\ { LG; 5% ; \ '2 5 '1 . ,-_ '5 , V L m. - - r *r "” M ANN—4.3.x -\.. w A _ _ ._ DRAUGHT SMANS HAND BO 0K , 01:; ) PLAN AND MAP DRAWING. , . WITH COLORED ILLUSTRATIONS. _ew idea to preserve a. soft pencil is the useful article and pie." ‘13 the; new How to Use a Bunsen—It is singular to notice how few of the many expe habit of using this popular burner are node of using it. at the cheapest form in which d use, for the great value but it cannot be power to This lowering can- rtain point unless the air adjustment for cutting ly. The secret of use is with the prope‘g 1 place we may say th it is sold is of very limite of the burner is in its economy; economically employed unless lower the flame when needed. not be done beyond a co holes are supplied with an oil? a ortion of the air supp to re nee the air supply if there be insufficient. air, if the air is in excess, the flame will “1 . —-that is to say, ignite inside the tube at the ponit as issues—under which circumstances it is should then be extinguished for a lessened by the regulating air holes, and relighted. thing, but by no means generally l Journal of 1’11010grapley. where the g useless. moment, the air supply bands that encircles the This is a simple known.——1>’risto éin > It used" twice as long under “ *.. . , ghanel durable, ry‘ usefu and saving, an , y rimenters in the acquainted In the first there is as the gas is lowered ; then, the flame Will be white ; flow down” [79589.]——Equatorial Drawings—I would poinply yery gladlyavith the courteous request of ‘ 1\emesis ” to supply him with complete drawings of my 3m. equatorial, but it is far too elaborate to serve his purpose. being all brass, with finely- marked R.A. and Dec. circles, vei'niei's, strident levels._ worin motions, 830., &c. Such a piece of work is not within reach of an amateur. I can. however, tell him where he can find everythine he wants. If iie will look at E M..” 'Voi. iv. p; 508,11e Will find a vs ‘V good'type of stand. Alsoin Vol. ELIX. p. ‘156110‘ 11 find an altogether different kind. And in Vol. XLIII. p. 292 he will find Dollond’s equatorial, V iich is extremely simple and. I should think good indeed. ”For RA: and Dec. ' " s Sir. . ‘ spasteliorml eircles‘accurately (ilYlded, which lea s I]Oil1l]l“‘t0 be domed. I). H. Si’iiniiind. V Tracing on \ this added to the Indian ink makes" . A"; (Ilofh.——Engineors and surveyor: are frequently troubled With the excessive glaze on tracing cloth preventing the ink of their drawing pens from running. I’ure otegall is 'Vsometinies used to. mix with the ink to over- come the difficulty, but the Following; flux is pre- ' ferred :-——Filtereii oxigall boiled and strained to ;,keep back the scum. is heated over a fire. and. powdered chalk added. When the efferveSoeneQ ceases the mixture is again filtered, and at” ,colduriess liquid is obtained. .1 Wrofigr ' , . "11m tracingeloth, and will also 'efi'aoelé (-7". marks. When the tracings are to b graphed, rawsiemia is added to the ink, f . colour unites with it most intimately and? Q1“ .cepts‘tliegreates’t quantity oi light. ' ‘f‘ .. Hw- ‘_,__‘ _____,. THE DBAUGHTSMAN’S HANDBOOK OF PLAN AND MAP DRAWING. ! BI‘IBLE LAND ES TA TE PLAN snawmc PRINCIPAL CHARACTERS OF .WORK USED IN MAPPING. 1;; ngssemwnw p m“, ‘ \ gs... “‘ 7/“ “'3?“ fl ~ I“ .‘ ' aw!“ VILLAGE “ram .0 ' Chapel A? ’f/tth‘xLX - U‘fifryt;7‘w.iv , ‘ ‘9'? , . " lfi§‘ O )> \;I FORT IV 3 ' ‘ 1 "4. I. 5"“ ' '«m. '_'. E 80F.N.Spon,Londcn JaNewYork. .3 PREFACE. Tim main purpose of the present work is to be- a handy book of reference for draughtsmen engaged chiefly in Topographical Drawings. But to have limited its use to one class of draughtsmen, and especially to the skilled members of that class, would have necessitated the discovery of more cogent reasons for its publication than its author has yet been able to adduce. Works of such a character exist already, and though their imperfections are numerous, they fulfil their purpose in a fairly satisfactory manner. But had the field been clear in this direction, it is so restricted in extent that to have entered upon it would have been to undertake a labour that. promised little fruit, for such a work could be only of small utility even to those for whom it was specially intended. It was, therefore, determined to make the present handbook generally useful by giving it a much wider scope. And Hence, if the intention has been efficiently carried out, it may claim a place in every drawing office, be it that of the Topographer, the Hydrographer, the Surveyor, the Military, Civil, or Mechanical Engineer, or the Architect. Whether or not this degree of success has been achieved, is not for the author to judge. But should he have failed to reach the high mark at which he has aimed, he hopes, with some degree of confidence, that he has at least succeeded in producing a book which the experienced draughtsman will find valuable as a book of reference, and which the pupil may constantly consult with profit. A want has long been felt by draughtsmen for some work of this kind to which they might refer their pupils in the office, and it may not be presumptive to suppose that the present work has supplied that want. To render it convenient for this twofold purpose, it has vi PREFACE. been divided into two parts. In the first part the principles and prac- tices of the art have been clearly but briefly explained and illustrated ; while in the second part, the application of the principles previously learned has been treated of, and such information given as relates directly to the duties of the practitioner. Of course, in a work of the present character, originality in the matter is neither to be expected nor desired; enough if the manner shows some novelty, and is such as to add value to the matter. Although the preparation of maps and plans has received the chief share of attention, engineering, architectural, and mechanical drawings have been largely treated of. Projection, orthographic, isometric and perspective, has been altogether omitted as beyond the scope of the work; but Colouring and Shading have been fully con- sidered and profusely illustrated. The Plates appended as examples for reference are numerous and varied in character ; they have been specially prepared by B. Alexander, to whom the author offers his warmest thanks for the truly admirable manner'in which he has executed the work entrusted to him. 16, CRAVEN STREET, CHARING Cnoss, September 7th, 1874‘. CONTENTS. PART I.—THE ESSENTIAL ELEMENTS. SECTION I.——THE DRAWING OFFICE AND ITs FURNISHINGS. I'AGE The Drawing Oflico .. .. .. .. .. .. .. .. 1 Instruments .. .. .. .. .. .. .. .. .. 2 Materials .. .. .. .. .. .. .. .. .. .. 5 Precautions and Remarks .. .. .. .. . .. .. 9 SECTION II.—GEOMETRIOAL PROBLEMS .. .. .. .. .. .. 15 SECTION III.—LINEs, DOTS, AND THEIR COMBINATIONS. Straight and Curved Lines .. .. .. .. .. . . .. 27 Lines of uneven thickness .. .. .. .. .. .. .. 30 The Broken Line .. .. .. .. .. .. .. .. 30 The Dotted Line .. .. .. .. .. .. .. .. 31 Combinations of Straight, Broken, and Dotted Lines .. .. .. 31 The Wavy Line .. .. .. .. .. .. .. .. 33 Grass-land .. .. .. .. .. .. . . .. .. 34 Swamps and Marshy Ground .. .. .. .. .. .. .. 35 Sand and Gravel .. .. .. .. .. .. .. .. 35 Woodland .. .. .. .. .. .. .. .. .. 36 Uncultivated Land .. .. .. .. .. .. .. .. 37 Contour Lines .. .. .. .. .. .. .. .. .. 37 SEUTION IV.——COLOURs. Flat—tints .. .. .. .. .. .. .. .. .. 40 Conventional Colours .. .. .. .. .. .. .. .. 44 Water .. .. .. .. .. .. .. .. .. .. 45 Grass-land .. .. .. .. .. .. .. .. .. 45 Marsh ., .. .. .. .. .. .. .. .. 45 Sand and Gravel .. .. .. .. .. .. .. .. 46 viii . CONTENTS. SECTION IV.——COLouns-—continued. mom Mud .. .. .. .. .. ., .. .. .. .. 46 Woodland .. .. .. .. ,. .. .. .. .. 46 Cultivated Land .. .. .. .. .. .. .. .. 47 Uncultivated Land .. .. .. .. .. .. .. .. 47 Buildings ., .. .. .. .. .. .. .. .. 47 Roads and Streets .. .. .. .. .. .. .. ., 47 Fences .. ., .. .. .. .. .. ,. .. .. 47 SECTION V.~SHADING. Application of Shade Lines 48 Cylindrical Surfaces 50 Shading Lines .. 50 Shading Lines on Cylindrical Suifaccs 51 Shading Lines 111 Topogiaphical Drawings .. 52 The Vertical System of Shading 57 Shading in Colours (53 Hill Slopes ,. . .. G3 Cylindiical Surfaces 111 Mechanical Diawings 34 PART IL—APPLICATIONS. SECTION I.—~—LETTERING, BORDERING, AND NORTH POINTS. Lettering .. .. .. .. .. .. .. .. 66 Borders .4 .. .. .. .. ,. .. .. A. (‘19 North Points .. .. .. .. .. .. ,. ,. .. 60 SECTION II.——SCALES. Scales of Distances .. .. .. .. .. .. .. .. 70 Scales of Construction .. .. .. ,. .. .. ' .. 74 SECTION III.—~PLOTTING. Reference Lines and Points 78 Plotted Points .. .. .. 78 To Plot Reference Lines and Points .. 78 To Plot Traverse Reference Lines . x h- CONTENTS. ix' SECTION III.—-PLOTTING"continued. PAGE TO Plot Detail .. .. .. . .. .. .. .. 80 To Plot Contours .. .. .. .. .. 00 To Plot Sounded Points In Submerged Districts .. .. .. .. 90 E1r01s and EIror-sheets .. .. .. .. .. .. .. 91 To Plot Vertical Sections .. .. .. .. .. .. .. 92 To lay down Gladients .. .. .. .. .. .. 95 TO Plot a Section from a Contour Map .. .. .. .. .. 96 SECTION IV.—CIVIL ENGINEERS’ AND SURVEYOES’ PLANS. Standing Orders of Parliament .. .. .. .. .. .. 98 ,, . ,, ,, Documents required .. .. .. 99 ,, ,, ,, Plans .. .. .. .. .. 100 ,, ,, ,, Book of Reference .. .. .. .. 101 a) a; ,, Sections .. .. .. .. .. 101 Working Sections .. .. .. .. .. .. .. .. 103 Regulations of Local Government Board :— Boundary Maps .. .. .. .. .. .. .. .. 104: Maps for Division into Wards .. .. .. .. .. .. 104 Plans of Proposed Works .. .. .. .. .. .. 105 General Plan .. .. .. .. .. .. .. .. 105 Detailed Plan .. .. .. .. .. .. .. ,. 106 Mining Plans .. . .. .. .. .. .. .. .. 106 Estate and Town Plans .. .. .. .. .. .. .. 107 SECTION V.—MAP DRAWING. Single Stroke Streams .. .. .. .. .. .. .. 109 Double Line Streams and Rivers .. .. ,. .. .. .. 110 Colouring Streams 01 Rivers. . . .. .. 110 Islands and Sand-banks, Sandy and Pebbly Beds of Rivels .. .. 110 Roads and Pathways .. .. .. .. .. .. .. 111 Mountain Passes .. . .. .. .. .. .. .. 111 Fouls and Ferries, Toll—gates .. .. .. .. .. .. 111 Telegrapll Lines and Stations .. .. .. .. .. .. 112 Railways, Stations, and Termini .. .. .. .. .. .. 112 Size of Cities, Towns, and Villages .. .. .. .. .. .. 112 Sketching, Shading, and Copying Hills .. .. .. .. .. 113 Field Sketching .. .. .. .. .. .. 114 Examination Of Maps In the Eield .. .. .. ,. .. 118 X . CONTENTS. SECTION VI.'—MECHANICAL AND ARCHITECTURAL DRAWINGS SECTION VII.»——CCPYING AND REDUCING. Drawing from Copy Copying by Tracing Copying by Transfer .. Reducing and Enlarging The Pantograph The Eidograph .. .. .. Drawings for Lithographcrs and Engravers .. TRIGONCMETRICAL FORMULZE INCLINED MEASURE .. CURVATURE AND REFRACTION INDEX PAGE 121 127 128 129 130 131 136 141 142 143 143 144 {a LIST OF ILLUSTRATIONS. ——oo:£x:o<>—— ALPHABETS, examples of Angle, to bisect .. Angles, to construct Arch, equilateral , horse-shoe , lancet ,obtuse ,Ogec . .. :semi-elliptical . . ,Tud or .. . Architectu1al drawings, colouring of. BORDERS . . Boundaries, parish, &c. .. CANAL LOCKS .. Cha1t, exa uple of. Cinquefcil, Gothic .. Circle, to desc1ibe tlnough given points , to find the centre of Cliffs . .. .. .. Colouring architectural drawings. maps and plans mechanical drawings Copse . . Corners Cylinders shaded Cyma recta rcvcrsa DOCKS . .. .. . . Drawings, architectural, colouring of. , isometrical , mechanical, colour- ing of. Page. Plate. 16 16,17 23 24 24 25 23 24 23 17 18 51,52 25 25 4,5,6 24 1,3,8,9, 13 3,15 1,11 18 1,11,14 24 1,3,13, 17,28,33 22, 23, 27 13,8,,9 13 1,11 24 27 EIDOGRAPH . . 22, 23, 27 i . 3 —, to b1sect Ellipse, to d1 aW l .. l Equilateral tliangle, tol construct. I l FLOURISHES I‘01t1ficat1ons, plans -——, sections. GEOLOGICAL MAPS .. .. l sections, coloured .. \ Grass .. .. .. .. ‘1 Gravel .. .. ' HARBOURS Hexagon, to deScribe Hill shading Hills —— in colour .. ISOMETRICAL DRAWINGS .. LAKES Land, cultivated . ‘ , uncultivated .. .. ‘ Lettering, examples of Line, to divide into equal parts. 1 Lines, broken .. .. .. E ———, contour L. = —-—, dotted —, section .. .. —, shade .. .. .. Page. 22 16 34 35 21 53,55,56, 58,61,62, 63 32 37 Plate. 26 25 31 28 20,21 1,17 1 11 1,12,14, 17 12,14 1,3,11, 17 1,13 4, 5; '6. 7, 5 , xii LIST OF ILLUSTRATIONS. MAPS, geological -——-, Ordnance, example of. —— and plans, colouring of. Marsh .. . .. .. Mechanical drawings, colouring of. Mining plans .. NORTH POINTS .. OVAL, to construct .. PANTOGRAPH Parabola, to draw Pentagon, to describe Perpendicular, to erect .. Plans, estate , fortifications .. -——, mining .. —, office .. , parliamentary , reducing or enlarging ————, town improvements and maps, colour- ing of. Plotting, examples of QUARRIES .. .. Quatrefoil, Gothic .. RADII 0F CIRCLE, to draw Railways. Rectangles, similar, to con— stiuct. Rivers —, outlines of Roads Rocks Roofs ; Swamps Page. ' Plate. I ' 28 18 1,3,13, 17, 28, 33 35 1,10,11‘ .. 22, 23, 27 33 9 18 .. 26 21 .. 2O . 15 .. H 3,17 .. 32 33 1‘ 2 13,19 1 26 13 1, 3, 13, 17, 28, 33 82,85,86, H 88,93 .. 1 26 .. 18 .. .. 1, 3 20 .. 1,11,12, 17 3O .. .. 1,3,12 17 .. 1,11 30 .. ' SAND banks Scales Section plotting, example of Sections, fortifications , parliamentary . —— of strata, examples of colouring. Shade, scales of, for bills Signs, various, used in In- dian and Colonial maps. , —, used in maps, plans, &c. , —, used in military maps and fortifications. S011ndings Square, to construct ,multiple of, to con- struct. Squares, proportional, to construct. and marsh y ground. TANGENT, to draw . Titles, examples of .. Towns Traverse ample of. Trees plotting, ex- Trefoil, Gothic Triangles, to construct VILLAGES WATER, flowing , standing — in section VVOOd-graining Wood In section VVoods. Page. 35 71,73,76 93 53, 58 18 19 19,20 18 85,86,88 36 25 1317 33 29 30 32 32 36 1,10 3,7,8 1,3,11, 3 1,3,10, 13,17 11 1,11 1,3,10, 17 PLAN AND MAP DRAWING. PART l.—THE ESSENTIAL ELEMENTS. ._oo§ec'_oo—-—- SECTION I.—TIIE DRAWING OFFICE AND ITS FURNISHINGS. THERE are few occupations so dependent for their correct performance upon minute matters of detail as that of the draughtsman. Things apparently the most trivial are sufficient to render inaccurate or to mar the appearance of the otherwise most carefully and skilfully executed design, and as the value of a drawing depends wholly upon its accuracy and its appearance, it is obvious that such matters of detail, however trivial they may be in themselves, demand careful attention. We have, therefore, deemed it desirable to preface our remarks on Plan and Map Drawing with a brief description of the instruments and materials required, and of the mode of using them which experience has shown to be the best. lee Drawing 0flice.—The first essentials of a room for drawing in are—that it shall be quite free from damp and be well lighted. The position of the windows is a matter of some importance, and though persons have largely to accommodate themselves to circum- stances in this respect, it is desirable to know what are the most suitable conditions, in order that they may be complied with as far as circumstances permit. Skylights are unsuitable, because the light entering from above is liable to be intercepted by the body, and especially by the hands of the draughtsman; besides which, the light from a skylight is seldom sufficient. For the same reasons, a window I; 2 PLAN AND MAP DRAWING. placed very high in the room is objectionable. When possible, a western aspect is to be preferred, as the light from this direction is less variable and lasts later in the day than from other directions. Blinds of some kind are necessary to modify the light when the sun shines directly upon the window. Gaslights should be situate about 3 feet above the drawing table, and there should be two burners, placed not less tha112 feet apart, as otherwise the hands and the inst1uments will cast shadows which will prevent fine lines and pOints from being seen. The drawing table should be placed under the window; it should have a breadth of about 2 feet (3 inches, and its height should be 3 feet 8 inches at the back and 3 feet 6 inches at the front. The front edge should be roundedover. Dusters and means for washing the hands must also be provided, as it is requisite to frequently dust the paper and the instruments, and to keep the hands perfectly clean. Inshumem‘s —-All drawing instruments should be of the best workmanship, f01 it is impossible to obtain accuracy with imperfect tools, and theyn must be kept in o1der by careful handling. For all kinds of drawing, compasses of three sizes are required, the ordinary compass, the bows, and the spring bows. The best compasses are those which are sector-jointed. The points should be kept suffi- ciently sharp not to slip on the paper, but not so sharp as to readily penetrate it. It is also important that the points be thin and round, as otherwise, when several arcs have to be struck from the same centre, the compass leg is apt to make a large hole, which is utterly destructive of accuracy. The pencil leg should be kept exactly equal in length to the steel leg, for true circles cannot be drawn when one leg is shorter than the other. In removing the movable leg, care should be taken to draw it straight out, as nothing spoils the instru- ment so soon as wrenching the leg from side to side. In using the compasses, the instrument should be held lightly between the thumb and the forefinger only. It should not be pressed upon the paper; but it should rest equally upon both points. If the weight of the THE ESSENTIAL ELEMENTS. 