THE Construction of Maps Relief. ILLUSTRATED. BY JOHN 11. HARDEN, MINING ENGINEER, PHIKNIX IRON CO., PHCENIXVII.LE, PA. AND EDWARD B. HARDEN, CHIEF TOPOGRAPHER, GEOLOGICAL SURVEY OF I'ENN'A, PHILADELPHIA, Pi. Transactions of the American Institute of Mining Engineers, Duluth Meeting, July, 1887. AUTHORS' EDITION. 18 8 7. [TRANSACTIONS OF THE AMERICAN INSTITUTE OF MINING ENGINEERS.] THE C0NSTBUCT10N OF MAPS IN BELIEF. BY JOHN II. HARDEN, PIICENIXVILLE, PA., AND EDWARD B. HARDEN, PHILADELPHIA, PA. The practical use to which topographical models or relief-maps have been put, has within the last few years taken a wider range. They are rapidly coming into favor for other than purely scientific purposes, and their value for illustration and instruction is being more fully appreciated. Topographical maps, representing by contour-curve lines the elevations and depressions of the earth's surface, are now demanded in engineering work of nearly every description, and afford a ready means of bringing out the configuration of the country in a simple manner. A beautiful example of recent topographical mapping is seen in the seventeen sheets just issued by the Geological Survey of New Jersey. By reason of the inability of unskilled persons to understand the nature of a topographical map, it is sometimes necessary to con struct the same in relief, with the rivers, canals, railroads, etc., delin eated upon it. With the aid of such a map, problems in engineer ing science which would otherwise require expert assistance to explain them, are reduced to a simple and understandable form. Relief-maps are also of value to the geologist in working out the geological structure. To the instructor they present the most ready and efficient means of imparting clear and accurate knowledge of topography and kindred subjects. To the lawyer they are invalua ble in enabling him to bring into the court-room a representation of a part of the country with al! its features accurately shown, to ex plain to the court and jury the special points about which litigation is pending and which would otherwise require long and laborious description. The application of the topographical map to business purposes is shown in a relief constructed by the writers for the Cumberland Valley Railroad Company and used by that company in the various ways of calling attention to the desirability of its route. This model is based partly on actual survey and partly on 1 2 THE CONSTRUCTION OF MAPS IN RELIEF. sketch topography. The horizontal scale is §poo; tne vertical 19^0 of nature, an exaggeration in excess of that desirable for models used for other purposes. An illustration of this relief by the Ives pro cess, taken from a phototype of the model by Gutekunst, is given in Mr. Lehman's paper (see Trans., xiv. 446). The foregoing are a few of the avenues through which has come a demand for relief-maps. The practical advantages yet to be ob- FlG. 1. Part of the South Mountains in Pennsylvania, from Geological Survey Maps. tained from their use can scarcely be conjectured, since ways are con stantly being found for their profitable employment. The writers have for some years made relief-maps by various methods of construction ; and a description of some of the forms employed, together with the results obtained, may be interesting to some, as well as helpful to others who may desire to undertake the construction of these beautiful relief-pictures. The person attempting the work should have a fair knowledge of field and office-practice, with some mechanical skill in the use of tools and the manipulation of material. A contour-line map (Fig. 1) THE CONSTRUCTION OF MAPS IN RELIEF. 3 or one on which the elevations are marked at numerous points, is the first requisite in relief-map-making. Fig. 2. Sf^-' Method of Modeling by sections in one direction. One of the earliest methods of constructing relief-maps is that of drawing section-lines across the topographical map (in intricate Fig. 3. y Method of Modeling by sections in two directions. topography, also at right angles, as in Fig. 1), and transferring these lines to thin boards or metal strips ; the height, as shown at the 4 THE CONSTRUCTION OF MAPS IN RELIEF. point crossed by each contour, being measured from the base of the strips, and the profile thus obtained cut out. The position of these section-lines is transferred from the map to a baseboard, as a guide to adjust and fasten the profile-strips. Fig. 2 shows the topography of the map (Fig. 1) drawn on pro file-strips in one direction only. Fig. 3 represents the same area with profile strips also at right angles. This method of making models was described in a work on Iso- metrical Drawing, by T. Sopwith (London, 1838), who says: " Several sections being cut out in pasteboard, or, what would be better, in thin plates of copper so prepared with a covering of paint as to admit of being drawn upon with ink and colors, are to be joined crossways by what is termed half-lapping, that is, by cutting eacli section half way down where it crosses another section cut in like manner on the other edge, and the whole being