc- 
 tions, and, consequently, a part of them wiU be re- 
 flected upwards on the mouldings above, and, there- 
 fore, will show hght and shade on the mouldings 
 according as the reflected rays fall, more or less, per- 
 pendicular on their surfaces. 
 
 Hence the reason why all perpendicular sides of 
 fillets will be darker in shade than the horizon- 
 tal sides. 
 
 An ovolo, having a projecture over it, so as to pre- 
 vent the sun's rays from falling upon it, the reflected 
 rays being more and more mclined from the under 
 edge towards the upper edge, wiU be lightest below, 
 and will be gradually darker and darker upwards. 
 
 A cavctto or hollow, immersed m shade, will, for 
 the same reason, be darkest below, and will be con- 
 tinually lighter to the upper edge. 
 
 A cima reversa, in shade, will be darkest above and 
 below, and lightest in the middle ; for this moulding 
 is composed of an ovolo above and a cavetto below. 
 
 A cima recta, in shade, will be hghtest above and 
 below, and darkest in the middle. 
 
 These are general rules for shading horizontal 
 mouldings. 
 
 CASE II. 
 Observations on vertical Mouldings. 
 
 All upright perpendicular mouldings, in shade, or 
 being in part so, will receive a reflection from those 
 smrfaces which are next to them ; for they cannot 
 receive a reflection from the contrary side, by reason 
 of their projection, which wiU prevent the ray, re- 
 flected from that side, from falling on them. 
 
 Therefore, it is plain, in these cases, the forms of 
 mouldings may be known by reflection. 
 
 Artists give this rule for shadowing: that is, to 
 shade all mouldings or other ornaments which are in 
 shade, inverse to those on which the sun's rays fall, 
 from the contrary side of the reflected rays. But this 
 rule is not only very uncertain, depending much on 
 the situation of other objects which surround thcs* 
 
SHADOWS. 
 
 75 
 
 mouldings or ornaments, but in some cases very erro- 
 neous, as in the example of mouldings perpendicular 
 to the horizon ; for mouldings in this situation, as has 
 been observed, will receive a reflection from that side 
 which is next to the front of the moulding, if some- 
 thing else docs not project to a great distance from 
 that surface from wliich the reflection comes. K a 
 cylinder or column is attached to a wall in a vertical 
 position, and if it has any projecture over it, so as to 
 cause that part under the projecture to be in shade 
 quite round the cylinder, there will not only be a re- 
 flection from the wall on the contrary side of the 
 cylinder, to the sun upon that side of the cylinder 
 which is next to it, but also from that part of the wall 
 on that side of the cylinder next to the sun, which 
 will make that part of the cylinder which is in shadow 
 lightest at the two sides and darkest in the middle. 
 Something of the same kind may be seen in Ionic 
 columns attached to a wall, where it may be observed 
 when the sun shines upon one side of them ; suppose 
 that side of the column which is on the right hand, 
 then the right hand volute will throw a shadow upon 
 the light side of the column, which shade Avill be 
 lightest on that edge which is next to the wall and 
 to the luminary, and darkest at that edge next to the 
 middle of the column. 
 
 CASE III. 
 
 Observations on Mouldings in Shade, when situate on 
 the Side of an Object ivhich is entirely in Shade^ 
 and also the Ground under that Side in Shade. 
 
 In one building where one end or side is entirely 
 in shade, and also a great part of the ground under 
 that end in shade, there wUl be little or no reflection 
 from the ground upwards, nor from the surface of 
 the building, and, consequently, little reflection upon 
 the mouldings from below ; the only light which they 
 receive is from a kind of scattered or confused rays 
 in the atmosphere, and small reflections from the 
 horizon ; and, therefore, horizontal mouldings, or or- 
 naments, in this situation, which have but small pro- 
 jectures over them, will have a contrary effect to 
 mouldings in shadow situate on the light side of an 
 object. 
 
 An ovolo, placed horizontally, and whose greatest 
 projecture is upwards, upon the dark side of an ob- 
 ject, will be lightest above, and continually darker and 
 darker to the under edge. 
 
 A cavello, having its greatest projecture upwards, 
 placed horizontally on the dark side of an object, will 
 be darkest above, and continually lighter and lighter 
 to the under edge. 
 
 Kcima reversa, placed horizontally on tlie dark side 
 of the object, having its greatest projection upwards, 
 will be darkest in the middle, and lightest above ajid 
 below. 
 
 A cima recta, whose greatest projecture is upwards, 
 and placed horizontally, will be darkest above and 
 below, and lightest in the middle. 
 
 All horizontal projectures on the dark side of an 
 object will condense the shade under them, and, con- 
 sequently, will appear more or less dark according 
 as the projecture is more or less. 
 
 These are general rules for shading mouldings on 
 the dark side of an object from scattered light ; how- 
 ever, there are some exceptions to these rules — that 
 is, when any of these mouldings have a very great 
 projecture over them, this projecture will hinder the 
 scattered rays from falling upon the mouldings ; but 
 as they will receive a small reflection from the hori- 
 zon below, the most of the scattered and reflected 
 rays will fall obliquely on the moulding; thus the 
 lighted place of an ovolo will not be exactly on 
 the under edge, but somewhere between the under 
 and upper edge, and will be nearest to either, ac- 
 cording as the shadow on the ground is less or 
 more distant from that side of the object, and ac- 
 cording as the projecture over the moulding is 
 more or less, and also according to the position 
 and distance of other surrounding objects ; all these 
 different circumstances combining together wUl vary 
 the places of light and shade on horizontal mould- 
 ings, which are situate on the dark side of an 
 object. 
 
 An horizontal cavetto on the dark side of an object 
 having a projecture over it as before, the lightest 
 place will be somewhere between the upper and 
 under edge, as in the ovolo, and both mouldings 
 would have actually the same appearance if their 
 profiles could not be observed, when most of the 
 scattered and reflected rays are in a plane, making 
 equal angles with the horizon, and with that side 
 of the object in shade — that is, forty-five degrees 
 with each other ; and, consequently, mouldings in 
 this situation will be less distinct than mouldings 
 in shade on that side of the object which the sun 
 shines on. 
 
76 
 
 SHADOWS, 
 
 Further Observations on the Effect that reflected Light 
 tcill have on Cornices which have ModiUions or 
 Mutules, Dentils, Sfc, or any other projecting Or- 
 naments of a Nature similar to them. 
 
 The reflected light from the ground and from the 
 object being scattered in all directions, it will there- 
 fore follow, if there are any projecting parts from 
 mouldings or cornices, which are in shadows, such 
 as mutules, modillions, dentils, &c., these projecting 
 parts will hinder a great part of the scattered rays 
 from falling in the spaces between them ; and there- 
 fore the spaces will be deprived of reflection, and, 
 consequently, will be much darker than the promi- 
 nent parts, even if these prominent parts were also 
 in shadow. 
 
 For this reason, the intervals between mutules, mo- 
 dillions, dentils, &c., are darker than on their fronts, 
 for every projecture will condense the shadow on 
 each side of it, if recessed on both sides ; therefore, 
 the spaces will be lightest in the middle, and darkest 
 nearest to the edges of the mutules, modillions, den- 
 tils, &c. ; but to show on which side of the mutules, 
 &c., the greatest shade would fall, according to the 
 place of the luminary, would be almost impossible, 
 as it depends so much on the situation of other ob- 
 jects. But suppose all the surrounding objects in the 
 vicinity to be removed, and the ground and building 
 to be of a light color, and suppose the rays to pro- 
 ceed from the right to the left hand of the object, and 
 parallel to a vertical plane which is inclined at an 
 angle of forty-five degrees with the elevation of the 
 object ; then it is plain that, since the angle of reflec- 
 tion is equal to the angle of incidence, the greatest 
 part of the rays which fall upon the horizon will be 
 reflected from the ground parallel to the vertical 
 plane ; and seeing that the vertical plane would be 
 on the right hand of another vertical plane, perpen- 
 dicular to the face of the object and to the horizon, 
 it follows that most of the rays will come from the 
 right hand, and be reflected towards the left on the 
 object ; and, consequently, any projectures from cor- 
 nices, as mutules, &c., which are in shadow, will con- 
 dense oi darken the shade upon the left hand of the 
 projecture, and that vertical side of the mutules 
 which is next to the luminary will be lighter than the 
 other vertical side on the left of the mutule, &c. As 
 to the direction and effect which most of the re- 
 flected rays would take from the face of the object, 
 
 imagine a plane parallel to the sun's rays, and per- 
 pendicular to the face of the building or object; then 
 most of the rays will be reflected from the building 
 or object downwards, parallel to this last-mentioned 
 plane ; and that part of those rays which are reflected 
 upwards would take no particular direction to the 
 right or to the left, and, therefore, would cause no sen- 
 sible difference upon the vertical sides of the mutules, 
 but would reflect most light upon the horizontal or 
 under sides, &c. 
 
 What has now been said of mouldings in shade 
 having projectures from them, or of the recessed parts 
 of any object, will apply to ornaments in shade which 
 are deeply relieved ; for their recessed parts, according 
 to the foregoing observations, will be deprived of reflec- 
 tion by the more prominent parts of them ; they will, 
 therefore, be darkest in their receding parts, and light- 
 est on the prominent parts. 
 
 Observations on the Shades of Projectures from 
 Buildings, or from any other plain Surface which 
 is made of light Materials. 
 
 If there is any vertical plane, and if a rectangular 
 prism is attached to that plane, having two of its 
 sides parallel to the plane, — and, consequently, the 
 other two sides perpendiciilar to it, — then, if the sun- 
 shine on the plane be on either side of the prism, the 
 other opposite side of the prism will cause a shadow 
 to be projected from its edge upon the plane ; and if 
 the shadow upon the plane be of ^o considerable 
 breadth, and if the plane be extended at any consid- 
 erable distance beyond the shadow, then the lightest 
 part of the plane on which the rays fall will reflect 
 a great part of the rays towards the prism ; but as 
 these reflected rays will not fall upon the shadow, it 
 will be deprived of reflection ; but as the side of the 
 prism which projects the shadow is opposed to the 
 reflected rays, that side of the prism will receive a 
 strong reflection, which will cause it to appear much 
 lighter than the shadow it throws on the plane ; but 
 if the shadow be projected farther on the plane, it will 
 diminish the reflecting surface behind the prism, and 
 will also cause the reflecting surface to be at a gi'catcr 
 distance from the side of the prism, and, consequent- 
 ly, will receive less reflection from the plane ; and, in 
 general, the reflection on the prism will be continually 
 diminished, according as the shadow on the plane is 
 increased, till at last there will be no difference be- 
 tween the shadow on the plane and the side of the 
 
Pl.l'.-J 
 
 •swM)mv^ 
 
 M N 
 
 O V K. 
 
 
l".-l- 
 
 ::?y>?TSi 
 
SHADOWS. 
 
 77 
 
 prism which projects that shadow ; and if the plane 
 be entirely deprived of light, by the extensive breadth 
 of the shadow, the side of the prism will in general 
 be darker than the shadow on the plane : but this 
 will depend very much on the situation of other 
 objects. 
 
 A building consisting of light-colored materials, 
 having a break in the front which projects a shadow 
 on the building, at a small distance from the break, 
 will, for the reason before mentioned, be much lighter 
 on the side of the break than the shadow projected 
 by it on the building behind it ; also, columns which 
 are attached to a wall will project a darker shadow 
 on the wall than any part of the columns which 
 throw the shadow, provided that the shadow is not 
 any considerable distance from the column ; for, ac- 
 cording to the above observations, the broader the 
 shadow, the less the column will appear to be relieved 
 from it. 
 
 Observations on the light Side of the Prism, and the 
 Effect that a Reflection from the Horizon and from 
 the Object will have on the Plane behind the Prism. 
 
 The rays of the sun being reflected from the hori- 
 zon in all directions, the projecture of the prism will 
 prevent a part of the reflected rays from proceeding 
 to the plane behind the prism, and, consequently, the 
 plane would be something darker than the face of 
 the prism which is parallel to it ; but the side of the 
 prism adjoining to the plane will throw a reflection 
 upon the plane, and, therefore, it would be difficult to 
 perceive the difference between the face of the prism 
 and the plane parallel behind the prism. As to the 
 difference of light between the side of the prism, 
 which is perpendicular to the plane, and the plane, it 
 will very much depend on the situation of the lumi- 
 nary ; for if the luminary is in a plane equally in- 
 clined to both, there will be nearly the same degree 
 of light on each ; for very little difference will arise 
 from the reflection, except the luminary is more in- 
 clined to one surface than another; and then that 
 surface will be darker than the other, accordmg to the 
 obliquity of the rays of the sun on that surface. 
 
 PROBLEM I. 
 Plate 24. 
 
 Given the ichnography and elevation of a base 
 and capital, and the seat of the sun's rays 
 
 on the ichnography, and on the elevation ; 
 to project the shadows caused by the several 
 parts of itself, and the line of shade upon 
 the base. 
 
 Imagine the object to be sliced, or cut, by as many 
 planes, parallel to the axes of the columns,* and to 
 the sun's rays, as may be thought convenient for the 
 purpose : then it is plain, if a ray of light enter any 
 of those planes, that every part of the ray ^vill be in 
 that plane, and that the projecting parts upon the 
 edges of these planes will withhold the rays from a 
 part of the edge of the plane ; and the lowest point 
 of that part will give the edge or projection of the 
 shadow of the part which throws the shadow : then, 
 if a sufficient number of these points are found, a 
 line drawn through ihern, with a steady hand, will 
 give the shadow ; the line of shade will be found by 
 drawing lines to touch the several sections parallel to 
 the seat of the sun's rays on the elevation ; and a 
 line being drawn through the points of contact of 
 the sections, will give the line of shade. 
 
 Let H I K be the ichnography of the abacus ; 
 H S K the ichnography of the ovolo ; and M P L 
 that of the astragal ; the lines G Y, F X, E W, D V, 
 C U, B T, and A S are lines drawn parallel to the 
 ichnography, cutting the front I K, of the abacus, and 
 from the seats on the ichnography, and the several 
 seats on the elevation, the shadows may be described, 
 as is shown in the elevation : then lines are drawn to 
 touch the most prominent parts of those sections ; 
 and the places where they cut the other parts of the 
 sections will be the projections of the several points 
 as before, and a line being drawn through these points 
 will give the shadow. 
 
 The part G F E is the shadow from the abacus, and 
 D C B the shadow from the ovolo ; thus the point g in 
 the elevation is the shadow of P ; / is the shadow of 
 N, and E the shadow of m ; and the shadow of the 
 other part of the abacus would be where the dotted 
 curved line is represented ; but as the sun shines on 
 the ovolo, in the middle of the abacus, it will throw 
 the shadow lower than the dotted lines. This will 
 be found by drawing lines to touch the several sec- 
 tions, which will give the points B, C, D. 
 
 * It is not absolutely necessary to suppose the plane parallel to 
 the axis of the column, as in this problem ; but the sections formed 
 by planes in this position are more easily found than in any other, 
 for Tvhich reason I prefer the above position of planes. 
 
78 
 
 SHADOWS, 
 
 Note. — That the line of shade on the torus might have been 
 found in a very different manner than is 8ho>vn ia this example, 
 may be seen by the circular ring, plate 19. 
 
 Much after the same manner may the shadow and 
 lines of shade be found on the attic base, as is shown 
 in plate 24. 
 
 PEOBLEM II. 
 Plate 35. 
 
 Fig. 1. To find the shadow of a cylindrical 
 recess in a wall, whose axis is perpendicular 
 to the plane of the wall ; having the seat of the 
 sun's rays on the ichnography and elevation. 
 
 Let Fig. 1 be the elevation of the wall, and C D 
 the diameter of the cyUndrical recess ; and let E F G H 
 be the ichnography ; bisect C D at a ; draw A a per- 
 pendicular to E H, cutting it at A ; through A draw 
 A B parallel to the seat of the sun's rays on the ich- 
 nography, cutting F G at B ; through B draw B b 
 parallel to A. a; and through a draw a b parallel to 
 the seat on the elevation, cutting B Z> at i ; then on 
 B as a centre, with one half of C D, describe a part 
 of a circle, as is shown by the dark line, and it will 
 be the edge of the shadow. 
 
 Much in the same manner may the shadow of a 
 recess, which has a back parallel to the plane of the 
 wall, be found, as is shown at Fig. 2. 
 
 PROBLEM III. 
 
 Fig. 3. To find the shadow of a recess con- 
 structed as in Fig. 2, when the sides of the 
 ichnography are inclined to the intersection 
 of the two planes of the ichnography and 
 orthography given, the intci-section of a num- 
 ber of planes passing through the luminary 
 perpendicular to the plane of the elevation. 
 
 Let Z 6, W Y, T V, and Q S be the intersection 
 uf as many planes passing through the sun perpen- 
 dicular to the elevation, and let Q, R be the projec- 
 tion of one of the sun's rays on that plane ; also, let 
 H I be the scat of the sun on the ichnography, cut- 
 ting the back F G of the elevation at I ; from I draw 
 I N perpendicular to I d, the common intersection of 
 the ichnography and orthography; from M, draw 
 M N parallel to Q R, cutting I N at N ; tlu-ough N 
 draw N O parallel to M U ; on O as a centre, and 
 with the distance O N, describe the arc N R, cuttijig 
 
 the side of the recess at R ; through the points S, V, 
 Y, b, draw S R, V U, Y X, and B a, parallel to I d; 
 and through the points Q, T, W, Z, draw the lines 
 Q R, T V, W X, and Z a, cutting the lines S R, 
 V U, Y X, and B a, at the points U, X, a; then 
 through the points R, U, X, a, draw the curve 
 R U X a, and the line I N R U X a will be the 
 edge of the shadow required. 
 
 PROBLEM IV. 
 
 Fig. 4. To find the shadow of a hemisi^here 
 niche ; given the seat and altitude of the 
 sun's rays on the elevation. 
 
 Let I N, G M, E L, and C O be liiies parallel to 
 the seat of the sun's rays ; and on these hues, as 
 diameters, describe semicircles I K N, G H M, and 
 E F L ; draw the line A B, bisecting O C ; from any 
 of the points C, E, G, I, as C, make the angle O C I) 
 equal to the sun's altitude, cutting the side of the 
 niche at D ; through the other points E, G, I, draw 
 E F, G H, and I K, parallel to C D, cutting the semi- 
 curcles E F G, G H M, and I K N, at the points 
 F H K ; through the points D, F, H, K, draw lines 
 D rf, F /, H //, and K k, perpendicular to the diam- 
 eters, cutting them at the points d, f, h, k; and 
 through the points A k, h, /, d, draw a curve, which 
 will be the edge of one half of the shadow, from 
 which the other half may be drawn, as is shown 
 by the figure ; and this will give the shadow com- 
 plete. 
 
 OBSERVATIONS. 
 
 I have given one example of the cflect of light and 
 shade on mouldings of different curvature : I shall 
 endeavor to show the effect of light and shade also 
 on many other examples, especially on the five orders 
 of Architectiue. 
 
 From what has been said on this subject, many 
 practical and useful rules in shadowing may be de- 
 duced ; but as I have far exceeded the bounds first 
 assigned for this part, I must end with observing, 
 that, from a consideration of the foregoing examples, 
 the shadows of all objects, however complicated, may 
 be found, as every object may be considered as com- 
 pounded of prisms, cylinders, spheres, and annuluses ; 
 

 F/<i.2. 
 
 
 '-'" ^u:^--^ 
 
 
 /C ^ ^^ 
 
 
 il\\ 
 
 
 
 
 1 
 
 ■'' z, 
 
 ' ] 
 
 / 
 
 
 1 \ 
 
 / 
 
 
 \ 1 
 
 f' 
 
 
 
 
 
 / 
 
 
 
 
 1 / 
 
 / 
 
 
 
 
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 / 
 
 
 
 
 ■ / -■ 
 
 ' 
 
 
 
 
 1 /-' 
 
 
 
 
 
 U' 
 
 
 
 
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 \ 
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 F 
 
 
 
 
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 A 
 
 H 
 
MOULDINGS. 
 
 79 
 
 therefore, each part being projected separately, ac- 
 cording to the rules for its particular kind of figure, 
 the projection of all the shadows in that object will 
 be completed. 
 
 Although I have given correct methods for shad- 
 owing, I have no reason to think that the artist will 
 always be at the trouble to project his shadows, for 
 as drawings, in general, are shadowed to an angle of 
 forty-five degrees, and as I have made choice of that 
 angle, he will still find these examples to be his only 
 guide in practice, as all the forms will be sufficiently 
 
 near when copied by the eye and drawn by the hand 
 of a judicious artist. 
 
 Note. — The treatise on shadows, like the preceding, has not been 
 changed, but has been inserted in the form and manner in which 
 it came from the author's pen. "Wc should have been pleased to 
 have inserted a few plates, to elucidate more fully the effect of light 
 and shade upon different objects ; but as this could not be done with- 
 out swelling our volume to a much larger extent than was at first 
 designed, we have given the original as it was in the previous edi- 
 tions. For those who may wish for a more extensive knowledge of 
 shadows, we would refer them to Gwilt's Shades and Shadows, as 
 being one of the clearest and most comprehensive works on the 
 subject with which we have ever met. — Editoks. 
 
 MOULDINGS. 
 
 Although, as observed in the Introduction of this work, (to which 
 the student is referred,) the shaft of a column may not admit of any 
 ornament on its body, yet in the base and capital various ornamen- 
 tal parts are introduced, which are called mouldings, because they 
 are always of the same shape, as if they proceeded from the same 
 mould or form. Mouldings are generally di-\-ided into Grecian and 
 Roman, with reference to the existing remains of the architecture 
 of those nations. The difference consists in this, that the Romans 
 usually employed segments of circles in their ornaments, while the 
 Greeks often introduced parts of an ellipsis, or some other section 
 of a cone, varying from the circle. 
 
 The regular mouldings are variously disposed in different orders, 
 and may reasonably be supposed to have had their origin in the in- 
 genuity of man rather than in any essential necessary law in nature 
 or art. The annexed figure represents their form and character. 
 
 ~r 
 
 The fillet, listel, annulet, or square. 
 
 Astragal, or bead. 
 
 Torus, or tore. 
 
 Scotia, trochilus, mouth, or casement. 
 
 Echinus, ovolo, or quarter round. 
 
 Grecian echinus. 
 
 Inverted cj-ma, talon, or ogee. 
 
 C)'ma recta, or cymatium. 
 
 Cavetto, or hollow. 
 
 Of these, the Roman ovolo and cavetto are never found in Gre- 
 cian architecture, nor the Greek echinus in that of the Roman ■ the 
 rest they possess in common. 
 
 DEFINITIONS. 
 
 1. Mouldings are figures composed of various 
 curves and straight lines. 
 
 K the mouldings are only composed of parts of a 
 cu-cle and straight lines, they are called Roman, be- 
 cause the Romans, in their buildings, seldom or 
 never employed any other curve for mouldings than 
 that of a circle ; but if a moulding be made part of 
 an ellipsis, or a parabola, or a hyperbola, the mould- 
 ings are then in the Grecian taste. 
 
 Corollary. — Hence it appears that mouldings in 
 the Greek taste are of a much greater variety than 
 those of the Roman, where only parts of circles are 
 concerned. 
 
 Mouldings have various names, according to the 
 manner in which they are curved. 
 
 2. The straight-lined part under or above a mould- 
 ing, in general, is called a fillet. 
 
 3. K the contour of the moulding be convex, and 
 a part of a circle, equal to or less than a quadrant, 
 then the moulding is called a Roman ovolo, or an 
 echinus, such as Fig. B, plate 26. 
 
 4. If the contour of the moidding be concave, and 
 equal to or less than a quadrant, it is called a cavetto 
 or hollow, such as Fig. D, plate 26. 
 
 Corollary. — Hence, a cavetto is just the reverse of 
 an ovolo. 
 
80 
 
 MOULDINGS. 
 
 5. A bead is a moulding, whose contour is simply 
 a convex semicircle. 
 
 6. If the contour be convex, and a complete semi- 
 circle or a semi-ellipsis, having a fillet above or below 
 1 he moulding, it is called a torus, as Fig. A, plate 26. 
 
 Corollary. — Hence, a torus is a bead with a fillet, 
 and is more particularly distinguished in an assem- 
 blage of mouldings from a bead, by its convex part 
 being much greater. 
 
 7. If the contour of a moulding be a concave semi- 
 ellipsis, it is called a scotia, as Fig. 2, No. 2, plate 28. 
 
 8. If the contour be convex, and not made of any 
 part of a circle, but of some other of the conic sec- 
 tions, having a small bending inwards towards the 
 to]j, the moulding is called a Grecian ovolo or echi- 
 7ms, such as Fig. 1, Nos. 1, 3, 3, 4; Fig. 4, Nos. 1, 2, 
 and 3, plate 29. 
 
 9. If the contour be partly concave and partly 
 convex, the moulding in general is called a cimatium, 
 such as Fig. 2, Nos. 1 and 2 ; Fig. 8, Nos. 1 and 2, 
 plate 29. 
 
 10. If the concave parts of the curve project be- 
 yond the convex part, the cimatium is called a cima 
 recta ; such as Fig. 2, Nos. 1, 2, and 3, plate 29. 
 
 11. If the convex part project beyond the con- 
 cave, the cimatium is called a cima reversa or ogee, 
 as Fig. 3, Nos. 1, 2, and 3, plate 28. 
 
 12. The bending or turning inwards of a small 
 part of the convex curve of a Grecian moulding is, 
 by workmen, called a quirk. 
 
 ROMAN MOULDINGS. 
 
 Plate 26. 
 
 To describe an ovolo in the Roman taste ; the 
 projections at a and b being given at each 
 extreme of the curve. 
 
 Figs. A, B, and C. Take the height of the mould- 
 ing ; on the points a and b, as centres, describe an arc 
 at c ; on c, as a centre, with the radius c a or c ft, 
 describe the arc a b, and it will be the contour of the 
 moulding required. 
 
 To describe a cavetto, hanng the extremes of 
 the curve. 
 Fig. D. The cavetto is described in the same man- 
 ner, but on the opposite side. 
 
 To describe a hollow, to touch with two straight 
 lines, b d and d a, one of them at a given 
 point a. 
 
 Figs. E and F. Let d be the point of their meet- 
 ing; make d b on the other line equal to da; from 
 the points a and b draw perpendiculars to each of 
 the lines d b and d a, meeting at c ; on c, as a centre, 
 with the radius c ft or c a, describe an arc ft a, and it 
 is done. 
 
 To describe a cima recta, the projections at a 
 and b being given. 
 
 Fig. G. Join « ft; bisect it at e; then on the 
 points a and ft describe arcs meeting each other on 
 the opposite sides at c and d; on the points c and d, 
 with the same radius, describe the opposite curves 
 a e and e d, and it is done. 
 
 Fig. H. The cima reversa is described in the same 
 manner, but in an opposite direction. 
 
 To describe a torus. 
 
 Bisect the diameter at a ; on it, with the 
 radius, describe a semicircle, and it is done. 
 
 Fig. I. 
 
 Fig. J is a semi-hollow. 
 Fig. K is a bed mould. 
 Fig. L is an ogee and bead. 
 
 GRECIAN MOULDINGS, COMPARED WITH THOSE OF 
 THE ROMAN, TO SHOW THE DIFFERENCE OF THEIR 
 FORM AND APPLICATION. 
 
 L Of a Bead. — This moulding is similar in both 
 Greek and Roman architecture. 
 
 II. Of the Torus. — The torus in most cases is 
 similar to a bead : it is always so in Roman archi- 
 tecture, but not always in Grecian, as may be seen 
 in various examples where the contour of the mould- 
 ing is elliptical. The bases of the columns of the 
 temple of Minerva Polias, and also the bases of the 
 columns on the monument of Lysicrates, are in- 
 stances of the elliptical forms of toruscs. 
 
 III. Of the Ovolo, or Echinus. — The Greek ovolo 
 differs greatly from that of the Roman : its contour 
 is generally a part of the ellipsis ; in some cases it is 
 hyperbolical, and even in some a straight line ; the 
 elliptical ovolo is always used in cornices, architraves, 
 and likewise in all mouldings projecting from plain 
 surfaces. It is also to be met with in the capitals of 
 columns. 
 
 Of such forms are the echinus of the capitals of 
 
I'l . Hi 
 
 J3©(iffli\RI EQ®iyiL©[ira©3 
 
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 (i 
 
 
 
 A 
 
 
 
 
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 "f 
 
 
 Vf 
 
 
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 ^ 
 
 / 
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 X 
 
 
 c 
 
 L. . " 
 
 
MOULDINGS. 
 
 81 
 
 the Doric portico at Athens, the temple at Corintii, 
 and the temple at Poestum, in Italy, which are all 
 elliptical ; but the hyperbolical form is oftcner to be 
 met with in the capitals of Athenian buildings than 
 any other. 
 
 Of such arc the echinus of the capitals of the 
 temples of Rlinerva and Theseus, and also the capi- 
 tals of the columns of the Prophylea, or gi-and en- 
 trance into the citadel. These are all Athenian 
 buildings, which were erected during the administra- 
 tion of Pericles ; and the portico of Philip, King of 
 Macedon, is an instance in which the echinus is in a 
 straight line. 
 
 Li Roman architecture, the echinus is always 
 some part of a circle, never exceeding a quadrant, 
 but often less. 
 
 IV. Of the Cavctlo. — The cavetto is the same 
 both in Roman and Grecian architecture, except in 
 its application. There is not an instance to be met 
 with in Greece * where the crown moulding is a ca- 
 vetto, but there are many in the Roman. 
 
 V. 0/ the Doric Cimatiiun. — This moidding is 
 constantly used in Greek buildings, under the fillet 
 of a finishing or crown moulding; but in Roman 
 buildings, there are no instances whatever of any 
 such moulding. 
 
 VI. Of the Cima Recta. — This moulding is nearly 
 of the same form, both in the Grecian and Roman 
 arcliitecture, and is also applied for the same pur- 
 pose in both. 
 
 VII. Of the Cima Reversa. — This moulding is 
 nearly similar in the Grecian and Roman architec- 
 ture, and is, in general, applied under the fiUet of the 
 crown moulding of the cornices of Roman buildings ; 
 but is never so apjDlied in Greek buildings, one in- 
 stance excepted, which is the Portico of PliUip, King 
 of Macedon. 
 
 THE EFFECT OF GRECIAN MOrLDINGS, COJIPAHED 
 WITH THE ROMAN OF THE SAME KIND. 
 
 I. Of the Ovolo. — The bending or turning in- 
 wards of the upper edge of the Grecian ovolo 
 causes, when the sun shines on its surface, a beauti- 
 ful variety of light and shade, which gi-catly relieves 
 it fi-om plane surfaces ; and if it be entirely in shadow, 
 but receive a reflected light, the bending or turning 
 
 * There are some out of Greece ; but of these there are few in- 
 stances -which may not be looked on as deviations from the estab- 
 lished methods that ■were used bv the Greeks. 
 
 11 
 
 inwards at the top will cause it to contain a great 
 quantity of shade in that ])lacc, but softened down- 
 wards round the moulding to the under edge. 
 
 In the Roman ovolo there is no turning inwards ; • 
 at the top, therefore, Avhcn the sun shines on its sur- 
 face, it will not be so bright on its upper edge as the 
 Grecian ovolo ; nor will it cause so beautiful a line 
 of distinction from other mouldings which it is com- 
 bined with when it is in shadow, and when lishtcd 
 by reflection. 
 
 II. Of the Cima Reversa. — Li the Greek cima re- 
 versa, the turning in of its upper edge, and the turn- 
 ing out of its under edge, will cause it, when the sun 
 shines, to be very bright on these edges, which will 
 greatly relieve it from other perpendicular surfaces 
 when combined together ; and when it is in shadow, 
 and lighted by reflection, the inclination of the upper 
 and under edges will also make a sti-ong line of dis- 
 tinction on both edges, between it and other mould- 
 ings or planes connected with it ; whereas the upper 
 and under edges of the Roman cima reversa f being 
 perpendicular to the horizon, the lightest place on its 
 surface wiU not be brighter than a perpendicular 
 plane surface, nor will it be better relieved in shad- 
 ows than perpendicular plane sui'faces also in shadow. 
 
 THE EFFECT OF GRECIAN MOULDINGS, COJIPARED 
 WITH ROMAN MOULDINGS OF A DIFFERENT KIND, 
 BUT IN SIMILAR SITUATIONS. 
 
 I. Of the Greek Ovolo, compared with the Roman 
 Cavetto, ivhen used as finishing Mouldings. 
 
 The upper moifldings, in all the remains of anti- 
 quity, are either entirely destroyed or much defaced. 
 It is certain, that if ovolos, which are sti-ong moiddings, 
 had been employed instead of cavettos, \ many of 
 them would have been almost entire ; and as the de- 
 grees of light and shade on the surface of the ovolo, 
 
 * That is to say, the upper edge of the moulding does not recede 
 &om a plane touching its surface, and perpendicular to the horizon. 
 
 t There are some instances in Roman buildings where the cima 
 reversa is turned inwards at the top, and outwards at the bottom ; 
 but this seldom occurs, except there is not sufficient projection to 
 its height. 
 
 X Some authors say, that the cima recta and cavetto were always 
 used as finishing mouldings ; but it is quite the reverse ; for in the 
 antique buildings now remaining in Greece there is not a single 
 instance where a cavetto is used for the upper member of a cornice ; 
 but in Doric buildings, the cornice always finishes with an ovolo ; 
 and in buildings of the Ionic and Corinthian orders, they are fin- 
 ished with cima rectas. 
 
82 
 
 MOULDINGS. 
 
 whether firom sunshine or from any other light, is 
 beautiful and soft, the shadow of the cavetto from 
 sunshine is very hard, and will not contain so great 
 a variety of light and shade on its surface ; it will, 
 therefore, be less pleasing to the eye. 
 
 II. The Doric Cimatium used hj the Grecians under 
 the Fillet of the Croicn Moidding, compared tvilh 
 the Cima Reversa in the same Situation. 
 The front of the Doric cimatium is a convex ellipti- 
 cal curve, and is sunk at the upper edge in the manner 
 of a Grecian ovolo ; therefore, tlie light and shade on 
 its front will be nearly similar to an ovolo ; and as 
 the sinking upwards behind the front will cause it 
 to contain a quantity of shade, — which will form a 
 line of separation from the corona, and, consequent- 
 ly, make it appear more distinct at a distance, but 
 the Roman cima reversa, being so very flat, would 
 not be well relieved, — its profile would be lost en- 
 tirely at a distance. 
 
 MODERN MOULDINGS. 
 
 I have given several modern designs for mould- 
 ings, not that in my own opinion they are more 
 tasteful than the Grecian or Roman, but that by com- 
 bining them it affords a greater variety ; and, as some 
 are fond of new things, they may be preferred. 
 Plate 27. 
 
 A is a cima recta. B is a cima reversa, or ogee. 
 C is a bed mould. These differ from the Roman 
 only in their curves being more graceful, but are 
 formed on the same principle. 
 
 D, E, F, G, II, I, J, K, and L are formed on the 
 principle of the Grecian, with a slight alteration in 
 their curves. 
 
 GRECIAN MOULDINGS. 
 Plate 29. 
 
 To describe the Grecian echinus or ovolo ; the 
 tangent A B, at the bottom, the point of con- 
 tact A, and the greatest projection of the 
 moulding at C being given. 
 
 Fig. 4, No. 2. From A, draw A D E perpendicu- 
 
 lar ; tlirough C draw C D parallel to the tangent 
 B A, cutting A E at D ; make D E equal to A D 
 then v.'ill D be the centre of an ellipsis, and C D and 
 D A will be two semi-conjugate diameters, from 
 wliich the ellipsis may be described by plate 6, Ge- 
 ometry. 
 
 Fig. 4, No. 1. This figure is described in the same 
 manner, and shows a greater projection, the tangent 
 being also taken in a higher position. 
 
 The same things being given, to describe the 
 moulding nearly, when the point of contact A 
 is at the extremity of the transverse axis. 
 
 Fig. 4, No. 3. From A, draw A D E perpendicular 
 to the tangent B A ; parallel to it draw C G, cutting 
 the tangent A B at G ; also, through C draw C D 
 parallel to the tangent A B, cutting A D E at D, the 
 centre of the ellipsis, for which D C and D A are the 
 semi-transverse and semi-conjugate axis, and pro- 
 ceed as before. 
 
 Plate 2S. 
 
 The semi-transverse and semi-conjugate axis 
 being given, to describe the moulding. 
 
 Fig. 1, Nos. 2 and 3. Proceed as in plate 6, Ge- 
 ometry, and you will have the contour of the mould- 
 ing required. 
 
 To describe the cima recta, the perpendicular 
 height, II L, being given, and its projection, 
 L I. 
 
 Fig. 2, No. 1. Complete the rectangle I L H F, 
 and divide the whole rectangle into four equal rec- 
 tangles ; then inscribe the concave quadrant of an 
 ellipsis in the rectangle I K C B, and a convex quad- 
 rant in the rectangle C G H D, and it is done. 
 
 To describe a cima reversa, the point A being 
 nearly the greatest projection at the top ; D 
 the extremity of the curve at the bottom ; 
 and D C a line parallel to a tangent, at the 
 point of junction of the opposite curve. 
 
 Fig. 3, No. 3. Draw A C at right angles to C D, 
 cutting C D at C, and complete the rectangle A C D E ; 
 then proceed as before, but in a contrary direction, 
 and you will have tlie contour required. 
 
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THE ORDERS. 
 
 83 
 
 To describe an echinus having the depth of 
 the moulding C D, the greatest projection 
 at D, and to be quirked at the top and 
 bottom. 
 Fig. 2, No. 3. Complete the rectangle C B A, and 
 
 proceed as in plate 6, Geometry. 
 
 To describe a scotia. 
 Fig. 2, No. 2. Join the ends of each fillet by the 
 right line A B ; bisect A B at D ; through D draw 
 C D E parallel to the fillets, and make C D and D E 
 equal to the depth of the seotia ; then will A B be a 
 diameter of an ellipsis, and C E its conjugate. Pro- 
 ceed as in plate 6, Geometry. 
 
 How to describe Grecian mouldings, whether 
 elliptical, parabolical, or hyperbolical ; the 
 greatest projection at B being given, and 
 the tangent C F at F, the bottom of the 
 moulding. 
 Fig. 4, Nos. 1, 2, and 3. Draw G F a continuation 
 
 of the upper side of the under fillet ; through B draw 
 
 B G perpendicular to B F, cutting it at G, and the 
 tangent F C at the pohit C ; also, through B draw 
 B E parallel to G F ; and through F draw F D E A 
 parallel to G B, cutting B E at E ; make E A equal 
 to E F, E D equal to C G, and join B D ; then divide 
 each of the lines B D and B C into a like number 
 of equal parts ; from the point A., and through the 
 points 1, 2, 3, 4, in B C, draw lines, cutting the former, 
 which will give the points in the curve. 
 
 If the point C, where the tangent cuts the line B G, 
 be less than one half of B G, from G the moulding 
 will be elliptical, as in Fig. 4, No. 2. 
 
 K G C be one half of B G, then the moulding is 
 parabolical, as in Fig. 4, No. 1. 
 
 If G C be gi-eater than half of B G, then the mould- 
 ing is hyperboLieal, as in Fig. 4, No. 3. 
 
 By this means you may make a moulding to any 
 form you please, whether flat or round. 
 
 [On plate 30 will be found four designs for archi- 
 traves, for the finish of doors and windows, full size. 
 These are substituted for plates 83 and 84 of the last 
 edition, as being more in keeping with the taste of 
 the times, &c. — Editors.] 
 
 THE OEDERS. 
 
 The term order seems to sustain the same relation 
 to architecture that the term harmony does to music, 
 or the ancient term ordonnancc to painting. It is, in 
 fact, no more nor less than an assemblage of parts 
 and mouldings, so disposed as to give an effect 
 at once pleasing to the eye, and proportioned and 
 adapted to the ofiice each has to perform. 
 
 Vitruvius, who was nearly, if not the first writer 
 on architecture who flourished in the first century 
 after the birth of Christ, expresses the idea as fol- 
 lows : " It is an apt and regular disposition of the 
 members of a work separately, and a comparison of 
 the universal proportion with symmetry." This, in 
 his work, (chapter 2d,) he calls ordonnancc. Scamozzi, 
 the son of an architect, and himself one of the old 
 masters, the rival of Palladio, and who after the death 
 of that artist, in 1580, had no competitor, is, we be- 
 lieve, the first of the ancient \%Titers that has given 
 
 us what may be termed the description of an order. 
 He observes in his book, (2d chapter, 2d part,) " that 
 it is a kind of excellency which infinitely adds to the 
 shape and beauty of buildings, sacred or profane." 
 He seems to have attempted to convey the same idea 
 as the author before quoted, which idea is compre- 
 hended in the terms propriety and harmony. Having 
 now given the idea which the ancients would seem 
 to have us entertain by the Latin word order, we wUl 
 proceed to illustrate more fully the composition and 
 use of the orders. First, then, an order is composed 
 of two parts, viz., the column and the entablature ; 
 these are again each divided into three other parts, 
 which parts are composed of an assemblage of mould- 
 ings, each respectively proportioned and adapted to 
 the order of which it is a part. The parts of the entab- 
 lature are called the architrave, frieze, and cornice ; 
 those of the column are the base, shaft, and capital, as 
 
84 
 
 THE ORDERS. 
 
 may be seen on plate 50. These are again subdivided 
 into other parts, as will be seen by the description 
 of the respective orders. The species of orders are 
 five in number — the Tuscan, Doric, Ionic, Corin- 
 thian, and Composite ; each is a composition peculiar 
 to itself, and is calculated to produce the expression 
 it is intended to possess, viz., strength, grace, ele- 
 gance, and richness. The orders above named rightly 
 understood, and correctly applied, are the foundation 
 upon which architecture has long rested as an art. 
 The oldest of these is the Doric, the next the Ionic, 
 and the last the Corinthian. The Tuscan is said to 
 have been invented by the inhabitants of Tuscany ; 
 and Vitruvius has first given it a name and placed 
 it in his book, a copy of which is shown on page 31 ; 
 but he docs not inform us of a single building on 
 which it has been employed, and as no examples 
 exist to warrant the belief of its frequent use in his 
 day, we are led to suppose that its rustic plainness 
 did not suit the Roman taste of his time. It has, 
 however, received the approbation of the principal 
 masters who have succeeded him, and is now ranked 
 with the regular orders. The Composite is a Roman 
 invention, and has been termed by Sii' Henry Wotton, 
 in his Parallel of Ancient Architecture with the Mod- 
 ern, the compounded order. It is composed of parts 
 of the other orders, but principally of the Ionic and 
 Corinthian. The proportion of the parts of the or- 
 ders are as various as the examples — no two authors 
 agreeing. In the examples given, the parts are fig- 
 ured, as will be seen ; and the proportion assigned to 
 each, as the example or author has directed explana- 
 tions of the orders more in detail, will be found at- 
 tached to them under their respective heads. — Eds. 
 
 TUSCAN ORDER. 
 
 The Komans added the Tuscan, or Etruscan, to the tlncc Grecian 
 orders, as they subsequently did the Composite. The idea of the 
 Tuscan is undoubtedly derived from the Doric order, from ■which it 
 differs, according to the view taken of it by Aldrich, as much as the 
 appearance of an inhabitant of the country does from one of a cit}'. 
 There is extant no ancient specimen of it with an entablature. It is the 
 first of the Italic orders, and is called Tuscan, as having been origi- 
 nally employed by that ancient people, once powerful in Italy. 
 " Vitruvius speaks of it as rustic even to deformit)' ; nor were the 
 later masters more favorable to it, except Palladio." Having no 
 complete exaraide from antique buildings, that which is given in 
 this work is taken from the description by Vitruvius. 
 
 Plate 31. 
 
 From Vitruvius, tvith lite Proporlion of the Parts in 
 Numbers. 
 
 A^'e have no complete example of this order re- 
 maining from antique buildings ; and all that we 
 know of it is from the description by Vitruvius, from 
 which this example is taken, and is, therefore, the only 
 standard. 
 
 The proportions of the parts are exhibited by equal 
 divisions on the plate. 
 
 That celebrated building, St. Paul's, Covent Gar- 
 den, is the only true specimen there is of the Tuscan 
 order in England. It may be adapted with great 
 propriety to market-places, as the simplicity of its 
 parts and the extraordinary projection of the cornice 
 render it suitable for that purpose. 
 
 Fig. 1. Elevation of the order, from Vitruvius. 
 
 Fig. 2. The ichnography of the mutulcs in the 
 cornice. 
 
 Fig. 3. Profile of the upper part of the cornice. 
 
 The column is seven diameters high ; the base and 
 capital are each half a diameter ; the base is divided 
 into two equal parts, one of which is given to the 
 plinth, the other to the torus and fillet ; divide the 
 capital into three equal parts, give one to the hypo- 
 traehelion, one to the ovolo and fillet, and the upper 
 one to the abacus. The mutulcs in the cornice are 
 to project one fourth of the length of the column. 
 
 Fig. 4. A modern example of the Tuscan order, 
 with the proportional measm'es in numbers. 
 
 On plate 32, we have given a design for the regu- 
 lar Tuscan order. No example, except that on plate 
 31, is in any of the previous editions. The design 
 here given is a composition from Chambers and Pal- 
 ladio. In his example of the Tuscan, Chambers has 
 followed Vignola and Serlio, in omitting the break 
 in the architrave, and making it consist of only two 
 members. This, it is acknowledged, is according to 
 the example given us by Vitruvius ; but as liberty 
 has been taken to adapt it to other times, there seems 
 to be no excuse why the method pursued by Palladio 
 should not be entitled to as much attention as that 
 by Vignola. The majority of authors have approved 
 the practice of the former ; in the example we have 
 composed, we have retained the bold and classic pro- 
 portions, as given by Chambers, for the cornice, add- 
 ing to it the architrave by Palladio. The column 
 is according to that given us by Chambers, and it is, 
 we believe, the most approved proportion with which 
 
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THE ORDERS, 
 
 85 
 
 we are acquainted. No. 1, on plate 32, is the order 
 figured to a scale of minutes. No. 2 is the impost 
 and archivolt of the same. — Editors. 
 
 ROMAN DORIC. 
 
 Some architects have maintained that the Doric order h unfit for 
 sacred edifices, by reason of its irregularity. This opinion was held 
 by Tarchesius, Pytheus, and Ilermogenus. The latter, after having 
 prepared marble materials for building a Doric temple, changed the 
 order, and made it Ionic, dedicating it to Bacchus. The Doric or- 
 der, however, is not deficient in grandeur, but an inconvenience 
 arises in the distribution of the triglyplis and lacunaria ; for it is 
 necessary that the triglyphs should bo placed over the middle quar- 
 ters of the columns, .md the metopes, which are between the tri- 
 glyphs, must be as long as high; also, the triglyphs at the angles are 
 placed at the extremities, and not over the middle of the columns ; 
 therefore, the metopes which are next the angular triglyphs will 
 not be square, but longer by half the breadth of a trigljqih. Some, 
 who wish to make the metopes equal, lessen the extreme inter- 
 columniation by half the breadth of the triglyph. However, the 
 metope or the contracting of the intercolumniatiou is a defect. 
 Though the ancients have been observed to neglect exact regularity 
 in Doric buildmgs, it is shown in its proper place how far we ought 
 to follow our masters. 
 
 The front of a Doric temple, where the columns 
 are placed, is divided, if it be terastyle, into twen- 
 tj'-eight parts ; if hexastyle, into forty-four. One of 
 these parts will be the module, which, in Greek, is 
 called Embafcs, and by which all the other parts are 
 proportioned. 
 
 The thickness of the column must be tw^o mod- 
 ules ; the height, with the capital, fourteen ; the 
 height of the capital one module, the breadth two 
 modules and a sixth. The height of the capital is 
 divided into three parts, of which one is given to the 
 abacus, with the cimatium ; another to the echinus, 
 with the annulets ; and the third to the hypotra- 
 chelion. The columns are diminished as described 
 on the plates. 
 
 The height of the epistilium, with the tenia and 
 drops, is one module. The tenia has the seventh of 
 a module, the length of a gvittse under the tenia 
 coinciding with the perpendicular of the triglyphs. 
 Their height with the regula is one sixth of a 
 module. The breadth of the epistilium also answers 
 to the hypotrachelion of the column. 
 
 On the epistilium are placed the triglyphs with 
 the metopes, having the height of one module and a 
 
 half, and the breadth in front one module. They 
 must be so distributed that they may be over the 
 centre of tlie columns at the angles, and two be- 
 tween each column. The breadth of the triglyphs 
 is divided into twelve equal parts, of which tlie 
 breadth of the femur in the middle will be two parts ; 
 then a channel is cut on each side of the femur, the 
 breadth of each channel being equal to two parts. 
 Next to the channels two other femurs are left, one 
 on the right and the other on the left, each equal to 
 the breadth of the middle femur, or two parts ; then 
 a part will remain next to the edge of each triglyph, 
 which is to be cut away in the form of a semi- 
 channel. On either side of this channels are sunk, 
 as if imprinted by the elbow of a square. To the 
 right and left of these another femur is formed. In 
 the same manner, semi-channels must be sunk at the 
 extremities. The triglyphs being thus disposed, the 
 metopes are as high as long; on the angles, also, the 
 semi-metopes are made half a module in width. 
 
 Thus all the errors arising from the wrong disti-i- 
 bution of the metopes, intcrcolumniations, and lacu- 
 naria will be rectified. 
 
 The capitals of the triglyphs must have one sixth 
 of a module. On these capitals is placed the coro- 
 na, projecting a half and a sixth part of a modiUe, 
 having a Doric cimatium below, and another above. 
 The corona, with the cimatiums, are half a module 
 in thickness. In the under part of the corona, per- 
 pendicularly over the ti-iglyphs and metopes, the 
 guttse in the mutules are so distributed that there 
 may be six in length, and three in breadth. The 
 spaces between the metopes being rather broader 
 than the triglyphs, are either left plain, or carved ; 
 and at the edge of the corona a channel is cut, 
 called Scotia; all the remainder, as the tympanum, 
 the cima, and corona, are the same as in the Ionic 
 order. 
 
 Concerning the diminution of the column, accord- 
 ing to Vitruvius, he gave the following rule for all 
 kinds of columns, the Tuscan excepted : — 
 
 The diminution of the top of the column at the 
 hypoh-achelion is thus regulated : If the column be 
 not less than fifteen feet high, the thickness at the 
 bottom is divided into sis parts, and five of these 
 parts are given as the thickness at the top. 
 
 " If the height is from fifteen to twenty feet, the 
 bottom of the shaft is divided into six parts and a 
 half, and five and a half of these parts make the 
 
86 
 
 THE OKDEKS. 
 
 thickness of the column at top ; and if from twenty 
 to thirty feet, the bottom is divided into seven parts, 
 and six of these make the diminution at the top. 
 If it is from thirty to forty feet high ; the bottom 
 thickness is divided into seven parts and a half, of 
 which six and a half is the measure of the diminu- 
 tion at the top. If from forty to fifty feet, it is 
 divided into eight parts, whereof seven will make 
 the thickness of the hypotrachelion at the top of the 
 shaft. And if it is still higher, the same propor- 
 tional method is observed ; for, as a greater height 
 causes them to appear more diminished, they are, 
 therefore, to be corrected by an addition of thickness, 
 beauty being the provmcc of the eye, which, if not 
 satisfied by the due proportion and augmentation of 
 the members, con-ccting apparent deficiencies with 
 proper additions, the aspect will appear coarse and 
 displeasing. 
 
 Plate 33. 
 
 This plate shows the elevation of the Roman 
 Doric, as given by Palladio. 
 Fig. 1. The elevation. 
 Fig. 2. The cornice inverted. 
 Fig. 3. The capital inverted. 
 
 Plate 34. 
 
 Elevation of the Doric Order from the Baths of Bio- 
 clesian, at Rome, with the Proportions in Numbers. 
 
 The cornice of this example is not Doric ; it is too 
 abundant with mouldings, and overcharged with 
 enrichments. 
 
 The disposition of the triglyphs and metopes in 
 the fi-ieze is according to the rules of Vitruvius. 
 
 The capital is not Doric, but of another kind ; nor 
 could this composition be known to have the least 
 resemblance to the Doric order, if the triglyphs in 
 the frieze were omitted. 
 
 Fig. 1. The elevation of this example. 
 
 Fig. 2. A section of the column, showing the 
 flutes. 
 
 ROMAN IONIC, 
 Plate 35, 
 
 Is the Roman Ionic as approved by Chambers, 
 and is inserted to supply the place of plates 56 and 
 57 of the previous edition, which contained the 
 
 example of the Temple of Concord, at Rome. This 
 was a very singular example, which was, perhaps, 
 the best authority the author had for introducing it. 
 The cornice contains mutulcs resembling the Doric, 
 and dentils as in the Ionic. The frieze and archi- 
 trave are plain, with the exception of two breaks, 
 the top one of which contains a cavetto or hol- 
 low. There is no band moulding to separate the 
 firieze from the architrave. The capital is angular, 
 volutcd, and is not without merit ; but the extreme 
 plainness of the space between the cornice and the 
 top of the capital, and the connection between the 
 cornice and frieze, is so inelegant, that the anath- 
 emas of those who would have used it have been 
 called down upon it, and it is now scarcely if ever 
 used. The example given by Chambers is, perhaps, 
 as good as any wc have ; and we have, therefore, in- 
 serted it to complete the Roman orders. Fig. 1 is 
 the order, and figs. 2, 3, and 4 the details of the cap- 
 ital. — Editors. 
 
 CORINTHIAN ORDER. 
 
 The Corinthian order took its rise in the flourishing days of 
 Corinth, a celebrated city commanding the communication of the 
 peninsula of Feloponncsus with the continent of Greece. It is 
 generally regarded by writers on architecture as being more delicate 
 than the Ionic, and is thought to resemble the graceful figure of a 
 virgin. Among the ancients, it had much resemblance to the Ionic. 
 According to Vitruvius, it imitated that order in every part but in 
 the capital of the pillar. In the introduction to this work, we have 
 alluded to the pretty Greek story told of the origin of the capital. 
 Villapandus gives another equally dubious account of its origin ; and 
 Aldrich conjectures as more probable that, as the shaft of a pillar 
 represents the trunk of a tree, so the tree being lopped, and sprout- 
 ing again, furnished the hint for the design of this capital. But, 
 however this may be, wc believe it will be generally conceded that, 
 in attempting too much, this order has deviated firom the true sim- 
 plicity of nature. It marked an age of luxury and magnificence, 
 when pomp and splendor had become the predominant passion, but 
 had not yet extinguished the taste for the sublime and beautiful; 
 and in this, attempts were made to unite these characters. 
 
 DEFINITIONS. 
 
 1. An order which has two annular rows of leaves 
 in the capital, each leaf of the upper row growing 
 between those of the lower row, in such a manner 
 that a leaf of the upper row may be in the middle 
 of each side or face of the capital, — and if between 
 
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THE ORDERS. 
 
 87 
 
 each space of the upper leaves there spring stalks 
 with volutes, two of which meet at the angles of the 
 abacus, and two in the middle of the capital, either 
 touching or interwoven with each other, — a capital 
 so constructed is called Corinthian. 
 
 2. An order wliich has a Corinthian capital, and 
 an Ionic or any other entablature, is called the Corin- 
 thian order. 
 
 Plate 38. 
 
 The Corinthian Order, from the Pantheon, at Rome. 
 
 This example, though plain, is yet beautiful and 
 chaste, and is an excellent model of the order. 
 
 Fig. 1. Elevation of the order in numbers. 
 
 Fig. 2. Section of one quarter of the column next 
 the capital ; also a section of one quarter of the col- 
 umn next the base. 
 
 Fig. 
 
 Elevation of the base of a larger size. 
 
 Plate 37. 
 
 Fig. 1. Is the outline of the leaves and elevation 
 of the capital, from the Pantheon, as shown in 
 plate 38. 
 
 Fig. 2. The capital inverted, showing an angle of 
 the architrave. 
 
 Fig. 3. The elevation of a leaf in the same. 
 
 Fig. 4. The elevation of a leaf in the capital of a 
 column, Ixom the Temple of Jupiter Stator, at Rome. 
 
 Fig. 5. The side elevation of the modiUion, from 
 the Temple of Jupiter. 
 
 Fig. 6. The modillion inverted. 
 
 Plate 36. 
 
 From the three Columns in the Campo Vaccina, sup- 
 posed to be the Remains of the Temple of Jupiter 
 Stator, at Rome. 
 
 The engi'aving exhibited in this plate, of that cel- 
 ebrated example of the remains of Jupiter Stator, is 
 as accurate as any yet published: the capital and 
 entablature are restored from the drawings of an 
 artist, who was so obliging as to favor me with 
 sketches of the ornament which he had from the 
 original. The elegance and beauty of the capital, 
 its graceful form, the grandeur and excellent propor- 
 tion of the entablature, wdth the delicacy of the or- 
 nament, render this one of the most complete exam- 
 ples now existing of the Corinthian order. 
 
 Fiff. 1. Elevation of the order in numbers. 
 
 Fig. 
 
 The cornice inverted, showing the enrich- 
 
 ments of the modillions and mouldings. 
 
 COMPOSITE ORDER. 
 
 The second Italian order, and last of the five orders of architec- 
 ture, is the Composite ; which some -writers have divided into three 
 species, or orders. The first, called the Composite, is composed of 
 the Ionic and Corinthian, " which two esliibit more graces in com- 
 bination than either of them would if joined with the Doric. The 
 Composite is more slender than the Corinthian, and more ornamented 
 with sculpture ; if the latter bears any resemblance to a young maid, 
 the former represents an harlot." 
 
 The second species, as given by Aldiich and Smyth, is " Dorico- 
 lonic ; the only remaining instance of which may be seen at Home, 
 in the ruins of the Temple of Concord. The base of the column is 
 Attico-Ionic, and without a plinth, except in angular pillars. The 
 capital is lonico-Doric, with the volutes projecting, as in the Italian ; 
 the abacus is Corinthian ; the frieze is sculptured, but the larmier 
 is plain. It has a beautiful appearance." 
 
 The third species of Composite is where the column is of one 
 order, and the entablature of another ; for instance, when the col- 
 umn is Corinthian, and the entablature Doric ; in which case, it 
 would, therefore, be very properly termed Dorico-Corinthian. " This 
 is approved of even by Vitruvius ; and, in fact, was introduced into 
 the Temple of Solomon, whose columns were Corinthian, supporting 
 a Doric entablature." 
 
 The Romans first introduced the Composite order into their tri- 
 umphal arches, to show their dominion over the people whom they 
 conquered. 
 
 Of this order we have many examples from the 
 ancients ; but the following is the most celebrated : 
 it is taken from the Arch of Titus, which was executed 
 soon after the destruction of Jerusalem, in order to 
 commemorate that remarkable event. 
 
 Plate 39. 
 
 From the Arch of Titus, at Rome. 
 This most beautiful and elegant example is made 
 choice of as the most proper model for this order. 
 
 TABLE, 
 
 Showing the relative Proportions of Grecian Doric 
 Columns contained in this Work. 
 
 Names of Buildings. 
 
 Colmnns. 
 
 Capital. 
 
 Architrave. 
 
 Frieze, i Cornice. 
 
 Modules. Min. 
 
 Minutes. 
 
 Minutes. 
 
 Minutes. Minutes. 
 
 Portico of Philip, K. of Macedon 
 
 The Temple of Theseus 
 
 The Temple of Minerva 
 
 13 21^ 
 11 12i 
 
 11 4 
 
 12 2i 
 
 4i 
 30J. 
 27^ 
 21f 
 20^ 
 
 38 
 
 50 
 
 43i 
 
 40 
 
 37 
 
 44 
 
 48 
 43i 
 42i 
 35 
 
 25 
 32 
 
 23A 
 
 21 A 
 25 
 
 Found in Asia, near the Tem- ( 
 pie of M inerva Polias \ 
 
88 
 
 PILASTERS, 
 
 PILASTERS. 
 
 Pilasters are, it is believed, a Roman invention, and certainly an 
 improvement. The Greeks cmiiloyed anta; in their temiiles, to re- 
 ceive the architraves -nliere they entered upon the walls of the cell. 
 Tlicsc, though they were, in one direction, of equal diameter with 
 the columns of the front, were in flank extravagantly thin in pro- 
 portion to their height, and neitlier their bases nor capitals bore any 
 resemblance to those of tlie columns they accompanied. The Ro- 
 man artists, disgusted, probably, with the meagre aspect of these 
 antx, and the want of accord in their bases and capitals, substituted 
 pilasters in theii- stead, which, being proportioned and decorated in 
 the same manner mtli the eolumns,-arc certainly more seemly, and 
 preserve the unity of the composition much better. The reader will 
 find some additional, and perhaps not unimportant, remarks iu re- 
 lation to the pilaster in tlie introduction to this work. 
 
 Pilasters differ from columns in their plan only, 
 whicli is square, while that of the column is round. 
 Their bases, capitals, and entablatures have the same 
 parts, with all the same heights and projections, as 
 those of columns ; and they are distinguished in the 
 same manner, by the names of Tuscan, Doric, Ionic, 
 Corinthian, and Composite. Of the two, the col- 
 umn is doubtless most perfect. Nevertheless, there 
 are occasions in which pilasters may be employed 
 with gi-eat propriety ; and some where they are, on 
 various accounts, even preferable to columns. 
 
 If we go back to the origin of things, and consider 
 pilasters, cither as representing the ends of partition 
 walls, or trunks of trees reduced to the diameter of 
 the round trunks which they accompany, but left 
 square for greater strength, the reason for dimin- 
 ishing them will, in either case, be strong and evi- 
 dent. 
 
 It is likewise an error to assert that pilasters are 
 never necessary, but that columns will at all times 
 answer the same end ; for, at the angles of all build- 
 ings, they are evidently necessary, both for solidity 
 and beauty, because the angular support, having a 
 greater weight to bear than any of the rest, ought to 
 be so much the sti-ongcr ; so that its diameter must 
 cither be increased, or its plan altered from a circle 
 to a square. The latter of which is certainly the 
 most reasonable expedient on several accounts, but 
 chiefly as it obviates a very strildng defect, occa- 
 sioned by employing columns at the angles of a 
 building; which is, that the angle of the entablature 
 is left hanging in the air without any support — a 
 sight very disagreeable in some oblique views, and 
 in itself very unsolid. 
 
 It is indeed customary, in porches and other de- 
 tached compositions, to employ columns at the an- 
 gles ; and it is judicious so to do, for, of two defects, 
 the least is to be prcfeiTcd. 
 
 Engaged pilasters are employed in churches, gal- 
 leries, halls, and other interior decorations, to save 
 room, for, as they seldom project beyond the solid of 
 the walls more than fifteen minutes of their diameter, 
 they do not occupy near so much space as engaged 
 columns. They are likewise employed in exterior 
 decorations ; sometimes alone, instead of columns, 
 on account of their being less expensive ; at other 
 times they accompany columns, being placed behind 
 them to support the springing of the architi'avcs ; or 
 on the same line with them, to fortify the angles : 
 they may lilcewise be employed instead of columns, 
 detached to form peristyles and porticoes, but there is 
 no instance of this, that I remember, in all the re- 
 mains of antiquity ; neither has any modern archi- 
 tect, I believe, been so destitute of taste as to put it 
 in practice. 
 