3 hand be thrown upon the instrument the points will penetrate the paper. Care should also be taken to bend the joints so as to keep both legs perpendicular to the paper. If attention he not given to this matter, the steel leg will make a large hole in the paper, and the ink leg will make a ragged line, because only one of the nibs will touch. Next in importance to the compass, and of more frequent use, is the drawing pen. The draughtsman should possess at least two of these instruments, one for fine, and another for medium lines. When the proper opening of the nibs for fine lines has once been obtained, it is desirable not to change it; the pen can always be cleaned by passing a piece of drawing paper between the nibs. The cleaning of the pen should be carefully attended to; it should never be put away without having every particle of dried ink removed from it; and frequently, while in use, it should be wiped out to remove the dust, which is constantly settling in it, as well as the particles of lead that are taken Up from the paper. The ink is supplied by breathing between the nibs and dipping them in the liquid, or by means of a camel’s hair brush. When the latter method is adopted, care should be taken to protect the brush from the dust floating in the atmo- sphere of the room. After considerable wear, the drawing pen will require setting. The operation of setting requires some judgment and considerable practice, and is one of those mechanical niceties which it is difficult to describe. Generally it will be found advantageous to have the pen set by an instrument maker. As, however, this resource is not always at hand, it is desirable that the draughtsman should be able to set his own pen. The following description of the operation given by W. Binns, in his admirable work on Projection, is the best we have seen. “ The nibs must be precisely of the same length, rounded in two directions, and as sharp as it is possible to make them without pro- ducing to the touch a sensation of cutting, and without scratching the surface of the paper when drawing a line, which is generally the case when one nib is longer than the other. This irregularity may be B 2 fax“ ,4 4 ”’ PLAN AND MAP DRAWING. detected by placing alternately the sides of the pen at an acute angle with the forefinger, and slipping the edge of the nail over the point, when the difference in length will be at once perceived; and it may be reduced by drawing a few lines, as it were, on a turkey stone, with the pen applied to the edge of a set square in the same manner as if drawing lines upon paper, but with this difference, that during the longitudinal motion of the pen the handle must be turned over in a circular manner, so as to give a rounded form to the point of the pen. If the pen be now held with the point directed towards the eye, and gently moved about so as to catch the angle of reflexion, a bright speck on one or both nibs will be observed, which must be reduced by rubbing the pen to and fro upon the stone, giving at the same time a slight rotary motion to the handle, which must be held at an angle of about 20° with the face of the stone: the point of the pen being examined from time to time, and the process of reducing the bright specks continued until the point is as fine as can be used without cutting or scratching the paper. If at this stage the two nibs are of the same length, a perfectly solid and fine line can be drawn. The beginner, however, must not be disappointed if sixty minutes are thus expended before he can produce a satisfactory result; whereas two minutes in the hands of a practitioner would suffice.” The instrument most frequently in the hands of the draughtsman is the lead pencil. These are required of various degrees of hardness, but for lines that are to be ruled an H H is the best. The most suit- able qualities of lead are those which are the most easily rubbed out ; these qualities are sometimes gritty, but this defect is more than com- pensated by the facility with which a line may be removed from the paper. There is some art in cutting a pencil properly. If the point is intended for sketching, it should be cut equally from all sides, so as to produce a perfectly acute cone. But for line-drawing a flat or chisel point should always be used. This point is much stronger, and will last much longer than the cone point. To produce the chisel point, first cut the pencil from two sides only with a long slope, and afterwards cut the other sides away only just sufficiently to round the THE ESSENTIAL ELEMENTS. Arty; first edge a little. This side wood is needed both to afford a support to the lead, and to show in what direction the point stands. To avoid breaking the lead, the knife should be held at an acute angle with it. A point out in this manner may be kept in order for some time by rubbing it upon a fine file or upon a piece of glass-paper or fine sand- stone. Of the other instruments used in drawing, nothing need be said in this work, as their use presents no difficulties. It may, however, be well to remark that no straight-edge employed for ruling lines should be less than a fourteenth of an inch thick, for if the edge be very thin, it will be impossible to prevent the ink from escaping from the pen on to it. Materials. —The drawing papers known as Whatman’s are the best prepared of any obtainable, and they are almost universally employed. Of these there are two kinds, the smooth and the rough; the former is technically called not paper, and is the more suitable for mechanical and architectural drawings; the rough is more effective for perspectives and Gothic elevations. A third kind is known as the hot-pressed, but as it does not take colour so well as the not and the rough, it is not often used. The various sizes are indicated by their names, which are the following :— Antiquarian .. .. .. .. .. .. .. .. 53 x 31 inches. Atlas .. .. .. .. .. .. .. .. .. 34 x 26 ,, Columbier .. .. .. .. .. .. .. .. 34% x 23% ,," Demy .. .. .. .. .. .. .. .. 20 x 15 ,, Double Elephaiit .. .. .. .. .. .. .. ‘étff‘bw 26%- ,, Elephant .. .. .. .. .. .. .. 28 x 23 ,, Emperor.. .. .. .. .. .. .. .. .. 68 x 48 ,, Imperial.. .. .. .. .. .. .. .. .. 30 x 22 ,, Medium .. .. .. .. .. .. .. .. .. 22% x 17 ,, Royal .. .. .. .. .. .. .. .. .. Zl x 191- ,, Super Royal .. .. .. .. .. .. .. .. 27; x 19% ,, The sizes considered best, and almost universally used for en- gineering and architectural drawings, are the elephant, the double elephant, and the imperial. If smaller sizes are required, the half or quarter sheet is used. Antiquarian has generally a good surface to draw upon, and it is preferred by some architects. The atlas is also a G PLAN AND MAP DRAWING. very good paper. Besides the foregoing, there is the machine-made or cartridge paper, which is very commonly employed for detail draw- ings. It has not so good a surface as the other kinds, nor is it so white; its chief advantage is found in its dimensions, it being made uniformly 53 inches wide and continuous. Hence the exact length required may be obtained. For large plans and competition drawings, either cartridge or emperor paper is used. Paper that is to receive an elaborate drawing must be stretched and glued to the board. This operation is one requiring a little skill and some practice to perform successfully. The following is the best manner of proceeding. The sheet to be strained is laid face upward upon the board, and a wet sponge is passed rapidly along the margins, and then across the face, including the margins, until the whole surface is sufficiently and uniformly wetted. The object of wetting the margins first is to prevent coekling by allowing them a longer time to expand in than the middle of the paper. The sheet must now be left for about ten minutes, or until the wet gloss has entirely disappeared. The process of glueing to the board is as follows. A straight-edge is laid along one end of the sheet, and about % of an inch of the margin is turned up against it, and glued by means of a brush. The margin is then turned down and rubbed quickly with a knife-handle or, still better, a paper-knife. The" opposite end of the sheet is next pulled outwards and glued in the same way, and the same method is afterwards applied to the top and bottom margins. Some draughtsmen prefer to glue down the adjoin- ing edges, but generally it will be found that laying down successively opposite edges will. give more satisfactory results. The contraction of the paper in drying should leave the face quite flat and solid. During the process of drying, it is important to keep the board in a perfectly horizontal position, as otherwise the water will gravitate towards the lower side and soften the glue, and as the sheet will dry unequally, the lower edge will break away. The thinner the glue used the better, and for this reason the best quality should be obtained, and care should be taken to keep the THE ESSENTIAL ELEMENTS. 7 water supplied that is lost by evaporation. When it becomes necessary to replenish the glue-pot, the cake should be soaked in cold water for at least eight hours. The removal of a drawing from the board presents no difficulty. A. pencil line is drawn along the margin at a sufficient distance from the edge to be clear of the glue, and a pen-knife is guided along this line by a straight-edge not used for drawing. AS duplicates of drawings, especially if they be working draw- ings, are usually tracings, tracing paper is an important material in every drawing office. It is too well known to need a description. It is sold in various sizes, and of various prices, but the most usual sizes are 30 X 20 inches, and 40 x 30 inches, the price of the former being 3d. and that of the latter 6d. a sheet. It may also be purchased in continuous lengths of 24 yards, 42 inches wide, for about 8.9., or if extra stout, 163. A much less expensive mode of obtaining tracing paper is to make it one’s self. Common silk or tissue paper may be pur- chased in quantities at less than a halfpenny a sheet of the ordinary size. This may be prepared by placing a single sheet at a time flat upon a board or other smooth horizontal surface, and applying a mixture of boiled linseed oil and turpentine. This mixture should be composed of one part of oil to five of turpentine, and it should be applied with a small sponge. One coating is sufficient, and it should not be put on too thickly. Each sheet as prepared should be hung over a string stretched across the room to dry, and when all the clear oily marks have entirely disappeared, it will be ready for use. Five gills of turpentine and one of oil is enough for two quires of double-crown tissue paper. That tracing paper is best which is toughest, most transparent, and most free from greasiness. The continuous papers are more economical than those in sheets, because just the quantity required can always be taken from the roll. For durability, tracing cloth is to be recommended; it is sold in continuous lengths of 24 yards, and it may be had from 18 inches to 41 inches in width. That known as “Sager’s vellum cloth” is of excellent quality, both for transparency and strength. 8 PLAN AND MAP DRAWING. Some. kinds of drawings, such as specifications for Letters Patent, plans upon deeds, &c., have frequently to be made upon parchment. Special kinds of parchment can be obtained for these purposes. There is a kind made Which is quite transparent, and which can be purchased cut to the Patent Office regulation size. As parchment has always a more or less greasy surface, before commencing to ink or to colour, it should be pounced over with pouncet of finely-powdered French chalk. Besides this precaution, it will be necessary to add a little ox-gall to the ink or colour. Blacklead and carbonic paper are used to transfer a drawing. The former is prepared by rubbing thin paper over with a soft block of Cumberland lead; the latter by painting one side of the paper with lamp-black ground to perfect fineness in slow drying oil. Carbonic paper is used for coarser work than blacklead paper. Both may be purchased, properly prepared, at a trifling cost. The drawing to be copied is laid over the sheet of paper which is to receive the copy, with a sheet of the blacklead or carbonic paper interposed, and a tracer is passed with a light pressure over the lines. This method is mostly used to reproduce a drawing from a tracing, to obtain a finished copy from a rough draught that has become soiled and marked in designing, or to avoid errors or small alterations in the first drawing. A very convenient kind of paper for small working drawings, or for sketching to scale, is that known as sectional paper. This is paper ruled into small squares to a given scale with pale ink. The spaces in ordinary use are 1—15, é, %, 7E, and i inch. Thicker lines are drawn either to mark off the inches or to count the spaces in tens. With this paper, the scale may be dispensed with, as the eye is capable of sub- dividing the spaces with sufficient accuracy for practical purposes. Sectional paper is much used for sections of railway cuttings and embankments, as it affords a ready means of calculating the contents. It is also made up into sketching books and architects’ pocket-books, for which purposes it is peculiarly convenient. Indian ink is used for all kinds of geometrical drawings. Being THE ESSENTIAL ELEMENTS. 9 free from acid, it does not corrode the steel points of the instruments, and it preserves its colour unchanged. It is difficult to get the genuine ink, but even that, as it is imported from China, varies considerably in quality. For line-drawing, that is the best quality which will wash up least when other colours are passed over it. This quality is ascertained in the trade, though not with absolute certainty, by breaking off a small portion. If it be of the right quality, it will show a very bright and almost prismatic-coloured fracture. The ink is prepared for use by rubbing it with water on a slab or in a saucer. The saucer should be quite smooth inside, so as not to ab ‘ade the ink. When mixed to the requisite thickness, which may be ascertained by drawing a line With a common pen, it should be covered to protect it from the particles of dust floating about the room. Ink should be rubbed up perfectly black, for pale ink makes the boldest drawing look weak. But after it has become black, any further mixing will only injure it by rendering it viscid. It is best to use it immediately after it is mixed, for if re-dissolved, it becomes cloudy and irregular in tone. The addition of a little ox-gall will make it flow more freely from the pen. For erasing Cumberland lead-pencil marks, native or bottle india- rubber is sufficient; but for other kinds of pencils, fine vulcanized indiarubber is better. This, besides being a more powerful eraser, possesses the important quality of keeping clean, as it frets away with the friction of rubbing, and thus presents a continually renewed sur- face. Vulcanized rubber is also very useful for cleaning off drawings. Precautions and Remarks—It is essential to the good appearance of a drawing that the paper be preserved perfectly clean. The hands especially should be kept as much as possible from resting on it, as the perspiration makes it greasy, and when once it has acquired this defect, clear, sharp lines become impossible. A sheet of clean paper should be constantly interposed between the draughtsman’s hands and the drawing upon which he is Working. Brown or printed paper is unfit for this purpose, as the former is either greasy or tarry, and the latter is apt to soil from the printed matter. White paper can be 0 10 PLAN AND MAP DRAWING. had of large size, or, if necessary, several sheets may be pasted together. To prevent risk of smearing the lines when inking in, it is well to begin at the top of the drawing and to work downwards, also from the right to the left for vertical lines. The ink slab or saucer should be kept on one side and never in front of the drawing. Should a drawing get a grease spot, it may be removed by the application of a hot smoothing iron to a piece of clean blotting-paper laid over the spot, but not sufficiently to be coloured over. Great care should be taken to correctly place the centre lines of a drawing; these lines should be drawn very fine and distinct. In working drawings the centre lines are of great importance, as the dimensions are always measured from them; in such cases it is customary to draw them in red or blue colour. In all cases where a plane figure is symmetrical with respect to a given line, whether the line exists in the figure or may be considered as existing in it, that line should be drawn first, and such a line is known as a centre line. The centres of all arcs should be marked for the ink compasses at the time the arc is struck by the pencil, by placing a small hand- drawn circle around it. It is also necessary to mark distinctly by short intersecting straight lines the exact points at which the arc begins and ends. \Vhen a number of concentric circles have to be struck, the smaller ones should be struck first, as it is more difficult when the hole in the paper becomes enlarged to draw a small circle than a large one. thenever it is practicable, lines should be drawn from a given point rather than to it; and if there are several points in one of which two or more lines meet, the lines should be drawn from that one to the others; thus, for example, radii should be drawn from the centre to the points in the circumference of a circle. IVhen a point has to be determined by the intersection of circular arcs or straight lines, these should not meet at an angle less than 300. In dividing a line into a number of parts, instead of setting off the part repeatedly THE ESSENTIAL ELEMENTS. 11 along the line, it is better to set off a convenient multiple of the given part, and subdivide it; that is, to work from the whole to the parts, rather than from the parts to the whole. This is an important principle 111 s111vey mg as well as in plan drawing, and 111 the construction of scales it ought always to be observed. Ink lines should never be erased with a knife, nor should an ink- eraser be used, especially if the drawing is to be coloured. A needle point will take out a short line in a way that leaves little trace of the error. A very good means of taking out a line is furnished by a piece of Oakey’S N0. 1 glass-paper folded several times until it presents a round edge; the application of this leaves the surface of the paper in a much better condition for drawing upon than it is left in by the knife. When the drawing is to be coloured, it is best to wash out a wrong line with a small hard brush, and to Slightly sponge over the place through a hole of the requisite size cut in a scrap of drawing paper, to save the other parts of the drawing. When a line has been drawn a little beyond the point at which it should terminate, it will generally be found better to avoid erasure by laying a little Chinese white over the line with a fine sable-brush. Sometimes, when erasures are unavoidable upon a drawing that is to be coloured, it will be found expedient to take the surface off the whole of the paper with glass-papei, the colour will then flow equally. In copying from a tracing, it is well to put a sheet of drawing paper underneath the tracing, for it not only Shows up the lines more distinctly, but it prevents the dividers from tearing the drawing while taking off measurements. Before commencing a drawing, a cutting-off line should be drawn all round the sheet clear of the glued portion. The portions outside of this line are useful to try the drawing pen upon before diawing a line, or for t1 y1n0~ a tint when colouring. Care should be taken not to leave too nariow a margin, for nothing detracts more from the appearance of a good drawinO‘. For a drawing occupying a space of 1 foot or 15 inches square over all, there should be a margin of at least 5 inches all round, with the border line from 1% to o 2 12 PLAN AND MAP DRAWING. 