properly painted with sec tions and joined together in this manner, will afford an interior view of the geo logical structure of the district. The model of squares thus formed is to be placed on a plane surface, and the several spaces may be filled with pieces of wood or Paris plaster carved or moulded on the upper surface so as to represent the surface of the earth. The several strips on which the sections are drawn may at any time be taken out for examination or for delineating any new discoveries upon them." Mr. Sopwith published in 1841 an admirable series of small models to illustrate various geological phenomena connected with practical mining. They were constructed of various kinds of wood fitted together to scale from actual measurements of the strata in the North of England. A method of construction for relief-maps, with or without the aid of contour-lines, is as follows. A baseboard is prepared, as in the method above described, and the contour-lines or points of eleva tion on the map are transferred to it. Nails are then driven into the baseboard at intervals and allowed to project above the board to the required height represented by the contours or points of eleva tion. The space between the nails is filled with wax or other suita ble materia], and tooled down to the heads of the nails, the finer detail being put in by reference to the map. This method may be used with advantage where the elevations are given at irregu lar intervals or where the topography is not shown by contour- lines. The method adopted by Mr. E. E. Howell, of Rochester, N. Y., in the construction of a relief of the United States Geological Survey map in the vicinity of Leadville, Colorado, is thus described in Ward's Natural Science Bulletin, vol. iii., No. 2. THE CONSTRUCTION OF MAPS IN RELIEF. 5 " The model is built up with cardboard representing twenty-five feet in thickness with the edges cut to the contour-lines. Theoretically this should work perfectly, provided the cardboard is of the proper thickness, but practically it will not. The sheets are sure to be closer in some places than in others, and just where they will do so is not always possible to tell, although as a general rule, small surfaces will lie more closely than larger ones. To meet this difficulty the main thickness of the model was built up of solid dry wood, which can be worked very exactly, and serves as a constant check in putting on the cardboard contours.' After these are all on, the model will be finished with clay mixed with glycerine and then moulded." A method used by Professor F. H. King, River Falls, Winconsin, is thus described in a letter to the writers. " I have come finally to use a block of plaster of Paris, cast in a suitable frame of the desired size and thickness, as the best material to work upon. There are several methods of realizing the final end. First, as you know, whatever the method, the map with contours must be prepared. This secured, a tracing on cloth is laid upon the block of plaster and, with a pointed instrument, contours are transferred to the plaster before it has had time to dry thoroughly. You will begin then with the lowest contour and cut the plaster down to the desired level, this being determined upon by means of a sliding scaie for measuring vertical elements. This done, the next contour is taken, and so on until there results a map like one made by building up with wood or other material. The details of relief have then to be worked in by carving down the shoulders as in any method of building up." " The chief difficulty in this method is to be found in cutting up to the contours and securing a perfectly vertical edge, in order that the contour may stand prop erly when transferred to the lower level. The material carves easily, shrinks and swells so Tittle, and may be revised with such great facility, that I prefer it to any other I have seen recommended. A little skill will enable one to work out the details.'' We have found, that in using tracing-cloth upon damp plaster it is liable to change its shape and size, and thus destroy the accu racy of the result. In using tracing-cloth for transferring the map in the various methods above described, care should be used, since even on a dry surface, the pressure of the stylus will spread the drawing. A method similar to that described by Professor King was prac ticed by Professor J. P. Lesley, at the University of Pennsyl vania. Instead of using one solid block of plaster, a number of blocks of uniform size to coyer the area of the map were taken, and a profile was drawn upon the sides of each block. They were then carved down to these lines, the spaces between the profiles being shaped by the eye. One of the early models made in this country, that of the Morri son's Cove Region, Blair County, Pa., was constructed by Professor 6 THE CONSTRUCTION OF MAPS IN RELIEF. Lesley on this plan, the blocks being of wood, three inches wide, and was carved with wood-cutters' tools. Fig. 4 is an illustration of what may be done by the block method of construction, the two blocks shown being taken from a large model of Blair