 When pilasters are used alone, as principal in the 
 composition, they should project fifteen minutes of 
 their diameter beyond the walls, which give them a 
 sufficient boldness, and, in the Corinthian and Com- 
 posite orders, is likewise most regular, because the 
 stems of the volutes, and the small leaves in flank 
 of the capital, arc then cut exactly through their mid- 
 dles. But if the cornice of the windows should be 
 continued in the inter-pUaster, as is sometimes usual, 
 or if there should be a cornice to mark the separation 
 between the principal and second story, or large im- 
 posts of arches, the projection must, in such cases, 
 be increased, provided it is not otherwise sufficient to 
 stop the most prominent parts of these decorations ; 
 it being very disagreeable to see several of the upper- 
 most mouldings of an impost or cornice cut away 
 perpendicularly, in order to make room for the pilas- 
 ter, Avhile the cornice or impost on each side projects 
 considerably beyond it. Mutilations are, on all oc- 
 casions, studiously to be avoided, as being destructive 
 of perfection, and strong indications cither of inatten- 
 tion or ignorance in the composer. 
 
 Where pilasters are placed behind columns, and 
 very near them, they need not project above seven 
 and one half minutes of their diameter, or even less, 
 excepting there should be imposts or continued cor- 
 nices in the inter-pilaster ; in which case, what has 
 been said above must be attended to. But if they 
 
PILASTERS. 
 
 89 
 
 be far behind the columns, as in porticoes, porches, 
 and peristyles, they should project ten minutes of 
 their diameter at least ; and when they are on a line 
 with the columns, their projection is to be regulated 
 by that of the columns ; and, consequently, it can 
 never be less than a semi-diameter, even when the 
 columns are engaged as much as possible. This 
 extraordinary projection, however, will occasion no 
 very great deformity, as the largest apparent breadth 
 of the pilaster will exceed the least only in the ratio 
 of eleven to ten, or thereabouts. But if columns be 
 detached, the angular pilasters should always be 
 coupled with a column, to hide its inner flank ; be- 
 cause the pilasters will otherwise appear dispropor- 
 tionate when seen from the point of view proper for 
 the whole building, especially if the fabric be small 
 and the point of view near. 
 
 It is sometimes customary to execute pilasters 
 without any diminution. In the antiques there are 
 several instances thereof, as well as of the contrary 
 practice ; and Palladio, Vignola, Inigo Jones, and 
 many of the greatest architects have frequently done 
 so. Nevertheless, it is certain that diminished pilas- 
 ters are, on many accounts, nmch preferable. There 
 is more variety in their form ; their capitals are better 
 proportioned, both in the whole and in their parts, 
 particularly in the Composite and Corinthian orders ; 
 and the irregularities occasioned by the passage of 
 the architraves, from diminished columns to undimin- 
 ished pilasters, are thereby avoided, as are likewise 
 the difficulties of regularly distributing the modil- 
 lions and other parts of the entablature, either when 
 the pilasters are alone or accompanied with columns. 
 
 Another disagreeable effect of undiminished pilas- 
 ters is likewise obviated by rejecting them. Indeed, 
 I am at a loss to account for it, and it is diametri- 
 cally opposite to a received law in optics. I im- 
 agined it might be the result of some defect in my 
 own sight, till, by inquiry, I found others were af- 
 fected in the same manner. It is this — the top of 
 the shaft always appears broader than the bottom. 
 
 The shafts of pilasters are sometimes adorned 
 with flutings in the same manner as those of col- 
 umns, the plan of which may be a trifle above a 
 semicircle ; and they must be to the number of 
 seven on each face, which makes them nearly of the 
 same size with those of the columns. The interval 
 between them must be either one third or one fourth 
 of the flute in breadth ; and when the pilaster is 
 12 
 
 placed on the pavement, or liable to be broken by 
 the touch of passengers, the angle may be rounded 
 off", in the form of an astragal ; between which and 
 the adjoining flute there must be a fillet or interval 
 of the same size with the rest, as in the porch of the 
 Pantheon, at Rome. 
 
 The flutes may, like those of columns, be filled 
 with cablings to one thurd of their height, either plain, 
 and shaped like an astragal, or enriched, according as 
 the rest of the composition is simple or much adorned. 
 Scamozzi is of opinion that there should be no flut- 
 ings on the sides of engaged pilasters, but only in 
 front; and, whenever cornices or imposts are con- 
 tinued home to the pilaster, this should be partic- 
 ularly attended to, that the different mouldings of 
 these members, by entering into the cavities of the 
 flutes, may not be cut off" in irregular and disagreea- 
 ble forms. But if the flanks of the pilasters are en- 
 tirely free, it may be as well to emich them in the 
 same manner as the front, provided the flutes can be 
 so distributed as to have a fillet or interval adjoining 
 to the wall — which is always necessary to mark the 
 true shape of the pilasters distinctly. 
 
 The capitals of Tuscan or Doric pilasters are pro- 
 filed in the same manner as those of the respective 
 columns; but in the capitals of the other orders, 
 there are some trifling differences to be observed. In 
 the antique Ionic capital, the extraordinary projection 
 of the ovolo makes it necessary either to bend it in- 
 wards considerably towards the extremities, that it 
 may pass behind the volutes, or instead of keeping 
 the volutes flat in front, as they commonly are in the 
 antique, to twist them outwards, till they give room 
 for the passage of the ovolo. Le Clerc thinks the 
 latter of these expedients the best ; and, that the arti- 
 fice may not be too striking, the projection of the 
 ovolo may be considerably diminished, as in plate 56, 
 Fig. 2 ; which, as the moulding can be seen in front 
 only, will occasion no disagreeable effect. 
 
 The employing half or other parts of pilasters that 
 meet, and, as it were, penetrate each other's inward 
 or outward angles, should, as much as possible, be 
 avoided, because it generally occasions several irreg- 
 ularities in the entablatures, and sometimes in the 
 capital also. Particular care must be taken never to 
 introduce more than one of these breaks in the same 
 place, for more can never be necessary. In many of 
 the churches at Rome we see half a dozen of them 
 together, which produce a long series of undulated 
 
90 
 
 ARCADES AND ARCH E S. — PEDESTALS. 
 
 capitals and bases, and a number of mutilated parts 
 in the entablature, than which nothing can be more 
 confused or disagreeable. 
 
 ARCADES AND ARCHES. 
 
 The arch is, without doubt, a Roman invention ; * 
 and from this circumstance the oldest, which is the 
 semicircular, is called the Roman arch. The time of 
 its introduction may be looked upon as a new epoch 
 in the science of architecture, for by this change the 
 Romans succeeded in laying the foundation for a 
 complete revolution of taste and conception. Says 
 Gwilt, in his Encyloptedia of Architecture, " This 
 change, by various steps, led through the basilica to 
 the construction of the extraordinary Gothic cathe- 
 drals of Europe, in its progress opening beauties in 
 the art of which the Greeks had not the remotest 
 conception." The principal feature of the Roman 
 architecture is the use of the arch and circle, each 
 moulding being composed of some portion; while 
 those of the Grecian are composed entirely of sec- 
 tions of the cone. An arcade is a series of arches, 
 separated by one or more columns, with their imposts 
 and piers, and is often one of the most pleasing, as 
 well as imposing, objects which architecture affords ; 
 
 * We are aware that, -n-ere we to pass oyer this point without al- 
 luding to the discovery of an arch at Thebes, we should not feel 
 warranted in making the above assertion. An account of this arch 
 may be found in "Wilkinson's Customs of the Ancient Egyptians, 
 vol. iii. pp. 221 and 263. To the arch of Thebes Mr. W. assigns 
 the date of 1500 B. C. But as this structure, if one may judge from 
 his delineation, is so purely Roman in its character, its antiquity is 
 doubted by most authors. The arch in the tomb of Saccara is the 
 other to which he alluded, and is from his delineation simply a lining, 
 and is not capable of sustainmg any weight, which is the office of 
 the arch. Mr. Wilkinson assigns as a reason for the Egyptians not 
 using the mode of construction requiring the arch, that there would 
 be difficulty attending the repairing of any accident that might befall 
 it. In regard to this argument, it would seem, at any rate, that, to 
 an engineer who could erect the Pyramid of Cheops, some way 
 would suggest itself for the repairs of a simple arch, had he ever 
 conceived of its construction. lie again speaks of the consequences 
 attending the decay of a single block, &c. In regard to this it is 
 argued, that, in the case alluded to, the balance on the outer side or 
 back of each course would preserve the opening in some form with- 
 out any arch at all. And besides this, when we take into considera- 
 tion the fact that so much time and labor was expended to procure 
 the immense stones for architraves, which could have been avoided 
 in many instances by the use of the arch, it seems that, had it ex- 
 isted in their very midst, some, to say the least, would have ven- 
 tured to use it- — Editohs. 
 
 and the utility of them in some climates, for shelter 
 from rain and heat, is obvious. We have given, in 
 plate 40, designs for arcades with and without pedes- 
 tals. The proportions are very nearly the same as 
 given by Chambers ; and, as will be seen by exami- 
 nation, they are different in each of the orders. We 
 should have been pleased to have given examples of 
 arcades above arcades ; but our limits would not allow 
 it. We will state here, however, that as in orders 
 above orders the Tuscan invariably stands at the bot- 
 tom, and above it the Doric ; immediately above tlus 
 the Ionic, and next the Corinthian ; and, should the 
 Composite be used, its place is above the Corinthian. 
 The lower diameter of the shaft immediately above 
 the base of each column is of the size of the one 
 next below it at the top just below the capital ; these 
 dimensions will, of course, govern the proportions of 
 the entire order. If the balustrade be used in the 
 openings, it should extend from pier to pier at the 
 side of the column, and its whole height should be 
 the top of the pedestal, the height of the baluster, or 
 its dimension, is the die of the pedestal. The rails 
 above and below them are a continuation of its cor- 
 nice and base. The use of arcades above arcades 
 is pretty generally confined to public buildings, as, 
 among the Romans, to their theatres and amphithea- 
 tres ; they have, however, been much employed in 
 Europe ; and in the magnificent design made by Inigo 
 Jones, for the palace at Whitehall, are to be found 
 some very fine examples. — Editors, 
 
 PEDESTALS. 
 
 Most writers consider the pedestal as a necessary part of the order, 
 without which it is not esteemed complete. It is, indeed, a matter 
 of small importance whether it be considered in that light or as a 
 distinct composition. Vitruvius only mentions it as a necessar)- part 
 in the construction of a temple, without signifying that it belongs to 
 the order, or assigning any particular proportions for it, as ho does 
 for the parts of the column and the entablature. But triangular, 
 circular, or polygonal pedestaLs, or such as are swelled and have 
 their die in the form of a baluster, or are surrounded with cinctures, 
 are, in no case, to be made use of in buildings. Such extravagances, 
 though frequent in some foreign countries, are now laid aside wher- 
 ever good taste prevails. 
 
 A pedestal, like a column or an entablature, is com- 
 posed of three principal parts, which are the base, the 
 body or the die, and the cornice. The die is always 
 
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 A 
 
 
 1 
 
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 ¥ 
 
 ! -.- 
 
 VI'}.: 
 
 L_ 
 
 -— '/i-^r - 4 
 
PEDESTALS. 
 
 91 
 
 nearly of the same figure, being constantly either a 
 cube or a parallclopiped ; but the base and cornice 
 are varied, and adorned with more or less mouldings, 
 according to the simplicity or richness of the compo- 
 sition in which the pedestal is employed. Hence 
 pedestals are, like columns, distinguished by the 
 names of Tuscan, Doric, Ionic, Corinthian, and Com- 
 posite. 
 
 Some authors are very averse to pedestals, and 
 compare a column raised on a pedestal to a man 
 mounted on stilts, imagining that they were first in- 
 troduced merely through necessity and for want of 
 columns of a sufficient length. 
 
 It does not seem proper to suppose that they were 
 first introduced merely through want of columns of 
 a sufficient length, since there are many occasions on 
 which they are evidently necessary, and some in 
 which the order, were it not so raised, would lose 
 much of its beautiful appearance. Thus, within our 
 churches, if the columns supporting the vault were 
 placed immediately on the ground, the seats would 
 hide their bases and a good part of the shafts ; and 
 in the theatres of the ancients, if the columns of the 
 scene had been placed immediately on the stage, the 
 actors would have hid a considerable part of them 
 from the audience ; for which reason it was usual to 
 raise them on very high pedestals, as was likewise 
 customary in their triumphal arches ; and in most of 
 their temples the columns were placed on a basement 
 or continued pedestal, so that the whole order might 
 be exposed to view, notwithstanding the crowds of 
 people with which these places were frequently sur- 
 rounded. And the same reason wiU authorize the 
 same practice in our churches, theatres, courts of jus- 
 tice, and other public buildings where crowds fre- 
 quently assemble. And in a second order of arcades 
 there is no avoiding pedestals, as without them it is 
 impossible to give the arches any tolerable proportion. 
 These instances will sufficiently show the necessity 
 of admitting pedestals in decorations of architecture. 
 With regard to the proportion which their height 
 ought to bear to that of the columns they are to sup- 
 port, it is by no means fixed — the ancients and mod- 
 erns, too, having in their own works varied greatly 
 in this respect, and adapted their proportions to the 
 occasion, or to the respective purposes for which the 
 pedestals were intended. Thus, in the amphitheatres 
 of the ancients, the pedestals in the superior orders 
 were generally low, because in the apertures of the 
 
 arches they served as rails to enclose the portico, and 
 therefore were, for the conveniency of leaning over, 
 made no higher than was necessary to prevent acci- 
 dents ; and the case is the same in most of our mod- 
 ern houses, where the height of the pedestals in the 
 superior orders is generally determined by the sills of 
 the windows. The ancients, in their theatres, made 
 the pedestals in the first order of their scene high, for 
 the reason mentioned in the beginning of this chap- 
 ter ; but the pedestals in the superior orders were very 
 low, their chief use being to raise the columns so as 
 to prevent any part of them from being hid by the 
 projection of the cornice below them ; and thus, on 
 different occasions, they used different proportions, 
 being chiefly guided by necessity in their choice. 
 
 Nevertheless, writers on architecture have always 
 thought it incumbent upon them to fix a certain de- 
 terminate proportion for the pedestal, as well as for 
 the parts of the order. It would be useless to enu- 
 merate in this place their different opinions ; but I 
 must beg leave to observe that Vignola's method is 
 the only true one. His pedestals are all in the orders 
 of the same height, being one third of the column ; 
 and as their bulk increases or diminishes, of course 
 in the same degree as the diameters of their respec- 
 tive columns do, the character of the order is always 
 preserved, which, according to any other method, is 
 impossible. 
 
 With regard to the divisions of the pedestals, if 
 the whole height be divided into nine parts, one of 
 them may be given to the height of the cornice, two 
 to the base, and the remaining six to the die ; or if 
 the pedestal is lower than ordinary, its height may 
 be divided into eight parts only, of which one may 
 be given to the cornice, two to the base, and five to 
 the die, as Palladio has done in his Corinthian order, 
 and Perault in aU the orders.* 
 
 The plan of the die is always made equal to that 
 of the plinth of the column ; the projection of the 
 cornice may be equal to its height ; and the base, 
 being divided into three parts, two of them will be 
 for the height of the plinth, and one for the mould- 
 ings, of which the projection must be somewhat less 
 than the projection of the cornice, so that the whole 
 base may be covered and sheltered by it. 
 
 These measures are common to aU pedestals ; and 
 in plate 41 there are proper designs for the Tuscan, 
 
 Ordonnance dcs cinq Especes de Colonnes, 1 Partie, ch. 6 et 7. 
 
92 
 
 IMPOSTS. 
 
 Doric, Ionic, and Corinthian orders, in which the 
 forms and dimensions of the minuter parts are 
 acciuately drawn and figured. With regard to the 
 application of pedestals, it must be observed that 
 when columns are entirely detached, and at a consid- 
 erable distance from the wall, as when they are em- 
 ployed to form porches, peristyles, or porticoes, they 
 should never be placed on detached pedestals, for 
 then they may indeed be compared to men mounted 
 on stilts, as they have a very weak and tottering 
 appearance. 
 
 The base and cornice of these pedestals must run 
 in a straight line on the outside throughout; but the 
 dies arc made no broader than the plinths of the 
 columns, the interv'als between them being filled 
 with balusters, which is both really and apparently 
 lighter than if the whole pedestal were a continued 
 solid. 
 
 TABLE, 
 
 Showing the Height of Pedestals in antique and 
 modem Works in Minutes, each one sixtieth of 
 the Diameter of the Shaft, 
 
 Doric, . 
 
 lowic, 
 
 CoMPOSlTS, 
 
 {Palladio, 
 Scamozzi 
 
 ! Temple of Fortuna Virilis, 
 Coliseum, 
 Palladio, 
 Scamozzi, 
 
 IArcb of Constantine, ... 
 Coliseum, 
 Palladio 
 Scamozzi , ■ 
 
 Arch of Titus 
 
 Arch of the Goldsmiths, 
 
 Palladia 
 
 Scamozzi, 
 
 Arch of Sep. Severus, . . 
 
 26 
 
 30 
 
 44 
 
 33J 
 
 28§ 
 
 30 
 
 lli 
 
 23 
 
 23J 
 
 30 
 
 55 
 
 46 
 
 33 
 
 30 
 
 30 
 
 Mouldings 
 above 
 Plinth. 
 
 14 
 15 
 
 19f 
 
 9^ 
 14* 
 15 
 29 
 
 11* 
 
 14* 
 
 15 
 
 30 
 
 25i 
 
 17 
 
 15 
 
 30| 
 
 80 
 
 68f 
 93f 
 
 97J 
 
 82i 
 153" 
 
 78 
 
 93 
 132J 
 141 
 144^ 
 133 
 112J- 
 140^ 
 
 20 
 
 22| 
 
 23^ 
 
 17 
 
 2U 
 
 22^ 
 
 29^ 
 
 19^ 
 
 19 
 
 22^ 
 
 29 
 
 25^ 
 
 17 
 
 221 
 
 29| 
 
 Total 
 Height 
 
 140 
 
 136Jj 
 
 180f 
 
 14U 
 
 162J. 
 
 150 
 
 228 
 
 131f 
 
 150 
 
 200 
 
 255 
 
 241 
 
 200 
 
 180 
 
 182^ 
 
 On plate 41 will be found designs for pedestals of 
 the different orders. They are figured by the same 
 scale with which the order should be drawn in which 
 they may be employed. 
 
 Fig. 2. In this figure is shown the manner of 
 striking or working a raking moulding to fit and 
 mitre with the same on a horizontal line or flank. 
 First divide the width of the moulding into 1, 2, 3, 
 
 and 4 parts, as in A ; raise a perpendicular line in 
 B, at O ; trace the cur^'e of the moulding from the 
 intersection of 1, 2, 3, 4, on the curve line of the 
 moulding ; draw a, b, c, d, e, f, g, h, at right angles 
 with the perpendicular line O, to the points /;,/, d, b, 
 in the curve or face of the moulding ; transfer to A. 
 a b, c d, ef, g h. In the like manner, the curve at C 
 may be found. All to mitre in their several parts 
 with each other. 
 
 IMPOSTS. 
 
 Imposts are explained in the glossary. By some, however, they 
 are called the walls back of the inserted column, rising from the 
 base to the spring line of the arch, and extending on each side of 
 the column about thirty minutes — forming the side of the apertures 
 of doors or mndows, and, when used without the columns, are 
 appropriately termed pilasters. But they are most generally used 
 for those assemblages of moulding which divide the perpendicular 
 part of the wall from the spring line of the arch. In some in- 
 stances regular pilasters are introduced, when the colimin may be 
 termed isolated, as it stands detached from the walls. We find 
 imposts introduced in the Temple of Solomon ; and they are com- 
 mon in Koman edifices ; as in the Arch of Titus, and most of theii 
 other triumphant arches, &c. In most parts of Europe imposts are 
 found, as also in some parts of the United States. The origin of this 
 style of building cannot be clearly traced. However elegant its 
 aspect in many instances may be, it seems now to be giving place to 
 a more magnificent and majestic style of architecture. Where we 
 once saw one range of columns rising above another, each support- 
 ing a distinct entablature, we now find the whole height supplied 
 by one length, thus preserving the principles of good taste. 
 
 An impost is the capital of a pier or pilaster which 
 receives the arch in the arcades of the Roman order. 
 On plate 42 we have given designs for the different 
 orders, and have figured them to be drawn by the 
 same scale of minutes with which the order is drawn 
 to which they may be applied. No. 4 is from a de- 
 sign by Vignola ; the rest are by Sir William Cham- 
 bers. 
 
 Bases. — No. 1 is the Tuscan base ; No. 2 is the 
 Doric; and No. 3 is the Attic. The last named 
 Chambers has used with all his orders, excepting 
 the Tuscan. This base was used by the ancients 
 to a great extent; and they have not, to say the 
 least, in many instances made any improvement 
 — Editors. 
 
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BALUSTRADES. 
 
 98 
 
 BALUSTRADES. 
 
 The baluster is not found in the works of the an- 
 cients, but owes its origin to the restoration of the 
 art in Italy. It, like the column, consists of the cap- 
 ital, shaft, and base. The most ancient examples 
 were of the shape of a stunted column, and not un- 
 frequently were crowned with a disproportioned Ionic 
 capital. Many forms have been given to them by 
 the later masters, and we may safely say that the 
 invention is one of the most useful as well as orna- 
 mental that was produced by the Italians. A balus- 
 trade is a series of balusters standing upon a base, 
 and croAvned with a capital or rail, — this capital 
 and base being of the same outline in its detail as 
 those of the pedestal which accompany them. It is 
 proposed by Blondel that balusters and balustrades 
 should partake of the character of the edifice they 
 are to be employed upon ; and by some their species 
 has been so arranged as to appropriate a design to 
 each order, and in the works of such they are known 
 by the name of Tuscan, &c. The general riUes to 
 be observed in the construction of balustrades are, 
 that the balusters be of an odd number, and the dis- 
 tance between them equal to half their larger diam- 
 eter, which will produce an equality between the 
 open and solid spaces ; and a half baluster should 
 always be placed against the pedestal. When the 
 balustrade is formed without pedestals, as is often 
 the case where balusters are placed between columns, 
 the half baluster may be omitted. The pedestals of 
 balustrades should always be placed directly over the 
 column, and the die be of the same width as the di- 
 ameter of the column at the top. Where the columns 
 stand together as in what is termed coupled columns, 
 as seen at A, in plate 43, the pedestal should extend 
 over both entire. Also, where a balustrade terminates 
 against a roof or pediment, the termination should 
 be by a pedestal, and it should commence where the 
 balustrade begins to diminish, be the distance more 
 or less ; and in no case should the baluster be cut to 
 the roof. The pedestals, as before stated, should 
 stand directly over the columns, — the distances be- 
 tAveen them would, of course, depend upon the in- 
 tercolumniation, — but where no columns are used, 
 either seven or nine whole balusters, with the half ones, 
 
 have been recommended as producing the best efiect ; 
 for when the pedestals stand too near each other, 
 they present a heavy and clumsy appearance to the 
 work ; and where they are too far apart, the work will 
 appear weak. The bulbs or bellies of balusters are 
 often enriched ; which, for stairs and highly-finished 
 interiors, is quite requisite. In regard to the heights 
 of balustrades, when they are used as a protection to 
 terraces, or before windows, they should be not less 
 than two feet six inches, nor more than three feet 
 high ; but when they are used as merely ornamental 
 appendages to a building, they should be, according 
 to the majority of authors, not more than two 
 thirds of the height of the entablature over which 
 they stand, nor less than two thirds, without count- 
 ing the plinth, the height of which must be sufii- 
 cient to leave the entire baluster exposed to view 
 from the best point of sight for viewing the building. 
 Palladio has, however, in some instances, made the 
 balustrade the height of the entire entablature, as at 
 the Valmarana Palace. Inigo Jones has, in some 
 instances, followed his example ; but this was not the 
 usual practice of either. We have before stated, 
 that the moderns have given to the baluster a variety 
 of shapes. On plate 43 we have given the designs 
 recommended by Chambers, with the method of pro* 
 portioning them, in the manner adopted by him. 
 No. 1 is the Tuscan ; No. 2 the Doric and Ionic ; 
 No. 3 the Corinthian and Composite. No. 4 is a 
 design for a Tuscan baluster, and has generally been 
 executed square. Nos. 5, 6, and 7 are designs for 
 double-bellied balusters, and are intended principally 
 for balconies and terraces, the rail and pedestal being 
 the same height as in other designs. Chambers has 
 designated them respectively the Tuscan, Doric, and 
 Ionic and Corinthian. The method of proportioning 
 them to the order is as follows : After ascertaining 
 the height, as before directed, divide it into thirteen 
 parts ; of which, give two to the rail, eight to the 
 baluster, and the remaining three to the base : if the 
 baluster is required to be less, divide the height into 
 fourteen parts, giving two to the rail, eight to the 
 baluster, and four to the base. One of these parts 
 is a module for determining the rest, and is divided 
 into nine other parts, called minutes. From what 
 has been said, the whole on plate 43 will, without 
 doubt, be clearly understood. — Editors. 
 
94: 
 
 GRECIAN ORDERS. 
 
 GRECIAN ORDERS. 
 
 The Doric, the Ionic, and the Corinthian were the only orders of 
 architecture employed by the Greeks. The Tuscan and Composite 
 were used only in Italy — the one more rude, the other more orna- 
 mented, than the Greek orders, -which occupied a middle rank. To 
 attain, therefore, a proper knowledge of the true principles of archi- 
 tecture, the student shoiJd devote most of his attention to the three 
 Greek orders ; not only because in them these principles arc the 
 most displayed, but because of all the monuments of antiquity 
 which have subsisted to modem times few, or perhaps none, can be 
 pointed out ra which the Roman or Italic mode of construction is 
 certainly to be traced. 
 
 DEFINITIONS. 
 
 1. If any number of frustums of cones, or frus- 
 tums of conoids of similar solids and equal magni- 
 tudes with each other, be so arranged that their 
 bases, which are the thickest ends of the frustums, 
 may stand upon or in the same horizontal plane, 
 and their axes in the same plane with each other 
 and perpendicular to the horizon ; and if on the tops 
 of these frustums be laid a continued beam ; and if 
 over this beam be laid the ends of a number of equi- 
 distant joists, the other ends being either supported in 
 the same manner, or by a wall or any piece of build- 
 ing whatever, so that the upper and under surfaces 
 may be in the same horizontal planes ; and if over 
 the ends of these beams be laid another beam paral- 
 lel to the former, which lays upon the fr-ustums, but 
 projecting farther out from the axis of the columns 
 than the vertical face of the lower beam which is 
 over the frustums ; and if this beam supports the 
 ends of rafters whose upper surfaces lay in the same 
 inclined plane, so as to support a covering or roof, — 
 the whole of this mass, together with the frustums 
 supporting it, is called an order. 
 
 2. K the bottom or lower end of the frustum 
 finish with an assemblage of mouldings, projecting 
 equally aU round beyond the bottom of the frustum, 
 then this assemblage is called a base. 
 
 3. If the upper end of the frustum finish with 
 mouldings or any kind of ornaments, and if these 
 ornaments or mouldings be covered with a solid, 
 whose upper end and lower sides are square, and the 
 vertical or perpendicular sides rectangles, then this 
 solid, together with the ornaments or mouldings 
 under it, is called a capital. 
 
 4. If the frustum has no base, then the capital 
 and frustum together are called a frustum column ; 
 but if the frustum has a base, then the base, frus- 
 tum, and capital, taken together, are simply called a 
 column. 
 
 5. The mass supported by the columns is called 
 an entablature. 
 
 6. The under beam of the entablature is called an 
 architrave or epistylium. 
 
 I. The space comprehended bet^veen the upper 
 side of the epistylium or architrave and the under 
 edge of the beam over the joists, is called the frieze 
 or zophorus. 
 
 8. The edge or profile of the inclined roof sup- 
 ported by the joists or cross beams, jetting out be- 
 yond the face of the zophorus or frieze, is called a 
 cornice. 
 
 9. The lowest or thickest part of a column is 
 called the diameter of the coluinn. 
 
 10. Half of the diameter of the column is called 
 a module. 
 
 II. If a module be divided into thirty, or any 
 other number of equal parts, then these parts are 
 called minutes. 
 
 12. The shortest distance from the bottom of the 
 frustum of one column to the bottom of the frus- 
 tum of the next column is called the intercolumni- 
 ation. 
 
 13. When the ijitercolumniation is one diameter 
 and half a column, it is called pijcnostyle, or col- 
 timns thick set. 
 
 14. When the intercolumniation has two diam- 
 eters of the columns, then it is called si/style. 
 
 15. When the space bct^-een the columns is two 
 diameters and a quarter, then the intercolumniation 
 is called evstyle. 
 
 16. When the intercolumniation is three diam- 
 eters of the columns, then it is called decastyle. 
 
 17. When the distance betw'een the columns has 
 four diameters of the columns, then that intercolum- 
 niation is called arccostyle, or columns thin set. 
 
 18. When there are four columns in one row, then 
 that number is called tetrastyle. 
 
 19. When there are six columns in ojic row, then 
 it is called hexastyle. 
 
 20. Wlicn there are eight columns in one row, 
 then it is called octastyle. 
 
GRECIAN DORIC. 
 
 95 
 
 GRECIAN DORIC. 
 
 The first Grecian order in point of antiquity is the Doric, so 
 called from the Dores, a small tribe in Greece ; or, as some say, 
 from Dorus, an Achaian chief, who first employed the order in 
 erecting a temple to Juno, at Argos. 
 
 DEFINITIONS. 
 
 1. If through the axis of the shaft be supposed to 
 pass twenty vertical planes, making equal angles 
 with each other, which wiU cut the surface of the 
 column in twenty places ; and if the surface of the 
 column be curved or hoUowcd between each two 
 lines, from the bottom to the top of the shaft, ter- 
 minating immediately under the lowest annulet, — 
 then the shaft will have twenty curved sides, and as 
 many angles ; and if nearly at the upper end of the 
 shaft be cut one or more grooves, of an equal depth 
 from the surface of the hollowing, each groove being 
 parallel to the annulets under the echinus, then a 
 column so formed is called Doric. 
 
 2. That part of the column contained between the 
 upper channel and the lower annulets is called the 
 hypotrachelion, neck, or frieze of the capital. 
 
 3. That part of the Doric column comprehending 
 the abacus, echinus, annulets, and hypotrachelion, is 
 called a Doric capital. 
 
 4. If the ends of the cross beams in the frieze 
 which lay upon the architrave be at right angles 
 to the sides of the beams, and parallel to the front 
 or the architrave ; and if the two vertical right angles 
 of each beam formed by the two vertical sides and 
 the ends be cut away by vertical planes, making 
 equal angles wath the sides and ends, — that is, 135 
 degrees with each, — and if two other vertical chan- 
 nels are cut on the end, so that the planes, which are 
 three in number, left on the ends of each beam, may 
 be equal rectangles, and the two sides of each chan- 
 nel make 135 degrees with the ends of the joists, 
 and are so disposed that there may be a rectangle 
 next to each semi-channel, and then two whole 
 channels, leaving a rectangle in the middle, — the end 
 of the beam so formed is called a trigli/pk. 
 
 5. K the spaces between the triglyph be filled up 
 with planes parallel to the front of the triglyphs or 
 to the front of the architrave ; and if these planes 
 be in the same plane with each other and recessed 
 
 beyond the ends of the triglypn, so as to show a 
 small part of the vertical sides of the beams, — that is, 
 to be farther in than the channels of the triglyph, — 
 then these spaces so filled up are called metopes. 
 
 6. If the front of the beam which supports the 
 rafters that lay upon the joists projects at some dis- 
 tance beyond the face of the triglyph, the plane of 
 the front being parallel to the ends of the beam ; 
 and if a recess be cut from this beam directly over 
 the metopes, the plane of the front of the recess 
 being parallel to, and having a small projecture over, 
 the metopes, and the ends of the recesses over the 
 metopes be in the same plane with the vertical sides 
 of the beam, — then that part of the front of the 
 beam over the triglyph is called the capital of the 
 triglyph. 
 
 7. The whole face of the work comprehended 
 between the upper edge of the beam which forms 
 the capital of the triglyphs, and the lower end of the 
 triglyphs and metopes, is called a Doric frieze. 
 
 8. If from the top of the architrave project a 
 fillet whose upper edge is in the same plane with the 
 top of the architrave or the lower end of the trigljrph, 
 the front of the fillet being a vertical plane parallel 
 to the front of tlie architrave, having a small projec- 
 ture beyond the front of the triglyph, this fillet being 
 supposed to be continued the whole length of the 
 architrave, and returning in the same manner round 
 its ends ; and if fillets be placed under this fillet, 
 whose fironts stand a little within the firont of the 
 upper fillet, but projecting beyond the face of the 
 architrave and the ends of these fillets, in the same 
 plane with the sides of the triglyph, and, conse- 
 quently, each fillet equal in length to the breadth of 
 the triglyph ; and if under each of these fillets be 
 fixed six equal similar finistums of cones, at equal 
 distances from each other, whose axes are perpen- 
 dicular to the horizon, and the same distance from 
 the face of the architrave, so that the extremities of 
 these frustums may not reach beyond the perpen- 
 dicular of the ends of the fillets above them, — then 
 the front of the architrave so formed is called a 
 Doric architrave. 
 
 9. The upper fillet of the Doric architrave is 
 called a tenia. 
 
 10. The fillets under the tenia of the Doric archi- 
 trave are each of them called a regula. 
 
 11. The little conical finistums under each regula 
 are called guttce, or drops. 
 
96 
 
 GRECIAN DORIC. 
 
 12. The plain part of the architrave under the 
 tenia and regute is called /acia. 
 
 13. If over the capitals of the triglyph be laid 
 another beam, whose front is parallel to the metopes 
 or to the front of the triglyphs in the frieze, having a 
 small projecture from the front of the metopes ; and 
 if over this beam be laid the ends of the rafters 
 which support the covering, the ends having a pro- 
 jecture forward and parallel to the beam under them, 
 one rafter over each triglyph, and also one over every 
 metope, placed directly in the middle of each ; that 
 is to say, a vertical plane perpendicular through the 
 middle of every metope, and also through the middle 
 of every triglyph, would pass through the ends of all 
 the rafters, and divide them into two equal rectan- 
 gles ; and if over the rafters be laid a beam, the front 
 of which, being a plane parallel to the ends of the 
 rafters, has a projectiire ; and if the void spaces be- 
 tween each two rafters and the under side of the 
 beam above the rafters and the upper side of the 
 beam below the rafters be covered in, so that the 
 front of the spaces so covered may be in the same 
 vertical plane with the face of the beam under the 
 rafters, — then those ends of the rafters projecting over 
 the face of the beam under them are called mutules. 
 
 14. If to the under side of the mutules be hung 
 three rows of small conical frustums, of the same 
 size as those under the regula; of the architrave, so 
 that there may be six in length in each of the rows, 
 and three in width, then these conical frustums are 
 also called gutta;, or drops, as those in the archi- 
 trave. 
 
 15. The front of the beam lying over the mutules 
 is called corona, or drip, or larmier. 
 
 16. The under side of the beam lying over the 
 mutules is called soffit, or lacunar. 
 
 17. A building, whether of wood or stone, or any 
 other material, having columns supporting an entab- 
 lature over them, as described in the preceding defi- 
 nitions, — such a building, so constructed, is said to 
 be of the Doric order. 
 
 Having defined the principal parts of this order, it 
 may not be improper to observe that the Doric order 
 lias, in general, more mouldings in the cornice ; but 
 ;is these vary in different buildings, and as the mem- 
 bers already described form its most striking features, 
 i, would have been useless to have taken any ac- 
 i;,;int of them in the definitions. 
 
 PROBLEM I 
 
 To draw the elevation of a Grecian Doric 
 order. 
 
 Make the lower diameter of the shaft of the col- 
 umn one eighth of the entire heiglit of the order; 
 divide the diameter of the column into two equal 
 parts ; then one of these parts is a module ; divide 
 the module into thirty equal parts, and each of these 
 parts will be a minute ; make the height of the col- 
 umn twelve modules, the height of the capital one 
 module ; divide the height of the capital into five 
 equal parts ; give one to the hypotrachelion, and two 
 parts to the annulets and echinus ; make the annu- 
 lets one quarter of the echinus, and the remaining 
 two parts to the abacus ; make the upper diameter 
 of the shaft three quarters of the lower diameter of 
 the shaft, the length of each side of the abacus two 
 modules and one fifth, or two modules and twelve 
 minutes ; the height of the entablature will be four 
 modules, of which the height of the cornice will 
 have one module, and the frieze and architrave each 
 forty -five minutes, or one module and a half; divide 
 the height of the frieze into eight parts ; give the 
 upper one to the capital of the triglyph, and the 
 three lower for the channels ; make one edge of the 
 triglyph in the columns at the angles of the building, 
 directly over the axis of the column, the breadth of 
 the triglyph tAventy-eight minutes, having the other 
 edge of the triglyph dncctly at the angle of the 
 building ; and make the distance between the 
 triglyph, or width of the metopes, equal to the height 
 of the frieze, forty-two minutes ; place all the col- 
 umns between the two extreme ones directly under 
 the middle of the triglyphs. Make the height of the 
 tenia one tenth of the height of the epistilium ; and 
 the height of the regula, together with tlic guttae, 
 equal to the height of the tenia. The height of the 
 cornice being one module, make tlie height of the 
 small bead on the lower part of the cornice one min- 
 ute ; the height of the mutules, including the guttse, 
 four minutes and a half; the length of tlie mutules 
 equal to the breadth of the triglyplis, and their pro- 
 jection beyond the faces of the triglyphs two thuds of 
 their length, observing that one should be directly 
 over the middle of every triglyph, and one over the mid- 
 dle of every metope ; make a fillet above the mutules 
 
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GRECIAN DORIC. 
 
 97 
 
 one minute and a half higli, to project beyond the 
 mutules half a minute over this fillet; make the 
 height of the corona one third of a module, or ten 
 minutes, having a projccture over the fillet one min- 
 ute ; make the height of the small echinus one min- 
 ute and a quarter ; over the echinus make a fillet of 
 the same height ; over the fillet make another echi- 
 nus six minutes and a half high, and two minutes 
 will remain for the height of the fillet above the 
 echini;.-?. 
 
 In order to establish the proportions and true taste 
 of the original Doric order, the following examples 
 are taken from the most celebrated biiildings now 
 remaining of this order. The module is divided into 
 thirty parts, or minutes ; the measures are all num- 
 bered in these parts ; the projections are reckoned 
 from a line representing the axis of the column, and 
 are figured at the extremities of each member. 
 
 Plate 44. 
 
 ELEVATION- OF THE DORIC ORDER ON THE TEMPLE 
 OF MINERVA, AT ATHENS, CALLED RARTHENON. 
 
 This temple, dedicated to Minerva, the chief god- 
 dess of the Athenians, is the most beautiful piece of 
 antiquity remaining. It was built by Pericles, who 
 employed Ictimus and Callicrates for his architects. 
 The entablature is charged with historical figures of 
 admirable workmanship ; the figures of the pediment, 
 though seen at so gi-eat a height, appear to be as 
 large as life, being in alto rilicvo, and well executed ; 
 the figure in the middle seems to have been made 
 for Jupiter, its right arm being broken off, which prob- 
 ably held the thunder. It is likely that between his 
 legs was placed the eagle ; for the beard, and majesty, 
 and expression of his countenance, and the figiu-e 
 being naked, as he was usually represented by the 
 Greeks, sufficiently show it to have been made for 
 Jupiter. At his right hand is another figure, covered 
 half way down the legs, coming towards him, which 
 perhaps was a Victory, leading the horses of INIiner- 
 va's triumphal chariot, which follows it. The horses 
 are finished with great art ; the vigor and spirit pe- 
 culiar to those animals seem here to receive addition, 
 as if inspired by the goddess they chew. Minerva, in 
 the chariot, is represented as the goddess of learning 
 rather than of war, without helmet, buckler, or a Me- 
 dusa's head on her breast, as Pausanias describes her 
 image within the temple. Behind her is another 
 
 13 
 
 figure of a woman sitting. The next two figures in 
 the corner are the Emperor Hadrian, and his empress 
 Sabina. On the left hand of Jupiter are five or six 
 figures, which appear to be an assembly of the gods, 
 where Jupiter introduces Minerva, and acknowledges 
 her his daughter. 
 
 The pediment at the other end of the temple was 
 adorned with figures, expressing Minerva's contest 
 with Neptune about who should name the city of 
 Athens, of which there only remains a part of a sea 
 horse. 
 
 The frieze is charged with basso rilievos, of excel- 
 lent workmanship, on which are represented the bat- 
 tles of the Athenians with the Centaurs ; these appear 
 to be as old as the temple itself. 
 
 Within the portico on high, and on the outside of 
 the cella of the temple, is another border of basso 
 rilievos around it, at least on the north and south 
 sides of it, which is without doubt as ancient as the 
 temple, and of admirable workmanship, but not in 
 so high a rilievo as the other. On it are represented 
 sacrifices, processions, and other ceremonies of the 
 heathen worship. 
 
 This temple is now turned into a Turkish mosque. 
 
 Fig. 1. Elevation of the Doric order ; the propor- 
 tions of the parts m numbers. 
 
 Fig. 2 is a design, showing the order, with the col- 
 umn and entablature entire. 
 
 Plate 45. 
 
 Fig. 1. This example shows the return of the flank 
 at the angle of the building. The figm-es in the 
 metope are omitted. 
 
 Figs. 2 and 3 show the forms of the moulding and 
 upper part of the cornice. 
 
 Fig. 4. Elevation of the capital, and of striking 
 the ovolo by conic sections. 
 
 Fig. 5. Section of one half the column. 
 
 Fig. 6. Section tlu'ough the annulets, of a large 
 size. 
 
 Fig. 7. Plan of the soffit inverted. 
 
 Plate 46. 
 
 ELEVATION OF THE DORIC ORDER ON THE TEMPLE 
 OF THESEUS, AT ATHENS. 
 
 This temple is one of the most ancient examples 
 of the Doric order now existing ; it was erected about 
 ten years after the battle of Salamis, by Cimon, the 
 son of Miltiades. The ceiling of the porch is re- 
 
98 
 
 GRECIAN IONIC. 
 
 markable for its construction ; there are great beams 
 of marble, the upper sides of which are level with the 
 bed of the cornice, and the ends corresponding ex- 
 actly to the triglyphs in the frieze, which give the 
 idea of the disposition of the timbers which were 
 first used in buildings, and from which the Doric 
 order is said to have had its origin. 
 
 This buUding is adorned with beautiful sculpture ; 
 the metopes of the frieze are charged with historical 
 figures, on which are represented various exploits of 
 Theseus ; the battle he had with Sinis, the notorious 
 robber, who dwelt in the Isthmus of Corinth. The- 
 seus is represented making Sinis undergo those tor- 
 ments which he had inflicted on others. 
 
 In the basso rilievo is represented a man taking 
 hold of another by his middle, and endeavoring to 
 throw him down ; this is, doubtless, intended to rep- 
 resent Theseus throwing Sch-on from a rock; the 
 combat of Theseus with the wild sow of Crommyon, 
 which was killed by that hero. In another basso 
 rilievo is represented a man presenting his hand to 
 a woman, perhaps to express the rape of Ai-iana, or 
 Helen, by Theseus. 
 
 Some others of the basso rilievos in the metopes 
 are less distinguished. The two mentioned by Pau- 
 sanius arc still to be seen on the front of the temple ; 
 one represents the battle of the Athenians with the 
 Amazons, the other the dispute of the Centam-s and 
 the Lapithw, in which Theseus kills a Centaur with 
 his own hand. 
 
 The first seems to represent the instant when the 
 Athenians granted peace to the Amazons, for there 
 the women are represented as sitting. 
 
 The inside of the temple is not ornamented like 
 the outside. 
 
 This temple is now a Greek church, dedicated to 
 St. George, and is at present in high esteem among 
 the Athenians. 
 
 Fig. 1. The elevation of the order, with the heights 
 and projections of the members in numbers. 
 
 The figures in the metopes are omitted. 
 
 Fig. 2. Represents the ovolo above the facia of 
 the cornice. 
 
 Fig. 3. Plan of the sofilt inverted. 
 
 Fig. 4. Plan of the ovolos and annulets of the 
 column. 
 
 Fiff. 5. Section of one half of the column. 
 
 Plate 47. 
 
 ELEVATION OF A URECIAX DOHIC, OF A LIGHTER 
 PUOrOKTIOX THAN ANY OF THE I'KECEDIXG, WITU 
 THE PIlOrORTIOXAL MEASURES IX NUMBERS. 
 
 The ratio of the parts of this elevation is the same 
 as that on the portico of Philip, King of Macedon, in 
 the Island of Delos ; but the profile of the cornice 
 diflcrs as follows : Instead of the ovolo, which I have 
 introduced in this example, a cima recta in the origi- 
 nal occupies its place ; and instead of the next ovolo 
 under the fillet in this, there is in the original a cima 
 rcversa. The profile in this plate I conceive to be 
 more beautiful than the original, as it will produce a 
 greater variety of light and shade, and, consequently, 
 the mouldings will be more clearly defined ; but as 
 the reader may be desirous of a knowledge of the 
 true form and taste of the original mouldings, I have 
 shown them in Fig. 3. 
 
 Fig. 1. Elevation, with the jiroportional measures 
 in numbers. 
 
 Fig. 2. A section through the 
 
 upp 
 
 er part of the 
 
 cornice, showing the form and taste of the mouldings 
 inti'oduccd into this elevation, by P. Nicholson. 
 Fig. 4. A section of the anta3 of the same portico. 
 
 Plate 48. 
 
 FROM THE CHGRAGIC MONUMENT OF THRASYLLUS. 
 
 Fig. 1. The proportional measm-es in irumber. 
 Fig. 2. Section through the cornice. 
 Fig. 3. Section throvigh the capital. 
 
 GRECIAN IONIC. 
 
 Plate 49. 
 
 THE IONIC TEMPLE. 
 
 Fig. 1. A grouml plan of the Temple on the Ilissu.'!, irith a por- 
 tico at each end. The colums G G are wanting ; but in the place 
 •where they stood circles are marked on the pavement, which are 
 exactly of the same dimensions with the remaining columns, and 
 were evidently designed as an accurate guide to the workmen, when 
 they erected those columns which are now destroyed ; for wliich 
 reason it was thought necessary to make these circles like\rise on 
 the plan which is here given. The capitals of the antip, belonging 
 to the posticus or back front, remain entire, and are of the same 
 form and dimensions with those of the portico, except only that the 
 sides contiguous to the hack wall of the cell are but half so broad 
 as the faces next to the columns ; whereas, in the antce oi the por- 
 
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 VLJ 
 
GRECIAN IONIC. 
 
 99 
 
 tico, the sides next tlie pronaos and the faces next the columns 
 are equal. The architraves of the back front project considerably 
 beyond the ant;c, and there arc sufficient remains of them to show 
 exactly how far the columns of the back front were distant from 
 the back wall of the cell. 
 
 Fig. 2. The elevation of the south side of the temple. 
 
 Note. — The ground plan and elevation are here given as meas- 
 ured by Stuart and Ilcvctt, in feet, inches, and decimals. 
 
 It has been already observed, in the general definitions of the 
 orders, that every order consists of a column and an entablature ; 
 that every column consists of a base, a shaft, and a capital, except 
 in the Doric, where the base is omitted ; that every entablature con- 
 sists of an architrave, a frieze, and a cornice ; that the base, shaft, 
 capital, architrave, frieze, and cornice are the principal members of 
 an order ; and that the peculiar mode or form of the members de- 
 termines the particular name of the order. But since many of the 
 mouldings are common to all the orders, and are generated in a 
 similar manner, what has been said in the general definition, and 
 also on the Doric order, will render it unnecessary to repeat the 
 same things in the Ionic, as such mo\ildings cannot form any partic- 
 ular feature of any particular order. It is therefore sho\vn, in the 
 subjoined definitions, how these members ought to be modified, so 
 that they may constitute the Ionic order. 
 
 DEFINITIONS. 
 
 1. If from the under side of the abacus of an or- 
 der there project two or more sphals on each end of 
 the fi'ont, in a plane, parallel to the frieze, so that the 
 extremity of each shall be at the same distance from 
 the axis of the column, and also two others upon the 
 opposite side of the abacus, parallel to the former 
 and projecting the same distance from the axis of the 
 column, so that each of the spirals shall have the 
 same number of revolutions, and equal and similar to 
 each other, the projecting part contained between 
 any two spirals is called a volute. 
 
 2. An order which has volutes and mouldmgs in 
 the capital of the annular kind, and the ichnogi-aphy 
 of the abacus square, as in the Doric order, the archi- 
 trave finishing of plain facia?, and mouldings either 
 plain or enriched, the frieze a plain surface, the cor- 
 nice to consist of a cima recta, then a fiJlet and an 
 echinus only ; and if to the under side of the corona 
 are hung a row of equal and similar parallclopipeds, 
 equidistant from each other, whose fronts arc in a 
 plane parallel to the plane of the frieze, then each of 
 these parallclopipeds is called a dentil. 
 
 3. An order so constructed is similar to that in- 
 vented by the lonians, and, consequently, is the Ionic 
 order. 
 
 Plate 30. 
 
 FROM THE IONIC TEMPLE ON THE lUYER ILISSUS, 
 AT ATHENS. 
 
 The simplicity and greatness of the parts, their 
 judicious arrangement, the beautiful turning on the 
 volutes, and the graceful curve of the hem hanging 
 between tliem, render this one of the most beautiful 
 and bold examples of this order. 
 
 The elegant base of the column, the grand propor- 
 tion of the entablature, the massy mouldings of the 
 cornice, and the spacious surface of the frieze, well 
 adapted for sculptured ornaments, and the architrave 
 for its strength, as it is not broken in two or more 
 facia;, arc considerations which shoidd recommend 
 this example. 
 
 Fig. 1. The elevation of the order and details fig- 
 ured in proportional parts for practice. 
 
 Fig. 2. A drawing of the order, by dividing the 
 whole height into twenty-one parts, which are dis- 
 posed of in modules and mmutes, as shown in the 
 example ; one of the parts makes a module, or thirty 
 minutes. 
 
 Fig. 3 shows how to form the curve of the fluting ; 
 the Grecians used the ellipsis form, while the Ro- 
 mans as uniformly made use of a semicucle, as in 
 Fig. 4. 
 
 Fig. 4. Explained the same as Fig. 3, in plate 58. 
 
 Fi£ 
 
 Plate 51. 
 
 1. The capital inverted, of the different tastes 
 
 of forming the volutes. 
 
 Fig. 2. The elevation of the same. 
 
 Plate 52. 
 
 FROM THE TEMPLE OF mXERVA POLIAS, AT PRIENE, 
 IX IONIA. 
 
 The small projection of the cima recta, and its 
 great height, is of itself beautiful and well contrived 
 for the ornament, as it is less obsciircd by the shadow 
 from the concave and convex parts of the moulding. 
 This small projecture is also well adapted for a low 
 corona ; for the greater the projecture of the cima 
 recta, the more it will predominate over the corona, 
 by the principles of optics ; and, on the contrary, the 
 less the projecture of the cima recta, the less it will 
 predommate over the corona. It follows, therefore, 
 that a low corona wiU require a cima recta of a 
 
100 
 
 GRECIAN IONIC. 
 
 small projccture; but a gi-eater height of the corona 
 will require a greater projecture of the cima recta, 
 and a less height. The dentils, which are a striking 
 feature in this order, show here to very great advan- 
 tage, their bold and singular projecture greatly reliev- 
 ing tlicm from each other. 
 
 The architrave is well proportioned to itself, and 
 also to the cornice ; the capital is elegant, and the 
 spirals of the volutes arc beautifully drawn. 
 
 The surprising delicacy of the ornaments, and thck 
 bold relief, with the grand ratio of the parts and 
 mouldings to each other, I'cnder this one of the most 
 beautiful examples of the Ionic order. 
 
 Fig. 1. The elevation of this example, the propor- 
 tional measures in numbers. 
 
 Fig. 2. Ichnography of the dentils. 
 
 Fig. 3. Profile of the mouldings in the base to a 
 larger size. 
 
 The cimatium, or crown of the arcliiti-ave, was 
 taken from the designs of Mr. Wood, who visited 
 this temple before Mr. Revett. 
 
 The base of the column is true Ionic : it has no 
 plinth ; the upper scotia is inverted, which diversifies 
 and gives the contoiu* a greater beauty than is the 
 Vitruvian base, in which the scotiaj are one over the 
 other, uninvertcd. The torus is elli2:)tical, and 
 fluted. 
 
 The eyes of the volutes are bored two inches and 
 a half deep ; the hem, or border, with its fillets rest- 
 ing on the echinus, and connecting with a gi-aceful 
 curve the spirals of the volutes, seeming to keep 
 them secure in their place, adds greatly to the beauty 
 of this capital. 
 
 Plate 53. 
 
 FROM THE TEMPLE OF MINERVA POLIAS, AT RRIENE. 
 
 Fig. 1. Section through the cornice of the pediment. 
 
 Fig. 2. Front of tlie cornice, showing the orna- 
 ments on the mouldings. It is remarkable, that the 
 enrichment of the upper moulding dificrs from that 
 on the lateral cornice. 
 
 Fig. 3. The mouldings of the capital, with then- 
 proportion in numbers. 
 
 Fig. 4. Volute, with the measure in feet, inches, 
 and tenths. 
 
 Fig. 5. A section through the upper torus of the 
 base, which is of an elliptical form, the transverse 
 axis being inclined to the plane of the horizon. 
 
 Plate 54. 
 
 FROM THE SAME TEMPLE. 
 
 Fig. 1. The elevation of the front of the capital, 
 to larger size. 
 
 Fig. 2. The ichnography of half of the capital. 
 Fig. 3. Side elevation of the same. 
 
 Plate 55. 
 
 FROM THE TEMPLE OF BACCHUS, AT TEOS, IN IONIA. 
 
 This temple was first begun of the Doric order, by 
 Hermogenus ; but afterwards he changed it into the 
 Ionic, and dedicated it to Bacchus. 
 
 This example is drawn from accurate measures, 
 taken from that celebrated building. 
 
 The dentils, in the cornice, add gi-catly to the char- 
 acter of the order. 
 
 Fig. 1. The elevation of the order. It may here 
 be observed, that no measiues have been taken of 
 the parts which are marked in this example with 
 letters, as none of them could be found. They arc 
 here supplied by mere conjectTire. 
 
 The base of the columns. It is thought, from the 
 little differences between the shaft at the base and 
 that immediately under the capital, that the base 
 which is here exhibited did not belong to the capital 
 shown at Fig. l,but to some of the interior columns; 
 for the ancients always made the interior ranges of 
 columns less in diameter than the exterior, as is to 
 be found in the celebrated Athenian buildings, the 
 Temple of Minerva, and the Propylea. 
 
 Fig. 2. Profile of one half the fi-ont of the capital, 
 with the measure of the volute, and proportional 
 measures in numbers. 
 
 Plate 56. 
 
 FROM THE TEMPLE OF MINERVA, AT ATHENS. 
 
 Fig. 1. Another example of a volute, showing the 
 different sections and formation of the face mould 
 ings thereof. 
 
 Fig. 2. A section through A B. 
 
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GRECIAN ARCHITECTURE. 
 
 101 
 
 GRECIAN AllCHITECTURE. 
 
 CORINTHIAN ORDER. 
 
 On the archih-avc of the Choragic Monument at Lysicrates was 
 the following inscription : — 
 
 " Lysicrates, of Kikyna, the son of Lisithetdcs, teas citoraffiis, (or gave 
 the chorus at his own expense.) T/ie tribe of Akamantis obtained 
 tlte victory in the chorus of boys. T/ieon teas the performer on the flute ; 
 Lysades, an Athenian, was the teacher of the chorus. Eeaenatus was 
 archon." 
 
 From this we conclude that on some solemn festival, which was 
 celebrated with games and plays, Lysicrates of Kikyna, a demos 
 or borough town of the tribe of Akamantis, exhibited at his own 
 expense, on behalf of the tribe to which he belonged, a musical or 
 theatrical entertainment, in which the boys of Akamantis obtained 
 the ■(■ictory ; also, that, in commemoration of the victory, this mon- 
 ument was erected to perpetuate the same to posterity, by the name 
 of the archon, or magistrate, in whose time this took place. It ap- 
 pears that the buUding was erected about three hundred and thirty 
 years before the Christian era, in the time of Demosthenes, ApeUcs, 
 Lysippus, and Alexander the Great. The tripod seems to have 
 been the peculiar reward bestowed by the people of Athens on that 
 choragus who exhibited the best musical or theatrical entertain- 
 ment ; and we find this particular custom obtained for these tripods 
 the name of choragic tripods. It was customary for the victor to 
 dedicate the tripod he had won to some divinity, and to place it 
 either on one of the temples abrcady built, or on the top of some 
 edifice erected and consecrated by him for the purpose. Tlius they 
 participated of the sanctity of the place, and were secured from in- 
 jury or violence. 
 
 A tripod thus dedicated was always accompanied with an inscrip- 
 tion, so that it became a permanent, authentic, and public monu- 
 ment of the victory and of the person who had obtained it. 
 
 Stuart and Eevett deduce many circumstances to prove that it 
 was erected for the above purpose, which appears rational and 
 conclusive. 
 
 Description of the Choragic Monument. 
 
 The Choragic JMonviment of Lysicrates, which we 
 are about to describe, is commonly called, by the mod- 
 ern Athenians, to *ava|i tou Arnxotfl^vioj, or the Lantern 
 of Demosthenes. 
 
 This monument of antiquity, which is exquisitely 
 \\Tonght, stands near the eastern end of the Acropo- 
 lis, and is partly enclosed in the hospitium of the 
 Capuchins. It is composed of three distinct parts : 
 first, a quadrangular basement ; secondly, a circular 
 colonnade, of which the intercolumniations were en- 
 tirely closed ; and thirdly, a tholus, or cupola, with the 
 ornament that is on it. There is no entrance or aper- 
 ture in the basement, which is entirely closed on 
 every side. The basement supports the circidar col- 
 onnade, and was constructed in the following man- 
 ner : SLx equal panels of white marble placed con- 
 
 tiguous to each other, on a circular plan, formed a 
 continued cylindrical wall, wlxich was divided from 
 top to bottom into sL\ equal parts by the junction of 
 the panels. On the whole length of each juncture 
 was cut a semicircular gi-oove, into which a Corin- 
 thian column was fitted with great exactness, so as 
 eflcctually to conceal the junctures of the panels.* 
 These columns projected somewhat more than half 
 their diameters from the surface of the cylindrical 
 wall, and have the Attic base. The shaft of the col- 
 umn is fluted in a singular manner ; it contains thir- 
 teen flutes : the lower extremities of these flutings 
 descend below their usual limits, and are cut into the 
 apophyges, or scape of the column, and the upper 
 extremities terminate in the form of leaves ; the an- 
 nular channel, immediately above them, which di- 
 vides the shaft of the column from the capital, waa 
 probably filled with an astragal or collarino of bronze. 
 Under this terminated the fluting in the form of an 
 annular tier of leaves, turning outward from the shaft 
 of the column. 
 
 This capital exhibits a specimen of the Grecian 
 art. The annular tier of leaves springing from the 
 neck in fonn of the palm, the acanthus forms the 
 second tier with the flowers. Li the third tier is 
 shown the beautiful branches and the scrolls, termi- 
 nating under the angular extremity of the abacus, 
 the points of which are cut short ; it in this respect, 
 as well as in the disposition of the foliage, differs con- 
 siderably from any other example of the Grecian 
 Corinthian capitals. 
 
 The entablature. The architrave is divided into 
 four divisions, the band or ogee and three parallel 
 planes or faces projecting one over the other ; the 
 lower edges stand out one or two degrees from a per- 
 pendicular line. 
 
 The frieze of this entablature is ornamented with 
 sculpture, representing the story of Bacchus and the 
 Tyrrhenian pirates. The figure of Bacchus himself, 
 the fauns and the satyrs who attended on the mani- 
 festation of his divinity, the chastisement of the 
 pirates, their terror and their transformation into dol- 
 phins, are expressed in this basso riUevo with great 
 spirit and elegance. 
 
 The cornice is very plain, composed of dentils and 
 
 * The two tripods are -wrought in basso rilievo on each of the 
 panels ; they are probably of the kind described by Homer and 
 Hesiod. 
 
102 
 
 BASES. 
 
 plain moiUduigs, in the place of the cima or cima- 
 tium, having an upright front ; it is ornamented with 
 scrolls and honeysuckle foliage in basso rUievo, in 
 the Yitruvian style. This cornice is composed of 
 several pieces of white marble, and bound together 
 by a cupola of one entire piece. 
 
 The cupola is ornamented with elegant workman- 
 ship ; its covering imitates that of thatch or of laurel 
 leaves ; the turret standing du-cctly over the wall re- 
 sembles a Vitruvian scroll ; next above the lam-el 
 leaves, the covering of the dome, spring three scrolls, 
 at equal distances from each other, in imitation of 
 those branches in the capital shown in this plate. 
 The flowers that ornament the top rise from the cen- 
 tre, and are composed of workmanship of foliage, 
 which terminate in three divisions of scrolls, of great 
 richness, on the top of which it is believed was sup- 
 ported the tripod gained as the prize, from the ck- 
 cumstancc that cavities are cut on the three principal 
 projections in an equilateral triangle, into which the 
 feet of the tripod were probably fixed ; and in the 
 fourth cavity, which is in the centre, and much the 
 largest, was erected a baluster to support the tripod. 
 Plate 57. 
 
 Fig. 1. This figure represents the elevation of the 
 Grecian Corinthian order, from the Choragic Monu- 
 ment of Lysicrates, proportioned to modules and 
 minutes. 
 
 Fig. 2. The inverted projection of the cornice. 
 
 Fig. 3. The base is attached to the basement. 
 
 Fig. 4. The capital inverted. 
 
 Plate 3S. 
 
 To draw the flutes of the columns of the Doric 
 order. 
 
 Divide the semi-circumference into ten equal parts ; 
 then with one of those parts, as a radius, and the 
 extremities of any division, as at 3 and 4, describe 
 arcs, cutting each other in C, and through C describe 
 a circle, or a part, and draw lines from the centre, 
 cutting that circle, which will give the centres for de- 
 scribing the flutes. 
 
 Or thus, for deeper Flutes. 
 
 Bisect any division, as 5, 6, at /; then on 5, 
 with the distance 5 /, describe an arc / D, cutting 
 the radius produced through 5 at D, and draw 
 the radii through the points 5, 6, 7, 8, 9, 10, cut- 
 
 ting that circle, which will give the centies of the 
 flutes. 
 
 Fig. 2. The elevation drawn from the plan. Fig. 1. 
 
 To ckaw the flutes of the Ionic and Corinthian 
 orders. 
 
 Fig. 3. Divide the semi-circumference into twelve 
 equal parts ; divide any division, as between 5 and 
 6, into eight equal parts ; then with a radius of three 
 of these equal parts, on the points 1, 2, 3, 4, 5, 6, 7, 
 8, 9, 10, 11, 12, as centres, describe the flutes, which 
 will leave the fiUets. 
 
 Fig. 4. The elevation drawn from the plan. Fig. 3. 
 