2 inches from the cut-off line. Other sizes should be in proportion. This rule is given by Maxton in his ‘Enginecring Drawing,’ who also has the following remarks on cutting off and preserving drawings. “The opposite side should never be out first, for if so cut, upon nearly completing the cutting of the third side the paper undergoes con— traction, and the fourth side pulling against it, is apt to snap off the remaining inch or so, and generally in towards the sheet, seldom in the margin on the outside of the cutting-off line. The sheet should be cut off all round, taking care, by applying the knife-blade under the edge of the sheet, that it is free from the board before proceeding to cut off the side or end adjoining. When the sheet has been removed, the strips of drawing paper left on the board should be simply sponged over two or three times, and they will peel off easily. “For preserving a rolled drawing, a common substitute for string, and one less likely to crease the drawing, is made as follows :——Take a strip of drawing paper from 1% to 2 inches wide and an inch longer than the circumference of the rolled drawing. About half an inch from each end make incisions, at one end in the middle and one-third of the breadth across, and at the other end at the sides, each one- third of the breadth across. Fold in these sides, so that they may pass through the incision in the opposite end of the strip; on being opened again after they have passed through, the whole will form a hoop, which, when slipped over the drawing, will keep it secure.” As cartridge paper is not always suitable, it sometimes becomes necessary to join the smaller sizes end to end. To do this neatly the edges should be cut straight, and a straight-edge laid upon the paper, allowing % inch to project beneath it. This portion of the paper should then be rubbed down with sand or glass-paper until the outer edge is quite thin. The edges of both sheets to be joined must be treated in this way, and covered with a thin coating of gum. Having placed these edges in contact, a strip of paper 1}; or 2 inches wide should be laid upon the joint and well rubbed with the handle of a paper-knife. If the paper thus joined has afterwards to be stretched THE ESSENTIAL ELEMENTS. 13 on a board, it should be done while the joint is damp. In sponging the paper, care must be taken not to go over the joint. In joining sheets of tracing paper, the joint should never be made more than i inch bread. The gum used for this purpose should be very thin, and a strip of drawing paper should be placed upon each side of the joint until it is quite dry. It is a good plan to roll the joined sheet upon a roller with the joint in a line with the roller and the strips infolded over the joint. When left to dry in this position, the joint will be perfectly smooth. Drawings have frequently to be mounted on stretchers, and the operation of mounting is one requiring some care and practice. Generally it will be found more convenient to purchase the stretcher ready made complete; but when this is not done, care must be taken to have the frame made of sufficient strength to resist the tension of the paper when dry. The sides and the ends of a stretcher, 8 or 9 feet long, should be 4 inches broad and not less than g inch thick, and for any length above 18 inches there should be one or more bars across. A frame 6 feet long should have two cross-bars dividing the length into three equal parts, and they should be of such a thickness as not to come up flush with the sides and ends by about é inch. The inner edges on the face of the latter should be rounded down to the level of the cross-bars, and the same degree of rounding should be given to the edges of the cross-bars themselves. This is necessary to prevent the edges from showing a soiled mark on the paper. When the frame has been thus prepared, the linen or calico should be spread out on some flat surface and the frame laid upon it face downwards. The ends of the linen should then be pulled over and nailed to the back; next, the middle of the sides should be pulled over and fixed in the same way. The intermediate spaces are afterwards tacked down by placing a tack alternately on opposite sides, care being taken to pull the linen tight and smooth before inserting the tack. It is a good plan to fold the edge, as the double thickness will hold the tacking better than if single. To mount the paper on the stretcher, it should be laid face down- l4 PLAN AND MAP DRAWING. wards upon a clean flat surface, which will be all the better if covered with a clean cloth, and sponged with clean water. When the water has soaked in, apply with a flat brush some cold flour paste, and, if necessary, remove all knots or particles of gritty matter, as these would prevent the paper from lying close to the linen. The addition of:mhtfle:flun1tothe pame hnproww:fisadheflvernopmmy,andsz) tends to make the drawing less stiff when dry. When a good coating of paste has been well distributed over the paper, place the stretcher upon the paper and rub the back ofthe hnen vmfll;then turn the stretcher over and rub down the edges of the paper. Air-bubbles between the linen and the paper may be got rid of by puncturing the spot with a fine needle and rubbing it down. Paper thus mounted may be drawn upon nearly as well as when stretched on a board. To give an edge for the T-square, a strip of wood with parallel edges may be temporarily nailed on. ' Some drawings, such as large plans of estates, have frequently to be varnished. This operation requires some skill, and can be satisfac- torily accomplished only by a practised hand. The process generally adopted is to stretch the drawing upon a frame, and to give it three or four coats of isinglass size with a flat broad brush, taking care to well cover it each time, and to allow it time to dry between each coat. The best varnish is Canada balsam, diluted in oil of turpentine. This requires to be put on evenly in a flowing coat with a fine flat brush, and to be left in a warm room free from dust until it is thoroughly dry. The drawing must be in a perfectly horizontal position while the size and the varnish are being applied. In drawings to be var- nished, thick lines, such as shade lines, and chalky colours should never be put on before sizing, as they are apt to blot during the process. Should a fir drandngfboard getzuxfidentauy dented, an apphca- tion of water to the part will, within certain limits, bring it up to its proper level. 'I‘IIE, ESSENTIAL ELEMENTS. 15 SECTION IL—GEOMETRICAL PROBLEMS. T 0 Need a git-fen Straight Lina—Let A B (Fig. 1) he the given line. From A and B, with any radius greater than g A B, draw arcs cutting each other in C and D; then the line joining C D will hisect the line A B as at E. FIG. 1. FIG. 2. T 0 erect a Perpendicular to a given Straight Line.—-—Let it he required to erect a line perpendicular to the point B (Fig. 2) in the line A B. From any point Oabove the line, with radius B 0, describe an are as A BD; join A C and produce the line until it cuts the arc in D, and join D B; then will D B be perpendicular to A B. To divide a Line into any number of equal parts. — Let it be required to divide the line A B (Fig. 3) into five equal parts. From B, at any angle, draw B C, and on the line B C lay off five equal parts, 1, 2, 3, 4, 5; then take a set square E, and make one of the sides containing the right FIG. 3. angle coincide with the points A and 5, and to the other side apply a straight-edge F; then by passing the set square along the edge of the straight—edge and drawing lines from the points 4, 3, 2, 1, through the line A B, we shall have the line A B divided into five equal parts through the points 1’, 2’, 3", 4’. T 0 draw a Line making, with (mot/(er line, a given Angle—Let it be required to draw a line making with the line AB (Fig. 4) an 16 PLAN AND MAP DRAWING. angle of 350. From a scale of chords, which will be found on most scales supplied with a set of instruments, take off 600; from the point A, with this distance for radius, describe an arc CD; lay off on this are the distance of 350 taken from the same scale of chords; from A draw a line through this point. Then will the line A E make with the line A B an angle of 350. The same result may be more readily arrived at by means of a protraetor. If the centre point of the protractor be placed on the point A and its base made to coincide with the line AB, we FIG. 4. can from its circumference prick off the distance of 350, and a line drawn from A through the point thus found will make, with the line A B, the required angle of 350. T0 Insect an Angle—Let B A C (Fig. 5) be the angle which it is required to bisect. From A, with any radius, describe an are cutting the lines A B and A C in D and E; from D and 14], with the same or any other radius, describe arcs cutting each other in F, and from A draw a line through F ; this line will bisect the angle as required. FIG. 5. Fm. 7. FIG. 6. Let A B (Fig. 6) be the given base. From A and B, with radius A B, describe T 0 construct an Equilateral Triangle on (t given base. arcs cutting each other in C ; join A C and C B, which will complete the required triangle. T 0 construct a Triangle, the lengths of the Sides being given—Let it be required to construct a triangle whose sides shall be equal respectively to G, 5, and 4. Lay down the base A B (Fig. 7), making it equal to G divisions of the scale; from A with radius equal to 4 divisions, and from B with radius of 5 divisions of the scale THE ESSENTIAL ELEMENTS. 17 describe arcs cutting each other in C ; join A C and CB, which will complete the required triangle. To construct an Angle equal to a given angle—It is required to draw a line making with the line D E (Fig. 8) an angle equal to that contained by the lines BAG. From A, with any radius, draw an arc FGr, and from D, with the same radius, draw the arc H I, and make H I equal F Gr ; then a line drawn from D through I will make, with the line D E, an angle equal to the angle B A C. FIG. 8. \G 0 FIG. 9. A r A g. B /-/ E t l A ’1 D Ia‘ I: To construct a Triangle, the length of the base and the angles at the base being given—It is required to construct a triangle whose base shall equal 1 inch, and the angles at the base be 30° and 4.50 respec- tively. Having made the base AB (Fig. 9) of the required length, make the angles at A and B of the required magnitude in the manner already described (see Fig. 4), and the continuation of these lines meeting in the point Gr will complete the construction of the required triangle. T 0 describe a Circle which shall pass through three given points—Let AB C (Fig. 10) be the points through which it is required to draw the circle. From each of these points, with any radius, describe arcs cutting each other in D and E; join the points D and E, and the point where these lines intersect will be the centre from which to describe the circle which will pass through the points AB C as required. To draw a Tangent to a circle—I. Let B (Fig 11) be the point from which it is required to draw the tangent. Draw the radius 0 B, D 18 PLAN AND MAP DRAWING. and at B erect a perpendicular (see Fig. 2) ; then will the line B D be a tangent to the circle. 11. It is required to draw a tangent from the point E in the same circle. Draw the radius OE extending beyond the circumference to F, and make E G equal to E F. From F and G, with any radius, describe arcs cutting each other in II and I; then a line drawn through these points will be a tangent to the circum- ference at E. FIG. 11. FIG. 12. T 0 find the Centre of a circle—From any point in the circum- ference, as B (Fig. 12), describe an are cutting the circumference in A and G, and from A and C, with the same radius, describe arcs cutting the first are in two points ; through the points of intersection draw lines to the interior of the circle, and the point 0 where these lines intersect will be the centre of the circle. To draw lines which s/zall be Radiz' of a circle, t/ze centre being inaccessible—Having laid off on the circum- F .13. . . a, 2; JG ferencc of the arc, the distances apart of the ilk \K I 3K radii, as A, B, C, &c. (Fig. 13), from each of A 1) \ these Joints, with radius ~reater than a l g division, describe arcs cutting each other as at a, b, c, &c., join Aer, B b, Cc, &c., and the lines so drawn will be radii of the circle as required. To construct an Oval, t/ze widtb being given—Draw the line A B (Fig. 14) equal to the width, and bisect AB by C D (see Fig. 1). From the point of intersection E, with radius E A or E B, describe the circle A C B F, and from A and B through F, draw the lines A G THE ESSENTIAL ELEMENTS. . 19 and B H. From A, with radius A B, describe the arc B G, and from B, with the same radius, describe the are A H; also from F, with radius F Gr or F H, describe the arc GD H, which will complete the required oval. FIG. 14. ' C FiG. 15. 9-" - / P ,/ / / / . .\\ / ./ A ‘_‘ n // C i) To construct a Square on a given line—Let AB (Fig. 15) be the given line. At A erect a perpendicular (see Fig. 2), and from A, with radius A B, describe an are cutting the perpendicular in C; also from B and C, with the same radius, describe arcs cutting each other in D ; join 0 D and B D, which will complete the required square. T 0 construct a square that shall be a .Multiple of any given square. —Let A B C D (Fig. 16) be the given square, and let it be required to construct a square that shall contain 2, 3, 4, 850., times its surface. Draw the diagonal BC, then the square described on BC will be double the square A B C D. Lay 011‘ D E, equal to B C, and draw C E ; then the square described on C E will be three times the square A B CD. In the same manner lay off DF, equal to CE, and the square described on O F will be four times the square A B C D ; and so for any multiple of the square A B C D. T 0 construct a square that shall be equal to g, :1, (Sc, of any given square. Let ABCD (Fig. 17) be the given square. On AB, as a diameter, describe the semicircle A Gr B, and erect at the centre E the perpendicular E G. Draw Gr B, which will be the side of a square equal to one-half of ABCD. Lay off BF, equal to one-fourth of AB, and erect the perpendicular FH; then the square described D 2 20 PLAN AND MAP DRAWING. upon H B will be equal to one-fourth of A B C D. In the same manner a square may be constructed equal to any part of A B C D. FIG. 17. FIG. 18. G F H A] 1‘ F 0 A l ‘3 C D C T 0 construct a square that sball be in any Proportion to a given square—Let ABC D (Fig. 18) be the given square. It is required to construct a square which shall be to A B CD as 2 is to 5. Upon the side A B as a diameter describe the semicircle A F B, and divide the line AB into five equal parts. At the second point of division erect the perpendicular E F and join A F ; the square described upon A F will be to the given square A B C D as 2 is to 5. To construct, upon a given base, a Rectangle, which shall be similar to a given rectangle—Let AEFG (Fig. 19) be the given rectangle. It is required to construct upon the base FIG-19- . AB, one that shall be similar to AEFG. C / Produce A E and lay off the given base from 1: / (I. A to B; draw the diagonal A Gr and pro- /// duce it indefinitely. Erect a perpendicular A / .. n to A B at B, and from the point D where it intersects the diagonal produced, draw DC perpendicular to 7A F produced. Then ABCD will be similar to A E F G. All rectangles having their diagonals in the same line are similar. I To describe a regular Pentagon on a given line. —— Let AB (Fig. 20) be the given line. Bisect A B at C, draw 0 F perpendicular to AB, and make CD equal to AB. Draw AD and produce it THE ESSENTIAL ELEMENTS. 21 indefinitely; make D E equal to half A B. From A as a centre, with A E as a radius, describe an are cutting the perpendicular C D in F ; and from A F and B as centres, with radius A B, describe arcs cutting each other in G and H; join A Gr, B H, F G and F H; then AGF H B will be the pentagon required. FIG. 20. T 0 describe a regular Hexagon—With a radius equal to the length of one side of the required hexagon, describe a circle (Fig. 21), and set Off the same radius round the circumference of the circle, which will be thus divided into six equal parts. Join the points thus found, and the required hexagon will be completed as A B C D E F. T 0 draw a Parabola, the base and height being given.—Lct CA (Fig. 22) equal half the base, and C D the height. From the point D draw D E parallel and equal to A C, and from the point A draw A E parallel and equal to C D. Divide DE and A E similarly, making the end E of A E correspond to the end D of E D. Through l, 2, &c., in DE draw 1, l; 2, 2, &c., parallel to D 0. Join D to the several points 1’, 2', &c., in AE. The parabola will pass through the points of intersections of these lines With the verticals drawn from DE to C A. To draw an Ellipse—I. By means of a piece of string and pins. Place the diameters AB and C D (Fig. 23) at right angles to each other, and set off from C half the major axis at E and F; then will E and F be the two foci in the ellipse. Fix a pin at E and another at F; take an endless string equal in length to the three sides of the triangle E FC and pass it round the pins, stretch the string with 22 PLAN AND MAP DRAWING. a pencil G, which will then describe the required ellipse. II. From the ' centre 0 (Fig. 24) describe a circle of the diameter of the minor axis FIG. 23. FIG. 24. FIG. 25 b. C 112v r ,/g;,%¢.., /' /‘/ 117’ of the required ellipse. From the same centre, describe another circle with a diameter equal to its major axis. Divide the inner circle into any number of equal parts as 1, 2, &c., and through these points draw radii cutting the outer circle in 4, 3, &c. From 1, 2, &c., draw horizontals, and from 3, 4, &c., draw perpendiculars cutting each other in E F, &c.; the curve traced from 0 through the points C E F A, 650., will complete the curve of the required ellipse. III. Let ., A B (Fig. 25 a) be the major and C D the minor axis of the required ellipse. On any convenient part of the paper draw two lines FG, FH (Fig. 25 b) at any angle with each other. From F with the distance E C or E D, the semi-axis minor, describe an are cutting the lines F G, F H, in I and K; and from F with the distance E A or E B, the semi-axis major, describe the are L M. Join I M, and from L and K draw lines parallel to I M, cutting F G, F H, in N and O. From A and.B (Fig. 25 a) set off the distance FN (Fig. 25 b) in points N', and from these points as centres, with FN as radius, describe an arc of about 150 on each side of the major axis. From 0 and D THE ESSENTIAL ELEMENTS. 23 (Fig. 25 a) set off on the minor axial line the distance FO (Fig. 25 b) in points 0', and from these points as centres, with radius F 0, describe arcs of about 15° on each side of the axis 0 D. To obtain any number of intermediate points take a slip of paper (Fig. 25 a) and mark upon one edge, with a sharp-pointed pencil, 1, 3, equal to the semi-axis major, and 2, 3, equal to the semi-axis minor. If the slip of paper be now applied to the figure and moved over it in such a manner that the point 2 is always in contact with the major axis, and the point 1 in contact with the minor axis, the outer point 3 will describe a perfect ellipse, any number of points in which can be marked off as the “ trammel ” is moved into successive positions. For this last method, which in practice is by far the best, we are indebted to Binns’ ‘ Orthographic Projection.’ To construct a Send-Elliptical Arc/z.—The span A B (Fig. 26) and rise CD being given, divide C A and C B into any number of equal parts. Through the point D, draw E F parallel to A B, and from the points A and B erect the perpendiculars AE and BF. Divide AE and B F similarly to C A and C B. Produce C D and make C G equal CD. From D draw lines to the points 1, 2, 3, &c., in the lines AE and B F; also from G draw lines through the points 1, 2, 3, &c., in the line A B, and produce these lines until they out those drawn from D to the corresponding numbers in A E and B F. Through the points thus obtained draw the curve of the ellipse. FIG. 26. To draw the Got/tic Equilateml Arch—From the points A and B (Fig. 27), with radius A B equal to the span, describe the arcs B C and AC. By joining C to A and B we obtain an equilateral triangle from which this arch derives its name. 24 PLAN AND MAP DRAWING. To draw the Gothic Lancet Arch—In this arch, the centres E and D (Fig. 28) from which the arcs are struck, are situate outside of and in a line with the points of springing A and B; thus it is constructed on an acute-angled triangle, as will be seen by joining C to A and B. FIG. 28. “o 0D E" To draw the Gothic Obtase Arch—This arch, called sometimes the Drop-Arch, is constructed on an obtuse-angled triangle; the centres E and D (Fig. 29) being situate below and within the points of springing A and B. To draw the Gothic Tudor Arch—On the line of springing A B, (Fig. 30) take any two points as F and G, so that A F is equal to Gr B. Draw FE and GD cutting each other on the bisecting line through 0; from F and G, with radius F A or Gr B, describe the short arcs, and from E and D, with radius E0 or D 0, describe the arcs meeting in 0. FIG. 31. FIG. 30. A -——___'_‘r B To draw the Moom'sh Horse-Shoe Arch—The centres E and D (Fig. 31) from which the arcs forming this arch are struck, are situate above and within the points of springing A and B. One of THE ESSENTIAL ELEMENTS. 25 the most graceful forms of this arch is obtained when the height of the points E and D above the line of springing and their distance from the bisecting line through C are equal to one-third of the span A B. To draw the Gothic Ogee Arch—The most pleasing form of this arch is that constructed on FIG. 32. an equilateral triangle, in the following manner. Having drawn the equilateral triangle A B C (Fig. 32), draw F Gr parallel to A B. Bisect the sides A C and CB and produce the bisecting lines to FGr and H, which will complete the triangle F G H similar and equal to the triangle ABC. From H, with radius HA or H B, describe the arcs AE and B D, and from F and Gr, with the same radius, describe the arcs E C and C D. To draw the Roman Cyma Recta and Cyma Reversa.——Join AB (Fig. 33) and bisect A B in C. From the points 0 and B, with the distance B C, describe arcs cutting each other in E; and from A and (.7, with the same radius, describe arcs cutting each other in D ; from D, with the same radius, describe the are A C, and from E describe the are C B. The projection of the upper end of the curve over the under, as F B, is generally equal to the height, AF, of the moulding. The same description applies to the Cyma Reversa (Fig. 34) letter for letter. To draw the Gothic Trefoil.—Having drawn the equilateral triangle A B C (Fig. 35), bisect the angles and produce the bisecting E 26 ‘ PLAN AND MAY DRAWING. lines D E F which will hisect the sides of the triangle in G H I. From A B and C as centres, with radius A H or A 1, equal to half the side of the triangle, describe the arcs K L M, and'those concentric with them, and from the centre 0 of the triangle describe the outer circles and concentric arcs, which will complete the figure. To draw the Gothic Quatmfoil. — Draw the square A B U D (Fig. 36); hisect the sides of the square at IKLM and produce the hisecting lines to E F Gr II. From the angles ABC 1) of the square as centres, with radius A I or A M equal to half the side of the square, describe the arcs P N R S, and draw the outer concentric arcs. The circles, completing the figure, are drawn from the centre 0 of the square. To construct t/cc Gothic 0inquc/hz'l.———Ilaving drawn the regular pentagon AB ODE (Fig. 37), liiscct the angles and produce the hisecting lines to F Gr IT I K, which will cut the sides of the pentagon in a, I), 0, (Z, c. From A B C D and E as centres, with radius A a or A (2, equal to one-half of the side of the pentagon, describe the arcs L M N P R, and draw the outer concentric arcs and those concentric with them. The circles are drawn from the centre 0 of the pen~ tagon, as in the preceding example. THE ESSENTIAL ELEMENTS. 27 SECTION III.—LINEs, Do'rs, AND THEIR COMBINA’I‘IONS. All kinds of drawings are made up of lines and dots; these are the constituent parts, the materials which the draughtsman has to employ. It is therefore essential that he should make himself acquainted with their various forms and uses, and familiar with those means of producing them which experience has shown to be the best, before commencing the study of the principles by which the repre— sentation of an object is delineated. And moreover, it is desirable that he should acquire a familiarity with the operations required in the delineation of isolated objects, previously to making any attempt to place them in combination for the purpose of producing a complete drawing. The student will, therefore, do well to study carefully and to practise diligently the forms and examples given in this Section. Straight and Curved Linea—All straight lines, however short, should be ruled, whether they be drawn with the pencil or the pen. Pencil lines, which are intended to serve merely as guides to the pen, should be drawn lightly, as otherwise it will be difficult to rub them out without injuring the ink. They should also be drawn a little beyond the point at which the line is required to terminate, because the intersection of the lines at that point makes it more distinctly visible, and there is, consequently, less danger of passing beyond that point or of stopping short of it when inking in. It is very important not to stop short of the required length when ruling a straight line with a pen, for it is extremely difiieult to lengthen the line subsequently without leaving the join visible. An accurate line cannot be drawn unless the point of the pencil or the pen be kept close up to the rule, and to do this the top should be inclined a little outward. Before inking in a line that has been drawn in pencil, the indiarubber should be passed lightly over it, to remove the particles of lead adhering to the paper, for if these particles are allowed to remain, they get between the nibs of the pen and prevent the ink from flowing freely. The chief diliiculties in ruling a straight line with E ‘2 28 PLAN AND MAP DRAWING. the pen are, to keep it of a regular thickness throughout, and, when numerous parallel lines have to be drawn, to keep them at equal distances apart. To draw an even line, a first requisite is that the pen be in good condition. Frequently it will be found when drawing fine lines that the pen ceases to mark before the end of the line is reached, and as we have already said, it is very difficult to join a line without leaving visible traces of the operation. To remedy this defect, the pen must be reset as described in Section I. If a very hard pencil has been used, or if the pencil has been pressed heavily upon the paper, the pencil line will lie in a groove in the paper, and as the nib of the pen will not touch the bottom of this groove, the line drawn will be ragged. Another cause of unevenness is unduly pressing the pen against the rule; this pressure closes the nibs, and besides producing an irregularity in the thickness of the line, is very apt to cause a blot by forcing out the ink, which adheres to the rule when brought into contact with it. To prevent this, care should be taken to press the pen very lightly against the edge of the rule. A pen is manufactured by Stanley, of Holborn, London, which has the back nib much stiffer than the other, so that all danger of defect from this cause is removed by the construction of the instrument. To ensure a good line, the pen should rest lightly upon the paper, and the handle of the pen should make the same angle with the paper from the beginning to the end of the line. A considerable amount of practice is required to accomplish this, and to acquire the habit, the same attention should be given to the pencil as to the pen. The ability to draw a number of parallel lines at equal distances apart without measuring requires considerable training of the eye, and this training can be obtained from practice alone. This ability must be acquired before anything further is attempted, and the student who spends a good deal of time in its acquisition may have the satisfaction of knowing that while he is going through this somewhat monotonous practice, besides exercising himself in drawing accurate lines, he is acquiring a correctness of eye and a power of hand that will be of incalculable service to him later. THE ESSENTIAL ELEMENTS. 29 The straight line, besides being used for the outlines of regular objects, is employed conventionally for various purposes. When it is required to show an object in section, the part in section is covered with straight and parallel lines drawn at an angle of 45° and at equal distances apart, as in Fig. 38. To represent standing water, as ponds and lalies, horizontal straight lines are drawn parallel to each other and at equal distances apart over the surface, as shown in Fig. 39. FIG. 39. Curved lines, when arcs of circles, are drawn by the compasses. Other curves are drawn by hand through points previously found. To draw the curve correctly through these points, unless they be very numerous, a knowledge of the nature of the curve is necessary, which the draughtsman should in all cases endeavour to obtain. When the curved line is long, it is usually inked in with the drawing pen, with the aid of an instrument called the French curve, or cardboard moulds cut for the purpose; but for short lines an ordinary fine-pointed steel- pen point, or better, a good quill is used. In general, all lines drawn by hand should be drawn towards the body, as a better command of the pen can be obtained in that direction than in any other. In inking in curves by this means, the draughtsman Should proceed continuously along the pencil-drawn line by partly repeated touches with the pen point, so held that the divided points of the pen may follow partly in the same track. Each touch should be made about one-thirtieth of an inch in length, and it should begin and end fine. Each succeeding touch must begin half its length back, so that the line is advanced by one-Sixtieth of an inch. In map drawing all irregular lines are drawn in this way. Tracing maps 30 PLAN AND MAP DRAWING. will afford the student excellent practice in this mode of using the pen. Lines of uneven flab/mesa—Though generally a line is required to be of even thickness throughout, cases sometimes occur in which a variation in the thickness may be made to express some feature or quality of the landscape. The usual application of this kind of line is to mark the outline of rivers, lakes, and ponds, as shown in Fig. 40. The drawing of such a line presents no difficulty; the increz sed thickness is produced by going over those parts of the line again with the pen. Care must, however, be taken not to make a sudden increase in the breadth of the line, but to begin and end imperceptibly. FIG. 40. FIG. 41. KM FIG. 42. T he Bro/€672, Liner—The broken line, shown in Fig. zll, is of frequent occurrence in all kinds of drawings. In architectural and engineering drawings it is usually employed in roofs, as in Fig. 42, and for water in sections, as in Fig. 43. It is also used in combination with other lines for various purposes. In drawing a succession of broken lines, care must be taken not to allow the break in one line to be immediately over that in another. The effect may be varied con- siderably by increasing or diminishing the extent of the break. As in section lining, the lines should be at regular intervals apart, and be all of the same degree of fineness. Broken lines are sometimes used upon the face of stone buildings, instead of marking in the joints and THE ESSENTIAL ELEMENTS. 31 etching or colouring. In such a case the breaks are long, and the lines Widely spaced. The Dotted Lines—Of still more frequent occurrence is the dotted line. There are two kinds of dotted‘lines, distinguished by the shape of the dot, and known as the long and the round dotted line. These are *" shown in Fig. 44, as well as a combination of ___________________ the two. The round dotted line is of very general application. In archi- tectural and mechanical drawings, it is used to distinguish hidden parts, and to mark the path of a moving piece in a machine. In plans, it is used to show the position of proposed works, to denote the walks through pleasure grounds and gardens, to indicate lines chained over in surveying, and frequently for other purposes, at the pleasure of the draughtsman. The long dotted line is employed to mark the boundaries of a township, the navigable channel of a river or creek, and in large-scale maps to show farm and bridle roads, footpaths, and the divisions of land among difi‘ercnt tenants. The combination of the long and round dotted lines is used for the boundaries of a parish. Another combination of two round and one long dots, or sometimes of three round and one long, is used to denote proposed railways, canals, roads, and other similar works. To draw a good dotted line requires some care. The difliculty lies in keeping the dots at equal distances apart, and in making them equal in size; and unless both these conditions are fulfilled, the line will not present a pleasing appearance. To obviate this difficulty, an instrument is sold by mathematical instrument makers, called the dotting or wheel pen. But it requires very great care in using, as otherwise it frequently happens that the ink escapes from it and spoils the drawing. For this reason, its use has been generally aban- doned by draughtsmen. But if the instrument were better Constructed and carefully handled, it might be made to do good service. Combinations of Straight, Broken, and Dotted Linea—Combina- tions of the foregoing lines are used for various purposes. Some FIG. 44. 1-...__...._._.._..-_.——- 32 PLAN AND MAP DRAWING. draughtsmen employ alternate, full, and dotted lines, to denote wood in section, as in Figs. 45 and 46; when wood is used in combination with iron or other metal, this is a very good way of distinguishing it. Wood-graining, though not made up of straight, broken, or dotted lines, yet partakes somewhat of the nature of all three kinds, and FIG. 45. may therefore be introduced here. Oak-graining is shown in Fig. 47, and fir-graining in Fig. 48. The former is executed with the drawing pen, and requires some care and practice; the latter is most readily done with a common pen or a crow-quill. End wood is grained as shown in Fig. 49. The spring bows are very suitable for drawing in the circles, as a certain degree of turn to the nut will open the ink leg to the required distance after drawing each circle. A few broken wavy lines, called shakes, radiating from the centre, produce a good effect. When several pieces of end wood come together, the centres in each should not be in the same relative position. Cultivated land is represented by alternate broken and dotted lines, suggesting furrows, as shown in Fig. 50. For the sake of variety, these lines are put in in sets, and in different directions, one set being usually parallel to one side of the enclosure. The lines are first ruled in continuously with the pencil, and the “NW“ ill broken and dotted lines afterwards drawn in over them by hand. The portions of the broken lines must in this case be short, and the breaks still shorter. The dots must be FIG. 50. THE ESSENTIAL ELEMENTS. 33 fine and close together; they are made by touching the paper with the point of the pen, and immediately lifting it off without dragging it over the paper. All round dots must be made in this way. The W'aw/ Lina—The wavy line is very important in topogra- phical drawings, as it is employed to represent running water, and frequently large bodies of standing water to which motion is com- municated by the wind, as lakes and the sea. These rippled lines are intended to represent the ripples in the water, a purpose which they fulfil in a very pleasing manner. They must, however, be well executed, or the pleasing effect will not be produced. The operation of drawing these lines is usually regarded by the draughtsman as a tedious and an uninteresting one. But such ought not to be the case, for there is ample scope in it for the exercise of the taste and the judgment, and in proportion to the taste displayed and the judgment exercised, will be the effect of the work when executed. Fig. 51 shows the manner of employing these lines. In repre- senting water by this means, the lines should be drawn from the shores towards the middle of the stream or lake, and never from the middle outwards, for if the latter mode of proceeding be adopted, the proper graduation of the spaces between the lines becomes impossible. The shore line, or outline of the water, should be a moderately thick line, and of uniform thickness throughout. The first shading line may be of nearly the same thickness as the shore line, and it must be drawn as near to it as possible. Also this shade line, as well as all subsequent ones, must follow exactly all the windings of the shore line; this is essential to a correct expression. To effect this with accuracy, care should be taken to make the space between the shore and the shade line a fine white line. The second shade line must be drawn a little finer than the first, and at a slightly increased dis- tance from it. This gradual diminution of the thickness of the lines, and increase of the spaces, must be continued to the middle of the F 34 PLAN AND MAP DRAWING. current. The last line in the middle of a piece of water must always return to itself. When the shading lines meet the margin of the drawing, they should terminate in it, that is, they should be drawn out to the margin as though they had been continued beyond and cut off. These lines require to be drawn clean, and to do this the hand must be kept steady. This steadiness may be obtained by taking a very short hold of the pen, and resting the middle finger upon the paper. The lines, as we have already said, should be drawn towards the body, the drawing being turned about as required to facilitate this, and the last line drawn must be always kept on the left of the one being drawn. By this means the last line and the point of the pen are kept constantly in sight. It is also important that the lines should be completed successively, rather than that several should be carried on at once, because if the latter mode of working be adopted, the eye is apt to become confused by the different intervals, and an uneven distribution of the lines is the result. A principle to be attended to is that every line shall return to itself, spirals being altogether inadmis- sible. The distance of the lines apart and their thickness are expressive of the character of the object; thus, in a small pond, for example, they will be fine and close together; in a large pond or a lake they will be thicker and more widely spaced; and in the open sea they will be made to present a bold appearance by increasing still more their thickness and the distance between them. Gmss-land—Various combinations of lines and dots are used, conventionally, to represent certain natural features of common occur- rence. As far as convenient execution will FIG. 52. allow, these signs are made to resemble the "1“... A73». jf -» "fl objects denoted. Thus the sign for grass-land _d:‘7...fl l. consists of groups of short lines, arranged like ’“‘ r h - """ A“; tufts of herbage, as shown in Fig. 52. Each tuft is composed of five or seven lines con- verging towards a point situate below the base, the middle line being the longest, and the outside ones mere dots. In drawing these groups, the base must be kept quite straight, THE ESSENTIAL ELEMENTS. 