County, Pa., made by one of the writers. The geological structure is shown in section on the sides of the blocks. Fig. 4. Model showing Geological Structure in Blair County, Pa. A model was made in this way (using plaster blocks) of the cele brated Ironton Hematite mine, in Lehigh County, Pa., and is now in the museum of the University of Pennsylvania. Another method is that of Mr. Henry Brooks, Boston, described in Science, vol. vii., page 418, as follows : "Make a careful tracing of the contour lines on waxed or oiled tracing-paper. Linen must not be used, as it will distort the lines when wetted. Paste the tracing on a clear piece of white holly veneer, an eighth of an inch in thickness, and cut or have cut, with a fine fretsaw, the lines of contour, leaving spaces now and then, should the lines so run that the intervening wood would drop out. Fasten the ve neer to a board, being sure that the surface is flat. Fasten veneer by the edges, and not through the spaces between contour lines. Cut or have cut strips of thin brass, each strip being as wide as the height of each contour line, and insert the strip into the corresponding saw-cut in the veneer. They must be pressed down until they touch the board below the veneer. When all the contours are in place, paint the whole surface over with heated wax, which will prevent the moisture of the clay from distorting the wood. When all is coated, fill in the spaces between the strips with clay until only the edges of the brass show. Where spaces are THE CONSTRUCTION OF MAPS IN RELIEF. 7 left the strips are cut with a slanting end long enough to span the space uncut, and the line of contour is thus unbroken. By this method nothing is left to the eye, and perfect accuracy is gained." When a topographical map is engraved, a simple method of con structing a relief is to have a sufficient number of sheets printed directly upon cardboard of a proper thickness, to cut out the suc cessive contours, and to fasten them together with a paste that will not swell the paper. Some of the European models exhibited at the Centennial Exhibition in 1876 were beautifully made in this way. It is desirable that some other material than plaster be found to reproduce relief-maps in a rapid and inexpensive way. Papier mache is used by manufacturers of globes and other small reliefs, but it requires special apparatus. The writers have attempted a method in which blotting-paper is used, somewhat after the stereo typing process. After the plaster negative has been obtained, a large sheet of blotting-paper is thoroughly saturated with water and laid upon the mould. A brush with hard bristles is then used to beat the paper until it conforms to all the inequalities of the relief. It is then covered with paste made of: * Flour, 4 parts, made into paste. Whiting, 2 " Glue, 1 " Water, a sufficient quantity. Mixed with heat. A second sheet of blotting-paper is then put on in the same man ner, to be followed by another coat of paste, and a third sheet of paper, or more, if great stiffness is required. When the relief is very great, the paper may be broken in forcing it into the deeper parts of the mould, in which case small pieces of paper with paste can be used to fill up and repair the break. This must remain until dry before removal from the mould, when it may be given a thin coating of shellac-varnish and painted. The paper should be large enough to allow the edges to be turned up and glued at the corners, when the sheets will be stiff enough to frame without any further backing. Mr. James B. Jordan, of London, England, who has made several large models, for various purposes, writes as follows : " My method of modeling is by means of contours, which I believe is the only accurate one, but of course it involves the preparatjon of a carefully contoured map. My first large model was made in 1873, of the area of country drained for the 8 THE CONSTRUCTION OF MAPS IN RELIEF. Sheffield water-supply. It embraced an area of 100 square miles. The horizontal scale was 880 feet to one inch, the vertical 500 feet to one inch (1 : 1.76). The sur face was built up in contours of cardboard, at intervals of 25 feet, each card being ^jth of an inch thick, making the vertical scale a fair proportion for a moderately hilly country. The surface of the model was colored in distemper of a light buff- color, the reservoirs and rivers being shown in blue. The size of the model was 6 by 4 feet. "In 1874 I made another important model for the use of a Parliamentary com mittee. This was also built up in contours of cardboard, at intervals of 10 feet. The horizontal scale was Tu5j0, the vertical scale ^j00 (1:4.4). The surface was colored geologically. The model was divided into two parts, having deep vertical edges, on each of which was colored a section of the strata, showing coal-seams, etc. For the purpose required this plan was found very useful. "At every tenth contour a different colored cardboard was introduced to mark each 100 feet elevation. This is a great advantage and especially useful during Ihe process of construction. The size of this model is about 9 by 