 BASES. 
 
 In no example of antiquity is the Doric column provided Tvith a 
 base. Tliis circumstance, says Mr. Partington, has occasioned no 
 small perplexity to some of those 'vrriters -n-ho seek, in every point, 
 some analogy to the human figure. Vitruvius has indeed said that 
 the base is a slioc, first invented to cover the nakedness of the ma- 
 tronly prototyjie of the Ionic order. " But," says Monsieur Lc Clcrc, 
 "I must o^^•n I cannot consider a column without a base, comparing 
 it to a man ; but I am, at the same time, struck 'with the idea of a 
 person ■without feet, rather than without shoes ; for ■which reason, 
 I am inclined to believe, either that the architects liad not yet 
 thought of employing bases to their columns, or that they omitted 
 them in order to leave the pavement clear, the angles and projec- 
 tions of bases being stumbling-blocks to passengers, and so much 
 the more troublesome, as the arcliitects of those times frequently 
 placed their columns very near each other, so that, had they been 
 made ■with bases, the passages between them ■^•ould have been ex- 
 tremely narrow and inconvenient." To supply this defect, as it is 
 generally considered, most architects have employed the Allic base, 
 which is common to all the orders except the Tuscan, though be- 
 longing, perhaps, more peculiarly to the Ionic. We have, therefore, 
 here given a representation of it, as furnished by Mr. Partington, 
 from Yignola. 
 
 It is seen that it consists of two tori, 
 with a seotia and fillets between, the 
 upper of which, iu this version, resembles 
 an inverted ovolo. The fillet, above the 
 upper torus, is always connected with the 
 shaft by a curve, as is also that under the 
 capital, for which reason they arc com- 
 monly considered as part of the shaft. The plinth, or square mem- 
 ber beneath, is usually understood, in Roman architecture, as an 
 indispensable appendage to the base, though PaUadio has omitted it 
 in his Corinthian order; but it is rarely found in the Greek speci- 
 mens. To save tliis order, however, fiom the sad humiliation of 
 being obliged to borrow a shoe, when required to wear one, Vignola 
 provided it with this appendage. Ilis base consists of one largo 
 torus, with one considerably smaller resting upon it, smmountcd 
 by the fillet. 
 
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ENTABLATURES. 
 
 103 
 
 M. Le Clerc has, in the opinion of Mr. Partington, discovered the 
 true reason why, at least in the latter Greek specimens, the base is 
 omitted — namely, the very narrow intercolumniations. In the 
 Greek order, alteration is not probable, and, perhaps, not desirable; 
 but in the Roman, -nhero this addition has long been provided for 
 us, and the intercolumniations adjusted accordingly, the omission 
 would bo certainly improper. 
 
 ROMAN BASES. 
 
 Several designs for bases after the Roman taste 
 are given on plate 59, which may be applied to col- 
 umns, pilasters, and, in some instances, to rooms, 
 chimney-pieces, &c. 
 
 Plate 59. 
 
 Fig. G. The Tuscan order. 
 Fig. E and A. The Doric. 
 Fig. B and C. The Ionic. 
 Fig. D. The Corinthian. 
 
 ENTABLATURES. 
 
 The orders consist of a composition of parts. When considered 
 in gross numbers, they consist of two parts, viz., the column and 
 entablature. These divisions are subdivided : the column com- 
 prises the base, capital, and their appendages, as shown in the orders. 
 The entablature consists of the architrave, frieze, and cornice. The 
 architrave, in all the orders, has the band. The Grecian Doric, 
 however, does not furnish us with more than two divisions, — the 
 band and frieze. The band, or fillet, which constitutes the upper 
 part of the architrave, is projected under the trigljiA ; and an an- 
 nulet is dropped from the iillet, a little on the frieze, to tlie soffit of 
 which are attached six drops, as in the Grecian examples. 
 
 In the Ionic and Corinthian orders, the Greeks have divided the 
 frieze into three projecting parts, as sho'^^^l in the example from the 
 Temple of Jlincrva Polias. Tlie divisions arc, 1st, lOJ ; 2d, 12 j ; 
 3d, 144 minutes. The Romans, in this respect, have followed the 
 Greeks, except in the proportions of the divisions ; as seen in the 
 Doric elevation found at Albano, near Rome; in the Diocletian 
 Baths ; and in the example from Andrea Palladio. 
 
 2d. The frieze or entablature is ornamented, in the Doric order, 
 with triglyphs, and sometimes with sculpture, as shown in the ex- 
 ample from the Temple of Theseus, at Athens. Aldrich has intro- 
 duced triglyphs into the Composite order, which I consider a com- 
 position of the three orders. This practice, however, is seldom 
 adopted ; although there may not be much impropriety in borrow- 
 ing from the Doric, as well as from the two higher orders. 
 
 The capital of the triglyph is from 4 to 6 minutes wide. The 
 width of the triglyph is commonly fr-om 28 to 30 minutes, having an 
 angle of 135 degrees from the outer comers, cutting from the face 
 24 minutes. The intermediate space is divided into five parts, the 
 second and fourth being cut at right angles from the centre. 
 
 The fi'icze of the two higher orders, viz., the Ionic and Corinthian, 
 afford a variety of ornaments, of which the Romans have been very 
 
 profuse ; as on the Temple of Fortuna Virilis, at Rome. See also 
 the example from the Arch of Titus. 
 
 3d. Cornices. — This assemblage of parts affords much variety, from 
 the plain bed mould, mutules, dentils, and modillions. The mu- 
 tulcs are common in the Doric planceer. The dentils are common 
 in the Ionic, and are placed between the hollow and the (juarter 
 round, as shown in the bed mould. An example of this is found 
 in the Temple of Fortuna Vkilis, and in the Coliseiun, at Rome. 
 The quarter round is sometimes ornamented with the egg and dart. 
 The Corinthian order has dentils and modillions, as shown in the 
 example from Jupiter Stator. Tlie mouldings are often ornamented 
 with carvings of various designs. 
 
 The facia, in the Grecian Doric, projects from 27 to 30 minutes 
 from the triglyijhs. In the Roman Doric, it sometimes projects 
 from 34 to 37 minutes. The height of the facia varies from 7 to 11 
 minutes. The crown moulding is a cima recta, and, in modern 
 times, the ovolo has been introduced in many instances, which is 
 preferred on account of its superior strength, and the beautiful 
 variety of light and shade which it presents to the eye. "We find 
 some examples overcharged with mouldings, which are not only 
 offensive to the eye, but destroy the appearance of strength and 
 proportion. An error of this kind is found in the Diocletian Baths, 
 in which the graceful simplicity is lost, when compared with the 
 Grecian Temple of Theseus. In the cornice, the facia has too 
 much projection, and is not deep enough, and would have a far 
 better appearance were the dentils quarter round, and bead left 
 out. They are not considered as properly belonging to the Doric 
 order. Palladio and others (as shown in some of the Roman ex- 
 amples given in this work) made use of a plain, simple bed mould, 
 composed of a hollow and round, under the planceer. This is as 
 much as belongs to the Doric. 
 
 In the Ionic, the Greeks have made xise of the eclunus, dentils, 
 an angular fillet, and a quarter round, under the planceer, as in the 
 example from the Temple of Minerva Polias. The extraordinary 
 projection of the dentils, rising above a plain frieze, has a beautiful 
 effect, as well as the modillions in the Corinthian order. This mo- 
 dilUon is frequently ornamented with foliage ; a decoration properly 
 belonging to, and supporting, the planceer. The ornamented ovolo 
 under the modillions, as found in the portico of the Pantheon, by 
 its chaste appearance, occasioned by not adding a sui'plus of variety, 
 is rendered one of the best specimens of the Romans. The example 
 taken from the Temple of Jupiter Stator is very beautiful. The 
 majestic proportions of the capital and entablatui'o would give it 
 the superiority, were it not overcharged with too much finery. The 
 addition of dentils, however, can be no objection to its pleasing 
 effect, as, in cities, eave cornices are not often viewed to advantage 
 at a greater distance than the angle of forty-five degrees, and within 
 that distance the ornamented planceer shows to good advantage:. 
 The proportions of cornices should invariably be regulated according 
 to these distances. If at the angle of forty-five degrees, the height 
 should be equal to its projections. If short of tliis, its projections 
 should increase, in regular projiortion, in all its members. l"he 
 cro«ni moulding of the cornices should be projected i^-ith soma 
 variation, — the Grecian ovolo at forty-five degrees, — but the cima 
 recta shoiJd not project so much, in order to open it more to the 
 rays of light j for if the swell does not receive a strong light, it is 
 rendered obscure at any considerable height. 
 
 I have introduced in tliis place several designs for cornices, which 
 may assist, in some measure, the fancy of those who may wish to 
 vary from the original Greek and Roman styles and proportions. 
 They may be executed on frontispieces, and many other places, 
 to advantage. 
 
104 
 
 CHIMNEY-PIECES. 
 
 Plate 60. 
 
 Presents five cornices, with the scale to wiiich 
 they are drawn. The scale is supposed to be the 
 diameter of the shaft of the column, at the bottom ; 
 from which these designs arc figured in proportional 
 parts. Figs. 1 and 5 arc plain plancccrs ; 3 and 4 
 ornamented friezes and entablatures. No. 1, plan of 
 the plancccr of Figs. 3 and 4. 
 
 Plate 61. 
 
 Fig. 1. Design of a modillion cornice. No. 1, the 
 modillion and manner of drawing it, viz. : From A 
 radiate from 1 to 2 ; from B to 1 and 3 ; liom C to 
 3 and 4, which completes the lower curve. 
 
 Fig. 2. A cornice without the entablature. No. 2, 
 design of the planceer, with mutules and ornament. 
 
 Fig. 3. Design of a Doric entablature. No. 3, or- 
 namented planceer. 
 
 Fig. 4. A Doric entablature and cornice. No. 4, 
 mutules with a reset. 
 
 CHIMNEY-PIECES. 
 
 It is a remarkable fact that neither the Italian nor the French, 
 nor indeed any of the continental nations, hare over excelled in com- 
 positions of chimney-pieces. It is believed that Inigo Jones, em- 
 inently distinguished among the arcliitects of England, ■was the 
 first who arrived at any great degree of perfection in this important 
 branch of architectural science. Other architects have, smco his 
 time, wrought upon his ideas, or furaishcd good inventions of their 
 own ; and of our many ingcnions and very able artists, -whoso prov- 
 ince it is to execute magnificent chimney-pieces in marble, happily 
 much in vogue, it may be said that, for taste of design and excel- 
 lence of workmanship, they are not surpassed by those of any other 
 nation. It was facetiously observed by Sir W'illiam Chambers, that 
 chimney-pieces should be " so situated as to be immediately seen by 
 those who enter, that they may not have the persons already in the 
 room, who are generally seated about the fire, to search for." There 
 is much good sense in this remark. 
 
 As the Egyptians, the Greeks, and the Romans, 
 to whom architecture is so much indebted in other 
 respects, lived in warm climates, where fires in the 
 apartments were seldom or never necessary, they 
 have thrown but little light on this branch of archi- 
 tecture. Amongst the antiquities of Italy, I do not 
 recollect any remains of chimney-pieces. Palladio, 
 indeed, mentions two — the one at Baia, and tlie 
 other near Civita Vecchia, which stood in the mid- 
 dle of the room, and consisted of columns support- 
 ing architraves, whereon were placed the pyramids 
 or funnels through which the smoke was conveyed. 
 
 Scamozzi takes notice of three sorts of chimney- 
 pieces used in Italy at his time. One of these he 
 calls the Roman, the apcrtiure of which is surrounded 
 only with a clumsy architrave ; another he calls 
 Venetian, which is likewise adorned with an archi- 
 trave, upon which arc placed a frieze and cornice, 
 and on the sides thereof are pilasters with consoles. 
 The third sort he calls a Padiglione. 
 
 This last he particularly recommends where the 
 walls are thin, if not being hollowed into the wall, 
 as both the other sorts arc, but composed of a pro- 
 jecting entablatm'c supported by consoles, termini, or 
 caryatides, on which the pyramid is placed. This 
 sort of chimney-piece is still very common in Italy. 
 The Dutch are very fond of it, and it may be found 
 in many old English country-houses. 
 
 The size of the chimney-piece must depend upon 
 the dimensions of the room wherein it is placed. Li 
 the smallest apartments, the width of the aperture is 
 never made less than from three feet to three feet six 
 inches ; in rooms from twenty to twenty-four feet 
 square, or of equal superficial dimensions, it may be 
 four feet wide ; in those of twenty-five to thkty, 
 from four to four and a half; and in such as exceed 
 these dimensions, the aperture may be extended to 
 five, or five feet sbc inches ; but should the room be 
 extremely large, as is frequently the case with halls, 
 galleries, and saloons, and one chimney of these 
 last dimensions neither afford sufficient heat to warm 
 the room, nor sufficient space round it for the com- 
 pany, it will be much more convenient, and far hand- 
 somer, to have two chimncy-piec"cs of a moderate 
 size, than a single one exceedingly large, all the parts 
 of which would appear clumsy and disproportioncd 
 to the other decorations of the room. The chimney 
 should always be " so situated as to be immediately 
 seen by those who enter, that they may not have the 
 persons already in the room, who arc generally 
 seated about the fire, to search for." The middle of 
 the side partition wall is the most proper place in 
 halls and saloons, and Ihe other rooms of passage to 
 which the principal enlranccs are commonly in the 
 middle of the front, or of the back wall ; but in 
 drawing-rooms, dressing-rooms, and the like, the 
 middle of the back wall is the best situation, the 
 chimney being then farthest removed from the doors 
 of communication. Tlie case is the same with re- 
 spect to galleries and libraries, whose doors of en- 
 trance are generally cither at one or both ends. In 
 
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DOORS. 
 
 105 
 
 bed-chambers the chimney is always placed in the 
 middle of one of the side partition walls, and in 
 closets, or other very small places. It is, to save 
 room, sometimes placed in one corner. 
 
 Whenever two chimney? are introduced in tlie 
 same room, they must be regularly placed, either 
 directly facing each other, if in different walls, or at 
 equal distances from the centre of the wall in which 
 they are both placed. The Italians frequently put 
 their chimneys in the front walls between the win- 
 dows, for the benefit of looking out while sitting by 
 the fire. 
 
 The proportion of the apertures of chimney-pieces 
 of a moderate size is generally near a square ; in 
 small ones, a trifle higher ; and in larger ones, some- 
 what lower. Chimney-pieces are made either of 
 stone or marble, or of a mixture of these with wood, 
 scagUola, or molu, or some other unfragile substances. 
 Those of marble are most costly, but they are also 
 most elegant, and the only ones used in high-finished 
 apartments, where they are seen either of white or 
 variegated marbles, sometimes iidaid and decorated 
 with the materials just mentioned. All their orna- 
 ments, figures, or profiles are to be made of the pure 
 white sort ; but their friezes, tablets, panels, shafts 
 of columns, and other plain parts, may be of party- 
 colored marbles, such as the yellow of Sienna, the 
 brocatello of Spain, the jaspers of Sicily, and many 
 other modern as well as antique marbles firequently 
 to be had in this country. Festoons of flowers, 
 trophies, and foliages, frets, and other such decora- 
 tions cut in white statuary marble, and fixed on 
 grounds of these, have a very good effect. But there 
 should never be above two, or at the utmost three, 
 different sorts of colors in the same chimney-piece, 
 all brilliant and harmonizing with each other. In 
 the inferior class of houses, and in upper chambers, 
 wood is generally used in the construction of chim- 
 ney-pieces, painted and varnished so as to resemble 
 marble. The use of wooden chimney-pieces, when 
 judiciously applied, materially lessens the expense, 
 and answers every purpose of utility or ornament. 
 
 In many places, the wildest notions have been in- 
 dulged in the designs of this part of architecture. 
 Sometimes we see a chimney-piece, the shelf of which 
 is supported on a numerous variety of mouldings, piled 
 one above the other until they project nearly as much 
 as the shelf itself; this, I contend, is useless and out of 
 , good taste, for they cannot be seen to any advantage, 
 
 14 
 
 as in ordinary eases they fall below the eye, except 
 when seated, and then they are so nearly on a level 
 with it that they cannot be seen to any advantage. 
 If, therefore, one half of the expense of mouldings 
 should be laid out in the frieze and pilasters, or col- 
 umns, they would have a much better appearance, 
 and display a more refined taste. 
 
 Plate 62. 
 
 On tills plate will be found two designs for com- 
 mon chimney-pieces, drawn to a scale of feet and 
 inches. 
 
 Plate 63. 
 
 On this plate will be found two designs for chim- 
 ney-pieces, as executed by Isaiah Rogers, Esq., in the 
 Tremont House, Boston, Massachusetts, drawn firom 
 the same scale as plate 62. 
 
 DOORS. 
 
 In our northern climate, the fewer doors a room has the more it 
 ■will be comfortably habitable ; for as vre have much more cold than 
 hot weather, it is yery necessary to make the rooms as close as pos- 
 sible, otherwise they will not be fit to live in the greater part of the 
 year. Wherefore it will be advisable never to make either more 
 windows or doors than are absolutely necessary. In this country, 
 the real and feigned doors of a room, with their ornaments, fre- 
 quently cover so great a part of the walls that there is no place 
 left for either pictures or furniture. 
 
 Doors of entrance to private houses should not be 
 less than three feet wide, nor more than six feet ; but 
 to churches, theatres, and other public structures, 
 where there is a constant ingress and egress of peo- 
 ple, and firequently great crowds, the apertures must 
 be larger, and their width cannot be less than six feet, 
 nor should it exceed ten or twelve. 
 
 Li settling the dimensions of the apertures of doors, 
 regard must be had to the architecture with which 
 the door is surrounded. K it be placed in the inter- 
 columniation of an order, the height of the aperture 
 should never exceed three quarters of the space be- 
 tween the pavement and the architrave of the order, 
 otherwise there cannot be room for the ornaments of 
 the door. Nor should it ever be much less than two 
 thirds of that space, for then there will be room suf- 
 ficient to introduce both an entablature and a pedi- 
 ment without crowding; whereas, if it be less, it will 
 appear trifling, and the intercolumniation will not be 
 sufficiently filled. The apertures of doors placed in 
 arches are regulated by the imposts, the top of the 
 
106 
 
 DOORS. 
 
 cornice being generally made level with the top of 
 the impost. And when doors are placed in the same 
 line with windows, the top of the aperture should 
 level with the tops of the apertures of the windows ; 
 or if that be not practicable without making the door 
 much larger than is necessary, the aperture may be 
 lower than those of the windows, and the tops of all 
 the cornices made on the same level. 
 
 With regard to the situation of the principal en- 
 trance, Palladio observes, that it should be so placed 
 as to admit of an easy communication with every 
 part of the buUding. Scamozzi compares it to the 
 mouth of an animal; and as nature, says he, has 
 placed the one in the middle of the face, so the archi- 
 tect ought to place the other in the middle of the 
 front of the edifice, that being the most noble situa- 
 tion, the most majestic and convenient. In several 
 of the palaces at Rome, as those of the Pamfili in 
 the Corso, and of the Bracciano, at Santi Apostoli, 
 there are two principal entrances in the same aspect ; 
 but this is, in general, to be avoided, as it leaves 
 strangers in doubt where to seek for the state apart- 
 ments, which should always be contiguous to the 
 principal entrance. In interior dispositions, the doors 
 of communication must be situated, as much as pos- 
 sible, in a line ; the advantages of which are, that it 
 contributes towards the regularity of the decoration, 
 and facilitates and shortens the passage through the 
 apartments in summer ; or on public occasions, when 
 the doors are set open, it produces a free circulation of 
 air, and likewise gives a much more splendid appear- 
 ance to the apartments, by exposing to view at once 
 the whole series of rooms, which is more particularly 
 striking when the apartments are illuminated, as on 
 occasions of balls, routs, or other rejoicings. There 
 should, if possible, be a window at each end of the 
 building, directly facing the line of the doors of com- 
 munication, so that the view may be more extensive, 
 and take in at once not only all the rooms, but like- 
 wise parts of the gardens, or other prospects sur- 
 rounding the building ; and whenever this is not 
 practicable, it will do well to place mirrors at each 
 end of the apartment, or to counterfeit doors, and fill 
 them with large plates of glass, or with sashes and 
 squares of looking-glass, as is the custom in France, 
 which by reflection mu'tiply the rooms, the doors, 
 and other objects, making an apartment, though lim- 
 ited or small, appear very considerable. 
 
 The door of entrance from halls, vestibules, or ante- 
 
 chambers, either to the principal apartment or to any 
 even of the inferior ones, should be in the middle 
 of the room, if possible, and facing a window ; those 
 that lead to galleries, or any other long rooms, should 
 be in the middle of one of the ends ; and in general, 
 all entrances should be so contrived as to offer to 
 view, at the first glance, the most magnificent and 
 extensive prospect of the place they open into. The 
 doors of communication from one room to another 
 of the same apartment must be at least two feet dis- 
 tant from the front walls, that the tables placed against 
 the piers, between the windows, or other pieces of 
 furniture put there, may not stand in the way of 
 those who pass. In bed-rooms, care must be taken 
 to make no doors on the sides of the bed, unless it 
 be to communicate with a water closet, wardrobe, 
 bath, or other eonveniency of that kind, as well on 
 account of t"he draught of air as of the noise commu- 
 nicated through them, or attending their opening and 
 shutting; both of which are always troublesome, and 
 on some occasions dangerous. Neither ought doors 
 to be placed near chimneys, for the same reasons, 
 and as the opening of them would disturb those who 
 sit by the fire. 
 
 In composing doors, regard must be had, both in 
 their size and enrichments, to the place they lead to. 
 Those that give entrance to churches, theatres, state 
 apartments, or other places of consequence must be 
 large and profusely enriched ; but such as open to 
 humbler habitations may be small and sparingly 
 decorated, unless the nature of the building should 
 require otherwise. Where several doors are in the 
 same aspect, as on the inside of a hall, saloon, or gal- 
 lery, they should be all of the same size and figure, 
 unless there be many, in which case the principal 
 ones, provided they stand in the middle of a side, or 
 in the middle of the ends of the room, may be larger, 
 of a different form, and more abundantly adorned 
 than the rest. But, whenever more than two sorts 
 are introduced in one room, it always tends to con- 
 fuse the spectator. 
 
 The commonest sort of doors are made of pine, 
 painted in various manners, and the better kind of 
 them are of mahogany, or oak, or different sorts of 
 rare wood, inlaid. With regard to their construction, 
 strength, beauty, and straightness are to be consid- 
 ered ; all which purposes are answered by composing 
 them of several panels. The number of these must 
 depend on the size of the door, which should like- 
 
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WINDOWS. 
 
 107 
 
 wise regtilate the thickness both of the panels and 
 the framing. If the doors be adorned with orna- 
 ments of sculpture, as is sometimes usual in very rich 
 buildings, they must either be sunk in, or kept very 
 flat upon, the sm-face, both for tlic sake of lightness, 
 and to prevent their being broken. The panels may 
 be either raised or flat, and surrounded with one or 
 two little plain or enriched mouldings, contained in 
 the thickness of the framing, not projecting beyond 
 it, as is sometimes seen in old buildings. 
 
 Doors that exceed three feet and a half in breadth 
 are generally composed of two flaps, by which means 
 each part is lighter ; when open, does not project so 
 far into the room ; and when required, may be made 
 to fold entirely into the thickness of the wall. It is 
 to be observed, that all doors should open inwards ; 
 otherwise, in opening a door to give a person en- 
 trance, it must open in his face, and may chance to 
 knock him down. 
 
 For a variety of doors, in the modern taste, see 
 
 plates 64, 65, 66. 
 
 Plate 64. 
 
 On plate 64 will be found sLs designs for inside 
 doors, with the finish. The proportions of each part 
 are figured, and across each will be seen a sectional 
 plan, showing panels, &c., either raised or sunken, 
 as the case may be. A is an elevation of a circular 
 head door, and is designed for an outside door. The 
 architraves of each at 1, 2, and 3, are those on 
 plate 30. — Editors. 
 
 Plate 65. 
 
 Figs. 1 and 2. Designs for outside doors. 
 
 Figs. 3 and 4. Horizontal section of the same, with 
 a projection of the threshold, steps, and pilasters. 
 
 Fig. 5. Section of the style, panel, and moulding. 
 
 Fig. 6. Section of the pilaster and plinth. 
 
 Plate 66. 
 
 Fig. 1. Front door finished in the Ionic style, the 
 pillars supporting the cap in the wall. 
 
 Fig. 2. The recess and side view of the column. 
 
 Fig. 3. The recess of the door from the column 
 and step on which the pillars stand. 
 
 Fig. 4. The ceiling of the recess and inverted cap- 
 itals of the column. 
 
 Fig. 5. Style, panel, and moulding of the door. 
 
 Good taste has taught us to avoid the multiplica- 
 tion of small members on inside finishing, and to 
 adopt in their place plane surfaces, or appropriate 
 
 mouldings of a proper size with their necessary ar- 
 rangements, as it is much easier executing a proper 
 finish of painting : the necessary application of a 
 pumice stone or sand paper, to produce a smooth 
 surface, is rendered impracticable, by numerous close 
 quirks, without injuring the paint on the otJHT parts. 
 On a plane surface, the work is much easier cleansed ; 
 and by this style of finish, which rejects every thing 
 that is mean and trifling, that manly character is 
 given to the work which the refined taste of ancient 
 and modern architects have so much admired. 
 
 The Proportions of the Architraves and Pilasters for 
 inside Finish. 
 
 The architraves for windows and doors in any one 
 apartment should be nearly of the same width, where 
 a uniformity of appearance requires it. Add together 
 the width of the door and of the window and the 
 splay ; find the mean width ; then divide it by 7, which 
 gives the width of the architrave ; but where fancy 
 pilasters are required, divide by 6, which gives one 
 sixth of the width of the opening for the width of the 
 pilasters. The designs in plate 30 give the full size 
 that those in general use are executed. 
 
 CONSTRUCTION OF WINDOWS. 
 
 There has been in this branch of architecture, as well as all oth- 
 ers, a variety of changes and modifications to suit the taste and 
 fashion of the times. In civilized countries, convenience and beauty 
 are consulted ; whereas, in barbarous countries, strength and safety 
 are their most necessary requisites. In this enlightened and happy 
 country, every man of taste adorns his habitation with such as he 
 may deem to be most convenient, economical, and ornamental. The 
 enriching of windows with ornaments is of ancient date, and has 
 been handed down to us in common with most of the grand princi- 
 ples of the arts and sciences. 
 
 The proportions of the apertures of windows de- 
 pend upon their situation ; their width in all the 
 stories must be the same, but the different heights of 
 the apartments make it necessary to vary the heights 
 of the windows likewise. In the principal floor it 
 may be from two and one eighth of the width to two 
 and one third, according as the rooms have more or 
 less elevation ; but in the ground floor, where the 
 apartments are usually somewhat lower, the aper- 
 
108 
 
 WINDOWS. 
 
 tures of the windows should seldom exceed a double 
 square ; and when they are in a rustic basement, they 
 are frequently made much lower. The windows of 
 the second floor may be, in height, from one and a 
 half of their width to one and four fifths ; and those 
 of attics or mezzanines, either a perfect square or 
 somewhat lower. The character of the order in 
 which the windows are employed, and that of the 
 profiles with which they are enriched, must likewise, 
 in some measure, be consulted, and the apertures be 
 made more or less elevated, as the order of the whole 
 decoration, or of the window itself, is more or less 
 delicate. 
 
 The windows of the principal floor are generally 
 most enriched. The simplest method of adorning 
 them is with an architrave surrounding the aperture, 
 covered with a frieze, and cornice suited thereto ; but 
 when the aperture is remarkably high with respect to 
 its width, it becomes necessary to spread the orna- 
 ments on the sides thereof, by flanking the architrave 
 with columns, pUasters, or consoles, in order to give 
 the whole composition an agreeable proportion. 
 The windows of the ground floor are sometimes 
 left entirely plain, without any ornaments whatever ; 
 at other times, they are surrounded with an archi- 
 trave, or with rustics, or have a regular architrave 
 crowned with its frieze and cornice. Those of the 
 second floor have generally an architrave carried 
 entirely round the aperture; and the same is the 
 method of adorning attic or mezzanine windows. 
 But these two last have seldom or ever either frieze 
 or cornice ; whereas, the second floor windows, when- 
 ever their aperture approaches a double square, are 
 often adorned with both. 
 
 The sills of the windows on the same floor should 
 be on the same level, and raised above the floor from 
 two feet nine inches to three feet at the very most. 
 When the walls are thick, they should be reduced 
 under the aperture of the windows, for the conven- 
 iency of looking out, and seats may be contrived to 
 fit these recesses, as is the custom in many modern 
 houses. In France, and now too often here, the win- 
 dows are carried quite down to the floor, which, when 
 the building is surrounded with gardens or other beau- 
 tiful prospects, renders the apartments exceedingly 
 pleasant in summer, but then they become exceed- 
 ingly cold in winter ; and the iron work, which in 
 France, and latterly very nmch here, is placed on the 
 outside by way of fence against accidents, ought 
 
 never to take place where regular architecture is 
 intended ; for all the gilding and flourishing in the 
 world can never make it tolerably accordant with the 
 rest of the composition. 
 
 In regular built houses, the sills of the windows 
 on the ground floor should be raised six feet above 
 the pavement on the outside of the building, to hin- 
 der passengers from looking into the apartments ; 
 but when this cannot be done without raising the 
 floor itself more than may be necessary, the lower 
 parts of the windows may be furnished with blinds. 
 The tops of the apertures of windows should never, 
 within the apartments, be carried up close to the cor- 
 nice of the room. A sufficient space ought always 
 to be left for an architrave, or at least two or three 
 inches between the architrave and cornice — a space 
 usually occupied by the cvirtain lath. 
 
 The interval between the apertures of windows 
 depends, in a great measure, on their enrichments. 
 The width of the aperture is the smallest distance 
 that can be between them, and twice that width 
 should, in dwelling-houses, be the largest ; otherwise, 
 the rooms will not be sufficiently lighted, and the 
 building will have rather the appearance of a prison 
 than of a structure calculated for the conveniences 
 and enjoyments of life. The purpose for which the 
 building is intended should regulate the quantity of 
 light to be introduced ; and, therefore, in dwelling- 
 houses, and all places where comfort and pleasure 
 arc the main purposes, there cannot be too much. 
 But in sacred structures, which should affect the 
 mind with. awe and with reverence, or in other great 
 works where grandeur of style is aimed at, it should 
 be cautiously and rather sparingly distributed. 
 
 The windows nearest to the outward angles must 
 be at least the width of their aperture distant from 
 the angle, and a larger space will be still more seemly, 
 and render the building more solid. In all the stories 
 of the same aspect, the windows must be placed 
 exactly one above the other, and those to the left 
 symmetrize with those to the right, in size, situation, 
 number, and figure. 
 
 The reasons for all these things are obvious enough, 
 and, therefore, it is needless to mention them. The 
 licentious practice of intermitting the architrave and 
 frieze of an order in the intervals between the col- 
 umns or pilasters, to make room for windows and 
 their enrichments, which are carried close up to the 
 cornice, can on no account whatever be suffered in 
 
WINDOWS. 
 
 109 
 
 regular architecture, it being in the highest degree 
 absurd to carry the windows above the ceiling, and 
 great want of judgment in an architect to intermix 
 and crowd together such a number of rich complicat- 
 ed parts as are those of the entablature of the order 
 and the entablatures of the windows. Besides, the 
 whole beauty of the order, when so mutilated, is 
 destroyed, its proportions and figure being entirely 
 changed. An interruption of the whole entablature 
 to make room for a window, and converting it into 
 an impost to the architrave, is a license equally un- 
 pardonable. 
 
 The common sort of builders in this country are 
 extremely fond of variety in the ornaments of win- 
 dows, and, indeed, in every other part of a building, 
 imagining, probably, that it betrays a barrenness of 
 invention to repeat the same object frequently. I 
 have seen a house with only eleven windows in the 
 whole front, and yet there were seven different sorts. 
 At another place, the case is the same, there being 
 seven or eight sorts of windows in the same aspect ; 
 and the like is to be met with in many other build- 
 ings, both in town and in the country. These in- 
 ventive gentlemen would do well to give their atten- 
 tion to some professors of the mechanic arts, who, 
 though exercising their talents on meaner objects, are 
 nevertheless worthy of their imitation. No taUor 
 thinks of employing seven or eight kinds of buttons 
 on the same coat ; a cutler will not make ten dif- 
 ferent sorts of knives for the same set; and if a 
 cabinet maker be trusted to furnish a room, he sel- 
 dom introduces more than one or two sorts of 
 chairs : their practice is founded on experience ; the 
 general approbation of mankind is the standard they 
 go by. 
 
 We do not discover, either in the works of an- 
 tiquity or those of the great modern architects, any 
 traces of this childish hankering after variety. The 
 same object is frequently by them repeated a hun- 
 dred times over ; and this is one of the causes of that 
 amazing grandeur, that noble simplicity, so much to 
 be admired in their productions. 
 
 This sameness must, however, have its limits ; for, 
 when carried too far, the imagination of the beholder 
 stagnates for want of occupation. In the most ad- 
 mired marks of architecture, we find the same objects 
 generally continued throughout the same level : thus 
 one order and one sort of windows or niches gener- 
 ally reign throughout the story ; but in other stories. 
 
 where the eye and the imagination necessarily as- 
 sume a fresh course, the decoration is altered. 
 
 Sometimes, however, it may be necessary to in- 
 crease the size, and vary the figures, of the windows, 
 either in the centre break or in some other prominent 
 part of a front, in order to light a saloon, a gallery, or 
 a hall higher than the rest of the room. But then it 
 will always be advisable to repeat the same form if 
 simple, as an arch, three, five, or more times, accord- 
 ing to the extent of the plan, so that the mind may 
 be in some degree satiated before it is conducted to 
 a new object. 
 
 Venetian windows and Venetian doors, too, are 
 on some occasions necessary, particularly in small 
 buildings, to light a hall, a vestibule, or such other 
 rooms as cannot admit of two windows, and yet 
 would not be sufficiently lighted with one. But 
 where they can be avoided, it is best ; for the col- 
 umns which separate the large interval from those 
 on the sides form such slender partitions, that, at a 
 distance, they are scarcely perceived, and the whole 
 looks like a large, irregular breach made in the 
 wall ; and, however advisable it may be to repeat the 
 same form as has above been mentioned, the repeti- 
 tion of these Venetian windows should always be 
 avoided. 
 
 The sashes of windows are generally made of pine, 
 cherry, or mahogany, and sometimes of iron, copper, 
 or other metals. Our artificers excel in these works ; 
 they make them very neatly, and though in appear- 
 ance slight, very strong. The lights of glass are 
 proportioned to the size of the windows, there being 
 commonly three in width and four in height, what- 
 ever be the dimensions of the window ; each sash is 
 composed of two equal parts, placed one above the 
 other, and either the lowermost, or both of them, 
 being hung on pulleys and counterpoised with weights, 
 and moved up and down with great ease, the 
 weights being concealed. 
 
 The shutters are always within the apartments 
 wherever beauty is aimed at, those on the outside 
 destroying the appearance of the front. They are 
 divided into several vertical slips, folding behind 
 each other, for the conveniency of ranging or boxing 
 them, when open, in the thickness of the wall. Each 
 slip or fold is framed and composed of several pan- 
 els, either raised or flat, surrounded with small 
 mouldings contained in the thickness of the fram- 
 ing, which, when the profiles in the room are en 
 
110 
 
 WINDOWS. 
 
 
 riched, should likewise be so, at least on the fold that 
 faces the aperture, when the shutters are turned 
 back ; the front of which must stand flush with the 
 inner edge of the architrave surrounding the window, 
 all the other folds being ranged behind it. I have 
 given, in plate 67, the mode of finishing window 
 frames, sashes, and shutters. 
 
 Plate 67. 
 
 Fig-. 1 shows the disposition of the members of a 
 windoio frame and shutters. 
 
 No. 1. The outside moulding against the wall. 
 
 No. 2. The outside casing. 
 
 No. 3. The pulley style. 
 
 No. 4. The inside casing. 
 
 No. 5. The back casing. 
 
 No. 6. The parting slip. •,, . 
 
 No. 7. The parting bead. 
 
 No. 8, 8. The weights. 
 
 No. 9. The recess of the wall. 
 
 No. 10, 10, 10, 10. The styles of the shutters. 
 
 No. 11, 11. The panels of the shutters. 
 
 No. 12. The back furring for the splay of the 
 window. 
 
 No. 13. The ground. 
 
 No. 14. Section of the pilaster. 
 
 No. 15. The back Uning. 
 
 No. 16. The thickness of the plastering. 
 
 Fig-. 2 shows the disposition of shutters folding- 
 back on a right line toith the plastering. 
 No. 1. The inside casing. 
 No. 2. Hinge casing. 
 No. 3, 3, 3, 3. Styles of the shutters. 
 No. 4, 4. Panels. 
 No. 5. Back casing. 
 
 No. 6. Box casing. , 4 
 
 No. 7. Plastering. 
 No. 8. Band moulding. 
 
 Fig. 3. Section of part of a shutter. 
 No. 1. The style. 
 No. 2. Panel. 
 No. 3. Moulding. 
 
 Fig. 4. Moulding, different from Fig. 3. 
 
 Fig. 5. Section through the frame and sash, and 
 shows the manner of selling the sash into the frame. 
 No. 1. The manner of joining the soffit to the frame. 
 No. 2. Cap of the frame-. 
 No. 3, 3. Casings of the frame. 
 
 No. 4. Top rail of the sash. 
 
 No. 5. Munten of the sash. 
 
 No. 6, 6. Meeting rails. 
 
 No. 7. Munten. 
 
 No. 8. Bottom rail. 
 
 No. 9. Window sill. 
 
 No. 10. Stop bead. 
 
 No. 11. Back. 
 
 No. 12. Back bead. 
 
 No. 13. Outside moulding. 
 
 Figs. 6 and 7. Sections of sash muntens. 
 
 Plate 68. 
 
 On plate 68 will be found a plan, elevation, 
 and section of a French window, with the scale by 
 which it was drawn. No. 1 shows the elevation ; 
 No. 2, the plan ; No. 3, a section ; No. 4, a section of 
 a part of the sUl and the sash ; A is a small fillet to 
 prevent the water being driven beneath the sash ; and 
 B is a channel to receive the water that may run 
 down on the outside behind the fillet ; the dotted line 
 C is another channel at right angles with B, to take 
 the water to the outside. B shows the manner of 
 constructing the meeting styles. The finish for the 
 window may be either of the architraves shown on 
 plate 30 ; and the manner of constructmg the shutters 
 is shown on plate 67. 
 
 Plate 69. 
 
 Plate 69 is a design for an oriel window. Figure 1 
 shows the front elevation ; figure 2, the side elevation ; 
 figure 3, the plan ; and figure 4, the detail of the base. 
 The scale is placed with the plan, by which the sev- 
 eral parts may be ascertained. 
 
 Plate 70. 
 
 Plate 70 * is a part of the details of plate 69. Figs. 
 1 and 2 are the trusses at D and A, and B is a de- 
 lineation of the leaf at C. Fig. 3 is a truss or console. 
 
 * This plate, with plate 69, was dcslgued and drawn by Mr. Shaw, 
 and we have inserted it as being the modern production of one who 
 has the honor of being among the earliest of the American architect- 
 ural ■writers. Mr. Shaw's first edition of Civil Architecture was 
 pubUshed more than twenty-five years ago ; and since then he has 
 contributed, in no small degree, to the advancement of his much- 
 beloved science, both practically and theoretically. He is now in 
 the 65th year of his age ; but, notwithstanding his advancement in 
 years, his desire is as strong as ever for the application of the correct 
 principles of architecture in buildings of every kind. — Editors. 
 
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ELEMENTS OF FOLIAGE. 
 
 Ill 
 
 FOLIAGE. 
 
 Both the elements and composition of foliage arc here consid- 
 ered, and illustrated by plates. The examples are taken from the 
 remains of the most esteemed buildings of Grecian and Roman an- 
 tiquity. The learner is recommended to go through all the variety 
 of ornaments exhibited in this department, by which means he will 
 be enabled to apply himself to any other species, however different. 
 
 DEFINITIONS. 
 
 1. An artificial arrangement or disposition of leaves 
 is caMed foliage. 
 
 2. The subdivisions of single leaves are called 
 raffles. The leaves which are chiefly used in architec- 
 ture are the acanthus, olive, parsley, laurel, and lotus. 
 
 3. All artificial arrangement of leaves, branches, 
 fruit, flowers, drapery, &c., either singly or combined 
 in any manner with each other, are called ornaments 
 in architecture. 
 
 4. A string, consisting of flowers, imit, leaves, and 
 branches, either singly or intermixed with each other, 
 and supported at the tsvo extremes, the middle part 
 forming itself into a curve by its gravity, is called a 
 festoon. 
 
 5. A curve line, which is continually changing its 
 position in conb-ary directions on the same side of it, — 
 that is, first concave and then convex, concave again 
 and then convex again, and so on alternately, in this 
 manner, to any number of curves of contrary flex- 
 ure, — is called a serpentine line. 
 
 6. If fi-om a stalk, in the form of a serpentine line, 
 a number of branches issue out, twisting themselves 
 in the form of spiral lines, on each side of the ser- 
 pentine, in all the concave parts on the alternate 
 sides of it, and if these spirals and the stalk be deco- 
 rated with foUage, — a composition so formed is 
 called tvindiriff foliage. 
 
 TO DRAW ORNAMENTS, 
 
 PROBLEM. 
 
 The learner should, in the first place, draw a great 
 variety of curve and spiral lines of different descrip- 
 
 tions, and compare these figures with each other, by 
 which means he will be able at sight to distinguish 
 each particular species of curve from another ; then 
 he ought to endeavor to imitate, with precision, the 
 same things by hand in every variety of position 
 which he can suggest to himself, and hence he will 
 acquire a freedom of hand in every direction. When 
 he proceeds to copying leaves, a general outline ought 
 to be drawn, circumscribing the whole leaf; he should 
 then form outlines of aU the raffles, and round every 
 compartment, circumscribing all the different sets of 
 points or raffles, and afterwards proceed to draw the 
 raffles themselves. 
 
 The learner having after sufficient practice in copy- 
 ing acquired a freedom of hand, he is advised to 
 draw from nature a variety of such things as will be 
 most suitable for the purposes to which they are to 
 be applied. By so doing, the parts of his composi- 
 tions will always appear rich and natural, and hence 
 he will obtain a greater facility of invention. Hav- 
 ing had sufficient practice in drawing from nature, 
 he may then apply himself to the designing of orna- 
 ments ; for which purpose he wiU find the first part 
 of the problem, viz., that of drawing curve and spiral 
 lines by hand, to be of the utmost utility in forming 
 the general outline of his design ; and for finishing the 
 smaller parts, such as raffles, flowers, fruit, &c., he 
 must apply the knowledge he has acquired in drawing 
 from nature, which will complete his composition. 
 
 LEAVES. 
 
 Of the acanthus, bear's breech, or brank ursine, 
 there are several species. 
 
 1. The moUis, or common bear's breech, a native 
 of Italy. 
 
 2. The spinosus, or prickly bear's breech, the leaves 
 of which are deeply jagged in very regular order, and 
 each segment is terminated with a sharp spine, as is 
 also the complement of the flower, which render it 
 troublesome to handle them. 
 
112 
 
 ELEMENTS OF FOLIAGE. 
 
 3. The ilictfolious, or shrubby bear's breech, grows 
 in both the Indies. It is an evergreen shrub, which 
 rises about four feet high, and is divided into many 
 branches, garnished with leaves like those of the com- 
 mon holly, and armed with spines in the same man- 
 ner ; the flowers are white, and shaped like those of 
 the common acanthus, but smaller. 
 
 4. The nigra, or Portugal bear's breech, with 
 smooth sinuated leaves, of a livid green color. 
 
 5. The middle bear's breech, with entire leaves, 
 having spines on their borders. 
 
 EXAMPLE. 
 Plate 71 
 
 Shows the method of beginning to draw leaves, as 
 given in the general problem 1. 
 
 Suppose it were required to draw or copy plate 72, 
 either of the same size, or in any other ratio to it. 
 First inspect plate 72, and draw with a pencil a faint 
 curve line, circumscribing the contour or general out- 
 line of Fig. 1 ; then describe curve lines similar to it, 
 as at Fig. 1, plate 71 ; then draw lines faintly with 
 a pencil, circumscribing the compartments or divis- 
 ions of Fig. 1, plate 72 ; then draw lines in a similar 
 manner, as at Fig. 1, plate 71, observing that all the 
 parts are similar to Fig. 1, plate 72 ; next draw the 
 raffles and veins in the compartments of Fig. 1, plate 
 71 ; and, lastly, with a pen draw in ink all the parts 
 of the leaf represented by Fig. 1, plate 72; then rub 
 your drawing clean ; the pencil lines wiU be rubbed 
 out, and the ink lines will be left, and will represent 
 a figure similar to Fig. 1, plate 72. 
 
 This explanation will be sufficient for aU the fol- 
 lowing examples, however dissimilar they may be. 
 In the following descriptions, it wUl be only neces- 
 sary to mention the names of the buildings from 
 which the examples were taken. 
 
 Fig.l 
 No. 1. 
 
 Fig. 2 
 Athens, 
 tlienes. 
 
 No. 2. 
 
 Fig. 1. 
 No. 1. 
 
 Plate 72. 
 
 is taken from the Arch of Adrian, at Athens. 
 The profile of Fig. 1. 
 
 . From the Monument of Lysicrates at 
 commonly called the Lantern of Demos- 
 Profile of ditto. 
 
 Plate 73. 
 
 From the Temple of Pola, in Istria. 
 Profile of ditto. 
 
 Fig. 2. From the Arch of Adrian, at Athens. 
 
 No. 2. A profile of ditto. 
 
 Fig. 3. Elevation of a leaf taken from the capi- 
 tals of the columns on the Baths of the Diocletian, 
 at Rome. 
 
 No. 3. Profile of ditto. 
 
 KOSES IN THE CAPITALS OF COLUMNS. 
 
 Plate 74. 
 
 Fig. 1. Elevation of the rose in the abacus in the 
 Temple of Vesta, at Tivoli. 
 
 Fig. 2. The elevation of a rose taken firom the 
 Temple of Jupiter the Thunderer, at Rome. 
 
 Fig. 3. Elevation of a rose from the abacus of the 
 capitals of the Temple of Vesta, at Rome. 
 
 Fig. 4. Elevation of a rose in the abacus of the 
 
 capitals of the pilasters of the frontispiece of Nero, 
 
 at Rome. 
 
 Plate 75. 
 
 Fig. 1. Elevation of a rose in the abacus of the 
 capitals of the Arch of Titus, at Rome. 
 
 Fig. A. Elevation of a rose in the abacus of the 
 capitals of the Pantheon, at Rome. 
 
 Figs. 2 and 3 are designs for the ornaments of mo- 
 dillions in cornices or corner pieces for pilasters. 
 
 Plate 76. 
 
 Fig. 1, the outline ; and Fig. 2, the shadowed leaf 
 taken from a frontispiece. 
 
 Plate 77. 
 
 Fig. 1. From the portico of the Temple of Anto- 
 ninus and Faustina, at Rome. 
 
 Figs. 2, 3, and 4. For corners and centres of panels. 
 
 ORNAMENTS FOR MOULDINGS. 
 
 Plate 7§. 
 
 No. 1. A general outline of Example 1. 
 
 No. 2. The outline of Example 2, from the cima- 
 tium of the Temple of Minerva Polias, at Priene. 
 
 Example 3. From the cima recta in the cornice 
 of the Temple of Bacchus, at Teos. 
 
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CARPENTRY. 
 
 113 
 
 Example 4. From the cima recta of the cornice of 
 the Temple of Peace, at Rome. 
 
 Plate 79. 
 
 Fig. 1. From the Arch of Titus, at Rome. 
 
 Fig. 2. From an impost moulding in the Arch of 
 Septimius Severus, at Rome. 
 
 Fig. 3. From the cima recta of the cornice of the 
 Frontispiece of Nero, at Rome. 
 
 Plate 80. 
 
 Fig. 1. The side, and Fig. 2, the front, of a key- 
 stone of the Arch of Septimius Severus, at Rome. 
 
 Fig. 3. The ichnography of the modillion in the 
 cornice of the Temple of Jupiter Stator, at Rome. 
 
 Fig. 4. Side of the modillion in the cornice of the 
 Portico of the Pantheon, at Rome. 
 
 Fig. 5. Ichnography of ditto, inverted. 
 
 CAHPENTRY. 
 
 The art of Carpentry, in the general acceptation of the term, in- 
 cludes every method of -n-orking or employing timber, or its substi- 
 tutes, in the construction of buildings ; but as it is evident that 
 coarse, rough work requires very different management from the 
 delicate finish of interior arrangement, most ■writers have very prop- 
 erly divided it into two classes : Carpentry, properly so called, to 
 which belongs flooring, roofing, framing, and the working of all 
 large pieces of wood ; and Joinery, which includes all ornamental 
 works in wood, (except what are obviously within the pro-v'ince of 
 the cabinet maker,) besides doors, windows, sashes, and other objects 
 intended for close inspection. The former, of course, is treated of 
 in this department. 
 
 THE ORDER OF CARRYING ON A BUILDING ; THE DI- 
 JIENSIOXS OF THE TIMBERS ; THEIR DISTANCES, 
 AND PLACES OF INSERTION. 
 
 The designs of buildings being of such a variety, 
 they not only require various methods of construc- 
 tion, but some require appendages which are unne- 
 cessary in others, and thus the order of proceeding 
 will be varied. The order, however, of proceeding 
 with any description of edifice will easily be under- 
 stood, when that of the usual manner is given. 
 
 Lintellings very soon occur ; their thickness ought 
 never to be less than as many inches as the aperture 
 has feet in width. Some recommend that lintels 
 should be laid on templets ; but when the mortar 
 dries, this practice, though it may seem to bind a 
 new building together, is injurious to the strength of 
 the walls. The old authors say that bond timbers 
 should be dovetailed at the angles ; but this method 
 of joining timbers is not sufficient to prevent, in two 
 return walls, the one from descending, while the other 
 keeps its place ; halving and bolting is much more 
 secure. 
 
 Where bond timbers are carried all round apart- 
 15 
 
 ments or rooms, or entu-ely round a building, the 
 thickness of these timbers will depend upon the mass 
 of the work over tlicm ; but where they are only par- 
 tially inserted for finishings, their thickness must be 
 the thickness of a brick. Some old authors think it 
 would not be amiss to place bond timbers at the dis- 
 tance of six feet through the whole height of the 
 building ; but, in our opinion, they ought to be used 
 with great caution ; for as the moisture dries out of 
 the timber, these ligatures will shrink and cause the 
 walls to bulge, which will not only produce a very 
 unpleasant effect to the eye, but will endanger the 
 building, by weakening the walls, and make them 
 liable to fall. Therefore, in good work, bond timbers 
 ought to be dispensed with ; and, if necessary, other 
 means ought to be resorted to, which will be equally 
 effective in point of strength ; but as neither stone 
 nor iron will answer the purpose of fixing, we will 
 recommend plugging, built in with the brick work. 
 
 FLOOES. 
 
 We now come to the consideration of floors. Li- 
 stead of mortising the ceiling joists, we would rather 
 recommend to notch them upon, and fasten them to, 
 the binding joists by means of nails. In some single 
 joisted floors, every third or fourth joist is made 
 deeper than the intermediate joists, and the ceiling 
 joists are fixed to the deep joists. This construction 
 is adapted to the prevention of sound, by reason of 
 the space which destroys or cuts off the conducting 
 power. 
 
114 
 
 CARPENTRY. 
 
 As no timbers must enter a wall where there arc 
 fireplaces or flues, the ends of the joists, instead of 
 being supported by the wall, must be supported by- 
 trimmers and trimming joists. As the trimming 
 joists have to support the trimmers, and these again 
 the ends of the joists, the trimming joists should be 
 increased in their thickness about one fifth part more 
 than the breadth of a common joist. 
 
 In double floors, the under sides of the binding 
 joists are frequently framed flush with the under side 
 of the girder, and about three or four inches below 
 the top, in order to receive the bridging joists. Some 
 old authors direct that the bridging joists should be 
 pinned down to the binding joists ; but this is unne- 
 cessary, and, besides, it weakens the binding joists ; 
 this method is therefore inadmissible. It w^as for- 
 merly the practice to place the binding joists about 
 three feet or three feet six inches distant from each 
 other ; the mean distance of the present practice is 
 about five feet. Single floors, consisting of the same 
 quantity of timber, are much stronger than framed 
 floors ; but a preference is sometimes given to framed 
 floors in superior buildings, on account tliat they are 
 not so liable to fracture the ceilings, and because they 
 conduct sound more imperfectly than a common joist 
 floor ; and hence it is that single floors can only be 
 employed in inferior buildings. Framed floors differ 
 from double floors only in the binding joists being 
 framed to girders. 
 
 In single floors, where the joists exceed eight feet 
 bearing, pieces of board ought to be inserted in the 
 spaces between the joists, in a vertical position, and 
 nearly the whole depth of the joists, and in one con- 
 tinued line at right angles to the joisting. The pieces 
 of timber thus inserted are called bridges, and the 
 floor is said to be bridged; the bridges ought not to be 
 driven in with groat force, but their ends should be in 
 close contact with the vertical sides of the joists, and 
 should be fixed thereto with a nail at each end. 
 
 The bridging of a floor is of great use, when the 
 joists are thin and deep, in preventing their buckling 
 by pressure; but for this purpose there is another 
 method, called keying, which consists of framing short 
 pieces of timber between the joists ; but as the mor- 
 tises which receive the tenons weaken the joists, and 
 as the keys cannot be in a straight line, and since 
 this method adda considerably to the expense, this 
 practice is not so eligible as that of bridging. Single 
 joist flooring may be used to any extent not exceed- 
 
 ing sixteen feet : but when it is desirable to prcrfcrve 
 the ceiling free from cracks, and prevent the passage 
 of sound, a framed floor is necessary. 
 
 The ceiling joists in double floors arc generally put 
 in after the building is up ; if, therefore, they are fixed 
 by means of mortises in the sides of the binding 
 joists, to receive the tenons on their ends, the space 
 between every other two mortises must be grooved 
 out alternately upon the opposite sides of the two 
 adjacent binding joists : by this means, the ceiling 
 joists may easily be put in their places, by inserting 
 the tenons in each coiling joist in the mortises at one 
 end, and sliding the tenon on the other end along the 
 groove in the arc of a circle, until the ceiling joist 
 come at a right angle with the binding joist. The 
 long mortises or grooves in the sides of the binding 
 joists are called chase mortises, or pulley mortises. 
 The ceiling joists may be thirteen or fourteen inches 
 apart ; the thickness of the bridging joists and ceiling 
 joists need nqt be greater than what is sufficient to 
 resist splitting by the driving in of the nails in order 
 to fix them. It has been found, by experience, that 
 two inches is a sufficient thickness for the purpose. 
 
 In double-framed floors, the distance of bridging 
 joists, in the clear, ought to be about twelve inches, 
 and should never exceed thirteen. It is a good prac- 
 tice to plane the upper edges of the bridging joists 
 straight, because, w^hen the boarding is laid, the faces 
 for walking upon will be more regular than if the 
 boards had been laid down upon the edges of the 
 bridging joists when rough from the saw. The 
 straightening of the edges of the bridging joists will 
 not only give greater facility to the making of a level 
 floor, but will contribute greatly towards making 
 sound work, and will prevent that disagreeable 
 creaking noise which arises from the parts not being 
 brought into contact ; for when the tops of the joists 
 on which the flooring boards are laid are uneven, it 
 wUl be impossible to avoid furring up the joists, or, 
 what is still worse, inserting chips in the hollows, 
 which will give way in the nailing of the boards to 
 the joists. The general practice is to make binding 
 joists half as thick again as common joists ; so that, 
 if a common joist be two inches thick, the binding 
 joists may be three inches thick. 
 
 Girders should always be placed upon walls which 
 are solid underneath ; but when it becomes necessary 
 to lay them over apertures, the lintels should be suffi- 
 ciently strong to support them. We cannot recom- 
 
 I 
 I 
 
CARPENTRY. 
 
 115 
 
 mend the practice of laying girders obliquely across 
 the room, since it divides the binding joists so very 
 uneqvially. 
 
 All joists should be laid with a camber upwards, 
 so as to raise the middle of the floor about three 
 quarters of an inch higher than the sides of the room ; 
 and a similar observation applies to ceiling joists, 
 viz., that the under horizontal sides should rise with 
 a concavity, so that the middle of the ceiling should 
 be three quarters of an inch above the margins at the 
 cornices or walls. The distance of girders from each, 
 or the walls, shovild never exceed twelve feet. 
 
 Girders should always be made of timber of 
 the best quality that can be found, and particularly 
 
 those which have long bearings. 
 
 When the bearing 
 
 exceeds twenty feet, it is difficult to procure timber 
 of sufficient dimensions; and the only method is 
 to allow a sufficient thickness between the surface 
 of the boarding and the ceiling, since it is found, by 
 experiments that have been made, that a truss girder 
 is not even so strong as a solid beam of the same 
 depth. The reason is obvious, for braces which have 
 only a small inclination to the horizon throw the 
 most enormous compression on thek abutments, 
 which is liable to give way, and the effect of truss- 
 ing would be rendered useless ; but if a sufficient 
 height were allowed for trussing, girders might be 
 made capable of supporting any weight whatever. 
 Two feet, or even three feet, in the height of a build- 
 ing, would be an ample allowance for framing girders 
 of sufficient strength, and would not occasion any 
 considerable expense to the structure, but would give 
 solidity to the walls, by having a greater distance 
 between the apertures. But where the depth is lim- 
 ited, and the bearing considerable, girders ought to 
 be made solid, and of cast iron. In order to equal- 
 ize the strength of solid girders, builders frequently 
 cut them longitudinally along the middle, and turn 
 the ends of the flitches contrary to what they were 
 at first in the solid, and apply the sawn sides so 
 as to face each other, and then bolt the two pieces 
 together in a sufficient number of intervals; but 
 it is evident that, since the holes made for the 
 passing of the bolts will weaken the timber, very 
 little strength will be gained. This process, however, 
 affords the opportunity of examining the timber, as, 
 in large trees, the heart is frequently found in a state 
 of decay. When this process of reversing and bolt- 
 ing is used, the tsvo'sawn sides of the timber should 
 not be brought in contact, but should be separated 
 
 by parallel pieces of wood, so as to allow a sufficient 
 circulation of air to pass between the two sides of 
 the flitches of the beams thus bolted. 
 
 To prevent the sagging of short girders, it is usual 
 to cut them camber ; that is, to cut them with an 
 angle in the middle of their lengths, so that their cen- 
 tres shall rise above the level of their ends as many 
 half inches as the girder contains ten feet lengths. 
 And, indeed, girders of the greatest length, al- 
 though trussed, should be cut crowning in the 
 same manner. 
 
 It may be proper here to notice, that the cambering 
 of girders does not prevent them from sagging, though 
 perhaps it may obviate their becoming concave on 
 the upper side. With regard to trussing girders, the 
 flitches should not be cut to a camber, but brought 
 into this state in the ac*^ of trussing. 
 
 PARTITIONS. 
 
 Partitions are usually lathed and plastered; and 
 sometimes the spaces between the timbers are filled 
 with brick work. A partition ought to be so con- 
 structed as to be capable of supporting its own 
 weight, in whatever situation the door is placed, or 
 whether there is a door in the middle, or two doors 
 near the ends. Partitions that rest upon a solid wall 
 do not require trussing ; but when there is no sup- 
 port, except at the ends, or at two given fixed points, 
 the braces ought to be so disposed as to discharge 
 the weight of the whole mass upon these points ; 
 and it is better to support a partition by the extreme 
 walls it is connected with than upon any solid from 
 the bottom ; for, in the settlement of the walls, the 
 partitions will be carried along with them ; but if 
 supported from the ground by light materials, the 
 walls and partitions will descend unequally, and 
 cause large fissures and cracks in the ceilings and in 
 the plaster upon the walls and partitions. 
 
 When a partition is supported at each end by 
 walls of unequal heights, the wall, which is the most 
 ponderous, will sink in a much greater degree than 
 that which is the lighter; therefore, in this case, 
 whatever care may be taken with the framing of the 
 partitions, it will not be possible to avoid the crack- 
 ing and splitting of the plaster upon the walls and 
 ceiling. Such consequences should be guarded 
 against in the design of the architect. 
 
116 
 
 CARPENTRY. 
 
 FRAMING. 
 
 This mechanical science is divided into t^^'•o princi- 
 ples — the Scribe and the Square Rule. 
 
 THE SCRIBE RULE. 
 
 1. First, the mortises should be made, and the 
 faces got out of wind. Second, after finding the 
 length of the timber in which the tenons are to be 
 made, for convenience apply the two-foot square. 
 Third, take out the size of the mortised timber on the 
 end of the square ; suppose ten inches to be the one 
 mortised, then fourteen inches remain on the square ; 
 make a distinct mark at the end of the square, wliich 
 is called the two-feet mark. Fourth, measure from 
 this mark, for the shoulder, fifteen inches, which 
 leaves one inch to be scribed; after the tenon is 
 made and entered, the mortise and the shoulders are 
 brought together or to a bearing ; then cut the shoul- 
 ders to the scribe, and when put together they will 
 remain out of wind, as when scribed. The process 
 is generally applied to sills, posts, and principal rafters. 
 
 2. A process called tumbling, is applied to timbers, 
 both ends of which are to be tenoned, as girders, &c. ; 
 also to sides and ends in section framing. 
 
 The girder should be placed so that both ends shall 
 come directly over the lower end of the mortises. 
 For the tenons you are about to strike, place the 
 lower edges of the girder to the line of the lower 
 end of the mortises ; make a scratch on the girder at 
 both ends, exactly to the face of the mortise. Cant 
 the girder so as to leave those marks up ; fetch the 
 girder again over the mortise, and apply the edge of 
 the square to the face of the mortise, the square ex- 
 tending above the girder. Move the girder by a 
 hammer for that purpose, until the scratch on the 
 corner of the girder is brought to the outer edge of 
 the square. Then with your compasses draw a line 
 across the girder by the edge of the square ; then 
 move the square on the opposite side of the girder, 
 and draw another line; in the same manner draw 
 lines at the other end of the girder. Strike a line 
 across the top and bottom of the girder, meeting the 
 end of those which give the exact length of the 
 shoulders; then strike the tenons. 
 
 3. Cant or plumb marks are those which are ap- 
 plied to all principal timbers that are to be employed 
 in section framing, after having been put together 
 in the sides. At some part of the post try on the 
 square, and fit that part (which may be up, in the 
 
 laying out of the section) to a right angle with the 
 level plane of the side framing, provided the section 
 should be at right angles with the sides. But if the 
 section should be required at any other angle with 
 the side, the plumb should be made according to that 
 angle. The angle should be taken with a bevel set 
 for that purpose ; and on these fittings of the posts 
 a right angle should be struck, to guide the direction 
 of the square across the section framing. The posts 
 should be brought by means of wedges in a horizon- 
 tal plane across the section. 
 
 THE SQUAHE RULE. 
 
 This principle is considered more simple than the 
 Scribe Rule, as it can be applied in many cases with 
 less help and more convenience. 
 