35 and parallel to the base of the drawing whatever the shape of the enclosure may be. Beginners usually experience considerable difficulty in keeping the base straight, the tendency being to make it curved. Great care is needed to distribute the groups evenly over the paper, and to avoid the appearance of being in rows, for the latter arrange- ment is destructive of that natural aspect which this sign otherwise possesses. Swamps and Ilfarshg/ Ground—As the surface of marshy ground consists of water and grass, a combination of the signs for these objects is employed to represent it. An illustration of this is given in Fig. 53. The lines representing the water should always be ruled parallel to the base of the drawing, and they should be grouped in an irregular manner so as to leave small islands inter- spersed throughout the locality. These islands should be covered with grass, and to show them out more distinctly, there should be nothing but water immediately around them. The division between the land and the water should be sketched in lightly before proceeding to rule in the lines. Sometimes dotted lines are used for the water, but full lines are to be preferred. The addition of a tree here and there improves the appearance of a drawing. A distinction is frequently made between a swamp and a marsh by watering the former more extensively than the latter. In drawing in marsh land, care should be taken to make the fineness of the lines in accordance with the scale of the map, as other— F“? .M' wise an offensive appearance will be produced. This caution applies equally to all signs. Sand and Gravel—Sand and gravel are represented by dots, the dots being made larger for the latter than for the former, as shown in Fig. 54. Simple as the operation of filling in these dots is, it is one that requires some degree of care. Beginners are apt to mar the F 2 36 PLAN AND MAP DRAWING. H appearance of their drawings by inattention in this respect. The dots should be made in the manner already described when speaking of the dotted line, that is, the point of the pen should be brought slowly down upon the paper, and lifted without dragging it; and no dot should be made without a deliberate intention respecting its position. All arrangement in rows must be carefully avoided. In sand-hills, the slopes should be made darker than the level parts by placing the dots closer together. Mud in tidal rivers may be represented by very fine dots placed close together. IVoodland.——Trees are generally shown in plan (as in Fig. 55). The outline is circular in character, and, to have a good effect, 1t should be made up of simple curves firmly drawn ; small indentations should be avoided as bad. A few touches of the pen are given on the interior and towards the shadow. The latter is ast by parallel rays of light inclined 450 to the horizon, and is detached from the outline of the tree. When the scale is large, the shadow will be elliptical in form, but in small scales it Will become a simple circle. FIG. 56. In representing woodland, the trees and masses of trees should be disposed in every possible variety of position, care being taken, however, to avoid all regular figures and arrangements in lines. In parks and gardens, where the arrangement of the trees is artificial, it is usual to represent a grove in a rectangular form. Orchards are shown by placing single trees with their shadows at the points of intersection of two sets of equidistant parallel lines drawn at right angles to each other. These lines are drawn in pencil and afterwards erased. Some draughtsmen prefer to draw trees in elevation, as shown in Fig. 56. This method allows the various THE ESSENTIAL ELEMENTS. 37 kinds of trees to be distinguished on the plan, and gives scope to .artistic skill. Uncultivated Land.—Uncultivated land, other than woodland, is represented by drawing bushes in plan, similar to trees, but of smaller dimensions, and mixing tufts of grass with them, as shown in Fig. 57. Contour Linea—Suppose a cone A B C (Fig. 58) cut at regular vertical intervals apart 1;;1; .ééafiié/firm by a series of horizontal planes 1, 2, 3. The ‘fifii‘flfi-‘frfifl intersections of these planes With the surface of 5§*§‘J’i‘«§§, 7;". the cone will give lines upon that surface; and $9332- it is obvious that the cone may be represented FIG. 58. in plan by the projection of these lines, as shown A in the figure. To obtain this projection, draw /:3 the horizontal line D E, and from the apex of /~ 2 the cone and from the intersections of the cutting planes let fall vertical lines. From the point where the line from the apex meets the line D E as a centre, with radii equal to the dis- tances from this point to those where the lines from the sections meet D E, describe circles. These circles will be the horizontal projections of the lines on the surface of the cone produced by the cutting planes; and these lines are called contour lines. Also it is obvious that, from the plan of the cone so obtained, we may as readily project the elevation, provided we know the vertical distance apart of the sections denoted by the contour lines. To obtain the eleva- tion, we have only to draw horizontal lines at the given distance apart, and from the points in D E erect perpendiculars to meet them. Lines drawn through the points of intersection will give the elevation of the cone. To find the inclination of the surface of the cone, upon a I), a portion of the normal D E, as a base, erect a perpendicular b 0, equal in height to the distance of the sections apart, and join ac. The hypothenuse ac then represents that portion of the surface of the cone which is included between the two contour lines, and of which 38 PLAN AND MAP DRAWING. the angle of inclination is b a c. The space between two contour lines is called a horizontal zone. The cone being a regular figure, its contour lines are circles. For irregular figures, the contour lines will be irregular curves. The regular inclination of the surface of the cone causes the projec- tions of the contour lines to be at equal horizontal distances apart. But when the inclination varies, the horizontal distance between the contour lines also varies, the distance decreasing as the inclination increases. Thus the method of representing objects in plan by contour lines, not only gives the correct form of the object, but shows the relative inclination of every portion of its surface. This may be clearly seen in Figs. 59 and 60, the former of which is a representa- tion in plan by contour lines of an irregularly shaped object, and the latter an elevation of the same object projected from the plan. The system of representation by contour lines is generally adopted by topographers to distinguish and define the variation of the surface of the ground in regard to hill, valley, and plain. By intersecting a mountain, for example, by a sufficient number of horizontal planes, its correct form may be delineated, and the declivity of its surface accurately shown. The relative declivity of any portion of its surface is indicated by the difference in the horizontal distance of the curves apart; and by constructing a triangle upon a normal to the upper curve in the manner already described for the cone, the absolute; slope at any point between any THE ESSENTIAL ELEMENTS. 39 two curves may be readily determined. The ground is supposed to slope uniformly from one curve or contour line to the next. Such, however, is rarely the case; but provided the curves are taken at frequent intervals, the error is of no practical importance. Hollows are represented in the same way; and whether the representation is that of a hill or a hollow, is known from the other parts of the map. Thus, if Fig. 59 represent a hill, the vertical projection will be as shown in Fig. 60; but if it denote a hollow, the outer curve must be projected highest, and the vertical section will be Fig. 60 inverted. In practice the contour lines are numbered, the number of any contour indicating its height above a plane of reference called a datum plane. The vertical distance of the contour lines apart varies with the character of the ground and the object of the survey; but it is seldom less than 25 feet. The lines are obtained by the surveyor by fixing a number of points on the same level by means of instruments. SECTION IV.—COL0URs. The preceding Section treats exclusively of representation by lines and dots, or that mode of delineating objects and natural features known as line or pen drawing. There is, however, another mode of representation by means of colours that is fast coming into general use. This latter mode is far more expressive than the former, and, besides affording a wider scope for artistic effect, shows with greater distinctness and precision the character of the object represented. For these reasons it is almost always adopted for plans of estates and geological sections, and also very frequently for other kinds of topo- graphical as well as for engineering and mechanical drawings. The colours used for this purpose are not applied in the way the artist applies them; but they are laid on in thin washes to produce a faint tint rather than a body of colour. The process is called tinting or 40 PLAN AND MAP DRAWING. flat-washing, and though it cannot be described as a work of art, considerable practice and skill are requisite to execute it properly. Flat-tints.—-A drawing to be coloured must be previously stretched and gummed to the board, in the manner described in Section I. Unless the paper be prepared in this way, it will remain blistered after being wetted by the laying on of the tints. The lines of the drawing must be very fine, and the ink, though black, should not be thick. Great care should be exercised in drawing in the outlines, that there be always a piece of clean paper between the hand and the drawing, for the least degree of greasiness will prevent the colours from working freely. Should the surface of the paper, however, from inattention to this matter, or from accident, become slightly greasy, the defect may be partially remedied by adding a little prepared ox-gall to the water with which the colours are mixed. When all the outlines have been drawn in and the pencil lines erased, the drawing is prepared for the colouring by being washed. The washing is effected by passing a soft sponge well saturated with clean water gently and rapidly over the surface. The purpose of this washing is twofold; first, to remove those portions of the ink which a wet brush would detach from the paper in laying on the colours, and which, by becoming mixed with the tint, would injure its purity ; and second, to damp the surface of the paper in order to prevent the colour from drying too rapidly. The latter is an important matter, for if the tint which is being applied dries quickly, it is impossible to unite the edges properly, and the tint, especially if the surface be large, will have a cloudy and blotchy appearance. As the operation of washing renders the paper too wet to imme- diately receive the colour, it must be allowed to remain in a perfectly horizontal position for a short time to dry, and during this time any tendency to dry unequally must be corrected by means of blotting- paper. ‘Vhile the paper is drying, the tints may be prepared. To ensure satisfactory results, care must be taken in the prepara- tion and preservation of the tints. They should never be made by artificial light, and a sufficient quantity should be made at first to cover all the portions required, as it is very difficult to match a tint THE ESSENTIAL ELEMENTS. 41 exactly. When a drawing is several days in hand, it is best to prepare a fresh tint for every coat, for the colours will change in the course of a day or two, even if protected from the light. A few drops of water should be added now and then, to make up for the loss by evaporation, especially in warm weather. Tints left to dry upon the palette should never be wet up again for use, but they should be washed clean out and a fresh tint made; if this precaution be not attended to, the colour will not be pure. When a tint is to be mixed, the end of the cake of colour should be moistened and allowed to soften for a minute or two, as this will cause it to rubsmooth and free from fragments. The palette should then be moistened and the end of the cake rubbed gently and evenly upon it till a sufficient quantity of colour has been obtained, which may be added to the requisite quantity of water by means of a brush. A precaution necessary to be observed is never to rub one colour down upon another, as it will probably be laid aside to dry with the other colour on it. The brush used should be as large as the nature of the work will allow, and it should be of the best sable hair; the quality is judged by the length of the hair, the longest and stiffest being the best. Draughtsmen frequently do all their work with a couple of sable brushes attached to one holder, one being for colour and the other for water; in this case the brushes should be of different colours to prevent mistakes. The art of laying on a flat-tint consists in allowing the coloured water to flow equally over the paper, which thus becomes uniformly tinged. To facilitate this, the surface of the drawing should be inclined towards the draughtsman at an angle of about five degrees during the process of laying on the colour. Having taken as much colour on the brush as it will safely carry without dropping, the operation of applying it should be begun in the upper left-hand corner, the brush being carried along towards the right, so as to make the colour lie neatly along the upper outline. The brush should then be struck unhesitatingly from right to left and from left to right alternately, so as to bring the colour down in horizontal bands or stripes, taking care not to pass the brush a second time over the same G 4-2 PLAN AND MAP DRAWING. surface during the same wash, and to control it neatly within the proper limits. If the surface of the paper be in this way kept well wetted with the colour, or if, in other words, a flow of colour be kept in motion with the point of the brush, the tint can be carried on with perfect continuity. It is important to keep as nearly as possible the same quantity of colour in the brush until the lower outline is nearly reached, when the quantity must be diminished so as to finish at the lower outline without a great excess of tint, for the excess must be taken up by a damp brush. No accumulations should be allowed to take place anywhere, as on drying, these places would show a darker tint. \Vhen the colour has once flowed over the surface, the tint is finished, and must not, as we have said, be touched a second time, for any attempt to remedy defects while the colour is drying will only make them worse. Generally it will be found that the more quickly a tint is laid on, the better is its appearance. A little practice will enable the student to lay on a wash in the proper manner, but to keep within the outlines is a matter of greater difficulty and one that requires some dexterity in the handling of the brush. If the boundary should be exceeded, a finger of the left hand should be instantly applied to brush the colour back. Though the foregoing directions can be followed strictly only on large surfaces, the principles involved in them must in every case be observed. The alternate or double tint consists of two colours applied alter- nately, their edges being made to blend into each other. The appli- cation of the double tint involves no particular difficulty. Having prepared two tints of equal intensity and provided a brush for each, lay on one of the colours at the upper outline of the figure, and before this dries, take the brush charged with the other colour, and run round its edge, allowing them to blend together. Repeat the first tint in the same manner, and continue the tints alternately till the surface is covered. The forms of the masses of each colour should be varied, and not made in stripes or spots, but irregularly clouded. All flat-tints should be made very light, and intensity of colour should be produced by repeating the wash. As every surface looks Q |) THE ESSENTIAL ELEMENTS. 