th	Wm
4961
C45
1893	=f=
ENVI ==S=
Geometry for Gardeners ; |Sun Dials & Dialling* * GreenlipuseBuildincf •NO STABLE IS COMPLETE WITHOUT
ELLIMAN’S royal EMBROCATION
THE LAME HUNTER.
[TRADE MARK ]
THE ROYAL HUNTER CURED.
From the Royal Hunt, Windsor Gt. Park.
Cumberland Lodge, July ^thy 1851.
Sirs,—I feel great pleasure in testifying to the successful application of your Embrocation for green wounds, the removal of strains, and enlargement of horses* legs, &c.—Yours truly.
Charles Bryant.
Glass Houghton Collieries, nr. Castleford.
Nov. 22nd, 1880.
Gentlemen,—Please supply as under, and charge to our account: one gross of Elliman’s Royal Embrocation for Horses, 3s. 6d. size. Send to our Colliery Siding, near Pontefract, (Lane, and Yorks Railway).
J. D. Thorp’s Executors.
Castle Weir, Kington, Herefordshire.
Deceitiber, 1878.
Gentlemen,—I use the Royal Embrocation in the stables and Kennels, and have found it very serviceable. I ha ve also used the Universal Embrocation for Lumbago and Rheumatism for the last two years, and have suffered very little since using it. R. H. Price, Lieut.-Col.,
Master of Radnorshire Hunt.
From His Grace the Duke of Rutland, Master of Belvoir Hunt.
Belvoir. Grantham, Dec. 1 sty 1879. Sirs,—Elliman s Royal Embrocation is used in my stables ; I think it very useful.
Rutland.
From J. Bellamy, Esq., Master of the Isle of Wight Hunt.
December, 1878.
Sirs,—I use Elliman’s Royal Embrocation, and have found it most efficacious in many cases of sprains and wounds, but especially for sore throats, and when used with a bandage as a mild blister.
J. Bellamy.
El/iman’s Royal Embrocation for Horses and Cattle,
Introduced to the public 30 years since, has maintained its world-wide reputation, not only by reason of its possessing remarkable healing properties, quickly restoring an injured limb or part to a healthy state, but also on account of the ease with which it is applied, its use being unattended by the slightest risk of blemish. A large proportion of the Masters of the Foxhounds and Harriers throughout the United Kingdom use it constantly in their Stables. The testimony of these men as to its efficacy all must recognise as unimpeachable. The Embrocation is very generally used by Contractors, Builders, Farmers, Brewers, Colliery Owners, Livery Stable Keepers, and owners of Carriage and Draught Horses ; in fact, by all those who see that it is the strictest economy to keep their horses' legs sound and fit for hard work.
From Major J. M. Browne, Master of South Staffordshire Hounds.
Fossewav, Lichfield, Oct. ijtky 1879.
Sirs,—I find Elliman’s Embrocation exceed-inglygood for sprains and cuts in horses, and also for cuts in hounds’ feet. I shall strongly recommend it to all my friends.
Yours faithfully, J. M. Browne.
Sold everywhere by Chemists and Saddlers in Bottles, 2/-, 2/6, and 3/6 each,NALDIRE’S TABLET!
A Medicated Soap (free from Poison),
FOR WASHING DOGS.
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Sold by all Chemists and Perfumers—Price One Shilling per Packet, With full directions for Use.
N.B.—Beware of low-priced Imitations, which are worthless. Manufactured only by
WRIGHT and HOLDSWORTH, London, S.W. j
E N B OW'S
WORLD-RENOWNED DOG MIXTURE.
In Bottles, 2j., 5s.,	10s. each ; and One Gallo?t Cans, for the use of Kennels, 45$. each. |
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Dear Sir,—I have pleasure in informing you that I have now decided to use your Buffalo Meat Biscuits in the Royal Kennels After an experience of upwards of twenty years, during which time every description of dog food has been submitted to my notice, 1 am enabled to judge of what is most suitable for the Canine race. Your Buffalo Biscuits has convinced me that a more nourishing and suitable Food for Dogs has not yet been invented, combining as they do, all the qualities of a most perfect food, and to all that dt-sire to keep their dogs in good health and condition, I can with the greatest confidence recommend them.—Yours truly, FRANK (IOOI)ALL.
Mr. W. G. Clarke.
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ESTABLISHED 1851.'Xi___
Is by far the most popular of any Greenhouse Boiler for Amateurs. It is easiest to fix; most economical in fuel; readily managed; and thoroughly reliable in operation if the orifji-nol jmttern only is obtained of the Inventors. IMPORTANT TESTIMONY.
“2, Vicar’s IIii.l, Lahywiu.l, S.E., May 5, 1S91.
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“W. E. BERRY, F.R.II.S.”
Any handy man can fix it through out as delivered by us.
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TORTOISE STOVE WORKS, HALSTEAD, ESSEX.MECHANICAL WORK
IN
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LOCK & BOWDEN’S
AMATEURS’ PRACTICAL! AID SERIES.
MECHANICAL WORK
IN
IN THREE PARIS.
33 art I.	art II.
GEOMETRY for GARDENERS SUN-DIALS AND DIALLING.
ByF. CHILTON-YOUNG, F.R.II.S. |	By ARTHUR YORKE.
5Part III.
GREENHOUSE BUILDING ANU HEATING, ETC.
By VARIOUS WRITERS.
Illustrated with Numerous Diagrams, Sketches & Working Drawings to Scale.
EDITED BY
FRANCIS CHILTON-YOUNG
Author o/“ Evert Man His Own Mechanic,** ** The House and its Furniture,’* and Editor o/“ Amateur Work,** First Series of Seven VeA&mm,
WARD, LOCK & BOWDEN, Limited,
LONDON : WARWICK HOUSE, SALISBURY SQUARE, E.C.
NEW YORK : EAST 12TH STREET.
MELBOURNE : ST. JAMES’S STREET. SYDNEY : YORK STREET,
1893.
(All rights reserved.)£MV!
UNIFORM WITH THIS WORK.
CARPENTRY FOR RIVER AND GARDEN.
Comprising Boat-Buii.ding and Rustic CARPENTRY. Illustrated.
London : Ward, Logic, & Bowden, Limited.PREFACE.	~\\j \/1
It is not unreasonable to suppose that, at this time of year, viz., the month of May, the garden is the chief focus of attraction to many an amateur, and it is on this account that the Second Volume of Ward, Lock and Bowden’s “Amateurs’ Practical Aid Series ” has been devoted entirely to work which belongs to the garden, and, therefore, may be properly regarded as garden-work. This, as will be seen from the title page, is disposed in three parts so as to give a maximum of variety in a minimum of space, and so satisfy, as far as it is possible to do so, as many diverse tastes as the space at command will permit. Of Part I.—“ Geometry for Gardeners ”—I need not, perhaps, say much. Although there are numerous treatises on Geometry, some general and others special, that is to say—some intended for learners generally, as educational manuals, and others to meet the requirements of special trades and callings, there exists, to the best of my belief, nothing of the kind for gardeners, conveying the first principles of the science as applied to the formation of flower-beds, etc., of various shapes. It will not be in the power of any one to say as much again, for here is a brief treatise, entirely, I hope, to the point and purpose, and written, I trust, in a manner which will render the study interesting to the reader, because it savours in no way of the barely-worded, skeletonised appearance which invariably belongs to the matter-of-fact problems of which any ordinary work on geometry is usually composed.
Regarded from an ornate and decorative point of view, the Sun-dial may be looked upon as an attractive feature in a garden, whether mural, or crowning a tasteful pedestal, and with a view to doing horological business in times of sunshine in a quick andiv
preface.
easy way, it is possible that many an amateur may be induced, by the explanatory description and excellent designs of dials of different forms given by our versatile friend, Arthur Yorke, in his “ Sun-Dials and Dialling,” to devote a few hours to constructing and setting up a sun-clock in his garden. As the work is not so difficult as it may appear to be at first sight, the hours thus appropriated to it will be found at its completion to have been passed not only pleasantly but profitably.
A Greenhouse, larger or smaller, according to extent of garden and length of pocket of the amateur gardener, is now an absolute necessity instead of a costly luxury, as heretofore, and I am sure that amateurs in general, who may be led by “ Mechanical Work in Garden and Greenhouse” to set to work, and become possessors of greenhouses before the chilly winds of autumn and winter’s biting frosts are again upon us, will thank the various writers on “ Greenhouse Building and Heating,” by whose clear and lucid instructions they will be enabled to form glazed shelters—frost-proof if properly warmed—for their choicer florai treasures of half-hardy and even more delicate constitution. It will be difficult, I may say, to find a greenhouse of better design and greater utility, as far as size is concerned, for an ordinary garden.
Further, that pleasant work may be found even for the amateur who may prefer a summer-house to a greenhouse—and I suppose there are some who do —directions for building such a structure have been appended to “ Greenhouse Building and Heating:” and this, I hope, will be accepted as a full and satisfactory explanation of the mysterious “etc.’’ which forms a pendant to the title ot Part III. as set forth in the title page of this Volume./
/
CONTENT

J3art I.
GEOMETRY FOR GARDENERS.
CHATTER I.	PAGE
Some Simple Preliminary Exercises in Geometry .	. i
CHATTER IE
Theory Exemplified in Practice—Formation ok Garden
Beds in Reciilinear Shape	.	.	.	.12
CHATTER HE
Formation of Garden Teds in Curved Shapes .	.	23
CHATTER IV.
The Geometrical Construction of Elower Reds .	.	31
CHAPTER V.
The LayiXG OUT of Geometrical Gardens,
40vi
CONTENTS.
^Jiirf II.
SUN-DIALS AND DIALLING.
CHAPTER I.	page
Dials, Horizontal and Vertical—How to Set out a Dial 49
CHAPTER II.
Hints and Suggestions for Making Ornamental Dials .	62
^.1 art III.
GREENHOUSE BUILDING AND HEATING
CHAPTER I.
A Useful Span-Roof Greenhouse .	.	.	.77
CHAPTER II.
How to Warm a Small Greenhouse .	.	.	.	91
CHAPTER III.
A Summer-House for a Small Garden
99i
•3?
PART I.
BP§i« GEOMETRY
GARDENERS.
I

geometry eor gardeners.
CHAPTER I.
SOME SIMPLE PRELIMINARY EXERCISES IN GEOMETRY.
Simple elementary work in geometry—Working drawings—Apology for procedure— Instruments and appliances required—Preliminary exercises— Bisection of a straight lino—Theory reduced to practice—To draw a perpendicular to a straight line from any point in it—Simple mode of drawing parallel straight lines—-Things to be noted in connection with the exercises given—About the protractors and angles—Right angles—Acute angles— Obtuse angles—The protractor, how used.
N the present day, when education is pumped into the rising generation at high pressure, it may be supposed that every youth who aspires to be a gardener has acquired some little knowledge of Elementary Geometry, and is able to work out for himself, on paper, such simple work as the bisection, or division into two equal parts, of any given straight line, the drawing of a straight line at right angles, or, in other words, perpendicular to another straight line, either from any point within its length, or from one or both of its extremities, or even from a point without it. And, further, that he is able to draw, without the assistance of a parallel simple ruler, a straight line parallel to another given straight line, a procedure which, to say the least of it, is helpful, geometry, if not absolutely necessary, in laying out, especially on paper, beds, borders, and paths of equal width throughout. The word parallet', when applied to two straight lines, or to two curved lines, for a matter of'hat, merely means that the lines which run in the sameGEOMETRY FOR GARDENERS.
direction and take the same course, are equally distant one from die other throughout their entire length. I have said that parallelism, or the state or condition of being parallel, applies to curved lines as well as to straight lines, in the property of equidistance, as may be seen at once by any one who will take his compasses and draw two circles, one within the other, from the same centre, or call to mind the continuous rails of a railroad, which are parallel to, or equidistant from, each other throughout from terminus to terminus, let its course be turned and twisted about in whatever direction it may have been found necessary to carry it.
Now, I have laid considerable stress on ability to draw on paper, for every workman who has to shape out or fashion any kind of work, whether in wood, or in metal, or, indeed, in any kind of material, or in tracing patterns on ground or grass, as must often be done in gardening, is far better able to do the work, whatever it
Working rnay be, if he can draw its form in outline on paper, drawings, than one who cannot. Such a sketch, or diagram, especially if somewhat complex, is generally spoken of as a working drawing, and it is usually drawn to scale, that is to say, the relative dimensions of the small drawing on paper are precisely the same as those of the work itself when made or done, although the proportion of the former may be in inches or parts of an inch, while those of the latter may be, and, indeed, usually are, in feet.
Well, it is just possible that this book may come into the hands of a working gardener who has not had the chance of picking up the rudiments of Geometry at school, and he may, perchance, wish that he could do the few simple things that have been mentioned above—problems they are usually called ; but, as I am a matter-of-fact man, and am writing chiefly in the interest, and for the benefit of matter-of-fact people, I will not introduce such words as these, because I should have to explain their meaning for the sake of the uninitiated, and these, as well as other readers who may have all these things at their fingers’ ends, would regard the explanation as Apology for being tiresome, if not a nuisance. So I will first say procedure. a few words about the instruments that the gardener-draughtsman will require, and then pass on to show, as briefly as may be consistent with clearness, how best to perform the few simple operations to which allusion has already been made. The remarks, however, must be taken as being wholly and solely forNECESSARY INSTRUMENTS AND APPLIANCES.
the instruction of those who may possibly know nothing about these things, and those who do may skip the next two or three pages, and leave them unread.
Now, I am not going to put any one who wishes to follow me in what I am about to say, and to draw the diagrams that I am about to bring under his notice, to any great expense in the way of instruments and appliances ; and, contrary to the general custom of writers on Geometry, I shall make the list as short instruments and as simple as I possibly can. The draughtsman appi^nces will want a lead pencil—an H. B. (hard black) is the required, best suited for his purpose ; two or three sheets of cartridge paper or cheap drawing paper ; a piece of india-rubber ; a flat ruler, which will be all the more useful if it be divided into inches, halt-inches, and eighths of a;3 inch, and which should not be less than twelve inches in length ; a hard steel pen or two ; and a pair of compasses with a shifting leg, which may be withdrawn when required for the insertion of a pencil-leg and a pen-leg, that may be obtained with the compasses. This is all that is absolutely required, and the whole outfit may be bought for 2s. or 3s. A brass protractor for the purpose of marking angles will be found to be a valuable addition to the stock of instruments and appliances enumerated above, and I strongly advise the draughtsman to purchase one. It may cost him another shilling.
Having got thus far, let us turn our attention to the geometrical processes to which I have alluded above, and which I will call preliminary exercises, to be taken very much in the same light as the preliminary canter of a horse before the race. Let us first see what must be done to bisect any given straight line, or, as I have already explained, to divide it into two equal parts, preliminary Let us suppose that the straight line A B is the line to exercises, be thus treated. You will notice that I have twice used the term ‘straight line” instead of line, and I do so because there are two kinds of lines, namely, straight lines and curved lines, and, as we are now operating on straight lines, it may be as well to be particular in showing precisely what kind of lines they are. It is equally possible to bisect a curved line, if it be a regular line, but if it be an irregular or serpentine line, that is to say, a line that twists about in various directions, as is sometimes the case with paths in gardens and pleasure grounds, its biseotion; although it
3GEOMETRY FOR GARDENERS.
could be accomplished, would be found to be a somewhat difficult and complex matter.
Eut we are running away a little from the bisection of our straight line which we will suppose to be A B in Fig. i. All points are designated by single letters, and all lines, whether straight or curved, by two letters, namely, those used to designate the two points that form their extremities, although it is useful
Bisection of r	°
a straight and more usual to denote a curved line by three letters. Looking then at A B, you will at once see that it lies evenly between its extreme points, and this, I may say, is the definition of a straight line given by the old Greek geometrician Euclid, against whom many a poor suffering schoolboy, myself included, has taken up his parable. Now having drawn
the straight line A B on your paper, first put the point of one leg of your compasses at A—remember that before doing this you should have taken out the movable pointed leg and put in the pencil-leg instead— and having opened the compasses to an extent that you take to be greater than half the length of A B, draw with the pencil the curved line (or arc, as it is generally called) c F D ; then without altering the distance between the steel point and pencil point of the compasses, put the steel point at B, and trace the arc CGD. Now take your ruler, and, through the points C and D, where the curved lines or arcs c F D,uc r>, intersect or cut each other, draw the straight line c E n. Take out the pencil leg of your compasses and put in the movable leg, and open the compasses till the points of the legs fall on the points a e. Now try them on the points E B, and you will find that the points
4PRACTICAL WORK BASED ON THEORY.
of the legs of the compasses fall exactly on these points, just as they did on A E. From this you see at once that A F, is equal to 6 E, and this being so, you find that you have bisected the straight line A B in the point E, or, in other words, divided it into two equal parts, which is just what you wished to do.
Now, whenever you -wish to divide a straight line into two equal parts, you have nothing more to do than to go through the operation described above, and it is just as easy to do this on grass lawns, or on any ground with two stakes and a bit of garden
line, as it is to do it on paper with pencil, ruler, and
’	i r	i i !	Theory re-
compasses. It does not matter, remember, where	duceato
the points F and G may be taken in a b, provided	PriioaCi--
always that G is the same distance from B that F is from a. The result w’ould be precisely the same if you had placed one leg of the compasses on a and then, having opened the legs to the full extent of a b, have drawn an arc through the point B, and then, reversing the points of the compasses, and placing the sharp steel point of one leg on b, have drawn with the pencil point another arc through the point A, finishing up by drawing the upright line C D through the points in which the arcs intersect. I have not done this, because the diagram thus drawn would be much larger than Fig. i, and waste space, but you can try it by way of exercise, and it will be good practice for you to do so. Try it even with the points of the legs of the compasses further apart than the length of A B, and you will still obtain the same result by joining the points in which the arcs intersect. There are always more ways of killing a cat than one.
Perhaps you will infer from the last sentence that I am somewhat frivolous in my nature and inclined to treat a serious matter as a joke. Well, I do not like too much “ Gradgrindism,” and “ prunes and prism,” and “ deportment,” and I think that if boys and girls were taught oftener in the manner in which I have been trying to teach you, cat-killing and all included, the road to learning that they have to tread, if not rendered “ royal ” would, at least, be macadamised, and that they would thus be more effectually and quickly brought past what old Lilly, the grammarian, was wont to term “ the bitterness of their learning.” I must not be so prolix, however, in that which is to follow, or I shall have my publishers, good worthy men, pulling long faces, so I will hurry
5
BGEOMETRY FOR GARDENERS.
on to the next step, which, to put it in the briefest of terms, is to
draw a perpendicular to a straight line from any point in it. Now
To draw a y°u so°n find that the method of doing this is
perpendicular identical in principle with that which you have been to a straight	.	.	.	.	,
line from any doing m the previous exercise. As before, let A B
point m i.	straight line, and c the point in it at or from
which it is desired to draw a straight line that shall be perpendi-
FIG. 2.—»DRAWING PERPENDICULAR TO STRAIGHT LINE FROM ANY POINT IN IT.
cular, or at right angles to A B, for when one straight line is perpendicular to another straight line, it must be at right angles to it, and the other way about, when one straight line is at right angles to another straight line it must be at right angles to it, so this is merely a conversion of terms and nothing more. All you have to do is to measure off a space from c along c B, equal in length to C A, and this will give you the point D. Now open out your compasses till the points are just as far apart as the length of A D. Then, to be stricter in geometrical phraseology than I have hitherto been :—From the point A at the distance A D, describe the arc D E, and from the point D at the distance D A, describe the arc A E. Through this point of intersection of the arcs, E, draw a straight line to the given point C ; the straight line C E is perpendicular, or at right angles to the straight line A B. “ Ah,” you may say, “ but supposing it had been the point A or B, instead of C, at which the perpendicular had to be drawn, how would you have managed then.” Well, as in cat-killing, to which I have already alluded, there are more ways than one of doing it, but I will take a very simple method, the simplest, perhaps, that can be hit on, because it is in reality the pursuance of the system of erecting a perpendicular that you have already learned, and, I hope, practised, and
6HOW TO DRAW PARALLEL STRAIGHT LINES.
you will not be worried with any further explanatory remarks which I must make if you and I, my reader, go off at a tangent and start on a new track. All you have to do is extend A B— “ produce is the orthodox geometrical term ”—as far as you like towards F, taking care, however, that you extend it far enough, a necessary procedure, for if it happened that you did not extend it far enough, you would have to make it still longer, and there is the same objection to performing two operations where one is sufficient as there is in making two bites of a cherry. And now you will see why a fair amount of extension is an absolute necessity From the point r. measure off B D along B A, and along b f measure off B G, which must be of the same length as B D. From the point D, at the distance D G, describe the arc G K, and from the point G, at the distance G D, describe the arc D K. These arcs-intersect in the point K ; draw a straight line through B and K, and the line B K thus drawn is perpendicular to A B, and is drawn from the extremity B.