 Li order to make a good frame of any considerable 
 magnitude, it should be the first care of the master 
 workman (after examining the plan of the firame with 
 care) to make out a proper schedule of the various 
 sizes of the timber. Set down their appropriate 
 marks on the schedule ; and when you have finished 
 Nos. 1, 2, &c., check them on the schedule. It is of 
 importance that all mortises, tenons, pin holes, &c., 
 should be struck with a pattern. All the timber 
 should be lined to its proper size, and the mortises 
 faced to the same. Care should be taken in applying 
 the pattern ; for striking, it should be governed by the 
 appropriate lines. This method has the preference 
 in detached framing ; the timber admitting of being 
 framed in different places, and not tried together until 
 its raising. 
 
 TRUSSES. 
 
 Plate 81. 
 
 Fig. 1 represents a truss partition, a, the truss 
 plate, b, the sUl. c c, the posts, d, the truss beam. 
 e e, the struts. / /, the studding, g g, the bridg- 
 ing, h h h, the door frames. 
 
 Fig. 2. Design for a truss gallery or floor. 
 
 Fig. 3. Method of scarfing and splicing timber. 
 
 Fig. 4. The horizontal section of Fig. 5. 
 
 Figs. 5 and 6 show the best method of trussing 
 girders. 
 
 The king bolts through Figs. 5 and 6 show the 
 two sides which incline to each other so as to form a 
 wedge, and thereby force the trusses upon their abut- 
 ments. 
 
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CARPENTRY. 
 
 117 
 
 To lighten the Girders. 
 
 Having grooved the sides of the flitches for the 
 trussing pieces, so as only to be close at the ends, 
 about an inch and a half deep on each side, and 
 having greased the head of the lung bolt, and put 
 the whole slackly together sideways by the screws, 
 proceed then to turn the nut of the Idng bolt, and let 
 another person strike the head with a mallet ; the 
 stroke will make the king bolt start every time it is 
 hit, and give fresh ease for the turning of the nut. By 
 this means, the girder may be cambered or crowned 
 at pleasure : the deflection from the straight line is 
 generally one inch in twenty feet. 
 
 Fig. 7 shows the manner of joining the beam to 
 the wall plate. 
 
 Fig. 8. The manner of keying the tenon through 
 the girder. 
 
 Fig. 9. Profile of the tusk tenon. 
 
 PLANS OF FLOORS. 
 
 Plate 83. 
 
 Fig. 1. Plan of the floor, suitable for buildings of 
 any magnitude. 
 
 a a a a a, girders resting upon the walls, b b b bi 
 binding joists, c c c, trimmers, d d d d d, bridging 
 joists. 
 
 Fig. 2. Section of the floor. 
 
 Fig. 3 shows the method of framing floors with 
 plank or deep joists. 
 
 a, the girder resting upon the walls, and should be 
 10 by 12 inches, b b b b, trimmer joist, 4 by 12 
 inches, e e e, joist, d d d d, wall girders, 6 by 12 
 inches, c c c, bridging joist, 2 by 12 inches. 
 
 This floor is adapted to rooms 16 or 18 feet square, 
 and the size of the joist should be 12 inches by 2^ or 
 3 inches. 
 
 . DESIGNS FOR ROOFS. 
 
 A roof, in architecture, is a cover of a building for 
 protecting its inhabitants from disagreeable changes 
 of weather, and from the depredations of evil-dis- 
 posed persons ; but a roof in carpentry is the timber 
 framing made to support the actual covering of 
 
 boards, shingles, slate, lead, &c. As the roof may 
 be made one of the principal ties of a building, it 
 should not be made too heavy to burden the walls, 
 nor too light to be incapable of keeping them to- 
 gether. 
 
 The principal timbers of a roof arc the wall plates, 
 tie beams, principal rafters, common rafters, pole 
 plates, purlines, king posts, queen posts, struts, strain- 
 ing beams, strong sUls, &c. Hence, since the pres- 
 sure of the roof is wholly discharged upon the wall 
 plates, these should be made of sufficient thickness 
 and breadth to distribute the weight of the roof to 
 the best advantage. 
 
 Plate 83. 
 
 Fig. 1, a a a a, wall plate ; b b, jack beams; c c c c, 
 tie beams ; d d, ridge line and jack beam ; e e e e, 
 dragon piece ; ////, angle tie ; g- g- g, hip rafters ; 
 h h, jack rafters ; i i, principal rafters ; j, king post ; 
 k k, strut braces. 
 
 To find the length and backing of hip rafters. 
 
 Draw 7, 4, 8, the base lines ; then draw 4, 5, at 
 right angles with 8, 4, which will give the perpen- 
 dicular height of the backing of the hip rafter. 
 From 9, extend one foot of the dividers to 10 ; de- 
 scribe the arc, cutting the base line at 2 ; then the 
 lines from 2 to 1 and from 2 to 3 give the angle 
 required for the backing, c, a section of the hip 
 rafter. 
 
 To find the angle and intermediate ribs of 
 octagon roofs. 
 Fig. 2 is the plan of an octagon dome, a b being 
 the base line of the given rib. No. 2 shows the 
 curve of the dome, in this case half of a circle 
 drawn from the centre a. Draw a 1, cutting the 
 circle at 1 and at right angles with d b, and produce 
 it to a ; divide b 1 into seven or more equal parts. 
 Make a b No. 3 parallel and equal to a b No. 1, b e 
 equal to 6 c No. 1, and draw e a. Then draw ordi- 
 nates from a b No. 2 to a e No. 3, parallel to a 1, 
 cutting the circle in No. 2 at 2, 3, 4, 5, 6, 7, and a e 
 No. 3 at 2, 3, 4, 5, 6, 7. Draw a 1 at right angles 
 with a e, also 2 2, 3 3, 4 4, 5 5, 6 6, and 7 7, parallel 
 to a 1, and equal to 7 7, 6 6, 5 5, 4 4, 3 3, 2 2, and 
 a 1 in No. 2, and then trace the curve c 7 6 5 4 3 2 
 and 1, which will, when placed in its right position, 
 correspond with the given circle. 
 
118 
 
 CARPENTRY. 
 
 To find the form of a board to bend upright to 
 the crown. 
 
 Fig. 2. Produce the line a fto e No. 1. Take the 
 divisions 2 3 4 5 6 7 on the curve line b 1 No. 2, and 
 lay them from / in F along the line 1111, &c., to 
 e; then the line/e No. 1 will be equal to the curve 
 line i 1 No. 2. Transfer the ordinates 2 3 4 5 6 7 in 
 the angle a b e No. 3, and lay them from / in F 
 No. 1 along the Ime 1111, &c., at right angles with 
 the line/e, and set them off on each side to 1 7, 1 7, 
 1 6, 1 6, 1 5, 1 5, 1 4, 1 4, 1 3, 1 3, and 1 2, 1 2. 
 
 Those, when traced, will give the form of the 
 board F. 
 
 Fig. 3. An octagon roof of a different curvature 
 from that represented in Fig. 2, but is formed on the 
 same principles. 
 
 Plates 84, 85. 
 
 On plate Nos. 84 and 85 we have given designs for 
 framing large roofs without wooden king or queen 
 posts, substituting iron rods in their stead. To 
 whom we are indebted for this method of framing 
 we have not been able to learn with any degree of 
 certainty. It may, however, be considered of quite 
 modern invention ; for, as the result of a careful in- 
 vestigation, we have found no example of longer 
 standing than thirty years, and have not found the 
 idea in any published work, with the exception of 
 some of the recent writings of the late Asher Ben- 
 jamin, Esq. This method was vised by him as early 
 as the year 1828, and after that time it was intro- 
 duced into nearly all the large roofs he constructed ; 
 and although he may not have been the first who 
 has used it, yet, as far as we can learn, he has done 
 as much as any other person to introduce it into 
 general use. It was published by him in his Build- 
 er's Guide, in 1839, and the principle involved has 
 received the approbation of nearly all the principal 
 architects of Boston. Mr. Charles G. Hall, archi- 
 tect of this city, adopted it some eighteen years 
 since, and used it in some of the largest buildings in 
 this vicinity. The roof over the large hall of the 
 Fitchburg depot, in this city, is a fine example of 
 this method of framing, and has fully dcmonstr,ated 
 its utility. The floor of this hall is 166 feet long, 
 and 76 feet wide, and is entirely supported by the 
 roof. On the occasion of one of Jenny Lind's con- 
 certs which was held there, it was filled, together 
 
 with the large passage, to its utmost capacity, which, 
 according to the experiments of Tredgegold, Rennie, 
 etc., was no less than the enormous weight of 
 1,873,960 pounds, or nearly 937 tons ; and, so far as 
 can be ascertained, this roof resisted the immense 
 strain without any material settlement. Although 
 by this system no new principle is established, yet it 
 may be looked upon as one of the most successful 
 achievements in the science of carpentry, and it has 
 added as much to the science as did the arch to 
 masonry. It has been introduced in many forms, 
 and employed in many ways ; and in every case 
 where a due propriety has been observed in regard to 
 the size of timber employed in the truss, it has given 
 entire satisfaction. But the great simphcity of the 
 theory has, in some cases, led to its abuse ; and as an 
 illustration of this, we have but to refer to a design 
 for an arched roof as constructed by the author of 
 the Builder's Guide, and shown on plate 64 of that 
 work. In this example are two rods, some forty feet 
 long, and they must necessarily be expanded so 
 much by the heat of oux summer as to relieve itself 
 from the strain it is intended to support, so that at 
 times the whole weight must come directly on the 
 tie beams, which would materially loosen the whole 
 truss. We speak of this with all deference to the 
 knowledge and experience of the author, yet we can- 
 not see that the experiment can philosophically rec- 
 ommend itself in a roof of seventy feet span. We 
 are aware that the sanie objection can be brought to 
 a certain degree against the whole theory of substi- 
 tuting rods for the posts ; yet when we take into con- 
 sideration the fact that, in nearly all roofs framed with 
 rods in the ordinary way, the purlines are well sup- 
 ported by the large truss rafter and the collar beam, — 
 that the truss without the rods would, if well executed, 
 almost sustain itself, and that the rods are not only 
 proportionably shorter, but differently applied, — we 
 cannot see that any fears need be entertained in case 
 of the latter, as may be with the former. With a de- 
 gree of propriety, therefore, and an adherence to the 
 principles of strength and support, the new method 
 may be used in an endless variety of ways ; and 
 there is now no reasonable excuse for the uneven 
 roofs which are so often presented to view in many 
 of our churches and other large buildings. — Editors. 
 
 Plate 86. 
 
 Fig. A shows how to glue up the head of a niche 
 
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 fill. r. 
 
STAIRS. 
 
 119 
 
 in five or more blocks, or rings, according as the 
 workmen shall deem expedient. 
 
 Fig. B is the plan of a circular dome; C the sec- 
 tion, which shows at d and d how to square the pur- 
 lines, so as to make them tend to the centre, or to 
 stand square to the surface of the dome ; but there 
 is not the least occasion for the squaring of any pur- 
 lines, which is attended with a deal of trouble and 
 waste of stuff; you need only to get them out of the 
 same curve as that of a great circle of a sphere, of 
 which the dome is a segment, and quite square at 
 the same time, which purlmes being fixed between 
 the ribs, the middle of them will be above the level 
 at the joints, but will be in the true surface of the 
 dome, and stand in a plane surface to the centre. 
 
 To find the form of a board to bend upright 
 to the crown. 
 
 Divide E into eight parts ; that is, one quarter or 
 any other number — the more the truer ; set one on 
 the outside of 1 1 1, &:c. ; draw 7 e and 1 e to e in 
 the centre ; take the divisions 12 3 4, &c., round E, 
 and lay them from 8, in F, along the line 1111, &c. ; 
 then circle them round e, and take 1 1, 1 2, 1 3, &c. 
 in E, and set them off on each side to 1 1, 1 1, 1 2, 
 1 2, 1 3, 1 3, &c. ; those, when traced, will give the 
 form of the board F. 
 
 To find the centres for bending the boards 
 horizontal in D. 
 
 It is evident, the more parts any thing of this na- 
 ture is divided into, the truer it will be ; but I shall 
 only divide into four, for the sake of eonvcniency. 
 Draw 4 3, to meet the perpendicular at d ; and 3 2, 
 to meet at c, &c. ; then d c b a will be the centres for 
 the boards G, H, I, K. 
 
 Fig. C is a method of finding the length and bevel 
 of hip and jack rafters. 
 
 Tlie Hip Rafter. — a bis the base line ; c the per- 
 pendicular height ; draw a line ac; then c is the bevel 
 at the highest point of the king post, a the bevel at 
 the beam, and a c the length of the hip rafter. 
 
 To find the bevel and length of the jack rafters. 
 
 d e is the base line, e f the height equal to eg; 
 then d e gis the right angle ; describe an arc g h, of 
 which dg is the radius, cutting a b at h ; then draw 
 the line hd; gis the down bevel, and h the top bevel, 
 and h d is the length of the jack rafter. 
 
 For this method of finding the length and bevel ol 
 jack rafters I am indebted to the politeness of Mr. 
 Salmon Washburn, whose skill and ingenuity first 
 discovered this mode, which has met with the decid- 
 ed approbation of the few to whom it has been com- 
 municated ; and it is now published for the first time. 
 
 STAIRS. 
 
 This is one of the most important subjects connected with the art 
 of building, and should he attentively considered, not only with 
 regard to the situation, but as to the design and execution. The 
 convenience of the building depends on the situation, and the 
 elegance on the design and execution of the workmanship. In con- 
 triving a grand edifice, particular attention must be paid to the sit- 
 uation of the space occupied by the stairs, so as to give them the 
 most easy command of the rooms. 
 
 " Staircases," says Palladio,' " will be commendable if they are 
 clear, ample, and commodious to ascend, inviting, as it were, people 
 to go up. They will he clear if they have a bright and equally dif- 
 fuse light; they will be sufficiently ample if they do not seem 
 scanty and narrow to the size and quality of the fabric. But they 
 should never be less than four feet in width, that two persons may 
 pass each other. They will bo convenient with respect to the whole 
 building if the arches under them can bo used for domestic pur- 
 poses ; and witli respect to persons, if their ascent is not too steep 
 and difficult, to avoid which, the steps should be t'wicc as broad as 
 high. 
 
 With regard to the lighting of a good staircase, a 
 skylight, or, rather, lantern, is the most appropriate, 
 for these unite elegance with utility ; that is, admit 
 a powerful light, with elegance in the design. In- 
 deed, where the staircase does not adjoin the exterior 
 wall, this is the only light that can be admitted. 
 Where the height of a story is considerable, resting- 
 places are necessary, which go under the name of 
 quarter paces and half ptaces, according as the pas- 
 senger has to pass one or two right angles ; that is, 
 as he has to describe a quadrant or semicircle. In 
 very high stories, which admit of sufficient head 
 room, and where the space allowed for the staircase 
 is confined, the staircase may have two revolutions 
 in the height of one story, which will lessen the 
 
120 
 
 STAIRS. 
 
 height of the steps ; but in grand staircases only 
 one revolutiou can be admitted, the length and 
 breadth of the space on the plan being always pro- 
 portioned to the height of the building, so as to 
 admit of fixed proportions. 
 
 The breadth of the steps ought never to be more 
 than fifteen inches, nor less than nine ; the height not 
 more than eight, nor less than five. There are cases, 
 however, which are exceptions to all rule. When 
 the height of the story is given in feet, and the 
 height of the step in inches, you may throw the feet 
 into inches, and divide it by the number of inches 
 the step is high, and the quotient will give the num- 
 ber of steps. 
 
 It is a general maxim, that the greater breadth of 
 a step requires less height than one of less breadth. 
 Thus, a step of 12 inches in breadth will require a 
 rise of 7 inches, which may be taken as a standard 
 to reffulate those of other dimensions. 
 
 Though it is desirable to have some criterion as a 
 guide in the arrangement of a design, yet workmen 
 will, of course, vary them as circumstances may re- 
 quire. Stairs are constructed variously, according to 
 the situation and destination of the buildmg. 
 
 Geometrical stairs are those which are supported 
 by having one end fixed in the wall, and every step 
 in the ascent having an auxiliary support from that 
 immediately below it, and the lowest step from the 
 floor. 
 
 Bracket stairs are those which have an opening or 
 well with strings and newels, and are supported by 
 landings and carriages. The brackets are mitred to 
 the ends of each riser, and are fixed to the string 
 board, which is moulded below like an architrave. 
 
 Dog-legged stairs are those which have no opening 
 or well hole, and have the rail and balusters of both 
 the progressive and returning flights falling in the 
 same vertical planes, the steps being fLxed to strings, 
 newels, and carnages, and the ends of the steps of 
 the inferior kind terminating only upon the side of 
 the string, without any nosing. In taking dimen- 
 sions and laying down the plan and section of stair- 
 cases, take a rod, and, having ascertained the num- 
 ber of steps, mark the height of the story by stand- 
 ing the rod on the lower floor ; divide the rod into as 
 many equal parts as there arc to be risers ; then, if 
 you have a level surface to work upon below the 
 stair, try each of the risers as you go on, and this 
 will prevent any excess or defect ; for any error, how- 
 
 ever small, when multiplied, becomes of considerable 
 magnitude, and even the dilTerence of an inch in the 
 last riser will not only have a bad effect to the eye, 
 but will be apt to confuse persons not thinking of 
 any such irregularity. In order to try the steps 
 properly by the story rod, if you have not a level 
 surface to work from, the better way will be to lay 
 two rods on boards, and level their top surface to 
 that of the floor. Place one of these rods a little 
 within the string, and the other near or close to the 
 wall, so as to be at right angles to the starting line 
 of the first riser, or, which is the same thing, parallel 
 to the plan of the string ; set off" the breadth of the 
 steps upon these rods, and number the risers; you 
 may set not only the breadth of the fliers, but that 
 of the winders also. In order to try the story rod 
 exactly to its vertical situation, mark the same 
 distances of the risers upon the top edges as the 
 distances of the plan of the string board and the 
 rods are firom each other. 
 
 In bracket stairs, as the internal angle of the steps 
 is open to the end, and not closed by the string as in 
 common dog-legged stairs, and the neatness of work- 
 manship is as much regarded as in geometrical stairs, 
 the balusters must be neatly dovetailed into the ends 
 of the steps, two in every step. The face of each 
 front baluster must be in a straight surface with the 
 face of the riser, and, as all the balusters must be 
 equally divided, the face of the middle baluster must 
 stand in the middle of the face of the riser of the 
 preceding step and succeeding one. The risers and 
 heads are all previously blocked and glued together, 
 and, when put up, the under side of the step nailed 
 •or screwed into the under edge of the riser, and then 
 rough brackets to the rough strings, as in dog-legged 
 stairs, the pitching pieces and rough strings being 
 similar. In gluing up the steps, the best method is 
 to make a templet, so as to fit the external angle of 
 the steps with the nosing. 
 
 The steps of geometrical stairs ought to be con- 
 structed so as to have a very light and clean appear- 
 ance when put up ; for this purpose, and to aid the 
 principle of strength, the risers and treads, when 
 planed up, ought not to be less than one eighth of 
 an inch, supposing the going of the stair or length 
 of the step to be four feet ; and for every six inches 
 in length, another one eighth may be added. The 
 risers ought to be dovetailed into the cover, and, 
 when the steps are put up, the treads are screwed up 
 
STAIRS. 
 
 121 
 
 from oclow to the under edge of the risers. The 
 holes for sinlciiig the heads of the screws ought to 
 be bored with a centre bit, then fitted closely in with 
 wood, well matched, so as entu-cly to conceal the 
 screws, and appear as one uniform surface. Brack- 
 ets are mitred to the riser, and the nosings are con- 
 tinued round. In this mode, however, there is an 
 apparent defect ; for the brackets, instead of giving 
 support, are tliemselvcs unsupported and dependent 
 on the steps, being of no other use, in point of 
 strength, than merely tying the sisers and treads of 
 the internal angles of the step together; and, from 
 the internal angles being hollow, or a reentrant 
 angle, except at the ends, which terminate by the 
 wall at one extremity, and by the brackets at the 
 other, there is a want of regiilar finish. The cavetto 
 or hollow is carried round the fi-ont of the riser, and 
 is returned at the end and mitred round the bracket ; 
 and if an open string, — that is, the under side of the 
 stairs open to view, — the hollow is continued along 
 the angle of the step and riser. 
 
 The best plan, however, of constructing geometri- 
 cal stairs, is to put up the strings, and to mitre the 
 brackets to the risers, as usual, and enclose the soffit 
 with lath and plaster, which will form an inclined 
 plane under each flight, and a winding surface under 
 the winders. Lr superior staircases, for the best 
 buildings, the soffit may be divided into panels. K 
 the risers are made from two-inch planks, it will 
 greatly add to the solidity. 
 
 Li constructing a flight of geometrical stairs where 
 the soffit is enclosed as above, the bearers should all 
 be fi-amed together, so that, when put up, they will 
 form a perfect staircase. Each piece of framework 
 which forms a riser should, in the partition, be well 
 wedged at the ends. This plan is always advisable 
 when strength and firmness are requisite, as the steps 
 and risers are entirely dependent on the framed car- 
 riages, which, if carefully put together, will never 
 yield to the greatest weight. 
 
 In preparing the string for the \\Teath part, a 
 cylinder should be made of the size of the well-room 
 of the stau-case, which can be done at a trifling ex- 
 pense ; then set the last tread and riser of the fliers 
 on one side, and the first tread and riser of the re- 
 turning flight on the opposite side, at their respective 
 heights ; then, on the centre of the curved surface of 
 this cylinder, mark the middle between the two, and 
 with a thin slip of wood bent round with the ruling 
 
 edge, cutting the two nosings of these fliers, and, 
 passing through the intermediate height marked on 
 the cylinder, draw a line, which will give the wreath 
 line formed by the nosmgs of the winders; then 
 draw the whole of the winders on this line by 
 dividing it into as many parts as you want risers, 
 and each point of division is the nosing of such 
 winder. Having thus far proceeded, and carefully 
 examined your heights and widths, so that no error 
 may have occurred, prepare a veneer of the width 
 intended for your string, and the length given by the 
 cylinder, and, after laying it in its place on the cylin- 
 der, proceed to glue a number of blocks about an 
 inch wide on the back of the veneer, with their 
 fibres parallel to the axis of the cylinder. When 
 dry, this wiU form the string for the wreath part of 
 the staircase, to be framed into the straight strings. 
 It is here necessary to observe, that about five or six 
 inches of the straight string should be in the same 
 piece as the circular, so that the joints fall about the 
 middle of the first and last fliers. This precaution 
 always avoids a cripple, to which tlie worlc w'ould 
 otherwise be subject. 
 
 The branch of stair building that falls under our 
 next and last consideration is that of hand railing, 
 which calls into action all the ingenuity and skill of 
 the workman. This art consists in constructing 
 hand rails by moulds, according to the geometrical 
 principles, that, if a cylinder be cut in any direction 
 except parallel to the axis or base, the section will 
 be an ellipsis ; if cut parallel to the axis, a rectangle ; 
 and if parallel to the base, a circle. 
 
 Now, suppose a hollow cylinder be made to the 
 size of the weU-room of the staircase, the interior 
 concave and the exterior convex, and the cylinder be 
 cut by any inclined or oblique plane, the section 
 formed will be bounded by two concentric similar 
 ellipses ; consequently, the section wUl be at its 
 greatest breadth at each extremity of the larger axis, 
 and its least breadth at each extremity of the smaller 
 axis. Therefore, in any quarter of the ellipsis there 
 will be a continued increase of breadth from the 
 extremity of the lesser axis to that of the greater. 
 Now, it is evident that a cylinder can be cut by a 
 plane tlu-ough any three points ; therefore, supposing 
 we have the height of the rail at any three points in 
 the cylinder, and that we cut the cylinder through 
 these points, the section wiU be a figure equal and 
 similar to the face mould of the rail ; and if the 
 
122 
 
 STAIRS. 
 
 cylinder be cut oy another plane parallel to the sec- 
 tion, at such a distance from it as to contain the 
 thickness of the rail, this portion of the cylinder wiU 
 represent a part of the rail with its vertical siu'faccs 
 already worked : and again, if the back and lower sur- 
 face of this cyliiidi'ic portion be squared to vertical 
 lines, either on the convex or concave side, through 
 two certain parallel lines drawn by a thin piece of 
 wood, which is bent on that side, the portion of the 
 cylinder thus formed will represent the part of the 
 rail intended to be made. 
 
 Though the foregoing only relates to cylindrical 
 well-rooms, it is equally applicable to raUs erected on 
 any seat whatever. 
 
 The face mould applies to the two faces of the 
 plank, and is regulated by a line drawn on its edge, 
 which line is vertical when the plank is elevated to 
 its intended position. This is also called the raking 
 mould. 
 
 The falling mould is a parallel piece of thin wood 
 applied and bent to the side of the raU piece, for the 
 purpose of drawing the back and lower surface, which 
 should be so formed that every level straight line di- 
 rected to the axis of the well-room, from every point 
 of the side of the rail formed by the edges of the fall- 
 ijig mould, coincide with the surface. 
 
 Li order to cut the portion of raU required out of 
 the least possible thickness of stuff, the plank is so 
 turned up on one of its angles that the upper surface 
 is nowhere at right angles to a vertical plane passing 
 through the chord of the plane ; the plank in this po- 
 sition is said to be sprung. 
 
 The pilch board is a right-angled ti-iangular board 
 made to the rise and tread of the step, one side form- 
 ing the right angle of the width of the tread, and the 
 other of the height of the riser. When there are both 
 winders and fliers, two pitch boards must be made 
 to their respective treads, but, of course, of the same 
 height, as all the steps rise the same. 
 
 The bevel by which the edge of the plank is re- 
 duced from the right angle when the plank is sprung, 
 is termed the spring of the plank, and the edge thus 
 bevelled is called the sprung edge. 
 
 The bevel by which the face mould is regulated to 
 each side of the plank is called the pitch. 
 
 The formation of the upper and lower surface of 
 a rail is called tlie falling of the rail; the upper sur- 
 face of the rail is termed the hack. 
 
 In the construction of hand rails, it is necessary to 
 
 spring the plank, and then to cut away the super- 
 fluous wood, as directed by the drawings, formed by 
 the face mould, which may be done by an expe- 
 rienced workman so exactly with a saw as to require 
 no further reduction ; and when set in its place, the 
 surface on both sides will be vertical in all parts, and 
 in a surface perpendicular to the plan. In order to 
 form the back and lower surface, the falling mould is 
 applied to one side, generally the convex, in such a 
 manner that the upper edge of the falling mould at 
 one end coincides with the face of the plank, and 
 the same in the middle, and leaves so much wood to 
 be taken away at the other end as will not reduce 
 the plank on the concave side ; the piece of wood to 
 be thus formed into the wreath or twist being agree- 
 able to their given heights. 
 
 Plate 87. 
 
 To find the projection of a helinet, on a plane 
 parallel to the axis of the cylindromc and per- 
 pendicular to the cutting plane of the solid. 
 
 Figs. 3 and 4. Let A B C D E F G H I K L M A, 
 (Fig. 3,) be the plan of a helinet, the quadrantal part 
 being B CDEFGHIKLB, and the straight 
 part being A B L M A. 
 
 Let Fig. 4 be the falling mould, corresponding to 
 the concave side of the semi-cycloid, found in the 
 usual manner, viz., draw any straight line X V W u; 
 make U V equal to the breadth of one of the fliers, 
 and V X equal to the stretch of B F ; draw X n per- 
 pendicular to U X, equal to the height of as many 
 winders as are contained in the circular part, together 
 wdth the height of the flier ; draw V t perpendicular 
 to U X, equal in height to a step, and join t n; then 
 complete the falling mould, of which the under edge 
 i&n p qr aV, and the upper edge z s < M V W X ; 
 make V W equal to B A, in Fig. 3 ; di-aw W a per- 
 pendicular to X U, cutting the under side of the fall- 
 ing moidd at «, and «/ parallel to U X; then a / is 
 the stretch of A B C D E F, Fig. 3. In Fig. 3, di- 
 vide the quadrant B F into any equal parts, B C, 
 C D, D E, E F, which stretch upon a f Fig. 4, ac- 
 cording to the corresponding letters. In Fig. 3, bisect 
 C D at I ; ch-aw I P radiating to the centre N, cut 
 ting the convex side of the plan at P ; draw F P R 
 and F O and P Q. parallel to each other, making an 
 angle with F R. In Fig. 4, bisect c d in y, and draw 
 y y perpendicular to a f uniting the under edge of 
 the falling mould at y ; divide fn and y y each into 
 
ir'Lf') K\'i:' 
 
 (yif ;rLiu:£ iF^.^iJM^o moQJia,®. 
 
 ,v ^ 
 
 n. 117 
 
 f e_ d v' r. h 
 
ts i3?j ^Y^fycBtf a®R ®[? is[is5ifUMie [pceuray^-s • 
 
 :• ICQOQJJIL®. 
 
 /;...■; 
 
 //« 4. 
 
 A 
 
 ■■v>' 
 
 /'/;/. / 
 
 /f^- 
 
 /■'it' / 
 
 ^^tejmLiiiipTr '' 
 
STAIRS. 
 
 123 
 
 the same number of equal parts as here into three. 
 In Fig. 3, make F O equal to one third of/ n, and 
 P Q equal to one third of y 1/ ; join O Q, which pro- 
 duce to meet F P in R. Draw R M, which produce 
 to s. La R s take any point m, and draw m f per- 
 pendicular to R s ; then, parallel to R s, draw A a s, 
 B b r t, C c q 11,1) dp r, E e iv, Ffn x. 
 
 From Fig. 4 transfer the heights b r, c q, dp, e 0, 
 and / n, to the corresponding lines b r, c q, dp, e o, 
 f n, Fig. 3 ; also, from Fig. 4 transfer the lines a s,rt, 
 q n, p V, o ic, and n x, to a s, r t, q v, p v, ti', and n x, 
 Fig. 3 ; then through the points 11 o p q r a draw a 
 ctirve, which will be the line representing the under 
 edge of the inside falling mould ; also, di-aw the curve 
 X IV V n t s, which is the line representing the upper 
 edge of the same falling mould. The upper and 
 lower edges of the outside falling mould will thus 
 be found — N being the centre of the quadrants 
 B C D E F and G H I K L; draw N E H, N D I, 
 N C K, N B L, cutting the convex side at H, I, K ; 
 and draw H W, I V, K U, L T, parallel to R 5 ; and 
 E W, D V, C U, B T, paraUel to / m. Also, draw 
 s s,tt, ti n, V V, parallel to / m ; and make 1 1, u u, v v, 
 respectively equal to T B, U C, V D ; and complete 
 the parallelogram 1 1, s s, and draw the curve t uv 3, 
 which will meet the curve s t u v tu x at J, the point 
 where a perpendicular drawn from the centre N of 
 the quadrant meets it. In the same manner, find the 
 curve nor; and we shall have the whole projection 
 of the helinet, which will give the thickness of the 
 stuff reqrured to make the rail ; by drawing a straight 
 line iji contact with two points on the under side 
 without cutting the solid, and another parallel to it 
 from the point X, then the distance between these 
 paraUel lines is the thickness of the stuff. 
 
 ON THE rORMATION OF THE FALLING MOULD. 
 
 To find tlie falling mould for a semicii'cular 
 stair, with winders round the semicii-cular 
 part ; or the falling mould for a semicu'cular 
 staircase level roimd the semiciixle, joined 
 below and above the fliers. 
 
 No. 1, Fig. 1, is in the plan of the rail round the 
 circular part, and of a small portion of the straight 
 part with the seats or plans of the risers round the 
 semicircular part. 
 
 Make a b, No. 2, equal to the height of the wind- 
 
 ers; draw a c and b d at right angles with a b; make 
 a e and b /each equal to the development oi I p or 
 pm, (No. 1 ; ) draw e I and d k parallel to a b ; make 
 e I and d k each equal to the height of a step ; and 
 join e g- and / k. This description so far applies both 
 to Figs. 1 and 2. 
 
 Li Fig. 1, No. 2, join c f; make e h equal to e g; 
 and / i equal to f k, and draw the touching curves 
 g-r h and i s k ; and g- r h i s k will be the line of the 
 rail. 
 
 In Fig. 2, No. 2, produce g- e to t, and k f to u; 
 bisect a b at s, and through 5 draw t u parallel to a c 
 or b d; from g t cut off t iv, and fi-om u k cut off u x, 
 each equal to g- e or / k ; and describe the touching 
 curves g z s and 5 y x, and giv z s y xk will be the 
 line of rail. 
 
 The breadth of the falling mould in common cases 
 is about two inches ; therefore, di-aw the curve lines 
 each at an inch distance from the line of the rail, and 
 the falling mould will be completed. 
 
 Plate S8. 
 
 OX THE RESTING POINTS. 
 PROBLEM. 
 
 To find the position of the plane of the plank, 
 and the resting points, so that the thickness 
 of stuff required to make the helinet may be 
 the least possible. 
 
 Fig. 1. Let abed efg h be the plan of the rail, 
 of which the part b c d efg is the quadrant of a cir- 
 cle, and the part a b g h of a rectangular figure ; the 
 straight lines a b and A g being tangents to the outer 
 and inner arcs at b and g, and the circular quadrants 
 bed and g- f e terminated by the radii b I and g I ; 
 then suppose two equal straight lines, one erected 
 upon c and the other upon /, perpendicular to the 
 plane of the plan of the rail, and let c Z be any inter- 
 mediate radius, cutting the interior quadrant at // 
 produce a h and e Ito meet each other in k. 
 
 Now, if a straight line be supposed to extend from 
 k to the top of the line which stands upon /, the 
 straight line thus extended, if produced, would be 
 higher than the top of the line which stands upon c ; 
 therefore, if a plane pass through a k and through the 
 top of the line insisting upon /, the plane will pass 
 above the top of the line standing upon c, and this 
 will be the case with every section, except the section 
 b g, which is parallel to a k; therefore, if the plane 
 
124 
 
 STAIRS. 
 
 of the plank rest upon the lower section a h, and upon 
 
 any other two points in the circular part, these points 
 must be in the concave side ; therefore, in this case, 
 the resting points are upon /(,/, e, in the concave side 
 of the rail. 
 
 Again : in Fig. 2, let I c and a 6 be produced to 
 meet each other in k ; then if a straight line be ex- 
 tended from k to the top of the line which stands 
 upon c, the straight line thus extended, if produced, 
 would be higher than the top of the line which stands 
 upon/; therefore, the plane which passes through a b, 
 and through the top of the line which insists upon c, 
 will be above the point which terminates the top of 
 the line insisting upon /; whence the resting points, 
 a, c, cl, are all upon the convex side of the rail. 
 
 Lastly : in Fig. 3, if a plane rests upon the top of 
 the two lines insisting upon c and /, and pass through 
 the point a, — and if a line be supposed to stand upon 
 e, perpendicular to the plane of the base, of such a 
 length as to meet the plane which passes through a, 
 and through the upper ends of the lines insisting 
 upon c and /, — it is evident that if another line be 
 supposed to be erected upon d, also perpendicular to 
 the plane of the base and equal in height to the line 
 insisting upon e, the plane wliich passes tlu'ough the 
 point a, and through the tops of the lines insisting 
 upon c,f, e, must be above the top of the line insisting 
 upon d; and that the intersection p q oi the plane 
 passing through a, and the points in the line insisting 
 upon c and/, must be parallel to c /. 
 
 It is now evident that if a & be produced to r, and h a 
 to 5, and as the intersection always passes tlirough a, 
 the line a p oi the intersection of the plane must al- 
 ways fall withm the right angle r a s. 
 
 It is likewise evident, if the resting section of the 
 rail fall between c / and a h, as at b g, the middle 
 resting point will be over b in the convex side of the 
 rail ; and if the resting section fall between c / and 
 d e, the resting point of the middle section must be 
 on the concave side. 
 
 SCHOLIUM I. 
 In stairs constructed upon the letter D plan, with 
 winders in the semicircular part, joined to a series of 
 fliers below and above, where the winders have a 
 higher pitch than the fliers, the first two resting 
 points, beginning at the lowest point, will be on the 
 convex side of the rail, while that at the highest point 
 is on the concave side. 
 
 Fig. 4. When the lower line of heights is nothing, 
 and the highest double to the middle one, the line of 
 intersection will be found by drawing a line through 
 the seat of the highest and middle resting point, and 
 producing the line on the other side of the seat of 
 the middle resting pomt, until the part produced be 
 equal to the part between the two seats, and drawing 
 a line through the lowest point a, and through the 
 extremity of the point thus found ; then the line thus 
 drawn will be the intersection. 
 
 Thus, in the present case, a c and e are the resting 
 points ; join c c, and produce e c to A; ; make c k equal 
 to c c, and join a k; then akis the intersection ; and 
 this agrees with what has been observed ; for if a k 
 and Z c be produced, they will meet in ?» ; therefore, / 
 is not the seat of the resting point : if/ were the seat 
 of the restmg point, maldng/ i equal to/ c, and join- 
 ing a i, then a i would be the intersecting line ; but it 
 is not, for the point c is nearer to a m than /. 
 
 Corollary. — From what has been observed, (see 
 Fig. 5,) that the intersecting line m v never falls 
 within the right angle at o, or upon the plan acdeh, 
 therefore, the point e is always nearer to u v than the 
 point d; therefore, the point e is the seat of a resting 
 point. 
 
 SCHOLIUM II. 
 
 Fig. 5. From the same given heights, and from 
 the same three resting sections of the rail, there can- 
 not be more than four intersecting lines by maldng 
 choice of one resting point irom each section. 
 
 For, suppose we make choice of the points d and c 
 as the seats of the resting points, and join the line 
 d c, and produce d c, suppose to some imaginary point 
 X, and find the point X from the heights upon d and 
 c, in such a manner that the line thus drawn may 
 not cross the plan, even if produced. The same 
 thing may be done through the points d and /, also 
 through the points e and c, and through the pomts 
 e and /; then, whichever of the points, d or e, is near- 
 est to the intersecting line ?f v, that point is the seat 
 of the resting point. 
 
 With regard to the ratio between the whole line 
 drawn through the seats of the resting points and 
 the part of it between the said seats, it is the same 
 as the ratio between the highest line and the line 
 insisting on the seat of the middle section. 
 
 Suppose (in Fig. 5) the seats of the resting points 
 are c and r; join c c, and produce it to i; draw e I 
 and c k perpendicular to e i; make e I equal to the 
 
SlriJ.3 P' 
 
 n 1)11 
 
 \:- 
 
 F{^,2. 
 
 I' t i 3 V 
 
S.Ii.ll 
 
 ,''1 'III 
 
STAIRS. 
 
 125 
 
 height insisting upon e, and c k equal to the height 
 insisting upon c ; join Ik, and produce it to i. Then, 
 because of the similar triangles e i I and c i k, i e : 
 i c : : e I : ck; that is, i c is the same part of i e that 
 c A; is of e I; therefore, if e / be double of c k, e i will 
 be double of c i, or i c will be equal to c e. 
 
 If the workman should not understand the demon- 
 stration now given, he may proceed mechanically 
 thus, the seats of the resting points being a, c, e. 
 
 Join e c, and produce ecioi ; draw e I and c k per- 
 pendicular to i e ; make e I equal to the height upon 
 e, c k equal the height upon c ; join I k and produce 
 it to /, and join i a; then i a is the intersecting line. 
 Produce i a both ways to ti and v, cf to o and i', and 
 d e to o and m; di-aw d r, e m, and o q perpendicular 
 to du; draw o p, fia, and c n perpendicular to o v; 
 make c n equal to c k, and join v n; produce v nto 
 p ; mak o q equal to o p, and e m equal to e I; join 
 m q ; then, if m g be produced, it will meet uv in ii. 
 This may easily be conceived by raising the triangles 
 i e I, V p, and u e m, upon their bases, i e, v c, and 
 d u ; then c k will coincide with c n, e I with e m, 
 and o p with o q ; and the lines i 1, v p, and r u will 
 all be in the inclined plane of which its intersection 
 is u V. 
 
 COXSTRTJCTION OF THE FACE MOULD. 
 
 Fig. 7. Let a d e f g h i be the plan of the rail, ef 
 g h a portion of the straight part, i being the upper, 
 and/ the lower, resting points. But as the place of 
 the middle resting point d vrSi. affect the tliickjiiess of 
 the stuff, it ought not to be arbitrarily assumed j 
 though it would be diiScult to show upon any prin- 
 ciple where it should be exactly. It is, however, 
 ascertained by trial that its position may vary to a 
 considerable distance without affecting the thickness 
 of the stuiT hi any great degree ; and as experiment 
 shows that it is nearly in the middle of the develop- 
 ment of a d ef, it is here taken in the middle, so that 
 the stretch-out of ad may be equal to the stretch-out 
 of df. 
 
 Figs. 6 and 7. In the figure of the falling mould, 
 produce the base a e of the winders to /, then a e 
 (Fig. 6) bemg equal to the development of a e, (Fig. 
 7,) make a d (6) equal to the development of ad, (7,) 
 and make e f (6) equal to e f, (7 ;) draw / 1 parallel 
 to a b, (6,) cutting the upper side of the falling mould 
 at 1, (6 ;) parallel to/a draw I i, cutting a b at i, (6 ;) 
 in i I make i d (6) equal to i d, (7 ;) draw d m (6) par- 
 
 allel to a b, cutting the upper side of the falling 
 mould at m ; draw vi n parallel to / a, cutting a 6 at 
 n ; draw d r parallel to a b, cutting m n at /•, (G.) 
 
 Join o r, and produce it to meet i I at q ; make i q 
 (7) equal to iq, (6;) join/ 7, (7,) and produce f q to 
 k i. Through g draw k I perpendicular to k q. 
 Through i draw i z parallel to k q, cutting k I at z. 
 Make z z equal to io, (6 ;) and join k z, (7,) and pro- 
 duce k z tx) I : draw a I parallel to z z. 
 
 TO FI>rD THE FACE MOTJLD. 
 
 Fig. 7. Draw I a and z b perpendicular to kl; 
 make I a equal to I a, z i equal to z i, and join i a; 
 then i a will form the part of the face mould repre- 
 sented by i a on the plan. Draw k f perpendicular 
 to k I, and make kf equal to kf. Draw g g parallel 
 to z z, cutting k I 2A, g, and join gf. Again : draw 
 h u parallel to z z, cutting k I at u and k I at tt. 
 Draw w h perpendicular to k I, and make u h equal to 
 uh; draw h e parallel to gf, and/ e parallel to g h ; 
 then e f g h will form the part of the face mould 
 corresponding to the straight part e f gh, in the plan. 
 The intermediate points of the face mould, which 
 form curves of the outside and inside of the rail, are 
 thus found. Through any pomt c, in the convex side 
 of the plan, draw c y parallel to z z, cutting k I at 
 y i, and k I at y, and the concave side of the plan at t. 
 Draw y c perpendicular to k I, and in y c make y t 
 equal to y t, and y c equal to y c ; then tis a. point in 
 the concave side, and c a point in the convex side, of 
 the face mould. A sufficient number of points being 
 thus found, the curved parts of the face mould may 
 be drawn by hand, or by a sfip of wood bent to the 
 curve. 
 
 It will be perceived that I have been obfiged, in 
 some instances, to use the same letter of reference 
 t«'ice ; but they are so placed, that the one referred 
 to can be ascertained without any difficulty. 
 
 Plates 89 & 90. 
 
 REdPROCAL SPIRAL AND SCROLL. 
 
 To draw the reciprocal spiral for a scroll. 
 
 Suppose the ordinate q (Fig. 1) to be given. 
 Make a b (Fig. 2) equal to q, and through b draw 
 c d, making an angle with ab ; then take & c in a 
 greater or less ratio to 6 1, as a less or greater part of 
 the scroll is wanted, or as the scroll is required to 
 
126 
 
 STAIRS. 
 
 have a flatter or qmcker curve at the remote extrem- 
 ity ; for instance, b c in this example is double to b 1. 
 
 Suppose the point c to be now fixed ; draw c e 
 parallel to a b, and a e parallel to c d; make 1, 2; 
 2, 3 ; 3, 4 ; &c., each equal to b 1, and draw the lines 
 1 e, 2 e, 3 e, 4 e, &c., cutting a b respectively at 
 e/g", &c. 
 
 Li Fig. 1, divide the space round the centre o into 
 eight equal angles, which will be easily done by 
 drawing a circle through q, and dividing the circum- 
 ference into eight equal parts, beginning at q ; draw 
 the portions o p, o q, o r, o s, &c. Make o p (Fig. 1) 
 equal to twice a b, (Fig. 2;)oq (Fig. 1) is equal to 
 a b, (Fig. 2;) also, make o r, o s, of, &c., (Fig. 1,) 
 respectively equal to a e, a f, a g, &c., (Fig. 2.) 
 Through all the points p q r s t, &c., draw the curve 
 p q r s t, &c., which will be the spiral required. 
 
 For want of room, a b (Fig. 2) is only made equal 
 to half the length it ought to have been ; for a & wiU 
 be divided into parts of the same length, whether a b 
 is double and b c equal to b 1, or a b as it is, and b c 
 double of & 1. 
 
 SCHOLIUM. 
 
 This spiral is well adapted to the purpose of hand 
 railing, for it may be made close or to extend at 
 pleasure, as may be seen by the subsequent examples. 
 
 This spiral may be extended so as to form the rail 
 itself by a gentle curve, which will approach nearer 
 to a straight line the more it is extended. The forms 
 of stairs attached to pulpits are often very fanciful ; 
 thek plan requires to be formed in the most graceful 
 manner ; the reciprocal spiral may be applied to this 
 purpose with advantage, as the effect produced will 
 be both beautiful and elegant. It may also be ap- 
 plied to form the plan of the riser of the curtail step 
 into a gentle curve, which will be in perfect unison 
 with the scroll itself. The plans of the other steps 
 may be formed to the same curve ; but the curvature 
 may be made less in each, as the other risers recede 
 from that of the curtail step, till at last the risers be- 
 come straight. The property of this scroll may be 
 shown arithmetically, thus : let any given radius be 
 called unity, or one, and let this radius, so called, be 
 the gi-catest radius ; let « be any constant number, 
 which must be in the same scroll, but variable in 
 difTcrent scrolls, and let a; be a variable number in the 
 same scroll, then will j^_ represent any ordinate ; thus 
 the first, second, third, &c., ordinates, by making x 
 
 respectively 0, 1, 2, 3, &c., will be respectively 
 
 By giving n a value, the form of the 
 determined. Thus, make 71 = 2, and 
 
 _!! ^ &c 
 
 scroll will be 
 we shall have the series of ordinates, |, f , f , f , |, &c. 
 This will give the scroll Fig. 1, plate 91. 
 
 Make n^A: then 
 
 -XI, 4t;, -^,,&c. will become 
 
 n-f- 1' n + 2' n-j- J' 
 
 f ) &) I) t, &c., respectively. These are the respective 
 ratios of the ordinates o a, o b,o c,o d,o e, Sec, Fig. 1, 
 plate 88. 
 
 Lastly : make n = 8; then ;, „-^, ~, ;^,&c.,wm 
 become f , |, j?^^, /j, &c., respectively. These are the 
 respective ratios of the ordinates oa, o b, o c, o d, &c.. 
 Fig. 3, plate 88. 
 
 So that we have both a geometrical and an arith- 
 metical rule for drawing the reciprocal spiral. 
 
 It may be here observed that this spiral is the only 
 one that can be employed in forming the volutes of 
 the Corinthian capital. 
 
 Fig. 3, plate 90, exhibits the scroll with the scale 
 drawn on the first radius. 
 
 Plate 91. 
 
 To describe the face and falling mould for pre- 
 paring the scroll. 
 
 Let a b he the first quarter of the scroll, c the cen- 
 tre ; draw d e parallel to b c, touching the outer spiral 
 at d ; draw e G parallel to c a, and through a draw 
 F G parallel to c b ; make G F equal to the breadth 
 of a step ; di-aw F H perpendicular to G H ; make 
 F H equal to the height of a step, and join H G ; 
 then G H is the pitch line of the stair. Draw lines 
 parallel to a c, cutting the inner edge of the scroll at 
 the points /, g; h, the outer edge at i, k, I, m, n, the 
 straight line F G in the points n, o, p, q, r, and H G 
 at the points N, O, P, Q, R ; let a c cut the concave 
 side of the scroll at t, and let it be produced to cut 
 H G at A ; from the point //, where the line d c cuts 
 the concave spiral of the scroll, draw h W parallel 
 to a c, cutting A G at W, F G at r, and the con- 
 vex spiral at ?/. Draw W H and G E perpendicular 
 to II G. 
 
 Make W H and G E each equal to v h or G e, 
 and join H E ; through the points N, O, P, Q, R, 
 draw lines perpendicidar to H G ; in the perpendicu- 
 lars make AT, N F, O G, each respectively equal 
 to a, t, n, f, o,g; also, make N I, O K, P L, Q, M, 
 R N, each respectively to « i, k, p 1, q m, r n ; draw 
 T X paraUel to H G, and draw the curves T F G H 
 
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 ri.:n 
 
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aif-pfLo^inro^Ri ®[? Trsaig im.ss sa®aj(L©. 
 
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 Pi.y.i 
 
 F,<,. 2 
 
 
 
 
 
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 '^ 
 
 
 
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 f 
 
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 / • 
 
 
 f 
 
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 u - 
 
 
 /. 
 
 L 
 
 f 
 
 fXi 
 
 
 h 
 
 "^ 
 
 ^ 
 
STAIRS. 
 
 127 
 
 and A I K L M N E, which will complete the face 
 mould for the twisted part of the scroll, which is to 
 be glued to the other part formed in one level piece. 
 The falling mould is constructed as follows : Fig. 2. 
 Let F G H be the pitch board, as in Fig. 1. Divide 
 F G into eight equal parts, and make F a equal to 
 three of the parts ; through a di'aw d q perpendicular 
 to F G, cutting H G at ^ ; produce H G io d; draw 
 any line q s parallel to F G, and make q s equal to 
 the sti'ctcli out of the first two quarters, a, b, v, of the 
 outward spiral. Fig. 1 ; through s draw u d parallel 
 to H F ; in H d take any distance d b, and draw b a 
 parallel to F G, cutting u d at a. Again : in H d 
 take b c equal to b a, and join c a; through ^j draw 
 p t parallel to c a, cutting n b in t ; draw t v parallel 
 to F G, cutting H fZ at w ; then will v t ha equal to 
 
 V p; divide v p and v t each into the same number 
 of equal parts, and draw the intersecting lines to the 
 points of division, and the curves formed will be the 
 upper edge of the falling mould ; the other edge will 
 be formed by gauging off the thickness of the rail. 
 
 Plate 92. 
 
 APPLICATION OF THE FACE MOULD TO THE PLANK. 
 
 To form the figure of tlie face mould upon each 
 side of the plank, so that, when the super- 
 fluous wood is cut away, the carved surfaces 
 formed thereby may stand perpendicular to 
 the plan, supposing the piece thus formed set 
 in due position. 
 
 Let abed e f g be the Fig. 1 of the face mould, 
 placed in due position to the pitch line g i, as when 
 traced from the plan ; and let Fig. 2 represent a de- 
 velopment of the plank where X represents the top, 
 
 Y the edge, and Z the under side of the plank. 
 
 The face mould is first applied to the top X, so 
 that the points g and the chord line g e oi the mould 
 may make the same angle at g with the arris line g e 
 of the plank that the figure of the mould at Fig. 1 
 makes with the pitch line ; di-aw g K, making the 
 same angle with i g that the pitch line makes with 
 any connecting line or perpendicular, and draw the 
 figure of the mould on the plank ; apply the same 
 mould to the other side Z of the plank to the point 
 K, so that the chord may make the same angle with 
 the other arris as on the first side, and draw the fig- 
 ure of the mould on this last side ; then the soUd 
 
 which is formed by cutting away the superfluous 
 wood is the piece required. 
 
 But as it may be desirable to apply the tips of the 
 mould g and e close to the edge of the plank. Fig. 3 
 shows how the plank is to be lined out according to 
 this application. Here the pitch line g K makes the 
 same angle with the upper arris of the plank as be- 
 fore ; di-aw g L perpendicular to either arris, cutting 
 the lower arris at L ; make the angle K L G equal 
 to the angle e g i, Fig. 1 ; make L g equal to L K, 
 and draw the chord g" e, in the plane Z, parallel to 
 the arris line ; in the plane Z apply the tips g and e 
 of the face mould to the line g e, as exhibited in the 
 figure ; then draw the form of the face mould as before. 
 
 DEMONSTRATION. 
 
 Fig. 2. Draw g L in the plane Y, cutting the lower 
 arris of the plank at L ; draw the ciiord K e of the 
 face mould in the plane Z, and draw L M in the same 
 plane parallel to K e ; also draw L s perpendicular 
 to K e, cutting K e at s. Now, imagine the figure 
 M L K e to be moved so as to revolve on the point 
 L, until L M come into the arris L m; it is evident 
 that the point K will move in the circumference of 
 the circle K k, and wiU come into the position k ; and 
 that the angle K L A* will be equal to the angle »i L M ; 
 but the angle 7ii L M is equal to the angle agi, Fig. 1. 
 Again : reverting to Figs. 2 and 3, it is plain in Fig. 3, 
 that if the angle KTi g in the plane Z be made equal 
 to the angle e g i, Fig. 1, and if L g- be made equal 
 to L K, and the mould applied to each side of the 
 plank as in the figure, the solid, when cut out, by 
 taking away the superfluous wood, will be equal and 
 similar in all its corresponding parts to that cut out 
 according to the oblique chords. Fig. 2. 
 
 Fig. 4 shows another application where the chord 
 of the face mould is neither applied to the angle e g i, 
 nor paraUel to the arris lines ; but as this application 
 is rather curious than useful, the bare inspection of 
 the diagram wiU render it sufficiently clear to those 
 who will take the trouble to consider it. 
 
 Plate 93. 
 
 ON THE FORMATION OF THE STRING. 
 PROBLEM. 
 
 To form the soffit of a stair with easings at the 
 junctions of the fliers and winders. 
 
 Let Fig. 1 be the plan of the staur, the breadth of 
 
128 
 
 STAIRS. 
 
 the steps being divided equally along the middle 
 line. Suppose the winders to begin at riser C, and 
 let the string from the riser of the curtail step to the 
 point C be straight. 
 
 The first thing to be done is to stretch out the 
 string; but in this development it will not be neces- 
 sary to exhibit it entirely, the circular part and a small 
 portion of the straight part at each end will be suffi- 
 cient; therefore, beginning at A, we shall take in the 
 two fliers over A B and B C. 
 
 In Fig. 2, draw;? I parallel to the rail, and makep I 
 equal to the length of tlie line abed e f g h. Draw 
 I K perpendicular to p I, make 1 1 ; 1, 2 ; 2, 3 ; equal 
 to tlie heights of the three risers over ABC, Fig. 1 ; 
 also, in Fig. 2, make 3, 4 ; 4, 5 ; 5, 6 ; 6,7; 7, 8 ; 
 each equal to the height of the winders over D, E, F, 
 G, H. h\ the plan Fig. 1, suppose a line drawn tlirough 
 the centre x perpendicular to the rail, cutting the mid- 
 dle line at D, and let this line be produced to ?;, Fig. 2 ; 
 in Fig. 2, draw 3 c parallel to p I, cutting xuatu; 
 join up and m 7 ; draw^j a in the same straight line 
 with the riser A, b b in the same straight line with 
 the riser B, and c c in the same straight line with the 
 riser C, to cut p ti at b and q ; make ti r equal to u q, 
 then form the easing curve q r ; draw 2 c, i d, 5 c, 
 €/, 7 g; parallel to^ I, cutting the easing curve at d 
 and e, and m 7 at / and g ; draw d d, e e, f f, g g^ 
 parallel to I K ; make c d equal to c d, d e equal to 
 d e, e/ equal to ef, fg equal to fg, and g h equal 
 to g h; then D H being divided into equal parts at 
 the points E, F, G, join D d, E e, F/, G g-, and pro- 
 duce them to the wall line ; in Fig. 2, draw the curve 
 P Q, R parallel to p q r zt a proper distance, which 
 completes one half of the string. The manner of 
 completing the other half is evident. 
 
 OBSERVATIONS. 
 
 Having given the details of finishing, I shall now 
 proceed to offer a few general remarks in relation to 
 this subject. 
 
 The selecting of biiilding materials has not, in gen- 
 eral, received that care and attention wliich this im- 
 portant subject demands. Many buildings have been 
 ruined, the owners of others have been displeased, 
 and not without just cause ; and the workman has lost 
 his reputation, and forfeited his claim to public patron- 
 age, solely firom neglect in this important particidar. 
 
 The first care of a master builder should be to see 
 that his lumber is properly seasoned. The best 
 method of seasoning is, after boards or plank have 
 
 been sawed at the mills, they should be immersed in 
 salt or fresh water for the space of one or two months ; 
 larger lumber should remain in this situation till the 
 sap is properly extracted from tlie wood ; this opera- 
 tion preserves the lumber in some degree fi-om the 
 dry rot. Next take the boards or plank out of the 
 water, and pile them in a situation where the air 
 may have a free circulation through and on all sides 
 of the piles. They should remain in this situation 
 for one year ; then take them down and select such 
 as are suitable for finishing : these should again be 
 stuck in a buUding, or covered in such a manner as 
 to be secure from the weather ; they should remain 
 in this situation at least sLx months before they are 
 used. While preparing the stuff for finishing, it 
 should be spread to the sun every fair day, and put 
 under cover at night for three or four weeks before it 
 is put together. The mechanic will feel himself well 
 paid for his time and trouble when he shall examine 
 his work at any subsequent period. 
 
 Framing timber should be squared up soon after 
 being taken out of the water, and stuck up under 
 cover for the space of six months before it is worked 
 into buUdings ; this wUl correct the erroneous idea, 
 in many cases, where the settling of the floor has been 
 attributed to bad workmanship, when, in fact, it has 
 been occasioned by the shrinking of the timber. 
 
 The Idnd of lumber in general use for building in 
 the New England States is white, yellow, pitch, and 
 Norway pine ; spruce, cedar, and sometimes hemlock, 
 white and basswood. The hard woods are oak, ma- 
 hogany, maple, cherry, and ash. In the Southern 
 States there is found a superior species of pine, which, 
 for durability, is preferable to northern pine, when 
 used for floor boards or joists. 
 
 Pine boards and joists are sorted into different 
 qualities, known as Nos. 1, 2, and 3. No. 1 is square 
 edged, free from knots, shakes, and rot. No. 2, the 
 second quality, is sound, not entirely free from knots, 
 and is square edged. No. 3 has Imots, shakes, is wane 
 edged, and has some rot. No. 1 is used for the best 
 of finishing ; No. 2 for rough boarding, such as roofs, 
 side and end boarding, &:c., where the edges are re- 
 quired to be tongucd and grooved, or rabbeted. From 
 this quality, by properly sorting them, good floor 
 boards may be selected, which should be sawed from 
 four to seven inches wide ; many of them will be 
 clear, and, after they arc A^TOught to a thickness, the 
 clearest may be used for the best rooms, and the others 
 as they may be suitable for the different rooms. 
 
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BRIDGES. 
 
 129 
 
 BRIDGES. 
 
 Mr. Ithiel To\vn's improvement in the construction of bridges 
 being considered preferable to any mode of bridge building yet laid 
 before the public, it has been thought best, in this department of the 
 work, to give his arguments and description in his own words, and 
 to refer the reader to the introduction for such additional facts and 
 remarks as has been thought necessary to lay before him, in order 
 to give him a more perfect understanding of this important branch 
 of his profession. 
 
 Plate 94 
 
 A Description of Ithiel Toioi's Improvement in the 
 Construction of icooden and iron Bridges., intended 
 as a general System of Bridge Building for Rivers, 
 Creeks, and Harbors, of whatever Kind of Bottoms, 
 and for ani/ practicable Width of Span or Opening, 
 in every Part of the Country. 
 
 To establish a general mode of constructing 
 wooden and iron bridges, and which mode of con- 
 struction shall, at the same time, be the most simple, 
 permanent, and economical, both in erecting and 
 repairing, has been for a long time a desideratum of 
 great importance to a country so extensive, and in- 
 terspersed with so many wild and majestic rivers as 
 ours is. It has been too much the custom for archi- 
 tects and builders to pUe together materials, each 
 according to his own ideas of the scientific principles 
 and practice of bridge building, and the result has 
 been, first, that nearly as many modes of construc- 
 tion have becH adopted as there have been bridges 
 built ; second, that many have answered no purpose 
 at all, and others but very poorly and for a short time ; 
 while most of the best ones have cost a sura which 
 deters and puts it out of the power of probably five 
 sixths of those interested in ferries to substitute 
 bridges which would obviate the many dangers and 
 delays incident to them. 
 
 That architects and builders adhere to their own 
 ideas in the construction not only of bridges, but of 
 buildings, is most universally true. They are obsti- 
 nately opposed to the adoption of any other mode 
 than their own ; consequently it is true, and it is 
 seen to be so throughout the country, (and it is much 
 to be regretted,) that in very few instances, either in 
 erecting bridges or buildings, there is any model, 
 
 17 
 
 either uniform or in genera!, very good. But in 
 bridges and public buildings, it would .seem some- 
 thing better might be expected if men scientifically 
 and practically acquainted with such subject.s would 
 step forward in a disinterested manner, and deter- 
 mine between principles which arc philosophical and 
 those which ase not, and between modes of execution 
 which are founded in practice and experience and 
 those which are founded in ignorance and inexperi- 
 ence ; and in matters of taste, if they would deter- 
 mine in favor of classic and well-established usage, 
 and not that which is the offspring of unimproved 
 minds and whimsical fancies, which are ever upon the 
 rack to establish new things — the creation of their 
 own imaginations, and which are, therefore, sure to 
 be wrong, for this good reason — that their authors 
 are so. 
 
 Perhaps the following propoeition comprises what 
 is the most important to be determined with regard 
 to a general system of bridge building, viz. : — 
 
 By what construction or arrangement will the 
 least quantity of materials and cost of labor erect a 
 bridge of any practicable span or opening between 
 piers or abutments, to be the strongest and most per- 
 manent, and to admit of the easiest repair. 
 
 In giving the best answer to this proposition 
 which I am capable of after a number of years' 
 attention to the theory and practice of this subject, I 
 shall refer to plate 94. The mode of construction is 
 so simple and plain to inspection as to require little 
 explanation of it. 
 
 Fig. 3 is an elevation of one of the trusses of a 
 bridge ; one, two, or three of those trusses placed 
 vertically upon piers are to be considered as the sup- 
 port of the bridge, and are to be of a height, at least, 
 sufficient to admit a wagon to pass under the upper 
 beams which lie horizontally upon the top string 
 piece of the side trusses ; and on these same side 
 string pieces rest the feet of rafters, which form a 
 roof to shingle upon. In this case a middle truss is 
 used, which will always be necessary in bridges of 
 considerable width. The height of it wiU be as 
 much greater than the side ones as the height or 
 pitch of the roof. The height of the trusses must 
 
130 
 
 BRIDGES. 
 
 be equal to the whole height of the bridge required, 
 and is to be an exact continuation of the work 
 represented in Fig. 1. 
 