4.) better with two washes than with only one, the strength of the tint should be such as to allow two coats to be laid over the lightest parts. If the colours have been laid on too dark, or the general effect be uneven and disagreeable, the defect may be remedied by sponging. This operation should be performed with a close-grained 6-inch sponge, and be commenced at the upper end of the inclined board. A basin of clean water having been provided, and an empty basin to receive the dirty water from the sponge, first moisten all the white surface of the paper to prevent the tint taken off by the sponge from adhering to it; then, having filled the sponge with water, pass it gently to and fro across the sheet. Press out the dirty water into the basin, refill the sponge, and repeat the operation until hardly any tint comes off. Sponging after five or six coats have been laid on generally improves the appearance of a drawing; it softens down asperities, and makes the tints blend into each other; the surface of the paper also takes the tints more readily after sponging. Small defects may frequently be remedied by a process called stippling. This consists in making a number of dots with the point of a brush containing an almost imperceptible quantity of colour. The process, though a tedious one, produces a very beautiful effect, similar to that of dotted engravings. Excesses beyond the boundary lines may be washed out with the water-brush, and the stains removed by a piece of clean blotting-paper. ‘Vhite spots left in a tint may be filled up, after the tint is dry, with the point of the brush; but care must be taken not to touch beyond the edges of the tint, as that would double the intensity at the edges and produce a ring. All flat surfaces in a drawing should be lighter or darker, in accordance with their distance from the eye. In laying on flat-tints when the surface is not in shade, it must be borne in mind (1) that all snrthces which are parallel to the plane of the picture, and therefore equally distant from the eye, should receive a tint of uniform inten- sity ; (2) that those surfaces which are farthest from the eye should receive the darkest tint; and (3) that surfaces which are inclined to the plane of the drawing should receive a tint of varying intensity, the G 2 44 PLAN AND MAP DRAWING. depth of the tint increasing as the surface recedes from the eye. When the surfaces are in shade, the converse of these rules holds good. Conventional Colours—In representing objects by means of colours, the natural colours of the objects are in some cases adhered to; and in others, for the sake of greater distinctness, a conventional colour is adopted. In engineering, architectural, and mechanical drawings, the latter mode is nearly always resorted to, while in plans of estates the former is very frequently employed. Unfortunately, practice is not uniform among draughtsmen in the conventional use of colours; but the following Table shows the colours mostly employed, and represents the general practice. Carmine or crimson lake .. .. For brickwork in plan or section to be executed. Prussian blue Flintwork, lead, or parts of brickwork to be removed by alterations. Venetian red .. .. .. .. Brickwork in elevation. Violet carinine .. .. .. .. Granite. Raw sienna .. .. .. .. English timber, not oak. Burnt sienna .. .. .. .. Oak, teak. Indian yellow .. .. .. .. Fir timber. Indian rcd.. .. .. .. .. Mahogany. Sepia .. .. .. .. .. .. Concrete works, stone. Burnt umber .. .. .. .. Clay, earth. Payne’s grey .. .. .. .. Cast iron, rough wrought iron. Dark cadmium or orange .. .. Gun metal. Gamboge .. .. .. .. .. Brass. Indigo ' .. .. . .. \Vrought iron—bright. Indigo, with a little lake .. .. Steel—bright. Hooker’s green .. .. .. .. Meadow land. Cobalt blue Sky effects. And some few others occasionally for special purposes. Sections are represented either by lines of the colour drawn with the pen or the point of the brush, or by a darker shade of the colour. In mechanical drawings, sections are frequently shown by ink lines drawn over the colour. In plans and maps, as we have said, some attempt is made to give the true appearance of things. As this—which may be called the natural mode of representation—allows more scope for artistic skill than the conventional, a great deal must be left to the judgment and the taste of the draughtsman. But there are general principles and .s‘; «Loci O TIIE ESSENTIAL ELEMENTS. 45 features that may be laid down and described, and such are the following :—— lVatew—For water, a flat-tint of pure indigo is used. To produce the clear, transparent effect of water, there should be two coats of the tint, which, to allow of this, must be very light coloured. Grass-land.—For grass or cleared land, a flat~tint of green is employed. This tint is composed of indigo and gamboge, and should be of a lively hue, which may be. produced by giving predominance to the gamboge. Care must always be taken in preparing greens for maps and plans, that the blue be kept subordinate to the yellow; for a predominance of the former colour produces a cold quality, which is utterly destructive of that natural appearance it is intended to give. The intensity of the tint for this and for other purposes should be such as to distinguish it clearly from others, and to allow somewhat for fading, without masking any of the details of the drawing; and it must be clear and transparent. We may here remark that all tints which are much extended should be balanced, that is, no one should obtrude itself upon the eye by its relatively too great intensity. Alwyn—Marsh and swamp are represented, as in line drawing, by a combination of the signs for water and grass-land. The tints are laid on horizontally, that is, parallel to the base of the drawing. They are not, however, laid on in bands or strips across the drawing, but are made to project in irregular points from each side, with here and there a long and narrow patch to represent an island. The land should cover a larger portion of the space than the water, and it should be washed in first, care being taken to make the white spaces left for the blue colour resemble the green in form, which spaces should project their horizontal points into the green as the latter projects its points into the white. The outer limits of a marsh should consist of an outline of projecting green points. The land portion of the marsh is finished by drawing a light shading line of indigo and burnt sienna along the lower edge of the green. This line must be drawn upon the edge and not against it upon the white space. In washing in the water, care must be taken not to overlay the edges of the green. A good 46 PLAN AND MAP DRAWING. efi‘eet is produced by introducing a tree here and there upon the land. Sand and GraveZ.—Sand is shown by a flat-tint of yellow ochre. Sand and gravel are represented by dotting the flat-tint with burnt sienna by means of the point of the brush held in a vertical position. Stones and rocks in sand should be first outlined with the pen in burnt sienna and sepia in equal proportions, and afterwards filled in with the brush with the same colour. Mud.—In the survey of rivers, creeks, and coasts, it frequently becomes necessary to show tracts of mud between the lines of high and low water. For this purpose a fiat-wash of sepia or Indian ink may be used dotted with Indian ink of greater intensity. The dots in this case must be very minute and thinly placed, and they should be evenly distributed. A fine-pointed pen will be found more effective in putting in these dots than the point of the brush. Woodland—To represent woodland, a flat-tint of green is first laid over the ground, as for grass-land. The groups and masses of trees are next drawn in outline, in the manner described in the last Section, with a hard and sharp lead pencil, or with a pen and pale ink. To fill in these outlines, a colour made up of indigo and gamboge in the same proportions as the ground tint, but of greater intensity, is laid on the lower and right-hand portion of each tree and mass of foliage, so as to occupy about two-thirds of the figure. The remaining portion,'which will be the side towards the light, is then touched with an orange tint composed of gamboge and burnt sienna. It only remains to add the shadow. As the light is supposed to enter the drawing in parallel rays from the upper left-hand corner, the shadow of every object will surround its lower and right-hand outlines. It is laid close up to the outline in masses of foliage; but for single trees, as in orchards, it is detached. The form of the shadow was described in the last Section. To produce the shadow, the same tint is used as for the ground, two or three successive applications being sufficient to increase the intensity to the requisite degree; or a neutral tint may be used, composed of indigo, burnt sienna, and a little lake. After THE ESSENTIAL ELEMENTS. 47 the shadow has been put in, the outlines on that side should be strengthened by going over them again with the pen. By drawing the trees in elevation, an opportunity is afforded for the display of artistic skill far greater than the foregoing method admits of. When drawn in this way, the work partakes somewhat of the nature of landscape painting. Cultivated Land.——Cultivated land is represented by a flat-tint of burnt sienna. Uncultivated Land.-—Uncultivated land or brushwood is repre- sented by a double tint of green, as for grass-land, and burnt sienna, as for cultivated land, laid on in the manner already described for the double tint. As this is the only double tint used, it may be made, if thought desirable, with alternate green and crimson lake. Buildings.~—~Buildings, including all structures of masonry, as bridges, locks, walls, and such like, are coloured with crimson lake, and shadowed with a neutral tint composed of indigo, burnt sienna, and a little lake, as given above for forest land. Roads and Streets—Roads and streets, and generally all those portions of a drawing not particularly described, are tinted with yellow ochre. Fences.—Hedges are represented by green dots, varied in size for bushes; stone or brick walls, by a line ruled in red; and wooden fences by lines of neutral tint, either ruled or drawn in by hand, according as the line is to be straight or otherwise. In every case the shadow must be put in. In determining the intensity of the various tints employed on a topographical drawing, care must be taken that everything be “in keeping.” A cardinal rule of art is that nothing shall unduly obtrude itself; and in a coloured plan, spottiness, as it is called, should be studiously avoided. Forest, brushwood, and cultivated land, should be represented by tints of about equal intensity, and the same equality may be observed for grass-land, marsh, water, and sand, but the intensity should be less than in the former case. Tints that are of small extent may be a little exaggerated in intensity for the purpose 48 PLAN AND MAP DRAWING. of giving them greater distinctness, especially when the object repre- sented is a building. Gardens and orchards require a little exaggera- tion in depth of tint, to distinguish them from the surrounding country; but care must be taken not to make the distinction too marked. It will generally be found conducive to a maintenance of “keeping,” to lay the lightest tints on first. SECTION V.—SHADING. In mechanical and architectural drawings, shade lines must be considered rather as embellishments than constituent parts of the drawing. They are, however, frequently employed; and as their incorrect use may deceive the eye with respect to the intention of the designer, it becomes an important matter to know when to apply them with propriety. Application of Shade Linea—As we have already explained, the light is supposed to fall upon the objects in a drawing in parallel rays from the upper left-hand corner for elevations, and from the lower left—hand corner for plans. To determine whether or not a given line should be a shade line, we have only to ascertain whether or not the light, introduced in such a manner, falls upon that edge of the object which the line represents. All those parts of a body upon which the rays of light fall directly, are said to be in light; all those parts upon which the rays of light do not fall directly, are said to be in shade; and those parts of a surface which are deprived of light by another body intercepting the rays, are said to be in shadow. These defini- tions should be borne in mind. Lines representing the boundaries of surfaces in light should be fine lines, and lines representing the boundaries of surfaces in shade should be thick or shade lines. Let it be required, for example, to determine the shade lines of the cube shown in elevation in Fig. 61. The extreme rays of light falling THE ESSENTIAL ELEMENTS. 49 upon the cube meet the edges in b and 0; hence the surfaces at b, a c, are in light, and the surfaces d 6, dc, are in shade. The foregoing rule will thus make a b and a 0 fine lines, and d b and d c shade lines. If the cube were turned so that ab should be at right angles to the rays of light, the extreme rays would fall on the edges a and b, and the middle ray which now falls on a, would fall on the middle of the line a b. The rays immediately beyond those which are arrested by the edges a and I), may be considered to pass along in contact with the surfaces at c and b d; and these surfaces must, therefore, be regarded as in light. Thus we shall have in this case the lines a I), a c, and I) d, fine lines, and the line cd a shade line. It is the practice of some draughtsmen to make ac and 6d in such cases a medium line, and the practice has propriety to recommend it. The foregoing explana- tions of the shade lines in the elevation of the cube, render any further remarks concerning those in the plan, Fig. 62, unnecessary.. In practice, whether or not a surface is in light may be determined by placing the set square of 45° against it. FIG. 61. FIG. 62. FIG. 63. fl The same principles are Observed in the end elevation of the hollow cylinder, shown in Fig. 63. The extreme rays meet the cir- cumference in the points a, and I); consequently the surface acb is in light, and the surface adb is in shade. The middle ray meets the surface perpendicularly at the point 0, which will be the lightest part of that surface; similarly, d will be the darkest part. To show this, the shade line must be gradually increased in thickness towards the point (I. The shading of the inner circle will be the converse of the outer. Fig. 64 shows a plan of the same object. II 50 PLAN AND MAP DRAWING. , Cylindrical Surfaces.—Let abcd, Fig. 65, be a plan, and kl am an elevation of a cylinder. The portion 050?) is in light, and the FlG. 65. f. My cm. portion a, d I) is in shade, of which latter portion a and b are the edges. From the points a and c draw vertical lines 6 f, git. Then will e f be that part of the cylinder upon which the light falls perpendicularly, or the lightest part, and git the edge of the surface in shade, or that portion of the sur- face of the cylinder that would cast a shadow upon the plane of projection. Hence this will be the darkest part, and consequently it is obviously improper to make the line [cl a shade line. This demonstration, which is given by Binns, shows that shade lines must never be applied to cylindrical surfaces. If this principle be observed, cylindrical may be readily distinguished from flat surfaces. Shading Linea—Shade lines are applied only to the edges or boundaries of surfaces; when lines are put upon a surface to show the effects of light and shade, they are called shading lines. The use of the latter is determined by the same principles as that of the former; indeed, a shade line may be practically considered as an end view of a number of shading lines. In Fig. 66, which is an elevation of a lllll i hexagon, the surface 0 is in shade, and to representthis surface correctly, it must be made darker than the others. This darkening of the surface is effected by drawing the shading lines heavier or closer together, or by both of these means combined. The surface I) is in light, but the rays fall upon it oh- liquely; the shading lines on this surface will therefore be lighter and more widely spaced than on c. The surface a is also in light, and receives the rays normally, that is, the THE ESSENTIAL ELEMENTS. 51 direction of the rays is normal to the surface. Hence this surface will reflect most, or, in other words, will be the lightest. This is shown by making the shading lines still lighter, and spacing them still more widely than those on I). The greatest care is needed in applying shading lines to keep their thickness and the spacing regular, as an error in these respects will frequently produce an effect quite opposed to what is intended. Shading Lines on Cylindrical Surfaces.—— If the demonstration previously given concerning shade lines on cylindrical surfaces be understood, the application of shading lines to these surfaces will pre- sent no difficulty. The darkest and the lightest part of the cylinder having been determined, and in practice this can be accomplished with sufficient exactness by the eye, the shading lines are applied according to the principles explained above with respect to the hexagon. The first shading line is drawn upon the darkest part; and each successive line on each side of this first line is drawn lighter and spaced more widely than the preced- ing. At the lightest part, a clear space is left to represent the reflexion of the rays that occurs strongly there, and beyond this part the shading is made equal to that of the corresponding part 011 the other side. The thicken- ing of the lines is effected by going over them a sufficient number of times. Fig. 67 shows a vertical and a horizontal cylinder shaded in this manner. In outline drawings of machinery, this mode of shading with parallel lines is frequently resorted to. It will be evident, on reflection, that when the cylindrical body stands parallel with the direction of the rays of light, as shown in Fig. (38, the lightest part will be in the middle, and the shade will increase in intensity as it approaches the edges. The shading of the interior of a cylinder is, as we have already remarked when treating II 2 t 5‘ PLAN AND MAP DRAWING. of shade lines, the converse of that of the exterior. This is shown in the sectional elevation, Fig. (39. When parallel with the direction of the rays of light, as in Fig. 70, the internal shading is the same as the external. On bright circular surfaces, such as that of a circular saw, or the polished end of a shaft, the light is radiated from the F10. 68. Fro. 69. centre, as shown in Fig. 71. This mode of shading is strictly in accordance with the appearance presented by such surfaces. It may be remarked here, that if, through inadvertence, any part should be made too dark, the error may be corrected by darkening all the other parts in a corresponding degree. Shading Lines in Topographical Drawings.—The shading lines put upon mechanical drawings are merely accessories used for pur- poses of embellishment. But in topographical drawings, shading lines are applied to give expression, and they constitute an essential element in the representation. We have shown how undulations of the ground, constituting hill and valley, are represented by contour lines. But it is obvious that these lines furnish information respecting THE ESSENTIAL ELEMENTS. 