G	L
I said at the commencement of my remarks on the first simple
steps in geometry, that a learner should be able to draw a straight
line parallel to another straight line without the aid of a parallel ruler, and I will now show how this may be done. Let us suppose that it is desired to draw a straight line parallel to a given straight
line A B, and, further, let us suppose that the straight simple mode line c D represents the distance at which the two ofparaUeiI * * * S parallel straight lines, namely A B and the straight straight lines, line that is to be drawn parallel to it, should be apart. Take any two points, F, and F, in A B, sufficiently distant from each other, and
then from the point E as a centre, with a radius or distance equal to c D, describe the semicircle N G n, and with F as centre, with the same radius or distance describe the semicircle K L M. Then place the flat ruler against the semicircles thus drawn, and it will be
7GEOMETRY FOR GARDENERS.
found that it touches the semicircles at the points G and L. Through these points draw the straight line O P, wnich is parallel to A B, and has been drawn at the required distance, for E G and L F being radii of the same semicircle are equal to E N, E II, F K, F M, which are also radii of the two semicircles, and are all of them equal to C D. I may add that the straight lines EG, F L are the shortest distance possible between the parallel straight lines A B and O P, as will be found by taking points on each side of G and L, and drawing straight lines to them from the points Bj and F. By taking a number of points on each side of G and I,, and drawing straight lines to them from E and F, it will be found that the further any point thus taken is from E or F, the longer will be the straight line drawn to it from E or F, which shows that E G and F L must be the shortest possible distances between A B and o P. These two straight lines E G and F E are parallel, the one to the other, and any straight line drawn parallel to either of these between A B and O P will be parallel to the other and equal in length to both, and, therefore, the shortest possible distance between the parallel straight lines A B, o P.
Now the reader will have learnt, or, at all events, ought to have learnt, a good deal of geometry, and pretty well as much as he needs for gardening purposes, from these preliminary exercises, but there are a few more things that he ought to know yet, and these I will proceed to point out to him. All the lines that are upright in Figs, i, 2, and 3 are perpendiculars, and they are perpendicular to the lines that lay in a direction across the page, which are called horizontal lines. Turn the page in which any one of these figures occur half round, either to the right hand or the left, Thing- to ho anc^ horizontal lines will become perpendiculars,
noted in con- and the perpendiculars horizontal lines. And let the
nection -with	,	.	.	.	,	,	,,	. ,
ihe exercises student bear 111 mind that all straight lines dtawn
from the centre of a circle to the circumference, as E N, E G, and E H, which are drawn from the centre E to the arc or semicircle N G h, arc radii of the circle, which may be completed by drawing another semicircle from the centre E, below ab, and with either of the straight lines just named as radius. Also let him note that any two radii in the same straight line, as are N E and E 11, form what is called a diameter, or through-measure of the circle. Thus N n i“ ' "'Mueter ot the circle n g it, if it
aTHE PROTRACTOR-ANGLES DEFINED AND EXPLAINED.
were completed by drawing another semicircle in the way already described below a l>, and if this were done and G E extended or produced in a downward direction until it reached the curved line that forms the boundary of the new semicircle, G E and its extension would be another diameter of the same circle. Thus all straight lines drawn through the centre until they meet the circum-fe rente of the circle in directly opposite points of it are diameters of the circle.
I must not bring this chapter to an end without saying something about angles, and I will, when doing this, take the opportunity to mention the protractor again, and to explain what it is and what is its use. A protractor for gardeners’ use will be described in a future chapter, but the mathematical instrument so called is a thin plate of brass, of which the outer edge, and the inner edge as well, form perfect semicircles. Its shape About thQ is shown in Fig. 4 : its use is to set out angles protractor correctly on paper. Now an angle is the space enclosed by two straight lines that meet together in a point. Thus B a d, d A E, E a f, and fac are all angles, or spaces enclosed by straight lines which meet respectively in the point A, the angle
dab being enclosed by the straight lines B A, D A, which meet in the point A, and so on for the rest. Further, B A E, D A F, and E A c are also angles for the same reason, and so are B A f and CAD. They are, in fact, all angles, some larger and some smaller, but they belong to three different classes of angles, which are distinguished by different names.
Now', it will be recognized at once that A E is perpendicular to B c, or at right angles to it in other words, for when one straight line is perpendicular to another straight line, it must be at right angles to it, and, conversely, when one straight line is at right
9GEOMETRY FOR GARDENERS.
angles to another straight line it must be perpendicular to it. Thus
it is that the angles B A E, E a C are right angles, and fright angles.	.	&	.	, r .	.	’
D A F is also a right angle, for it is equal to the
angles just named, and AF,AD are at right angles, or perpendicular, in point of fact, the one to the other, as may be seen by turning the page till one becomes a horizontal line and the other a perpendicular. Therefore one of the tlnxe classes of angles comprises right angles.
Again, the angles bad, d a e, e a f, and FAC, are angles
that are smaller or less than right angles, because the lines by
which they are bounded enclose less space than is enclosed by
straight lines that form right angles. They form a second class
of angles known as acute angles, or, in other words, Acute angles.	°	°	1	’
sharp angles, because they are more pointed than
right angles. And the student must remember that all angles
that are less than a right angle are included in this second class,
and called acute angles, even if they be less or greater than the
angles shown as acute angles in Fig. 4. The only thing necessary
to constitute an acute angle is that the space enclosed by the
straight lines by which it is bounded shall be less than the space
enclosed by the lines that bound a right angle.
Lastly, the third class of angles comprises those that are known
as obtuse angles, and all angles that are greater than right angles,
or, in other words, blunter than right angles, are in-Obtuse angles. ’	,	'	,	,
eluded in this class. Obtuse angles, then, are angles
w'hose boundary lines enclose a greater space than is enclosed by
straight lines which bound a right angle. Thus in Fig. 4 the
angles I! A F, C A D, are obtuse angles, because the spaces enclosed
by the lines that bound them are greater than the space enclosed
by the boundary lines of a right angle, as may be seen from the
figure itself.
I have said that the use of the protractor is to set out angles of any opening with accuracy, without having recourse to any of the geometrical processes by which angles of certain openings may be constructed. The shaded part of Fig. 4 represents a protractor. The protrac- The semicircular part is graduated or divided into tor, how used. equaj spaces by straight lines that all converge or bend towards the point A, which is the central point in the outer boundary line of the straight part, and in which a mark or nick is
10CONSTRUCTION AND USE OF PROTRACTOR.
made, the better to determine and show its position. When the edge of the straight part is applied to any straight line, and the central mark to any particular point in the straight line, and a mark is made on the paper at the outer point of the line on the semicircular part which shows the angle required, a straight line drawn from the point thus obtained to the point in the straight line to which the outer edge of the straight part of the protractor has been applied, will form one of the boundaries enclosing the required angle, and part of the horizontal line to the right or left of the point identical with A will form the other. I do not say anything now about the graduation of the protractor, but will leave it until I describe the protractor that may be made and used for actual work in gardening.CHAPTER II.
THEORY EXEMPLIFIED IN PRACTICE—FORMATION OF GARDEN P.EDS IN RECTILINEAR SHAPES.
Working plans—Drawing to scale—Construction and use of scale—Appliances for working on the ground—McIntosh’s instrument for striking circles — Construction of regular geometrical figures—The hexagon and equilateral triangle—The square, pentagon, heptagon, and octagon—Other figures based on the regular polygons—Division of the circle—Angles measured by arcs of circles—Determination of size of angles by arcs of circles—Arcs bounding angles other than right angles—Angles subtended by sides of regular polygons—How to draw a polygon with the protractor.
NY one who has studied the preceding chapter, and can perforin with facility the simple geometrical operations described therein on paper, will now know sufficient of Geometry to enable him, first of all, to trace a plan of the garden on paper, and then, having done this, to trace it on the ground. There will be just this difference between the working plan on paper and the actual plan on the Working ground—the former will be very small, and the latter plans. will be full size. Nevertheless, the small plan will be an exact counterpart of the plan on the ground, and it will be so, because it is drawn to scale. It is necessary, therefore, before the working plan is constructed, to determine on what scale it shall be drawn—that is to say, what proportion the working plan shall bear to the full-size plan on the ground. I do not say anything about making what may be termed a map of the garden, in which its outlines and extent are accurately laid down, as this would involve the description of the method by which this is done, and require a chapter at least on Mensuration, which the reader, perhaps, will be Drawing to just as WfH pleased to dispense with. All that is scale. necessary for the gardener-geometrician to do is to set out a base line on paper, and erect a perpendicular to it, and then
12NECESSITY OF IVOR KING PLANS TO SCALE.
to proceed to lay out the garden in little on either side. But, first.,
he must settle the scale on which his drawing is to be made—thal
is to say, what is to be the unit of length on paper which is tc
correspond to a foot in length on the ground. It does not mattei
whether the plan on paper is drawn on a scale of an inch to the
foot, half an inch to the foot, or a quarter of an inch to the foot, as
long as the proportions are preserved throughout. The extent of
the ground will have considerable influence on the determination
of the scale, for, if it be a small piece, a larger scale can be adopted;
but, if it be of considerable extent, a smaller scale will be found to
be better suited to the geometrician’s purpose. If the reader will
turn to Fig. 26, in page 34, he will find a scale of feet at the foot ol
the diagram, and whatever may be the scale he adopts, he must
make a scale of feet on this principle ; for example, if it be made
on a scale of a quarter of an inch to the foot, every straight line
drawn on the paper must be as many quarters of an
1	1	,	,	.	.	Construction
inch in length as there will be feet in the corres- and use of
ponding straight line on the ground. I cannot
possibly lay too strong a stress on this—namely, that in laying out a
garden, whatever may be the purpose to which it is to be devoted,
a working plan is absolutely necessary. All working plans, as they
are termed, should be drawn to a correct scale, the larger the
better, but it may be said that a quarter of an inch to a foot is a
convenient size.
We can now get away from paper to work on the ground, and we will take it as a matter of course that everything that is done on the ground in the tracing of beds and borders has been worked out on paper beforehand, so, having provided ourselves with a strong garden line, several smooth round stakes from Appliances 5 to 6 feet long, a quantity of small stakes to define the beds, a pair of wooden compasses, 5 feet in	ground,
length, the legs being connected together with a perforated quadrant-shaped piece of iron, for fixing them at any distance required, a straight-edged piece of wood, say 10 feet long, and a square, with one limb about the same length—we proceed to business. And here it may be pointed out that the compasses and ruler that we have been using for our work on paper are found on a larger scale in the compasses and garden measuring rod above mentioned, and that the graduations in feet, and quarter feet, or three inches,
13GEOMETRY FOR GARDENERS.
on the measuring rod, may be regarded as corresponding with the scale that has been previously made for the construction of the plan on paper. The small stakes further serve to fix and define the points from which measurements are made, and circles or arcs of circles struck, and the larger stakes and garden line for setting out straight lines and striking circles whose radii, perhaps, are of some length, our wooden compasses being more for the purpose of measurement than for striking circles.
Of course, there are contrivances used for striking circles and arcs of circles in garden work other than those which have just
2 feet in length, shod with iron, upon which revolves a metallic McIntosh’s tube, with a projecting shoulder, to which is attached forlstr™dng by a screw a wooden rod, 8, io, or more feet in length, circles. marked in feet and inches. Upon this rod there is a movable iron slide, with an iron sharp-pointed stud. The 2-feet pole being placed in the centre, or point from which the figure is to be described, the slide is moved along the rod to the proper distance, and fixed there by means of a screw. An iron handle, turned up at the end of the rod, about 18 inches in length, is taken hold of; and, as it is moved round, the iron stud in the horizontal rod describes the figure intended.” This instrument is shown in f'ig- 5-
The first operation in laying down a garden will generally con-
been mentioned. Mr. McIntosh, in his “ Book of the Garden,” gives a diagram and description of a very useful instrument, which it would be desirable to procure where there is much work to be done, although a line in a proper
loop round a stake will perform the same work, but not quite so expeditiously. The instrument
FIG. 5.—M’lNTOSIl’S SUB IN STRIKING CIRCLES
tosh is “an upright pole,CONSTRUCTION OF REGULAR GEOMETRICAL FIGURES.
sist in determining the centre of the ground to be occupied, and then drawing a base-line, intersected by a perpendicular, the whole length and width of the space to be occupied. These lines will furnish the starting-points of most of our measurements, and it is of the first importance that they should intersect each other exactly at right angles. Striking circles, whether on paper or construction ground, is easy enough, and all figures whose sides geometrical are part of a circle are formed by its division into figures, different parts. For instance, a pentagon is a circle whose circumference is divided into five, a hexagon six, a heptagon seven, an octagon eight, and so on. If the operator is not furnished with a pair of large compasses, all regularly-curved lines, as it has been said, can be described by a cord running loosely round a strong stake in the centre of the curve, and the divisions of the circumference can be easily made to furnish the polygon required by means of straight lines drawn from point to point. All regular figures, from an equilateral triangle to an octagon, are represented in Figs. 6, 7, 8, 9, 10, 11. These are so clear and suggestive of the method employed in describing them that little more need be said about them.
It is obvious that in a short treatise like this, it is impracticable
to give directions in detail for the construction of each figure
geometrically, and for this reason any reader who desires further
information of this kind must be referred to a work on “ Practical
Geometry,” of which there are many in existence. The mode of
describing a circle is well known, and it has been said that any
regular polygon can be formed by dividing the circumference of
the circle into as many parts as the figure has sides, and drawing
straight lines between each pair of adjacent points. Now, the
hexagon (Fig. 9) is the easiest figure to construct,
,	,	.	,	.	...	, The hexagon
because the circle m which it is inscribed may be and equiiate-
divided into six equal parts without any alteration of ral trianele-
the width between the extreme points of the legs of the compasses,
because any and all the sides of a hexagon are exactly equal to the
radius of the circle on which it is inscribed. Thus, if the radius of
the circle be 3 feet, each side of the hexagon inscribed in it will be
3 feet, and so on. The equilateral triangle (Figs. 6 and 9) is
equally easy to describe, when it is said that the circumference of
the circle may be divided into six equal parts as for a hexagon,
15GEOMETRY FOR GARDENERS.
and the triangle completed by drawing straight lines between the intermediate points.
The four points of a square (Fig. 7) may be easily determined by drawing or marking out on the ground two straight lines of sufficient length, and from the point of their intersection as a centre describing a circle cutting the straight lines already drawn at right angles to each other. The points in which the circumference of the circle cuts the straight lines at right angles to each other are those which must be joined by drawing straight lines The square, between each pair of adjacent points in order to form heptagon’ t^ie scluare- The pentagon and heptagon (Figs. 8 and and octagon. 10) can be readily determined by geometrical process, but as they are too long to enter on here, the points of division in the circumference of the circle must be determined by trial.3 The octagon (Fig. 11) can easily be made by describing a square within a circle first of all, and then dividing into two equal parts each portion or arc of the circumference subtended by a side of the square. When straight lines are drawn from point to point in succession of the eight points thus found, the octagon will be formed.
All that has been said above will be apparent on examination of Figs. 6 to 11 inclusive, but if the reader will look closely at each of the figures, and note the effect of the dotted lines drawn across them from point to point, he will see how many additional regular figures may be gained from them. These figures are indicated by other figures the shaded parts, the original figure in each case being baSr<^uiarh6 hounded and contained by solid black lines. Thus, poly go us.	the overlapping of two equal and similar equilateral
triangles, as in Fig. 6, forms a six-pointed star, and a similar disposition of two squares, as in Fig. 7, gives an eight-pointed star. By drawing straight lines from each point of the pentagon, as shown in Fig. 8, to the extremities of the side that is opposite to it, a five-pointed star, known in heraldry as a mullet, is obtained. A similar procedure with regard to the hexagon gives a six-pointed star of the same form as that shown in Fig. 6, or three equilateral triangles
* The writer in a treatise on Geometry that appeared in a popular educational work proceeded in the construction of regular geometrical figures b} geometrical means as far as the undecagon or regular figure with eleven sides. This, as far as he is aware, has never yet been done by any geometrician except himself.
16SOME REGULAR GEOMETRICAL FIGURES.
FIG. 6.—EQUILATERAL	FIG. 7.—SQUARE.
TRIANGLE.
*7GEOMETRY FOR GARDENERS.
meeting in a point, as shown by the shaded parts in Fig 9. Finally, by treating the heptagon in the same way as the pentagon was treated, a seven-pointed star is formed, as in Fig 10 ; and Fig. 11 suggests the formation of four rhomboidal beds, which should be divided by an intervening space of turf or gravel path.
Having got thus far, it will be convenient here to speak of the division of the circle and the use of the protractor, which has been mentioned in Chapter I., in laying out such beds as we have been considering. I mean, of course, the brass protractor for working out plans on paper, and not the gardener’s protractor for work on Division of ground, which will be described in another place, the circle. But before doing this, let us see how the circle is divided, and the useful purpose which this division serves. The circumference of the circle is divided into 360 parts, known as degrees, and each part or degree is further subdivided into 60 equal parts, called minutes, and each minute into 60 equal parts, called seconds, but with the seconds and any further subdivision we need not concern ourselves. This division and subdivision applies not to any particular circle of a certain size, but to every circle whether it be the largest or smallest possible. So, if a circle contains 360 degrees, a semicircle will contain half this number, or 180 degrees, a quarter of a circle, or quadrant, 90 degrees, and a sixth part of a circle, or sextant, 60 degrees. And thus it is that the arcs of circles are used to denote and show the number o Angies degrees that an angle contains. “ But,” I daresay mearcls6orby you will feel inclined to urge, “ there is a great deal circles. 0f difference in the size of angles, for in one angle the straight lines that contain it are very long, and in another these lines are very short.” This is so, but it must always be borne in mind that the length of the straight lines which contain an angle, sometimes called its “legs,” make no difference whatever, and, indeed, have nothing whatever to do with its size. Probably, when you are talking about the size of an angle, you are thinking of the area or space that would be enclosed by its legs if a straight line were drawn from the extremity of one leg to the extremity of the other, and a triangle were formed. On the contrary, when I am talking about the size of an angle, I mean the 1 umber of degrees contained in the arc of a circle that may be drawn by placing one leg of the compasses on the point in
18SIZES OF ANGLES EXPLAINED.
which the straight lines that contain the angle meet, opening the legs as far as you like from or as near to this point as you like, and then describing an arc of a circle cutting both legs. The size of the angle is determined by the number of degrees in the piece of the arc intercepted between the legs of the angle. And this is what I want you to understand thoroughly and realize completely.