 The height of the trusses is to be proportioned to 
 the width of the openings between the piers or 
 abutments, and may be about one tenth of the open- 
 ings, when the piers arc fifteen feet or more apart — 
 a less span requiring about the same height, for the 
 reasons before stated. 
 
 The diagonal bearing of these trusses is composed 
 of sawed plank, ten or eleven inches wide, and from 
 three to three and a half inches thick. It may be 
 sawed from any timber that will last well when kept 
 dry. White pine and spruce are probably the best 
 kinds of timber for the purpose, on account of their 
 lightness, and their not being so subject to spring or 
 warp as white oak. 
 
 The nearer those braces are placed to each other, 
 the more strength will the truss have, and in no case 
 are they to be halved or gained where they intersect 
 each other ; but they are to stand in close contact, 
 depending entirely on three or four trunnels which 
 go through each joint or intersection; and where the 
 string pieces pass over these joints, the trunnels go 
 through them also, and are each of them wedged at 
 each end to keep the timber in close contact. A 
 chain or clamp is necessary to bring the work tight 
 together. 
 
 Trunnels may be made of white oak, one and a 
 half inches in diameter. They are made very cheaply 
 and excellently by being rived out square, and driven, 
 while green or wet, through a tube fitted to a block, 
 and ground to an edge at the top end. They are 
 then to be seasoned before they are used. 
 
 The string pieces arc composed of two thicknesses 
 of plank, of about the same dimensions as the 
 braces, and they arc so put together as to break 
 joints, as shown at Fig. 4. This renders long-hewn 
 timber iinnecessary, as also any labor in making 
 splices and putting on iron work. 
 
 For any span or opening not exceeding one hun- 
 dred and thirty feet, one string piece at top and one 
 at bottom of each truss, if of a good proportion and 
 well secured, will be sufTicicnt ; but as the span is 
 extended beyond one hundred and thirty feet, two or 
 more at top and bottom would be required, as shown 
 in Fig. 1, where two string pieces run over the two 
 upper and lower series of joists or intersections of the 
 braces : and in wide spans the floor beams may be 
 
 placed on the second string piece, as shown at 
 
 Fig. 1. 
 
 Fig. 5 shows, on a larger scale, how each joint is 
 secured, by which it is seen that the trunnels take 
 hold of the whole thickness of each piece. 
 
 Fig. 4 is a section of a bridge of this construction, 
 and shows the manner in which the braces and 
 string pieces come together, and also the manner of 
 making the floor of the bridge, and of butting beams 
 and braces over head, which are to be connected 
 with the middle truss for the purpose of bracing the 
 bridge against lateral rack or motion. Very flat- 
 pitched roofs will be preferable, as- they will, in that 
 case, be a greater support to the upper part of the 
 bridge. 
 
 a a a a, Fig. 1, show the elevation of the roof. 
 
 Fig. 2 is the floor or plan of the bridge, showing 
 the mode of bracing and the floor joist. 
 
 Fig. 4 is a view of the bottom or top edge of the 
 string piece, and shows how the joints are broken in 
 using the plank, and also how the trunnels are dis- 
 turbed. 
 
 This mode of construction will have the same 
 advantages in iron as in wood, and some in cast 
 iron which wood has not, viz., that of reducing 
 the braces in size between the joints, and of cast- 
 ing flaunches to them where they intersect, thereby 
 making it unnecessary to have more than one bolt 
 and nut to each joint or intersection. 
 
 When it is considered that bridges, covered from 
 the weather, will last seven or eight times as long as 
 those not covered, and that the cheapness of this 
 mode will admit of its being generally adopted, with 
 openings or spans between piers composed of piles, 
 and at a distance of one hundred and twenty to one 
 hundred and sixty feet apart, then the construction 
 of long bridges over mud-bottomed rivers, like those 
 at Washington, Boston, Norfolk, Charleston, &c., wiU 
 be perceived to be of great importance, especially as 
 the common mode of piling is so exposed to freshets, 
 uncommon tides, driftwood, and ice, as not to insure 
 safety or economy in covering them, and, conse- 
 quently, continual repairs, and often rebuilding them, 
 become necessary. There is very little, if any, doubt 
 that one half of the expense, computing stock and 
 interest, that would be required to keep up, for one 
 hundred years, one of the common pile bridges, like 
 those at Boston, would be sufficient to maintain one 
 built in this new mode, keep it covered, and have all 
 
BRIDGES. 
 
 131 
 
 or nearly all, the piers built with stone at the end of 
 the one hundred years. If this be the case, it would 
 be great economy to commence rebuilding, by de- 
 grees, in this manner. The saving in the one article 
 of floor planks, if kept dry, would be very great, as, 
 by being so much wet, they rot and wear out in about 
 hair the time. 
 
 For aqueduct bridges of wood or iron, no other 
 mode can be as cheap or answer as well. This mode 
 has equal advantages also in supporting wide roofs 
 of buildings, centres of wide arches in masonry, 
 trussed floorings, partitions, sides of wood towers, 
 steeples, &c., 6cc., of public buildings, as it requires 
 nothing more than common planks, instead of long 
 timber — being much cheaper, easier to raise, less 
 subject to wet or dry rot, and requiring no iron work. 
 
 Some of the advantages of constructing bridges 
 according to this mode are the following: — 
 
 1. There is no pressure against abutments or piers, 
 as arched bridges have, and, consequently, perpendic- 
 ular supports only are necessary : this saving in wide 
 arches is very great, sometimes equal to a third part 
 of the whole expense of the bridge. 
 
 2. The shrinking of timber has little or no effect, 
 as the strain upon each plank of the trusses, both of 
 the braces and string pieces, is an end-grain strain or 
 lengthwise of the wood. 
 
 3. Suitable timber can be easily procured and 
 sawed at common mills, as it requires no large or 
 long timber ; defects in timber may be discovered, 
 and wet and dry rot prevented, much more easily than 
 could be m large timber. 
 
 4. There is no iron work required, — which, at best, 
 is not safe, — especially in frosty weather. 
 
 5. It has less motion than is common in bridges, 
 and which is so injurious and frequently fatal to 
 bridges ; and, being in a horizontal line, is much less 
 operated upon by winds. 
 
 6. A level road way is among the most important 
 advantages of this mode of construction. 
 
 7. The side trusses serve as a frame to cover upon, 
 and thereby save any extra weight of timber, except 
 the covering itself; and the importance and economy 
 of covering bridges from the weather is too well un- 
 derstood to need recommendation after the experi- 
 ence which this country has already had. 
 
 8. Draws for shipping to pass through may with 
 perfect safety be introduced in any part of the bridge 
 
 without weakening, as in arched bridges, where llu' 
 strength and safety of the arches depend so much on 
 their pressure against each other and abutments, tiiat 
 a draw, by destroying the connection, weakens the 
 whole superstructure. 
 
 9. The great number of nearly equal parts ov joints 
 into which the strain, occasioned by a great weight 
 upon the bridge, is divided, is a very important ad- 
 vantage over any other mode, as, by dividing!; the 
 strain or stress into so many parts, that which falls 
 upon any one part or joint is easily sustained by it 
 without either the mode of securing the joints, or the 
 strength of the materials being sufficient. 
 
 10. The expense of the superstructure of a bridge 
 would not be more than from one half to two thirds 
 of other modes of constructing one over the same 
 span or opening. This is a very important considera- 
 tion, especially in the Southern and Western States, 
 where there are many wide rivers, and a very scat- 
 tered population to defray the expenses of bridges. 
 
 11. This mode of securing the braces by so many 
 trunnels gives them much more strength when they 
 are in tension strain than could be had in the com- 
 mon mode of securing them by means of tenons and 
 mortises ; for tenons being short, and not very thick, 
 compared with this mode, nor having so much hold 
 of the pins or trunnels as in this case, will, of course, 
 have much less power to sustain a tension or pulling 
 strain ; and it is obvious that this strain is in many 
 cases equal to, and in others greater than, the thrust 
 or pushing strain. It is also very obvious that this 
 pushing or thrust strain in the mode of tenons and 
 mortises receives very little additional strength from 
 the shoulders of the tenons, as the shrinkage of the 
 timber into which the tenon goes is generally so much 
 as to let the work settle so far as to give a motion 
 or vibration, which, in time, renders them weak and 
 insufficient. 
 
 12. Should any kind of arched bridge, for any rea- 
 son, be preferred, however, it may be arched either at 
 top or bottom, or both ; still this same mode of com- 
 bining the materials will have all the advantages, as 
 to cheapness and strength, over the common ones of 
 framing, as in the case of the horizontal or straight 
 ones before described. Li cases where abutments 
 are already built, it may sometimes be preferred. 
 
 Sidewalks may with equal ease be constructed, 
 either on the outside or inside of the main body of 
 
132 
 
 BRIDGES. 
 
 the bridge, which particular, us also the great strength 
 of the mode, &c., may be better seen by examination 
 of the models, which are, or soon will be, placed in 
 most of the principal cities of the United States; and 
 no merit is either desired or claimed in this new mode 
 of construction by the patentee which the mode 
 itself docs not command, even on the most strict 
 philosophical investigation, as to its mathematical 
 principles, the easy, practicable, and advantageous 
 application of materials, the advantages it possesses 
 in mechanical execution, and its simplicity, strength, 
 economy, and durability, as a general and uniform 
 mode of bridge building. 
 
 Science and practice will, in a short time, decide on 
 this question, so important to this extensive country. 
 
 I shall conclude this article by a few ideas taken 
 from the celebrated Robert Fulton's Treatise on Ca- 
 nal Navigation, page 117 and subsequent pages. 
 
 In England, the attention of engineers has, of late 
 years, been much engaged on bridges of iron. These 
 bridges, as experience produces courage, are progres- 
 sively enlarging their dimensions ; nor should I be 
 surprised if genius should, in time, produce the me- 
 chanic rainbow of one thousand feet over wide and 
 rapid rivers. Li crossing the rivers in such countries 
 as Russia and America, an extensive arch seems to 
 be a consideration of the first importance, as the riv- 
 ers, or even rivulets, in time of rain, suddenly swell 
 to a great height ; and in the spring, on breaking up 
 of ice, the immense quantity which is borne down 
 with a rapid stream would, if interrupted by small 
 arches and piers, collect to such a weight as ulti- 
 mately to bear away the whole. It is, therefore, ne- 
 cessary that, in such situations, an arch should be 
 extended as far as possible, and so high as to suffer 
 every thing to pass through, or the inhabitants must, 
 without some other expedient, submit their passage 
 to the casualties of the weather. 
 
 The important objection to bridges of wood is their 
 rapid decay ; and this objection is certainly well 
 founded when particular situations are alluded to 
 where timber is scarce, and, consequently, expensive. 
 But in such countries as America, where wood is 
 abimdant, I conceive it will be a fair criterion to 
 judge of their application by calculating on the ex- 
 pense of a bridge of stone and one of wood, and 
 then compare the interest of the principal saved in 
 
 adopting the wood bridge with the expense of its 
 annual repairs. 
 
 I have before exhibited the necessity of construct- 
 ing bridges in America of an extensive span or arch, 
 in order to suffer the ice and collected waters to pass 
 without interruption ; and for this purpose, it must 
 be observed that a wood arch may be formed of a 
 much greater length or span than it is possible to 
 erect one of stone : hence wooden bridges are appli- 
 cable to many situations where accumulated waters, 
 bearing down trees and fields of ice, would tear a 
 bridge of stone from its foundation. 
 
 It therefore becomes of importance to render bridges 
 of wood as permanent as the natm'e of the material 
 will admit. 
 
 Hitherto, in bridges not covered from the weather, 
 the immense quantity of mortises and tenons, which, 
 however well done, will admit air and wet, and, con- 
 sequently, tend to expedite the decay of the weak 
 parts, has been a material error in constructing bridges 
 of wood. 
 
 But to render wood bridges of much more impor- 
 tance than they have hitherto been considered — first, 
 from their extensive span ; secondly, from their dura- 
 bility — two things must be considered: first, that the 
 woodworks should stand clear of the stream in every 
 part, by which it never would have any other weight 
 to sustain than that of the usual carriages ; secondly, 
 that it will be so combined as to exclude, as much as 
 possible, the air and rain. 
 
 When the true principle of building bridges of 
 wood is discovered, their progressive extension is as 
 reasonable as the increased dimensions of shipping, 
 which, in early ages, was deemed a great work, if 
 they amomited to one hundred tons' burden ; but 
 time and experience have extended the art of ship 
 building to two thousand tons, and in the combina- 
 tion and arrangement of the various and complicated 
 parts there certainly is more genius and labor re- 
 quired than in erecting a bridge of five hundred or 
 one thousand feet span. But the great demand for 
 shipping has rendered their formation familiar, and 
 their increased bulk has gradually grown upon our 
 senses. But had a man, in the infancy of naval 
 architecture, hinted at a vessel of two thousand tons, 
 I am inclined to think his contemporary artists would 
 have branded him as a madman. 
 
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BRIDGES. 
 
 133 
 
 WATERLOO BRIDGE. 
 
 Plate 95. 
 
 This bridge, thrown over the River Thames, at 
 London, was projected by Mr. George Dodd, about 
 the year 1805. Considerable time, however, elapsed 
 before the iiltimate arrangements necessary to carry 
 it into execution were made. The first act was ob- 
 tained in the month of June, 1809, and incorporated 
 the proprietors under the name of the " Strand Bridge 
 Company," empowering them to raise the sum of 
 £500,000 in transferrable shares of £100 each ; and 
 the further sum of £300,000, by the issuing new 
 shares, or by mortgage, in case it should be found 
 necessary. In July, 1813, a second act was passed, 
 enabling them to raise an additional sum of £200,000 ; 
 and in July, 1816, a third act was obtained, granting 
 the company further powers, and changing the name 
 from Strand Bridge to Waterloo Bridge, which name 
 it now bears. 
 
 IVIr. Rennie, having been appointed engineer to the 
 company on the 23d day of June, 1810, furnished two 
 designs, one of seven and the other of nine arches, 
 the latter of which was finally approved by the com- 
 mittee and ordered to be put in execution. 
 
 This noble bridge is situated about half way be- 
 tween the Bridges of Blackfriars and Westminster. 
 The river at this place is about 1326 feet wide at 
 high water ; and ordinary spring tides rise about 13 
 feet, and ordinary neap tides about 9 feet 6 inches. 
 The greatest depth at low water is about 9 feet. The 
 bed of the river is composed principally of a stratum 
 of sand and gravel resting upon clay. 
 
 The bridge is level, and consists of nine semi-ellip- 
 tical arches, each having a span of 120 feet, and a 
 rise of 35 feet ; thus leaving for the navigation 30 
 feet of clear height above the high water of spring 
 tides, and forming an ample water way of 1080 feet. 
 The abutments are 40 feet thick at the bases, and 
 diminish to 30 feet at the springing of the arches. 
 Their lengths, including the stairs, are 140 feet. The 
 piers are 30 feet broad at the base, and diminish to 
 tw^o thirds at the springing of the arches. Their 
 lengths at the bases are 87 feet. The points or sa- 
 lient angles of the piers are in the form of a Gothic 
 arch, and are terminated above by two three-quarter 
 columns, supporting an entablature which forms a 
 recess. The whole is surmounted with a balustrade 
 and a frieze and cornice of the Grecian Doric. The 
 
 columns are Doric also, and were selected on account 
 of the extraordinary strength of their proportions, as 
 being best suited to a structure of this magnitude : 
 they are 23 feet 9 inches high, or, rather, more than 
 four diameters. 
 
 The clear width between the parapets is 42 feet 4 
 inches, allowing 28 feet 4 inches for the carriage-way, 
 and 7 feet for each of the footpaths. 
 
 Four plying places, or stairs, for watermen, are 
 formed by circular wings, projecting at right angles 
 to the bridge, with archways leading to the road way. 
 These wings are ornamented with columns, entabla- 
 tures, &c., as before described. 
 
 The bridge being level, and of so great a length, it 
 became necessary to provide means for carrying off 
 the rain water. This is efiectcd by having circular 
 openings in the centre of each pier, which enter the 
 river immediately below low-water mark ; these open- 
 ings are connected with iron branch pipes up to the 
 level of the road-way, where gratings are placed to 
 receive the water. 
 
 The roads, or approaches, to each end of the pier 
 are 70 feet wide throughout, except just at the en- 
 trance into the Strand, and are carried over a series 
 of semicircular brick arches of 16 feet span each. 
 The Surry, or southern approach, is formed by 39 of 
 these, besides an elliptical arch of 26 feet span over 
 the narrow wall road, and a small embankment 
 about 165 yards long, having an easy and gradual 
 ascent of not more than 1 foot in 34 feet. 
 
 Feet. 
 The length of the brick arches in the Surry 
 
 approach is 766 
 
 Ditto of those in the Strand approach, . . 310 
 Total length of the bridge from the ends of 
 
 the abutments, 1380 
 
 Total length of the bridge and brick arches, 2456 
 
 Fig. 1 exhibits a longitudinal section of one of the 
 arches, the adjacent piers, and part of the next adja- 
 cent arches, with the elevation of one of the trusses 
 forming the centre. The curve of equilibrium passes 
 through the middle of the length of the arch stones, 
 or very nearly so. The hollows over the piers are 
 raised to the level of the summits of the arches by 
 parallel brick walls, and connected with blocks of 
 stone from wall to wall, for supporting the road-way. 
 
 The centring was composed of eight trusses. It 
 is 1250 feet long, has nine elliptical arches of 120 feet 
 
134 
 
 RURAL VILLA.— CHURCH EDIFICE. 
 
 span over the river, with piers 20 feet thick, built en- 
 tirely of granite, and forty brick arches for a cause- 
 way on the Surry side. This plate is given with a 
 view of showing the construction of masonry, as gen- 
 erally applied to bridge building. The geometrical 
 principle of constructing arches, and drawing the 
 joint Lines so as to be perpendicular to the curve, is 
 sufficiently explained in plate 101. 
 
 Fig. 2. The horizontal section showing the brick 
 walls, as a, a, &c., which arc covered with stone ; 
 also, the foundation of the piers at b, b, &c. 
 
 RURAL VILLA AT MILFORD, MASS. 
 
 Plate 96. 
 
 On this plate we have given a front elevation, with 
 a transverse section, together with the entrance and 
 chamber-story plans of a villa that we have erected 
 during the past year, in the town of MUford, Mass., 
 for A. C. Mayhew, Esq. It was our intention at 
 first to place at the last part of this work a series of 
 six designs for buildings of this character, with their 
 plans and detailg ; but upon further consideration we 
 have concluded to omit them, and, at some future 
 time, publish them in a form more in keeping with 
 a work of a rural character; this plate, however, 
 being made, we have inserted it as plate 96. 
 The size of the building will be readily seen by 
 the figures on the drawing. The outside walls 
 are of hard-burnt bricks, and are twelve inches 
 in thickness, which are vaulted, or having an air 
 space of four inches between the exterior and inte- 
 rior courses. The angles of the buUding are laid 
 solid, as are also the sides of the openings in the 
 walls, such as the sides of the doors, windows, &e. 
 The vaulted portions are connected together by 
 means of ties of brick in every two feet in length. 
 The exterior walls are covered with stucco cement, 
 and colored in imitation of drab stone. The exte- 
 rior wood work is painted, and sanded with beach 
 sand. — Editors. 
 
 CHURCH EDIFICE AT MILFORD, MASS. 
 
 Plate 97. 
 
 On this plate will be found the t%vo plans, and the 
 front elevation of a small church which was erected 
 
 under our superintendence in 1850, for the Pearl 
 Street Universalist Society of JMilford, Mass. We 
 do not present it as containing any thing of pecu- 
 liar merit or of costly design ; but the arrangement 
 of the plans and tlie general features of the build- 
 ing having received the approval and approbation 
 of building committees and others interested in 
 such matters, we have, at their urgent solicitations, 
 and at the suggestions of many others, inserted this 
 plate for the benefit of those seeking the information 
 the plate and its description may contain. The fol- 
 lowing description of this edifice appeared in the 
 Trumpet and Universalist Magazine at the time the 
 budding was dedicated ; and, with a few slight alter- 
 ations, we transcribe it entire, as the description of 
 plate 97.* 
 
 ARCHITECTURAL DESCRIPTION OF THE NEW MEET- 
 ING-HOUSE IN MILrORD, IIASS. 
 
 This building is built of wood, erected upon a brick stylobate or 
 basement, and is of the following dimensions, viz., length, 72 feet 
 8 inches; width, 51 feet, outside; with a projecting vestibule on 
 the front end, 13 feet wide by 26 feet long, and the posts are 25 feet 
 in height. Upon the roof of the vestibule stands a pedestal, 19 feet 
 square and 13 feet high, finished with suitable projections ; upon 
 this is a clock tablet, 15 feet square and 12 feet high, covered with 
 a roof showing an entablature and pediment on each side ; the tab- 
 let is finished with heavy mouldings, and a recess 8 inches deep is 
 made on each side, to receive a dial 7 feet in diameter. Rising from 
 this is an octagonal bell tower, 12 feet in diameter and IG feet high, 
 including its base and entablature ; on each of its sides are arched 
 openings, 3 feet 3 inches in width, and in each of which is a balus- 
 trade, composed of heavy-turned balusters. Upon this tower is an 
 octagonal pedestal, 6 feet high and 11 feet in diameter, with deep 
 panels on each side, which is surmounted by a spire 45 feet high, 
 crowned with a carved finial, making the entire height from the line 
 of the grading 136 feet. The style of architecture Is the Roman- 
 esque, which is a combination of the Roman and the late Norman, 
 the latter being the prevailing style of the 11th century. The cor- 
 ners of the building, together with the vestibule, are finished with 
 heavy pUasters 2 feet 9 inches wide, in each of which is a deep 
 circular-headed panel ; upon these rests a dentil corniced entablature, 
 5 feet deep. The cornice of the entablature is continued up the 
 rakes of the main building and vestibule, which finish gives the 
 whole an imposing and massive appearance. 
 
 The building is Ughted on either side by three circular-headed win- 
 dows, which arc composed of two circular-headed parts, and separated 
 by a large mullion ; and the front of the main building, on either side 
 of the vestibule, by one of the same style, and of two thirds the width 
 
 * To OUn BELOVED FRIENU, THE ReV. HeNRT A. EaTON, PAS- 
 TOR OP TUE SOCIETY, AND UNDER WHOSE MINISTRATIONS TUB 
 BUILDING WAS ERECTED, THIS PLATE IS RESPECTFULLY DEDI- 
 CATED, A3 A SMALL TRIBUTE OF RESPECT AND ESTEEM, BY THE 
 ARCHITECTS. 
 
 THOMAS W. SILLOWAY, 
 GEORGE M. HARDING. 
 
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CHURCH EDIFICE. 
 
 of those on the sides, making them adapted to their location. The 
 choir-room, which is on the second floor of the vestibule, is lighted 
 by a largo window, composed of one in its centre, similar to those 
 before described ; to which is added on either, side another of one 
 half its width, and a proportionate height, and separated from it by 
 pilasters, the capitals of which are so disposed that the centre ■win- 
 dow is stilted 1 foot 6 inches ; the i\idth of the entire window is 1 1 
 feet. Beneath this window, on the front of the vestibule, is the 
 main entrance to the building, which is by three circular-headed 
 doors, the centre one of which is 5 feet wide suid 13A feet high ; the 
 arch of this door is stilted 3 feet. Those of cither side are 34 feet 
 wide and 10 feet 3 inches high; making an actual space in width 
 of 12 feet, which is 1 foot 6 inches more than the whole width of the 
 church aisles. The doors are entered by five steps, which are buUt 
 of southern pine, and extend the entire length of the vestibule, in- 
 cluding a buttress 3 feet wide at either end. This brings us to the 
 interior of the building. 
 
 As has been before stated, the entrance was but five steps from 
 the grading on the front end, so that the entrance floor is five feet 
 lower than the pew floor ; a space of four feet is left at the entrance 
 on the inside, the entire length of the vestibule, 24 feet. And at 
 that distance from the doors, a flight of eight stairs, 13 feet long, 
 lead up to the entry of the church ; which entry is 74 feet wide, 
 and runs the entire width of the church on the inside. These stairs 
 are very easy of ascent, and, being 13 feet long, amoimt to 24 feet 
 more than the width of all the aisles, so that these, together with 
 the outside doors, insure against any jam being produced in the 
 entry of the building, which is one of the evUs with which the 
 architect has often to contend. 
 
 On either side of the main stairs to the church arc those leading 
 to the vestry ; these are each 44 feet wide, making a passage-way 
 of 9 feet ; they are built of southern pine, as are also the floors of 
 all the entries, and are oiled over, leaving the natural color of the 
 wood. A large mahogany rail and southern pine balusters com- 
 mence at the foot of those to the vestry, and are continued up 
 around the well-room over those to the church, and returns at 
 the top railing in the space on the upper entry, which is not 
 occupied by those leading to the entrance floor. 
 
 An arch is sprung over each of the three openings at the top of the 
 church stairs ; these openings are made by a square pillar coming 
 down at the head of the stairs on either side, so that, beneath these 
 three arches, the whole space is open on the church entry floor the 
 entire ^vidth of the vestibule, which gives to the whole a spacious 
 and airy appearance. From this floor, stairs on either end lead to 
 the singing gallery. Beneath this entry, on the vestry floor, is one 
 of the same width, and from it is a door 4 feet wide, leading to the 
 outside of the building ; one leading to a room 12 feet square, for 
 wood and coal, beneath the church stairs ; also two others leading 
 to the vestry, the dimensions of which are 42 by 49 feet, and 1 1 feet 
 
 high in the clear ; connected with which arc two ante-rooms, each 
 20 feet 6 inches by 22 feet. Attached to each of these rooms is a 
 closet, 4 feet wide and U feet long. The ante-rooms are separated 
 from the vestry by largo doors, which move on castors, so that the 
 whole may be thrown into one large room. 
 
 The floor of the church contains 82 pews, 2 feet 10 inches wide, 
 and 9 feet 7 inches in length, which provides 19 inches to a person, 
 allowing G persons to a pew, making the house capable of seating in 
 all, including the gallery, 650 persons. Tlie side aisles are 3 feet 
 wide ; the one in the centre, 44 feet. 
 
 The pulpit is of an original design, and is in strict accord- 
 ance with the architectural character of the edifice. It is an im- 
 itation of rosewood, and the seven circular-headed panels on the 
 front are lined with garnet plush. The sofa connected with the 
 pulpit is of rosewood, and was designed for the place it occupies ; 
 the trimmings of the sofa, pulpit, and chairs are also of garnet 
 plush. 
 
 There is a choir gallery at the end of the church, over the 
 entrance, connected with which is a room for the choir's rehear- 
 sals, 24 by 12 feet, and 12 feet high. There ia a dado in each 
 of the side aisles of the main floor, to the height of the window 
 sUls, which is returned at the sides of each window, making a 
 pedestal of sufficient width to include the window and the fresco 
 pilasters at its sides. This dado has a capping and base, which, 
 together with the doors of the church, are grained black walnut. 
 
 The windows of the whole building, above the basement, are 
 furnished with blinds on the inside, and are painted Paris green. 
 The walls of the principal room arc 24 feet high, and these, with the 
 whole interior of the church, are finely painted in distemper fresco, 
 in the following manner : The side walls have a fine fluted Corin- 
 thian pilaster on each side of all the windows, which support an 
 entablature 3 feet deep, extending entirely around the church walls ; 
 between each of these is a sunken panel, and inside of these is one 
 which is raised ; over the windows is a rich moulding ornamented 
 with a console, and ending at the pilasters with an acanthus lea£ 
 On the back end, on either side of the recess, back of the pul- 
 pit, is painted a niche standing on a pedestal, and finished like the 
 windows. In the recess back of the pulpit is represented an arched 
 panelled recess or passage, leading to a rotunda, in the centre of 
 which stands a large cross ; the celling is very finely decorated by 
 large panels, and at the angles are ornaments of Roman foliage, 
 extending some 11 feet either way. In the centre of the ceiling is 
 a cast-iron register, 3 feet in diameter, to admit the foul air to one 
 of Emerson's ventilators, (which efi'ectually ventilates the room;) 
 around this is a beautiful design of foliage, and on two of its sidei 
 is seen a harp, supported by the leaves and scroUs. The tint of the 
 ground is a gray lilac. The building was raised in November last, 
 and has been entirely completed since that time. It has cost, 
 including the land and furnishing, not far from $10,500. 
 
 T. W. S. 
 
136 
 
 GOTHIC ARCHITECTURE. 
 
 GOTHIC ARCHITECTURE 
 
 Gotliic, or what may be termed, with more pro- 
 priety, English architecture, is that style which im- 
 mediately succeeded the Norman, and the most 
 prominent feature of which is the pointed arch, 
 slender columns, and a predominancy of vertical 
 lines. Wc should have been pleased to have given 
 a full description of this kind of architecture ; but 
 our limits not permitting, we shall content ourselves 
 with simply giving a synopsis of some of its char- 
 acteristics; and to those of our patrons who may 
 wish for a more extensive knowledge of this branch 
 of the science, we would refer them to a work 
 known as the Glossary of Architecture, the fifth 
 edition of which was published in London the past 
 year. This work contains a very elaborate description 
 of all that pertains to this branch of the science, and 
 is a production of inestimable value. We have 
 stated that this species of architecture immediately 
 succeeded the Norman — indeed, it is a work of 
 some nicety to draw the dividing line between them ; 
 but, before proceeding further, we will remark that 
 the Rev. Mr. Millers, of England, has divided the 
 architecture on which we treat into three distinct 
 classes, and his classification has met the approval 
 of Rickman and Pugin, who are among the principal 
 architectural \\Titers of England. The first style he 
 terms the Early English, the second the Decorated, 
 and the third the Perpendicular. We shall follow 
 him in this respect, and shall describe each style re- 
 spectively hereafter. 
 
 The Early English, then, is the style which is 
 nearest to the Norman, and it may be said to have 
 grown out of it ; and here we beg leave to differ 
 from the opinion that has at times found warm 
 advocates, which is, that the form of the arch which 
 characterizes this species of architecture was sug- 
 gested by the intersection of branches of trees. This 
 idea is, without doubt, the production of a fertile 
 imagination, and, like the famous story of Callima- 
 chus and the vase at Corinth, it may be regarded as 
 a play of the fancy and a freak of ideality. One of 
 the principal features of the Norman architecture is 
 
 the very frequent use of the Roman arch ; and, by 
 describing a second semicircle with a point in the 
 circumference of one already drawn as a centre, we 
 produce what is familiarly known as the Gothic arch, 
 and a series of these we term intersected arches. 
 This also is of firequent occurrence in the later 
 Norman architecture ; and we deem it no departure 
 from the principles of logic to deduce from this fact 
 that the arch used in the English architecture was 
 no invention, but simply a transfer to it from the 
 Norman, and that, even with those with whom it 
 originated, it was the result of accident rather than 
 design. We thus give our reasons for the intrusion 
 we make upon the favorite speculations of those 
 who may differ from us, for we do so with all re- 
 spect to their love of the ideal, and we would be the 
 last to deprive them of the pleasure they may de- 
 rive from the idea that those with whom one of the 
 most beautiful of the productions of architecture had 
 its origin were men endowed with great inventive 
 talent, and that, too, which often manifested itself to 
 an astonishing degree. But to proceed: we will 
 again remark, that the first style is the Early English, 
 and is, as its name suggests, the earliest of the three. 
 The intersecting arches to which we have before 
 referred characterized the Norman, as it was about 
 to merge into it, and, in some instances, we find 
 examples of the poiiited arch in the Norman, entirely 
 by itself; thus the one has produced the other. 
 
 The time when this style may be said to have had 
 its rise was about the year 1200, and continued from 
 this period to 1300, which extended through the reigns 
 of John, Henry III., and Edward I. It is stated that, 
 during the reign of Henry III. alone, no less a num- 
 ber than one hundred and fifty-seven abbeys, priories, 
 and other religious houses were founded in England ; 
 and the erection of these was considered as among 
 the most effectual means of obtaining the forgiveness 
 of sins, and, consequently, the favor of Heaven. 
 The principal characteristic of this style is, in the 
 language of Gwilt, as follows : The arches are 
 sharply lancet pointed, and lofty, in proportion to 
 
GOTHIC ARCHITECTURE. 
 
 137 
 
 their span. In the upper tiers, two or more are com- 
 preliended under one, finished in trefoil or cinquefoil 
 heads, instead of points, the separating columns 
 being slender. Columns on whicii the arches rest 
 are very slender in proportion to their iieight, and 
 usually consist of a central shaft, surrounded by 
 several smaller ones. The base takes the form of 
 the cluster and the capital is frequently decorated 
 with foliage, very elegantly composed. The tcin- 
 doics are long, narrow, and lancet-shaped, whence 
 some \\Titers have called this style the Lancet Gothic. 
 They are divided by one plain mullion, or, in upper 
 tiers, by two at most, finished at the top with some 
 simple ornament, as a lozenge, or a trefoil. They 
 have commonly small marble shafts on each side, 
 both internally and externally ; two, three, or more, 
 together, at the eas't or west end, and tier above tier. 
 Roofs arc high pitched, and the ceilings vaulted, 
 exhibiting the first examples of arches with cross 
 springers only, which, in a short period, diverged into 
 many more, rising from the capitals of the columns, 
 and almost overspreading the whole sm-face of the 
 vaulting. 
 
 The longitudinal horizontal line which reigned 
 along the apex of the vault was decorated with 
 bosses of flowers, figures, and other fancies. Walls 
 much reduced in thickness from those of the pre- 
 ceding period ; they arc, however, externally strength- 
 ened with buttresses, which, as it were, lean against 
 them for the purpose of counteracting the thrust 
 exerted by the stone vaults which form the ceil- 
 ings, and which the walls and piers, by their own 
 gravity, could not resist. The buttresses are, more- 
 over, aided in their office by the pinnacles, adorned 
 with crockets at their angles, and crowned with 
 fiuial flowers, by which they are surmounted. The 
 ornaments now become numerous, but they arc sim- 
 ple and elegant. The mouldings are not so much 
 varied as in the Norman style, and are generally, 
 perhaps universally, formed of some combination of 
 leaves and flowers, used not only in the cuxumference 
 of arches, especially of windows, but the columns or 
 pilasters are completely laid down with them — ti-e- 
 foils, quatrefoils, cinqucfoils, roses, mullets, bosses, pa- 
 terae, &c., in the spandrils, or above the keystones of 
 the arches, and elsewhere. The ornamental pinna- 
 cles on shrines, tombs, &c., are extremely high and 
 acute, sometimes with, and sometunes without, niches 
 under them. In east and west fronts, the niches are 
 
 18 
 
 filled with statues of the size of life, and larger, and 
 are crowned with trefoil, &c., heads, or extremely 
 acute pediments, formed by the meeting of two 
 straight lines, instead of arcs. All these ornaments 
 arc more sparingly introduced into large, entire edi- 
 fices than in smaller buildings or added parts. The 
 plans are, generally, similar to those of the preceding 
 period; but that important feature, the tower, now 
 begins to rise to a great height, and lanterns and 
 lofty spires arc frequent accompaniments to the 
 structure. It will natm'ally occur to the reader, that, in 
 tiie transition from the Norman to this style, the archi- 
 tects left one extreme for another, though it has been 
 contended that the latter has its germ in the former. 
 However that may be, the period of which we are 
 now speaking was undoubtedly the parent of the 
 succeeding styles, and that by no very forced or un- 
 natural relationship. 
 
 The principal examples of the early English style, 
 in the catheckal churches of England, are to be seen 
 at Oxford, in the chajiter-house ; Lincoln, in the nave 
 and arches beyond the transept ; York, in the north 
 and south transept ; at Durham, in the additional tran- 
 sept ; Wells, the tower and the whole western front ; 
 Carlisle, the choir ; Ely, the presbytery ; Worcester, 
 the transept and choir ; Salisbitri/, the whole cathe- 
 ch-al — the only unmixed example ; at Rochester, the 
 choir and transept. " It is well worthy of observa- 
 tion," says Ml-. Dallaway, " that though the gi-ound 
 plans of sacred edifices are, generally spealdng, simi- 
 lar and systematic, yet in no single instance which 
 occurs to my memory do we find an exact and un- 
 varied copy of any building which preceded it, in any 
 part of the structure. A striking analogy of resem- 
 blance may occur, but that rarely." 
 
 The second class or style is the Decorated, and oc- 
 cupied the period between 1300 and 1460. " Li the 
 early part of the period," continues Gwilt, " the change, 
 or rather progress, was extremely slow, and marked by 
 little variation ; and indeed, until 1400, the style can 
 scarcely be said to have been perfected ; but after 
 that time, it rapidly attained all the improvement 
 whereof it was susceptible, and so proceeded till 
 about 1460, after which it assumed an exuberance 
 of ornament, beyond which, as it was impossible to 
 advance, it was in a predicament from which no 
 change could be efiected but by its total abandon- 
 ment. This style exhibits arches, less acute and 
 more open, the forms varying." 
 
138 
 
 GOTHIC ARCHITECTURE. 
 
 Columns. — The central and detached shafts are 
 now -worked together into one, from experience of the 
 weakness of those of the previous style, exceedingly 
 various in their combinations. 
 
 The untulows are larger, divided by mullions into 
 several lights, spreading and dividing at the top into 
 leaves, flowers, fans, wheels, and fanciful forms of 
 endless variety. These marks are constant, but in 
 the proportionate breadth there is much variation ; 
 for, after having expanded in the reigns of Edward I. 
 and II., they grew narrower again in proportion to 
 their height in that of Edward III., and also sharper. 
 The head was then formed of lines just perceptibly 
 curved, sometimes even by two straight lines, some- 
 times just cur\-ed a little above the haunches, and then 
 rectilinear to the apex. The eastern and western win- 
 dows were very lofty and ample, and splendidly deco- 
 rated with painted glass. In regard to the roof or 
 ceiling, the vaulting is more decorated. The princi- 
 pal ribs spread from their imposts, running over the 
 vault lilie tracery, or, rather, with ti'ansoms divided 
 into many angular compartments, and ornamented 
 at the angles with heads, orbs, historical or legendary 
 pictures, &c., elaborately colored and gilded. The 
 ornaments are more various and labored, but not so 
 elegant and graceful in character, as in the preceding 
 style. Niches and tabernacles, with statues, are 
 used in great abundance. Tiers of small ornamental 
 arches are frequent. The pinnacles arc neither so 
 lofty nor tapering, but are more riclily decorated with 
 leaves, crockets, &c. Sculpture is introduced in 
 much profusion, and is frequently painted and gilt; 
 screens, stalls, doors, panelled ceilings, and other 
 ornaments in carved and painted wood. 
 
 Some of tlie principal examples of the ornamented 
 English style in cathedral churches are, at Exeter, 
 the nave and choir; Lichfield, uniformly; at Lincoln, 
 the additions to the central tower; at Worcester, the 
 nave ; York, nave, choir, and western front ; at Can- 
 terbury, transept ; at Gloucester, transept and cloisters 
 began ; Norwich, the spire and tower ; Salisbiiri/, spire 
 and additions ; Bristol, the nave and choir ; Chichester, 
 the spire and choir; Eli/, Our Lady's Chapel, and 
 the central louvre ; Hereford, the chapter-house and 
 cloisters, now destroyed. In the later part of the pe- 
 riod, the choir at Gloucester, the nave at Canterbury, 
 Bishop Beckington's additions at Wells, and from 
 the upper transept to the great east window at 
 Lincoln. 
 
 FLORID ENGLISH, OR PERPENDICU- 
 LAR STYLE. 
 
 " There is," as Dr. Henry obser^'es, " a certain per- 
 fection in art to which hmnan genius may aspire 
 with success, but beyond which it is the apprehen- 
 sion of many that improvement degenerates into false 
 taste and fantastic refinement." " The rude sim- 
 plicity of Saxon architecture was [ultimately] sup- 
 planted by the magnificence of the ornamental Gothic; 
 but magnificence itself is at last exhausted, and it 
 terminated dm-ing the present period in a style cen- 
 sm-able as too ornamental, departing from the gran- 
 dem- peculiar to the Gothic, without acquiring pro- 
 portional elegance; yet its intricate and redundant 
 decorations arc well calculated to rivet the eye, and 
 amaze, perhaps bewilder, the mind." The period of 
 this style is from 1460 to the dissolution of the re- 
 ligious houses in 1537, and comprehends, therefore, 
 the reigns of Edward IV. and V., Richard III., 
 Henry VII. and VIII. 
 
 Its principal characteristics are arches, univer- 
 sally flat, and wide in proportion to their height. 
 The windows arc much more open than in the 
 last period, flatter at the top, and divided in the 
 upper part by transoms, which are almost con- 
 stantly crowned with embattled work in miniature. 
 The ceilings, or vaultings, spread out into such a 
 variety of parts that the whole surface appears cov- 
 ered with a web of delicate sculpture or embroidery 
 thrown over it; and from different intersections of 
 this ribbed work, clusters of pendent ornaments hang 
 down, as Mr. Miller observes, like " stalactites in 
 caverns." The flying buttresses are equally orna- 
 mented, and the external sufaces of the walls are one 
 mass of delicate sculpture. The ornaments, as may 
 be deduced from the above particulars, are lavish and 
 profuse in the highest degi-ee. Fretwork, figures of 
 men and animals, niches and tabernacles, accompanied 
 with canopies, pedestals, and traceries of the most 
 exquisite workmanship, carried this style to the sum- 
 mit of splendor ; and all these combined had, perhaps, 
 no small share in producing the extinction it was 
 doomed to undergo. 
 
 Roslin and Holyrood Chapels, the first whereof was 
 erected by Sir William St. Clair, for richness and 
 variety of ornamental carvings camiot be exceeded. 
 Its plan is without parallel in any other specimen of 
 the fifteenth century. The latter was finished by 
 
GOTHIC AKCHITECTURE. 
 
 139 
 
 James, the second ol that name, in 1440, and is a 
 beautiful example, with flying buttresses, which are 
 more ornamented than any even in England. Ex- 
 amples of tlie Florid Gothic or Perpendicidar style 
 are to be seen at the cathedi-al churches of Glouces- 
 ter, in the Chapel of Our Lady ; at Oxford, in the 
 roof of the choir ; at Ely, in Alcock's Chapel ; at 
 Peterboro% in Our Lady's Chapel ; and at Hereford, 
 in the north porch. In conventual churches at 
 Windsor, St. George's Chapel at Cambridge, King's 
 College Chapel at Westminster, King Henry VII.'s 
 Chapel; at Great 3Ielverit, in Worcestershire, the 
 tower and choir; at Christ's Church, Oxford, the 
 roof of the choir ; and at Evesham Abbe?/, in Worces- 
 tershhe, the campanile and gateway. 
 
 Among other principal examples in this style, it 
 may be well to mention that Scotland boasts of many 
 fine specimens of ecclesiastical architectiure. The 
 Abbeys of Melrose and Kelso, founded by David I., 
 as well as those in Dryburgh and Jedburgh, — all in 
 Roxbm-ghshire, — prove that the art advanced to as 
 great perfection north of the Tweed as it did in 
 England. 
 
 For parochial churches, except in some very few 
 
 specimens in Somersetsliire, and there, perhaps, only 
 in parts, we are unable to refer the reader to a com- 
 plete specimen, in all its parts, of the perpendicular 
 style. The pulpit and screen at Dartmouth, in Dev- 
 onshire, are worthy of his notice. 
 
 The following synoptical view of the general di- 
 mensions of the above cathedrals, we think, may 
 prove occasionally useful to the reader, by enabling 
 him to compare the whole of them and their parts 
 with each other. Dallaway, without the remotest 
 idea of the principles in question, has observed, 
 with his usual sagacity, that there appears in them 
 " a distribution of parts wiiicli will hold ahnost gen- 
 erally, that the width of the nave is that of both 
 the aisles, measured in the place to the extremity of 
 the buttresses externally ; and that the breadth and 
 height of the whole building arc equal. In the more 
 ancient churches, the aisles are usually of the width 
 of the space between the dividing arches." Some 
 idea of the principle is conveyed in the plates of 
 jNIilan Cathedral, curiously introduced into the very 
 early translation of Viti-uvius by Ca;sar Cesarianus, 
 a work of great curiosity, and of which copies arc 
 now rarely met with. 
 
 A Synoptical Vieiv of the leading- Dimensions of the English Cathedrals. 
 
 
 Total 
 
 
 
 
 
 
 
 
 
 Cailiedral. 
 
 internal 
 
 Naves and Aisle 
 
 J. 
 
 
 Choirs. 
 
 
 Transepts. 
 
 Spires and Towers. 
 
 
 Lengtli. 
 
 
 
 
 
 
 
 
 
 
 
 Length. 
 
 Breadth. 
 
 Height. 
 
 Length. 
 
 Breadth. 
 
 Height. 
 
 Breadth. 
 
 Height. 
 
 Winchester, 
 
 545 
 
 247 
 
 86 
 
 78 
 
 138 
 
 
 
 73 
 
 186 
 
 
 Ely, . 
 
 517 
 
 327 
 
 73 
 
 70 
 
 101 
 
 73 
 
 70 
 
 178 
 
 Tower, . 210 
 
 Canterbury, 
 
 514 
 
 214 
 
 70 
 
 80 
 
 150 
 
 74 
 
 80 
 
 154 
 
 Do., . . 235 
 
 Old St. Paul's, . 
 
 500 
 
 a35 
 
 91 
 
 103 
 
 165 
 
 43 
 
 88 
 
 248 
 
 Spire, . 534 
 
 York, . 
 
 498 
 
 264 
 
 109 
 
 99 
 
 131 
 
 
 
 99 
 
 222 
 
 Tower . 234 
 
 Lincoln, 
 
 498 
 
 
 83 
 
 83 
 
 
 
 
 — 
 
 227 
 
 Do., . . 260 
 
 Westminster, 
 
 489 
 
 130 
 
 96 
 
 101 
 
 152 
 
 
 
 151 
 
 189 
 
 
 Peterboro', . 
 
 480 
 
 231 
 
 78 
 
 78 
 
 138 
 
 
 
 78 
 
 203 
 
 Louvre, . 150 
 
 Salisbury, . 
 
 452 
 
 246 
 
 76 
 
 84 
 
 140 
 
 — 
 
 84 
 
 210 
 
 Spire, . 387 
 
 Durham, . 
 
 420 
 
 
 — 
 
 — 
 
 117 
 
 33 
 
 71 
 
 176 
 
 Tower, . 214 
 
 Gloucester, 
 
 420 
 
 174 
 
 84 
 
 67 
 
 140 
 
 
 
 86 
 
 144 
 
 Do., . . 225 
 
 Lichfield, . 
 
 411 
 
 213 
 
 67 
 
 — 
 
 110 
 
 
 
 67 
 
 
 Spire, 258 W. 183 
 
 Norwich, . 
 
 411 
 
 230 
 
 71 
 
 — 
 
 165 
 
 — 
 
 — 
 
 191 
 
 Do., . . 317 
 
 Worcester, 
 
 410 
 
 212 
 
 78 
 
 — 
 
 126 
 
 
 
 74 
 
 130 
 
 Tower, . 196 
 
 Chichester, 
 
 401 
 
 205 
 
 91 
 
 61 
 
 100 
 
 
 
 — 
 
 131 
 
 Spire, . 267 
 
 Exeter, 
 
 390 
 
 173 
 
 74 
 
 69 
 
 131 
 
 
 
 69 
 
 140 
 
 Tower, . 130 
 
 Wells, 
 
 371 
 
 191 
 
 67 
 
 67 
 
 106 
 
 — 
 
 67 
 
 135 
 
 Do., . . 160 
 
 Hereford, anct. . 
 
 370 
 
 144 
 
 68 
 
 68 
 
 105 
 
 — 
 
 64 
 
 140 
 
 
 Chester, . 
 
 348 
 
 
 73 
 
 73 
 
 
 
 
 
 
 
 Tower, . 127 
 
 Rochester, . 
 
 306 
 
 150 
 
 65 
 
 — 
 
 156 
 
 
 
 — 
 
 123 
 
 Spire, . 156 
 
 Carlisle, . 
 
 213 
 
 
 71 
 
 71 
 
 137 
 
 71 
 
 
 
 
 
 Bath, . 
 
 210 
 
 136 
 
 72 
 
 78 
 
 
 
 
 — 
 
 126 
 
 Tower, . 162 
 
 Bristol, 
 
 175 
 
 100 
 
 75 
 
 73 
 
 100 
 
 
 
 «__ 
 
 128 
 
 Do., . . 127 
 
 Oxford, . 
 
 154 
 
 74 
 
 54 
 
 41 
 
 80 
 
 — 
 
 374 
 
 102 
 
 Spire,. . 184 
 
140 
 
 GOTHIC ARCHITECTURE. 
 
 To the above vvc subjoin the correspondent dimen- 
 sions of the several component parts of some of tlic 
 cathedral churches enumerated, which we consider 
 useful to the student as well as the general reader. 
 
 Total Length. 
 
 Feet. 
 
 Chichester cathedral church, 
 
 , 
 
 410 
 
 Norwich cathedral church. 
 
 . 
 
 . 411 
 
 Worcester cathedral church, 
 
 . 
 
 410 
 
 Durham cathedral church. 
 
 , 
 
 . 420 
 
 Gloucester conventual church, 
 
 • 
 
 420 
 
 Ucighls of Naves. Style. 
 
 
 Feet 
 
 
 Salisbury cathedral church, 
 
 . 84 
 
 Pointed arch. 
 
 Lincoln cathedral church, . 
 
 . 83 
 
 Pointed arch. 
 
 Canterbury cathedral churcli. 
 
 . 80 
 
 Pure Gothic. 
 
 Peterboro' conventual church, 
 
 . 78 
 
 Norman. 
 
 Winchester cathedi-al chm-ch, 
 
 . 78 
 
 Pure Gothic. 
 
 Durham cathedral church, . 
 
 . 71 
 
 Norman. 
 
 Ely cathedral chm'ch. 
 
 . 70 
 
 Norman. 
 
 Exeter cathedral church, . 
 
 . 69 
 
 Pointed arch. 
 
 Gloucester conventual church, 
 
 . G7 
 
 Norman. 
 
 Wells cathedral church. 
 
 . 67 
 
 Pointed arch. 
 
 Breadths of Naves 
 
 and Aisles. 
 
 Feet 
 
 Feet. 
 
 Feet. 
 
 Noi-wlch, . 71 Exeter, . 
 
 . 74 
 
 Durham, . 80 
 
 Bristol, . . 73 Salisbmy, 
 
 . 76 
 
 Lincoln, . 83 
 
 Chester, . . 73 Peterboro', 
 
 . 78 
 
 Gloucester, 84 
 
 Ely, ... 73 Worcester, 
 
 . 78 
 
 Winchester, 85 
 
 Canterbury, 74 
 
 
 
 The author just quoted, in reference to the tables 
 here given, says of them, that "the parallel will 
 afford VTs, at one view, authentic information con- 
 cerning the proportion of one constituent part to 
 another of every cathedral in England which is wor- 
 thy the notice of an architect. Such," he continues, 
 " a coincidence of dimensions as that which is found 
 in many of tlicm can scarcely be supposed to be the 
 effect of chance, especially where the buildings are 
 contemporary, and of an exactly correspondent style." 
 It appears that the equality of proportions is con- 
 fined to each era and style of ecclesiastical architect- 
 ure in so remarkable a degree as to lead us to con- 
 jecture that they might have been designed by the 
 same architect. " The constant rivalry," says Dalla- 
 way, "which subsisted between the magnificent prel- 
 ates, was excited upon the erection of any part of a 
 
 cathedral of superior beauty, and imitated in those 
 of the same kind which were then undertaken ; and 
 the architect who had once displayed great talents 
 was invited to repeat the more perfect performance 
 upon which he had rested his professional fame." 
 We have not considered it necessary to devote a 
 special portion of our work to the conventual archi- 
 tecture of England, because it followed the style of 
 the time. It was of great splendor. The ground 
 plans of their habitable portions were usually, though 
 not always, quackangular, and in the later ages par- 
 took of the improvements in domestic architecture, 
 as in the colleges built by Wykham and Waynflete, 
 and many of the episcopal residences. Glastonbury 
 and Reading presented exceedingly fine examples of 
 it ; the former comprised within its walls sixty acres 
 of gi'ound. 
 
 We have thus given, although very briefly, an ac- 
 count of the rise and progi'css of a species of archi- 
 tecture which is in itself a wonder, and which has set 
 up an eternal defiance to him who would speak light- 
 ly of the deep conception it develops, or the wonder- 
 ful fertility of the inventive genius it demonstrates. 
 It was the production of a peculiar age, and, true to 
 its time, it mirrors in every case a transcript of the 
 mind of him who conceived it. The low roof of the 
 Indian Temple of Elephanta, or the Egyptian Phila; 
 or Edfu, were lofty enough for their deities. The 
 Parthenon and the Erectheum of classic Greece were 
 sufficiently spacious and significant of the gods they 
 worshipped ; but to the mind of the Christian, whose 
 vision extended beyond the confines of temples that 
 were made with hands, the most gorgeous temple of 
 Grecian story, although composed of the purest mar- 
 ble and of the most classic design, was but mean and 
 grovelling. Their religion was of a. loftier nature, 
 and their aspirations could only be satisfied when, 
 with awful sublimity, they saw the spire of Salisbury 
 towering in majestic significance for four hundred 
 feet in the air. In that huge pile, awful yet majestic, 
 they recognized a divinity, the colossal grandeur of 
 which awakened and perpetuated in their bosoma 
 emotions of adoration and praise. Beneath the sky 
 of ancient Rome stands one of the seven wonders of 
 the world ; and, beneath that of London, the glory of 
 Roman architecture on the soil of Old England. But 
 in constructing the Cathedral Churches of St. Peter's 
 and St. Paul's, the conception of Raphael, and An- 
 
I'l.'i. 
 
 Kl.v.ili,.ii iin.l S.-,li..ii ..r llir ( 111. I M'm.li." Ill 111.- . Mir-.iii. .■ -^-ili-vi-av. 
 
i'i.;i;i 
 
 . yi ^ii aavW'.aji/ii. STTOIKlfu 
 
I'l.Klil 
 
I'l.ll' 
 
 
 
GOTHIC ARCHITECTURE, 
 
 141 
 
 gelo, and Wren were trammelled by the rules and 
 proportions of an order, and a Roman sternness 
 characterizes each pile. Li these is seen, it is true, 
 the great victory that science and skill have won over 
 disorder and ignorance, but in Gloucester and Win- 
 chester the very essence of art and ideality. The 
 perfect columniations and nicely-arranged entabla- 
 tures of the former speak to us, it is true, with a bold- 
 ness that well becomes the Roman ; but the flowing 
 tracery and lofty arches of the latter breathe an air 
 of poctiy : while the gTcat domes of the one fill the 
 mind with majesty and awe, the towering spires of 
 the others address their solemn eloquence to the soul. 
 We would not underrate the talent which produced 
 the great realities we place in contrast ; we give them 
 the glory which a matured science and a ripe skill 
 have hung around them ; but we claim for the others 
 that each conception is distinctly identified with the 
 time which gave it bu-th, and that they were the out- 
 gushings of souls who were striving to gain the mas- 
 tery over darkness and degradation, and whose lof- 
 tiest aspkations were the establishment and perpetuity 
 of a reformed religion ; that they are the mementoes 
 of a genius and invention which were lent to a peo- 
 ple who had been appointed to assist at an important 
 era in a reform which is to ultimately rid the race of 
 their vices and transgressions. It is to be acknowl- 
 edged that the means made use of by the clergy were 
 often censurable, and at variance with Lhe principles 
 of the religion they would inculcate ; but, notwith- 
 standing all this, behind the definite and sharp 
 scientific outlines with which the reason and expe- 
 rience of six centuries have bouirded the dominion 
 of religious duty, we see standing out fi-om it all a 
 detertnination and an accomplishment ; an intense 
 desire, amounting in itself to a demand, for a deeper 
 
 reverence for the principles of religion, as they under- 
 stood tlicm,and now, after sLx centuries have elapsed, 
 the crowded aisles of a hundred cathedrals speak out 
 their triumph and success, and the walls which en- 
 close them are but votive monuments of the immen- 
 sity of their wonderful genius. — Editors. 
 
 Plates 9§, 99, 100, 101. 
 
 On these plates we have given examples of Gothic 
 architecture, with their details. These plates are 
 transcripts of the examples they arc designed to rep- 
 resent, and are taken fi-om Pugin's Gothic Architect- 
 ure, with the figures and scale annexed. They are 
 not inserted as illustrations of cither of the styles we 
 have described, neither do we give them as elements 
 of those styles, for did we attempt to illustrate each 
 style in a manner that would do justice to the stu- 
 dent, some twelve plates, at least, would be required 
 to give him even a limited knowledge of the arches, 
 doors, windows, and columns belonging to each style ; 
 and to continue the illustration by examples of roofs, 
 ceilings, mouldings, &c., &c., all of which would be 
 demanded, twice that number would be reqiiired in 
 addition ; and as it was not the original design of the 
 work to treat upon this part of the science, we have 
 contented ourselves with giving our patrons a descrip- 
 tion of the principal elements which compose it, and 
 would refer them, in addition to the works we have 
 named, to Rickman's Gothic Ai'chitecture, and also 
 to the publications of Britton and Pugin. 
 
 The four plates alluded to contain so great a va- 
 riety of useful and practical information for the coun- 
 try artisan, or to those who do not have access to the 
 works to which we refer them, (and for those our 
 whole work is principally designed,) that we have been 
 induced to place them in our edition. — Editors. 
 
142 
 
 BUILDING. 
 
 BUILDING. 
 
 Aldrich tcUs us that, in choosing a situation for building, its vicin- 
 ity to public edifices should be principally attended to j that is, we 
 should build as near as convenient to the place Tvliere the business 
 of the o-micr chiefly calls him. " Every one would -ivish to be near 
 a church," (or, perhaps, should wish to be so,) " but especially a 
 priest ; the la-\\-yer near the hall of justice ; the merchant near the 
 exchange ; the trader in the principal street ; and every other citi- 
 zen, in the same manner, •n-ould choose his dwelling according to his 
 occupation — not far from the river, if any flow near the city ; at a 
 distance from a tallow chandler, a brewer, a soap boiler, or any other 
 business attended with an unsavory smell ; far from the noise of the 
 anvil, the hammer, and the saw ; and, above aU, (as Cato says,) at a 
 distance from bad neighbors. In short, that spot is most eligible in 
 which you can construct a regular house ; that is, one with right 
 angles — where room, leisure, and cleanliness may be obtained, and 
 you may procure to your house the advantages of a rural situation. 
 If all the above conveniences cannot be met >vith, (and it is very 
 seldom, if desired, that they can be,) it is prudent to aim at such as 
 may be desirable and are attainable. 
 
 Under this general term, which implies the con- 
 struction of an edifice, according to the rules laid 
 down by the different artificers employed, we purpose 
 to treat of the respective business of the mason, brick- 
 layer, plasterer, slater, plumber, painter, and glazier ; 
 previous to which it will be necessary to consider the 
 sinking of the foundation, the due mixture of the in- 
 gredients which compose the mortar, and the art of 
 making bricks, upon the whole of which materially 
 depends the stability of an edifice. 
 
 As firmness of foundation is indispensable, wher- 
 ever it is intended to erect a building, the earth must 
 be pierced by an non bar, or stuck with a rammer, 
 and, if found to shake, must be bored with a well- 
 sinker's implement, in order to ascertain whether the 
 shake be local or general. If the soil is in general 
 good, the loose and soft parts, if not very deep, must 
 be excavated until the laborers arrive at a solid bed 
 capable of sustaining the pier or piers to be built. 
 If not very loose, it may be made good by ramming 
 into it very large stones, packed close together, and 
 of a breadth proportionate to the intended weight 
 of the building ; but where very bad, it must be piled 
 and planked. 
 
 In places where the soil is loose to any great depth, 
 and over which it is intended to place apertures, such 
 as doors, windows, &c., while the parts on which the 
 
 piers are to stand are firm, the best plan is to turn an 
 inverted arch under each intended aperture, as then 
 the piers, in sinking, will carry with them the inverted 
 arch, and, by compressing the gi'ound, compel it to 
 act against the under sides of the arch, which, if 
 closely jointed, so far from yielding, will, with the 
 abutting piers, operate as one solid body ; but, on 
 the contrary, if this expedient of the inverted arch is 
 not adopted, the part of the wall under the aperture, 
 being of less height, and, consequently, of less weight 
 than the piers, will give way to the resistance of the 
 soil acting on its base, and not only injure the brick 
 work between the apertures, but fracture the window 
 heads and sills. 
 
 In constructing so essential a part as the arch, 
 great attention must be paid to its curvature, and 
 we strongly recommend the parabolic curve to be 
 adopted, as the most effectual for the purpose ; but 
 if, in consequence of its depth, this cannot conven- 
 iently be introduced, the arch should never be made 
 less than a semicircle. The bed of the piers should 
 be as uniform as possible ; for though the bottom of 
 the trench be very firm, it will, in some degree, yield 
 to the great weight that is upon it, and if the soil be 
 softer in one part than in another, that part which is 
 the softest wUl, of course, yield more to the pressure, 
 and cause a fracture. 
 
 K the solid parts of the trench happen to be under 
 the intended apertures, and the softer parts where 
 piers are wanted, the reverse of the above practice 
 must be resorted to ; that is, the piers must be buUt 
 on the firm jjarts, and have an arch that is not in- 
 verted between them. In performing this, attention 
 must be paid to ascertain whether the pier will cover 
 the arch ; for if the middle of the pier rest over the 
 middle of the summit of the arch, the narrower the 
 pier is the gi-eater should be the ciu'vature of the arch 
 at its apex. When suspended arches are used, the 
 intrados ought to be kept clear of the ground, that 
 the arch may have its due effect. 
 
 When the gi'ound is in such a state as to require 
 the foundation merely to be rammed, the stones are 
 hammer dressed, so as to be of as little taper as possi- 
 ble, then laid of a breadth proportioned to the weight 
 
BUILDING. 
 
 143 
 
 that is to be rested upon them, and afterwards well 
 rammed together. In general, the lower bed of 
 stones may be allowed to project about a foot from 
 the face of the wall on each side, and on this bed 
 another com-se may be laid, to bring the bed of 
 stones on a level with the top of the trench. The 
 breadth of this upper bed of stones should be four 
 inches less than the lower one ; that is, projecting 
 about eight inches on either side of the wall. In all 
 kinds of walling, each joint of every coiu'se must 
 fall as nearly as possible in the centre, between two 
 joints of the course immediately below it ; for, in all 
 the various methods of laying stones or bricks, the 
 principal aim is to procure the greatest lap on each 
 other. 
 
 MORTAR. 
 
 Li making mortar, particular attention must be 
 paid to the quality of the sand, and if it contain 
 any proportion of clay or mud, or is brought fi.-om 
 the sea-shore, and contains saline particles, it must 
 be washed in a stream of clear water till it be di- 
 vested of its impiuities. The necessity of the fii-st 
 has been clearly proved by Mr. Smeaton, who, in the 
 course of a long and meritorious attention to his 
 profession as an engineer, has found that when mor- 
 tar, though otherwise of the best quality, is mixed 
 with a small proportion of unburnt clay, it never 
 acquhes that hardness which, without it, it would 
 have attained ; and, with respect to the second, it is 
 evident that, so long as the sand contains any saline 
 particles, it cannot become hard and diy. The 
 sharper and coarser the sand is, the better for the 
 mortar, and the less the quantity of lime to be used ; 
 and sand being the cheapest of the ingredients which 
 compose the mortar, it is more profitable to the 
 maker. The exact proportions of lime and sand are 
 still undetermined ; but in general, no more lime is 
 required than is just sufficient to surround the parti- 
 cles of the sand, or sufficient to preserve the neces- 
 sary degree of plasticity. 
 