5 feet. "The cardboard I use for model work is made especially for the purpose and very hard. It is composed throughout of the best Whatman paper, cemented together with glue, instead of paste, as in the ordinary way. " Another model now in process of construction is that of the British Islands, with a portion of the Continent of Europe and surrounding sea-bottom,' in con tours of cardboard at every 250 feet, commencing at the greatest depth of the ocean, 20,000 feet below sea-level. The cardboards number 25 to an inch. At each 1000 feet a light blue cardboard is inserted which gives a very pretty effect where the features are so undulating as in this model. It is being made for the Science and Art Department for educational purposes." A notable geological model is that of the London area, based on the maps of the Geological Survey of Great Britain, and now in the Jermyn Street Museum, a description of which is given in a Guide to the Geology of London, by William Whitaker, F.G.S., published in the Memoirs of the Geological Survey, 1884. The horizontal scale is 6 inches to 1 mile, and the model represents an area 15 miles east and west, and 11 miles north and south. It was found necessary to increase the vertical scale, as the greatest difference in level in the area represented— that between the Thames and the top of Hamstead Heath — would be little more than half an inch on the scale; consequently all the minor features would be lost. The vertical scale was therefore made 200 feet to one inch, an excess of 4.4 times over the horizontal. Owing to the large size of the model it was constructed in nine separate pieces and the lines of separation were chosen in view of the geological sections which could be represented. The blocks are therefore irregular in shape. The four corner blocks are fixed and the other five are movable by suit able mechanism to exhibit the sections. We are indebted to Mr. J. B. Jordan, by whom the model was made, for a description of the method of construction : THE CONSTRUCTION OF MAPS IN RELIEF. V "A firm foundation table was made with great care, to avoid any alteration in the form by shrinkage or warping of the timber. Nine deep frames, of the proper form, were made and fitted together on the foundation. Each frame top was cov ered with cotton cloth, and on these were mounted a set of the six-inch ordinance maps of the district. "These maps were the datum plane on which the undulating surface of the model was raised. As there was no regular system of contour lines on the maps, then available, though they had elevations at numerous points, the system adopted was to drive measured pins into the points where the heights were marked, the pins, of which several thousand were used, being cut to exactly represent the ele vation above the datum plane at the point through which they were driven. After driving the pins over a space representing a square mile, that space was covered with soft wax above the pins, and then the wax was worked down so as to show the bright end of each wire. "Plaster casts were taken in suitable frames, and on completion of the nine areas they were fitted together, strengthened with sizing and a covering of muslin. "To finish the surface a set of maps were mounted directly on the undulating surface, a task needing much care and patience, on account of the paper having to be thoroughly saturated and nearly reduced to pulp before being fixed on the surface of the model. "Drawing paper was pasted on the sides of the blocks on which the geological sections were drawn, and the whole colored appropriately to represent the various formations." The method preferred, however, by the writers, and the one that has given the most satisfactory results in their hands, as regards both accuracy and ease of manipulation, is that of cutting out the con tours in wood of the proper thickness to represent the vertical interval selected, building up and finishing in wax. Having a baseboard one inch thick, with one planed surface, and the exact dimensions of the intended relief, either paper, card board, strawboard, or wood of a proper thickness to represent the contour-curves, is used to build up the model. Having at hand transfer paper, stylus, hammer, wire-nails, glue and a jig-saw, you have all the material necessary to begin the work. Suppose the scale of your map to be i^ of nature, or 1600 feet to the inch, and it is decided to build up in steps representing 50 feet vertically ; then the material should be BV °f an incn thick. Lay your map upon the baseboard and transfer to it the outline of the first 50-feet contour. Transfer the same outline to the material selected for the building up of your relief and also the outline of the 100-feet con tour as a guide for the position of the next layer. With the jig-saw cut to the outline of the 50-feet contour, then fasten it to the base board with glue and nails in the position marked for it. Proceed in like manner to transfer the outline of the 100-feet contour and 10 THE CONSTRUCTION OF MAPS IN RELIEF. make marks for the adjustment of the 150-feet layer, saw out the 100-feet line