Let me try to help you by a diagram. It has been said, and well and truly said, too, that a little showing is worth any amount of telling, which means that comprehension is arrived at more
quickly through the eye than through the ear, or that pictures tell their tale more speedily and completely than words, and that is why I say,
• “ Let me try to help you by a diagram.” In Fig. 12, A B and c D are two straight lines, which intersect or cut each other in the point E, and these two straight lines are at right angles to each other. Further, by the intersecting of these straight lines four angles are made, namely, the angles A E D, D E B, B E c, and c E A, and they are at right angles to each other, each and all of the angles just named are right angles. Now from E, as centre, at the distance, or with the radius E F, describe the circle F, it, L, N, and then taking another and shorter distance, E P, describe from the same centre e, another smaller circle p, R, T, v. Determination Now you will allow at once that the size of any of angfe^ty area these four angles is the same, and that whether we of circles, speak of the first of the four as A E B, F E H, or per, there is no difference whatever in the sizes of these angles, because, in point of fact, they are identical, or, in ether words, one and the same,
19
FIG. 12.—ANGLES AND TIIEIR SIZES.GEOMETRY FOR GARDENERS.
because the inclination of the straight lines which contain the angles is the same in each case, and it is only in the length of the legs that there is any difference, and this difference in length of leg makes no difference whatever in the sizes of the angles. Now in a circle, or circumference of a circle, whether large or small, there are 360 degrees, and the circumference of the circles F H L N, P R T V, each contain 360 degrees, and each circumference bounds four angles, which are equal angles and right angles. Consequently, the four arcs F H. H L, L N, and N F, and the four arcs F R, R T, T v, and V p, are two groups of four equal arcs, and as the fourth part of 360 is 90, each of the arcs contains 90 degrees, and each angle that has been named is therefore an angle of 90 degrees. And the angles A E D, D E B, EEC, C E A, with which we started, are angles of 90 degrees, and they would remain so if the straight lines which contain them were produced from their extremities for miles, if such a thing were possible, for the reason which has been already given, namely, that the size of an angle is determined by the number of degrees in the arc of a circle by which it is subtended, a short way of expressing by a single word what I have hitherto spoken of as the arc of a circle intercepted between the straight lines that contain or bound the angle, such circle in every case being described or struck from the point in which the sides of the angle meet, as centre.
The number of degrees in a semicircle is 180, and as nfh, H L N are semicircles, they each contain 1S0 degrees. “Well,'"’you will say at once, “ there are no angles bounded by these arcs as they stand, so to speak, on the straight line N H.” To this I must reply that, mathematically speaking, N E His regarded as an angle of 1S0 degrees, though, practically, the lines which contain it are in one and the same straight line, and, being so, in no way meet your notion of an angle, as the inclination of two straight lines, one to another, which meet in the same point. At all events, you Arcs bounding will see and allow that it is composed of two right atbanSrightr angles, H E F, FEN, and admit the principle that two angi03- angles put together must make one angle, which will help you somewhat in the difficulty. I will not attempt to explain it further than this, for if I did it would lead us into deep water, and perhaps bring you, my reader, out of your depth. Moreover, ni explaining satisfactorily, I should have to go on to such an
20SLDES AND ANGLES AT CENTRES OF TOL JDONS.
extent that you would suspect me of an attempt to rival Tennyson’s brook, which, despite the coming and going of men, goes “ on for ever.” Now open your compasses to the extent of the radius E F, and placing one point at F mark the point G on the circumference of the circle, and the points H, L, M, o successively. The circumference of the circle is divided into six equal parts, or arcs, at the points, and as the sixth part of 360, or 360 divided by 6, is 60, each of these arcs contains 60 degrees, and each bounds or , subtends an angle of 60 degrees, and by drawing straight lines through the opposite points o, K, and G, M, you get the angles of 60 degrees which these arcs subtend, namely, the angles feg,gek, K E L, L E M, M E o, and o E F. Further, at the points P, Q, 5, X, u, \v, you get the division of the circumference of the smaller circle into arcs of 60 degrees, which, as already explained, subtend the same angles as the six arcs of the larger circle.
From the preceding remarks it is clear that the number of degrees in an angle subtended by the side of any regular polygon is obtained by dividing 360 by the number of sides in the polygon. It may be convenient for many to have a table show- Angies sub-ing the angles at the centres of regular polygons sub- tended by
0	0	o r jo	sides ol
tended by each side of the polygon, to which recourse regular poly-may be had when using the protractor illustrated in eons.
Fig. 4. The angles are given for all regular polygons, from the equilateral triangle to the quindecagon, in degrees and minutes, as closely as can be done without resorting to seconds ar.d fractions of seconds.
Polygon.	Number of »Sides.	Angle at Centre of Polygon.	
Equilateral Triangle 		3	120°	0''
Square 		4	90	0
Pentagon		5	72	0
Hexagon				<>	60	0
I Ieptagon		7	51	26
Octagon		8	45	0
Nonagon ... ._ 		9	wm	0
Decagon		10	36	0
Un decagon 		11	32	44
Dodecagon 		12	30	O
Polygon of 13 sides 		13	27	42
,, of 14 sides 		14	25	43
Quindecagon 		IS	24	O
21
cGEOMETRY FOR GARDENERS.
It only remains now to show how the protractor is to be used. Suppose we want to set out a hexagon by its aid. First draw a base line A B (Fig. 13), and on this line set off c D equal in length How to draw to one of the sides of the required hexagon. Place wFth^tlie1 ^ie protractor on A B with the nick in the centre of protractor, the straight edge against the point D. Make a mark on the paper at the extremity of the line marked 60, and after removing the protractor draw from D, through the point thus obtained, the straight line D E, and set off along it from the point D,
D f equal in length to c d.
Then apply the protractor in the same way to the point F, the central nick in the straight edge of the protractor being placed at
the point F. Make another mark on the paper at 60, and through F and this last point draw a third straight line, along which set off the length F G equal to C D and D F. Proceed in this manner to obtain the sides G H, H K in continuation of the sides CD, D F, F G, already drawn, and, lastly, complete the hexagon by joining the points K and C. The student should finish this figure in the manner in which I have commenced it, and then, for practice’ sake, construct in the same manner from the table given above every regular polygon that is mentioned in it.
FIG. 13.—HEXAGON DRAWN WITH PROTRACTOR.
22CHAPTER III.
FORMATION OF GARDEN BEDS IN CURVED SHAPES.
Ellipse, or oval, with given length and breadth—Ovals formed of arcs of circles —Another oval of arcs of circles—Third mode of drawing oval of arcs of circles—Volutes and spiral lines—Mode of forming egg-shaped bed—Bed formed of semicircles described on sides of square—Crescent-shaped bed, etc.—Semicircular ribbon bed—Horseshoe bed—Bed of serpentine form— Another bed of serpentine form—Cordate or heart-shaped bed—Fan-shaped figure—Bird-shaped figure.
LLIPSES, or ovals, are figures which frequently occur in gardens, and as these present more difficulty in their formation than the circle or any polygonal bed based on the circle, it is better to describe here various ways of forming them to which the operator
bear in mind concerning them is that the length must always correspond with the width. In cases where both the length and the breadth are given, the easiest way to proceed is as follows : Mark out a line, A b (Fig. 14), equal to the given length, and another, c D, equal to the given breadth, and intersecting A B at right angles at E, itself being also intersected by a b in the Ellipse, or same point, E. Now take a distance or radius equal givln length to half the length of the ellipse—in this case equal to and breadth. A E or b — and with this radius, from the points C and D as
23
may have recourse. The chief point to C
FIG. 14.— ELLIPSE WHOSE LENGTH AND BREADTH ARE KNOWN.GEOMETRY EOR GARDENERS.
centres, describe the dotted arcs shown in the figure which cut each other and the length of the ellipse, A B, in F and G. Drive two stout stakes into the ground at F and G, and having taken a piece of cord with a loop	c
at each end, equal to A is, including the loops, slip one loop over F and the other over G, and then tightening the cord to the utmost with a stick or iron stake, extend the cord till it touches the point A, and, keeping it tight, trace the curved
line, A C B I) A, which is FIG< j.—oval formed of arcs of circles. the ellipse required.
Thus it will be seen that the distance from any point in the circumference of the ellipse to F and G, taken conjointly, is the same in all cases, for F A + A G = FC + c G = F c' + C G = F B -f Bd~CD |DF, and so on for any other point in the circumference of the ellipse that may be selected.
Ovals can also be formed by the aid of two, three, or four circles, as here shown. In Fig. 15, three circles are formed on A B, the central line of the oval, whose length is given.
The outer edges of the two end circles form the ends of the
Ovals formed
of arcs of ellipse. Then draw C d circles.	.	. , .	,	, •
at right angles to A B at
the point of contact of the end circles, fig. 16.—another oval of
and also drawr the straight lines, b c,	arcs of circles.
af e c, and a g. Then form a as centre, with the radius ag or af
describe the arc gf and from c as centre, with the radius cb or ce
describe the arc be. The four arcs, gf f c, and e b, together,
make up the circumference of the required ellipse.
To make the ellipse shown in Fig. 16 describe two circles, A
24VARIOUS MODES OF DRAWING OVALS.
and la whose circumference will touch each other. Take the
diameter of one of these circles as a radius, and placing one foot
of the compasses first in the centre of one of these ,
r	. Another oval
circles and then of the other, draw arcs, as shown in of arcs of
the diagram, intersecting each other at the points a circ c&'
and b. Then from a and b as centres draw two more circles of the
same diameter, and those will form the ends of the oval. Then
draw straight lines through A and by b and li, B and a, and a and a,
as shown in the diagram. Lastly, from A as centre, with a radius
A C or A D, describe the arc C D, and from B as centre, with a radius
I! E or B F, describe the arc E F. The four arcs, CD,DE, E F, and
f c, together form the circumference of the ellipse, and the figure
is complete. These circles may all be formed by means of a stake,
to which a string is attached.
The method shown in Fig. 17 is still more simple. Divide the length, A B, into three equal parts, A c, c D, and D B, Third modeof and let the two points c and D thus found be the dr0a™rcs of3*1 centres of two circles, whose outside edges will form circles, the ends of the ellipse. From the points E and F, in which the
circles intersect each
other, draw through c and D the straight lines, E G, E H, F K, F L. Then from E as centre, with E G or E H as radius, describe the arc G n, and from F as centre, with F K or F L as radius, describe the arc K L. The four arcs, G H, H L, L K, and K G, as in the cases already explained, make up the circumference of the ellipse.
Gardeners’ methods of forming curved spiral lines are found in the following systems :—(1) To form a volute with numerous spaces: Make a circle around the centre of your intended volute, as much in circumference as you intend the breadth volutes and of your circuitous border to be. Stick the circum- EPlral Hues, ferential line full of pegs, and tie one end of a garden line to one of them ; then, taking the other in your hand, go out to the point
?5GEOMETRY FOR GARDENERS.
where you intend the volute to begin, and, as you circumambulate, holding the line strained tight, you will delineate on the ground the figure required. (2) To form a spiral line where the border is narrower, towards the centre, like the shell of a snail: Make a circle as before, and, instead of driving the pegs upright, let them form a cone ; or, instead of pegs, use a large flower-pot whelmed, and, if necessary, a smaller one whelmed over it Measure the radius of your volute, and wind that complement of line round the cone in such a manner as to correspond with the varying breadth of your intended border, and commence making the figure at the interior by unwinding the line.
The method of forming an egg-shaped bed exhibited in Fig. 18 will be found useful.
First set out the	A	'
straight line A B, equal to the greatest width of the bed required.
Divide it into two equal parts in the point C, and through C draw the straight line D E, of indefinite length, at right angles to A B.
Then from the point c, where A B and D E
intersect each other, with the radius C A or c B, describe the circle A F B G. Next, taking a and B as centres with A B and B A as radii, describe the arcs B H, A K, and from the same points A
Mode of form-	'	’	...
ing egg- and B draw through G—one of the points in which the shaped bed. cjrcje ^ f B G cuts the straight line D E—the straight lines A L, B M, respectively cutting the arc B H in the point O and the arc A K in the point N. Lastly, from G as centre, with the radius G N or G O, describe the arc or quarter circle N o, which completes the figure. The outline of the bed thus obtained is shown Beds formed hV the solid line‘
of semicircle The forms shown in Figs. 19,20, 21, 22, and 23, on sides of are frequently found in beds cut in turf, or formed
square. wj^ box edging ; and it may be useful to show as briefly as possible, the modes by which they may be conveniently
26CRESCENT-SHAPED AND SEMICIRCULAR BEDS.
laid out. In Fig. 19, the first step to out two straight lines, A B, c D, intersectin| angles in E. Then from E as centre, with
be taken is to lay ; each other at right any length of radius
FIG. 19.—BEDS FORMED BY SEMICIRCLES DESCRIBED ON SIDES OF SQUARE.
that may be determined on> describe the circle FGHK, In this circle inscribe a square, F G H K, and from the points, L, M, N, o, in which the sides of the square intersect the straight lines i0 A B, c D, describe the arcs rF P G, GQH, H R K, K S F. A bed of the form shown by the solid arcs of circles will then be formed, consisting of four semicircles described on the four sides of a square. The simplest method of construction is to lay out a square first of all, as F G H K, next to bisect the four sides of the square in the points L, M, n, o, and from these points as centres to describe the semicircles F P G, G Q H, H R K, and K S F, that form the bed; but the more elaborate mode of procedure has been given because it is suggestive of the formation of other beds as a crescent, formed by the solid arc FPG and the
J	.	Crescent-
dotted arc F G, which is a fourth part of the circum- shaped bed, ference of the circle F G H K. Other forms are those which are bounded by the solid arc FPG, and the dotted arcs F E, G E, or by the dotted arcs, F G, G E, E F.
In Fig. 20, a semicircular ribbon bed is shown. To lay out a bed of this form, a straight line, A B, equal in length to the distance between the outer edges of the border, is drawn, and this is divided into any number of equal parts, according to semicircular the width of the bed that it is intended to make; if ribbt>11 bed-narrow, a greater number of parts will be required ; if wide, less. In this case it is supposed to be divided into four equal parts, in the points c, D, and E. From the centre, D, at the distance, D A, describe the semicircle a h b, and from the same centre a*
77GEOMETRY FOR GARDENERS.
K E. Bisect the
the distance D C describe the semicircle c lines A c, E B, in the points F and G, and from these points as centres, with the radii F A and G B, describe the semicircles A L c, B M E, which complete the end of the bed. A bed of horseshoe form may be produced by extending the circumference of the circles A n B, c K. E, and forming the extremities of the 2o-—SKMI circular R,l!BON or
.	.	.	HORSESHOE BEL).
bed by drawing straight lines, as
L) N, l> o, intersecting the circumferences of the circles. From Fi
Horseshoe Jt* ig. 20 it may be easily seen how to form a bed of an P- or serpentine form, by repeating the process
v. >
already described on the line A B produced towards A or B, or continuing it on the lines D N or D o produced towards N or o.
A bed in a serpentine form is shown in Fig 21, which is very easily laid out. Firstly, a straight line, equal to the bed from end to end, as A B, is marked out, and this is divided into three equal parts in the points C and D. The divisions A C, D B, are again subdivided into two equal parts in the points K and F. From E and F, as centres, with radii E A, F B, the semicircles, A G c, BHD are described, and from C and D as centres, with radii c A and D B, the semicircles akd,blc, are described, completing the outline of the bed. By dividing A B into two equal parts Bed of ser- in M, and from M as centre, with the distance M A pentino form. on M ^ describing the dotted circle A N B o, a bed of a curved pear-shaped form is obtained, as A G C L B o. The faultSERPENTINE AND HEART-SHAPED BEDS.
FIG. 22.—ANOTHER SERPENTINE EED.
of the serpentine bed shown by the solid lines in Fig. 21 is that it is too sharp at the extremities.
Another serpentine form that has not got this fault is shown in
Fig. 22. In this the straight line A B is divided, as .	„	. ,
&	&	’ Another bed
in the above, into three equal parts, and each of of serpentine ,	•	•	...	„	form,
these parts is again subdivided in E, G, and F. Perpendiculars on opposite sides of A B are erected to A B at E and
F, as E H and F K. In E H, take E L, equal to E A or E c, and In F K take F M, equal to F B or F D. Join L M, and from L through C draw L n, and from M through D draw M o. Then from L as centre, with radius L c, describe the arc A c P, and from M as centre, with radius M D, describe the arc BDQ, and next from the same centres, with radii L Q, M r, describe the
arcs Q R, P S. Join A R, B S, and bisect them in T and U ; erect perpendiculars T v, u X, to A R, B s, at the points T and U, and from v and X (where these perpendiculars cut L R, M s) as centres, with radii V R, x s, describe the arcs A R, B S, which complete the figure.
A cordate or heart-shaped bed is formed as in Fig. 23 by dividing a line A B into four equal parts in the points D, C, E. Then from D and E
B
FIG. 23.—HEART-SHAPED AND OTHER BEDS.
29GEOMETRY FOR GARDENERS.
as centres, with radii D A and D B, the semicircles A F c, C G B, „ , , are described, and from the same points as centres,
Cordate or .....
heart-shaped with radii D B, E A, the arcs B K H, A L H, are described, which intersect each other in H, and complete the figure. By dividing A B into six equal parts in the Fan-shaped P°ints M> N, C, O, P, and by describing the semicircle figure. a Q B from C as centre, with radius C A or C B, and the semicircles A T N, N R o, and OVB, from M, c, P, as centres, a fan-shaped figure, enclosed by dotted lines, is obtained, and by completing the circle A Q B S, a bed similar to that shown in Fig. 18, but in different proportions, is exhibited. Lastly, by the larger and Bird-shaped smaller semicircles disposed above the straight line guro. a B, a bird-like figure, with symmetrical wings is shown, and another bed bounded by the semicircles A F c, C G B above the line A B, and the semicircle A S B below it. All these forms may prove useful in various positions, and will suggest modes of setting out geometrical gardens in curved lines.
30CHAPTER IV.
THE GEOMETRICAL CONSTRUCTION OF FLOWER-BEDS OF COMPLEX FORMS.
liaison d'etre for following remarks—The heraldic fieur-de-lys—Difficulties presented by figure—How to be overcome—Attempt at conventional treatment cf fieur-de-lys—Axis or central line of bed—Preliminary steps—Construction cf upper central lobe of fieur-de-lys—Delineation cf upper arcs of side-lobes cf figure—-How to strike out lower arcs—How to trace transverse bar —Construct™ cf part below bar—Completion of figure—Setting out straight lines at right angles to each other—Contrivance for effecting this—Application of contrivance to construction cf other figures—Protractor for laying out flower-beds—Dimensions and construction—Division of circumference of circle—How to obtain number of degrees in angle of any rectangular polygon —Hew to form equilateral triangle, etc.—Measurements of fleur-de-lys of different sizes-
T frequently happens that a professional gardener is
called upon to cut a flower-bed in turf in a shape that
is somewhat out of the common, or that an amateur
wishes to do a piece of work of this kind
1	^	Half on a elre
for himself. Now a little knowledge of for following .	, remarks,
elementary geometry is surncient, perhaps, to enable
anyone who is fortunate enough to possess it to mark out any
of the simple geometrical forms ; but when a more complicated
outline is desired, involving many curves and arcs struck from
different centres, with as many salient and retiring angles as
occur in an elaborate piece of fortification, it is by no means so
easy, as the working out of the process involves no little thought
and consideration, with a great deal of planning and contrivance
to meet and overcome the difficulties of the proposed figure. Let
us suppose that a gardener is about to cut a fleur-de-lys in a lawn,
and let us see how it is possible to trace a bed in this shape which
shall be in every way suitable for the purpose for which it is
designed.
3iGEOMETRICAL CONSTRUCTION OF FLOWER-BEDS.
In Fig. 24 I have given what I conceive to be a good example of the fleur-de-lys, as used either as a heraldic emblem or charge, The heraidio *r for decoration of an ecclesiastical character. I tieur-de-iys. }iave done this to show how unsuitable is the fleur-de-lys in its ordinary form for any other than the purposes just mentioned, and especially for a flower-bed, unless it were carried out on a very large scale—so large, indeed, that it would not be possible for the eye to gather in at a glance the outline of the bed itself, much less its various details when fully stocked with all the floral treasures that so vast a bed would hold. If I am asked to
FIG. 24. TRUE HERALDIC FLEUR-DE-LYS.