 Mortar, in which sand forms the gi-eater portion, 
 requires less water in its preparation, and, conse- 
 quently, is sooner set. It is also harder and less lia- 
 ble to shrink in drying, because the lime, while dry- 
 ing, has a greater tendency to shrink than sand, 
 which retains its original magnitude. The general 
 
 proportions given by the London buUdcrs is 1^ cwt., 
 or 37 bushels of lime, to 2^ loads of sand ; but, if 
 proper measures be taken to procure the best burnt 
 lime and the best sand, and in tempering the mate- 
 rials, a greater portion of sand may be used. There 
 is scarcely any mortar that has the lime well cal- 
 cined, and the composition well beaten, but that will 
 be found to require two parts of sand to one part of 
 unslaked lime ; and it is worthy of observation, that 
 the more the mortar is beaten, the less proportion of 
 lime suffices. 
 
 Many experiments have been made, with a view 
 to obtain the most useful proportion of the ingre- 
 dients, and, among the rest. Dr. Higgins has given 
 the following : " Lime, newly slaked, one part ; fine 
 sand, three parts ; and coarse sand, four parts." 
 
 He also found that one fourth of the lime of bone 
 ashes greatly improved the mortar, by giving it 
 tenacity and rendering it less liable to crack in the 
 drying. 
 
 It is best to slake the lime in small quantities as 
 required for use, about a bushel at a time, in order to 
 secm-e to the mortar such of its qualities as would 
 evaporate were it allowed to remain slaked for a 
 length of time. But if the mortar be slaked for 
 any considerable time previous to being used, it 
 should be kept covered up, and, when wanted, should 
 be rebcaten. If care be taken to secure it from the 
 action of the atmosphere, it may thus remain covered 
 up for a considerable period, without its strength be- 
 ing in the least affected ; and, indeed, some advan- 
 tages are gained, for it sets sooner, is less liable to 
 crack in the drying, and is harder when dry. 
 
 Grout, wloich is a cement containing a larger pro- 
 portion of water than the common mortar, is used to 
 run into the narrow interstices and irregular courses 
 of rubble-stonc walls ; and as it is reqviired to con- 
 crete in the course of a day, it is composed of mor- 
 tar that has been a long time made and thoroughly 
 beaten. 
 
 Mortar, composed of pm-e lime, sand and water, 
 may be employed in the linings of reservoirs and 
 aqueducts, provided a sufficient time is allowed for it 
 to dry before the water is let in ; but if a sufficient 
 time is not allowed, and the water is admitted while 
 the mortar is wet, it will soon fall to pieces. There 
 are, however, certain ingredients which may be put 
 into the common mortar to make it set immediately 
 under the water ; or, if the quicklime composing the 
 
144 
 
 BUILDING, 
 
 mortar contains in itself a certain portion of burnt 
 clay, it wUl possess this property. For further in- 
 formation on this head, the reader is referred to the 
 sub-head — Plasterinff. 
 
 MASONRY. 
 
 Masonry is the art of cutting stones, and building 
 them into a mass, so as to form the regular sur- 
 faces which arc requu-ed in the construction of an 
 edifice. 
 
 The chief business of the mason is to prepare the 
 stones, make the mortar, raise the wall with neces- 
 sary breaks, projections, arches, apertures, &c., as in- 
 dicated by the design. 
 
 A wall built of unhewn stone, whether it be built 
 with mortar or otherwise, is called a rubble jvall. 
 Rubble worlv is of two kinds, coursed and uncoursed. 
 In coursed rubble, the stones are gauged and di-cssed 
 by the hammer, and thrown into different heaps, each 
 heap containing stones of equal thickness; and the 
 masonry, which may be of different thicknesses, is 
 laid in horizontal com'ses. In uncom-sed rubble, the 
 stones are placed promiscuously in the wall, with- 
 out any attention being paid to arrange them in 
 courses ; and the only preparation the stones under- 
 go is that of knocking off the sharp angles with the 
 thick end of a tool called a scabling hammer. Walls 
 are often built with an ashlar facing of fine stone, 
 averaging about fom- or five inches m thickness, and 
 backed with rubble work or brick. 
 
 Walls backed with brick or uncoursed rubble are 
 liable to become convex on the outside, from the 
 great number of joints, and the difficulty of placing 
 the mortar, which shrinks in proportion to the quan- 
 tity, in equal portions, in each joint ; consequently, 
 walls of this description are much inferior to those 
 where the facing and backing are built of the same 
 material, and with equal care, even though both of 
 the sides be uncoursed. When the outside of a wall 
 is faced with ashlar, and the inside is coursed rubble, 
 the courses of the backing should be as high as pos- 
 sible, and set within beds of mortar. Coursed rub- 
 ble and brick backings are favorable for the insertion 
 of bond timber ; but in good masonry, wooden 
 bonds should never be in continued lengths, as, in 
 case of cither fire or rot, the wood will perish, and 
 
 the masonry will, by being reduced, be liable to bend 
 at the place where the bond was inserted. 
 
 When timber is to be inserted into walls for the 
 purposes of fastening buttons for plastering or skirt- 
 ing, (kc, the pieces of timber ought to be so disposed 
 that the ends of the pieces be in a line with the wall. 
 
 In a wall faced with ashlar, the stones are gen- 
 erally about 2 feet or 2i feet in length, 12 inches in 
 height, and 8 inches in thickness. It is a very good 
 plan to incline the back of each stone, to make all 
 the backs thus inclined run in the same direction, 
 which gives a small degree of lap in the setting of 
 the next course ; whereas, if the backs arc parallel to 
 the front, there can be no lap where the stones run 
 of an equal depth in the thickness of the waU. It is 
 also advantageous to the stability of the wall to se- 
 lect the stones, so that a thicker and a thinner one 
 may succeed each other alternately. In each course 
 of ashlar facing, cither with rubble masonry or brick 
 backing, thorough stones should occasionally be in- 
 troduced, and their number be in proportion to the 
 length of the course. In every succeeding course, 
 the thorough stones should be placed in the middle 
 of every two thorough stones in the course below; 
 and this disposition of bonds should be punctually 
 attended to in all cases where the courses are of any 
 great length. Some masons, in order to prove that 
 they have introduced sufficient bonds into their work, 
 choose thorovigh stones of a greater length than the 
 thickness of the wall, and afterwards cut off the ends ; 
 but this is far from an eligible plan, as the wall is not 
 only subject to be shaken, but the stone is itself apt 
 to split. In every pier, between windows and other 
 apertures, every alternate jamb stone ought to go 
 through the wall with its bed perfectly level. When 
 the jamb stones are of one entire height, as is fre- 
 quently the case when architraves are ^\Tougllt upon 
 them, upon the lintel crowning them, and upon the 
 stones at the ends of the courses of the pier which 
 are adjacent to the architrave jamb, every alternate 
 stone ought to be a thorough stone : and if the piers 
 between the apertures be very narrow, no other bond 
 stone is required ; but where the piers arc wide, the 
 number of bond stones are proportioned to the space. 
 Bond stones must be particularly attended to in all 
 long courses below and above windows. 
 
 Iron clamps are now used in all cases where it is 
 practicable, instead of thorough stones. The shrink- 
 ing of the mortar in the backing is very apt to start 
 
BUILDING. 
 
 145 
 
 the thorough stone from its true position, which either 
 fractures it, or causes the wall to bulge, and open the 
 seams on the outside. This inconvenience is obvi- 
 ated by the use of clamps. 
 
 All vertical joints, after receding about an inch 
 with a close joint, should widen gradually to the 
 back, thereby forming hollow spaces of a wedge-like 
 figure for the reception of mortar, rubble, &c. The 
 adjoinmg stones should have their beds and vertical 
 joints filled from the face about three quarters of an 
 inch inwards, with oil putty, and the rest of the beds 
 must be fiUed with well-tempered mortar. Putty 
 cement will stand longer than most stones, and will 
 even remain permanent when the stone itself is mu- 
 tilated. All walls cemented with oU putty, at first 
 look unsightly ; but this disagreeable effect ceases in 
 a year or less, when, if care has been taken to make 
 the color of the putty suitable to that of the stone, 
 the joints will hardly be perceptible. 
 
 In selecting ashlar, the mason should take care that 
 each stone invariably lays on its natural bed, as, from 
 carelessness in this particular, the stones frequently 
 flush at the joints, and sooner admit the corrosive 
 power of the atmosphere to take effect. 
 
 It ought also to be observed, that, in building walls 
 or insulated piUars of small horizontal dimensions, 
 every stone should have its bed perfectly level, and 
 be without any concavity in the middle ; because, if 
 the beds are concave, the joints wUl most probably 
 flush when the piUars begin to sustain the weight of 
 the building. Care should also be taken that every 
 course of masonry in such piers be of one stone. 
 
 Having thus given to the practical mason an out- 
 line of the subject of walling, we will proceed to the 
 consideration of the more difficult branches of the 
 art — that of constructing arches and vaults. 
 
 DEFINITIONS. 
 
 An arch, in masonry, is that part of a building 
 which is suspended over a given plane, supported 
 only at its extremities, and concave towards tlie plane. 
 
 The upper surface of an arch is called the extrados ; 
 and the under surface, or that which is opposite the 
 plane, the intrados. 
 
 The supports of an arch are called the spring ivalls. 
 
 The spring-ing lines are those common to the sup- 
 ports and the intrados, or the line which forms the 
 intersection of the arch with the surface of the wall 
 which supports it. 
 
 19 
 
 The chord or span is a line extending from one 
 springing line to the opposite one. 
 
 Section of the hollow of the arch is a vertical plane, 
 supposed to be contained by the span and the in- 
 trados. 
 
 The height or rise of the arch is a line drawn at 
 right angles from the middle of the chord, or span- 
 ning line, to the intrados. 
 
 The croivn of the arch is that part which the ex- 
 tremity of the perpendicular touches. 
 
 The haunches or flanks of the arch are those parts 
 of the curve between the crown and the springing line. 
 
 When the base of the section, or spanning line, is 
 parallel to the horizon, the section will consist of two 
 equal and similar parts, so that, when one is applied 
 to the other, they will be found to coincide. 
 
 Arches are variously named, according to the fig- 
 ure of the section of a solid that would fill the void, 
 as circular, elliptical, cycloidal, catenarian, parabolical, 
 &c. There are also pointed, composite, and lancet or 
 Gothic arches. 
 
 A rampant arch is when the springing lines are of 
 two unequal heights. 
 
 When the intrados and extrados of an arch are 
 parallel, it is said to be extradossed. 
 
 There are, however, other terms much used by ma- 
 sons : for example, the semicircular are called perfect 
 arches; and those less than a semicircle, imperfect, 
 surbused, or diminished arches. 
 
 Arches are called stilted when they are higher than 
 a semicircle. 
 
 A vault is an arch used in the interior of a build- 
 ing, overtopping an area of a given bomidary, as a 
 passage, or an apartment, and supported by one or 
 more walls, or pillars, placed without the boundary 
 of that area. 
 
 Hence an arch in a wall is seldom or never called 
 a vault ; and every vault may be called an arch, but 
 every arch cannot be termed a vault. 
 
 A groin vault is a complex vault, formed by the 
 intersection of two solids, whose surfaces coincide 
 with the intrados of the arches, and are not confined 
 to the same heights. An arch is said to stand upon 
 splayed jambs when the springing lines are not at 
 right angles to the face of the wall. 
 
 In the art of constructing arches and vaults, it is 
 necessary to bmld them in a mould, until the whole 
 is closed ; the mould used for this purpose is called 
 a centre. 
 
146 
 
 BUILDING. 
 
 The intrados of a simple vault is generally formed 
 of a portion of a cylinder, cylindroid, sphere, or sphe- 
 roid ; that is, never greater than the half of the solid ; 
 and the springing lines which terminate the walls, 
 or when the vault begins to rise, are generally straight 
 lines, parallel to the axis of the cylinder or cylindroid. 
 
 A circular wall is generally terminated with a 
 spherical vault, which is either hemispherical, or a 
 portion of a sphere less than a hemisphere. 
 
 Every vault which has a horizontal, straight axis 
 is called a straight vault; and, in addition to what 
 we have ab-eady said, the concavities which two sol- 
 ids form at an angle receive likewise the name of 
 arch. 
 
 An arch, when a cylinder pierces another of a 
 greater diameter, is called cylindro-cylindric. The 
 term cylindro is applied to the cylinder of the greatest 
 diameter, and the term cylindric to the less. 
 
 If a cylinder intersect a sphere of greater diameter 
 than the cylinder, the arch is called a sphero-cylindric 
 arch; but, on the other hand, if a sphere pierce a 
 cylinder of greater diameter than the sphere, the 
 arch is called a cylindro-spheric arch. 
 
 If a cylinder pierce a cone, so as to make a com- 
 plete perforation through the cone, two complete 
 arches will be formed, called cono-cylindric arches; 
 but, on the contrary, if a cone pierce a cylinder so 
 that the concavity made by the cone is a conic sur- 
 face, the arch is called a cylindro-conic arch. 
 
 If , in a straight wall, there be a cylindric aperture 
 continuing quite through it, two arches will be formed, 
 called plano-cylindric arches. 
 
 Every description of arch is, in a similar manner 
 to the above, denoted by the two preceding words — 
 the former ending in o, signifying the principal vault, 
 or surface cut through ; and the latter in ic, signify- 
 ing the description of the aperture which pierces or 
 intersects the wall or vault. 
 
 When groins are introduced merely for use, they 
 may be built either of brick or stone ; but, when in- 
 troduced by way of proportion or decoration, their 
 beauty will depend on the generating figures of the 
 sides, the regularity of the surface, and the acuteness 
 of the angles, which should not be obtruded. In the 
 best buildings, when durability and elegance are 
 equally required, they may be constructed of wrought 
 stone ; and, when elegance is wanted, at a trifling 
 expense, of plaster, supported by timber ribs. 
 
 In stonecutting, a narrow surface formed by a 
 
 point or chisel on the surface of a stone, so a# to 
 coincide with a straight edge, is called a draught. 
 
 FORMATION OF STONE ABCHES. 
 
 The formation of stone arches has always been 
 considered a most useful and important acquisition 
 to the operative mason ; in order, therefore, to remove 
 any difficulties which might arise in the construction 
 of arches of different descriptions, both in straight 
 and circular walls, we shall here introduce a few ex- 
 amples, which, it is hoped, with careful examination, 
 will greatly facilitate a knowledge of some of the 
 most abstruse parts of the art. 
 
 Plate 102. 
 
 To find the moulds necessary for the construc- 
 tion of a semicircular arch, cutting a straight 
 wall obliquely. 
 
 Fig. 1, No. 1. Let A B C D E F G H be the plan 
 of the arch ; I K L M the outer line ; and N O P Q 
 the inner line on the elevation. 
 
 a b c d e, on the elevation, shows the bevel of each 
 joint or bed from the face of the wall ; and a b c d e, 
 below, gives the mould for the same, where x y on 
 the elevation corresponds with xy 2it a. 
 
 The arch mould, No. 2, is applied on the face of 
 the stone, and, on being applied to the parts of the 
 plan, gives, of course, the bevel of each concave side 
 of the stone with the face — that is, K to O, on the 
 elevation. 
 
 To find the mould for constructmg a semicir- 
 cular arch in a circular wall. 
 
 Fig. 2, No. 1, is the elevation of the arch, and No. 2 
 the plan of the bottom bed from q to r. 
 
 a to b is what the arch gains on the circle from the 
 bottom bed k o to I ; and c to d is the projection of 
 the intrados to p, on the point /, p. 
 
 Nos. 2, 3, and 4 are plans of the three arch stones, 
 1, 2, 3, in the elevation ; and Nos. 5 and 6 are moulds 
 to be applied to the beds of stones 1 and 2, in which 
 s c equals 5 c in No. 2, and t to equals t to in No. 3. 
 
 In No. 1, k Ip is the arch or face mould. 
 
 When the reader is thoroughly proficient in the 
 construction of arches under given data, as the cir- 
 cumstances of the case may point out, he may pro- 
 ceed to investigate the principles of spherical domes 
 and groins. 
 
A(a®rai£3. 
 
 I'l.KU 
 
« 
 
 I 
 
 I 
 
BUILDING. 
 
 147 
 
 Figs. 3 and 4 show the principles of developing 
 the sofRts of the arches in the two preceding exam- 
 ples. In each the letters of reference are alike, and 
 the operation is precisely the same. 
 
 Let A B D E be the plan of the opening in the 
 wall, and A F B the elevation of the arch ; produce 
 the chord A B to C, divide the semicurcle A F B into 
 any number of parts, the more the better, and with 
 the compasses set to any one of these divisions, run 
 it as many times along A C as the semicircle is 
 divided into ; then draw lines, perpendicular to B C, 
 through every division in the semicircle and the line 
 C A, and set the distance 1 b, 2 d, 3 f, &c., respec- 
 tively equal to ab c d ef, &c., and then, by tracing a 
 curve through these points and finding the points in 
 the line G D, in the same manner, the soffit of the 
 arch is complete. 
 
 Fig. 5 shows the method of constructing spherical 
 domes. 
 
 No. 1 mould is applied on the spherical surface to 
 the vertical joints, and No. 2 mould on the same 
 surface to the other joints, and, in both cases, the 
 mould tends to the centre of the dome. 
 
 3, 4, 5, 6, 7, and 8 are moulds which apply on the 
 convex surface to the horizontal joint, the lines a b, 
 c d, e f, &c., being at right angles to the different 
 radii, b c, d c,f c, &c., and produced until they inter- 
 sect the perpendicular a c ; the different intersections 
 are the centres which give the circular leg of the 
 mould, and the straiglit part gives the horizontal 
 joint. 
 
 Fig. 6 exhibits the plan of a groined vault. 
 
 Lay down the arch, either at the full or half size, 
 on a floor or piece of floorcloth, then divide and draw 
 on the plan the number of joints in the semicircular 
 arch, and from the intersections with the diagonals 
 draw the transverse joints on the plan, and produce 
 them tUl they touch the intrados of the elliptical arch, 
 the curve of which may be found by setting the cor- 
 responding distances from the luie of the base to the 
 curve ; thus a b equal to a b. This being accom- 
 plished, di-aw the joints of the elliptical arch in the 
 manner of which we give c rf as a specimen. To 
 draw the joint c d, draw chord e c and bisect it, draw 
 a line from the centre c through the bisecting point, 
 and produce it tUl it touches the perpendicular ef; 
 and c d, being at right angles to c /, will be the joint 
 required. In the same manner the others are found. 
 By examination, it will be seen that a rectangle 
 
 circumscribing the mould 3, 3, gives the size of the 
 stone in its square state, and that, if each stone in 
 both arches be thus enclosed, the dimensions for 
 each will be found, as also the position in which the 
 moulds must be placed. The dark lines give the 
 different bevels, which must be carefully prepared 
 and applied to the stones in the manner represented 
 in the figure. 
 
 To draw the joints of the stones for an elliptical 
 arch in a wall, &c. 
 
 Fig. 7. The curve is here described by the inter- 
 section of lines, which certainly gives the most easy 
 and pleasing curve, as segments of circles apply only 
 under certain data, or in the proportion which the 
 axis major has to the axis minor, while the intersec- 
 tion of lines apply to any description of ellipses. 
 Find the foci F. In an ellipsis, the distance of either 
 focus from one extremity of the axis minor is equal 
 to the semi-axis major ; that is, D F is equal to c C. 
 Then, to find any joint, a b, draw lines from both foci 
 through the point b, as F e, / d, and bisect the angle 
 d b ehy the line a b, which is the joint required. 
 
 BRICKLAYING. 
 
 In building upon an inclined plane, or rising ground, 
 the foundation must be made to rise in a series of 
 level steps, according to the general rise of the ground, 
 to insure a firm bed for the courses, and prevent them 
 from sliding ; for if this mode were not adopted, the 
 moisture in the foundations, in wet weather, will in- 
 duce the inclined parts to descend, to the manifest 
 danger of fracturing the walls and destroying the 
 building. 
 
 Li walling, in dry weather, when the work is re- 
 quired to be firm, the best mortar must be used, and 
 the bricks must be wetted or dipped in water as they 
 are laid, to cause them to adhere to the mortar, which 
 they would not do if laid dry ; for the dry, sandy na- 
 ture of the brick absorbs the moisture of the mortar, 
 and prevents adhesion. 
 
 In carrying up the wall, not more than four or five 
 feet of any part should be built at a time ; for, as 
 all walls shrink immediately after building, the part 
 which is first carried up will settle before the adja- 
 cent part is carried up to it, and, consequently, the 
 
148 
 
 BUILDING. 
 
 shrinldng of the latter will cause the two parts to 
 separate ; therefore, no part of a wall should be car- 
 ried higher than one scaffold, without having its 
 contingent parts added to it. In carrying up any 
 particular part, the ends should be regularly sloped 
 off, to receive the bond of the adjoining parts on the 
 right and left. 
 
 There are two kinds of bond in brick work, which 
 differ materially from each other. Bricks laid length- 
 wise in the direction of the wall are called stretchers, 
 and those laid in an opposite way, crossing the direc- 
 tion of the wall, are called headers. The old English 
 bond is a continuation of one Idnd throughout in the 
 same course or horizontal layer, and consists of alter- 
 nate layers of headers and stretchers — the headers 
 serving to bind the wall together in a longitudinal 
 direction, or lengthwise, the stretchers to prevent 
 the wall splitting crosswise, or in a transverse direc- 
 tion. Of these two evils, the former is by much the 
 worst kind, and is, therefore, the most dreaded by the 
 bricklayer. The brick work of the Romans was of 
 this kind of bond. 
 
 The other description of bond, called Flemish bond, 
 consists in placing a header and a stretcher alternately 
 in the same course. The latter is deemed the neat- 
 est and most elegant ; but, in the execution, is at- 
 tended with great inconvenience, and, in most cases, 
 does not unite the parts of a wall with the same de- 
 gree of firmness as the English bond. In general, it 
 may be observed, that whatever advantages are gained 
 by the English bond in tying a wall together in its 
 thickness, are lost in the longitudinal bond, and vice 
 versa. To remove this inconvenience in thick walls, 
 some builders place the bricks in a cone at an angle 
 of forty-five degrees, parallel to each other, through- 
 out the length of every course, but reversed in the 
 alternate courses ; so that the bricks cross each other 
 at right angles. But even here, though the bricks in 
 the cone have sufficient bond, the sides are very 
 imperfectly tied, on account of the triangular in- 
 terstices formed by the oblique direction of the in- 
 ternal bricks against the fiat edges of those in the 
 outside. 
 
 Concerning the English bond, it may be observed, 
 that, as the longitudinal extent of a brick is nine 
 inches and its breadth four and a half, to prevent two 
 vertical joints from running over each other at the 
 end of the stretcher from the corner, it is usual, after 
 
 placing the retiu-n corner stretcher, which occupies 
 half the length of this stretcher, and becomes a header 
 in the face, as the stretcher is below, to place a quar- 
 ter brick on the side, so that the two together extend 
 six inches and three quarters, being a lap of two 
 inches and a half for the next header. The bat in- 
 troduced is called a closer. A similar effect may be 
 obtained by introducing a three-quarter bat at the 
 corner of the stretching course, so that the corner 
 header being laid over it, a lap of two inches and 
 a quarter will be left at the end of the stretch- 
 ers below, for the next header, which, being laid on 
 the joint below the sti-etchers, will coincide with its 
 middle. 
 
 In the winter, it is very essential to keep the un- 
 finished wall from the alternate effects of rain and 
 frost ; for, if it is exposed, the rain will penetrate into 
 the bricks and mortar, and, by being converted into 
 ice, expand, and burst or crumble the materials in 
 which it is contained. 
 
 The decay of buildings, so commonly attributed 
 to the effect of time, is, in fact, attributable to this 
 source ; but as finished edifices have only a vertical 
 surface, the action and counteraction of the rain 
 and frost extend not so rapidly as in an unfinished 
 wall, where the horizontal surface permits the rain 
 and frost to have easy access into the body of the 
 work. Great care, therefore, must be taken, as soon 
 as the frost or stormy weather sets in, to cover the 
 unfinished walls either with straw, which is the most 
 common, or weather boarding. 
 
 When weather boarding is employed, it is advi- 
 sable to have a good layer of straw between the 
 work and the boarding, and to place the boarding in 
 the form of stone coping, to throw the water off 
 equally on both sides. 
 
 A number of very pleasing cornices and other 
 ornaments may be formed in brickwork, by the mere 
 disposition of the bricks, without cutting; and if 
 cut, a simple chamfer will be sufficient. A great de- 
 fect, however, is very often observable in these orna- 
 ments, particularly in the bulging of arches over 
 windows, which arises fi-om mere carelessness in 
 rubbing the bricks too much on the inside ; whereas, 
 if due care were taken to rub them exact to the 
 gauge, their geometrical bearings being united, they 
 would all tend to one centre, and produce a well- 
 proportioned and pleasing effect. 
 
BUILDING. 
 
 149 
 
 PLASTERING. 
 
 The plasterer is a workman to whom the decora- 
 tive part of architecture owes a considerable portion 
 of its effect, and whose art is requisite in every kind 
 of building. 
 
 The tools of the plasterer consist of a spade or 
 shovel of the usual description ; a rake, with two or 
 three prongs bent downwards from the line of the 
 handle, for mixing the hair and mortar together; 
 troicels of various kinds and sizes; stopping' and 
 picking-ont tools; rules called straight edges; and 
 wood models. 
 
 The trowels used by plasterers are more neatly 
 made than tools of the same name used by other 
 artificers. The laying and smoothing tool consists of 
 a flat piece of hardened iron, about ten inches in 
 length, and two inches and a half wide, very thin, 
 and ground to a semicircular shape at one end, but 
 left square at the other ; and at the back of the plate, 
 near the square end, is riveted a small iron rod with 
 two legs, one of which is fixed to the plate, and the 
 other to a round, wooden handle. With this tool all 
 the first coats of plaster are laid on, as is also the 
 last, or, as it is technically termed, the setting. The 
 other kinds of trowels are made of three or four 
 sizes, for gauging the fine stuff and plaster used in 
 forming cornices, mouldings, &c. The longest size 
 of these is about seven inches on the plate, which is 
 of polished steel, about two inches and three quar- 
 ters broad at the heel, diverging gradually from a 
 point. To the heel or broad end a handle is adapted. 
 
 The stopping and picking-ont tools are made of 
 polished steel, of different sizes, though most gener- 
 ally about seven or eight inches in length, and half 
 an inch in breadth, flattened at both ends, and ground 
 somewhat round. These tools are used in modelling 
 and finishing mitres and returns to cornices; as, like- 
 wise, in filling up, and perfecting the ornaments at 
 the jomings. 
 
 The straight edges are for keeping the work in an 
 even or perpendicular line ; and the models or moulds 
 are for running plain mouldings, cornices, &c. : of 
 these latter, the plasterers require a greater number, 
 as very little of his finishing can be done without 
 them. 
 
 Experienced workmen keep their tools very clean, 
 and have them daily polished. 
 
 Plasterers have technical divisions of their work, 
 
 by which its quality is designated and value ascer- 
 tained; as, lathing; laying; pricking up; lathing, 
 laying, and set; lathing, floating, and set; screed, set, 
 or putty ; rendering and set ; or rendering, floated, 
 and set ; trowelled stucco, &c. ; each of which, here- 
 after, we shall very minutely explain. 
 
 In all the operations of plastering, lime exten- 
 sively abounds ; we shall, therefore, first offer some 
 observations on the properties of this important 
 article. 
 
 All who have written on the subject of lime, as a 
 cement, have endeavored to ascertam what is the due 
 proportion of sand for making the most perfect cem- 
 ent ; but, with a little attention, it is evident that 
 aU prescribed rules must be so very vague and un- 
 certain, as to be of little utility to the workman ; for, 
 besides the variation which is occasioned by a more 
 or less degree of calcination, it is a certain fact, that 
 some kinds of limestone are much more pinre, and 
 contain a much smaller proportion of sand, thaa 
 others ; consequently, it would be absurd to say that 
 pure lime requires as small a proportion of sand, 
 when made into mortar, as that which originally 
 contained in itself a large proportion. 
 
 The variation thus produced, in regard to the pro- 
 portion of sand, is found to be extremely great. It 
 is, however, stated that the best mortar which has 
 come under examination was formed of eleven parts 
 of sand to one of lime ; to which was added, by 
 measure, between twice and thrice its own bulk of 
 sand, which may be allowed to have been at least 
 three times its quantity by weight. Supposing, 
 therefore, that every particle of the lime had been so 
 perfectly calcined as to be in a caustic state, there 
 could not be less than forty-seven parts of sand to 
 one of lime ; but it is hard to suppose that above 
 one hundredth part of this mass, independent of the 
 water, consisted of pure caustic calcareous earth. 
 
 From these considerations, it is conceived that it 
 is impossible to prescribe any determinate proportion 
 of sand to lime, as that must vary according to the 
 nature of the lime and other incidental circum- 
 stances, which would form an infinity of exceptions 
 to any general rule. But it would seem that it 
 might be safely inferred that the moderns, in general, 
 rather err in giving too little, than in giving too much, 
 sand. It deserves, however, to be noticed, that the 
 sand, when naturally in the limestone, is more inti- 
 mately blended with the lime than can possibly be 
 
150 
 
 BUILDING. 
 
 ever effected by any mechanical operation ; so that it 
 would be in vain to hope to make equally good mor- 
 tar artificially from pm-e lime, with so small a pro- 
 portion of caustic calcareous matter, as may some- 
 times be effected, when the lime naturally contains a 
 very large proportion of sand. Still, however, there 
 seems to be no doubt, that if a much larger propor- 
 tion of sand than is common were employed, and 
 that more carefully and expeditiously blended and 
 worked, the mortar would be made much more per- 
 fect, as has been proved by actual experiments. 
 
 Another circumstance, which greatly tends to vary 
 the quality of cement and to make a greater or 
 smaller proportion of sand necessary, is the mode of 
 preparing the lime before it is beaten up into mortar. 
 When for plaster, it is of great importance to have 
 every particle of the limestone slaked before it is 
 worked up ; for, as smoothness of surface is the most 
 material point, if any particles of lime be beaten up 
 before sufficiently slaked, the water still continuing 
 to act on them, wUl cause them to expand, which 
 will produce those excrescences on the surface of the 
 plaster termed blisters. Consequently, in order to 
 obtain a perfect kind of plaster, it is absolutely ne- 
 cessary that the lime, before being worked, be allowed 
 to remain a considerable time macerating or souring 
 in water : the same sort of process, though not abso- 
 lutely required, would considerably improve the lime 
 intended for mortar. Great care is required in the 
 management, the principal thing being the procur- 
 ing of well-burnt lime, and allowing no more lime, 
 before worked, than is just sufficient to macerate or 
 sour it with the water : the best-burnt lime will re- 
 quire the maceration of some days. 
 
 It has been almost universally admitted, that the 
 hardest limestone affords the lime which will consol- 
 idate into the finest cement ; hence, it is generally 
 concluded that lime made of chalk produces a much 
 weaker cement than that made of marble or lime- 
 stone. It would seem, however, that, if ever this be 
 the case, it is only incidentally, and not necessarily. 
 In making the mortar, other substances are occasion- 
 ally mixed with lime, which wc shall here proceed to 
 notice, and endeavor to point out their excellences 
 and defects. Those commonly used, besides sand 
 of various denominations, are powdered sandstone, 
 brickdust, and sea shells; and for forming plaster 
 where closeness, rather than hardness, is required, 
 lime which has been slaked, and kept in a dry place 
 
 till it has become nearly effete, and powdered chalk, 
 or whiting, and gypsum, in various proportions, be- 
 sides hair and other materials of a similar nature. 
 Other ingredients have been more lately recom- 
 mended, such as earthy balls, slightly burnt and 
 pounded, old mortar rubbish, powdered and sifted, 
 and various things of the like kind, the whole of 
 which are, in some respect or other, objectionable. 
 
 Plaster of Paris is employed by the plasterer to 
 give the requisite form and finish to all the superior 
 parts of his work. It is made of a fossil stone 
 called gypsum, which is excavated in several parts 
 of the neighborhood of Paris, where it derives its 
 name, and is calcined to a powder, to deprive it of 
 its water of crystallization. 
 
 The stones are burnt in kilns, which are generally 
 of very simple construction, being not unfrequently 
 buUt of .the gypsum itself. The pieces to be cal- 
 cined are loosely put together in a parallelopiped 
 heap, below which are vaulted pipes or flues, for the 
 application of a moderate heat. 
 
 The calcination must not be carried to excess, as 
 otherwise the plaster will not form a solid mass when 
 mixed with a certain portion of water. During the 
 process of calcination, the water of crystallization 
 rises as white vapor, which, if the atmosphere be dry, 
 is quickly dissolved in air. 
 
 The pounding of the calcined fragments is per- 
 formed sometimes in miUs constructed for the pur- 
 pose, and sometimes by men, whose health is much 
 impaired by the particles of dust settling upon their 
 lungs. 
 
 On the River Wolga, in Russia, where the burning 
 of gypsum constitutes one of the chief occupations 
 of the peasantry, all kinds of gypsum are burnt pro- 
 miscuously on grates made of wood ; afterwards, the 
 plaster is reduced to powder, passed through a sieve, 
 and finally formed into small, round cakes, which are 
 sold at so much per thousand. 
 
 These balls are reduced into an impalpable powder 
 by the plasterer, and then mixed with mortar. 
 
 The less the gypsum is mixed with other sub- 
 stances, the better it is qualified for the purpose of 
 making casts, stucco, &c. The sparry gypsum, or 
 selenite, which is the purer kind, is employed for 
 taking impressions from coins and medals, and for 
 making those beautiful imitations of marble, grahite, 
 and porphyry, known by the name of scagliola, which 
 is derived from the Italian word scagli. 
 
BUILDING. 
 
 151 
 
 Finely-powdered alabaster, or plaster of Paris, 
 when heated in a crucible, assumes the appearance 
 of a fluid, by rolling in waves, yielding to the touch, 
 steaming, &c., all of which properties it again loses 
 on the departure of the heat. If taken from the cru- 
 cible and thrown upon paper, it will not wet it, but 
 immediately be as motionless as it was before being 
 exposed to the heat. 
 
 Two or three spoonfuls of burnt alabaster mixed 
 up thin with water will, at the bottom of a vessel 
 filled with water, coagulate into a hard lump, not- 
 
 withstanding the water that surrounds it. 
 
 The coag- 
 
 ulating or setting property of burnt alabaster will be 
 very much impaired or lost if the powder be kept for 
 any considerable time, and more especially in the 
 open au-. When it has been once tempered with 
 water, and suffered to grow hard, it cannot be ren- 
 dered of any further use. 
 
 Plaster of Paris, diluted with water into the con- 
 sistence of a soft or thin paste, quickly sets, or grows 
 firm, and, at the instant of its setting, has its bulk 
 increased. This expansive property, in passing from 
 a soft to a firm state, is one of its valuable properties, 
 rendering it an excellent matter for filling cavities in 
 sundry works, where other earthy mixtures would 
 shrink and leave vacuities, or entirely separate from 
 the adjoining parts. It is also probable that this ex- 
 pansion of the plaster might be made to contribute 
 to the elegance of the impressions it receives from 
 medals, &c., by properly confining it when soft, so 
 that, at its expansion, it would be forced into the mi- 
 nutest traces of the figures. 
 
 Other cements are iised by plasterers for inside 
 work. The first is called lime and hair, or coarse 
 stuff, and is prepared as common mortar, with the 
 addition of hair from the tan yards. The mortar is 
 first mixed with a requisite quantity of sand, and the 
 hair is afterwards worked in by the appKcation of a 
 rake. 
 
 Next to this is fine stuff, which is merely pure lime, 
 slaked first with a small quantity of water, and 
 afterwards, without any extraneous addition, super- 
 saturated with water, and put into a tub in a half 
 fluid state, where it is allowed to remain till the water 
 is evaporated. In some particular cases, a small por- 
 tion of hair is incorporated. When this fine stuff 
 is used for inside walls, it is mixed with very fine 
 washed sand, in the proportion of one part sand to 
 three parts of fine stuff, and is then caUed trowelled 
 
 or bastard stucco, with which all walls intended to be 
 painted are finished. 
 
 The cement called ^augc stuff consists of three 
 fifths of fine stuff" and one fifth plaster of Paris, mixed 
 together with water, in small quantities at a time, to 
 render it more ready to set. This composition is 
 mostly used in forming cornices and mouldings run 
 with a wooden mould. When great expedition is 
 required, plasterers gauge all their mortars with plas- 
 ter of Paris, which sets immediately. 
 
 MASTIC CEMENT. 
 
 This useful invention consists in making a cement 
 or composition, which may be applied in the for- 
 mation of ornaments and statues, and of bricks, or 
 an imitation of bricks, tiles, and stones, and joining 
 and cementing the same, and in erecting, covering, 
 and decorating buildings internally and externally ; 
 and the said cement or composition may be mixed 
 and moulded upon any sort of material, and whole 
 and entire erections and substances may be worked 
 and moulded therewith. 
 
 The cement consists in a mixture of earths and 
 other substances that are insoluble in water, or nearly 
 so, either in their natural state, or such as have been 
 manufactured, as earthen ware, porcelain, and such 
 like substances ; but it is preferred that those earths, 
 either in their natural or manufactmred state, are the 
 least soluble in water, and have, when pulverized, or 
 reduced to powder, the least color. To the earth or 
 earths as before named, either in their natural or man- 
 ufactured state, and so pulverized, add a quantity of 
 each of the oxides of lead, as litharge, gray oxide, and 
 minium, reduced or ground to powder, and to the 
 whole of the above-named substances a quantity of 
 pulverized glass or flint stone 
 
 These various earths, oxides, and glass, or flijit stone, 
 reduced to a pulverized state, in proper and due pro- 
 portions, and being mixed with a proper and due 
 proportion of vegetable oil, as hereinafter named, 
 form and make a composition or cement, which, by 
 contact or exposure to the atmosphere, hardens and 
 forms an impenetrable and impervious coating or 
 covering, resembling Portland or other stones. 
 
 The cement or composition is composed in the 
 following manner and proportions : To any given 
 
152 
 
 BUILDING. 
 
 weight of earth or earths, commonly called pit sand, 
 river sand, rock sand, or any other sand of the same 
 or like nature, or pulverized earthen ware, or porce- 
 lain, add two thirds of such given weight of the earth 
 or earths commonly called Portland stone, Bath 
 stone, or any other stone of the same or like nature, 
 pulverized. To every five hundred and sixty pounds' 
 weight of these earths so prepared add forty pounds' 
 weight of litharge, prepared as before described, and, 
 with the last-mentioned given weights, combine two 
 pounds' weight of pulverized glass or flint stone. 
 
 Then join to this mixture one pound weight of min- 
 ium and two pounds' weight of gray oxide of lead. 
 
 This compound of earths, oxide, and glass, or flint 
 stone, put into a circular or other proper machine, 
 that will, by its rotary or other motion, mix them well, 
 and their proper intermixture may be ascertained by 
 the shade or colors, which should appear of one even 
 and regular shade or hue ; but any particular shade 
 or color may be given by a proper selection of earths, 
 or by adding a small quantity of vegetable, mineral, 
 or other coloring matter. 
 
 This composition being thus mixed, pass the same 
 through a wire sieve, or dressing machine, of such 
 fineness or mash as may be requisite for the purposes 
 it is intended for, preferring a fine sieve, mash or wire 
 work, when the composition is to be used for works 
 of a fine or even surface. The composition thus 
 formed and mixed is a fine dry powder, and may be 
 kept open in bulk or in casks for any length of time 
 without deterioration. 
 
 When this composition is intended to be made 
 into cement for any of the purposes described, it is 
 spread upon a board or platform, or mixed in a trough ; 
 and to every six hundred and five pounds' weight of 
 the composition are added five gallons of vegetable 
 oil, as linseed oil, v^^alnut oil, or pink oU. 
 
 The composition is then mixed in a similar way 
 to that of the mortar, and is afterwards subjected to 
 a gentle pressure by treading upon it ; and this oper- 
 ation is continued until it acquires the appearance 
 of moistened sand. The mixture being thus com- 
 posed is a cement fit and applicable to the enume- 
 rated purposes. It is requisite to observe, that this 
 cement should be used the same day the oil is added, 
 otherwise it wiU fix or set into a solid substance, and 
 be unfit for use. 
 
 When this cement is to be used or applied to any 
 thing, — to making of decorations, ornaments, and 
 
 statues, or artificial bricks, tiles, and stones, — running 
 or casting moulds, prepared, suited, and applicable 
 for the purposes for which they are intended, are made 
 use of. The moulds for making ornaments, statues, 
 or other fancy works are prepared and made of gyp- 
 sum, or plaster of Paris, or seasoned or dry wood, 
 and must be prepared by rubbing the internal parts 
 well with raw linseed oil, until they are brought to a 
 dry, smooth, and polished surface, to prevent adhe- 
 sion ; and in some instances, to obtain a more per- 
 fect, dry, smooth, and polished surface, pulverized 
 plumbago is used. In all cases it is requisite to de- 
 tach or remove, with convenient speed, the mould 
 from the body of the cement or composition to which 
 it is intended to give form. 
 
 The statue, ornament, bricks, tiles, and stones, or 
 the imitations of all or either of them, thus formed, 
 must be removed with care, and placed upon a bench 
 or platform, which must be previously covered with 
 fine dry sand to prevent adhesion ; and, in some 
 cases, for statues and ornaments, a bed of fine dry 
 sand is necessary to receive them, where they must 
 remain in both cases for the purpose of setting for 
 twenty-four hours, or a longer period, according to 
 the temperature to which they are exposed. 
 
 When it is applied for the purpose of cementing 
 and joining of bricks, tiles, stones, and other sub- 
 stances, the surfaces to which the cement or compo- 
 sition is to be applied are prepared by brushing and 
 cleaning them from dust and all loose matter ; the 
 said surfaces are then covered with boiled linseed 
 oil, with a brush, as in painting. This application 
 of the boiled linseed oil prevents the too rapid ab- 
 sorption of the oil employed or mixed with the cem- 
 ent or composition. A thin coating of the cement is 
 then applied between the two bodies to be joined. 
 When the cement is used for the purpose of covering 
 buildings intended to resemble stone, the surface of 
 the buildings is washed in oil. 
 
 The cement is then applied of the thickness of a 
 quarter of an inch, or any greater thickness, accord- 
 ing to the nature of the work, joint, or stone it is 
 intended to resemble. 
 
 It is requisite to observe, that when a joint, in- 
 tended to resemble a plain stone joint, is to be made 
 upon the surface of the cement or composition, the 
 cement or composition must be partly set or hardened 
 previously to the impression of the joint upon its sur- 
 face, and the joint is made by a rule and steel jointer. 
 
BUILDING. 
 
 153 
 
 When the cement is used for the covering of sub- 
 stances less absorbent than briclcs, or tiles, (as wood, 
 lead, iron, or tin,) a much less quantity of boiled 
 linseed oil in preparing the surfaces is required. 
 
 LATHING, PLASTERING, &c. 
 
 Lathinff, the fii-st operation, consists in nailing 
 laths on the ceiling or partition. Laths are made of 
 spruce or pine, and are fastened with cut nails. They 
 are made in fom'-foot lengths ; and, with respect to 
 their thiclaaess and strength, are either smgle, lath 
 and half, or double. The single are the thinnest and 
 cheapest ; those called lath and half are supposed to 
 be one third thicker than the smgle ; and the double 
 laths are twice that thickness. In lathing ceilings, 
 the plasterers should so dispose them that the joints 
 be as much broken as possible, that they may have 
 the stronger key or tie, and thereby strengthen the 
 plastering with which they are to be covered. The 
 thinnest laths are used in partitions, and the strongest 
 for ceilings. 
 
 Latlis are also distinguished into heart and sap 
 laths : the former should always be used in plain 
 tiling ; the latter, which are of inferior quality, are 
 most frequently used by the plasterer. 
 
 Sawed laths have within a few years been inti-o- 
 duced, and are nov/ in general use. They are not 
 subject to so much waste, cost less, and do not re- 
 quire so much mortar as the split lath; the last 
 named, however, retains the mortar most firmly. 
 
 Having nailed the laths in then- appropriate order, 
 the plasterer's next business is to cover them with 
 plaster, the most sim.ple and common operation of 
 which is laying ; that is, spreading a single coat of 
 lime and hair over the whole ceiling or partition, 
 carefully observing to keep it smooth and even in 
 every direction. This is the cheapest kind of plas- 
 tering. 
 
 Pricking up is performed in the same manner as 
 the foregoing ; but it is only a preliminary to a more 
 perfect Idnd of work. After the plaster is laid on, it 
 is crossed all over V;dth the end of a lath, to give it a 
 tie or key to the coat which is afterwards to be laid 
 upon it. 
 
 Lathing, laying, and set, or what is termed lath and 
 plaster, one coat and set, is, when the work, after 
 
 20 
 
 being lathed, is covered with one coat of lime and 
 hair, and aftei-^ards, when sufficiently dry, a thin and 
 smooth coat is spread over it, consisting of lime only, 
 or, as the workmen call it, putty or set. This coat is 
 spread with a smoothing trowel, used by the work- 
 man with his right hand, while his left hand moves 
 a large flat brush of hogs' bristles, dipped in water, 
 backwards and forwards over it, and thus produces a 
 sm-facc tolerably even for cheap work. 
 
 Lathing, floating and set, or lath and plaster, one 
 coat, floated and set, differs from the foregoing, in 
 having the first coat pricked up to receive the set, 
 which is here called the floating. In doing this, the 
 plasterer is provided with a substantial straight edge, 
 frequently from ten to twelve feet in length, which 
 must be used by two workmen. All the parts to 
 be floated arc tried by a straight edge, to ascertain 
 whether they be perfectly flat and level ; and whenever 
 any deficiency appears, the hollow is filled up with a 
 trowel full or more of lime and hair only, which is 
 termed fllling out ; and when these preliminaries are 
 settled, the screeds are next formed. The term screed 
 signifies a style of Hme and hair, about seven or 
 eight inches in width, gauged quite true, by drawing 
 the straight edge over it until it be so. These screeds 
 are made at the distance of about three or four feet 
 from each other, in a vertical dh-cction, all round 
 the partitions and walls of a room. When all are 
 formed, the intervals are filled up with lime and hair, 
 called by the workmen stuff, till flush with the face 
 of the screeds. The straight edge is then worked 
 horizontally on the screeds, by which aU the super- 
 fluous stuff projecting beyond them in the intervals 
 is removed, and a plain sm-face produced. This 
 operation is termed floating, and may be applied to 
 ceilings as well as to partitions or upright walls, by 
 first forming the screeds in the dkcction of the 
 breadth of the apartment, and filling up the intervals 
 as above described. As great care is requisite to 
 render the plaster sound and even, none but skilful 
 workmen should be employed. 
 
 The set to floated work is performed in a mode 
 similar to that aheady prescribed for laying; but, 
 being employed only for best rooms, is done with 
 more care. About one sLxth of plaster of Paris is 
 added to it, to make it set more expeditioiisly, to 
 give it a closer and more compact appearance, and 
 to render it more firm, and better calcidated to re- 
 ceive the whitewash or color when dry. For floated 
 
154 
 
 BUILDING. 
 
 stucco work, the pricking up cannot be too dry ; but 
 if the floating which is to receive the setting coat 
 be too dry before the set is laid on, there will be 
 danger of its peeling off, or of assuming the appear- 
 ance of little cracks or sliclls, which would disfigiu-e 
 the work. Particular care and attention, therefore, 
 must be paid to have the under coats in a proper 
 state of dryness. It may here be observed, that 
 cracks, and other unpleasant appearances in ceilings, 
 are more frequently the effect of weak laths being 
 covered with too much plaster, or too little plaster 
 upon strong laths, rather than of any sagging or 
 other inadequacy in the timbers or the building. If 
 the laths be properly attended to, and the plaster laid 
 on by a careful and judicious workman, no cracks or 
 other blemishes are likely to appear. 
 
 The next operation combines both the foregoing 
 processes, but requires no lathing ; it is called render- 
 ing- and set, or rendering, floated, and set. What is 
 understood by rendering, is the covering of brick or 
 stone wall with a coat of lime and hair, and by set is 
 denoted a superficial coat of fine stuff or putty upon 
 the rendering. These operations are similar to those 
 described for setting of ceilings and partitions ; and 
 the floated and set is laid on the rendering in the 
 same manner as on the partitions, &c., akeady ex- 
 plained, for the best kind of work. 
 
 Trowelled stucco, which is a very neat kind of 
 work, used in dining-rooms, halls, &c., where the 
 walls are prepared to be painted, must be worked 
 upon a floated ground, and the floating be kept quite 
 dry before the stucco is applied. In this process, the 
 plasterer is provided with a wooden tool, called a 
 Hoat, consisting of a piece of half-inch board, about 
 nine inches long and three wide, planed smooth, 
 with its lower edges a little rounded off, and having 
 a handle on the upper surface. The stucco is pre- 
 pared as above described, and afterwards beaten and 
 tempered with clear water. The ground intended to 
 be stuccoed is first prepared with a large trowel, and 
 is made as smooth and level as possible ; when the 
 stucco has been spread upon it to the extent of four 
 or five feet square, the workman, with a float in his 
 right hand and a brush in his left, sprinkles with 
 water and rubs alternately the face of the stucco, till 
 the whole is reduced to a fine, even surface. He 
 then prepares another square of the ground, and pro- 
 ceeds as before, till the whole is completed. The 
 water lias the effect of hardening the face of the 
 
 stucco. When the floating is well performed, it will 
 feel as smooth as glass. 
 
 Rovgh casting, or rough tvalling, is an exterior fin- 
 ishing, much cheaper than stucco, and, therefore, more 
 frequently employed on cottages, farm-houses, &c., 
 than on buildings of a higher class. The wall in- 
 tended to be rough cast is first picked up with a coat of 
 lime and hair ; and when this is tolerably dry, a sec- 
 ond coat is laid on, of the same materials as the first, 
 as smooth as it can possibly be spread. As fast as 
 the workman finishes this surface, he is followed by 
 another 'with a pailful of rough cast, with v\'^hich he 
 bespatters the new plastering, and the whole dries 
 together. The rough cast is composed of fine gravel, 
 washed from all earthy particles, and mixed with 
 pure lime and water, till the whole is of a semi-fluid 
 consistency. This is thrown from the pad upon the 
 wall with a wooden float, about five or six inches 
 long, and as many wide, made of half-inch board, 
 and fitted with a round handle. While, with tliis 
 tool, the plasterer throws en the rough cast with his 
 right hand, he holds in his left a common wliite- 
 washer's brush, dipped in the rough cast also, with 
 which he brushes and colors the mortar and the 
 rough cast he has already spread, to give them, when 
 finished, a regular, uniform color and appearance. 
 
 Cornices are either plain or ornamented, and some- 
 times embrace a portion of both classes. The first 
 point to be attended to is, to examine the drawings, 
 and measure the projections of the principal mem- 
 bers, which, if projecting more than seven or eight 
 inches, must be bracketed. This consists in fixing 
 up pieces of wood at the distance of about ten or 
 twelve inches from each other, all round the place 
 proposed for the cornice, and nailing laths to them, 
 covering the whole with a coat of plaster. In the 
 brackets, the stuff necessary to form the cornice must 
 be allowed, which, in general, is about one inch and 
 a quarter. A beech mould is next made by the car- 
 penter, of the profile of the intended cornice, about 
 a quarter of an inch iii thickness, with the quirks, or 
 small sinkings, of brass or copper. All the sharp 
 edges are carefully removed by the plasterer, who 
 opens with his knife all the points v/hich he finds 
 incompetent to receive the plaster freely. 
 
 These preliminaries being adjusted, two workmen, 
 provided vdth a tub of putty and a quantity of plas- 
 ter of Paris, proceed to run the cornice. Before 
 using the mould, they gauge screed of putty and 
 
BUILDING. 
 
 155 
 
 plaster upon the wall and ceiling, covering so much 
 of each as will correspond with the top and bottom 
 of the intended cornice. On this screed, one or two 
 slight board straight edges, adapted to as many 
 notches or chases, made in the mould for it to work 
 upon, are naUed. The putty is then mixed with 
 about one third of plaster of Paris, and brought to 
 a semi-fluid state by the addition of clean water. 
 One of the workmen, with two or three ti'owels full 
 of this composition upon his liau'k, which he holds 
 in his left hand, begins to plaster over the surface 
 intended for the cornice, wuth his trowel, while his 
 partner applies the mould to ascertain when more or 
 less is wanted. When a sufficient quantity of plas- 
 ter is laid on, the workman holds his mould firmly 
 against both the ceiling and the wall, and moves it 
 backwards and forwards, which removes the super- 
 fluous stuff, and leaves an exact impression of the 
 mould upon the plaster. This is not effected at 
 once ; for while he works the mould backwards and 
 forwards, the otlicr workman takes notice of any de- 
 ficiencies, and fills them up by adding fi-esh supplies 
 of plaster. In this manner, a cornice from ten to 
 ttt^elve feet in length may be formed in a very short 
 time; indeed, expedition is essentially requisite, as 
 the plaster of Paris occasions a very great tendency 
 in the putty to set ; to prevent which, it is necessary 
 to sprinkle the composition frequently with water, as 
 plasterers, in order to secure the truth and coiTectness 
 of the cornice, generally endeavor to finish aU the 
 lengths or pieces between any two breaks or pro- 
 jections at one time. In cornices which have very 
 large proportions, and in cases where any of the or- 
 ders of arcliiteeture are to be introduced, three or 
 four moulds are required, and are sim.ilarly applied, 
 till all the parts are formed. Litcrnal and external 
 mitres, and small returns or breaks, are afterwards 
 modelled and filled up by hand. 
 
 Cornices to be enriched with ornaments have cer- 
 tam indentations, or sinldngs, left in the mould in 
 which the casts are laid. These ornaments were 
 formerly made by hand, but now are cast in plaster 
 of Paris, from clay models. When the clay model 
 is finished, and has, by exposure to the action of the 
 atmosphere, acquired some degree of firmness, it is 
 let into a wooden firame, and, when it has been re- 
 touched and finished, the frame is fiUed with melted 
 wax, which, when cold, is, by turning the frame up- 
 side down, allowed to fall ofl', being an exact cameo. 
 
 or counterpart of the model. By these means, the 
 most enriched and curiously-wrought mouldings may 
 be cast by the common plasterer. These wax mod- 
 els are contrived to east about a foot in length of the 
 ornament at once, such lengths being easily got out 
 from the cameo. The casts are made of the finest 
 and purest plaster of Paris, saturated with water; 
 and the wax mould is oiled previously to its being 
 put in. When the casts or intaglios arc first taken 
 from tlie mould, they are not very firm ; but being 
 suffered to dry a little, either in the open air or in an 
 oven, they acquke sufficient hardness to allow of 
 being scraped and cleaned. 
 
 Basso rUievos and friezes are executed in a similar 
 manner, only the wax mould is so made that the 
 cast can have a back ground at least half an inch 
 thick of plaster cast to the ornament or figure, in 
 order to strengthen and secure the proportions, at the 
 same time that it promotes the general effect. 
 
 The process for capitals to columns is also the 
 same, except that numerous moulds arc required to 
 complete them. In tlic Corinthian capitals, a shaft 
 or belt is first made, on which is afterwards fixed the 
 foliage and volutes, the whole of which require dis- 
 tinct cameos. 
 
 In running cornices, which arc to be enriched, the 
 plasterer takes care to have proper projections in the 
 running moulds, so as to make a groove in the cor- 
 nice for the reception of the cast ornament, v/hich is 
 laid in and secured by spreading a siuall quantity of 
 liquid plaster of Paris on its back. Detached orna- 
 ments intended for ceilings or other parts, and where 
 no running mould has been employed, are cast in 
 pieces corresponding with the design, and fixed upon 
 the ceiling, &c., with white lead, or with the compo- 
 sition known by the name of iron cement. 
 
 The manufacture of stucco has, for a long time 
 past, attracted the attention of all connected with 
 this branch of building, as well as chemists and other 
 individuals ; but the only benefit resulting from such 
 investigations is, a more extensive -knowledge of the 
 materials used. It would seem that the gi-eat moist- 
 m-e of our climate prevents its being brought to any 
 high degree of perfection ; though, among the various 
 compositions which have been tried and proposed, 
 some, .comparatively speaking, are excellent. 
 
 Common stucco, used for external work, consists 
 of clean-washed river sand and ground lime, which are 
 mixed dry, in the proportion of three of the latter to 
 
156 
 
 BUILDING. 
 
 one of the former : when well incorporated together, 
 these should be secured from the air in casks till re- 
 quired for use. Walls to be covered with this com- 
 position must first be prepared, by raking the mortar 
 from the joints, and picking the bricks or stones, till 
 the whole is indented ; the dust and other extraneous 
 matter must then be brushed off, and the wall well 
 saturated with clean water. The stucco is supersat- 
 luatcd with water till it has the appearance and con- 
 sistence of ordinary whitewash, in which state it is 
 rubbed over the wall with a flat brush of hogs' bris- 
 tles. When this process, called roughing in, has been 
 performed, and the work has become tolerably chy 
 and hard, which may be known by its being more 
 white and transparent, the screeds are to be formed 
 upon the wall with fresh stucco from the cask, tem- 
 pered with water to a proper consistency, and spread 
 on the upper part of the wall, about eight or nine 
 inches wide ; as also against the two ends, beginning 
 at the top, and proceeding downwards to the bottom. 
 Li this operation, two workmen arc required ; one to 
 supply the stucco, the other to apply the plumb ride 
 and sh-aight edge. When these are truly formed, 
 other screeds must be made in a vertical direction, 
 about fom" or five feet apart, unless apertures in the 
 wall prevent it ; in which case, they must be formed 
 as near together as possible. When the screcding is 
 finished, compo * is prepared in larger quantities, and 
 both the workmen spread it with their trowels over 
 the wall, in the space left between each pair of 
 screeds. When this operation is complete, the 
 straight edge is applied, and dragged from the top to 
 the bottom of each pair, to remove whatever super- 
 fluous stucco may project above the screeds. If 
 there be any hollow places, fresh stucco is applied, 
 and the straight edge is again drawn over the spot, 
 till the compo is brought even to the face of the 
 screeds, and the whole is level with the edge of the 
 rule. Another interval is then filled xip, and the 
 workmen thus proceed till the whole of the wall is 
 covered. The wall is finished by floating; that is, 
 hardening the surface by sprinkling it with water, 
 and rubbing it with the common wood float, which 
 is performed similarly to trowelling stucco. 
 
 This description of compo is frequently used by 
 plasterers for cornices and mouldings, in the same 
 manner as described in common plastering; but if 
 
 * A name often given to Parker'i? cement. 
 
 the workman finds it necessary, he may add a small 
 quantity of plaster of Paris, to make it fix the better 
 while running or working the mould. Such addition 
 is not, however, calculated to give strength to the 
 stucco, and is only made through the necessity of 
 having a quick set. 
 
 Scag-Uola is a distinct branch of plastering, dis- 
 covered or invented, and much used, in Italy, and 
 thence introduced into France, where it obtained its 
 name. 
 
 Columns and pilasters are executed in this branch 
 of plastering in the following manner: A wooden 
 cradle, composed of thin strips of pine or other wood, 
 is naade to represent the column designed, but about 
 two inches and a half less in diameter than the shaft 
 is intended to be when finished. This cradle is lathed 
 round, as for common plastering, and then covered 
 with a pricking-up coat of lime and hair. Wlien 
 this is quite dry, the artists in scagliola commence 
 operations, by imitations of the most rare and pre- 
 cious marbles, with astonishing and delusive effect ; 
 indeed, as the imitation takes as high a polish, and 
 feels as cold and hard, as the most compact and solid 
 marble, nothing short of actual fracture can possibly 
 discover the counterfeit. 
 
 In preparing the scagliola, the workman selects, 
 breaks, and calcines the purest gypsum, and as soon 
 as the largest fragments, in the process of calcination, 
 lose their brilliancy, withch-aws the fire, and passes 
 the calcined powder through a very fine sieve, and 
 mixes it, as required for use, with a solution of glue, 
 isinglass, &c. In this solution, the colors required in 
 the marble to be imitated arc diffused ; but when the 
 work is to be of various colors, each color is prepared 
 separately, and afterwards mmgled and combined, 
 nearly in the same manner as a painter mixes oia his 
 palette the primitive colors to compose his different 
 tints. 
 
 When the powdered gypsum is prepared, it is laid 
 on the shaft of the intended column, over the pricked- 
 up coat of lime and hair, and is then floated with 
 moulds of wood, made to the requisite size : the artist 
 iises the colors necessary to the imitation dm'ing the 
 floating, by which means they mingle and incorpo- 
 rate with the surface. To obtain the glossy lustre, 
 so much admired in works of marble, the workman 
 rubs the work with one hand with a pumice stone, 
 while with the other he cleans it with a wet sponge ; 
 he next polishes it with tripoli, charcoal, and a piece 
 
BUILDING. 
 
 157 
 
 of fine linen ; aftenvards with a piece of felt, dipped 
 in a mixtnre of oil and tripoli ; and finally completes 
 the work by the application of piu-e oil. This imita- 
 tion is, certainly, the most complete that can be con- 
 ceived ; and wlion the bases and capitals arc made 
 of real marble, as is the common practice, the de- 
 ception is beyond discovery. K not exposed to the 
 weather, it is, in point of durability, little inferior to 
 real marble, retains its lustre full as long, and is not 
 one eighth of the expense of the cheapest kind. 
 
 There is another species of plastering, used in the 
 decorative parts of architecture, and for the frames 
 of pictures, looking-glasses, &c., which is a perfectly 
 distinct branch of the art. This composition, which 
 is very strong, and, when quite dry, of a brownish 
 color, consists of the proportion of two pounds of 
 powdered whiting, one pound of glue in solution, 
 and half a pound of linseed oil, mixed together, and 
 heated in a copper, and stin-ed with a spatula till the 
 whole is incorporated. When cool, it is laid upon a 
 stone, covered with powdered whiting, and beaten till 
 it assumes a tough and firm consistence ; after which 
 it is covered with wet cloths, to keep it fresh till re- 
 quu-ed for use. 
 
 The ornaments to be cast in this composition are 
 modelled in clay, as in common plastering, and af- 
 terwards a cameo, or mould, is carved in boxwood. 
 This carving requires to be done with the utmost 
 care, otherwise the symmetry of the ornament which 
 is to be cast from it will be sjjoUed. The composi- 
 tion, when required for use, is cut with a knife into 
 pieces of the requisite size and forced into the mould ; 
 after which it is put into a press worked by an iron 
 screw, and still further compressed. When the mould 
 is taken from the press, the composition, which is 
 generally cast about a foot in length, is dislodged 
 from the mould, and the superfluous parts pared 
 off with a knife and cast into the copper for the 
 next supply. 
 