and nail it down. Proceed in this way to the greatest elevation of the relief, always marking your material with two lines, one for cutting, the other for a guide for the position of the next layer above. Should the final layer, representing the tops of the hills, be less than 50 feet, it may be rubbed down with sandpaper to its proper height. When this is completed the relief appears in terraces J.2 of an inch in height, each step representing 50 feet and corresponding in outline to the contours at 50, 100, and 150 feet, and so on to the highest elevation, as shown in the cardboard model, illustrated in Fig. 5. If wood is used each alternate layer should be laid down with the grain at right-angles to the preceding layer, to counteract the con- Fig. 5. Cardboard Model oi a part of the South Mountains. traction or expansion of the wood, which will otherwise seriously interfere with the accuracy of the result. It is also necessary to take precautions to prevent the baseboard giving trouble from the same defect. Should the model, after finishing, be cut along certain section- lines to exhibit the geological structure, these lines should be marked upon the map and transferred to each layer at the same time as the contour lines, and when nailed down care must be taken to keep the nails far enough away from these lines to allow the saw to pass. THE CONSTRUCTION OF MAPS IN RELIEF. 11 The model is now ready for the waxing process. For this pur pose the following formula is recommended : Beeswax, 16 parts. Venice turpentine, 4 " Corn starch, 8 " Venetian red, 1 " Sweet oil 1 " Melt the wax, add the Venice turpentine, and sift in the corn starch, stirring the mixture thoroughly, after which the Venetian red or other coloring matter may be "added, together with the sweet oil. This preparation, poured into flat dishes, and allowed to cool, is used to fill up the angles or steps. The skill of the topographer now comes into play in forming the finer details of the topography from the map, between the successive steps formed by the boards, it being assumed that the original is in contours 10 feet apart; and it is in this part of the work that the mere mechanic fails. The tools employed are of various rounded forms and sizes, to suit the intricate shapes of the finished model. They can be made of hard wood or bone. The wax should be of a consistency to work easily, which can be obtained by regulating the quantity of sweet oil in the above formula. In some first attempts by one of the writers, a mixture of resin and tallow was used to cover the wood before applying the wax. In practice this was found unnecessary, the wax adhering to the wood without it. A little sweet oil used on the tools when giving the final touches, will be found advantageous. If the above method of waxing is followed, the relief may be kept for years without danger of separation from the wood ; or it may be finished for immediate use when time is an object. Usually, how ever, the wax relief is only used to cast a mould in plaster, from which any number of duplicates may be made. At this stage of the process help may be had from a plasterer, who will cast copies for a small sum, depending upon their size. When a modeler desires to make his own casts, it may be done in the following manner :- Enclose the relief in a wood frame, oiled or soaped to prevent the adhesion of the plaster, and place the whole on a flat surface to secure an even distribution of the liquid mass when poured into the mould. A sufficient quantity of water is then taken in a suitable vessel, into which plaster of Paris is carefully sifted through a fine- mesh sieve, rapidly stirring to prevent the formation of lumps and Fig. 6. oc cc5 d oHO c*3 Model prepared for Photo- mechanical Printing. THE CONSTRUCTION OF MAPS IN RELIEF. 13 air-bubbles in the mixture. When it arrives at the consistency of cream, it should be poured into the mould and allowed to stand until partially set. A straight-edge should then be drawn across the top of the frame to remove the surplus plaster, level with its upper edge. Large casts may be strengthened with iron rods or with wire netting inserted soon after the plaster is poured into the mould ; and the weight of a thick cast may be reduced by hollowing out the plaster from the under side before it gets thoroughly hard. In a short time the plaster will be sufficiently hard to turn over, when the frame may be removed and the wax original separated from the cast. The writers prefer to dry the mould after retouching and to apply a coat of thin shellac varnish to the plaster negative before casting a positive. When time is an element, a positive may be made immediately by brushing the mould with a solution of soap-water before casting. The finish of a model depends on the purpose for which it is to be used. For photographic prints or photo-mechanical reproduc tion, the surface features can be put directly upon the plaster in black, India-ink, or paint. Fig. 6 is a relief of the western end of the Northern anthracite coal-field, prepared in India-ink for photo-mechanical printing by the Ives process. If it