FIG. 25. SKETCH OF FLEUR-DE-LYS FOR GEOMETRICAL. TREATMENT.
explain why this would be so, I need only point to the narrow w. spaces that intervene between the central member of
DUhculties 1
presented the fleur-de-lys and those at the sides, both above and
jjy firwrg,	*
below the transverse bar that crosses and breaks the continuity of the three parts ; and say that it would be impossible unless these spaces were at least iS inches wide at the narrowest part—and for all practical purposes 3 feet would be better—to utilise them as a means of obtaining access to the interior of the bed, and at the same time to keep the turf of which they are composed in proper condition, and the verge or edge of the bed cleanly cut and well kept.
llow, then, is the difficulty to be got over ? Simply by conven-How to be tional treatment of the form that is desired—that is to overcome. say, by effecting such changes in its general outline that, while they do not in any way destroy its identity with4X/S OR CENTRAL LINE OF FED.
the object, natural or otherwise, from which it is taken, render it better adapted, and more suitable for the purpose which it is ntended to serve. In Fig. 251 give another sketch, which was made by a gardener who wished to cut a flower-bed in this form. Whether or not the absolute need for conventional treatment was felt by the delineator of this sketch, I cannot say ; but be this as it may, it is clear that, for the reasons above stated, the Attemptat sketch is far more suitable for a flower-bed than the t™at™entoJ true heraldic fleur-de-lys, and is, in fact, this form fleur-de-lys. conventionally treated for the special requirement in view. I will now proceed to show how this design may be drawn geometrically, being mainly formed by arcs struck from certain centres. It is in the determination of these centres that the difficulty chiefly lies in laying out this or any other bed whose outline is chiefly composed of arcs of circles.
Referring now to Fig.26, having determined the position of the bed, it is first necessary, by means of a garden-line and a couple of stakes, to lay down a central line, or axis, on either . . side of which the bed itself will be symmetrically dis- central line posed. This central line is represented in the figure by the straight line A B. In this straight line, at a suitable dis. tance from the end A, select a point c, and through c draw the straight line D E at right angles to A B, and measure off along the line D E, c F, and C H, each equal to 2} feet. The figure is constructed on a large scale, and is shown on a scale of £ inch to a foot; the size of the bed, however, may be regulated preliminary at pleasure by changing the scale ; for example, if the steps, scale of the bed be taken at | inch to a foot, then c F and c H will be each equal to ij feet, and the actual size of the bed when cut will be just one-half of what it would be if carried out on a scale of i inch to a foot.
By what has been done we have now obtained two points, F and H, at a distance of 2j- feet from the point c, and therefore at a distance of 5 feet from each other. From the point F, Construction with the radius F H, describe the arc k h l, and from °tra?iobeCcf^" the point H, with the radius H f, describe the arc fleur-de-lys. K. F 1.. These arcs give the outline of the upper end of the central lobe of the fleur-de-lys. To trace these arcs, drive in stakes at F and h, and have a piece of garden-line with a ring at one end that
33GEOMETRICAL CONSTRUCTION OF FLOWER-BEDS.
A- 5 S V & S ID H SCALE. ^jlN.GH! IQ 1 FOOT
12	13	14SIDE LOBES AND TRANSVERSE BAR.
may be slipped over each stake in turn, and a pointed iron at the ?ther, round which the free end of the line may be wound until the required length of radius is obtained.
From c now measure off along A B and towards B, C M = 7 feet if the scale be taken at inch to a foot, or = 3jfeet if taken at i inch to a foot, and from C as centre, with the Delineation radius c M, describe the arc N M O. From the point of sFde-iobTs3 M set off along A B, and towards B, M P, P Q, and Q R, of figure-each equal to 1 foot (I shall from this point leave off calling attention to any difference in reading the scale, as my readers can work this out for themselves), and through Q draw the straight line S T at right angles to A B. Along this line, in opposite directions from Q set off Q s and Q T, each equal to feet, and from K draw the straight lines K s and K T, through the points S and T. These lines cut the arc N M o in the points u and v, at which, as also at the points p and R, stakes should be driven in. From the point u, with the radius u x equal to 3! feet, describe the circle w X Y ; and from the point v, with the radius v A'describe the circle za'b'. In these circles we obtain the upper arcs of the side lobes of the figure, whose extent will be determined presently.
Through the points P and R, now set off the straight lines e' f' and g' h', each at right angles to A B, and therefore „ parallel to the central line s T, and along s T, in oppo- strike out site directions from Q, set off Q c' and Q D', each equal lower aros• to 6 feet. Then, from c' as centre, with radius c u, describe the arc w k' l'm', cutting e' f' and g' H in K' and L', and from d' as centre, with radius D' v, describe the arc z n' o'p', cutting e'f' and G' h' in N and O'. In the arcs W K' and zn' we obtain the lower arcs of the side lobes of the figure, and the arcs L' M' and O' P' of the extremity of the figure below the transverse bar.
Now set off P e' and P f' in opposite directions from P along
the straight line e' f', each equal to 3.)feet, and rg' „
|	°	7	^	’	How to trace
ana R H, each equal to 3^ feet, along the straight transverse
line g' h' from R, and also in opposite directions from
this point. Join E' G', f' h', and the transverse bar of the fleur-
de-lys is completed. Then from K', with a radius _
equal to 4J feet, describe the arc m' q', and from n', of part
with the same radius, describe the arc P' R'. Lastly,
from P' as a centre, with a radius equal to 5 feet, describe the arc
35GEOMETRICAL CONSTRUCTION OF FLOIVER-BEDS.
Q' s', and from M' as centre, with the same radius, describe the* arc r' s'.
The lower part of the figure is now completed, and all that is left to be done is to connect the upper part of the central lobe with the upper arcs of the side lobes. This is done by laying down from P the straight line P V', touching the circumference of the Completion circle W X V in T' and the arc K F L in u', and the of figure. straight line P y' touching the circumference of the circle Z A' b' in w' and the arc KHL in x'. By the addition of the straight lines T'u', w'x', the outline of the fleur-de-lys is now completed in every part, and is exhibited in the diagram by a thick and solid line, the portions of arcs and straight lines that are not included in the outline of the figure being in dotted lines.
The conventionally treated fleur-de-lys has been assimilated as closely as possible to the sketch originally sent, and copied in Fig. 25, and its outline has been geometrically traced as requested. If space permitted, a handsome cross might be formed of four beds similar to this, disposed so as to bring the lowest point s' in each to the distance of about three or four feet from each other.
It is possible that many gardeners, professionals as well as
amateurs, may find a little difficulty in setting out straight lines at
Setting out right angles to each other, or, in other words, in
straight lines setting oat one or more straight lines at right angles at right	&	0	....	,	,
angles to to another straight line as the straight lines D e, E F,
each other, g ^ ancj G» at fight angles to the straight line A B in Fig. 26. A contrivance for doing this without any trouble what-Contrivanoe ever’s sh°wn 'n Fig.27, and this may be easily made for effecting by anyone who can accomplish a little simple joinery.
The first thing to be done is to cut out and plane up two slips of wood, 3 or 4 feet in length, about 3 inches broad, and
FIG. 27. CONTRIVANCE FOR SETTING OUT LINES AT RIGHT ANGLES.PROTRACTOR FOR LAYING OUT FLOIVER-BEDS.
£ inch thick, as represented by BC, DE in the figure. These pieces, when accurately halved together and secured by screws, will present the form of a cross whose arms are at right angles to one another. Notch the ends of the arms of the cross with rectangular notches, their points or apexes being exactly in the straight line running through each slip from end to end, equidistant from its edges. Paint the cross itself black, and the straight lines forming the central line of each slip, white, and at their point of intersection at A bore a hole from i inch to 5 inch in diameter. Now when a straight line has been set out by means of stakes and a garden line, as A B in Fig.26,it is manifest that when the cross is passed under this line, that is to say the garden line, the line itself will lie along the white line, D E, if de be the slip that is placed beneath it, and that when the hole at A is brought directly over the point C in Fig.26,and another line is laid along and over the white line B c, the line thus laid down will be at right angles to the first line, A B. And provided that the four arms of the .	..
cross are of equal length, as they should be, a square, ofcontriv-L • J- ,	,	.7,	, , auce to con-
b d c E, may be immediately and quickly traced by Btruction of
putting in stakes in the ground, one in each notch at otlier figureb-the ends of the arms, and laying down lines from stake to stake. Or if marks be set between A and B, and A and c, at equal distances from A, as at L and M, a diamond may be formed by laying down the lines D L, D M, EM, EL; and, by turning the cross so that the white line, D E, is brought into the position F H, and B C into that of K G, by laying down the lines fk,k h, H g, g f, forming another square, an eight-pointed star, having the points B, F, D, G, c, H, E, K, will be produced.
In laying out beds and determining the inclination of straight
lines at certain angles to each other, a protractor on a large scale,
as shown in Fig. 27,will be found useful. This will „ ,
assume the form of a broad ring, whose inner and for laying out ,	. T	,	.. ilower-beds.
outer edges are concentric circles. It may be easily
made by cutting out arcs of wood of the necessary radius, in board
| inch thick, and arranging them in a double circle, so that the
joints in the circle above come about the centres of the pieces
forming the circle below, and vice versa, and then screwing the
whole firmly together to form a solid ring of -4 inch in thickness.
For the inner edge of the ring, 2 feet vll be found a sufficient
C 7
3J
DGEOMETRICAL CONSTRUCTION OF FLOWER-BEDS.
,93
radius, and from 2 feet 4 inches to 2 feet 6 inches for the radius of
the outer edge. The surface of the ring should be Dimensions .	0	.	.
and con- painted black, and two circles traced on it, one at the
distance of 1 inch within the outer edge, and the other at the same distance within the inner edge. The inner zone thus formed, and the central zone also, may be divided into spaces of 10 degrees, but the outer zone should be perfectly graduated in spaces of 1 degree, as shown in the figure. It will be useful to indicate the common centre of the concentric circles forming the ring, and traced upon it by wires traversing the central space from the points marked o and 180 ; and 90 and 270. These wires are not shown in the illustration.
The circumference of a circle, as it has been already Division of explained, is Ce£cemofr' divided into 270 circle. 360 degrees, a semicircle into 180 degrees, and a quadrant into 90 degrees. The number of degrees in an angle subtended by the side of any regular polygon, is obtained F,G_ 23_—protractor for gardeners. by dividing 360 by the
How to ob- number of sides in the polygon ; thus the angle sub-o^degrees In tended by the side of an equilateral triangle is obtained angle of any by dividins 360 by 3, which gives 120. If then stakes polygon. be placed at intervals of 120 degrees round the inner or outer edge of the protractor, and straight lines traced from
stake to stake, an equilateral triangle will be formed, Howto form	.	,	.	,
equilateral as shown by the dotted lines traced in the interior of
triang.e, eic. t^e figure. Similarly as an angle of 60 degrees is
subtended by the side of a regular hexagon, or six-sided figure,
this figure may be obtained by setting stakes round the protractor
at intervals of 60 degrees, and drawing lines from stake to stake,
as also shown in the interior of Fig. 28. Larger figures may be
obtained by laying out lines from the centre across the proper
38SCALE OF MEASUREMENTS.
marks of division to any extent, and taking points in the lines thus
obtained, equi-distant from the centre from which to lay down
lines to form the boundary of the regular figure required.
For the convenience of those who are not able to read a plan
by scale, I will conclude by giving the proportions of mentlfof
the various measurements above mentioned in terms fleur-de-iya -	.	, . .	.	ir	of different
of scales of \ inch, f inch, and h inch to the foot, sizes.
which, if followed, will give the fleur-de-lys, exhibited in Fig. 3 in
three different sizes.
			SCALE.			
MEASUREMENTS.						
			;} ill. tO		-3- in. to	£ in.to
			foot.		foot.	foot.
Semi radius, c F == c ll ...	...		2h	feet	11 feet	i $ feet
Radius F H = II F 			=	5	a	a	2è „
Radius c M		==	7	» >	5i a	3i
M P — P Q — Q R ...	...	=	1	>>	9 inch	6 inch
Q S = Q T ...	...	=	6i	>>	4 J feet	3* feet
Radius u x = V a'		=	01 02	a	2 8 if	a
Q C' = Q D' 			=	6	}i	4i f f	Ó
P f/ =PF, = RG/=RIi/		=	11 02	))	oh. b i i	T 3 i-f if
Radius c' U = D' V 			=	4	if	3 a	n — a
Radius of arcs, m'q', P' r' from k', n' 		centres .	_	4l	)*	■2?. OS if	2\ if
Radius of arcs, q' s', r' s' from P', M'		centres	-	5	ff	3Ì »	ol ■*2 if
B' G' = F' II' 			=	2	u	li »	I »
I trust that what has been said will be suggestive and helpful to many, both professional and amateurs, in designing and tracing the outline of flower-beds on geometrical principles. My next and last chapter must consist of a few remarks on design with respect to geometrical gardens, with some simple examples.
39CHAPTER V.
THE LAYING OUT OF GEOMETRICAL GARDENS.
Setting out geometrical garden on ground—Design suitable for square or circular garden—Garden in Dutch or French style—Garden in formal style —Necessity for working plans—Width of paths should be uniform—Suitable widths for paths—Gardens on mixed plan—Basket and tent beds—Edgings —Flower beds on sterile soils—Diversification of sky outline—Conclusion.
DESIGN for a geometrical garden is shown in Fig. 29, which may be cut in turf or formed with box edging, with gravel walks between the beds. The entire centre of the design is shown in the illustration, and a full quarter in the upper right-hand corner. From this a working drawing, showing the garden complete, may easily be made. In forming this design, the first step will be to drive in a stake at A, which is the centre of the eight Setting out concentric circles that form the main path in succes-^aiMenmi1 s've rin§s> fr°m the middle to the exterior limit of the ground. garden. This done, set out the straight lines BC,D K, intersecting each other in A at right angles, and the diagonals F G, H K, which also intersect each other in A at right angles, and make angles of 450 with the lines A B, c D, at the common point of intersection, A. If a point be taken on any of the straight lines passing through A, midway between Nos. 2 and 3 of the concentric circles, and another concentric circle be struck through this point, as M, for example, the centres, L and N, of the circles in the first zone of borders next the borders forming the centre, and the centres, K, M, H, G, of the inner curves of the elliptic borders arranged round the central border, and of the curves of the central border itself, will be found at the points in which the dotted concentric circle intersects the straight lines proceeding from the central point, A. The centres, O, P, Q, of the small circles of the outer zone of borders arc in the points in which the straight lines drawn through
40SETTING OUT GEOMETRIC GARDENS.
A are intersected by another concentric circle described from A as its centre midway between the circles numbered 6 Design suit-and 7. With regard to the curves that form the beds ab^®^irouia^6 in the second zone of borders, R is the centre of the garden, curves lettered T and u, and s the centre of the curves lettered V and w. Lastly, x and Y are the centres of the curves that form the spear-headed corner bed at F and the paths on the inner sides
B
of it. From the data given, the figure can be easily completed. With the corner beds, the design may be used for a square geometrical garden ; without them, it represents a circular garden.
Fig. 30 represents the centre and a quarter of a garden in the Dutch or French style. It is most readily formed by <3araenin drawing the centre and the four semicircles at the Dutch or sides, then drawing the diagonal lines, and, finally, Frencl1 style-the straight ones. This garden, if sunk about t8 inches or 2 feet
4iGEOMETRY FOR GARDENERS.
beneath the surrounding surface, would have a beautiful effect when looked down upon.
Fig. 31 represents a quarter of a geometrical garden in a more stiff and formal style, the other three-fourths being exactly the Garden in counterpart of that which is given. Beginning at the formal style, centre, it would be easily transferred to paper by dividing the dotted circle into an octagon, having the horizontal pides at top and bottom, and the perpendicular sides to right and left, longer than the four diagonal ones; the other lines being mostly straight, no instructions for their construction are necessary.
Irregular figures and elaborate patterns in box are not so easily managed as beds cut in turf, although many of them are susceptible of being formed upon certain and easily-ascertained principles. In cases, however, where it is otherwise, and the tracery is capricious and difficult to reduce to rule, there is no better mode of transference to the ground than by running lines across it in all directions, so that the ground is divided into a series of squares of equal size, corresponding to the same squares on the paper reduced to a scale. Holding the paper in one hand and a pointed stick in the other, almost any design may be copied in this manner. Of course, the plan on the paper will be divided into squares in the same manner as the ground. It would also facilitate the transference of all plans, if the chief points of formation were boldly indicated.
Generally, gardeners make rough plans for their own use ; and certainly, as I have already strongly urged, every design must be fully mastered on paper before there can be the
Necessity for
working slightest hope of success in placing it on the ground.
plans.	w-jj ke observed in the plans that are given in
Figs. 29, 30, and 31, that the spaces between the beds are of uniform width throughout. No plan ever looks satisfactory on
the ground if this desideratum is not carefully
•Width of ,	&	,	.	,	,	i , 3
paths should observed. Sharp, irregular, angular pieces ot turt or
e uniform. grave]; leading nowhere, may look very well on paper, but are most disappointing on the ground. Unless there are embroidery patterns of box or different-coloured surfaces, lay it down as a rule never to be infringed, that the spaces between the beds, whether occupied with turf or gravel, shall be of one
42WIDTH OF GARDEN WALKS AND PATHS.
uniform width throughout. The distance between them and the
main walks should also be the same at all points ; and,
as a rule, this distance should be greater than the widths for
width between the beds. The distance of one figure
from another must be determined by the size of the figures. On
grass, however, it should never be less than 3 feet, and need never
exceed 12 feet. Small gardens on gravel may have the figures
FIG. 30.—DESIGN FOR GEOMETRICAL GARDEN IN DUTCH OR FRENCH STYLE.
closer together ; but if the paths between them are much under 3 feet, the beds will have a miserable puny appearance. For large gardens, 5 feet will be a good average width for the paths ; for large gardens on grass, 6 is also an excellent average ; and 5, 4, down to 3, for those of smaller dimensions.
Sometimes gardens are laid down on a mixed plan of grass and gravel. When each bed is edged with brick, stone, tile, or
43GEOMETRY FOR GARDENERS.
cement, these edgings are occasionally surrounded with from 2 to Gardens on 4 feet S* Srave^ succeeded by the same or a greater mixed plan. Vvidtli of turf. Flagstones are also used for this purpose instead of gravel, as well as to subdivide groups of figures
close to the dwelling-house. Beds on grass, however, unless much elevated above the surface, are most effective without any edgings whatever : although, in certain situations, raised beds, with massive
44ORDERINGS AND EDGINGS FOR FLOWER BEDS.
edgings of stone or rustic work, look well. Single beds of this description often have their tops converted into the Basket and orm of baskets, tents, etc., to be covered with climb- tent beds, .ng plants or roses, with excellent effect. For beds on gravel, an edging of some kind becomes imperative. Of all living edgings box is the best; thrift, echeverias, sedums, and saxifrages of various kinds, follow each other in value and adaptability for this purpose, in the order in which they are here named. Ornamental stone, tile, brick, or cast iron edgings, are probably better than any living edging whatever. They can neither harbour insects, exhaust the soil, nor look patchy through dying off; and although perhaps
more expensive in the first instance, the first expense _
’	,	,	Edgings,
is the only one. They can be purchased on the most
reasonable terms, and of the most chaste patterns and varied and
elegant designs. Whatever edgings are used, they must vary in
height and thickness with the size of the beds they define. Nothing
can be in worse taste than a heavy, massive edging surrounding a
small, delicate pattern, or vice versa.
On sterile, uncongenial soils, it has been recommended by
Mr. Loudon and others to enclose all the flower beds with a brick
wall to the depth of 2 or a feet, so that the soil may _	. ,
r	/ Flower beds
be entirely removed at pleasure. Where this is on sterile
attempted, such walls would form an excellent base for the edging to rest on ; and where such an operation is unnecessary, a layer of concrete 6 inches deep will afford the requisite solidity and stability. Groups of beds, or single figures for roses, may often be edged with tiles of good design and embellished overhead with Gothic or other arches of wire-work, to be covered with the climbing varieties. Such
Diversifica-
erections, while objects of great beauty in themselves, tion of sky also diversify the sky outline of our gardens, and relieve that monotonous beauty which seems almost to be incident to our present methods of furnishing them.