 The ornaments thus formed are glued upon wooden 
 grounds, or fixed by means of white lead, &c. ; after 
 which they are painted or gUt, according to the pur- 
 poses for which they are intended. This composition 
 is at least 80 per cent, cheaper than carving, and, in 
 most cases, equally calculated to answer all the pur- 
 poses of the art. 
 
 It is much to be wished, that the art of plastering 
 could be restored to its ancient perfection, for the 
 Romans possessed an art of rendering works of this 
 
 kind much more firm and durable than can be ac- 
 complished at the present time. 
 
 The specimens of ancient Roman plastering still 
 visible, which have not been injured by force, are 
 found to be fnm and solid, free from cracks or crev- 
 ices, and as smooth and polished on the surface as 
 when first applied. The sides and bottoms of the 
 Roman aqueducts were lined with this plastering, 
 and endured many ages. 
 
 At Venice, some of the roofs of houses and the 
 floors of rooms are covered with a sort of plaster of 
 later date, and yet sti-ong enough to endure the sun 
 and weather for several ages without either cracking 
 or spoiling. 
 
 The method of making the Venetian composition 
 is not known in England ; but such might probably 
 be made by heating the powder of gypsum over a 
 fire, and when boiling, which it wUl do without the 
 aid of water or other fluid, mixing it with rosin, or 
 pitch, or both together, with common sulphur, and 
 the powder of sea shells. K these be mbced together, 
 water added to it, and the composition kept on the 
 fire till the instant of its being used, it is not improb- 
 able that the secret may be discovered. Oil of tur- 
 pentmc and wax, which are the common ingredients 
 in such cements as are accounted firmest, may also 
 be tried as additions, as also may strong alewort, 
 which is by some directed to be used instead of 
 water, to make mortar of limestone of more than 
 ordinary strength. 
 
 SLATING. 
 
 This branch of building, which is principally em- 
 ployed in the covering of roofs, is not unfi-equently 
 combined with that of plastering. The slates chiefly 
 used in London are brought from the quarries at 
 Bangor, in Cacrnarvonshii-e, which supply all parts 
 of the United Kingdom. Another kind of slate, of 
 a pale blue-gi-een color, is used, and most esteemed, 
 being brought from Kendal, in Westmoreland, called 
 Westmoreland slates. These slates are not large, but 
 of good substance, and weU calculated to give a neat 
 appearance to a roof The Scottish slate, which as- 
 similates in size and quality to a slate from Wales, 
 called ladies, is in little repute. 
 
 The slates produced in this country are principally 
 from the quarries in the State of Vermont. In point 
 
158 
 
 BUILDING. 
 
 of durability, they are equal to the Welsh slates, but 
 have not that uniformity of color which distinguishes 
 the latter. 
 
 The height of roofs at the present time is very 
 rarely above one third of the sjian, and should never 
 be less than one sixth. The most usual pitch for 
 slates is that when the height is one foiu'th of the 
 span, or at an angle of 26i degrees with the horizon. 
 Taking this as a standard, the following table vn\l 
 show the degree of inclination which may be given 
 for other materials : — 
 
 Kind of Covering. 
 
 Inclination 
 to tlie hori- 
 zon. 
 
 Height of 
 
 roof in parts 
 
 of span. 
 
 Weiglit 
 
 upon a square 
 
 of roofing. 
 
 Copper, . . . 
 
 . 
 
 3 50 
 
 A 
 
 100 
 
 Lead, .... 
 
 
 3 50 
 
 -r'^ 
 
 700 
 
 Slates, large, . . 
 
 
 22 00 
 
 Iff 
 
 J, 
 
 5 
 
 1120 
 
 Slates, ordinary, 
 
 . . 
 
 26 33 
 
 1 
 f 
 
 From 900 
 to 500 
 
 Stone slate, . . 
 
 • 
 
 29 41 
 
 2380 
 
 Plain tiles, . . 
 
 . . 
 
 29 41 
 
 -? 
 
 1780 
 
 Pan tiles, . . . 
 
 . , 
 
 24 00 
 
 2 
 
 650 
 
 Thatch of straw or i 
 
 eeds, 
 
 45 00 
 
 i 
 
 
 Slaters class the "^ 
 
 kVelsh 
 
 and America) 
 
 1 slates in 
 
 the following order : 
 
 — 
 
 
 
 Doubles, averag 
 
 e size 
 
 Ft. In. 
 
 11 b 
 
 Ft. In 
 
 y 6 
 
 Ladies, " 
 
 a 
 
 1 3 
 
 8 
 
 Countesses, " 
 
 (1 
 
 1 8 
 
 10 
 
 Duchesses, " 
 
 u 
 
 2 
 
 1 
 
 Welsh rags, " 
 
 a 
 
 3 
 
 2 
 
 Queens, '' 
 
 (( 
 
 3 
 
 ' 2 
 
 Imperials, " 
 Patent slate, « 
 
 11 
 
 2 
 2 
 
 6 
 6 
 
 2 
 2 
 
 The doubles are made from fragments of the larger 
 kinds, and derive their name from their diminutive 
 size. Ladies are similarly obtained. Countesses are 
 a gradation above ladies ; and duchesses above coun- 
 tesses. 
 
 Slate, like most other stony substances, is separat- 
 ed from its bed by the ignition of gunpowder. The 
 blocks thus obtained arc, by the application of wedges, 
 reduced into layers, called scantling-s, from four to 
 nine inches in thickness, and of any requked length 
 and breadth, which are afterwards sawed to the re- 
 spective sizes by raachmery. The blue, green, and 
 
 for buildings 
 stables, and other 
 
 purple, or darker kinds of slate, are, in general, found 
 capable of being split into very thin laminae, or sheets ; 
 but those of the white or brownish freestone land can 
 seldom be separated or divided so fine ; consequently, 
 these last form heavy, strong, thick coverings, proper 
 in exposed situations, siich as barns, 
 outhouses. 
 
 The instruments used in splitting and cleaning 
 slates are slate knives, axes, bars, and wedges ; the 
 three first being vised to reduce the slates into the 
 required thicknesses, and the last to remove the ine- 
 qualities from the siuface. 
 
 Imperial slating is particularly neat, and may be 
 known by having its lower edge sawed ; whereas, all 
 other slates used for covering are chipped square on 
 their edges only. 
 
 Patent slate was first brought into use by Mr. 
 Wyatt, the architect; but a patent was never ob- 
 tained. It derives its name from the mode adopted 
 to lay it on the roofs ; it may be laid on a rafter of 
 much less elevation than any other, and is considera- 
 bly lighter, by reason of the laps being less than is 
 necessary for the common sort of slating. This slat- 
 ing was originally made from Welsh rag-s ; but it is 
 now very frequently made from imperials, which ren- 
 der it lighter, and also somewhat neater in appearance. 
 
 Westmoreland slate, from the experiments made by 
 the late Bishop of LlandafT, appears to differ a little 
 in its natural composition from that obtained from 
 Wales. It must, however, be remarked, that this 
 kind of slate owes its lightness, not so mucli to any 
 diversity in the component parts of the stone, as to 
 the thinness to which it is reduced by the workman ; 
 consequently, it is not so well calculated to resist 
 violent winds as those which are heavier. 
 
 Slates, when brought from the quarry, are not suf- 
 ficiently square for the slater's use ; he therefore 
 picks up and examines the slates separately, and 
 observes Avhich is the sti-ongest and squarest end; 
 then, seating himself, he holds the slate a little slant- 
 ing upon, and projecting about an inch over, the 
 edge of a small block of wood, which is of the same 
 height as his scat, and cuts away and makes straight 
 one of its edges ; then, with a slip of wood, he 
 gauges and cuts off the other edge parallel to it, and 
 squares the end. The slate is now considered pre- 
 pared for use, with the exception of perforating 
 through its opposite ends two small holes for the 
 reception of the nails which are to confine it to the 
 
BUILDING. 
 
 159 
 
 roof. Copper and zinc nails, or iron nails tinned, arc 
 considered the best, being less susceptible of oxida- 
 tion than nails made of bar iron. 
 
 Before we proceed fiu-thcr with the operations 
 necessary in the slating of buildings, we shall give 
 some account of the tools used by this class of ar- 
 tificers. 
 
 Slaters' tools are very few, whicli sometimes are 
 found by the masters, and sometimes by the men. 
 The tool called the saixe is made of tempered iron, 
 about sixteen inches in length, somewhat bent at one 
 end, with a handle of wood at the other. This tool 
 is not unlilcc a large knife, except that it has on its 
 back a projecting piece of iron, about three inches in 
 length, drawn to a sharp point. This tool is used to 
 chip or cut all the slates to the required sizes. 
 
 The ripper is also of iron, about the same length 
 as the saixe ; it has a very thin blade, about an inch 
 and three quarters wide, tapered somewhat towards 
 the top, where a round head projects over the blade 
 about half an inch on each side; it has also two 
 little round notches in the two internal angles, at 
 their intersections. The handle of this tool is raised 
 above the blade by a shoulder, which enables the 
 workman to hold it firm. This instrument is used 
 in repau-ing old slating, and the application consists 
 in thrusting the blade under the slates, so that the 
 head, which projects, may catch the naU in the little 
 notch at its intersection, and enable Lhe workman to 
 di-aw it out. During this operation, the slate is suffi- 
 ciently loosened to allow of its beuig removed and 
 another inserted in its place. 
 
 The hammer, which is somewhat different in shape 
 to the ordinary tool of that name, is about five inches 
 in height on the hammer or driving part, and the top 
 is bent back, and gi'ound to a tolerably sharp point, 
 its lower or flat end, which is quite round, being 
 about three quarters of an inch in diameter. On 
 this side of the di-iving part is a small projection, 
 with a notch in the centre, which is used as a claw 
 to extract such nails as do not drive satisfactorily. 
 
 The shaving tool is used for getting the slates to a 
 smooth face for skirtings, floors for balconies, &c. It 
 consists of an iron blade, sharpened at one of its 
 ends like a chisel, and mortised through the centre 
 of two round wooden handles, one fixed at one end, 
 and the other about the middle of the blade. The 
 blade is about eleven inches long and two inches 
 wide, and the handle is about ten inches long ; so 
 
 that they project about four inches on each side of 
 the blade. In using this tool, the workman places 
 one hand on each side of the handle that is in the 
 middle of the blade, and allows tlie other to press 
 against both his wrists. In this manner, he removes 
 all the uneven parts from off the face of the slate, 
 and gets it to a smooth surface. 
 
 The other tools used by the slater consist of chisels, 
 gouges, and files of all sizes ; by means of which he 
 finishes the slates into mouldings and other required 
 forms. 
 
 Li slating roofs, it is necessary to form a base or 
 floor for the slates to lay compactly and safely upon ; 
 for doubles and ladies, boarding is requii-ed, which 
 must be laid very even, with the joints close, and 
 properly secm-ed by nails to the rafters. This being 
 completed, the slater provides himself with several 
 slips of wood, called tilling fdlets, about ten inches 
 and a half wide, and three quarters of an inch thick 
 on one edge, and chamfered to an arris on the other, 
 which he nails down all round the extreme edges of 
 the roof, beginning with the hips, if any, and if not, 
 with the sides, eaves, and ridge. He next selects the 
 largest of the slates, and arranges them regularly 
 along the eaves, with their lower edges to a line, and 
 naUs them to the boarding. This part of the work 
 being completed, he takes other slates to form the 
 bond to the under sides of the eaves, and places 
 them under those previously laid, so as to cross and 
 cover aU their joints. Such slates are pushed up 
 lightly under those which are above them, and are 
 seldom nailed, but left dependent for support on the 
 weight of those above them, and then* own weight 
 on the boarding. The countesses and all other de- 
 scriptions of slates, when intended to be laid in a 
 good manner, are also laid on boards. 
 
 When the slater has finished the eaves, he stretches 
 a line on the face of the upper slates, parallel to its 
 outer edge, and as far from it as he deems sufficient 
 for the lap of those he intends shall form the next 
 course, which is laid and nailed even with the line, 
 crossing the joints of the upper slates of the eaves. 
 This lining and laying is continued close to the ridge 
 of the roof, observing throughout to break the differ- 
 ent joints, by laying the slates one above another. 
 The same system is universally followed in laying aU 
 the different sorts of slates, with the exception of 
 those called patent slates, as hereafter explained 
 
 The largest kind of slates are found to lay firm on 
 
160 
 
 BUILDING. 
 
 battens, which are, consequently, much employed, 
 and produce a very considerable saving of expense 
 in large buildings. A batten is a narrow portion of 
 board, about two inches and a half or three inches 
 wide, four of them being commonly procm'ed from 
 an eleven-inch board. 
 
 For countess slates, battens three quarters of an 
 inch thick will be of adequate substance ; but for 
 the larger and heavier kinds, inch battens will be 
 necessary. In battening a roof for slates, the battens 
 are not placed at a uniform distance from each other, 
 but so as to suit the length of the slates ; and as 
 these vary as they approach the apex or ridge of the 
 roof, it follows that the slater himself is the best 
 judge where to fix them, so as best to support the 
 slates. 
 
 A roof, to be covered with patent slates, requh-es 
 that the common rafters be left loose upon then- pur- 
 lines, as they must be so arranged that a rafter shall 
 lie under every one of the meeting joints. Neither 
 battening nor boarding is required for these slates. 
 The number of rafters will depend on the width of 
 the slates ; hence, if they be of a larger size, very 
 few will suffice. This kind of slating is likewise 
 commenced at the eaves ; but no crossing or bond- 
 ing is required, as the slates arc laid uniformly, with 
 each end reaching to the centre of the rafter, and 
 butted up to each other throughout the length of the 
 roof. When the eaves-course is laid, the slates which 
 compose it are screwed down to the rafters by two or 
 three strong inch and half screws at each of then- 
 ends. A line is then sti-ained about two inches be- 
 low the upper edge, in order to guide the laying of 
 course, which is laid with its lower edge 
 
 the next 
 touching 
 
 the line. This lining, layhig with a lap, 
 and screwing down, is continued till the roof is com- 
 pletely covered. The joints are then secured by fil- 
 leting, which consists in covering all tlic meeting 
 joints with fillets of slate, bedded in glaziers' putty, 
 and screwed down through the whole into the rafters. 
 The fillets are usually about three inches wide, and 
 of a length proportionate to that of the slates whose 
 joints they have to cover. These fillets are solidly 
 bedded in the putty, and their intersecting joints are 
 lapped similar to those of the slates. The fillets 
 being so laid, and secm-cd by one in the middle of 
 the fillet, and one in each lap, arc next neatly pointed 
 all round their edges with more putty, and then 
 painted over with the color of the slate. The hips 
 
 and ridges of such slating are frequently covered by 
 fillets, which produce a very neat effect ; but lead, 
 which is not much dearer, is by far the best kind of 
 covering for all hips and ridges. The patent slating 
 may be laid so as to be perfectly water tight, with 
 an elevation of the rafters considerably less than for 
 any other slate or tile covering. The rise in each 
 foot of length in the rafter is not required to be more 
 than t«-o inches, which, in a rafter of fifteen feet, will 
 amount to only two feet six inches — a rise scarcely 
 perceptible from the gi-ound. 
 
 Slating is performed in several other ways, but the 
 prmciples aheady explained embrace the most of 
 them. Some workmen shape and lay their slates in 
 a lozenge form. This kind of work consists in get- 
 ting all the slates to a uniform size, of the shape of a 
 geometrical square. When laid on the roof, which 
 must be boarded, they are bonded and lapped as in 
 common slating, observing only to let the elbow, or 
 half of the square, appear above each slate that is 
 next beneath it, and be regular in the courses all over 
 the roof. One naU or screw only can be used for 
 such slating; hence it soon becomes dOapidated. It 
 is commonly employed in places near to the eye, or 
 where particular neatness is required. 
 
 It has been ascertained that a slate one inch thick 
 will, in a horizontal position, support as much in 
 weight as five inches of Portland stone similarly sus- 
 pended. Hence slates are now ^^^.■ought and used in 
 galleries, and other pm'poses, where it is essential to 
 have strength and lightness combmed. Slates are 
 also fashioned into chimney-pieces, but arc incapable 
 of receiving a polish like marble. It makes excellent 
 sku'tings of all descriptions, as weU as casings to 
 walls, where dilapidations or great wear and tear are 
 to be expected. For these purposes, it is capable of 
 being fLxed with joints, equally as neat as wood ; and 
 may, if required, be painted over so as to appear like 
 it. Staircases may also be executed in slate, which 
 vrill produce a resemblance of marble. 
 
 PLUMBING. 
 
 Plumbing is the art of casting and working in 
 lead, and using the same in the covering and for 
 other purposes in building. 
 
 To the plumber is also confided the pump work, 
 
BUILDING. 
 
 161 
 
 , as well as the making and forming of cisterns and 
 reservoirs, large or small closets, &c., for the purposes 
 of domestic economy. The plumber does not use a 
 great variety of tools, because the ductility of the 
 metal upon which he operates does not require it. 
 The tools used consist of an iron hammer, rather 
 heavier than a carpenter's, with a short, tliick handle ; 
 two or three wooden mallets of different sizes, and a 
 Iressing and flatting tool. Tliis last is of beech, 
 about eighteen inches long and two inches square, 
 planed smooth and flat on the under surface, and 
 fouiaded on the upper, and one of its ends tapered 
 off round as a handle. With this tool he stretches 
 out and flattens the sheet lead, or dresses it to the 
 shape required, using first the flat side, then the round 
 one, as occasion may require. 
 
 The plumber has also occasion for a jack and 
 trying plane, similar to that of the carpenter. With 
 this he reduces the edges of sheet lead to a straight 
 line, when the purposes to which it is to be applied 
 require it. His cutting tools consist of a variety of 
 chisels and gouges, as well as knives. The latter of 
 these are used for cutting the sheet lead into slips 
 and pieces after it has been marked out by the chalk 
 line. 
 
 Files of difierent sizes ; ladles of three or four sizes, 
 for melting the solder ; and an iron instrument called 
 g-rozing irons. 
 
 These grozing irons are of several sizes, generally 
 about twelve inches in length, tapered at both ends, 
 the handle end being turned quite round, to allow 
 of its being firmly held whUe in use ; the other end 
 is a bulb, of a spindle or spherical shape, of a size 
 proportioned to the soldering intended to be ex- 
 ecuted. They are, when required for use, heated to 
 redness. 
 
 The plumber's measm-ing ride is two feet iii length, 
 divided into three equal parts of eight inches each ; 
 two of its legs are of boxwood, duodecimally divided ; 
 and the third consists of a piece of slow-tempered 
 ^teel, attached to one of the box legs by a pivot on 
 which it turns, and falls, when not in use, into a 
 groove cut in such leg for its reception. This steel 
 leg can be passed into places where the others can- 
 not enter; and it is also useful for occasionally re- 
 moving the oxide or any extraneous matters from the 
 surface of the heated metal. 
 
 Scales and weights are also necessary ; and he 
 must be supplied with centre bits of all sizes, for the 
 
 21 
 
 purpose of making perforations in lead or Wood, 
 through which he may want to insert pipes, &c. 
 Compasses, to strike curcular pieces, to line or cover 
 figures of that shape, are occasionally required. 
 
 Lead is obtained from ore, and, from its being gen- 
 erally combined with sulphur, it has been denomi- 
 nated sulphuret. After the ore has been taken from 
 its bed it is smelted, fust being picked, in order to 
 separate the unctuous and rich or genuine ore from 
 the stony matrice, and other impurities ; the picked 
 ore is then pounded under stampers worked by ma- 
 chinery, and afterwards washed to carry off the re- 
 mainder of the matrice, which could not be separated 
 in picking. It is next put into a reverberatory fur- 
 nace to be roasted ; during which operation it is re- 
 peatedly stirred, to facilitate the evaporation of the 
 sulphur. When the surface begins to assume the 
 appearance of a paste, it is covered with charcoal, 
 and well shaken together ; the fire is then increased, 
 and the purified lead flows down on all sides into 
 the basin of the furnace, whence it runs off into 
 moulds prepared for its reception. The moulds are 
 capable of receiving one hundi-ed and fifty -four pounds 
 of lead each, and their contents, when cool, are, in 
 the commercial world, called pigs. 
 
 Lead is of a bluish-white color, and when newly 
 melted, or cut, is quite bright ; but it soon becomes 
 tarnished on exposure to the atmosphere — assuming 
 first a dirty, gray color, and afterwards becomes white. 
 It is capable of being hammered into very thin plates, 
 and may be drawn into wire ; but its tenacity is very 
 inferior to that of other metals, for a leaden wire, the 
 hundred and twentieth part of an inch in diameter, 
 is only capable of supporting about eighteen pounds 
 without breaking. Lead, next to tin, is the most fu- 
 sible of all metals ; and if a stronger heat be applied, it 
 boils and evaporates. If cooled slowly, it crystallizes. 
 The change of its external color is owing to its 
 gradual combination with oxygen, which converts its 
 exterior surface into an oxide. This outward crust, 
 however, preserves the rest of the metal for a long 
 time, as the air can penetrate but very slowly. 
 
 Lead is not acted upon immediately by water, 
 though that element greatly facilitates the action of 
 the air upon it ; for it is known that, when lead is 
 exposed to the atmosphere, and kept constantly wet, 
 the process of oxidation takes place much more rap- 
 idly than it does under other circumstances ; hence 
 the white crust that is to be obser\'ed on the sides of 
 
162 
 
 BUILDING. 
 
 leaden vessels containing water, just at the place 
 where the surface of the water terminates. 
 
 Lead is piurchased by plumbers in pigs, and they 
 reduce it into sheets, or pipes, as they have occasion. 
 Of sheet lead they have two kinds, cast and milled. 
 The former is used for covering flat roofs of build- 
 ings, laying of terraces, forming gutters, lining reser- 
 voirs, &c. ; and the latter, which is very thin, for cov- 
 ering the hips and ridges of roofs. This last they do 
 not manufacture themselves, but purchase it of the 
 lead merchants, ready prepared. 
 
 For the casting of sheet lead, a copper is provided, 
 and well fixed in masonry, at the upper end of the 
 workshop, near the mould or casting table, which 
 consists of strong boards, well jointed together, and 
 bound with bars of iron at the ends. The sides of 
 this table, of which the, shape is a parallelogram, vary 
 in size from four to six feet in width, and from six- 
 teen to eighteen feet and upwards in length, and are 
 guarded by a frame or edging of wood, three inches 
 thick, and four or five inches higher than the interior 
 surface, called the shafts. This table is fixed upon 
 firm legs, strongly framed together, about sLs or seven 
 inches lower than the top of the copper. At the up- 
 per end of the mould, nearest the copper, is a box, 
 called the pan, which is adapted in its length to the 
 breadth of the table, having at its bottom a long, hor- 
 izontal slit, from which the heated metal is to issue, 
 when it has been poured in from the copper. This 
 box moves upon rollers along the surface of the rim 
 of the table, and is put in motion by means of ropes 
 and pulleys, fixed to beams above. While the metal 
 is melting, the surface of the mould, or table, is pre- 
 pared by covering it with a stratum of dry and clean 
 sand, regularly smoothed over with a kind of rake, 
 called a strike, which consists of a board about five 
 inches broad, and rather longer than the inside of the 
 mould, so that its ends, which arc notched about two 
 inches deep, may ride upon the shafts. This being 
 passed down the whole length of the table, reduces 
 the sand to a uniform surface. The pan is now 
 brought to the head of the table, close to the copper, 
 its sides having previously been guarded by a coat 
 of moistened sand, to prevent its firing from the heat 
 of the metal, which is now put in by ladles from the 
 copper. 
 
 These pans, or boxes, it must be observed, are made 
 to contain the quantity of melted lead which is re- 
 quired to cast a whole sheet at one time ; and the 
 
 slit in the bottom is so adjusted as to let out, during 
 its progress along the table, just as much as wUl com- 
 pletely cover it of the thickness and weight per foot 
 required. Every thing being thus prepared, the slit 
 is opened, and the box moved along the table, dis- 
 pensing its contents from the top to the bottom, and 
 leaving in its progress a sheet of lead of the desired 
 thickness. When cool, the sheet is rolled up and 
 removed from the table, and other sheets are cast, 
 till all the metal in the copper is exhausted. The 
 sheets thus formed are then rolled up and kept for use. 
 
 In some places, instead of having a square box 
 upon wheels, with a slit in the bottom, the pan con- 
 sists of a kind of trough, being composed of two 
 planks nailed together at right angles, with two tri- 
 angular pieces fitted in between them at their ends. 
 The length of this pan, as well as that of the box, is 
 equal to the whole breadth of the mould. It is placed 
 with its bottom on a bench at the head of the table, 
 leaning with one side against it ; to the opposite side 
 is fixed a handle, by which it may be lifted up in order 
 to pour out the liquid metal. On the side of the pan 
 next the mould are two iron hooks, to hold it to the 
 table, and prevent it from slipping while the metal is 
 being poured into the mould. 
 
 The mould, as well as the pan, is spread over about 
 two inches thick with sand sifted and moistened, and 
 rendered perfectly level by moving over it the strike, 
 and smoothing it down with a plane of polished 
 brass, about a quarter of an inch thick and nine 
 inches square, tiuned up on the edges. 
 
 Before they proceed to casting the lead, the strike 
 is made ready by tacking two pieces of old hat on the 
 notches, or by covering the notches with leather 
 cases, so as to raise the under side of the strike 
 about an eighth of an inch or more above the sand, 
 according to the proposed thickness of the sheet. 
 The face or under side of the strike is then smeared 
 with tallow, and laid across the breadth of the mould, 
 with its ends resting on the shafts. The melted lead 
 is then put into the pan with ladles ; and, when a . 
 sufficient quantity has been put in, the scum is swept 
 off" with a piece of board, and suffered to settle on 
 the coat of sand, to prevent its falling into the mould 
 when the metal is poured out. It generally happens 
 that the lead, when first taken from the copper, is too 
 hot for casting ; it is, therefore, suffered to cool in the 
 pan till it begins to stand with a shell or wall on the 
 sand with which the pan is lined. Two men ther 
 
BUILDING. 
 
 163 
 
 take the pan by the handle, or one of them takes it 
 by means of a bar or chain fixed to a beam in the 
 ceiling, and turn it down, so that the metal runs into 
 the mould ; while another man stands ready with the 
 strike, and, as soon as all the metal is poured in, 
 sweeps it forward and draws the residue into a 
 trough at the bottom, which has been prepared to 
 receive it. The sheet is then rolled up as before. 
 
 In this mode of operation, the table inclines in its 
 length about an inch or an inch and a half, in the 
 length of sixteen or seventeen feet, or more, accord- 
 ing to the required thickness of the sheets : the thin- 
 ner the sheet, the greater the declivity ; and vice 
 versa. The lower end of the mould is also left open, 
 to admit of the superfluous metal being thrown off. 
 
 When a cistern is to be cast, the size of the four 
 sides is measured out; and the dimensions of the 
 front having been taken, slips of wood, on which the 
 mouldings are carved, are pressed upon the sand. 
 Figures of birds, beasts, &c., are likewise stamped in 
 the internal area, by means of leaden moulds. K 
 any part of the sand has been disturbed in doing 
 this, it is made smooth, and the process of casting 
 goes on as for plain sheets ; except that, instead of 
 rolling up the lead when cast, it is bent into four 
 sides, so that the two ends, when they are soldered 
 together, may be joined at the back : the bottom is 
 afterwards soldered up. 
 
 The lead which lines the Chinese tea boxes is re- 
 duced to a thinness which our plumbers cannot, it is 
 said, approach. The following account of the pro- 
 cess was communicated by an intelligent East Lidian, 
 in a letter which appeared in the Gentleman's Mag- 
 azine : " The caster sits by a pot containing the 
 melted metal, and has two large stones, the lower 
 one fixed and the upper one movable, having their 
 surfaces of contact ground to each other, directly 
 before him. He raises the upper stone by pressing 
 his foot upon its side, and with an iron ladle pours 
 into the opening a sufficient quantity of the fluid 
 metal. He then lets fall the upper stone, and thus 
 forms the lead into an extremely thin and irregular 
 plate, which is afterwards cut into its required form." 
 
 Cast sheet lead, used for architectural purposes, is 
 technically divided into 5 lb., 5^ lb., 6 lb., 6^ lb., 7 lb., 
 7A lb., 8 lb., and S| lb.; by which is understood 
 that every superficial foot is to contain those respec- 
 tive weights, according to the price agreed upon. 
 
 The milled lead used by plumbers is very thin, sel- 
 
 dom containing more than five pounds to the foot. It 
 is by no means adapted to gutters or terraces, nor, in- 
 deed, to any part of a building that is much exposed 
 either to great wear or to the effects of the sun's rays : 
 in the former case, it soon wears away ; in the latter, 
 expands and cracks. It is laminated in sheets of 
 about the same size as those of cast lead, by means 
 of a roller, or flatting mill. 
 
 Lead pipes are sometimes made of sheet lead, by 
 beating it on round wooden cylinders of the length 
 and dimensions required, and then soldering up the 
 edges. 
 
 Solder is used to secure the joints of work in lead, 
 which, by other means, would be impossible. It 
 should be easier of fusion than the metal intended to 
 be soldered, and should be as nearly as possible of , 
 the same color. The plumber, therefore, uses what 
 is technically called soft solder, which is a compound 
 of equal parts of tin and lead, melted together and 
 run into moulds. In this state it is sold by the 
 manufacturer, by the pound. 
 
 In the operation of soldering, the surfaces or edges 
 intended to be united are scraped very clean, and 
 brought close up to each other, in which state they 
 are held by an assistant, while the plumber applies a 
 little resin on the joints, in Order to prevent the oxida- 
 tion of the metal. The heated solder is then brought 
 in a ladle and poured on the joint ; after which it is 
 smoothed and finished by rubbing it about with a 
 red-hot soldering iron ; when completed, it is made 
 smooth by filing. 
 
 Li the covering of roofs or terraces with lead, (the 
 sheets never exceeding six feet in breadth,) it be- 
 comes necessary, in large surfaces, to have joints, 
 which are managed several ways, but in all the chief 
 object is to have them water tight. The best plan 
 of effecting this is to form laps, or roll joints, which is 
 done by having a roU or strip of wood about two 
 inches square, but rounded on its upper side, naile<J 
 under the joints of the sheets, where the edges lap 
 over each other : one of these edges is to be dressed 
 up over the roll on the inside, and the other is to be 
 dressed over them both on the outside, by which 
 means the water is prevented from penetrating. No 
 other fastening is requisite than what is required 
 from the hammering of the sheets together down 
 upon the flat ; nor should any other be resorted to 
 when sheet lead is exposed to the vicissitudes of tho 
 weather, because it expands and shrinks, which, if 
 
164 
 
 BUILDING. 
 
 prevented by too much fastening, would cause it to 
 crack and become useless. It sometimes, however, 
 occurs, that rolls cannot be used, and then the method 
 of joining by seams is resorted to. This consists in 
 simply bending the approximate edges of the lead 
 up and over each other, and then dressing them down 
 close to the flat, throughout their length. But this is 
 not equal to the roll, either for neatness or security. 
 
 Lead flats and gutters should always be laid with 
 the current, to keep them dry. About a quarter of 
 an inch to the foot is a sufficient inclination. 
 
 In laying gutters, &c., pieces of milled lead, called 
 flushing-, about eight or nine inches wide, are fixed 
 in tlic walls, all round the edges of the sheet lead, 
 with which the flat is covered, and are suffered to 
 hang down over them, so as to prevent the passage 
 of rain through the interstice between the raised 
 edge and the waU. If the waUs have been previously 
 bmlt, the mortar is raked out of the joint of the 
 
 bricks next above the 
 
 edge 
 
 of the sheet, and the 
 
 ffushings are not only inserted into the crack at the 
 upper sides, but their lower edges are likewise dressed 
 over those of the lead in the flat, or gutter. When 
 neither of these modes can be resorted to, the flush- 
 ings are fastened by waU hooks, and their lower 
 edges dressed down as before. 
 
 Drips in flats, or gutters, are formed by raising one 
 part above another, and dressing the lead, as already 
 described, for covering the rolls. They are resorted 
 to when the gutter or flat exceeds the length of the 
 sheet; or, sometimes, for convenience. They are 
 also a useful expedient to avoid soldering the joints. 
 
 Sheet lead is also used in the lining of reservoirs, 
 which are made either of wood or masonry. As 
 these conveniences are seldom in places subject to 
 material changes of temperature, recourse may be 
 had to the soldering without fear of its damaging 
 the work, by promoting a disposition to crack. 
 
 The pumps which come under the province of the 
 plumber are confined generally to two or three kinds 
 used for domestic purposes, of which the suction and 
 lifting pumps arc the chief; these, as well as water 
 closets, are manufactured by a particular set of work- 
 men, and sold to the plumber, who furnishes the lead 
 pipes, and fixes them in thek places. 
 
 Plumbers' work is generally estimated by the 
 pound, or hundred weight ; but the weight may be 
 discovered by measurement, in the following manner : 
 Sheet lead used in roofing and guttering is commonly 
 between seven and twelve pounds to the square 
 
 foot ; but the following table exhibits the particular 
 weight of a square foot for each of the several 
 thicknesses : — 
 
 . Thickness. 
 
 lbs. to a sq. foot. 
 
 Thickness. 
 
 lbs. to a sq. foot. 
 
 .10 
 
 5.899 
 
 .15 
 
 8.848 
 
 .11 
 
 6.489 
 
 .16 
 
 9.438 
 
 i 
 
 6.554 
 
 i 
 
 9.831 
 
 .12 
 
 7.078 
 
 .17 
 
 10.028 
 
 ■h 
 
 7.-373 
 
 .18 
 
 10.618 
 
 .13 
 
 7.668 
 
 .19 
 
 11.207 
 
 .14 
 
 8.258 
 
 1 
 
 11.797 
 
 i 
 
 8.427 
 
 .21 
 
 12.387 
 
 In this table, the thickness is set down in tenths 
 and hundredths, &c., of an inch ; and the annexed 
 corresponding numbers are the weights in avoirdu- 
 pois pounds and xoVtt of a pound ; so that the 
 weight of a square foot of ^d in- thick, -^iP^, is 5 i%^^a 
 pounds ; and the weight of a square foot, } in. in 
 thiclcness, is 6 ^\^^ pounds. Leaden pipe, of an 
 inch bore, is commonly thirteen or fourteen pounds 
 to the yard in lengtli. 
 
 GLAZING. 
 
 The business of this class of artificers consists in 
 putting glass into sashes and casements. Glaziers' 
 work may be classed under three distinct heads — 
 sash work, lead work, and fret work. 
 
 The tools requisite for the performances of the 
 first of these departments are, a diamond, a ranging 
 lathe, a short lathe, a square, a rule, a glazing knife, 
 a cutting chisel, a beading hammer, duster, and sash 
 tool ; and, in addition, for stopping in squares, a 
 hacking knife and hammer. 
 
 The diamond is a speck of that precious stone, 
 polished to a cutting point, and set in brass on an 
 iron socket, to receive a wooden handle, which is so 
 set as to be held in the hand in the cutting direction. 
 The top of the handle goes between the root of the 
 forefinger and the middle finger, and the hinder part 
 between the point of the forefinger and thumb ; there 
 is, in general, a notch in the side of the socket, which 
 should be held next to the lathe. Some diamonds 
 have more cuts than one. Plough diamonds have a 
 square nut on the end of the socket next the glass, 
 which, on running the nut square on the side of the 
 lathe, keeps it in the cutting direction. Glass grinders 
 have these plough diamonds without long handles, 
 
BUILDING. 
 
 165 
 
 as, in cutting their curious productions, they cannot 
 apply a lathe, but direct them by the point of their 
 middle finger, gliding along the edge of the glass. 
 
 The ranging lathe must be long enough to extend 
 rather beyond the boundary of the table of glass. 
 
 Ranging of glass is the cutting it in breadths as 
 the work may require, and is best done by one unin- 
 terrupted cut from one end to the other. 
 
 The square is used in cutting the squares from the 
 range, that they may with greater certainty be cut at 
 right angles. The glazing knife is used for laying 
 in the putty in the rabbets of the sash, for binding 
 in the glass, and for finishing the front putty. 
 
 Of the glass used in building, tlu-ee qualities are in 
 common use, denominated best, second, and third. 
 The best is that which is the purest metal and free 
 of blemishes, as blisters, specks, streaks, &c. ; the 
 second is inferior, from its not being so free from 
 these blemishes ; and the third is still inferior, both 
 in regard to quality and color, being of greener hue. 
 They are sold at the same price per crate ; but the 
 number of tables varies according to the quality. 
 Best twelve, second fifteen, and third eighteen 
 tables. 
 
 These tables are circular when manufactured, and 
 about 4 feet in diameter, having in the centre a knot, 
 to which, in the course of the process, the flashing 
 rod was fixed ; but for the safety of carriage and con- 
 venience of handling, as well as utility in practice, a 
 segment is cut off about 4 inches from the knot. 
 The large piece with the knot still retains the name 
 of table ; the smaller piece is technically called a slab. 
 From these tables being of a given size, it is reason- 
 able to suppose that, v.^hen the dimensions of squares 
 are such as cut the glass to waste, the price should 
 be advanced. 
 
 A superior kind of glass may be obtained at some 
 of the first houses in London, which is very flat and 
 of large dimensions, some of it being 2 feet 8 inches 
 by 2 feet 1 inch ; these are sold only in squares. 
 
 Rough glass is vv'ell adapted to baths and other 
 places of privacy ; one side is ground with emery or 
 sand, so that no objects can be seen through it, though 
 the light be still transmitted. 
 
 Plate glass is the most superior in quality, sub- 
 stance, and flatness, being cast in plates, and pol- 
 ished. The quantity of metal it contains must be 
 almost, if not altogether, colorless; that sort which is 
 tinged being of an inferior quality. Plate glass, when 
 
 used in sashes, is peculiarly magnificent ; and it can 
 be had of larger dimensions than any other Idnd of 
 glass. 
 
 Stained glass is of diflerent color, as red, orange, 
 yellow, green, blue, and purple. These colors are 
 fixed by burning, and are as durable as the glass. 
 
 La this country, window glass is iised of various 
 sizes, from 7 inches by 9 inches to 12 by 20 inches. 
 It is packed by the manufacturers in boxes, contain- 
 ing 50 or 100 square superficial feet. There are 
 many manufactories of this article in the United 
 States which usually produce glass of good quality ; 
 but the reputation of Boston plate glass stands de- 
 cidedly higher than any other, either of foreign or 
 domestic manufacture. The " New England Com- 
 pany," in Boston, manufacture stained glass in a style 
 not surpassed in Europe. 
 
 Glass can be bent to circular sweeps, which is 
 much used in London for shop windows, and is car- 
 ried to great perfection in covers, for small pieces of 
 statuary, &c. 
 
 The application of stained glass to the purposes 
 of glazing is called fretwork. This description of 
 work consists of working ground and stained glass, 
 in fine lead, into different patterns. In many cases, 
 family arms and other devices are worked in it. It 
 is a branch capable of great improvement, but at 
 present is much neglected. Old pieces are very much 
 esteemed, though the same expense would furnish 
 elegant modern productions. They are placed in 
 halls and stancase windows, or in some particular 
 chrurch windows. La many instances, they are intro- 
 duced where there is an unpleasant aspect, iia a place 
 of particular or genteel resort. 
 
 Lead work is used in inferior offices, and is in 
 general practice all through the country. Frames 
 intended to receive these lights are made with bars 
 across, to which the lights are fastened by leaden 
 bars, called saddle bars; and where openings are 
 wanted, a casement is introduced either of wood or 
 iron. Sometimes a sliding frame answers the same 
 purposes. Church windows are generally made in 
 this manner, in quaaTies or in squares. 
 
 The tools with which this work is performed are, 
 in addition to the foregoing, as follows : — 
 
 A vice, with different cheeks and cutters, to turn 
 out the different lands of lead, as the magnitude of 
 the window or the squares may requure. 
 
166 
 
 BUILDING. 
 
 The German vices, which are esteemed the best, 
 arc furnished with moulds, and turn out lead in a 
 variety of sizes. The bars of lead cast in these vices 
 are received by the mUl, which turns them out with 
 two sides parallel to each other, and about f of an 
 inch broad, witli a partition connecting the two sides 
 together, about J of an inch wide, forming on each 
 side a groove, nearly | by ^ of an inch, and about 6 
 feet long. 
 
 Besides a vice and moulds, there are a setting board, 
 latterkin, setting knife, resin box, tin, glazing irons, 
 and clips. 
 
 The setting board is tliat in which the ridge of the 
 light is marked and divided into squares, struck out 
 with a chalk line, or drawn with a lathe, which serves 
 to guide the workman. One side and end is squared 
 with a projecting bead or fillet. 
 
 The latterkin is a piece of hard wood pointed, to 
 run in the groove of the lead, and widen it for the 
 easier reception of the glass. 
 
 The setting- knife consists of a blade with a round 
 point, loaded with lead at the bottom, and termiiiat- 
 ing in a long, square handle. The square end of the 
 handle serves to force the square of glass tight in the 
 lead. All the intersections are soldered on both sides, 
 except the outside joints of the outer sides — that is, 
 where they come to the outer edge. These lights 
 should be cemented by pouring thin paint along the 
 lead bars, and filling up the chasms with dry whitmg, 
 to which, after the oil in the paint has secreted a lit- 
 tle, a little more dry whiting, or white lead, must be 
 added. This will dry hard, and resist the action of 
 the atmosphere. 
 
 PAINTING. 
 
 Painting, as applied to purposes of building, is the 
 application of artificial colors, compounded either 
 with oil or w^ater, in embellishing and preserving 
 wood, &c. 
 
 This branch of painting is termed economical, and 
 applies more immediately to the power which oil and 
 varnishes possess, of preventing the action of the at- 
 mosphere upon wood, iron, and stucco, by interposing 
 an artificial surface ; but it is here intended to use 
 the term more generally, in allusion to the decorative 
 part, and as it is employed by the architect, throughout 
 every part of his work, both externally and internally. 
 
 In every branch of painting in oil, the general pro- 
 cesses are very similar, or with such variations only 
 as readily occur to the workman. 
 
 The first coatings, or layers, if on wood or iron, 
 ought always to be of ceruse or white lead, of the 
 best quality, previously ground very fine in nut or 
 linseed oil, either over a stone with a muUer, or, as 
 that mode is too tedious for large quantities, passed 
 through a mill. If used on shutters, doors, or wain- 
 scotings, made of pine, it is very requisite to destroy 
 the effects of the knots, which are generally so com- 
 pletely saturated with turpentine as to render it, per- 
 haps, one of the most difficult processes in this busi- 
 ness. The best mode in common cases is to pass a 
 brush over the knots with ceruse ground in water, 
 bound by a size made of parchment or glue ; when 
 that is dry, paint the knots with white lead ground 
 in oil, to which add some powerful siccative, or drier, 
 as red lead, or litharge of lead ; about one part of the 
 latter. These must be laid very smoothly in the di- 
 rection of the grain of the wood. 
 
 When the last coat is dry, smooth it with pumice 
 stone, or give it the first coat of paint, prepared or 
 diluted with nut or linseed oil; after which, when 
 sufficiently dry, all the nail holes or other irregulari- 
 ties on the surface must be carefully stopped with a 
 composition of oil and Spanish white, commonly 
 known by the name of putty. The work must then 
 be painted with white lead and oil, somewhat diluted 
 with the essence of oil of turpentine, which process 
 should, if the work be intended to be left of a plain 
 white or stone color, be repeated not lessi than three 
 or four times ; and if of the latter color, a small quan- 
 tity of ivory or lampblack should be added. But if 
 the work is to be finished of any other color, either 
 gray, green, &c., it will be requisite to provide for 
 such color after the third operation, particularly if it 
 is to be finished flat, or, as the painters style it, dead 
 white, gray, fawn, &c. Li order to finish the work 
 flatted or dead, which is a mode much to be preferred 
 for all superior works, not only for its appearance, but 
 also for preserving the color and pm-ity of the tint, 
 one coat of the flatted color, or color mixed up with 
 a considerable quantity of turpentine, will be found 
 sufficient ; although in large surfaces it will be fre- 
 quently requisite to give two coats of the flatting 
 color to make it quite complete. Indeed, on stucco 
 it will be almost a general rule. 
 
 In all the foregoing operations, it must be observed 
 
BUILDING. 
 
 167 
 
 that some sort of drier is absolutely requisite ; a very 
 general and useful one is made by grinding in lin- 
 seed, or perhaps prepared oils, boiled, are better, about 
 two parts of the best white copperas, which must be 
 well dried with one part of litharge of lead ; the quan- 
 tity to be added will much depend on the dryness or 
 humidity of the atmosphere at the time of painting, 
 as well as the local situation of the building. It may 
 here be noticed, that there is a sort of copperas made 
 in England, and said to be used for some purposes 
 in medicine, that not only does not assist the opera- 
 tion of drying in the colors, but absolutely prevents 
 these colors drying, which would otherwise have done 
 BO in the absence of the copperas. 
 
 The best drier for all fine whites and other deli- 
 cate tints is sugar of lead, ground in nut oil ; but be- 
 ing very active, a small quantity, about the size of a 
 walnut, \\dll be sufficient for twenty pounds of color, 
 when the basis is white lead. 
 
 It does not appear that painting in oil can be ser- 
 viceable in stucco, unless the walls have been erected 
 a sufficient time to permit the mass of brick work to 
 have acquired a sufficient degree of dryness. When 
 stucco is on battened work, it may be painted over 
 much sooner than when prepared on brick. Indeed, 
 the greatest part of the art of painting stucco, so as 
 to stand or wear well, consists in attending to these 
 observations ; for whoever has observed the expan- 
 sive power of water, not only in congelation, but also 
 in evaporation, must be well aware that when it 
 meets with any foreign body obstructing its escape, 
 as oil painting, for instance, it immediately resists it, 
 forming a number of vesicles or particles, containing 
 an acrid lime water, which forces off the layers of 
 plaster, and frequently causes large defective patches, 
 not easily to be eradicated. 
 
 Perhaps in general cases, where persons are build- 
 ing on their own estates or for themselves, two or 
 three years are not too long to suffer the stucco to 
 remain unpainted, though frequently, in speculative 
 works, as many weeks are scarcely allowed to pass. 
 
 The foregoing precautions being attended to, there 
 can be no better mode adopted for priming, or laying 
 on the first coat on stucco, than by linseed or nut oil, 
 boiled with driers before mentioned — taking care, in 
 aU cases, not to lay on too much, so as to render the 
 surface rough and irregular, and not more than the 
 stucco will absorb. It should then be covered with 
 
 three or four coats of white lead, prepared as de- 
 scribed for painting or wainscoting, allowing each 
 coat sufficient time to dry hard. If time will permit, 
 two or three days between each layer will be advan- 
 tageous. When the stucco is intended to be finished 
 in any given tint, as gray, light green, &e., it wiU 
 then be proper, about the third coat of painting, to 
 prepare the ground for such a tint, by a slight ad- 
 vance towards it. Gray is made with white lead, 
 Prussian blue, ivory black, and lake ; sage green, pea, 
 and sea greens, with white, Prussian blue, and fine 
 yellows ; apricot and peach, with lake, white, and 
 Chinese vermilion ; fine yellow fawn color, with 
 burnt terra sienna, or umber and white ; and olive 
 greens, with fine Prussian blues, and Oxfordshire 
 ochre. 
 
 Distemper, or painting in water colors mbced with 
 size stucco or plaster, which is intended to be painted 
 in oU when finished, but not being sufficiently dry to 
 receive the oil, may have a coating in water colors, 
 of any given tint required, in order to give a more 
 finished appearance to that part of the building. 
 Straw colors may be made with French whites and 
 ceruse, or white lead and masticot, or Dutch pink. 
 Grays, full, with some whites and refiners' verditer. 
 An inferior gray may be made with blue-black, or 
 bone black, and indigo. Pea greens, with French 
 green, Olympian green, &c. Fawn color, with burnt 
 terra de sienna, or burnt umber and white, and so of 
 any intermediate tint. The colors should all be 
 ground very fine, and mixed with whiting and a size 
 made with parchment, or some similar substance. 
 Less than two coats will not be sufficient to cover 
 the plaster and bear out with a uniform appearance. 
 It must be recollected, that when the stucco is suffi- 
 ciently dry, and it is desurable to have it painted in 
 oil, the whole of the water colors ought to be re- 
 moved, which may be easily done by washing, and, 
 when quite dry, proceed with it after the direction 
 given on oil painting in stucco. 
 
 If oil plastering has become disfigured by stains, 
 or other blemishes, and if it be desired to have it 
 painted in distemper, it is, in this case, advisable to 
 give the old plastering, when properly cleaned off and 
 prepared, one coat, at least, of white lead ground in 
 oU, and used with spurits of turpentine, which will 
 generally fix old stains ; and, when quite dry, take 
 water colors very readily. 
 
 D. H. HILL LIBRARY 
 
 North Carolina State College 
 
TABLES 
 
 Slwwing the Weight of different Materials, Strength of Columns, ^c, ^c. 
 
 OP THE COHESIVE FORCE OF METALS AND WOODS. 
 
 Weighl or Force necessary to tear asunder one Square Inch, in 
 .Avoirdupois Pounds. 
 
 Copper, cast 29-500 
 
 " wire 61-200 
 
 Iron, cast; gray, 2 fusion. 30-680 
 
 " « English 52-000 
 
 " " French 70-000 
 
 « " " soft... 63-600 
 « " German 68-300 
 
 Iron, wrought 60-000 
 
 « " Swedish... 72-000 
 
 " " German . . .69-000 
 
 Ib9. 
 Ash, wliite, seasoned 14-000 
 
 " red, seasoned 17-800 
 
 Birch 15-000 
 
 Bay, 14-500 
 
 Beech ,11-500 
 
 Box 20-000 
 
 Cedar 11-400 
 
 Chestnut, sweet 10-500 
 
 Elm 13-400 
 
 Fir, strongest 12-000 
 
 " American 8-800 
 
 Locust 20-500 
 
 lbs. 
 
 Iron, wire 85-700-113- 
 
 " medium bar 60-000 
 
 « inferior bar 30-000 
 
 Lead, cast -880 
 
 " milled 3-320 
 
 Silver wire 38-257 
 
 Steel, soft 120-000 
 
 " fine 135-000 
 
 " razor, tempered . . 150-000 
 
 lbs. 
 
 Mahogany 21-800 
 
 " Spanish 12-000 
 
 Maple 10-500 
 
 Oak, American, white. . .11-500 
 
 " English 10-000 
 
 " seasoned 13-600 
 
 Pine, pitch 12-000 
 
 " Norway 13-000 
 
 Sycamore 13-000 
 
 Walnut 17-800 
 
 Willow 13-000 
 
 ON THE RESISTANCE TO CRUSHING WOOD. 
 
 According to the experiments of Rondelet, made on a hydro- 
 static press, on cubes of an inch in lengUi, it required from 5000 
 to 6000 pounds per square inch to crush oak; and under this 
 pressure its length was diminished more than one third. To crush 
 fir, it required from 6000 to 7000 pounds per square inch ; and 
 the length was reduced one half. Mr. Rennes's trials, wliich are 
 considered the most precise on this subject, afforded results con- 
 siderably lower than those of Rondelet. The following are the 
 results of liis experiments : — 
 
 Base 1 inch square, height 1 inch, Elm was crushed by 1,284 lbs. 
 
 " " " " " White deal " 1,928 
 
 " " " " " American pine " 1,606 
 
 " " " " « English oak " 3,860 
 
 " " " '•• " African teak " 8,480 
 
 " " " length 4 inches, " " " 5,147 
 
 ' 3 inches square, length 6 to 9, " oak " 60,480 
 
 The load a piece of timber will bear, when pressed in the di- 
 rection of its length, without risk of being crushed, may be found 
 
 by the following rule, when the pressure is exactly in the axis of 
 
 the piece : — 
 
 Rule. — Multiply the area of the piece in inches by the weight 
 that has been found capable of crushing a square inch of the same 
 kind of wood. (Sec the preceding experiments.) Then one fourth 
 of the product will give the greatest load in pounds that the piece 
 would bear with safety. 
 
 TO SHOW THE WEIGHT OR PRESSURE 
 A Column of Cast Iron will sustain ivith Safely. 
 
 Length or 
 
 
 
 
 
 
 
 
 
 
 Heigbt io 
 feet. 
 
 8 
 
 10 
 
 12 
 
 14 
 
 IC 
 
 18 
 
 20 
 
 22 
 
 24 
 
 
 Weight 
 
 Weight 
 
 Weight 
 
 Weight 
 
 Weight 
 
 Weight 
 
 Weight 
 
 Weight 
 
 Weight 
 
 
 in cwts. 
 
 in cwts. 
 
 in cwts. 
 
 in cwts. 
 
 in cwts. 
 
 in cwts. 
 
 in cwts. 
 
 in cwts. 
 
 in cwta. 
 
 24 in. 
 
 91 
 
 77 
 
 65 
 
 55 
 
 47 
 
 40 
 
 34 
 
 29 
 
 25 
 
 3 " 
 
 145 
 
 128 
 
 111 
 
 97 
 
 84 
 
 73 
 
 64 
 
 56 
 
 49 
 
 34 « 
 
 214 
 
 191 
 
 172 
 
 156 
 
 135 
 
 119 
 
 106 
 
 94 
 
 a3 
 
 4 " 
 
 288 
 
 266 
 
 242 
 
 220 
 
 198 
 
 178 
 
 160 
 
 144 
 
 130 
 
 44 " 
 
 379 
 
 354 
 
 327 
 
 301 
 
 275 
 
 251 
 
 229 
 
 208 
 
 189 
 
 5 " 
 
 479 
 
 452 
 
 427 
 
 394 
 
 365 
 
 337 
 
 310 
 
 285 
 
 262 
 
 6 " 
 
 573 
 
 550 
 
 525 
 
 497 
 
 469 
 
 440 
 
 413 
 
 386 
 
 360 
 
 7 « 
 
 989 
 
 959 
 
 924 
 
 887 
 
 848 
 
 808 
 
 765 
 
 725 
 
 686 
 
 8 " 
 
 1289 
 
 1259 
 
 1224 
 
 1185 
 
 1142 
 
 1097 
 
 1052 
 
 1005 
 
 959 
 
 9 " 
 
 1672 
 
 1640 
 
 1603 
 
 1561 
 
 1515 
 
 1467 
 
 1416 
 
 1364 
 
 1311 
 
 10 " 
 
 2077 
 
 2045 
 
 2007 
 
 1964 
 
 1916 
 
 1865 
 
 1811 
 
 17.55 
 
 1697 
 
 11 " 
 
 2520 
 
 2490 
 
 2450 
 
 2410 
 
 2358 
 
 2305 
 
 2248 
 
 2189 
 
 2127 
 
 12 " 
 
 3020 
 
 2970 
 
 2930 
 
 2900 
 
 2830 
 
 2780 
 
 2730 
 
 2670 
 
 2600 
 
 SHOWING THE WEIGHT 
 
 Of solid Cylinders of Cast Iron, twelve Indies long, in .Avoirdupois 
 Pounds. 
 
 Inches 
 
 Weipht 
 
 Inches 
 
 ^Veifiht 
 
 Inches 
 
 Weight 
 
 Inches 
 
 Weight 
 
 diam. 
 
 in lbs. 
 
 diam. 
 
 in lbs. 
 
 dinm. 
 
 in lbs. 
 
 diam. 
 
 in lbs. 
 
 1 
 
 1-394 
 
 24 
 
 15-492 
 
 44 
 
 50-193 
 
 8 
 
 158-638 
 
 i 
 
 1-897 
 
 2§ 
 
 17-080 
 
 4i 
 
 55-926 
 
 84 
 
 179-087 
 
 
 2-478 
 
 21 
 
 18-745 
 
 5 
 
 61-968 
 
 9 
 
 200-774 
 
 ij 
 
 3-137 
 
 25 
 
 20-488 
 
 5.i 
 
 68-319 
 
 94 
 
 223-704 
 
 li 
 
 3-873 
 
 3 
 
 22-308 
 
 5i 
 
 74-981 
 
 10 
 
 217-872 
 
 13 
 
 4-686 
 
 31 
 
 24-206 
 
 53 
 
 81-925 
 
 104 
 
 273-278 
 
 14 
 
 5-577 
 
 3,i 
 
 26-181 
 
 6 
 
 89-234 
 
 11 
 
 299-925 
 
 IS 
 
 6-545 
 
 31 
 
 28-234 
 
 6.i 
 
 96-825 
 
 114 
 
 327-811 
 
 IJ 
 
 7-591 
 
 34 
 
 30-364 
 
 64 
 
 104-726 
 
 12 
 
 356-935 
 
 n 
 
 8-714 
 
 m 
 
 .32-572 
 
 m 
 
 112-936 
 
 13 
 
 418-903 
 
 2 
 
 9-915 
 
 m 
 
 34-857 
 
 7 
 
 121-457 
 
 14 
 
 485-830 
 
 2J 
 
 11-193 
 
 35 
 
 37-219 
 
 7.^ 
 
 130-287 
 
 15 
 
 557-712 
 
 2i 
 
 12-548 
 
 4 
 
 39-660 
 
 74 
 
 139-428 
 
 16 
 
 634-552 
 
 21 
 
 13-981 
 
 4i 
 
 44-771 
 
 7} 
 
 148-878 
 
 
 
 Note. — Cubic inches of cast iron X "263 = lbs. avoirdupois. 
 Circular inches of cast iron X -2065 = lbs. avoirdupois. 
 
TABLES. 
 
 169 
 
 WEIGHT OP CAST-METAL CYLINDERS. 
 
 The cylinders are solid, each one foot in lengtli. 
 
 Diameter. 
 
 Iron Cylinders. 
 
 Copper Cylinders. 
 
 Brass Cylinders. 
 
 Lend Cylinders. 
 
 inch. 
 
 lbs. 
 
 Ills. 
 
 lbs. 
 
 U.S. 
 
 1 
 
 2-5 
 
 3-0 
 
 2-9 
 
 3-9 
 
 2 
 
 9-8 
 
 12-0 
 
 11-4 
 
 ].->-5 
 
 3 
 
 22-1 
 
 27-0 
 
 25-8 
 
 •M-8 
 
 4 
 
 39-3 
 
 47-9 
 
 45-8 
 
 (11-9 
 
 5 
 
 Gl-4 
 
 74-9 
 
 71-(i 
 
 90-7 
 
 6 
 
 88-4 
 
 107-8 
 
 103-0 
 
 139-3 
 
 7 
 
 120-3 
 
 14ti-8 
 
 140-2 
 
 189-f. 
 
 8 
 
 157-1 
 
 191-7 
 
 183-2 
 
 347-7 
 
 9 
 
 198-8 
 
 242-7 
 
 231-8 
 
 313-4 
 
 10 
 
 245-4 
 
 299-5 
 
 28G-2 
 
 387-0 
 
 WEIGHT OF CAST-IRON PIPES. 
 
 This table shoivs the weiirht ot' pipes one foot long, of bores 
 from 1 inch to 1"2 inches in diameter, advancinjr by one fourth 
 of an inch; and of tiiickncsses from one fourth of an inch to one 
 and one fourth inch, advancing by one eighth of an inch. 
 
 Bore. 
 
 K 
 
 K 
 
 U 
 
 H 
 
 « 
 
 % 
 
 1 
 
 IH 
 
 IH 
 
 inch. 
 
 lbs. 
 
 lbs. 
 
 lbs. 
 
 lbs. 
 
 lbs. 
 
 lbs. 
 
 lbs. 
 
 lbs. 
 
 lbs. 
 
 1 
 
 3-1 
 
 5-1 
 
 7-4 
 
 10-0 
 
 12-9 
 
 16-1 
 
 19-6 
 
 23-5 
 
 27-6 
 
 u 
 
 3-7 
 
 6-0 
 
 8-6 
 
 11-5 
 
 14-7 
 
 18-3 
 
 22-1 
 
 26-2 
 
 30-7 
 
 1* 
 
 4-3 
 
 6-9 
 
 9-8 
 
 13-0 
 
 16-6 
 
 20-4 
 
 24-5 
 
 29-0 
 
 .33-7 
 
 li 
 
 4-9 
 
 7-8 
 
 11-1 
 
 14-6 
 
 18-4 
 
 22-6 
 
 27-0 
 
 31-8 
 
 3G-8 
 
 2 
 
 5-5 
 
 8-8 
 
 12-3 
 
 16-1 
 
 20-3 
 
 24-7 
 
 29-5 
 
 34-5 
 
 39-9 
 
 2* 
 
 6-1 
 
 9-7 
 
 13-5 
 
 17-6 
 
 22-1 
 
 26-8 
 
 31-9 
 
 37-3 
 
 43-0 
 
 24 
 
 6-7 
 
 10-6 
 
 14-7 
 
 19-2 
 
 2:1-9 
 
 28-9 
 
 34-4 
 
 40-0 
 
 46-0 
 
 2} 
 
 7-4 
 
 11-5 
 
 10-0 
 
 20-7 
 
 25-7 
 
 31-1 
 
 36-8 
 
 42-8 
 
 491 
 
 3 
 
 8-0 
 
 12-4 
 
 17-2 
 
 22-2 
 
 27-6 
 
 3:3-3 
 
 39-3 
 
 45-6 
 
 52-2 
 
 3* 
 
 8-6 
 
 12-3 
 
 18-4 
 
 23-8 
 
 29-5 
 
 35-4 
 
 41-7 
 
 48-3 
 
 55-2 
 
 Si. 
 
 9-2 
 
 14-2 
 
 19-6 
 
 25-3 
 
 31-3 
 
 37-6 
 
 44-2 
 
 511 
 
 58-3 
 
 3? 
 
 9-8 
 
 1.5-2 
 
 20-9 
 
 26-9 
 
 33-1 
 
 39-7 
 
 46-6 
 
 53-8 
 
 61-4 
 
 4 
 
 10-4 
 
 16-1 
 
 22-1 
 
 28-4 
 
 35-0 
 
 419 
 
 49-1 
 
 56-6 
 
 64-4 
 
 4i 
 
 11-1 
 
 17-1 
 
 2;3-4 
 
 .30-0 
 
 36-9 
 
 44-1 
 
 51-6 
 
 59-4 
 
 G7-6 
 
 44 
 
 11-7 
 
 18-0 
 
 24-5 
 
 31-4 
 
 38-7 
 
 46-2 
 
 54 
 
 62-1 
 
 70-6 
 
 4| 
 
 12-3 
 
 18-9 
 
 25-8 
 
 a3-o 
 
 40-5 
 
 48-3 
 
 56-5 
 
 64-9 
 
 73-6 
 
 5 
 
 12-9 
 
 19-8 
 
 27-0 
 
 34-5 
 
 42-3 
 
 50-5 
 
 .58-9 
 
 67-6 
 
 76-7 
 
 5* 
 
 13-5 
 
 20-7 
 
 28-2 
 
 36-1 
 
 44-2 
 
 52-6 
 
 61-4 
 
 70-4 
 
 79-8 
 
 54 
 
 14-1 
 
 21-G 
 
 29-5 
 
 37-6 
 
 46-0 
 
 54-8 
 
 63-8 
 
 73-2 
 
 82-8 
 
 53 
 
 14-7 
 
 22-G 
 
 30-7 
 
 39-] 
 
 47-9 
 
 56-9 
 
 66-3 
 
 76-0 
 
 85-9 
 
 6 
 
 15-3 
 
 23-5 
 
 31-9 
 
 40-7 
 
 49-7 
 
 59-1 
 
 68-7 
 
 78-7 
 
 88-8 
 
 6.1 
 
 1(5-0 
 
 24-4 
 
 33-1 
 
 42-2 
 
 51-5 
 
 61-2 
 
 71-2 
 
 81-2 
 
 92-0 
 
 64 
 
 16-6 
 
 25-3 
 
 34-4 
 
 43-7 
 
 53-4 
 
 63-4 
 
 73-4 
 
 84.2 
 
 95-1 
 
 6J 
 
 17-2 
 
 26-2 
 
 35-6 
 
 45-3 
 
 55-2 
 
 65-3 
 
 76-1 
 
 87-0 
 
 98-2 
 
 7 
 
 17-8 
 
 27-2 
 
 36-8 
 
 46-8 
 
 56-8 
 
 67-7 
 
 78-5 
 
 89-7 
 
 101-2 
 
 7| 
 
 18-4 
 
 28-1 
 
 .38-1 
 
 48-1 
 
 58-9 
 
 69-8 
 
 81-0 
 
 92-5 
 
 104-2 
 
 74 
 
 19-0 
 
 29-0 
 
 39-1 
 
 49-9 
 
 60-7 
 
 72-0 
 
 83-5 
 
 95-3 
 
 107-4 
 
 7? 
 