is desired to color the model geologically or otherwise, a thin coat of shellac-varnish is applied, and it may then be colored in oil. The artistic map-maker will have no difficulty in giving character and finish to his cast, but unskilful drawing and poor lettering will ruin the appearance of otherwise good work. The use of contour-curves to delineate underground topography originated with Mr. B. S. Lyman about 1865, and the first model based on his map was made to illustrate the complicated structure of the Cooper or Bennett coal-beds at the Hutchinson mine of the Plymouth Coal Company, Plymouth, Luzerne County, Pa. The method of modeling last described, is admirably adapted for the construction of underground relief; and a plate showing, on this plan, the workings in the middle member of the Mammoth coal-bed at Excelsior colliery, Columbia County, Pa., is given in Fig. 7. Other models of underground topography constructed in the same way are those of the Panther Creek coal-basin (floor of the Mam moth coal-bed) between Tamaqua and Mauch Chunk, in Schuylkill and Carbon counties, illustrated in the Pennsylvania Geological Survey Report, AA. p. 242 ; also of the floor of the Mammoth coal- 14 THE CONSTRUCTION OF MAPS IN RELIEF. bed in the Mahanoy and Shenandoah coal-basin, Schuylkill County, for the Geological Survey of Pa., and of the Salisbury coal-basin, Somerset County, for the University of Pennsylvania. The adaptability of this method for exhibiting artificial surface- contour made in open-work mining is shown in Fig. 8, taken from THE CONSTRUCTION OF MAPS IN RELIEF. 15 a ao O S 16 THE CONSTRUCTION OF MAPS IN RELIEF. a model of the extensive mining operations at the Cornwall magne tite mine, near Lebanon. Fig. 9. Part of the South Mountains, equal scales. There is great diversity of opinion in regard to the relative scales admissable in the construction of relief maps, though the weight of Fig. 10. Part of the South Mountains, vertical scale exaggerated. opinion seems to be in favor of a slightly exaggerated scale. The writers have avoided in their practice the distortion of the vertical, THE CONSTRUCTION OF MAPS IN RELIEF. 17 where possible, and believe it to be unnecessary in maps of a large scale, say of 100 to 1000 feet to one inch (Was to tsW) depending somewhat upon the nature of the topography. Fig. 9 exhibits a piece of South Mountain, Pa., topography, near Caledonia furnace, constructed on the true scale, vertical and horizontal alike, from map Fig. 1 where the greatest difference in elevation is 1000 feet. Fig. 10 shows the same territory with the vertical scale increased as 2 to 1. Mr. E. E. Howell, Rochester, N. Y. in a letter to us says, — " In nearly all the models I have made, the vertical scale and the horizontal scale are the same. In two maps covering a large area I doubled the vertical scale*; but I believe, in every case where it is practicable, the two scales should be the same ; and were I to-day re-modeling the two maps referred to, I would not exaggerate the vertical scales." Prof. J. P. Lesley expresses the same opinion in vol, vii., page 58, of Science, where he says : "I must personally thank you for your good words in behalf of non-exaggerated reliefs in your last issue, p. 24. I have had a long experience in this kind of work, and never found a case which required the vertical scale to be exaggerated. No relief of the surface is too delicate to escape the human eye when represented with sufficient skill and care in modeling. The demand for exaggeration in a relief comes from those who will not spend a sufficient amount of time and pains upon the intermediate contour curves, or from those who have not trained themselves in draw ing from objects. The habit of exaggerating the relief excuses itself at first on the plea that common people cannot appreciate heights when true to nature, but the fact- is that the difficulty is felt by the modeler himself, and, when the habit is once formed, it becomes incurable. If a relief-map be not true to nature, what is the good of it ? Geologists have been forced to abandon exaggerated cross-sections ; why should they permit relief-map makers to revive the discarded error, and put the representation of the whole in antagonism to the representation of the parts? " About the year 1865 or 1866 I made a wooden model of one of our lower Silu rian limestone valleys, with its bounding ridges, about 20 miles long. The model was about 18" by S6", in 12 bars of wood, each 18" long by 3" wide. On each side of each bar I painted the corresponding section of the valley, with its limonite horizons and faults. The model still exists. My purpose was first to get correct ideas of the country structure for my own work, and then to exhibit my conclusions to the Pennsylvania Bailroad Company, who employed me. The reliefs in the valley were very low ; but they were perfectly legible to the eye of a layman. What would have been the fate of my side-sections had I used an exaggerated vertical scale ? " In 1865 I made a model of the underground of the Plymouth anthracite mine, with its remarkable vertical