The art of laying out gardens on geometric principles has now been set forth at sufficient length to enable every _	, .
lover of a garden to form his own, and thus heighten his enjoyment by adding to his other pleasures the satisfaction of constructing, and even carrying out, if needs be, his own designs without the assistance of others. As a matter of r* irse. in soGEOMETRY FOR GARDENERS.
brief a treatise as this, on so wide and varied a subject, many things have been left unsaid, and many geometrical processes have been left without mention, much less description, which might have been said and described with advantage. For example, when a gardener desires to form a spiral line, or a volute, as it is sometimes called, if he does not follow one or other of the methods described in p. 25, in all probability the mode of procedure he will adopt is to take a rope of some thickness, so its weight will keep it on the ground fairly well in the position in which it is laid, and then, starting from the central point, to arrange it in such form as may seem to the eye best to harmonise with the form required. The
____1_____1_____1_____l i____1_____1_____1_____1______L____
a g	f	e	dnc	h	k	l	mb
FIG. 32.—INITIATORY STRAIGHT LINE FOR SPIRAL OR VOLUTE.
gardener who is possessed of some little geometrical knowledge would go to work in a very different way. He would set out a straight line A B, through c, the point selected for the commencement of the spiral, and from c, in opposite directions along c A and c B set out equal spaces, c D, D e, e f, f g, to the left of c, and C H, H K, K L, L M, to the right. He would bisect CD in the point N, and then, from N as centre, at distances N D, N E, N F, N G, describe semicircles on c D, E H, F K, and G L, above the line A B, and from C as centre with distances c D, C E, C F, c G, describe semicircles on D H, E K, F L, and G M, below the line A B. If the reader will go to work and complete the figure according to the directions given, he will find that he has traced geometrically an accurate volute, commencing at C and ending at M. And with this I must quit a subject over which it is pleasant to linger.
46-HjH- SUN-DIALS *MJh-
AND	/
DIALLING.
I








SUN-DIALS AND
DIALLING
CHAPTER I.
DIALS, HORIZONTAL AND VERTICAL—HOW TO SET OUT
A DIAL.
Curiosities in dialling—Treatment proposed—Theory of dialling—The gnomon: what it is—Simplest forms of dial—South Vertical Dial—East and West Vertical Dials—North Vertical Dial—Vertical dials for walls--Setting out horizontal dial—Determination of latitude—How to find the hour-lines— Gnomon for horizontal dial—The meridian—Regulation of sun’s time—South Vertical Dial—IIow to set it out—Gnomon for South Vertical Dial—Another method for setting out dial—Setting out East Vertical Dial—Gnomon of East Vertical Dial—West Vertical Dial—Setting out North Vortical Diaz—Gnomon of North Vertical Dial—Practical part of subject—Working out problems— Mode to be adopted—Tracing lines of drawing on dial—Allowance for thickness of gnomon—Materials for dials—Painted dials—Gnomon on painted dial—Dial on freestone masonry—Incised lines and numerals—Pencilling letters and lines cut in stone-work—Rubbing down face of dial.
O enter deeply into the theory and principles of dialling would be out of place in a practical treatise like the present. They rather concern the mathematician than the mechanic. Together with the actual construction of dials, they have, however, curiosities formed a favourite relaxation of philosophers in many in diallin2* ages. Thus rules have been deduced for the construction of many complex, and, for practical purposes, almost useless dials—things of value only as matters of curiosity, and as means of displaying the scientific skill of their makers. Among these are the reclining and declining dials, and the still more complex moon clial.
With these philosophical toys it will be little to our Treatment purpose to deal. In treating of the science of dial- proposed, ling, what I propose to do is to give the rules on which the simpler
49SUN-DIALS AND DIALLING.
and more useful dials are constructed, and to do so in such a manner that they may be carried out by any person of ordinary ability, without the aid of special instruments.
As regards the theory of dialling, it will be sufficient for me to state that a horizontal dial is assumed to represent, and to be Theory of parallel with, the plane of the horizon ; and with that dia mg. plane every vertical dial is assumed to be a plane at right angles ; whilst that edge of the gnomon by which the shadow is cast, represents, and should be parallel with, the axis of the earth. Bearing these assumptions in mind, it is easy to understand that a gnomon which will be correct for all places of the same latitude will be incorrect for all others, and that it must vary in its inclination, as it is used nearer to or farther from the equator ; and also why, before constructing a dial, it is necessary to ascertain the latitude of the place at which it is to be erected.
The gnomon, it may be explained, is that projection from the face of the dial by which the shadow is cast. It means, literally The gnomon: and simply, “that which indicates.” That edge of what it is.	gnomon by which the shadow is cast is called the
“ stile.” The line on the face of the dial from which the gnomon projects is the “ sub-stile.”
The two most ordinary, simple, and useful forms of dial are the Horizontal and South Vertical. The horizontal dial we commonly Simplest see placed on the top of a pedestal. As a teller of forms of dial. tjme stands first in utility, since it will mark all those hours in which the sun is fairly above the horizon ; that is to say, in the height of summer, from four o’clock till eight. Its disadvantage is, that, except under very unusual circumstances, it can only be read from near distances. Considered as an object of taste and decoration, it is rather the pedestal than the horizontal dial itself which is capable of much embellishment.
Next in importance is the South Vertical Dial. This dial must
South occupy a wall or other elevation facing due south. Vertical Dial. q£ ap dials js die most simple, complete, and symmetrical, and is in itself best adapted to be made ornamental. It tells the time from six in the morning till six at night.
?Ind East and West Vertical Dials—that is, dials to tical Dials, occupy walls facing due east and west—are not difficult of construction ; but the period during which they mark the
50VERTICAL DIALS FOR WALLS.
time cannot in the longest day exceed eight hours, and they want that symmetry which renders the south dial so well adapted for ornamental purposes.
North Vertical Dials are also sufficiently simple, but they tell time only before the south dials begin, and after North Ver-they cease to act; that is to say, before six a.m. ticalDials, and after six p.m. Practically, therefore, they are next to useless.
A
FIG. I.— HORIZONTAL DIAL FOR THE LATITUDE OF LONDON.
Vertical Dials for walls which do not face either of the cardinal points can be made, but their structure is complex and vertical difficult. I do not propose to waste space by giving Dials for rules for making them. If the diallist has a wall of this kind on which to work, it is simpler and better to make one side of his dial so project, that a cardinal point may be faced.
To Set Out a Horizontal Dial.—On a sheet of paper of the required size of the dial draw the central line A B (Fig. i). This
5*SUN-DIALS AND DIALLING.
tion of latitude.
is the twelve o’clock line. It represents the meridian of the place Setting out f°r which the dial is made, and is the line in which Horizontal the sun is, or ought to be, at twelve o’clock. At a little more than one-third from the bottom of this, draw the line C D, cutting it at right angles in E. This may be called the six o’clock line.
We now need to know our latitude. A terrestrial globe, a gazetteer, or the index of an atlas, will, if we cannot find our exact Deiermina- latitude, give us that of some place sufficiently near to serve for all practical purposes. On the line C E, and at any convenient point, as F, we set off a line making, with F E, an angle equal to the latitude of the place at which the dial is to be used. Thus for London we must allow 51?°, for York 540 (nearly). This	n
line, continued to the meridian, will cut it at G.
The triangle fge, will give us the form of the gnomon, but it has also to assist us . in finding what we need first—■ namely, the hour-lines.
To do this, from H, the centre of the line F G, we must let fall a perpendicular equal to half its length, as H I, and draw lines to I from F and G. Then with I as a centre, and with H 1 as radius, we must describe the quadrant J K. This we have to divide into six equal parts, and through the points thus gained we have next to draw lines from I till they meet the line F G. Through these points of contact on F G we may now draw lines from E to the circumference of the paper, and we shall have the hour-lines from six a.m. to twelve at noon. To get the afternoon hours we have merely to fold the paper at A, B, and prick through with a point to the opposite side, for the two sides of this dial are just alike. The hour-lines for four and five in the morning, and seven and eight in the evening, are to be obtained by merely continuing the morning seven and eight and the afternoon four and five hour-lines beyond F. The half and quarter hour
How to lind the hour-lines.REGULATION OF SUN'S LINE.
divisions are to be obtained by a continuation of the process which gives us the hour-lines.
Fig. 2 shows the gnomon for this dial. Its form is that of a triangle equal to F g E, in Fig. t, Its angle A is the same as F in
Fig. i, and is made to agree with that of the latitude
-	°	Gnomon
of the place, which, in the present example, will give forhori-,	-	10	’	H ,	,	zontal dial,
an angle ot 51$ . When placed perpendicularly on
the dial its position will be on the meridian line A, b, the point A falling on E, and the line A C falling along the meridian line in the direction of g. The point B will be that which projects farthest from the dial. The line A B will be the “ stile,” or that which casts the shadow, and the line a c will be the “ sub-stile.” The angle formed by these two is called the “ elevation ” of the stile.
At the beginning of the above rule I spoke of the meridian as the line in which the sun had, or ought to have, his place at twelve o’clock. This implies an amount of irregularity in the The sun of which he is not suspected by the majority of meridian, people. Even amongst the educated the greater number hold the belief that a true sun-dial will always tell true time. This, literally understood, is simply a vulgar error. When Pope bids presumptuous man “ Correct old time and regulate the sun,” he by no means commends him to a needless task. The sun is in reality a most indifferent timekeeper, and wants a great deal of _ j tion correcting. In this particular department of his « bub’s business he is outdone by clocks of even moderate punctuality. Apart from some minor disturbing influences, the fact that the plane of the ecliptic in which he moves is not parallel to the plane of the equator, necessitates that he should really come to the meridian precisely at twelve o’clock on four days in the year only, namely, the 20th of March, the 21st of June, the 23rd of September, and the 21st of December. At other times he w ill either be before or behind that time. About the 1st of November he comes more than sixteen minutes too soon. This, however, by no means renders the sun-dial valueless as a teller of time. He is regular in his irregularities. The daily difference between clock and sun can be, and has been, accurately calculated, and is given in most almanacks. So that by adding or subtracting the difference, as the case may require, to the time shown by the sun-dial,
53
SUN-DIALS AND DIALLING.SETTING OUT SOUTH VERTICAL DIAL.
absolutely correct mean time may be ascertained, and clocks and watches set right.
To Set Out a South Vertical Dial.—As in the last problem the meridian A B, Fig. 3, has first to be drawn, and at any convenient point upon it, as c, a perpendicular of indefinite length south ver-must be erected.	ticaiDiai.
For setting out this dial and its gnomon we require not the latitude itself, as in the last problem, but the complement to it, that is, so many degrees as will bring it to 90°, the how to degrees of a right angle. Still, as- set it out. suming that we are working for London, we must subtract the latitude of that place, 51 i° from 90°, which will leave 38A0, and that is the complement we require. From A we now set off a line at an angle of 38^°, which will cut the perpendicular at D. And from n we set off another line at the same angle of 3S30, or whatever the given complement may be, which will cut the meridian at E. Through E we draw the line F G at right angles with the meridian. Then taking E H equal to ED and with H as a centre, we describe the quadrant F. 1. This has to be ® divided into six equal parts, and through the points thus gained lines have to be drawn from H, cutting the line F G at K, L, M, F, and G. Lines drawn through these last-named points from A to the circumference of the paper will give the hour-lines from noon to six p.m.; and of these the morning lines will be the exact counterpart.
Fig. 4 shows the gnomon for this dial, in which the angle B must be equal to the complement of the latitude, that Gnomon for is 38^°. When it is fixed perpendicularly to the dial the angle B will fall upon the point A in Fig. 3, and the line B A will fall down the meridian line towards B; c being the projecting angle.
Another method of setting out this dial is by proceeding as
FIG. 4.—GNOMON OF VERTICAL SOUTH DIAL.
South Vertical Dial.
55SUN-DIALS AND DIALLING.
with the horizontal dial, Fig. i, but using instead of an angle equal Another to the latitude, one equal to its complement. The of setting method described above is, however, the one usually out dial. followed.
To Set Out an East Vertical Dial.—To do this we must first Setting out draw the horizontal line A B, Fig. 5, and at B draw the ticaiDiai. line B c, making the angle ABC equal to the complement of the latitude. Then at D, and with any convenient radius,
K
FIO. 5.—VERTICAL EAST DIAL FOR THE LATITUDE OF LONDON.
we have to describe a circle. Touching this circle at I and J, we have to draw two lines, E F, and G H, parallel to c B. Through the centre D, and at right angles to c B, we draw I J, which is our six o’clock line. To obtain the other hour-lines we divide each of the four quadrants into which the circle has been cut, into six equal pai cs, and from the centre D, through the points thus ascertained, we draw a series of lines till they cut E F and G H. By uniting the corresponding points of intersection on these two lines, we get the hour-lines 4, 5, 6, 7, 8, 9, 10, and 11 ; which include as long a portion of the day as this dial will mark.SETTING OUT NORTH VERTICAL DIAL.
Fig. 6 is the gnomon of this dial. Unlike the former examples, which are triangular, this is a parallelogram in shape. Its width must be equal to the radius I P, of the circle in Fig. 5, Qnomon of and its length should be somewhat greater than the Eastver-
•	* n ■>	Tii	tical Dial.
diameter of that circle. When fixed perpendicularly
to the dial, it should be placed lengthwise on the six o’clock line
I j, Fig. 5, with its centre A falling on D.	Wesfc
A West Vertical Dial is the exact converse of the Vertical •	•	Dial,
above, and its gnomon precisely the same.
To Set Out a North Vertical Dial.—This may be regarded as
the complement of the South Vertical Dial. It tells those hours
of daylight only in which the latter is useless. We getting out
shall construct it most easily by availing ourselves of North Ver-
.	T	tical Dial,
the diagram of the South Dial, Fig. 3. Let us take a
piece of paper, and so place it that its lower edge may lie on and
coincide with the six o’clock line through A, Fig. 3. To explain more fully, I show in Fig. 7 the upper part of the South Dial, and meeting with it and joining it at the line through A, the lower edge, Y z, of the paper w x Y z, on which the North Dial is to be drawn. First, we produce the meridian B A, upon our paper to C. Then we continue the hourlines five and four through the point A, to the opposite edge of the paper. These give us respectively the evening hours seven and eight. The morning hours four and five may be obtained in like manner by continuing the morning seven and eight hour-lines from the South Dial. The lower edge of the paper is the six o'clock line, and as our North Dial marks time from four to six a.m., and from six to eight p.m. only, we have now completed it.
The gnomon is precisely the same as that of the South Vertical, but must be placed upside down. Thus Gnomon of
1	,	T,.	r 11	1	•	.	North Ver-
the angle B, Fig. 4, must fall on the point A, Fig. 7, tical Dial.
and the line B A will lie along the meridian in the direction of c.
As much of what I may call the scientific part of dial- Practical J	1	part of
ling as is likely to be of general use, is included in the subject.
above rules ; we now turn to the more practical part of our subject.
57
FIG. 6.—GNOMON OF VERTICAL EAST DIAL.SUN-DIALS AND DIALLING.
When anyone of my readers proposes to make a dial, it will be well for him to work out the required problem to the same size as
the intended dial. This will be far better than working it on a small scale, and afterwards enlarging it. On a large scale errorsWORKING OUT PROBLEMS IN DIALLING.
are far less liable to occur, and it must be remembered that unless worked out with perfect truth and precision through- Working out. out, the dial will be worthless as a time-teller. If the problems, worker has not been in the habit of making mechanical or architectural drawings, I may observe that his better plan will be to use a drawing-board and strained paper. The sides Mode to be of a drawing-board will be straight lines, and its adopted, corners right angles, so that by working with a T-square he will have no difficulty in keeping his lines true. Paper is strained by damping it on both sides with a clean sponge, and then, after leaving it four or five minutes to soak and swell, gluing or pasting it round the edges to the board. As it dries, it shrinks and stretches itself as tight and smooth as the end of a drum, and thus allows of truer and more satisfactory drawing than when merely pinned down. When the drawing is finished, the paper can be cut from the board.
It can then be laid upon the surface of the actual dial, and its
lines traced off. There are various well-known ways Traoing lineg
of doing this : such as covering the back with chalk of drawing °	f	on dial,
or charcoal, and going over the design with a hard
point; pricking holes and rubbing some powdered colouring
matter through them; etc.
Before beginning the tracing one important fact has to be borne in mind. In theory, and consequently as shown in our diagrams, the gnomon is a mere line. In practice, how- Auowance
ever, it must have so much thickness of material as for thicknesa
of gnomon.
will enable it to resist any forces which might bend or break it. Due allowance must therefore be made for this thickness. Before we begin to trace, we must decide what the thickness of the gnomon will be; and then cutting our paper plan in two, up the line on which the gnomon is supposed to stand, we must fix the pieces on the actual dial just so far apart as to allow space between them for the actual gnomon to be placed.
The materials to be used by the diallist will much Materials depend on the locality in which, and the circum- fordials, stances under which, he works, and his own taste; yet I may perhaps be able to give some useful suggestions.
Against a house or other building of ashlar, brick, or stucco, if the workmanship is level and good, there can be no difficulty in
59SUN-DIALS AND DIALLING.
simply painting a dial. In ordinary oil colours it may stand for Painted years. With a trowel, any hollows or inequalities may
dials. be filled up with a little cement, the wall having first been damped. The space for the dial may be covered with a couple of coats of some light colour, which will throw up the figures and lines well—say a stone colour. If the porousness of the wall is found an objection, by absorbing the oil too rapidly, and thus causing the colour to clog rather than to work freely, going over it first with linseed oil will remove this difficulty. On the painted background it will be a simple matter to trace and pencil in the lines and figures of the dial.
The gnomon, if of metal, can have a couple of pins attached to it, and be fixed by letting these into two holes drilled into the Gnomon on wall, and there cementing them. A square should be pamted dial. use(j jn settjng t]ie gn0mon, that it may be set perfectly perpendicular to the dial. If the height and position of the dial are such as to render the danger of breakage small, the gnomon may well be made from a piece of slate, which is more easily worked by the amateur than metal, and of which the virtual cost is nothing. A slate gnomon will need cementing into a groove. Beyond the trouble of the diallist, it will be seen that the cost of erecting such a dial as this will scarcely be appreciable.
If the wall should happen to be of good freestone masonry, a more workmanlike and enduring thing may be made by incising ,	the lines and letters of the dial. A smooth face on
freestone	which to do this, may be obtained by rubbing down
masonry. ,	,	. .	, .	.	.
the required space with water and a flat piece of gritstone. Any stone wffiich, like Yorkshire paving-stone, is composed of a sharp, hard sand, will do this. When the surface has been gritted and washed clean, the paper plan of the dial can be stuck r	to it with wafers, and a tracing made. The lines and
lines and	numerals will then need to be cut pretty deeply into
numerals. ,	. ,	.. .	....	„
the stone with V-shaped incisions, freestone cuts easily. If the worker does not possess stone-cutting tools, he will find a carpenter’s or wood-carver’s chisel do equally well, and be little the worse for it.
As in this case the ground will not be painted, before the letters are painted black, it will, in order to prevent running of the colour, be well to pencil them over with japan size. There are two w'ays
60INCISED WORK ON DIALS.
in which black paint is applied to incised letters in stone-work;
One is to “ write ” them in with the pencil. Practice, Pencilling
patience, and a steady hand, are wanted to do this baeewitln
well. The other is to “ slush ” them in ; that is, to Btone-work-
dab the colour into the incisions with a big brush. In doing this
it matters nothing how much colour may be daubed upon the face
of the stone beyond the incisions, for when the paint Rubtin
has dried, the whole face has to be rubbed down with down face ■ 11	11	„	.	,	,	, of dial,
grit-stone, till all superfluous pamt has been ground
off. If the cutting has been well done, the letters will with this
process come out as well as if put in by the most skilful “ writer.”
6iCHAPTER II.
HINTS AND SUGGESTIONS FOR MAKING ORNAMENTAL DIALS.
Example of Elizabethan dial—Mottoes from old dials—Painting dial on wall— Suitable substance for painted dial—Emblematic decoration—Slate dials : their treatment—Facing to cardinal point—Oaken dial—Ornamentation for east dial—Dial on pedestal—Material for dial on pedestal—Metals for plates of dial—Stone and slate—Formation of pedestal—Carving in soft stone easy —Stones suitable for carving—Rustic wooden pedestal—Formation and material—Height of horizontal dial—Combination dial—Form of gnomon —Cost of casting brass—Gnomon of sheet copper—Care necessary in fixing dials—Situations suitable for dials—Dials on lawns—Choice of wall space— Present purposes of sun-dials—Dials now superseded by clocks—Dials mentioned in Scripture—Roman dials—Large dial near Delhi.