 19-6 
 
 29-7 
 
 40-5 
 
 51-4 
 
 62-6 
 
 741 
 
 85-9 
 
 98-0 
 
 110-5 
 
 8 
 
 20-0 
 
 30-8 
 
 41-7 
 
 52-9 
 
 64-4 
 
 76-2 
 
 88-4 
 
 100-8 
 
 11:3-5 
 
 8;J 
 
 20-9 
 
 31-7 
 
 43-0 
 
 54-5 
 
 66-3 
 
 78-4 
 
 90-8 
 
 103-5 
 
 116-6 
 
 84 
 
 21-7 
 
 32-9 
 
 44-4 
 
 56-2 
 
 68-3 
 
 80-8 
 
 93-5 
 
 106-5 
 
 119-9 
 
 8* 
 
 22-1 
 
 33-6 
 
 45-4 
 
 57-5 
 
 70-0 
 
 82-7 
 
 95-7 
 
 109-1 
 
 122-7 
 
 9 
 
 22-7 
 
 34-5 
 
 46-6 
 
 .59-1 
 
 71-8 
 
 84-8 
 
 98-2 
 
 111-8 
 
 125-8 
 
 9} 
 
 23-3 
 
 35-4 
 
 47-9 
 
 60-6 
 
 73-6 
 
 87-0 
 
 100-6 
 
 114-6 
 
 128-9 
 
 94 
 
 2:^-9 
 
 .36-4 
 
 49-1 
 
 62-1 
 
 75-5 
 
 89-1 
 
 10:3-1 
 
 117-4 
 
 131-9 
 
 m 
 
 24-6 
 
 37-3 
 
 50-3 
 
 63-7 
 
 77-3 
 
 91-3 
 
 105-5 
 
 120-1 
 
 135-0 
 
 10 
 
 25-2 
 
 38-2 
 
 51-5 
 
 65-2 
 
 79-2 
 
 93-4 
 
 108-0 
 
 122-8 
 
 1:38-1 
 
 10^ 
 
 25-8 
 
 39-1 
 
 52-8 
 
 66-7 
 
 81-0 
 
 95-6 
 
 110-4 
 
 125-6 
 
 141-1 
 
 104 
 
 26-4 
 
 40-0 
 
 54-0 
 
 68-3 
 
 82-8 
 
 97-7 
 
 112-9 
 
 128-4 
 
 144-2 
 
 lOJ 
 
 27-0 
 
 41-0 
 
 55-2 ! 69-8 
 
 84-7 
 
 99-9 
 
 115-4 
 
 131-2 
 
 147-3 
 
 n 
 
 27-6 
 
 41-9 
 
 .56-5 
 
 71-3 
 
 86-5 
 
 102-0 
 
 117-8 
 
 1.33-9 
 
 1.50-3 
 
 lU 
 
 28-2 
 
 42-8 
 
 57-7 
 
 72-9 
 
 88-4 
 
 104-2 
 
 120-3 
 
 i:3G-7 
 
 153-4 
 
 1U 
 
 28-S 
 
 43-7 
 
 ,58-9 
 
 74-4 90-2 
 
 106-3 
 
 122-7 
 
 139-4 
 
 156-4 
 
 111 
 
 29-5 
 
 44-6 
 
 60-1 
 
 75-9 920 
 
 108-5 
 
 125-2 
 
 142-2 
 
 159-5 
 
 12 
 
 30-1 
 
 45-6 
 
 61-4 
 
 77-5 93-6 
 
 110-6 
 
 127 6 
 
 145-0 
 
 162-6 
 
 22 
 
 WEIGHT OF MET.VL PLATES. 
 
 This table shows the weight of a square foot of different meta 
 (dates, of thicknesses from one si.\tcenth of an inch to one inch, 
 advancing by a sixteenth. 
 
 Inch. 
 
 Wrought 
 
 Cast 
 
 Cast 
 
 Cast 
 
 Cast 
 
 Cast 
 
 Cast 
 
 Cast 
 
 Iron. 
 
 Iron. 
 
 Copper. 
 
 Brass. 
 
 Lead. 
 
 Zinc. 
 
 Tin. 
 
 Silver. 
 
 IClbs. 
 
 lbs. 
 
 lbs. 
 
 lbs. 
 
 lbs. 
 
 lbs. 
 
 lbs. 
 
 lbs. 
 
 lbs. 
 
 1 
 
 2-5 
 
 2-3 
 
 2-9 
 
 2-7 
 
 3-7 
 
 2-3 
 
 2-4 
 
 3-4 
 
 2 
 
 5-1 
 
 4-7 
 
 5-7 
 
 5-5 
 
 7-4 
 
 4-7 
 
 4-7 
 
 6-8 
 
 3 
 
 7-6 
 
 7-0 
 
 8-G 
 
 8-2 
 
 11-1 
 
 7-0 
 
 71 
 
 10-2 
 
 4 
 
 10-1 
 
 9-4 
 
 11-4 
 
 11-0 
 
 14-8 
 
 9-4 
 
 9-5 
 
 13-6 
 
 5 
 
 12-7 
 
 11-7 
 
 14-3 
 
 13-7 
 
 18-5 
 
 11-7 
 
 11-9 
 
 17-0 
 
 6 
 
 1.5-2 
 
 14-0 
 
 17-2 
 
 16-4 
 
 22-2 
 
 14-0 
 
 14-2 
 
 20-5 
 
 7 
 
 17-9 
 
 16-4 
 
 20-0 
 
 19-2 
 
 25-9 
 
 16-4 
 
 16-6 
 
 23-9 
 
 8 
 
 20-3 
 
 18-8 
 
 22-9 
 
 21-9 
 
 29-5 
 
 18-7 
 
 19-0 
 
 27-:5 
 
 9 
 
 22-8 
 
 21-1 
 
 25-7 
 
 24-6 
 
 .^3-2 
 
 21-1 
 
 21-4 
 
 30-7 
 
 10 
 
 25-4 
 
 2.3-5 
 
 28-G 
 
 27-4 
 
 36-9 
 
 23-4 
 
 23-7 
 
 :34-l 
 
 11 
 
 27-9 
 
 25-8 
 
 31-4 
 
 30-1 
 
 40-G 
 
 25-7 
 
 26-1 
 
 37-5 
 
 12 
 
 30-4 
 
 28-1 
 
 31-3 
 
 32-9 
 
 44-3 
 
 28-1 
 
 28-5 
 
 40-9 
 
 13 
 
 32-9 
 
 ;50-5 
 
 37-2 
 
 35-6 
 
 48-0 
 
 30-4 
 
 30-9 
 
 44-3 
 
 14 
 
 35-5 
 
 32-9 
 
 40-0 
 
 38-3 
 
 51-7 
 
 32-8 
 
 33-2 
 
 47-7 
 
 15 
 
 38-0 
 
 35-2 
 
 42-9 
 
 41-2 
 
 55-4 
 
 3,5-1 
 
 35G 
 
 51-1 
 
 16 
 
 40-6 
 
 37-6 
 
 45-8 
 
 43-9 
 
 59-1 
 
 37-5 
 
 38-0 
 
 54-6 
 
 TIIE WEIGHT, IN POUNDS, OF A FOOT IN LENGTH OF CAST IRON 
 
 inch. 
 
 i 
 
 1* 
 15 
 14 
 
 -3* 
 II 
 
 f 
 
 ? 
 6i 
 
 Square. 
 
 •781 
 
 1-756 
 
 3125 
 
 4-881 
 
 7-031 
 
 9-.56S 
 
 12-.520 
 
 1.5-818 
 
 19-531 
 
 23-e31 
 
 28-12.5 
 
 33-009| 
 
 38-281 
 
 43-943 
 
 -50-000 
 
 56-443 
 
 63-281 
 
 70-506: 
 
 78-120I 
 
 86-131: 
 
 94-531 
 
 103-318; 
 
 112-.500I 
 
 122058, 
 
 Hexagon 
 
 ■bio 
 
 1-528 
 
 2-703 
 
 4-225 
 
 085 
 
 8-281 
 
 10-815 
 
 13-990 
 
 16-900 
 
 20-450 
 
 24-340 
 
 28-565 
 
 33-131 
 
 38-031 
 
 43-271' 
 
 48-3531 
 
 54-7681 
 
 61-021 
 
 67-5151 
 
 74-549| 
 
 81-815 
 
 89-421 
 
 97-368 
 
 105-640 
 
 Octagon. 
 
 Circle. 
 
 -65U 
 
 -012 
 
 1-471 
 
 1-387 
 
 2-603 
 
 2-454 
 
 4-065 
 
 3-8-54 
 
 5-8-56 
 
 5-.521 
 
 7-971 
 
 7-515 
 
 10412 
 
 9-815 
 
 iqiian-i bquore. 
 di-l 
 
 13-lGS 
 16-2.561 
 19-6711 
 23-412 
 27-475 
 31818 
 3G-581 
 41-621 
 46-990 
 52-681 
 58-69(5 
 65 040 
 71-701 
 78 696 
 86-015 
 93-656 
 101-621 
 
 12-42.5 
 15-337 
 18-559 
 22-087 
 25-921 
 30-065 
 31-512 
 39-268 
 44-331 
 49-700 
 55-375 
 61-3.59 
 67-709 
 74-243 
 81-r2G 
 88 354 
 95-871 
 
 inch. 
 
 64 
 
 6J 
 
 7 
 
 7{ 
 
 7.-1 
 
 P 
 8] 
 84 
 
 9^* 
 % 
 
 10 
 
 104 
 10.| 
 lO^j 
 
 u 
 
 11} 
 in 
 11} 
 
 12 
 
 Hexagon 
 
 031 114-271 
 ,231 
 528 
 ■162 
 037 
 449 
 099 
 
 Octagon. 
 
 125 219 
 
 78l'201- 
 031 214- 
 968 257- 
 500 270- 
 318-281- 
 .53l|'298- 
 131,312- 
 125,.327- 
 216342- 
 ■281.357- 
 023373 
 ■000 389^ 
 
 087 177^ 
 412187 
 078!l99 
 078 210- 
 418 222- 
 100 234^ 
 105 247^ 
 471,2fl0^ 
 1.59 273^ 
 193'286' 
 .5.59;300- 
 268,314- 
 315329- 
 693,344- 
 32-5 3.59 
 ■475.374 
 
 103-696 
 Ul-82.5 
 120-372 
 128-986 
 138-056 
 147-415 
 157-078 
 167-049 
 177-328 
 187-912 
 199-203 
 600 210-800 
 793,221-506 
 3151233-318 
 163,245-437 
 341 257-8.59 
 82s!270-593 
 646 283-633 
 796 296-978 
 
 310-631 
 324-587 
 338-8.56 
 353-428 
 
 OF TIIE MT3IGHT OF A CUBIC FOOT OF VARIOUS SUBSTANCES, 
 In common Use for Building. 
 
 lbs. 
 
 Sand, solid 112-5 
 
 Sand, loose 95 
 
 Earth 93-75 
 
 Common Soil 124 
 
 Strong Soil 127 
 
 Clay 120 to 1.35 
 
 Clay and Stone 158 
 
 Brick 119 
 
 Granite 169 
 
 Marble 166 to 169 
 
 Sand, one cubic yard 3037 
 
 Common Soil, one cubic yard 3429 
 
170 
 
 TABLES. 
 
 THE NIT.MDER OP NAILS AND SPIKES TO THE POUND, 
 
 Of various Sizes, as manufactured at the Troy Iron and .Vail Fac- 
 tory, JV. Y. 
 
 1 
 
 Size of 
 
 Number 
 
 Boat 
 
 Diam. 
 
 No.Spikes 
 
 Sliip 
 
 Diam. 
 
 No.Spikes 
 
 Nail9. 
 
 to the lb. 
 
 Spikes. 
 
 of Rod. 
 
 to the lb. 
 
 Spikes. 
 
 of Rod. 
 
 to the lb. 
 
 3 penny 
 
 600 
 
 No. 4 
 
 i 
 
 13 
 
 No. 4 
 
 A 
 
 8 
 
 4 " 
 
 3G0 
 
 " 5 
 
 tV 
 
 8 
 
 " 5 
 
 1 
 
 6 
 
 6 " 
 
 200 
 
 " 6 
 
 i 
 
 5 
 
 " 6 
 
 i 
 
 5 
 
 8 " 
 
 110 
 
 " 7 
 
 i 
 
 4 
 
 " 7 
 
 S 
 
 3i 
 
 10 " 
 
 88 
 
 
 
 
 " 8 
 
 1 
 
 3 
 
 12 " 
 
 68 
 
 
 
 
 " 9 
 
 T^if 
 
 2 
 
 20 « 
 
 40 
 
 
 
 
 " 10 
 
 t\ 
 
 14 
 
 FOE FINT)ING THE STRAIN THAT M.VY BE APPLIED TO A HEMPEN 
 ROPE WITH S.VFETY. 
 
 Circum- 
 ference. 
 
 Pounds. 
 
 Circum- 
 ference. 
 
 Pounds. 
 
 Circum- 
 ference. 
 
 Pounds. 
 
 Circum- 
 ference. 
 
 Pownds. 
 
 1-00 
 
 200-0 
 
 3-00 
 
 1800-0 
 
 4-75 
 
 4512-5 
 
 6-50 
 
 8450-0 
 
 1-25 
 
 312-5 
 
 3-25 
 
 2112-5 
 
 5-00 
 
 5000-0 
 
 6-75 
 
 9112-5 
 
 1-50 
 
 450-0 
 
 3-50 
 
 2450-0 
 
 5-25 
 
 5512-5 
 
 7-00 
 
 9800-0 
 
 1-75 
 
 612-5 
 
 3-75 
 
 2812-5 
 
 5-50 
 
 6050-0 
 
 7-25 
 
 10512-5 
 
 2-00 
 
 800-0 
 
 4-00 
 
 3200-0 
 
 5-75 
 
 6612-5 
 
 7-50 
 
 112.50-0 
 
 2-25 
 
 1012-5 
 
 4-25 
 
 3G12-5 
 
 6-00 
 
 7200-0 
 
 7-75 
 
 12012-5 
 
 2-50 
 
 1250-0 
 
 4-50 
 
 4050-0 
 
 6-25 
 
 7812-5 
 
 8-00 
 
 12800-0 
 
 2-75 
 
 1512-5 
 
 
 
 
 
 
 
 
 
 WEIGHTS OP COPPER 
 
 AND SPIKES 
 
 
 
 Size. 
 
 Weight of 1 
 
 Cop'r Bolts] 
 
 per foot. 
 
 Number of Composition 
 Spikes to tlio 100 lbs. 
 
 Weipht of Sheatbing Copper, and 
 
 Yellow Sheatiiing Metal, 
 
 per sheet. 
 
 4 
 
 i 
 
 i 
 
 1 
 
 11 
 
 li 
 
 lbs. 
 
 -7567 
 1-18-24 
 1-7027 
 2-3176 
 3-0270 
 3-8312 
 4-9298 
 
 5 in. round head, 500 
 
 5 " square " 434 
 54" " " 400 
 
 6 « " " 377 
 64" " " 295 
 
 7 " " " 275 
 74" " " 210 
 
 8 " " " 200 
 84" " " 148 
 
 Size. 
 
 Weight. 
 
 Size. 
 
 Weight. 
 
 ounces. 
 
 14 
 16 
 
 18 
 20 
 22 
 
 lbs. ozs. 
 
 4 1 
 
 4 10 
 
 5 4 
 
 5 13 
 
 6 7 
 
 ounces. 
 
 24 
 
 26 
 28 
 30 
 32 
 
 lbs. ozs. 
 
 7 
 
 7 9 
 
 8 3 
 
 8 12 
 
 9 5 
 
 WEIGHT OF LEAD PIPES, TWELVE INCHES LONG. 
 
 SHOWING THE CONTENTS OF BRICK WALLS, NO. OF BRICKS, &;c. 
 
 This table is calculated in round numbers, and is not far from 
 the average of waUs made of the Cliarlestown, Fresh Pond, or 
 eastern bricks — the latter being about two tlurds tlie size of the 
 two former. 
 
 
 Width of Bricks 
 
 Thickness 
 
 No. of Bricks 
 
 Contents of 
 
 
 to a superficial 
 
 of Wall, in 
 
 to a superlicial 
 
 Willi, in su- 
 
 
 foot. 
 
 inches. 
 
 foot. 
 
 perlicial feet. 
 
 1000 
 
 1 
 
 4 
 
 7 
 
 143 
 
 ii 
 
 2 
 
 8 
 
 14 
 
 71 
 
 ^^ 
 
 3 
 
 12 
 
 21 
 
 474 
 
 t( 
 
 4 
 
 16 
 
 28 
 
 354 
 
 (£ 
 
 5 
 
 20 
 
 35 
 
 28} 
 
 (t 
 
 6 
 
 24 
 
 42 
 
 23} 
 
 u 
 
 7 
 
 28 
 
 49 
 
 204 
 
 (( 
 
 8 
 
 32 
 
 56 
 
 17} 
 
 (I 
 
 9 
 
 36 
 
 63 
 
 15} 
 
 1 cask of lime will plaster about 50 yards. 
 1 cask will skim about 200 yards. 
 4 casks will ordinarily employ 45 bushels of sand. 
 1 cask will ordinarily employ 5 pecks of hair. 
 00 yards of plastering will cover 1000 laths. 
 100 pounds of tlireeponny nails will lay 900 yards. 
 
 § in, thick, from 1 to 3 inches bore. 
 
 1 in. thick, from 1 to 3 inches bore. 
 
 s-ize. 
 
 Weight 
 
 Size. 
 
 Weight Size. 
 
 Weight 
 
 Size. 
 
 Weight Size. 
 
 Weight Size. 
 
 Weight. 
 
 1 
 
 2-19 
 
 li 
 
 3-64 
 
 24 
 
 5-09 
 
 1 
 
 4-85 
 
 1} 
 
 7-76 
 
 24 
 
 10-66 
 
 u 
 
 2-43 
 
 li 
 
 3-8;j 
 
 2S 
 
 5-a3 
 
 IJ 
 
 5-34 
 
 15 
 
 8-17 
 
 2g 
 
 11-15 
 
 li 
 
 2-66 
 
 2 
 
 4-12 
 
 2} 
 
 5-57 
 
 li 
 
 5-81 
 
 2 
 
 8-73 
 
 2} 
 
 11-63 
 
 15 
 
 2-91 
 
 2J 
 
 4-29 
 
 25 
 
 5-82 
 
 15 
 
 6-3 
 
 25 
 
 9-21 
 
 25 
 
 12-12 
 
 14 
 
 3-15 
 
 21 
 
 4-61 
 
 3 
 
 6-06 
 
 14 
 
 6-79 
 
 2i 
 
 9-7 
 
 3 
 
 12-61 
 
 11 
 
 3-39 
 
 21 
 
 4-t)2 
 
 
 
 lis 
 
 7-27 
 
 25 
 
 10-25 
 
 
 OF CYLINDRIC.VL ME.VSURES, 
 
 Designed for the computation of the contents of lead pipes, from 
 1 inch diameter to 3 and upwards ; also, cisterns of 10 feet di- 
 ameter and under ; and the quantity and weight of water in 
 pumps, suction pipes, &c., of 1 inch diameter and upwards. 
 
 Indies 
 
 (liaiuetcr. 
 
 Cubic feet 
 
 and decimal 
 
 parts. 
 
 Ale gallons 
 and parts. 
 
 Wine gal- 
 lons and 
 parts. 
 
 Weight of 
 
 water in lbs. 
 
 and parts. 
 
 Dry bushels 
 and parts. 
 
 1 
 
 •0055 
 
 -033 
 
 •04 
 
 •34 
 
 •0044 
 
 2 
 
 •0218 
 
 -134 
 
 •16 
 
 1^36 
 
 •0175 
 
 3 
 
 -0491 
 
 •301 
 
 ■37 
 
 3^06 
 
 •0394 
 
 4 
 
 •0873 
 
 ■534 
 
 -65 
 
 5^45 
 
 •0700 
 
 5 
 
 -136 
 
 -835 
 
 1-02 
 
 8-.52 
 
 •110 
 
 d. 6 
 
 -196 
 
 1-20 
 
 1-47 
 
 12-'27 
 
 •158 
 
 g 7 
 
 -207 
 
 1-64 
 
 2-00 
 
 16-70 
 
 •215 
 
 ■^ 8 
 
 -349 
 
 2-14 
 
 2-61 
 
 21-82 
 
 ■281 
 
 ° 9 
 
 -442 
 
 2-71 
 
 3-30 
 
 27-61 
 
 •355 
 
 ^ 10 
 
 •545 
 
 3-34 
 
 4-08 
 
 34-09 
 
 •438 
 
 S " 
 
 •660 
 
 4-04 
 
 4-94 
 
 41-25 
 
 -530 
 
 :^ 12 
 
 •785 
 
 4-81 
 
 5-88 
 
 49-09 
 
 •631 
 
 ^ 24 
 
 S 36 
 
 3-14 
 
 19-25 
 
 23-52 
 
 196-.36 
 
 2-521 
 
 7-07 
 
 43-30 
 
 52-92 
 
 441-79 
 
 5-68 
 
 R 48 
 ■1 50 
 
 12-57 
 
 77-00 
 
 94-08 
 
 785-44 
 
 10-10 
 
 13-64 
 
 83-55 
 
 102-00 
 
 852-21 
 
 11-00 
 
 W 60 
 
 19-64 
 
 l'20-30 
 
 146-88 
 
 1-227-19 
 
 15-78 
 
 72 
 
 28-28 
 
 173-20 
 
 211-51 
 
 17(i7-15 
 
 22-72 
 
 84 
 
 38-49 
 
 235-81 
 
 287-88 
 
 2405-28 
 
 30-92 
 
 96 
 
 50-27 
 
 308-00 
 
 370-01 
 
 3141-,59 
 
 40-39 
 
 108 
 
 C):3-62 
 
 389-79 
 
 475-89 
 
 397608 
 
 51-12 
 
 120 
 
 78-54 
 
 481-25 
 
 587-.52 
 
 4903-74 
 
 63-11 
 
 N. B. If the diameter should fall between any of the numbers 
 in the first column, the mean proportional contents may be found 
 by adding the two contents between which it falls, and dividing 
 by 2. Suppose it falls between 108 and 120 of the diameters, re- 
 quired the wine gallons in 114 inches, or 9 feet 6 inches diameter, 
 which falls between 587-52 
 
 and 475-89 
 
 2)106.3-41 
 
 Answer, 531-704 
 
 Or, if between 60 and 7"2, say 64 inches, or 5 feet 4 inches ; one 
 third of 12 is 4 ; tlien required the cubic feet and parts. 
 
 28-28 
 Subtract 19-64 
 
 Divide 
 
 Add 
 
 3)8-64 
 
 2-88 
 19-64 
 
 Answer, 22-52 
 
 Any depth may bo found, by multiplying by the depth any of 
 the numbers in the contents; as, required the number of ale gal- 
 lons in 24 inches diameter, at 6 feet deep. 
 
 19-25 
 6 
 
 Answer, 
 
 115-50 
 
GLOSSARY 
 
 OF 
 
 ARCHITECTURAL TERMS 
 
 Abacus The upper member of the capital of a column whereon the 
 architrave rests. Scammozzi uses this term for a concave mouMing 
 in the capital of the Tuscan pedestal, whicli, considering its etymol- 
 ogy, is an error. 
 
 Aedimest. The solid part of a pier, from which an arch springs. 
 
 Acanthus. A plant called in English hears hrccch, whose leaves 
 are employed for decorating the Corinthian and Composite capitals. 
 The leaves of the acanthus arc used on the bell of the capital, and 
 distinguish the two rich orders from tlic three others. 
 
 Accompaniments. Buildings or ornaments having a necessary con- 
 nection or dependence, and which serve to make a design more or 
 less complete — a characteristic pcculiai-ity of ornaments. 
 
 AccouPLEMENT. Among carpenters, a tie or brace ; sometimes the 
 entire work, when framed. 
 
 AcKOTEKiA. The small pedestals placed on the extremities and apex 
 of a pediment. 
 
 Admeasukement. Adjustment of proportions ; technically, an esti- 
 mate of the quantity of materials and labor of any kind used in a 
 budding. 
 
 Alcove. The original and strict meaning of this word, which is 
 derived from the Spanish atcoba, is that part of a bed-chamber in 
 which the bed stands, and is separated from the other parts of the 
 room by columns or pilasters. 
 
 Amphiprostyle. In ancient architecture, a temple with columns 
 in the rear, as well as in the front. 
 
 AiipniTnEATRE. A double theatre, of an elliptical form, on the ground 
 plan, for the exhibition of the ancient gladiatorial tights and other 
 shows. 
 
 Ajtcones. The consoles or ornaments cut on the keys of arches, 
 sometimes serving to support busts or other figures. 
 
 Annulet. A small, square moulding, which crowns or accompanies 
 a larger. Also, that fillet which separates the flutings of a column. 
 It is sometimes called a list, or listdla, which see. 
 
 ANTiE. A name given to pilasters attached to a wall. 
 
 Apophyge. That part of a column between the upper fillet of the 
 base and the cylindi-ical part of the shaft of the column, which 
 is usually curved into it by a cavetto. 
 
 ABiEOSTYLE. That style of building in which the columns are dis- 
 tant four, and sometimes five, diameters from each other ; but the 
 former is the proportion to which the term is usually applied. This 
 columnar arrangement is suited to the Tuscan order only. 
 
 Akcade. a series of arches, of apertures, or recesses, a continued 
 covered vault, or arches supported on piers or columns instead of 
 galleries. In Italian towns, the streets are lined with arcades like 
 those of Covcnt Garden and the Koyal Exchange. 
 
 Ancn. An artful arrangement of bricks, stones, or other materials. 
 
 in a curvilinear form, which, by their mutual pressure and support, 
 perform the oflice of a lintel, and can-y superincumbent weights — 
 the whole resting at its extremities upon piers or abutments. 
 
 Arch Bcttress, or Flying Buttress, (in Gothic architecture,) an 
 arch springing from a buttress or pier, and abutting against a wall. 
 
 Archeion. The most retired and secret place in Grecian temples, 
 used as a treasuiy, wherein were depo.<itcd the richest treasures 
 pertaining to the deity to whom tlio temple was dedicated. 
 
 Architect. One who designs and superintends the erection of 
 buildings. 
 
 Architrave. The lower of the primary divisions of the entabla- 
 ture. It is placed immediately upon the abacus of the capital. 
 
 Astragal. From the Greek word for a bone in the foot, to which 
 this moulding was supposed to bear a resemblance. A small 
 moulding, whose profile is semicircular, and which bears also the 
 name of talon, or tondino. The astragal is often cut into beads 
 and berries, and used in ornamental entablatures to separate the 
 faces of the architrave. 
 
 Attic. A tenn that expresses any thing invented or much used in 
 Attica, or the city of Athens. A low story erected over an order 
 of architecture, to finish the upper part of the building, being chiefly 
 used to conceal the roof, and give greater dignity to the design. 
 
 Attic Base. See Base. 
 
 Attic Order. An order of low pilasters, generally placed over some 
 other order of columns. It is improperly so called, for the aiTange- 
 ment can scarcely be called an order. 
 
 AuRiEL, or Oriel, (in Gothic architecture,) a window projecting out- 
 wards for private conference ; whence its appellation. 
 
 Balcony. A projection from the siu-face of a wall, supported by 
 consoles or pillars, and surrounded by a balustrade. 
 
 Baluster. A small pillar or pilaster, serving to support a rail. Its 
 form is of considerable variety, in difltrent examples. Sometimes it 
 is round ; at other times square : it is adorned with mouldings and 
 other decorations, according to the richness of the order it accom- 
 panies. 
 
 Balustrade. A connected range of a number of balusters on bal- 
 conies, terraces around altars, &c. See Baluster. 
 
 Band. A term used to express what is generally called a face or 
 facia. It more properly means a flat, low, square, profiled member, 
 without respect to its place. That from which the Corinthian or 
 other raodillions or the dentils project is called the modilUon band, 
 or the dentil band, as the case may be. 
 
 Bandelet. A .liminutive of the foregoing term, used to express any 
 narrow, flat moulding. The ta;nia on the Doric architrave is called 
 its bandelet. 
 
172 
 
 GLOSSARY OF ARCHITECTURAL TERMS. 
 
 Baxkek. a stone bench, on which masons cut and square their work. 
 Banquet. The footway of a bridge raised above the carriage-way. 
 Babrel Drain. A drain of the form of a Iiollow cylinder. 
 Base. The lower part of a column, moulded or plain, on which the 
 
 shaft is placed. 
 Basement. The lower part or story of a building, on which an 
 order is placed, with a base or plinth, die, and cornice. 
 
 Basil. A word used by carpenters, &c., to denote the angle to which 
 any edge tool is ground and fitted for cutting wood, &c. 
 
 Basin, en Coquille, that is, shaped like a shell. 
 
 Basin is likewise used for a dock. 
 
 Basket. A kind of vase in tho form of a basket, Blled with flowers 
 or fruits, seri'ing to terminate some decoration. 
 
 Basilica. A town or court hall, a cathedral, a palace, where kings 
 administer justice. 
 
 Basso Eilieto, or Bas Relief. The representation of figures pro- 
 jecting from a background, without being detached from it. Though 
 this word, in general language, implies all kinds of rilievoes, from 
 that of coins to more than one half of the thickness from the back- 
 ground. 
 
 Bath. A receptacle of water, appropriated for the purpose of 
 bathing. 
 
 Batten. A scantling of stuff from two to six inches broad, and 
 from § to two inches thick, used in the boai'ding of floors ; also upon 
 walls, in order to secure the lath on which the plaster is laid. 
 
 Batter. 'When a wall is built in a direction that is not per- 
 pendicular. 
 
 Battlements. Indentations on the top of a parapet, or wall, first 
 used in ancient fortifications, and afterwards applied to churches 
 and other buildings. 
 
 Bat, (in Gothic architectm'c,) an opening between piers, beams, or 
 muUions. 
 
 Bat Window. See Auriel. 
 
 Bead and Flusu Work. A piece of panel work, with a bead ran on 
 each edge of the included panel. 
 
 Bead and But Work. A piece of framing in which the panels are 
 flush, having beads stuck or run upon the two edges witU the grain 
 of the wood in their direction. 
 
 Bed Mouldings. Those mouldings in all the orders between the 
 corona and frieze. 
 
 Billet Moulding, (in Gothic architecture,) a cylindrical moulding, 
 discontinued and renewed at regular intervals. 
 
 Boltel, (in Gothic architecture,) slender shafts, whether an-anged 
 round a pier, or attached to doors, windows, &c. The term is also 
 used for any cylindrical moulding. 
 
 Boss, (in Gothic architecture,) a sculptured protuberance at the inter- 
 jnnction of the ribs in a vaulted roof. 
 
 Bossage. (A French term.) Any projection left rough on the face 
 of a stone for the purpose of sculpture, which is usually the last 
 thing finished. 
 
 BouLTiN. A name given to the moulding, called the egg or quarter 
 round. 
 
 Broach, (in Gothic architecture,) a spire, or polygonal pjTamid, 
 whether of stone or timber. 
 
 Bracket, (in Gothic ai'chitceture,) a projection to sustain a statue, or 
 other ornament, and sometimes supporting the ribs of a roof 
 
 Bulk. A piece of timber from four to ten inches square, and is some- 
 times called ranging timber. 
 
 Buttress, fi" Gotliic architecture,) a projection on the exterior of a 
 wall, to strengtheii the piers and resist the pressure of the arches 
 within. 
 
 Cabling. The filling up of the lower part of the fluting of a column 
 
 with a solid cylindrical piece. Flutings thus treated are said to be 
 
 cabled. 
 Caisson. A name given to the sunk panels of various geometrical 
 forms, symmetrically disposed in flat or vaulted ceilings, or in sofiits, 
 generally. 
 Canopt, (in Gothic architecture.) the ornamented dripstone of an arch. 
 
 It is usually of the ogee form. 
 Canted, (in Gothic architecture,) any part of a building having its 
 
 angles cut off is said to be canted. 
 Capital. The head or uppermost part of a column or pilaster. 
 Carpenter. An artificer whose business is to cut, fasliion, and join 
 timbers together, and other wood, for the purjjose of building : the 
 word is from the French charpcnlicr, derived from charpentie, which 
 signifies timber. 
 Carpentry, or that branch which is to claim our attention, is divided 
 into three principal heads, viz.. Constructive, Descriptive, and Me- 
 chanical ; of these, Descriptive carpentry shows the lines or methods 
 for forming every species of work in piano, by tho rules of geometry j 
 Constructive carpentry, the practice of reducing the wood into par- 
 ticular foi-ms, and joining the forms so produced, so as to make a 
 complete whole, according to the intention of the design ; and Me- 
 chanical carpentry displays the relative strength of the timbers, and 
 the strains to which tliey arc subjected by their disposition. 
 Cartoucd. Tlic same as raodillions, except tliat it is exclusively used 
 to signify those blocks or modillions at the caves of a house. See 
 Modillion, 
 Caryatides. Figures of women, which serve instead of columns to 
 
 support the entablature. 
 Casement. The same as Scotia, which see. The term is also used 
 
 for a sash hung upon hinges. 
 Cauliculus. The volute or twist under the flower, in the Corinthian 
 
 capital. 
 Cavetto. a hollow moulding, whose profile is a quadrant of a circle, 
 
 principally used in cornices. 
 Cell. Sec Naos. 
 
 Cincture. A ring, list, or fillet, at the top or bottom of a column, 
 
 serving to divide the shaft of the column from its cajiital and base. 
 
 Chamfer, (in Gothic architecture,) an arch, or jamb of a door, 
 
 canted. 
 Cdamp, (in Gothic architecture,) a flat surface in a wall or pier, as 
 
 distinguished from a moulding, shaft, or panel. 
 CiNQUEFOiL, (in Gothic architecture,) an ornamental figure, with five 
 
 leaves or points. 
 Column. A member in architecture of a cylindrical form, consisting 
 of a base, a shaft or body, and a capital. It ditfors from the pilaster, 
 which is square on the plan. Columns should always stand per- 
 pendicularly. 
 Composite Order. One of the orders of ai'chitecture. 
 Cope, Coping, (in Gothic architecture.) the stone covering the top of 
 
 a wall or parapet. 
 CoRREL, (in Gothic architecture,) a kind of bracket. The term is 
 generally used for a continued series of brackets on tho exterior of 
 a building supporting a projecting battlement, which is called a 
 corbel table. 
 CoKiNiniAN Order. One of the orders of architecture. 
 Cornice. The projection, consisting of several mcmbci-s, which 
 crowns or finishes an entablature, or tho body or part to which 
 it is annexed. The cornice used on a pedestal is called the cap of 
 the pedestal. 
 Corona, is that flat, square, and massy member of a cornice, more 
 usually called the drip or larmier, whose situation is between the 
 cimatium above and the bed moulding below. Its use is to caiTV 
 the water, drop by drop, from the building. 
 
GLOSSARY OF ARCHITECTURAL TERMS. 
 
 173 
 
 Corridor. A gallery ov o])Cn communication to the diffoi-cnt apart- 
 ments of a house. 
 
 COKSA. The name given by Vitruvius to a platbancl or square facia, 
 whose height is more tlian its i)rojcctiiro. 
 
 Crenelle, (in Gothic architecture.) tlie opening of an embattled 
 parapet. 
 
 Crest, (in Gothic architecture,) a crowning ornament of leaves run- 
 ning on the top of a screen or other ornamental work. 
 
 Crocket, (in Gothic architecture,) an ornament of leaves, running up 
 the sides of a gable, or ornamented canopy. 
 
 CcPOLA. A small room, either circular or polygonal, standing on the 
 top of a clonic. By some it is called a lantern. 
 
 CnsuioxED. See Frieze. 
 
 Cusp, (in Gothic architecture.) a name for the segments of cutIcs 
 forming the trefoil, quatrcfoil, &c. 
 
 Ctma, called also Ci/malium, its name arising from its resemblance to 
 a wave. A moulding which is hollow in its upper part, and swelling 
 below. 
 
 Decagon. A plain figure, having ten sides and angles. 
 
 Decastyle. A building having ten columns in front. 
 
 Decejipeda. (Decern, ten, and pes, foot, Lat.) A rod of ten feet, 
 used by the ancients in measuring. It was subdivided into twelve 
 inches in each foot, and ten digits in each inch ; like surveyors' rods 
 used in measuring short distances, &c. 
 
 Decimal Scale. Scales of this kind are used by draughtsmen, to 
 regulate the dimensions of their drawings. 
 
 Decoration. Any thing that enriches or gives beauty and ornament 
 to the orders of architecture. 
 
 Demi Metope. The half a metope, which is found at the retiring or 
 projecting angles of a Doric frieze. 
 
 Dentils. Small, square blocks or projections used in the bed mould- 
 ings of the cornices in the Ionic, Corinthian, Composite, and some- 
 times Doric orders. 
 
 Details of an Edifice. Drawings or delineations for the use of 
 builders, othenvise called working plans. 
 
 Diagonal Scale is a scale subdivided into smaller parts by second- 
 ary intersections or oblique lines. 
 
 Diameter. The line in a circle passing from the circumference 
 through the centi'e. 
 
 Diamond. A sharp instrument formed of that precious stone, and 
 used for cutting glass. 
 
 Diapered, (in Gothic architecture,) a panel, or other flat surface, 
 sculptured with flowers, is said to be diapered. 
 
 Diasttle. That intercolumniation or space between columns, con- 
 sisting of three diameters — some say fom- diameters. 
 
 Die, or Dte. A naked, square cube. Thus the body of a pedestal, 
 or that part between its base and cap, is called the die of the pedes- 
 tal. Some call the abacus the die of the capital. 
 
 Dimension. (D/mrf/er, Lat.) In geometry, is either length, breadth, 
 or thickness. 
 
 Diminution. A term expressing the gradual decrease of thickness 
 in the upper part of a column. 
 
 Dipteral. A term used by the ancients to express a temple with a 
 double range of columns in each of its flanks. 
 
 Dodecagon. A regular polygon, with twelve equal sides and 
 angles. 
 
 DoDECASTVLE. A building having twelve columns in front. 
 
 Dome. An arched or vaulted roof, springing from a polygonal, circu- 
 lar, or elliptic plane. 
 
 Doric Order. One of the five orders of architecture. 
 
 Dormant, or Dormer Window, (in Gothic architecture,) a window 
 set upon the slope of a roof or spire. 
 
 DooKS. Flat pieces of wood, of the shape and size of a brick, in- 
 serted in brick walls, sometimes called plugs or wooden bricks. 
 
 Door. The gate or entrance of a house, or other building, or of an 
 apartment in a house. 
 
 Dormitory. A sleeping-room. 
 
 Drawing, or Witiidrawino-uoom. A lai-ge and elegant apart- 
 ment, into which the company witlidraw after dinner. 
 
 Dressing-room. An apartment contiguous to the sleeping-room, 
 for the convenience of dressing. 
 
 Drip, in (Gothic architectm-e,) a moulding much resembling the ci- 
 matium of Roman architecture, and used for the same purpose as a 
 canopy over the arch of a door or window. 
 
 Drops. Sec GiUkc. 
 
 EcniNUS. The same as the ovolo or quarter round ; but perhaps it is 
 only called echinus with propriety. 
 
 Edging. The reducing the edges of ribs or rafters, that they may 
 range together. 
 
 Elbows of a Window. The two panelled flanks, one under each 
 shutter. 
 
 Elevation. A geometrical projection drawn on a plane, perpendic- 
 ular to the horizon. 
 
 Embankments arc artificial mounds of earth, stone, or other materi- 
 als, made to confine rivers, canals, and reseiwou-s of water within 
 their prescribed limits ; also for levelling up of railroads, &c. 
 
 Embrasure, (in Gothic arcliitccture,) the same as Crenelle, which sec. 
 
 Encaepcs. The festoons on a frieze, consisting of fruits, flowers, and 
 leaves. See Festoon. 
 
 Entablature. The assemblage of parts supported by the column. 
 It consists of three parts — the architrave, frieze, and cornice. 
 
 Entail, (in Gothic architecture,) delicate carving. 
 
 Entasis. The slight curvature of the shafts of ancient Grecian col- 
 umns, particularly the Doric, which is scai'cely perceptible, and 
 beautifully graceful. 
 
 Entresol. See Mezzanine. 
 
 Epistylum. The same as Architrave, which see. 
 
 EusTYLE. That intercolumniation which, as its name would import, 
 the ancients considered the most elegant, namely, two diameters 
 and a quai-ter of a column. Vitravius says this manner of arran- 
 ging columns exceeds all others in sti'ength, convenience, and beauty. 
 
 Facade. The fi\ce or front of any considerable building to a street, 
 court, garden, or other place. 
 
 Facia. A flat member in the entablature or elsewhere, being in fact 
 nothing more than a band or broad fillet. 
 
 Fane, Phane, Vane, (in Gothic architecture,) a plate of metal usu- 
 ally cut into some fantastic form, and turning on a pivot, to deter- 
 mine the course of the wind. 
 
 Fastigium. See Pediment. 
 
 Feather-edged Boards are narrow boards, made thin on one 
 edge. They are used for the facings or boai-ding of wooden walls. 
 
 Festoon. An ornament of carved work, representing a wreath or 
 garland of flowers or leaves, or both, interwoven with each other. 
 
 Fillet. The small, square member which is placed above or below 
 the various square or curved members in an order. 
 
 FiNiAL, (in Gothic architecture,) the ornament, consisting usually of 
 four crockets, which is employed to finish a pinnacle, gable, or 
 canopy. 
 
 Flank. The least side of a pavilion, by which it is joined to the 
 main building. 
 
 Flatnino, in inside house painting, is the mode of finishing without 
 leaving a gloss on the surface, which is done by adding the spirits 
 of turpentine to unboiled linseed oil. 
 
174 
 
 GLOSSARY OF ARCHITECTURAL TERMS. 
 
 Flieks are steps in a series which are parallel to each other. 
 
 Fligut of Staies is a series of steps, from one landing-place to 
 another. 
 
 Floors. The bottom of rooms. 
 
 Flutings. The vertical channels on the shafts of columns, ■which 
 are usually rounded at the top and bottom. 
 
 Folding Docks arc made to meet each other from opposite jambs, 
 on which they are hung. 
 
 Foliage. An ornamental distribution of leaves or flowers on various 
 parts of the building. 
 
 FoREsnoKTEX. A term applicable to the drawings or designs in 
 which, from the obliquity of the \iew, the object is represented as 
 receding from the opposite side of the plane of the projection. 
 
 FonNDATiON. That part of a building or wall which is below the 
 surface of the ground. 
 
 Foot. A measure of twelve inches, each inch being three barleycorns. 
 
 Fbame. The name given to the wood work of windows enclosing 
 glass, and the- outward work of doors or windows, or window shut- 
 ters, enclosing panels ; and in carpentry, to the timber work sup- 
 porting floors, roofs, ceilings, or to the intersecting pieces of timbers 
 forming partitions. 
 
 Feet. A kind of ornamental work, which is laid on a plane surface. 
 The Greek fret is formed by a series of right angles of fiUcts, of 
 various forms and figures. 
 
 Fkieze, or Frize. The middle member of the entablature of an 
 order, which separates the architrave and the cornice. 
 
 Frontispiece. The face or fore front of a house; but it is a term 
 more usually applied to its decorated entrance. 
 
 Front. A name given to the principal interior facade of a building. 
 
 Frustum. A piece cut oft' from a regular figure ; the frustum of a 
 cone is the part that remains when the top is cut oft' by an intersec- 
 tion parallel to its base, as the Grecian Doric column without a base. 
 
 FuRRiNGS are flat pieces of timber, plank, or board, used by carpen- 
 ters to bring dislocated work to a regular surface. 
 
 FcST. The shaft of a column. See Shaft. 
 
 Gable, (in Gothic architecture,) the triangularly-headed wall which 
 covers the end of a roof. 
 
 Gable Window, (in Gothic architecture,) a window in a gable. 
 These are generally the largest windows in the composition, fre- 
 quently occupying nearly the whole space of the wall. 
 
 Gablet, (in Gothic architecture,) a little gable. See Canopij. 
 
 Gage. In carpentry, an instrument to strike a line parallel to the 
 straight side of any board or piece of stuft". 
 
 Gain. The bevelled shoulder of a binding joist. 
 
 Garland, (in Gothic architecture,) an ornamental blind surrounding 
 the top of a tower or spire. 
 
 Glyphs. The vertical channels sunk in the triglyphs of the Doric 
 frieze. 
 
 GoLA, or GuLA. The same as Ogee, which see. 
 
 Gorge. The same as Cavcilo, which see. 
 
 Gouge. A chisel of a semicircular form. 
 
 Granite. A genus of stone much used in building, composed chiefly 
 of quartz, feldspar, and mica, forming rough and large masses of 
 very great hardness. 
 
 Groin, (in Gothic architecture,) the diagonal line formed by the inter- 
 section of two vaults in a roof. 
 
 Groined Ceiling. A surface formed of three or more curved sur- 
 faces, so that every two may form a groin, all the groins terminating 
 at one extremity in a common point. 
 
 Groove, or Mortise. The channel made by a joiner's pUne in the 
 edge of a moulding, style, or rail, to receive the tenon. 
 
 Gbound Floor. The lowest story of a building. 
 
 Ground Plane. A line forming the ground of a design or picture, 
 
 which line is a tangent to the surface of the face of the globe. 
 Ground Plot. The ground on which a building is placed. 
 Grounds. Joiners give this name to narrow strips of wood put in 
 
 walls to receive the laths and plastering. 
 GuTT^, or Drops. Those frusta of cones in the Doric entablature 
 
 which occur in the arcliitrave below the ttenia under each triglyph. 
 Gutters are a kind of canals iu the roofs of houses, to receive and 
 
 carry off rain water. 
 
 Halving. The jtmction of two pieces of timber, by inserting one into 
 
 the other; in some cases, to be preferred to mortising. 
 Hand Railing. The art of forming liand rails round circular and 
 
 elliptic well holes without the use of the cylinder. 
 H-iNGiNG Style of a Door is that to which the hinges are fixed. 
 Heel of a Rafter. The end or foot that rests upon the wall plate. 
 Helical Line op a Hand Rail. The line, or spii-al line, represent- 
 ing the form of the hand rail before it is moulded. 
 Helix. The curling stalk under the flower iu the Corinthian capital. 
 
 See Caulicuhis. 
 Hem. The spiral projecting part of the Ionic cupital. 
 Hexastyle. a building having six columns in front. 
 Hood Mould, (in Gothic architecture.) See Drip. 
 Hook Pins. The same as draio bore pins, to keep the tenons in their 
 
 place, while in the progress of framing ; the pin has a head or notch 
 
 in the outer end, to draw it at pleasure. 
 Hyp.ethral. Open at top ; uncovered by a roof. 
 HvPERTnYROx. The lintel of a doorway. 
 HvpoTRACnELiUM. A term given by Vitruvius to the slenderest part 
 
 of the shaft of a column, where it joins the capital. It signifies the 
 
 part under the neck. 
 
 Inciinooraph Y. The transverse section of a building, which represents 
 the circumference of the whole edifice ; the ditfcrcnt rooms and 
 apartments, with the thickness of the walls ; the dimensions and sit- 
 uation of the doors, windows, chimneys ; the projection of columns, 
 and every thing that could be seen in such a section, if rcilly made 
 in a building. 
 
 Impost. The layer of stone or wood that crowns a door post or pier, 
 and which supports the base line of an arch or arcade ; it generally 
 projects, iind is sometimes formed of an assemblage of mouldings. 
 
 Inch. The twelfth part of a foot. For tlie purpose of reckoning in 
 decimal fractions, it is divided into ten parts or integers. 
 
 Inclined Plane. One of the mechanical powers used for raising 
 ponderous bodies, in many instances, of immense weight ; a declivity 
 of a hill, &c. 
 
 Insular Column is a column standing by itself. 
 
 Insulated. Detached from another building. 
 
 Intaglio. Any thing with figures in relief on it. 
 
 Intercolumnhtion. The distance between two columns. 
 
 Intrados. The undcr-cuned surface or soflit of an arch. 
 
 Inverted Arches. Such as have their intrados below the centre or 
 axis. 
 
 Ionic Order. One of the orders of arohitcctm-c. 
 
 Jack Plane. A plane about eighteen inches long, to prepare for the 
 trying plane. 
 
 Jack Rafters. The jack timbers, which arc fastened to the hip raft- 
 ers and the wall plates. 
 
 Jambs. The side pieces of any opening in a w.ill, which bear the piece 
 that discharges the superincumbent weight of such wall. 
 
 Joinery, in building, is confined to the nicer and more ornamental 
 parts. 
 
GLOSSARY OF ARCHITECTURAL TERMS. 
 
 stuff for joints, 
 
 Jointer. A tool used for straightening and preparing stud 
 &c. Tliis jointer is about two feet eight or ten inches Ion 
 
 Kerk. Tlio slit or cut in a piece of timber, or in a stone, by a saw. 
 Kjng Post. The middle post in a section of rafters. 
 
 LABEt, (in Gothic architecture.) a name for the drip or liood moulding 
 of an arch when it is returned square. 
 
 LACtrxAE, or Laqueae. The same as Soffit. 
 
 Laxtekjj, (in Gothic architecture,) a turret or tower placed above a 
 building, pierced either with windows to admit light, or liolcs to lot 
 out steam. 
 
 LARMiEn. Called also Corona, which see. 
 
 Lath. A naiTow slip of wood, 1} to \h inclics wide, 4 to 3 inch thick, 
 and fom- feet long, used in plastering. 
 
 Leaves. Ornaments representing natural leaves. The ancients used 
 two sorts of leaves, natural and imaginary. The natural were those 
 of the laurel, palm, acanthus, and olive; but they took such liberties 
 in the form of these, that they might almost bo said to be imagi- 
 nary, too. 
 
 Level. A surface which inclines to neither side. 
 
 Lining. Covering for the interior, as casing is covering for the exte- 
 rior surface of a building. 
 
 Lintel. A piece of timber or stone, placed horizontally over a door, 
 ■window, or other opening. 
 
 List, or Listel. The same as fillet or annulet. 
 
 Listing. The catting the sapwood out from both edges of a board. 
 
 Loop, (in Gothic architectui'C,) a small, narrow window. 
 
 Louvre, (in Gothic architecture.) See Lantern. 
 
 LuFFES Boarding. The same as blind slats. 
 
 Machicolations, (in Gothic architecture,) small openings in an em- 
 battled parapet, for the discharge of missile weapons upon the assail- 
 ants. Frequently these openings are underneath the parapet ; in 
 which case, the whole is brought forward and supported by 
 corbels. 
 
 SIechanical Cabpentrt. That branch of earpentiT which teaches 
 the disposition of the timbers according to their relative strength, 
 and the strains to which they ai-e subjected. 
 
 Mediaeval AKcniTECTUEE. The architecture of England, France, 
 Germany, &c., during the middle ages, including the Norman and 
 early Gothic styles. 
 
 Members. (Jicmfiriini, Lat.) The different parts of a building; the 
 different parts of an entablature ; the different mouldings of a cor- 
 nice, &c. 
 
 Metope. The square space between two triglyphs of the Doric order. 
 It is sometimes left plain, at other times decorated with sculpture. 
 
 Mezzanine. A low story introduced between two principal stories. 
 
 Minerva Polias. A Grecian temple at Athens. 
 
 Minute. The sixtieth part of the diameter of a column. It is the 
 subdivision by which architects measure the small parts of an order. 
 
 Mitre. An angle of forty-five degrees ; a half of a right angle. 
 
 Modillion. An ornament in the entablature of richer orders, resem- 
 bling a bracket. 
 
 Module. The semi-diameter of a column. This term is only prop- 
 erly used when speaking of the orders. As a semi-diameter, it con- 
 sists of only thirty minutes. See Minute. 
 
 Mosaic. A kind of painting representing cubes of glass, &c., and is 
 formed of different colored stones, for paving, &c. Specimens of 
 this kind have been found among the ruins of antiquity. 
 
 Mouldings. Those parts of an order which are shaped into various 
 curved or square foiins. 
 
 Mouth. The same as Cavetto, which see. 
 
 175 
 
 MuTULE. A projecting ornament of the Doric cornice, which occu 
 
 pies the place of the modillion, in imitation of the ends of rafters. 
 MuLLiON, (in Gothic architecture,) the framework of a window. 
 
 Naked. The unornamcntcd, plain surface of a wall, column, or other 
 
 part of a building. 
 Naos, or Cella. The part of a temple within the walls. 
 Newel. The solid, or imaginaiy solid, when the stairs are open in 
 
 the centre, round which the stops are turned about. 
 Niche. A square or cylindrical cavity in a wall or other solid. 
 
 Obelisk. A tall, slender frustum of a pyramid, usually placed on a 
 pedestal. The difference between an obelisk and a pyramid, inde- 
 pendent of the former being only a portion of the latter, is, that it 
 always has a small base in proportion to its height. 
 
 Octastyle. a building with eight columns in front. 
 
 Ogee, or Ogive. The same as Cijma, which see. 
 
 Order. An assemblage of parts, consisting of a base, sh.-vft, capital, 
 architrave, frieze, and cornice, whose several services, requiring some 
 distinction in strength, have been contrived or designed in five sev- 
 eral species — Tuscan, Doric, Ionic, Corinthian, and Composite; 
 each of which has its ornaments, as well as general fabric, propor- 
 tioned to its strength and character. 
 
 Oedonnance. The aiTangement of a design, and the disposition of 
 its several parts. 
 
 Oele. (Ttal.) A fillet or band under the ovolo of the capital. Pal- 
 ladio applies the term also to the plinth of the base of a column or 
 pedestal. 
 
 OvoLO. A moulding sometimes called a quarter round, from its pro- 
 file, being the quadrant of a circle. When sculptured, it is called an 
 echinus, which see. 
 
 Panel. A thin board, having all its edges inserted in the groove of a 
 
 suiTounding frame. 
 Paeapet. From the Italian Parapetto, breast high. The defence 
 
 round a terrace or roof of a building. 
 Pakastat^. Pilasters standing insulated. 
 
 Pavilion. A tuiTet or small building generally insulated, and com- 
 prised beneath a single roof. 
 Pedestal. The substruction under a column or wall. A pedestal 
 
 under a column consists of three parts — the base, the die, and the 
 
 cornice or cap. 
 Pediment. The low, triangular, crowning ornament of the front of 
 
 a building, or of a door, window, or niche. 
 Pend, (in Gothic architecture,) a vaulted roof without groining. 
 Pendant, (in Gothic architecture,) a hanging ornament in highly- 
 - enriched vaulted roofs. 
 
 Pinnacle, (in Gothic architecture,) a small spire. 
 Peripteral. A term used by the ancients to express a building 
 
 encompassed by columns, forming, as it were, an aisle round the 
 
 building. 
 Peristylium. In Greek and Roman houses, a com't, square, or 
 
 cloister. 
 Perspective is the science which teaches us to dispose the lines and 
 
 shades of a picture, so as to represent, on a plane, the image of ob- 
 jects exactly as they appear in nature. 
 Piazza. A continued archway, or vatilting, supported by pillars or 
 
 columns ; a portico. 
 Pier. A solid between the doors or the windows of a buildjng. Tie 
 
 square or other formed mass or post to which a gate is hung. 
 Pilaster. A square pillar engaged in a wall. 
 Pile. A stake or beam of timbers, driven firmly into the ground. 
 Pillar. A column of irregular form, always disengaged, and always 
 
176 
 
 GLOSSARY OF ARCHITECTURAL TERMS. 
 
 deviating from the proportions of tlie orders ; whence tlie distinction 
 between a pillar and a column. 
 
 Platband. A square moulding, whose projection is less than its 
 height or breadth. 
 
 Plinth. The square solid laider the base of a column, pedestal, or 
 wall. 
 
 PoKcn. An arched vestibule at the entrance of a church or other 
 building. 
 
 Portico. A place for walking under shelter, raised with arches in the 
 manner of a gallei7 ; the portico is usually vaulted, but has some- 
 times a flat soffit or ceiling. This word is also used to denote the 
 projection before a church or temple supported by columns. 
 
 Post. A4)iece of timber set erect in the earth. Perpendicular tim- 
 bers of the wooden frame of a building. 
 
 PoSTicnJi. The back door of a temple ; also the portico behind the 
 temple. 
 
 PiiiNCiPAL Eaftees. The two inclined timbers which support the 
 roof 
 
 Peofile. The contour of the different parts of an order. 
 
 Peojecture. The prominence of the mouldings, and members be- 
 yond the naked surface of a column, wall, &c. 
 
 Proscenium. The front part of the stage of the ancient theatres, on 
 which the actors performed. 
 
 Prostyle. A building or temple with columns in front only. 
 
 PuELiNS. Pieces of timber framed horizontally from the principal 
 rafters, to keep the common rafters from sinking in the middle. 
 
 PvcNOSTTLB. An intercolumniatiou equal to one diameter and 
 a half. 
 
 Pyramid. A solid, with a square, polygonal, or triangular base, ter- 
 minating in a point at top. 
 
 Quarter Eound. See Ocolo and Echinus. 
 
 QuATEEFOiL, (in Gothic architecture,) an ornament in tracery, con- 
 sisting of four segments of circles, or cusps, within a circle. 
 
 Quirk Mouldings. The convex part of Grecian mouldings, when 
 they recede at the top, forming a rcOnticcnt angle with the surface 
 which covers the moulding. 
 
 Quoins. The external and internal angles of buildings, or of their 
 members. The corners. 
 
 Radius, in geometry, is the semi-diameter of a circle, or a right line, 
 
 drawn from the centre to the circumference ; in mechanics, the spoke 
 
 of a wheel. 
 Rails, in framing, the pieces that lie horizontal j and the perpendicu- 
 lar pieces are called styles, in wainscoting, &c. 
 Raking. A term applied to mouldings whose arrises are inclined to 
 
 the horizon. 
 Resistance, in mechanics, that power which acts in opposition to 
 
 another, so as to diminish or destroy its effect. 
 Reticulated Work. That in which the courses are arranged in a 
 
 net-like form. The stones arc square, and placed lozengewise. 
 Return. {Fr.) The continuation of a moulding, projection, &c., in 
 
 an opposite direction, as the flank of a portico, &c. 
 Rib. (Sax.) An arched piece of timber sustaining the plaster work 
 
 of a vault, &c. 
 Ridge. The top of the roof, which rises to an acute angle. 
 Rilievo, or Relief. The projccture of an architectural ornament. 
 Ring. A name sometimes given to the list, cincture, or fillet. 
 Roman Order. Another name for the Composite. 
 Rose. The representation of this flower is carved in the centre of 
 
 each face of the abacus in the Corinthian capital, and is called the 
 
 rose of that capital. 
 Rustic. The courses of stone or brick, in which the work is jagged 
 
 out into an irregular surface. Also, work left rough without 
 tooling. 
 
 Sagging. The bending of a body in tlio middle by its own weight, 
 when suspended horizontally by each end. 
 
 Salon. [Fr.) An apartment for state, or for the reception of paint- 
 ings, and usually running up through two stories of the house. It 
 may be square, oblong, polygonal, or circular. 
 
 Saloon. A lofty hall, usually vaulted at the top, with two stages 
 of windows. 
 
 Sash. The wooden frame which holds the glass in windows. 
 
 Scaffold. A frame of wood fixed to walls, for masons, plasterers, 
 &c., to stand on. 
 
 Scantling. The name of a piece of timber, as of quartering for a 
 partition, when under five inches square, or the rafter, purlin, or pole- 
 plate of a roof. 
 
 ScAPUS. Tlie same as Shaft of a column, which see. 
 
 Scarfing. The .joining and bolting of two pieces of timber together 
 transversely, so that the two appear but as one. 
 
 Scotia. The name of a hollowed moulding, principally used between 
 the tori of the base of columns. 
 
 Severy, (in Gothic architecture,) a separate portion of a building. 
 
 SnAFT. That part of a column which is between the base and capital. 
 It is also called the/Hs(, as well as trmd; of a column. 
 
 Shank. A name given to the two intcrstical spaces between the 
 channels of the triglyph in the Doric frieze. 
 
 Shooting. Planing the edge of a board straight, and out of 
 winding. 
 
 Shoulder. The ])lane, transverse to the length of a piece of timber 
 from which a tenon projects. 
 
 Shutters. The boards or wainscoting which shut up the aperture of 
 a window. 
 
 Sill. The timber or stone at the foot of a window or door; the 
 ground timbers of a frame wbicli support the posts. 
 
 Skirtings. The narrow boards which form a plinth round the mar- 
 gin of a floor. 
 
 Socle. A square, flat member, of greater breadth than height, usu- 
 ally the same as plinth. 
 
 Soffit. The ceiling or under side of a member in an order. It 
 means also the under side of the larmier or corona in a cornice ; 
 also, the under side of that part of the architrave which does not rest 
 on the columns. Sec also Lacunar. 
 
 SoMMER. The lintel of a door, window, &c. ; a beam tenoned into a 
 girder, to support the ends of joists on both sides of it. 
 
 Spandrel, (in Gothic architecture,) the triangular space enclosed by 
 one side of an arch, and two lines at right angles to each other; one 
 horizontal, and on a level with the apex of the arch, the other per- 
 pendicular, and a continu.ition of the line of the jamb. 
 
 Spiral. A curve line of a circular kind, which in its progress recedes 
 from its centre. 
 
 Steps. The degrees in ascending a staircase. 
 
 Stereobata, or Stylobata. The same as Entasis. 
 
 Strap. An iron plate, to secure the junction of two or more timbers, 
 into which it is secured by bolts. 
 
 Stretching Course. Bricks or stones laid in a wall, with their 
 longest dimensions in the horizontal line. 
 
 SuRBASE. The mouldings immediately above the base of a room. 
 
 Systyle. An intercolumniatiou equal to two diameters. 
 
 Table, (in Gothic architecture,) any surface, or flat member. 
 
 TiENi. A term usually applied to the lastel above the architrave in 
 
 the Doric corder. 
 Templet. A mould used by bricklayers and masons for cutting or 
 
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