fault, from levels which I took in the mine. What good would this have been had I used a different vertical scale ? " I have myself made models on several plans ; the most satisfactory, but the most 2 18 THE CONSTRUCTION OF MAPS IN RELIEF. laborious, being to draw a good many cross-sections on the same vertical and hori zontal scale, along parallel lines, as nearly as possible at right angles to the general strike ; then cut strips of wood, lead, zinc, or stiff paper (I have used all four) to represent the cross-sections, set these up in their places, . fill in with wax or plaster, and finally tool the surface thus obtained. I prefer this method to the common one of jigging out the contour curves, and filling the terraces between them with slopes of wax. The latter method is easier and less costly; but it is sure to make the modeler slovenly in his geological representation, and it is a powerful seduction towards exaggeration of the vertical scale. Beginners and earnest scholars ought not to be allowed to use this method until they have been drilled to accuracy and to love the true natural aspect, by the compulsion of the method of cross-sec tions. I never see a false relief-map without indignation, and a touch of the con tempt we feel for all anachronism." Prof. F. H. King, River Falls, Wisconsin, who with Mrs. King has lately completed a model of the world on Mercator's projection, addresses the following letter to Science, vol. vii., page 120. " There are various uses for topographical models, and that for which they are designed must necessarily govern their construction. While the technical geologist, in considering orographic questions, finds it undesirable to exaggerate the vertical scale of his cross-sections, such profiles would be absolutely useless in the actual construction of a railroad. It should be equally evident that the needs of school children under sixteen years, and those of the field geologist, are not necessarily met by identical appliances. The construction of suitable topographical models for use in the common schools is educationally of the utmost importance, and, now that the matter has been referred to, I hope it may receive the consideration it demands. Almost every great physiographic and commercial problem requires the pupil to see his locality and State in its vertical relations to other States and coun tries ; and how best to enable him to do this, is not solved by Professor Lesley's dictum. "What we need to-day for educational purposes, as I see it, is an accurate topo graphic model of every State in the Union, constructed in such proportions as will enable the pupils, in their respective schools, to use it as a working-plan for the making of a larger model of their State. This map should not be isolated. The pupil must see it in its horizontal and vertical relationships to other States. Now, to meet these demands, a relief-map of the United States is required, in which both the horizontal and vertical elements for each State may be measured with sufficient accuracy and facility b'y the pupil. Such a model must be portable, very strong, and extremely cheap. I emphasize the last, because, unless they are cheap, the schools needing them most cannot have them. Now, a model of the United States might be constructed, as Professor Lesley suggests, but it would be useless for topo graphic purposes if made of any portable size. Our own map has the horizontal scale sixty-five miles to the inch, and it is certainly as large as can be conveniently handled in the average school-room. But taking the Grand Canon district as an example of what might be done with both scales alike, using Mr. Dutton's profile, extending from the Markagunt plateau southward across the Grand Canon, for data, we should have the following profile : • 10,000 . 4,659 ieet auove sea-ievt " below (1) " j, or tt .0138 . 1,250 " below (2) " it .0036 . 1,818 " above (2) " u .0053 . 1,363 " below (4) " u .0040 . 1,022 " above (5) " (1 .0030 . 568 " below (6) " (( .0016 . 1,022 " above (7) " " .0030 . 1,931 " below (8) " [( .0057 113 " above (9) " a .0004 . 1,363 " below (10)" ii .0040 THE_ CONSTRUCTION OF MAPS IN RELIEF. 19 1. Markagunt plateau, . 2. North bank of Parunuweap, 3. Depth of bed of stream, 4. Height of Vermilion Cliffs, 5. Foot of Vermilion Cliffs, . 6. Brink of Permian terrace, 7. Foot of cliff, 8. Brink of second terrace, . 