HE Elizabethan dial shown in Fig. 8, I have sketched from memory only. The original, on the front of an Elizabethan manor-house in Warwickshire, is in very low relief in pargetting-work, that is, in plaster. One of a similar design might very well be carved in stone, but I have introduced it in this place because it appears to me a Example of	calculated to be effective if simply painted in
EUzabethan ]3iac]< on a wan. The outline should be boldly made out, and the little shading necessary, indicated by a few lines only. From association, perhaps, the Elizabethan style seems peculiarly suited to the adornment of sun-dials ; and the cartouche form, on which the present example is placed, admits of being varied to infinity.
It will be noticed that this dial bears a motto, “ Orimur, Morimur ” (We are born, we die). The application of mottoes to Mottoesfrom dials is an ancient and praiseworthy practice. Many old dials, learned men have puzzled their brains to devise suitable ones. The Latin language has, on account of its terseness, always been the favourite vehicle for these things. Here are a few
62MOTTOES ON OLD SUN-DIALS.
examples, gathered from old dials. “Noli conjidere nodi" (Trust not to the night). “ Umbra sumus” (We area shadow). “ Lex Dei lux did” (The law of God is the light of day). “ Vigilate et orate” (Watch and pray). “ Per emit et imputantur” (They pass away and are laid to our account). “UIt imam time ’’ (Fear the last
AN EXAMPLE OF AN ORNAMENTAL SOUTH VERTICAL DIAL.
hour). “ Fugit irreparabile tempus” (Irredeemable time flies away). But English has at times been used ; as witness that not less humorous than practical motto which said to the loiterer, “ Begone about your business.” Sometimes, too, a couplet was employed, as in the following quaint and devout example :—
“Yield thou to God thy heart, thy time, thy gold,
The day fast weareth, and the years wax old.”
63SUN-DIALS AND DIALLING.
In the case of painting on the actual wall it has been assumed that the aspect has been due south, or at least that the wall has Painting dial faced one of the cardinal points. This having been onwai. satisfactorily ascertained, the plan of the dial can readily be traced and drawn in its place by the aid of plummet and level. But supposing that the wall does not duly face any point, or that its material is not suitable for painting upon ; or, even supposing that the diallist prefers to carry on his work in a place where he can pursue it with greater ease and leisure than against the actual wall, he will find various materials suited to form a ground on which he can paint, and he can afterwards fix up his dial with hooks.
As a good, cheap, and enduring substance on which to paint, and one on which any amount of colour and gilding may well be Suitable employed, zinc may be mentioned. Whether much substance for gay colour and gold about a dial are in good taste is a question for individual opinion. There are good old examples in favour of such decoration. One might be quoted in which a mediaeval ship—an emblem of the course of time—is Emblematic made to do service as the base of the dial, its mast is decoration.	meridian, and its ropes form the hour-lines.
Indeed, if the decorator has a taste for allegory, symbolical matter suited to his subject may be found in abundance. To come to more practical matters, however, it will be advisable to let the colour interfere with the hour-lines as little as possible. If thrown upon dark colour the shadow of the stile is much less easily seen than it should be, and, thus, the original purpose of the dial is sacrificed to mere ornament.
Another good and inexpensive material for painting upon is a slab of slate. Slate may be gritted down to a good, even surface . ...	in the same way as freestone, and afterwards still
their	farther smoothed by rubbing with pumice-stone. In
treatment. ....	.	,	.	.	.
fact it is a freestone. It may be treated as such—its face generally left of the natural colour, and lines and numerals incised. In this case, on the dark-coloured ground, gold tells best for picking-out the incisions. For this, as for every other kind of out-door gilding, oil-size must, of course, be used ; the lines and letters having previously received a coat of japan-size, and then one of chrome-yellow paint. A dial made of thin material, such as
64FACING DIAL 10 CARDINAL POINT.
zinc or slate, can readily be packed to any required angle, and one side brought farther forward than the other by fixing a Paclng to wedge of wood or stone behind it. If under the same cardinal
°	.	point.
necessity for bringing the dial to face a cardinal point, a slab of stone is used to work upon, the simplest way is to bring
it to the required angle by cutting it wedge-shape ; but on a block
of good stone I imagine that no diallist will care to paint, but will
rather incise and black his letters.
Wood, from its liability to warp and decay, can scarcely be
called a good material for the diallist. Yet against one .	..	.	....	Oaken dial,
of my buildings is a dial painted on a slab of oak
which bears the date 1834. It recently came into my possession,
65SUN-DIALS AND DIALLING.
and when I fixed it in its present position I found the wood perfectly sound and good. It had been well coated with white-lead paint, which is undoubtedly the best preservative in common use for woodwork exposed to the weather. This dial proves that, in the absence of better materials, a sound piece of oak may be made to serve the purpose of the diallist, with a reasonable prospect that it will at least last for his own lifetime.
The well-balanced arrangement of the south dial makes it easy of being rendered ornamental, but the lop-sided figures of the east Ornamenta- anc^ west dials causes them to be much less susceptible
tionfor of artistic treatment. In Fig. o, however, I give a east dial.	.	°	’ b
suggestion for the ornamentation of an east dial. As
an appropriate emblem of day the sunflower is introduced. This design is intended to be illuminated on zinc, in gold and colours.
The most usual and appropriate place for a horizontal dial is upon the top of a pedestal on a lawn, or in a garden. Thus the Dial on	dial itself cannot be a conspicuous object, however
pedestal.	mUch the pedestal may be so. It is indeed scarcely
seen except by those who examine it to learn thejame. To make it the subject of elaborate ornamentation would therefore be absurd, and the diallist who has to decide on the material from which to make it, will not have to consider what will best bear decoration, but simply what will practically be the most suitable.
A strong material will be necessary, for the position of a horizontal dial is a trying one, both as regards exposure to accidents Material	an<^ vveat^er- Ip spite of warnings to the contrary,
for dial on	garden tools are sure to be rested against or laid upon
pedestal. f	...	.	.	,
it. Being within reach of every one, it will now and
then have to receive hard knocks. As it will lie perfectly flat, every shower will wet it, and the water which it receives will not readily run off. The vertical dial can be, to some extent sheltered, or, at the worst, will throw off the rain and quickly dry again ; not so this. No painted surface could last long under these circumstances, and incised letters in soft stone would after rain hold puddles of water, which would soon tend to destroy the stone. If the diallist wishes his work to stand, he must be careful in his choice.
Metals for For these reasons metal is almost always em-piatesofdial, p^yg^ and generally brass. The diallist unaccustomed to work in metals, need not be afraid of this material. If
66AT A TERIALS FOR SUN-DIALS.
he gets a brass plate and a graver, which latter will cost about sixpence, he will, if used to handling tools, find it quite possible to engrave his dial with sufficient neatness and decision. The task looks much more formidable than it really is. Hard as the metal may seem, it yields to a properly tempered tool. A plate of copper, which is nearly as good for the purpose, he will find much more
FIG. IO.—DESIGN FOR A HORIZONTAL DIAL.
easy to engrave. A slab of hard, white stone, such as Sicilian marble, will stand well and be uninjured by weather, stone if the amateur possesses the tools and skill to cut it. and slate‘ More available and practicable, however, is a slab of slate not less than half an inch thick ; this is easily to be got, stands weather well, and may readily be incised. In the design for a horizontal dial, Fig. io, there is nothing that could not easily be engraved by any one on copper or slate.
67SUN-DIALS AND DIALLING*
How far the pedestal can be formed without professional help is more doubtful. Pedestals for dials are most commonly made of Formation of stone (in a style more or less following the Italian, see pedestal.	and comparatively few amateur workers care
to touch this material. Many who are perfectly at home in working or carving wood, look with a certain awe at stone, as a material quite beyond their power. I well remember having this feeling
myself in early life ; and when I had once overcome it, I was surprised to find how very much easier it was to carve in soft stone than in wood.
There is nothing in working a pedestal in freestone which need
alarm any ingenious person. Unlike wood-carving, stone-carving
Carving in demands no considerable outlay on tools. I remem* soft stone	,
easy. ber, years ago, the man who now stands pre-eminent
among English stone-carvers, talking on this subject, said to me,
68RUSTIC WOODEN PEDESTAL.
“ One can’t have too many tools for wood-carving ; but as for stone, I can carve it as well with a rusty nail.” This, if not literally true, expressed the broad fact correctly. Few and simple instruments will suffice for soft stone; and if wood tools are used, they will suffer no more injury than may be put right by re-grinding.
When resting on the earth, and still less when partly buried in
it, few kinds of soft stone will stand weather well. stones
Indeed, Caen, the best of all soft carving-stones, will suitable for
carving.
not stand anywhere out of doors. In Bath stone, there
is one description which bears weather well, but is unfitted for
carving, whilst that which is a good carving stone will not bear
frost. Among stones in general use, Portland is the only one
which at the same time will bear a reasonable amount of exposure,
and admit of easy, if not of very elaborate
carving. It will be found well suited for
the present purpose. Its cost, in London
stone-yards, is about is. 6d. per cubic foot.
Except in quite a formal garden, a
rustic wooden pedestal may Kusti0
be as pleasing to the eye, if wooden , . °	*	pedestal,
less enduring, than one of
stone. Merely the stump of a tree, twined round with creepers, will in many situations look well when applied to this purpose. In Fig. ii, I have given a somewhat more elaborate design for a rustic-work pedestal to exercise the skill of the amateur dial-list and carpenter. Its construction is explained by the plan, Fig. 12. It is formed of one larger length of rough wood, covered with bark—say of 6 or 7 inches diameter—and two smaller Formation lengths, sawn through their centres, and nailed against andmaterial-the sides of the larger. Larch is the wood to be preferred, both for appearance and durability. The base and top are of stout plank, over which are nailed strips of rough wood. The kind of “ dog's-tooth” ornament running up the hollows, is formed merely of fircones, fastened with brae's to the woodwork.
A horizontal dial is, it should be remembered, much more easily seen and consulted if kept well below the eye.	Height of
It is a lrequent mistake to make the pedestals for such Dial, dials too lofty. About 3 ft. 6 in. is a good height. The combina-
69
FSUN-DIALS AND DIALLING,
7oGNOMONS—FIXING DIALS.
tion dial (Fig. 13) is not unfrequently to be seen, mounted on an ancient stone shaft, in a country churchyard. With combination the horizontal, it comprises the north, south, east, and west, vertical dials. The four last certainly tell the time no farther than it is told by the first, but they may be seen more readily; and a dial of this kind derives a certain charm from its completeness. With a cube of hard stone, or oak, its construction need offer no difficulty whatever.
The gnomon of a horizontal dial is much more exposed to injury than that of a vertical one ; and as an unbent and un- Form o£ broken line in the stile is essential to true time-telling, gnomon, care must be taken to secure sufficient strength. In the horizontal dial, also, the gnomon is a conspicuous object, and is therefore a fit subject for ornament. Both strength and decoration can be got in cast brass. The diallist can cut a wooden pattern to any design that he pleases, and place it in the hands of a brassfounder to be cast. The usual charge for casting brass is about iod. costofcast-per pound. It must be remembered that the metal	mg brass,
shrinks in cooling, and will therefore be somewhat smaller than the pattern An ornamental gnomon is shown in Fig. 14.
If the situation is a comparatively safe one, whether on a horizontal or vertical dial, a sufficient gnomon may be Gnomon of made of sheet copper which any amateur can work for Eheet copper, himself. A tolerably thick sheet of copper can be cut through with a mallet and chisel, if laid on a lump of lead or a crosscut block of hard wood, and can afterwards be neatly finished with a file.
In fixing dials of all kinds, much care and exactitude are necessary. A horizontal dial requires to be laid perfectly Care neces
flat, and should be tested with a spirit-level, or, fail- nary in
,	.	. ,	,	'	fixing d ais,
ing such an instrument, with a mason s plummet. I hat
the meridian—the twelve o’clock line—runs due north and
south, may be ascertained by a mariner’s compass, or otherwise by
setting the dial on a sunny day, with the aid of a correct clock ;
but before doing so it will be necessary to consult the almanack,
and to make due allowance for the difference, if any, between the
Jock and the sun, on the day when the dial is fixed.
As regards the choice of situations in which to place sun-dials, it scarcely seems necessary to premise that the site should be one cn which no trees or buildings can throw shadows which will
71SUN-DIALS AND DIALLING.
Situations suitable for dials.
interfere with the working of the dial. In other respects much will have to depend on circumstances, and on individual taste. I may, however, observe that a horizontal dial, mounted on a carefully or elaborately shaped stone pedestal, never looks so well as when occupying a small bed in the centre of a geometrical flower garden, laid out in formal knots and paths. Such a garden, in fact, never looks complete without its central sun-dial.
In a garden arranged more in natural style, as for instance, where we have an irregularly-shaped lawn, broken upon in places
Dials by trees or shrubs, a horizontal dial will look more in on lawns, keeping if it be mounted on a mere tree-stump, or such a rustic pedestal as the one suggested above. Due regard paid to the fitness of things in such apparently slight matters, goes far towards creating a general effect of good taste.
In fixing upon wall-space erection of vertical dials, then one or two practical considera tions which it will be well to bear in mind. In the first place, it will be desirable to set the dial high enough,
that it may be out of harm’s way and easily seen. In the second Choice of place, to secure, if possible, a wall duly facing one of waU-space. tjie carcjjnai points. If this is not done extra labour will be involved, either in working out the problem of a more elaborate dial, or in the mechanical toil of giving one side of the simple dial the projection necessary to make it face the required point; and in either case the effect, aesthetically considered, will not be so good.
But apart from practical considerations, I own that for my part
I rather regard a sun-dial as a thing for the contemplation of myself
Present and niy friends than for that of the general public, purposes of	J	0	r
sun-dials. The days are gone past when the dial regulated the busy affairs of life, and stood in the market-place, and wherever
72
FIG, 14.—ORNAMENTAL GNOMON.Notable diale, ancient and modern.
men congregated. In such places it has been superseded by the
noisy clock. This old-world monitor seems better Dials now J	.	.	superseded
fitted now to mark our hours of quiet and retirement, by clocks.
I would rather place a dial where I could see it from my garden or private grounds, than in my street front.
Those interested in the sun-dial may feel an interest in knowing something of the antiquity of this time-honoured Eiaismen-
invention. According to the received Scripture chro- tioned in
.	.	.	Scripture,
nology, the dial of Ahaz, mentioned in Isaiah, and
which, by the bye, appears to have been divided into degrees not
hours, must have been set up about 750 years before Christ. Pliny,
however, ascribes the origin of the dial to Anaximander, some 200
years later. In any case, the use of the instrument appears to have
travelled, and travelled slowly, from the East to the West.
The first dial seen in Rome is said to have been set up on the
Temple of Quirinus, 293 B.c., at which period the „	,
....	r \	1	■	,	r	Roman dials,
present division of the day into hours was adopted.
Somewhat further on, in the days of the Emperors, sun-dials became so much the fashion in the Imperial City that no public building was without one. In the seventh century they began to be used on churches, and thenceforward they were to be seen throughout Christendom in every place where men met or passed, till they were gradually superseded in modern times by clocks.
Perhaps the most startling production in dialling is to be found in our Indian Empire, near Delhi. There we have a Large dial horizontal dial, whose gnomon, of solid masonry, near Delhi, measures 118 feet in the stile, and 104 in the sub-stile. The edge of the gnomon, and the graduated circle on which the shadow fell, were of white marble, which is now much broken. The Rajah Jeysing, who built it about 1710, honoured it with the title of “the Prince of Dials,” an appellation which it certainly merited, if size, and size only, be taken into account.
According to the French historian Nicolas Lenglet, Du Fresnoy dials were first set up in churches about the year 613 A.D. The poetry of the sun-dial, even if collected, would not occupy very much space ; for poets, though accustomed to dwell and moralise on the rapid flight of Time, have not drawn much inspiration apparently from the means by which the passage of the great destroyer, and equally great healer, is marked. From among the
73SUN-DIALS AND DIALLING.
poems that have been written on this subject, the following “ Lines to a Sun-Dial in a Churchyard,” by the Rev. William Lisle Bowles, may form an appropriate close and pendant to this brief account of dials and the mode of making them :—
So passes, silent o’er the dead, thy shade,
Brief Time ! and hour by hour, and day by day.
The pleasing pictures of the present fade,
And like a summer vapour steal away.
And have not they, who here forgotten lie—
Say, hoary chronicler of ages past—
Once marked thy shadow with delighted eye Nor thought it fled—how certain and how fast ?
Since thou hast stood, and thus thy vigil kept,
Noting each hour, o’er mouldering stones beneath ;
The pastor and his flock alike have slept,
And “ dust to dust ” proclaimed the stride of death.
Another race succeeds, and counts the hour,
Careless alike ; the hour still seems to smile,
As hope, and youth, and life were in our power ;
So smiling, and so perishing the while.
I heard the village bells with gladsome sound—
When to these scenes a stranger I drew near—
Proclaim the tidings of the village round,
While memory wept upon the good man’s bier.
Even so, when I am dead, shall the same bells Ring merrily when my brief days are gone;
While still the lapse of time thy shadow tells,
And strangers gaze upon thy humble stone !
Enough, if we may wait in calm content The hour that bears us to the silent sod ;
Blameless improve the time that Heaven has lent,
And leave the issue to Thy will, O God.
74<? 9
6 W ©
eyjvo
V
PART III.GARDEN BUILDINGS FOR AMATEUR GARDENERS.
CHAPTER I.
A USEFUL SPAN-ROOF GREENHOUSE.
Glass-houses in bygone times—Now universal—Pleasures afforded by green, house—How to build greenhouse—Position and site—Class to be described— Span-roofed house, why preferable—Mortising corner-posts to frame—How to secure ground-plate—Dimensions of house—Dimensions of ground-plate —Uprights at corners—Division of space between end-posts—Intermediate posts : their position, etc.—Doorways—Rafters : their dimensions—Provision for ventilation—Outward thrust of rafters, how counteracted—Glazing, doors, and painting— Explanation of diagrams—Working drawings to scale —Proportion of scale—Construction of full-sized working drawings—Material, whence obtained—Knotting and priming—Dimensions of glass—Painting— Modes of heating house—Best system—Old flue method—Why undesirable •—Construction of fireplace and flue—Dimensions of flue—Heating by hot air—Franklin, Hocking, & Co.’s boilers—Boiler without brick work—Suitable fuel—Concentric tubular boilers—Boiler, tank, and chimney—Diameter of pipes—Plants should be near glass —Flooring of house—Provision for carrying off water—Guttering to house—Disposal of rainfall—Cesspits and tanks for rain-water—Communication between potting shed and house—Alternative methods of building greenhouses.
T is not so very long ago that a “ glass-house M was an object of reverential awe to the mass of the population, when the tax on glass made the	.
smallest conservatory attached to a noble- in bygone man’s house a thing to look at and talk about, but which was far beyond the reach of the average country squire’s means. Subsequently, when this tax was removed, greenhouses began to increase in our gardens, but it is only within late years that these embellishments, alike to house and garden, have become as general, nay, universal, as they now are. Now I am not alluding to ti e “acres of glass* which	universal,
appear in the extensive gardens of those who can afford them, but rather to the little glass plant-house, which, built on to, or apart from, houses of moderate dimensions, keep the plants alive, and
77
if®
IjjilgA USEFUL SPAN-ROOF GREENHOUSE.
the house supplied with flowers during the dreary darkness of our English winter. One of our best poets has said, and most justly) Pleasures af- i Who loves a garden, loves a greenhouse too,” and
forded by be did not mean a lofty glazed pavilion, where the greenhouse.	....
gardencr-in-chief reigns supreme, and the owner enters with lowly mien and bated breath, but a snug little conservatory where one may pick this, repot that, tie up the other, grow winter salads, and cultivate one’s own vine. How to build such a snuggery for himself, at the cost only of the labour of his hands, How to buna his wood, and glass, is the object of the following green ouse. paper on ^he subject set down from practical experience, and sure, in intelligent hands, to produce a result which cannot fail to gratify. Instructions are given as to heating apparatus, which may or may not be added at the will of the builder.
Before proceeding to describe the greenhouse it will be well to say the position best suited for its erection, is one dry, and Position and exposed on the east, south, and west sides ; but, if site>	possible, sheltered on the north, and as the house is
mainly constructed of wood, it should be placed on a bank of earth or masonry io inches or I foot higher than the surrounding ground,- and some 6 or 8 inches wider than the base of the greenhouse.