9. Foot of second terrace, 10. Brink of Grand Canon, 11. Bed of Colorado, "These figures are a sufficient proof of the impracticability of making a model of any large section of country without exaggerating the vertical scale, to say nothing of cheaply reproducing it with any degree of accuracy. Our map, con structed with the horizontal scale 5000 feet to the inch, that is, the same as the vertical, would be about 16 rods long and 9 rods wide. Were it constructed with the vertical scale the same as the horizontal, Mount Whitney would be but .044 of an inch high ; Mount Washington, .018 of an inch ; and the highest point in Wis consin, .0053 of an inch. Our model has attached to it one of the summits of the White Mountains, both scales alike, covering a rectangle 9 by 5 inches, and shows in itself just what the effect of exaggeration is. For my part, when I think of a mountain valley represented on the model, I think of it as 65 times wider than it is in the model ; and I believe that pupils, if properly taught, will do so." In the catalogue of the Royal Geographical Society's exhibit of appliances used in geographical education, London, 1885, we find 11 reliefs constructed on the same horizontal and vertical scales; on 8 the information is not given; 9 were "exaggerated many times," or " considerably ;" and over 20 were exaggerated in their vertical scales from 2 to 72 times. Probably one of the largest relief-maps or models ever made was of the earth, 60 feet in diameter, covering 10,000 feet of surface and exhibited by Mr. Wyld in Leicester Square, London, in 1851. The horizontal scale was 10 miles, the vertical 1 mile to 1 inch (533^ to 83^). The view was taken from the interior, the delineation being on the concave instead of the convex surface. There was no writing upon the model ; the sea was colored blue, and the land of as natural a tint as possible. Lieutenant H. A. Reed, in his work on topographical drawing, recommends the following exaggeration as affording a pleasing relief: "For a map scale 6 inches to 1 mile; if mountainous, J; if only hilly, ^ ; if gently undulating, §. For smaller scales, except for very rugged tracts, the exaggeration should be correspondingly increased. For a tract consisting wholly of mountains, no exaggera tion is necessary." 20 THE CONSTRUCTION OF MAPS IN RELIEF. Relief-maps are invaluable to the instructor in geographical and geological teaching, and this fact was early recognized at the Uni versity of Pennsylvania, where, in 1873, Prof. J. P. Lesley had prepared by and under the direction of one of the writers, assisted by the students in the department of geology and raining, a number of models based on actual surveys, to illustrate special features of geological structure. A list of these is here given. 1. The Schuylkill Water Gap in the Blue Mountain, at Port Clinton, Pa., size 38 by 32 inches, scale j^. 2. The Delaware Water Gap in the Blue Mountain, size 27 by 25 inches, scale ggoo. 3. The Lehigh Gap in the Blue Mountain, size 25 by 21 inches, scale 4gu(j. 4. The Black Log Gap and environs of Orbisonia, Huntingdon County, Pa., size 25 by 22. inches, scale 9^5. 5. Part of the Northern Anthracite coal-field, from Shickshinny to Scranton, Luzerne and Lackawanna Counties, Pa., based on a topographical map by Mr. R. P. Roth well, size 180 by 40 inches, area 80 square miles, scale j^o. 6. Logan's Gap, in Jacks Mountain, Pa., size 18 by 18 inches, scale 4j$(j<). 7. The underground workings at the Oak Hill colliery, Drifts Nos. 1 and 2, Scranton, Lackawanna County, Pa., size 12 by 15 inches, scale i^. 8. The Ironton Railroad Company's brown hematite mine, Le high County, Pa., size 50 by 18 inches, scale ^5. 9. The Washoe Mining District, Nevada, based on United States Geological Survey maps. 10. The White Pine mining district, Nevada, based on United States Geological Survey maps. 11. The Iron Mountain, Mo., based on the State Survey map. 12. The New Jersey zinc-mining district, Franklin Furnace, Sussex County, based on the State Survey map. 13. The property of the Cambria Iron Company, adjacent to their iron-works, Cambria County, Pa., scale fzw. 14. A part of Big Sewell Mountain, Fayette County, West Va., showing the number and position of the coal and limestone beds on the lands of the Longdale Coal and Iron Company, from private surveys. The following is a list of models constructed for and based upon the work of the Geological Survey of Pennsylvania : THE CONSTRUCTION OF MAPS IN RELIEF. 21 1. A part of Blair County, published in report T, scale i^,.. 2. The Seven Mountains Regions, Union, Mifflin and Snyder Counties, Pa., scale j^ • 3. The same, cut into 14 sections to show the geological structure. 4. Part of the South Mountains, Adams and Franklin Counties, Pa., from sheets Al, A2, BI and B2, published in D5 atlas, scale 19,200" 5. Part of the Mahanoy and Shenandoah coal-basin, showing the floor of the Mammoth coal-bed, scale 9^5. 6. The Panther Creek coal-basin from Tamaqua to Mauch Chunk, showing the floor of the Mammoth coal-bed, scale g^. 7. Part of the Bald Eagle mountain and Tyrone Gap, Huntingdon County, Pa., showing faulted strata, horizontal scale f^o, vertical 9800- Published in report T3, page 369. 8. Rocky Ridge and East Broad Top coal-basin, Huntingdon County, Pa., horizontal scale j^, vertical A. Published in report T3, page 285. 9. The Loyalsock coal-basin, Sullivan County, Pa., scale j^. 10. The Jones magnetite mine, Berks County, Pa., scale m. 11. The Cornwall magnetite mine, Lebanon County, Pa., scale §ajj,. Annual Report, 1885, p. 490. 12. The Cornwall Mining Company's property, Lebanon County, Pa., scale j^. 13. The ancient channel of the Allegheny River at Parker, Clarion County, Pa., scale u^m- The following is a list of models made for private use : 1. Morrison's Cove and part of the Allegheny Mountains, Pa., scale