The class of greenhouse proposed to be described is a small span-roofed one, which is preferable, as being easier to construct Class to be than the lean-to, or half-span ones, and more useful described. when constructed than one of the latter would be. And also a span-roofed one, when made in the way proposed, may be easily moved at the will of the owner, not being a fixture ; so „	, . that should he desire to change his place of residence,
Span-roofed	°	r	’
house: why his greenhouse need not be' left behind, but may be
prclsrdiblCa	.	.
taken, and again secured in another suitable position. It is for this reason that the posts marked c and D are mortised Mortising 'n t'ie grourid-plate shown A, instead of being driven corner-posts in the ground, as they would have been had the house been intended for a fixture. But as the framing of it only rests on the surface, it will be necessary to fasten it down by some means, to prevent it being moved by high winds, as it otherwise would be. This will be best done by driving into the ground prepared for the greenhouse four posts, so that their heads are
78CONSTRUCTION OF HOUSE AND TOTTING SHED.
level with the surface, each post being about five inches square, and about two feet six inches long. These must be put in such positions that they arc under the ground-plate, which Howto secure must be secured to them by four I coach-screws, 6round Plate-screwed through it into the posts. The best positions for the posts is near the corners of the house.
A convenient size for the house (including the potting shed Fig. 6, which is at the north end) is about 18 feet long and 8 feet
wide, outside framing. In referring to the drawings it will be seen Dimensions there is a ground-plate	ofhouse-
running all round the base, this is lettered A A, and is IF inches deep and 5 inches wide, and is formed into a frame 8 feet i inch wide and 18 feet i inch long. Securely fastened at the corners, there are four up- Dimensions of right posts c, which are 4 ercu^-P18-16-inches square, these are kept in a vertical position by eight uprights at struts J, which greatly	corners,
help to stiffen the framework, until the boards are fastened over it. The space between the end-posts is divided on either side of the house into five equal spaces by four posts, three of them, D, being 4 inches by 3 Division of
inches, and the fourth tspace be-’	tween end-
marked X, 4 inches by 4 posts, inches. This latter divides the potting shecl from the greenhouse, as shown in Figs. 4 and 5. These are all 4 feet 9 inches long, and as they are mortised into the wall-plate at the top, and the ground-plate at the bottom, each of which are ii inches thick, the space between the wall-plate and ground-plate is 4 feet 6 inches. The Intermediata wall-plate B is 4 inches wide. Six other posts d, 7 feet posts, their 4 inches long, 3 inches thick, and 4 inches wide, must P°sitl011’etc-be provided. These are all mortised at one end to the ground-plate, and at the other are nailed to the rafters E. Of these two
79
Fir,. I.—TRANSVERSE SECTION OF RAFTER OR SASII-HAR. FULL SIZE.A USEFUL SPAN-ROOF GREENHOUSE.
at either end form the door-posts, of which the doorways are 6 feet 3 inches high by 2 feet 3 inches wide. The Doorways. rafterS) lettered E and F, are nailed at one end on the wall-plate, and on the other to the ridge-board H, which is 18 feet Rafters: their 3 inches long, 6 inches deep, and 1 inch thick. Those dimensions, lettered E are 2 inches by 3 inches, and those lettered F of the form shown (Fig. 1), which represents the actual size of the section, they are all 4 feet 9 inches long. These rafters can be
FIG. 2.—END ELEVATION—DOOR OF POTTING SHED.
purchased of the section shown, and should be all carefully placed at equal distances (see Fig. 4), when the width must be measured, and the glass ordered accordingly.
To ventilate the house about 9 inches next to the ridge-board on one side should be unglazed, and the space covered with half* Provision for inch board, hinged in four lengths to the ridge-board, ventilation. anci arranged so as to be easily opened from the inside, as shown at L (Figs. 3 and 7), and the same must be adopted
80CONSTRUCTION OF SIDES OF HOUSE.
at the bottom of the opposite rafters, where four lengths of board M are hinged to the wall-plate B. The outward thrust of the rafters over c, X, D, D, D, and c can be counteracted by pieces Outward of wood used as ties, as shown at G. The house raiter^how should be glazed with glass 16 ounces in weight to the counteracted, square foot. With regard to doors, the amateur had better get them made by a carpenter, as to look well they require good work, and they are not expensive. The framing of the sides must be
FIG. 3.—END ELEVATION—DOOR OF GREENHOUSE.
covered with or | inch boarding, tarred or painted on the outside, and the spaces between the inner and outer GlazJng boards filled with sawdust, which is a slow conductor doors, and
painting.
of heat. Perhaps some amateurs will require a little explanation with regard to follow'ing the drawings in cutting the timbers to the necessary length. To describe the Explanation dimensions of every piece of timber used in the fram- °f diagrams, ing would be tedious, and occupy too much space, and there would
$1H
References to Lettering in all the Figures.—A, Ground-Plate. B, Wall-Plate. C, Corner Posts. F), Intermediate Posts. J, Struts
to Stiffen Corner Pos's. X, Posts at Partition between Greenhouse and Potting Shed. E, Rafters. F, Sash bars. H, Ridge i Board. L, Vent lators. G, Ties to Rafters. N, Boiler. P, Tank. R, Pipes for Heating House.	1
USEFUL SPAN-ROOF GREENHOUSE,!	2	8 A-	S	6	7	fi	9	IO II	12	13	14 lò IS 17 fa
nmwnnmiw --------------------numihuhhiiu	twìiiìhihihi»»?!	n;iwinwimn	~	i<ni.;it»tW’»MtaT	- ^ìy^i.tha	-niEHpnanna»
SCALE OF FEET
PLAN OF HOUSE SHOWING STAGE, ETC.A USEFUL SPAN-ROOF GREENHOUSE.
be but very few who would require such minute instructions. If
anyone who is in difficulty on this point will look at the illustrations
Working	P^an> front, and end elevations and sections
drawings to of the house in the illustrations that accompany this de-scale.	.	.
scription, he will find that they are working drawings, drawn to scale, and that a scale from which he may ascertain the dimensions of any part of the house, by aid of a pair of compasses is given below the plan of the house in Fig. 5. The proportion in
which the scale is drawn is one-third of an inch to a foot ; that is Proportion to say, every linear dimension, as shown in the illus-of scale. trations, is one thirty-sixth part of its counterpart in the house itself when built, or of a full-sized working drawing. Construction Now, although it would be possible to make full sized °fworkinged working drawings of different parts of the building, drawings. jt js neither desirable nor necessary to do so ; but before setting to work, the amateur is recommended to prepare
84MATERIAL TOR WOOD-WORT OF HOUSE.
from the figures working drawings on a larger scale—say on the
scale of an inch to the foot—which would familiarize him with the
different pieces required for the structure, and their relative positions.
The best material for the construction of the wood-work of the
house will be thoroughly dry, soft deal, free from knots
•i	i - -ii i	Material,
as much as possible; and it will doubtless save the whence
constructor much trouble if he obtains the different ° tained>
required pieces of the sections shown in the drawing, only a little
_fi
larger, as he easily can do from saw-mills or elsewhere ; so that all he will find necessary will be to plane them, and follow the drawings in cutting them to the required length, and then nail, mortise, or screw them together as shown in the different diagrams.
When all the wood-work has been put together, and is thoroughly dry, the knots must be carefully stopped, and the Knotting ana whole framing giver, one coat of white lead ; this will pummg. make the putty in the glazing hold well. Then the glass must be
85
GA USEFUL SPAN-REST GREENHOUSE.
put on of the required width, the length of each piece being from
Dimension of 15 to 18 inches long, and each overlapping the next
gia,ss. tQ jt by about an inch and a quarter. When this is
completed, the whole of the inside and outside wood should receive
two good coats of paint, of pale stone colour or white; Painting.	- ?	, .	. .	.	.	’	,	, .	, ,	,	|
and in doing this it is strongly advised that the paint
used should be rather thick, and well rubbed on, a little only being
taken up in the brush at one time.
The subject of heating the greenhouse is such a very wide one
that in this article there is only space to treat it in a very cursory
.	, manner. However, an endeavour must be made to
Modes or
heating tell the amateur as much as possible about this house.	.
important matter in a lew words. I here are thiee well-known methods—namely, heating by brickwork flues, by hot air, and by hot water.
Each of these systems lias its admirers, who have, of course, claimed for it the advantages of effectiveness, economy, and Best	equality of temperature, amongst other less important
system. ones which want of space will not allow being here -numerated. The heating by flues was for many years after the introduction of the others the most popular, but it now is, and has been for some time past, rapidly giving place to the hot-water system, which appears to the writer by far the best arrangement for houses of all sizes.
Referring to the different systems in the above order, the chief quality which appears to recommend the use of the old flue method Old flue *n die small house which in this article we have method. endeavoured to show the amateur how to make, is its cheapness of construction; but this advantage is more than counterbalanced by the fact that greenhouses heated by it are liable to Why un- rapid changes of temperature, should the fire (which, desirable. therefore, requires constant attention) become either too great or too little, and that should the cement in the joints of the flue crack at all, the house is filled with a strong odour of sulphur, which is both unpleasant to those entering and very injurious to the plants inside ; besides which, there is the incon venience of the flues constantly requiring sweeping—an operation which, should the amateur be obliged to do for himself, though not taking long, it is difficult to believe however enthusiastic a
86HOIV TO HEAT THE HOUSE.
floriculturist he may be, he would not greatly dislike. However, should any reader decide, in spite of these objections, to adopt this form of heating his house, it will be well to say that
Construction
the fireplace, which must be built about ten inches ofttrepiace below the level of the flue (and of course is horizontal an ue‘ where it runs through the house), should be 20 in. long 10 in. high, and 91 in. wide, into which space must be built the fire-bars. The flue should be about 8 inches square inside, and Dimensions be fitted with a damper to regulate the draught, and a offlue‘ small wrought-iron or brick chimney at the other end to carry away the smoke.
With regard to the next system, that of heating by hot air. It can only be said it seems both expensive and generally unfit for a small house. The third method now remains, which, Heating by as I said before, appears best adapted for all sizes of hot air< greenhouses, and this opinion is much strengthened by the numerous boilers of so many shapes, sizes, and principles, which are to be seen advertised in every gardening paper of the present day. In fact, there are so many good arrangements of boilers, that it can only be said the most popular seem to be the “ horse shoe ” and “ saddle ” types ; but of the boilers which have come
i	31	•	r 1	,	,	, .r	Franklin,
under my notice of late, those made by Messrs. Hocking, & Franklin, Hocking.,	Co., of Liverpool, seem amongst C°‘ sboilers■
the best, and to these I shall again refer a little further on. However, in so small a boiler, perhaps the best way will be for the amateur to look through the advertisements in the gardening papers, and fix on one which the makers will tell him Bo}1
will do the work he requires, and is at a price he is out brick-.	.	work,
prepared to give. As is shown in the sketch, it will be
best for him to select some arrangement in which no brick work setting is required, as it would be more easily moved, and would occupy less room than it would otherwise do. The fuel should be small coke or gas, the latter has been found very _ .. ,, , , convenient in small houses, on account of the little attention which is required in keeping the house at a uniform heat. However, where this means of heating cannot be used, as is generally the case in the country, small coke is the most convenient.
This description of fuel, I should think, would burn for a con-
87A USEFUL SFAN-ROOF GREENHOUSE.
siderable time without attention in one of Messrs. Franklin, Hocking, & Co.’s small concentric tubular boilers, in which Concentrio	.	.	.	’
tubular the upper part is filled with a considerable quantity
bo ere.	Coke at a time, which works down, and slowly
takes the place of that which has been already burnt.
In the sketches is shown a small circular boiler and tank and piping (P, N, r), which are heated by gas, the fumes of which Boiler, tank, should be carried away as shown in the drawings, by andchimney. a piece of iron stove-pipe, capped by a conical covering raised a little distance above the top of the pipe to prevent the sudden down-rush of any gust of wind.
For a greenhouse of the size illustrated, the pipes should be two, or two and a half, inches in diameter. The stage marked K Diameter of is 2 feet 5 inches wide, and 2 feet 9 inches or 3 feet pipes. high, as will be seen in the drawings. The most important thing in its construction is that it should be made that Plants should the plants may be as near the glass as possible, which be near glass. wjjj prevent their being drawn into those long, sickly-looking objects one so often sees in conservatories and Flooring of greenhouses in which the old-fashioned step-stage is house. used. The centre of the house may be laid with tiles, or thick slates, which will help to make it more tidy and cleanly.
All minor details which have not been specially described, will be sufficiently understood on referring to the drawings, but there is yet one thing to which the attention of the amateur must Provision for drawn, and ^iat *s the necessity of providing means carrying off for carrying off the water that will fall from time to time on the glass roof when “the clouds drop fatness,” in order to prevent the drip on the earth below, and the disfigurement that it causes if it be allowed either to trickle down the front and back of the house or to fall and splash against its base. As the house that has been described has a span roof, and a door Guttering to at each end, zinc or iron guttering, supported on brackets, must be placed immediately under the eaves along the front and back, and two pipes must be provided to admit of the exit of the water caught in the gutters. Had one end of the house been permanently closed, one exit pipe would have been sufficient, as the gutters in front and back could have been connected by a third piece running across the closed end.
SSTANK FOR HOLDING AAD UTILISING RAINFALL.
The next thing to be considered is the provision of means for
the dispersion or absorption of the rainfall, or, what is better, for
its storage for use in the greenhouse. If it is not to Disposal of
be saved, the pipes must have their lower ends set in rainfeu.
drain pipes leading to a pit dug in the earth, and filled to about
half or two-thirds its depth with brickbats covered _
r	Cesspits and
with brushwood to prevent the entrance of the mould tanks for • i	Jr .	,	, rainwater,
with which it is filled in. If the water is to be stored,
a brick tank, well cemented, should be made under the potting
shed, from which receptacle the water can be raised communica-
when wanted by a small pump in the shed itself. A tp°uing'shed
sliding panel in the partition between the potting shed and house.
and the house, will be found useful for passing in newly-potted
plants, etc., without carrying them round in the front of the house,
which, to say the least of it, will be found somewhat inconvenient,
especially at times when it is necessary to pot, or re-pot, a great
many plants at the same time.
For reasons that have been already stated, a span-roof house is the most desirable structure of this kind for the amateur, and one
that can be re- Alternative
moved if con- methods of moveu, II con building
structed in the greenhouses, manner described, more easily than any other. If, however, the amateur be building on his own ground, and does not anticipate any necessity arising for removing the structure, or if, on the other hand, he is compelled to be as economical as possible, the house may be constructed as in Fig. 8, which is a sketch partly in section and partly of the end of a low span roof house, in which the necessary height is obtained within by excavating the earth at A to a distance equivalent to the length of the house, and a flight of steps leading to the level of the floor of the house from the level of the ground, which is indicated by the line B c, of which the dotted part shows the original level of the excavation. By this means half the material required for building thq
89
FIG. 8,—SECTION OF LOW SPAN ROOF HOUSE.A USEFUL SPAN-ROOF GREENHOUSE.
sides of the house according to the method described above is saved, and about a third of that which is necessary for making the ends. Indeed, the side-walls at P> and c might be reduced to the height of 12 or 18 inches, and so be pretty nearly done away with altogether. The earth on each side of the excavation serves as a stage for the plants, thus reducing the cost of building still further. There is no better kind of house than this for a small vinery, or for fruit-growing on a small scale ; for the little standard pyramids can stand on each side of the walk, close to the edge, and strawberry plants in pots be placed behind them on shelves, as at D D, close under the glass ; and it will be found equally convenient for flowers. The cost of the roof remains the same, inasmuch as its area and mode of construction is not affected by the height of the walls. A house built on this plan is, moreover, warmer, and more easily protected from without by matting, etc., during severe frosts, as the roof is easily reached from the level of the earth without. When the house is heated, the pipes may be brought along the centre^ immediately in front of one of the earthen stages, provision being made for them by cutting away the earth on either side of the central passage, as may be found most convenient. Or a trench may be cut in the earth on one side for the reception of the pipes and slates laid over it. It will be necessary to take means to support the earth on each side when the passage way has been excavated. This may be done by building a low brick wall on each side as high as the level of the earth, one brick thick ; or, more cheaply, by driving in uprights from end to end of the house, just in front of each earth-bank, and about two or three feet apart, and interposing a layer of stout, rough inch planks, piled one above another, edge to edge, between the posts and the earth, which may be rammed down behind the boards in order to press them tightly against the posts that support them. A neat coping may be formed by a 43-inch board, nailed down to the heads of the posts and the edge of the uppermost boards. The outer edge of the coping should be rounded like the nosing of a stair.
90CHAPTER II.
HOW TO WARM A SMALL GREENHOUSE.
Methods of warming glass house—Superiority of hot-water apparatus—Heating pips—IIow to determine quantity required—“Star Independent Boiler”— 'lop feeder of boiler—Gas boiler for greenhouse—Cost of gas per hour— Hot-water pipes : their sizes—Arrangement for boiler—Pipe connections and pipes—IIow to secure joints of pipes—Patent joints—Air pipe or tap— Supply cistern—Action of apparatus—Flow and course of water—Apparatus for gas boiler—Admission of fresh air—Relative cost of boilers and pipes— Another mode—Dimensions of small house heated by apparatus—Form and nature of box—Cubic content of box—Arrangements for lighting and carrying away products of combustion—Supply of air and diffusion of heat.
Methods of warming glass house.
AVING a small greenhouse for plants, etc., the next thing is how can the frost best be kept out, for one night of it will do immense damage. This, as already said, may be best effected by hot air stoves, which either warm air by passing it through them, or radiate heat from gills or plates which form part of the stove, or by hot-water pipes, warmed from a small boiler outside, which being placed round the sides of the greenhouse at a low level, radiate the heat from their surfaces, and as air in the process of warming expands, it becomes lighter than cold air and rises ; thus a constant upward current of warm air is maintained.
The hot-water apparatus is much the best if it can be conveniently fixed. As fire has to be kept up all night:	Superiority
as well as day in winter, inside the greenhouse there of hot-water would in all probability be an escape of unconsumed gases, etc., from an open stove, which would be detrimental to the plants ; also, there are very few stoves which would last all night without attention, and not be too large for the purpose, and expensive in fuel.
The next question is, what quantity of heating pipe would be required to heat a greenhouse of a given size. First find with a
91vD
to
H
HOW TO WARM A SMALL GREENHOUSE.QUANTITY OF HEATING PIPE REQUIRED.
rule the superficial glass surface of the greenhouse, also the cubical contents of the part below the level of the side lights,	Heating
etc., which is generally enclosed by brick or wood, pipe< and then apply the following rules, which will give the quantity of pipe necessary to heat greenhouses, etc., of any description, to any required temperature.
i foot of pipe surface at an excess temperature of 1250 to 130°, will heat p§ cubic feet of air 30° per minute. 1 square How to foot of glass in greenhouses will cool 1 i cubic feet of quantity0
air,as manydegrees required, per minute as the internal temperature exceeds that of the external air ; hence, 1 foot of pipe surface may be provided for every 5 feet of glass, where the temperature to be maintained does not exceed 30° above the external air. If the temperature is to be maintained at an excess of 40°, divide the superficial extent of glazing by 3}, if 50°, by 3, and if at 60° above the external air, divide by 2h. A more accurate approximation is, to the whole extent of glazing
FIG. 9.—GAS BOILER FOR HEATING GREENHOUSE.
exposed to the atmosphere, add t, and multiply the sum by the number of degrees that the temperature of the house is to be maintained above that of the external air. The product divided by 190 will give the quantity of piping to be provided, estimated in superficial feet ; or by 160 for feet run of 4 inch pipe. For the parts not glazed allowance must be made also ; 1 foot of 4 inch pipe for every 100 cubic feet of air thus enclosed, added to the quantity required by the glass, will be sufficient for the greenhouse.
One of the best boilers for the small greenhouses is the “ Star Independent Boiler” (Fig. 8) ; this boiler requires no brick setting, which is expensive ; but only requires Boikr.” to be sunk, so that the lowest level of the pipes in the greenhouse
93HOW TO WARM A SMALL GREENHOUSE.
for
greenhouse.
are above the boiler itself, as shown in the accompanying diagram, in which the method of fixing the boiler, and the arrangement of the flow and return pipes, the cistern, air pipe, etc., within the greenhouse are clearly exhibited—so clearly, indeed, as to require no further reference to the different parts by letters or numbers.
It will be seen from the illustration that the boiler has an extended top feeder, so that it will burn through a night without Top feeder attention, having an extra store of fuel; also, it costs of boiler. very little for feeding, as it will burn coal-dust, cinders, etc. The height of one as illustrated, of sufficient capacity to heat loo feet of 4 inch pipe, is 46 inches, and 12 wide. There is also a Gas boiler S00^ little gas boiler (Fig. 9), composed of a wrought and cast-iron casing, with copper tubes inside. This is heated by an atmospheric burner, which by means of a small arrangement at the back carries in air, and mixes it with the gas thus consuming the oxygen of the air, and giving a small blue flame of intense heat and producing nearly perfect combus-Costof gas tion. The smallest size of this boiler will heat 20 feet per hour. Gf ^ inch pipe, at a cost of one farthing per hour. This boiler can be placed inside the greenhouse at a low level, and a pipe taken off the top and turned outside to carry off any unconsumed gases, which are a mere nothing.
Having decided which boiler you will use, let us now pass on to the fixing. Let us in this instance take the “ Star.” Hot-water Hot-water P'Pes generally used, are either 2 inch, 3, or 4 inch
pipes:	internal diameter: a 2 inch pipe having half, and a
their sizes. .	....	.	.
3 inch, three-quarters of the heating surface a 4 inch
pipe of the same length has. They are cast either in 9 feet 01 6 feet lengths, and any shorter length must be cut from one of these. If the greenhouse be on the ground level, a small hole Arrangement large enough for the boiler to stand in and also allow for boiler. inching the bottom doors to clean out the fire, must be sunk so that the top of the boiler (not the feeder) is below the floor level of the greenhouse, or the level of the return pipe, but if it be built at a high level, any convenient position below will do, pipe for the higher the head of water, the better the cir-
connections culation. This boiler has on it two pipe connections, and pipes.	.	.
the one at the top being for the flow pipe, and the
lower for the return. From these connections 1 or 1} inch wrought-
94METHODS OF JOINING IRON PIPES.
iron pipe is generally carried into the greenhouse as it is more convenient than cast, not being large, and connected to the cast pipes by means of cast blank ends, drilled and tapped for the same. These pipes must be laid with a little rise, on the top pipe or flow all round till it reaches the turning point, where a syphon is fixed to connect it to the return or loiver pipe. This return pipe must follow or reach the boiler with a slight fall, if it goes back under the flow, as in sketch, it looks best to have the same fall as the flow has rise, and to fall directly before entering the boiler. Either way will work satisfactorily. These pipes have each	How to
on one end a socket, and the other end is called a	joints of
spigot; to make the joint the easiest way is, where pipes, there is no great head pressure of water, by india-rubber rings put on the spigot end and jammed into the socket; the farther the ring is back the better ; then fill up the open space left with Portland cement. Another way is with red lead and yarn, a piece of yarn being put round and caulked with a proper tool to the bottom of the socket, care being taken that the spigot is down as well; then a small roll of red lead pushed down, and the remaining space filled with yarn, and caulked. This last joint is not so likely to crack and leak with the expansion of the pipe, but is more costly. There are also patent joints which screw together with bolts Patent and nuts, with an indiarubber ring inside ; but pipes f -with these cost about 25 per cent, more than the ordinary pipes. At the highest point of the apparatus, which in this case is the syphon, an air pipe or tap is required to let out any Air pipe air in the pipes, or steam, if the boiler is over-fired. ortap-The pipe, which can be £ inch lead or iron, is the best, as it requires no attention after being fixed, but a tap would require to be opened once a day. This pipe will be carried up in any convenient place, till it is above the level of the supply cistern, and turned outside. The supply cistern, for supplying water to the pipes, Supply ought to have a ball valve and water supply laid on, cistern, but this is not necessary as long as it is kept filled by hand, for as soon as it gets empty by evaporation, drawing off water, etc., the circulation stops, and steam is formed, and here the use of the air pipe instead of the tap would be to let the steam escape. The cistern would be fixed on the staging, or on brackets to the wall, and connected to the return pipe as shown A plug or tap ought
95HOW TO WARM A SMALL GREENHOUSE.
to be put in at the lowest part of the return, to allow for emptying the apparatus when required. The action of the apparatus is this : Action of The fire being in the centre of the boiler, the water apparatus. i,as con(-aC{ ap r0und and heats rapidly, and the fuel only burns till about half way up, as the air can only get in at the bottom, where two doors are placed, one for cleaning the fire bars and the other for air inlet. As fast as it is consumed fresh fuel takes its place by falling down from the feeding hopper on top, which being filled up at night will last till the morning by regulating the damper in the smoke pipe and the air inlet. The water Flow and being heated at the bottom of the boiler, expands, and
course of becomes lighter than the cold, and so rises to the top water.	.	.
and enters the flow pipe, and passes on to the highest
point in the pipes. By this time it has become cooler, the pipes
having radiated the heat, and so begins to descend, the return
being pushed on by the hotter water behind, and drawn by the
vacuum being formed in the boiler by the hot water leaving, and
having passed all round the pipes, re-enters the boiler at the lowest
level, where the fire is burning the brightest, and so continues its
course again.
With the gas boiler (Fig. 2) the apparatus would be the same, only the boiler would have to be under the level of the pipes in the Arpara'tu greenhouse, if placed inside, although outside would f.rgas do just as well. Gas would have to be laid on to this, which could be done by anyone who will study the papers on Gasfitting in Vol. VI. of this Series. The pipes would either stand on little carriages and rollers to allow' for expansion, or slide on brackets fixed to the floor or walls. If fresh air is admitted to Admission of the greenhouse, the best way, and place, is, by means fresii air. Qf a sliding grating fixed in the external walls, at the floor level behind the pipes, so that the supply can be regulated, and the entering air become warmed before it reaches the plants. Relative cost The Star boiler, as here show n, can be purchased for
of toilers	/3 jos., the	gas	boiler,	costing	L.’k, is	dearer in pro-
and pipes.	J .	’	f .	’	,	,	^
portion, not being able to do so much work, and the
tubes being of copper, larger sizes of both are obtainable. The prices of hot-water pipes are about, for 4 inch, 2s. Sd., 3 inch, 25. id., and 2 inch, is. 6d. per yard, and the double brackets about gd. each, but these prices fluctuate with the iron market.
96DIMENSIONS OF SMALL HOUSE.
The mode described in the preceding pages, if adopted and well carried out, will be found to be both efficient and reliable. There may, however, be some who would not willingly incur the expense or encounter the labour involved in supplying the newly built house with such heating apparatus, Another especially if the greenhouse is not on the same mode, scale; or, I should rather say, of the same capacity as the greenhouse brought under the notice of the reader. Therefore, for the benefit of those who may have made, or who may be intending to make, a glazed house of far smaller size, another mode shall now be given, which is inexpensive and has the merit of being easily carried out.
The following description of a method of heating a small greenhouse with gas has been found most effectual for heating a small house, which is 6 feet 6 inches by 4 feet 6 inches, the Dimensions height at back being 7 feet 6 inches. Assuming the hou^heated height in front to be 5 feet 6 inches, the mean height ^apparatus, would then be 6 feet 6 inches, and the cubic content a trifle more than 190 cubic feet, which is probably very near the mark, and shows the number of cubic feet for which an apparatus of the s:ze described is suitable.
The form and nature of the box and its fittings are shown clearly enough in the accompanying illustration (Fig. Form and id). The box is made of zinc, with the exception of the	nature
top, which is of brass. The gas jet is fitted with a No. 6. nipple, and it is so arranged and placed within the box that the top of the flame is 1 inch below the top of the box when lighted. In Fig. 10 A is the box, which is 9 inches by 9 inches, and 7 inches in height, giving a cubic content of 567 cubic cubic con-inches or little less than 5 cubic foot. It is useful to tent of box. know this, because, if a box made in this manner and equal in cubic content to J cubic foot will heat 190 cubic feet of space, it will take a box § cubic foot in content, or two boxes of the size described, to heat a space 380 cubic feet, and so on. With regard to the other parts, B is the top of the box, which, as it Arrangements has been said, must be made of sheet brass ; c is a a'nd'carry-gas jet, fitted, as directed, with a No. 6 nipple, which is suitable for the size of the box. If the box be made combustion, larger, the number of nipples or burners must be increased, or a
97HOW TO WARM A SMALL GREENHOUSE.
nipple of a larger size must be used. An opening is shown at D for lighting the gas, fitted with a slide, which must be closed as soon as the gas is lighted. E is a pipe to carry away the fumes of the gas and the products of combustion , the pipe is 2 inches in dameter, and must be taken up through the roof or any suitable outlet, into the open air The p:pe for gas supply is shown at F. Another pipe, G, 2 inches in diameter, >s brought into the box from the outside, in order to a supply of air necessary for the maintenance of the flame, and a small pane cf glass is inserted in one side of the box at H. so that it may be seen whether or not the gas is alight. Heat is diffused through the house by radiation from the sides of
the box; and	hg. 10—apparatus for heating small greenhouse.
if the box be
well made no fume can possibly escape and cause injury to the plants in the house, because the constant influx of
Supply of air	.	.
and diffusion fresh air through the pipe G, not only tends to supply 0 ea ’ air to the flames, but helps to carry off the fumes by forcing the heated and vitiated air in the box into the exit pipe at E. If a moist air be required in the house, this may be effected by placing a shallow vessel—a small baking tin for example—on the top of the box.CHAPTER III.
A SUMMER-HOUSE FOR A SMALL GARDEN.
Incentives to building summer-house—Suitable time for building—Utility of summer-houses and green-houses—Dimensions of proposed arbour—Scale of elevations and plan—Advice to intending builders—Preparation of site— Posts to receive ground plate—Construction of ground-plate—LJprights in framing—Insertion of horizontal pieces—Wall-plate—Ridge of roof and rafters—Fitting parts together—Employment of coach-screws—Screws for -	ground-plate—Counter-sinking for screw-heads—Formation of roof—Orna-
mentation of crest-board, etc.—Skirting at base—Laying flooring—Arched pieces and lattice-work in front and at sides—Tongued boarding below— Interior lining and mouldings—Seats, table, and brackets—Construction of V-jointed panelling—Suggestions for painting—Guttering to carry off rainfall —Alternative methods of treatment—Plans for summer-houses in corners— Circular-fronted summer-house.
DVANCING spring covers hill and dale with verdure, and the amateur gardener, inspired by Nature’s awakening, sets to work heartily, as well-kept beds and trim borders soon manifest Being intent on the embellishment of his garden, he labours in the hope that summer’s advent will discover successful cultivation Incentives to
testified by sweet flowers in profusion, and seeks no building sum-i	11	,	. r i • i - i i	mer-house.
other reward than contemplation of their bright hues
and forms—a contemplation that will be better enjoyed and reward thoroughly realized if he rejoice in the possession of a summer-house, wherein he may cogitate upon plans for the future, or, perhaps, with family and friends, partake of the cup that cheers. But if his garden boast not such a pleasant shelter, let suitable time him make its erection one of his tasks ere the time forbluldlng-arrive when exposure to the broiling heat of noon is attended by danger, or, at least, discomfort. The time and trouble utility of expended thereon will be amply repaid and with its houses and completion summer’s joys be enhanced, just as the green-houses, possession of a green-house rendered less irksome the dreary hours of winter.
99A SUMMER-HOUSE FOR A SMALL GARDEN.
It is the purpose of this article to describe the construction of an arbour, simple in style, yet neat and pretty withal, therefore . to a slender purse better suited than a design more of proposed pretentious; and the dimensions (5 ft. 6 In. by 3 ft. 6 in.
arbour.	,	,	... ,	..	,	,	.
on plan) will be found to encroach not too greatly on
the garden space generally available. The elevations and plan are
drawn to a scale of i inch to the foot, and the method of building
Scale of may be easily understood anj followed ; but it is quite
elevations a probable contingency that the work in its progress
will present difficulty, assuming the intended builder
to be no adept at carpentry ; he is admonished, therefore, before
proceeding, to digest these few words of advice : Do not seek by
Advice to	slovenly subterfuge to evade doubtful points, but
intending	boldly set about their solution ; perseverance and •
builders.	.	,	,	,
patient thought must prevail, for in their exercise the
inconveniences attached to deficient skill or scantily furnished
tool-chest are minimised, and amateur work often saved from
bearing the impress of unprofessional labour.
The site should be one that affords an interesting view ; let it
be also dry, and, in order that no moisture hereafter collect
Preparation beneath the building, somewhat raised, or, better still,
of site. a course 0f bricks laid for a base. Then, taking into
consideration the desirability of easy disintegration and removal, let
four posts, each 3 in. square, be sunk into this base to the depth of
Post to 1	4 m., leav*ng 2 in. °f each protruding; upon
receive these the summer-house will rest, and, to insure ground-plate. . ,	,	TV’	,	,	r
stability be	secured to	them	by	means	of screws
through the ground-plate. Their positions, two at back and two
Construction at ^tont» near to but clear of the corners, are shown in
of ground- plan in Fig. 11, at A, A, A, A, by dotted lines. The ground-
plate beginning the actual building is a rectangular
framing, 5 ft. 6 in. by 3 ft. 6 in., of 3.! in. by 32 in. stuff, halved to
Uprights in join, and consisting of five pieces. When fixing, put
framing. the fonger pieces down first, then upon those the three
shorter ones ; this	provides support	for	the	flooring.	Ten up-
Insertion of riShts>	each	3 in- scl- b>' 5 ft-	8	m.	long, are	mortised
horizontal into this framing ; four for the back, B, B, B, B, may be placed equidistant, one each side midway, shown at c, c,
and four for the front, as at D, D, D, D ; but between the two that
tooTHE FOUNDATION OF THE BUILDING.
form the entrance allow for a clear way of 2 ft. 6 in. Having
arranged these, insert the horizontal pieces into the corner
uprights, halving where they cross the intermediate ones ; all these
uprights are in turn to be mortised into the wall-plate, a frame
similar to, but of less stout material than, the ground- „ , ,
Wall-plate.
plate. The apertures at the sides and front may be
furrowed or rebated on the inner, and stop chamfered on the outer
edges.
Then two pieces of the 3 in. stuff, 1 ft. 8 in. long, are inserted into the top of the wall-plate, and themselves connected by a length
Scale of feet.
FIG. II.-PLAN SHOWING FRAMING OF GROUND-PLATE*
of the same, to form the ridge of the roof. To each side of this
are screwed three rafters of proper length ; these rest Ridge of roof
upon and are secured to the wall-plate. In order that andrafters*
no wyeak and rickety affair be presented in the completed building,
it is incumbent on the amateur to make all joints pittingparts
closely yet not too tightly fitting; then, having in prac- together.
tice carefully followed the foregoing, he will find the arrangement
of the various parts lend itself to an easy taking apart, Empioyment
when needful, but in no way detract from the quality of coach-
screws.
of firmness requisite. Employ coach-screws with
washers and counter-sunk heads to fasten the corner uprights to ilia
iox
HA SUMMER-HOUSE FOR A SMALL GARDEN.
wall and ground-plates, thus : At each bottom corner a screw passed through the lower half of ground-plate will hold the end
of the upright mortised therein ; at each top corner one screw Screws for through the rafter into the upright will at once hold ground-plate. rafter) wall-plate, and upright together; the lower fastenings will then be hidden by the skirting, and the upper ones
102FRONT ELEVATION AND SIDE ELEVATION.
covered by the boards of the roofing. Stouter coach-screws must
be used to hold the ground plate to the sunken posts. counter
For Other sinking for screw-heads.
parts ordinary screws will suffice, their heads countersunk by the f centre-bit ; when these screws are driven home, the pits left must be stopped by turned wooden plugs, these plugs to be omitted in putting on the rafters.
The skeleton being now completed, the roof may be put on, either of Formation feather- of roof-edged boards, or, preferably, close-boarded, covered with felt, pitched and sanded ; whatever method be employed, of course, must leave all weatherproof. The strips of ornament may be manipulated with a keyhole saw, using the brace and bit 0rnamenta_
fo r the tion of crest-board, etc.
circles.
The spearhead should be turned, but, failing that, fashioned by the best means Skirting at
the amateur can command. The skirting round the base, base is 8 in. wide, bevelled on one edge; i and, to insure the
FIG. 13.—SIDF. ELEVATION. Scale, Half an inch to the foot.A SUMMER-HOUSE FOR A SMALL GARDEN.
passage of air beneath, a few holes are bored therein, forming trefoils to accord with other parts of the design. The space apparent in the apertures from the ground-plate to where the top of skirting reaches, will need to be made good ; the riser of step must also be provided for.
Having proceeded so far with the outside of the summer-house,
commence the interior work by laying the floor with inch boards,
Laying making the tread of the step rounded on the edge, and
flooring. to project somewhat beyond the riser. That done
satisfactorily, cut out with the keyhole saw, from f boards, the
Arched pieces arched pieces, and fix them in their respective places
work infront >n the upper apertures of the front and side ; then fill
and at sides, the remaining space of those with lattice work ; if the
work has been rebated, this must be kept in position by strips of
Ton d beading. The lower apertures are to be filled up by
boarding	narrow boards, tongued, and V-iointed, fixed upright
below.	„	. , ° j , , J ,	’ .	,	•
or diagonally right and left, as shown in elevation.
The back and lower portions of sides and front, and, if desired, the
interior roof, are to be lined with match-boarding, then with a
lining and moulding at the height of a dado, and at the head
mouldings.l	°	.
of the walls will leave a neat appearance. The seats must be of inch board, and arranged to rest upon ledges and Seats, table, brackets, or one or two perpendicular supports. The and brackets.	may manufactured, or a piece of rustic
formation utilised for the purpose. The small brackets flanking the entrance may now be affixed.
Clean deal will be found economical for all parts of this, and may be obtained in the sizes mentioned ; but it will be necessary to make, or have made, the small quantity required of the vj°'ntcd paneling; this consists of 3 in. by £ in. stuff, bevelled both edges on Construction ^;icc> an^ grooved for the reception of a false tongue.
of v-jointed This tongue must be glued in, and should be of hard panelling.	.	,	. ,	,
wood, not necessarily in one piece, but with the grain
at right angles with its length. The lattice work may be made,
or purchased prepared.
When completed so far as carpentry be concerned, give all two Suggestions coats of paint. It is suggested for finishing that the or painting, outside receive two shades of green, the lighter on the chamfers and panels only ; the slips of ornamental and plugs may
104CONCLUSION.
be white The interior may be a green grey, with a dado of a dark plum colour.
In conclusion may be mentioned the advisability of providing a
means for catching the rain-drip from the roof in wet
b	v	. Guttering to
weather; and whosoever desires to complete his job carry off
in a workman-like manner will not omit to effect this ralnfaii.
by fixing a gutter at each side, leading to a pipe at the back. These
precautions taken, and with a good coat of paint every year, will
largely contribute to the durability of the structure.
105
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MEAT“ FI Bl
N^r^hese Biscuits aie the onl although statements to tj
Purveyors by Appointment to National” Dog Shows; the New
Sporting Dog and Field Triai uiuu,	,	_____
d’Acclimatation, Paris; and to all the Important Canine Exhibitions and Kennels in the United Kingdom and Abroad.
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PATENT GREYHOUND
MEAT “F1BRINE” DOG- CAKES.
THESE SPECIAL BISCUITS contain 35 per cent, of Meat, and are Manufactured from the Best Scotch Oatmeal, Wheaten Meal, and other ingredients, forming the most successful food for Greyhounds in training. Used by all the principal Trainers, including many owners of Winners of the Waterloo Cup.
ROUND OATMEAL DOG BISCUITS
For Greyhounds, where preference is given to training on Meat. They contain 50 per cent, of Oatmeal, and can be had with a larger proportion if desired.
PET DOG- BISCUITS, PUPPY BISCUITS. PREPARED PUPPY FOOD
HIGHLY RECOMMENDED BY THE “FIELD.”
DOG MEDICINES AND DOG SOAP. CAT FOOD.
SPRATT’S PATENT, Bermondsey, S.E.
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