53 the character of the surface only at those points through which they pass. Thus we are necessarily left in ignorance of the irregularities existing between any two successive contours. T0 supply this in- formation which the contours fail to give, shading is resorted to. Another important object of hill shading is to represent the surface of the ground conventionally in a manner that will immediately afford an idea of its character without the aid of regular contours. The method adopted consists in employing lines varying in their thickness and in their intervals apart according to the slope of the ground FIG. ’72. to be represented. This method is 37% based upon the principle of the hori- ‘4 zontal contours, which is to give to the g same vertical interval the same absolute amount of shade, whatever the incli- nation of the ground may be. The shading lines are used, as we have said, to fill in the features of the ground be- tween contours already fixed; and to ensure accuracy and uniformity in the representation, a “ scale of shade” is employed. The accompanying Fig. 72 shows the standard scale of shade adopted by the Council of Military Education, and made use of for all the Government surveys. The second and the fifth columns of this scale show the spacing of the hachures and their thickness for different angles of slope, while the first and the last columns show the number of hachures to be interpolated between contours at every 25 feet vertical intervals, supposing the slope to be uniform. The slope is denoted both by the number of degrees in the angle it makes with the horizontal, 54 PLAN AND MAP DRAWING. and by a fraction showing the ratio of the vertical height to the base in a right-angled triangle, the hypothenuse of which is the slope in question. . The scale of shade is constructed for a horizontal scale of six inches to the mile, and the amount of shade has been chosen with a view of producing the best possible artistic effect. Of course, the most satisfactory results, both artistically and practically, will be obtained when the ground is delineated to this scale, but it can be readily applied to any other scale. For example, the horizontal interval for a slope of 510—, corresponding to a vertical interval of 25 feet, will be 20 X 25 = 500 feet, which, on a scale of six inches to a mile, will be represented by a length equal to 5520;)” X (i : 0'566 inches. In this case, therefore, supposing the slope of the ground to be uniform between two given contours 25 feet apart, we should represent it by means of the hachures shown opposite a slope of 51—“ continued over a space of 0'566 inch. In topographical drawings, the light is supposed to fall vertically upon the surface; hence a level surface will reflect all the light that falls upon it, while one of 450 will not reflect any. The drawing of the hachures presents certain difi‘iculties of execu- tion that can be overcome only “by continued practice and careful attention to the modes of proceeding which experience has proved to be the most effectual. Thus an important rule is always to draw “ from left to right and downwards.” To allow this to be done, the drawing must be placed with the summit of the hill to the left hand, and be turned round as the work progresses. The liacliures should always be commenced at the crest of the hill, working outwards towards the foot of the slope. They should be drawn firmly, and of a length varying from :1}— inch to g inch, according to the width of the zone, that is, according to the greater or less degree of the slope, as shown in Fig. 73, at a, I), c, d. When the hill is steep, the lines are made short and thick, and when the declivity is less, they are made longer and lighter, becoming fine and clean as the level is approxi« THE ESSENTIAL ELEMENTS. 55 mated to. A difficulty with beginners is to press upon the pen equally from the beginning to the end of the stroke, the tendency being to press more heavily towards the end, thus producing a whip-like appear- ance quite opposed to artistic effect, and conveying a false impression of the character of the ground. A good effect is produced by impart- ing a slightly tremulous motion to the pen when drawing the ba- chures. The form of the hill being accurately defined by the pencil contour lines, it is not necessary that the accessory curves formed by the shading lines should be rigorously continuous, and indeed a much better effect, artistically, is gained by avoiding such a manner of drawing them. The various sets of lines must be placed together, end to end, in such a way that the groups or sets shall not be separated by a vacant space, nor over- lap each other. Care must be taken that the junctions of sets in two contiguous zones do not form a continuous line from one zone to the other, but everywhere “break joint.” Each zone must be filled in before the next lower one is commenced, the drawing being turned as the work progresses to allow the rule enunciated above of “from left to right and downwards” to be complied with. The distance between the shading lines must be increased or diminished according as the width of the zone varies, so as to divide the space equally; and on reaching the part where the lines were begun, the ends must be brought neatly together. As this can be most satisfactorily accom- plished where the lines come close together, it is best to begin at the steepest part of the slope. in taking a set of hachures round a sharp bend, as in the case of a spur or a ravine, a practical difficulty occurs, which difficulty is increased as the angle becomes more acute. The most effective way of overcoming this difficulty is to draw a pencil line down the spur or 56 PLAN AND MAP DRAWING. re-entering angle, as shown at A B and C D in Fig. 74, and to mark of on this line, at the proper intervals, small arcs of the same radius, as near as can be judged by the eye, as the curve of the contour line. The sets of ha- chures on each side may then be drawn to these arcs. Guid- ing lines, as a b, c d, e f, and g It, should be drawn at right angles to the general direction of the contours to ensure the hachures being correctly placed before and after rounding the angle. FIG. 7 4. \ \f \ \V‘” \ \\ \\__ {,1 Lu Y. \ For this method of carrying a , l :1,{I(11 ./ A] set of hachures round a sharp curve, we are mainly indebted to Lieut. R. Pulford’s ‘Theory and Practice of Drawing.’ When this method is not employed, the hachures must be drawn on each side of the angle first, and those for the angle filled in separately. Great care must be taken in filling in the zones formed by the contour lines, that the drawing when finished do not present the appearance of separate layers or bands; for such an appearance is not only quite opposed to artistic effect, but it conveys a false notion of the character of the ground. The successive zones are not separate portions of the surface, but each is a continuation of the one adjoining it. The great principle to be observed in this, as in all matters of hill shading, is that changes of slope are gradual. When the contours are only pencilled in as guide lines to be afterwards erased, the above- mentioned defect may be avoided by drawing the hachures over them, without reference to exact spacing. But when, as is usually the case in regular surveys, the contours are inked in in dotted lines, the only means of avoiding it is to space the hachures on each side of a contour line at the same distance apart. The student of map drawing should practise assiduously this THE ESSENTIAL ELEMENTS. 57 system of shading in detached portions before undertaking the delinea- tion of a complete hill. For such exercises, either a soft, medium- pointed steel pen, or a quill may be used. The Vertical System of Shading—The foregoing system of shading is known as the Horizontal, and is now generally employed in this country for all kinds of surveys. There is, however, another system much used abroad, and frequently adopted here for engraved maps. In this system, which is known as the vertical, the shading lines are made to radiate from or converge into the curved parts of a hill, according as they project or re-enter. Such lines are called lines of greatest descent,- they are supposed to describe the same course that water would describe if allowed to trickle in streams down the slopes, and hence they exhibit both the direction and the degree of the slope. Having the horizontal sections given, we may obtain a complete knowledge of the direction in which the ground slopes by drawing perpendicular to them any number of lines of greatest descent; the degree of deelivity is expressed by purely conventional means. The means adopted for this purpose are of two kinds. One depends upon the principle of vertical illumination, in which the maximum quantity of light is reflected upwards to the eye by a horizontal surface, and a minimum by a surface inclined 45° to the horizon. This is the English and German convention, and it lays more stress upon the proportions of black to white in indicating the degree of slope, than upon the distance between the shading lines. The other convention, which is the French, on the contrary, makes its expression depend more upon the distance between the lines of greatest descent than upon the shade of colour produced, though in this also the tint is graduated from dark to light, according to the degree of declivity. A scale of shade is used for this system, founded upon the same principles as that already given for the horizontal system. The scale adopted is due originally to Major Lehmann, of the Saxon Infantry; but it has received some modification to adapt it to the requirements of practice. Fig. 75 shows Lehmann’s scale. It is constructed for every 50, from a level up to a slope of 45°, which is the steepest I . 58 Ed7i LEHMANE SCALE OF SHADE, £144.31 ‘ .J PLAN AND MAP DRA“TNG. slope at which earth will stand. Each division of the scale corresponding to a given slope is subdivided into nine parts, to show the proportions of black to white. For a level, the whole of these spaces are left white ; for a slope of 50, the proportion is one black to eight white; for a slope of 10°, two black to seven white; and so on up to 45°, for which slope we have all black. The longitudinal divisions of the scale below that against the outer edge A B contain the same proportions of black to white, but equally distributed to show the mode of applying it. Thus, in the division 0197’s, corresponding to a slope of 50, the single black space is, in E F GH, divided into two equal parts and distributed; in GHIK, these two parts are again equally divided and distributed ; and so on through- out the other longitudinal divisions. If now the scale be cut off along the line L M, the part LMCD will constitute a scale, the graduated edge L M of which will furnish us with a means of marking oil the distance between the centres of the shading lines. To find the proportion of black to white in the foregoing scale for any given slope z—Subtract the given inclination from 450 for a denominator, and put the given inclination for a numerator. In the scale, as drawn in the figure, the variations are by 50; but it is obvious that a scale may be drawn in the same manner to mark smaller variations, it' thought desirable. THE ESSENTIAL ELEMENTS. 59 In applying this method in the United States’ Coast Survey, it was remarked that “this scale of shade does not represent slopes greater than 45°, thereby limiting the graphic capabilities and effect of the map. It also makes the slopes too dark as they approach the inclination of 45°, and does not well represent slopes of less than 5° which latter it is often desirable and necessary to express distinctly.” The following modification was therefore made :— Proportlon of l l’i‘opoition of Slope. Slope. __. ___,-, A__M._. Black. White. Black. l White. | "to or 2%0 1 10 35° 6 l 5 5° ,, 5° 2 9 45° 7 l 4 10° 11° 3 8 60° 8 I 3 15° ,, 15° 4. 7 75° 9 | 2 25° ,, 26° 5 6 By this scale, the slighter slopes are represented distinctly. For slopes less than 16°, the shades are darker than in Lehmann’s scale; this makes their difference more noticeable. Above 25° the shades are lighter. A further modification, which for ordinary purposes possesses the advantages of simplicity and facility of application, has been made in England, and very generally adopted. This modification consists in fixing with accuracy only three proportions of black to white for three medium slopes, as follows :— Proportlon of l ‘ Proportion of Slope. _—_.—...— ‘ Slope. \ Black. 1 White. I \M Black. 1 w hue Level all 30° l 1 1 5o 1 2 all i 22 $0 1 1 l 1 l A scale of shade may at once be constructed from this Table, by assuming the thickness of the shading line for the medium slope of 2253, which thickness must be suited to the scale, and to the degree of fineness and finish it is intended to give the drawing. Generally, I 2 60 PLAN AND MAP DRAWING. if the lines have such a relation to the scale of the drawing as to present a well-connected appearance, it will be found that fewer shading lines and a rather coarse texture will conduce more to clear- ness of expression than a finer texture, which tends to produce a dryness of style. In shading to this scale, it should be applied to the drawing wherever the slope corresponds to one of the three on the scale. Intermediate slopes are indicated by graduating the thickness of the shading lines. In all cases a good deal must be left to correctness of eye and skill of hand. In the French method, as we have said, the inclination is expressed by the distances between the centres of the lines of greatest descent. The limits of the slopes that can be represented by this method are, % or 450 for the greatest and — or 00 53 ’43” for the 614 smallest. The largest scale that will admit of conveniently drawing the lines of g1eatest descent 1s 5—0—0 full size, or about 8% feet to a mile. The vertical distance between the horizontal sections is generally taken as 1 ya1d. Hence to a scale of— 6—1—00 the least width of zone will be ”LO inch, and the greatest~— ;0—0 X 64- _ 31—«800 inches. The distance between the shading lines 1s reckoned from centre to centre, and is determined by the rule :—-To the distance between the upper and the lower curves of any zone add —— of an inch, a sixteenth part of this sum will be the proper interval for the shading lines. The distance is measured along the line of greatest descent. Thus, if the inclination be 5‘3 and the scale GTO, the width of zone wigll9 be '06 X 60 = 3'60 inches, and by the rule we have 3301?: _—— _ —O 244 inch. Another rule is :——To a fourth of the distance between the upper and the lower curves of any zone, add 177,70 of an inch; a fourth part of the sum will be equal to the interval. The thickness or breadth of the lines is made to vary directly as the inclination to assist in expressing the declivity. This thickness is determined by the following rule. For a slope of % the thickness of the shading lines is equal to § of the distance between their centres, THE ESSENTIAL ELEMENTS. 61 and this thickness will diminish with the inclination down to 5;, where the lines will be as fine as they can be drawn. In a slope of % this rule will always make the breadth of the shading lines twice that of the white space contained between them. To represent declivities by the vertical system of shading a considerable amount of practice is required. This practice should be commenced by drawing repeatedly the scale of shade, and gradually applied, as proficiency is attained, to the varying inclinations of a hill- side. Having the horizontal sections of the hill given, the degree of slope. should be written upon it in pencil in as .many places as is necessary. The distances between the centres of the shading lines may then be marked off upon the upper curve of the zone from the scale of shade, and the lines of greatest descent drawn through the points thus determined. The exact proportion of black to white being then adopted, the colour will express the degree of the slope, and the line of greatest descent will show its direction. The principle of making the shading lines longer on a gentle slope than on a steep one should be adhered to generally; but in this matter much must be left to the judgment and the skill of the draughtsman. Frequently on slight, inclinations it will be desirable to divide and subdivide the zone by medial lines, as shown in Fig. 76, and on very steep slopes the shading lines may be drawn over two or more zones. For ordinary scales the extremes of length may be fixed at % of an inch on the steepest slopes, and f:— of an inch on the gentlest. It is not necessary to repeat the process of construction for every line, such a mode of proceeding would be too laborious and slow. It will be suflicient to determine the lines in this exact manner at those parts where the greatest changes of slope occur. Thus a group should be constructed in each zone where the slope is greatest and another FIG. 76. 62 PLAN AND MAP DRAWING. where it is least, after which a few intermediate ones may be put in. The vacancies may then be filled in, taking care to graduate the changes in passing from group to group. By this means we do not, of course, get a mathematically exact representation of the surface, but it is sufficiently accurate for practical purposes. When the preparatory pencil lines have been drawn in and the spaces for the shading lines laid off by dots, the shading should be commenced at the steepest part of the upper zone. The lines should be drawn firmly from curve to curve, taking care to make each row terminate evenly at the lower edge; they must always be drawn downwards and from left to right, proceeding in this direction round the zone till the point of setting out is reached, where the joining must be carefully effected. This can always be done most neatly where the lines are thickest, as we have previously pointed out. The succeeding zones should be filled up in the same manner. As changes must be gradual in every direction, care must be taken to make the contiguous zones blend into each other. When it is required to pass from a light zone to a darker one beneath it, the lower ends of the lines in the light zone should be thickened a little, so as to meet the upper ends of the lines in the dark zone with nearly the same colour. The upper ends of these latter lines should also be slightly lightened. The lines of one zone must not be continued into those of the next. Even on a uniform slope such a prolongation of the lines would produce a hard appearance, which should be avoided. But in the case of a conical hill, like that shown in RV Fig. 77, it would give rise to an error in principle ; {\\i\§\\\\ {/é; for soon after leaving the summit we should have too g??? “g few lines of descent. When the hill has been covered 1%? Rfi with shading lines, the base and the summit must be M ”k V softened off by tapering the lower end of each line at the base, and the upper end of each line at the summit. To give the taper to the latter, the drawing should be turned upside down. When the curves are parallel or nearly so, the shading lines are FIG. 77. THE ESSENTIAL ELEMENTS. 63 straight, and also nearly parallel. But when the curves depart widely from each other, the shading lines will themselves have a slight curva- ture, for being lines of greatest descent, they must be normal to FIG-78. . . \ \ . the curves. In such cases, a _\,\\;\\\\\\\\\§\\\\\\\‘ .r \\§\\\\\1\\\\\\\\\\‘\\\\\ \ number of normals should be put ,1 \ \\\\\\ \\\\\\\\\ . . . K \ \\‘~\.'\' i\\\\\\\ \\ in at short dlstances With the , wi;\\\\§\§_\ . . . .’ ‘S\ ,Q \ pencfl, as shown in Fig. 78, to 7§§~m ' ' |' l ‘-——‘1' .2-5 :5 serve as guides to the shading x g. /‘ . . . . ‘r’ ,—‘\ x" ‘ lines. The foregomg directlons x for shadincr a 11111 a 1 e uall J» a: PP)’ (1 Y iv“*'~.:‘£_... {Mum "Mame w W to the shading of a hollow, the shading lines in which are con- verging. Occasionally short slopes steeper than the “ natural slope” of 45° will be met with. Such being exceptions to the law of slopes, are marked in an exceptional manner. When the surfaces of these slopes are of earth, they are shown by black lines drawn parallel to the horizontal curves, and when of rock, by black lines drawn in all directions, not intersecting, but abutting abruptly upon each other in short heavy masses, as shown in Fig. 78. Shading in C Maura—Frequently in topographical drawings, and still more frequently in mechanical drawings, colour is resorted to to produce the efiect of shading lines. As the principles according to which colour is applied for this purpose are the same as those which determine the use of shading lines, there remains little to be said on this matter beyond describing the modes of applying the colour. IIill Slopes.—~In representing slopes, the tint employed to give the effect of that produced by the ink lines already described is com- posed of indigo and burnt sienna, and is applied as a flat-wash. A little lake is added to neutralize the greenish hue of this tint when it is to be laid over sand or cultivated ground. The different degrees of intensity required to express the inclination are produced by repeating the wash over those parts which are darker than the rest. To accom- 64 PLAN AND MAP DRAWING. plish this neatly, the darker portions must be washed in first, so that the final washings may cover the whole surface, and the edges of each successive wash must be softened off or blended into the next with a brush and clean water. In shading hills, the paper along the crest of the slope should be first moistened with the water-brush, and before it dries, the laying on of the colour should be begun on the moistened part, and proceeded with down the slope. The effect of representing hills by this method, which is a very expeditious one, is much improved by adding light shading lines with the pen, either in pale ink, or a mixture of indigo and burnt sienna. The ground is always covered with its appropriate sign before the shading tint is laid on. Cylindrical Surfaces in JIIcc/zanical Drawings—In shading cylin- drical surfaces and drawings generally, three methods are employed. One of these is known as softening of, and is employed on finished drawings of machinery. For shading by this method, a brush called a softener is required; this has a brush at each end of the handle, one being larger than the other. Having moistened the paper, and filled the smaller brush with colour and the larger one with water, a narrow strip of colour is laid along the darkest part of the cylinder, and immediately after, while the colour is quite moist, the water-brush is drawn along one edge of the strip and then. in like manner along the other, so as to cause the colour to flow over that portion of the surface which has been damped. The brush is then wiped upon a cloth and drawn lightly down the edge to take up the superfluous water. The colour should be light to begin with, and the quantity to be taken in the brush must be determined by experience. The same remark applies to the water-brush, for if too little be used the colour will not spread sufficiently, and if too much, the colour will be diluted and rendered uneven. These operations of laying on the colour and softening off are continued until the cylindrical appearance has been produced. Each succeeding coat should be laid on before the pre- ceding one is quite dry, as the colour will spread more evenly over a damp surface. The previously applied coat must, however, have been THE ESSENTIAL ELEMENTS. 65 sufliciently absorbed not to wash up, or a clouded appearance will be the result. Another method, known as the French, consists in applying a narrow strip of colour to the darkest part, and overlaying this with other strips, each wider than the one previously laid on. To regulate the breadth of the strips, a number of meridian lines are drawn upon the cylinder. When shaded in this manner, the cylinder presents the appearance of a pol rgon rather than that of a cylinder. The third method, by reason of the facility it affords of producing effect, is very suitable for large drawings and diagrams for illustrating papers and lectures. In shading according to this method, a thick line or a narrow strip of very thick and black Indian ink is laid on the darkest part of the cylinder with the point of the brush. The breadth of the strip will be regulated by the diameter of the object, and it should be previously lined out in pencil. When dry, a damp brush is passed over it so as to remove the sharp edges of the strip, and to cause the ink to run Slightly over the moistened surface of the paper. The flat colour washes are then applied as required, the washes being carried over the black strips, which will be further reduced in tone by a portion of the ink mixing with the colour. In shading, it will be found convenient to keep the light side of the object next to the operator, as it is easier to wash towards the body than from it with the water-brush. The brush should be held in as nearly a vertical position as possible, as it is more easy, when that position is observed, to keep within the boundary lines. ( 66 ) PART IL—APPLICATIONS. __°o§o for lateral, and thus for vertical dimensions. To enable the draughtsman to take T these with accuracy, he should be provided with a pair of g: callipers for measuring the diameters of shafts, a plumb-line for obtaining lateral distances when the objects are not in the \l/ same horizontal plane, and a two-foot rule. K 122 PLAN AND MAP DRAWING. The chief point to be attended to in commencing the drawing of a machine is to obtain the correct positions of the centre lines of its principal component parts, especial regard being had to the centres of motion. These centre lines have been explained in a former Section. Having laid down these lines accurately in their relative positions, separate sketches may be made on a large scale of each part of the machine, and the details of each part constructed upon each corre- sponding centre line in succession, until the whole machine is built up. The centre lines should be drawn in red, and the dimensions should be laid off on each side of them. It will frequently be necessary to take a careful section, to obtain sufficient information from which to draw the plan and the elevation. ‘ With respect to the written dimensions on a drawing, it may be remarked that they cannot be too full or too numerous. Indeed, without complete written dimensions a drawing is almost useless; for though a scale may and should in all cases be attached, great labour would be required to make use of the drawing by means of the scale only. Every dimension which an engineer is likely to require to know should, therefore, be plainly written. Nor is it sufficient to give a dimension once only, as on the plan, for example, and to omit it on the elevation or on the section. It should never be necessary to refer to another drawing to find a dimension. The lettering should be clearly executed, and the direction of the lettering should be the same as that of the figuring, an example of which has been given; that is, it should read from the front or from the right-hand side of the drawing. If a drawing is to be coloured, the lettering, and all dark lines, such as shade lines, must be left till after the colour has been applied. On all coloured drawings the draughtsman should endeavour to obtain a bright, clear tint by repeating the washes a sufficient number of times. In preparing a flat-wash the tint should be mixed up slightly darker than is required, and the solid colouring matter allowed to settle before using. The solution, being poured off without disturbing the sediment, will give a perfectly clear and pure tint. Tints for colouring perspective drawings should always be prepared in this APPLICATIONS. 123 manner. The methods of laying on flat-washes and of shading by colours have been described in former Sections. The following additional remarks on colour shading are taken from VVorthen’s ‘ Cyclopaedia of Drawing.’ A means of adding considerably to the definiteness of a coloured mechanical drawing, and of promoting, in a remarkable degree, its effective appearance, is obtained by leaving a very narrow margin of light on the edges of all surfaces, no matter what may be the angles they form with the surfaces that join them. This should be done invariably; we do not even except those edges which happen to have shadows falling upon them. In such cases, however, this margin, instead of being left quite white, should be slightly subdued. The difficulty of achieving this effect of imparting a clear, regular, un- broken appearance to these lines of light seems very formidable, and, indeed, almost insuperable. The hand of the colourist may be as steady and confident as a hand can be, and yet fail to guide the brush, at an almost inappreciable distance from a straight or a circular line, with that precision and sharpness so requisite for the production of this beautiful effect. \Ve shall, however, explain a novel and an effective method of arriving at this most desirable result. Suppose the object about to receive the colour to be the elevation of a long flat rod or lever, on the edge of which a line of light is to be left. Fill the drawing pen, as full as it will conveniently hold, with tint, and draw a broad line just within, but not touching, the edge of the lever exposed to the light. As it is essential to the successful accomplishment of the operation that this line of colour should not dry, even partially, before the tint on the whole side of the lever has been laid on, it will be well to draw the pen a second time very lightly along the line, so as to deposit as much tint as possible. Immediately this has been done, the brush, filled with the same tint, should be passed along so as to join the inner edge of this line of colour and the whole surface of the lever to be filled in. By this means a distinct and regular line of light is obtained Without sacrifice of time. A still more expeditious way of colouring such n2 124 PLAN AND MAP DRAWING. surfaces is to draw a second line of colour along and in contact with the opposite edge of the lever or other object, and to fill in the intermediate space between the two wet lines with the brush. In this way a clear, uniform outline to the tint is obtained. The blades of the drawing pen must not be sharp, and care must be taken not to press heavily upon it, as otherwise the blades will leave their course visible—an unsightly betrayal of mechanical means to obtain such regularity in the colouring. Flat circular surfaces may be treated in the same way, by using the pen compass instead of the drawing pen. “Then such surfaces are large it will be judicious to colour them in halves or in quadrantal spaces, but great care must be taken to join the parts neatly. The lines of junction may be obliterated by slightly washing them, or by laying a very light tint over the whole surface, taking care in crossing the lines of junction to rub them lightly with the brush. The line of light upon cylindrical objects may be beautifully produced by the same means. To indicate this line with perfect regularity is highly important, for if strict uniformity be not main- tained throughout its length, the object will appear crooked or distorted. Having marked in pencil the position of the light, and filled the drawing pen with a just perceptible tint, draw a line of colour on one side of the line of light. Then, with the brush filled with the same tint, fill up the space unoccupied by the shade tint, within which the very light colour in the brush will disappear. The portion of the surface on the other side of the line of light being treated in the same way, the desired effect, of a stream of light, clear and mathematically regular, will be obtained. The effectiveness and expeditiousness of this method will be most noticeable on long circular rods of small diameter, where a want of accuracy is more immediately perceptible. The extreme depth of shade, as well asthe line of light, may, on such rods, be marked by filling the pen with dark shade tint, and drawing it exactly over the line representing the deepest part of the shade. On either side, and joining this strip of dark colour, another, composed of lighter tint, is to be drawn. Others successively APPLICATIONS. 1 25 lighter should follow, until, on one side, the line of the rod is joined, and, on the other, the lightest part of the rod is nearly reached. The line of light is then to be shown, and the faint tint used at this part of the operation spread with the brush lightly over the whole of that portion of the rod situate on either side of this line, thus blending into smooth rotundity the graduated strips of tint drawn with the pen. For the correct representation of a building, plans, sections, and elevations are required. The plan is usually a horizontal section of the building close above the ground floor. The position and the dimensions of the walls and the rooms of a house are shown by this means. As the walls are shown in section in the plan, sections of the various walls must, of course, be supplied before the plan can be drawn. It is usual to colour the section of the walls in a ground plan; but not unfrequently a dark wash of Indian ink is preferred to colour. The number of sections required will depend upon the regularity of the building; but generally it will be found that two half-sections are sufficient. These two half-sections are usually placed side by side, separated by a single line. The lines on which they are constructed must be drawn distinctly on the plan, and lettered. The section is then described as “ Section ” or “ Half-section ” on A B, &c. Usually the line of section is broken in plan, and the section is then said to be on AB, C D, one half being on AB and the other half on C D. Separate sections to larger scales are required for the details of construction, such as joints of rafters, mouldings to windows, and other parts needing distinct representation. Elevations generally represent the whole of one side of the building, and every side that differs from the rest must have its own elevation. Such elevations are termed Front, Back, and End Elevations, or North, South, East, and West Elevations. In order to show the foundations, a section of the ground is sometimes given with an elevation ; in such a case the level of the ground should be shown by a distinct line. Sometimes the portions of the structure below the ground are shown by dotted lines. Such portions should not be coloured. In getting out the drawings the plan should first be drawn, then the sections, and finally 126 PLAN AND MAP DRAWING. the elevations. The colouring of elevations will afford the student an opportunity of applying the knowledge he may have acquired from a former Section of this work, and of displaying his artistic taste. In the accompanying Plates will be found examples of colouring mechanical and architectural drawings. These should be studied in conjunction with the Section on colouring in the first part of this work. Plate 22 shows a piece of marine engine carefully coloured to indicate the material of which the several parts are made, and Plate 23 contains a piece of permanent way, consisting of wrought-iron rail and bolt, cast-iron chair and wooden sleeper and block, and an elevation of a skew bridge, accurately coloured and shaded in accordance with the principles already explained. It is not within the scope of this work to treat the subject of projection, whether orthographic, isometri- cal, or perspective; but we have given examples of each of these for the purpose of illustrating the remarks and instructions on colouring given in the Section referred to above. Thus Plate 24 is a perspective drawing, such as are frequently made by architects, requiring a high degree of skill and taste 011 the part of the colourist. And Plate 27 contains two isometrical views of a building. These examples are intended to serve as models of finished colouring. The Plates relating to this Section are Nos. 22, 23, 24, and 27. SECTION VII.——COPYING AND REDUCING. Duplicates of drawings are very frequently required; so fre- quently, indeed, and in such numbers, that their production constitutes a large portion of the work executed in every drawing office. Gene- rally, these duplicates are required to the same scale as the original drawing; but often it becomes necessary to reduce or to enlarge the scale to render the drawing suitable to the purpose for which it is intended. The various means and methods by which such duplicates are produced are, therefore, important matters to the draughtsman, APPLICATIONS. 127 and especially to the young draughtsman, whose labours in the drawing office will for a long time be confined almost exclusively to their employment. These means and methods will now be described. Drawing from Copy—Drawing from copy is rarely resorted to for the purpose of obtaining duplicates, the process being too slow for practical requirements. But it constitutes the principal means, after the study of projection, by which pupils in the office are initiated into the art of producing drawings. A few hints concerning the best modes of proceeding in these operations will, therefore, be serviceable, both to the instructor and the instructed. First draw a horizontal and a vertical line through the middle, each way, of the sheet upon which the copy is to be made ; draw also similar lines upon the copy. As these lines divide the paper equally, they may, for the sake of distinction, be called “ divisional lines.” If the centre lines are not shown on the copy, these must next be drawn in lightly with the pencil, great care being taken to place them correctly. The position of these centre lines relatively to the divisional lines may then be transferred by means of the dividers from the copy to the fair sheet, upon which they must be drawn finely but distinctly. Sometimes it will be necessary to draw other lines upon the copy, and to transfer them in like manner to the fair sheet. The details may then be drawn in upon these cent-re lines, by transferring to them the measurements taken from the centre lines of the copy. In taking measurements from a centre line through an object that has both sides alike, the dividers should be turned over to ascertain whether the distance on the other side of the centre line is the same, so as to prove the accuracy of the drawing with respect to the centre line. All measurements must be taken in the exact direction of the distance to be measured, and be transferred in the same direction, or an obviously incmrect distance will be the result. In making the mark, the point of the dividers should not be pushed into the paper, a just visible mark being all that is required ; care must also be taken, when using the compasses, not to press the leg into the paper, as the holes thus made render circles and arcs inaccurate, are unsightly at all times, and 128 PLAN AND MAP DRAWING. completely destroy the unbroken appearance of a tint on a coloured drawing by retaining the colour. When drawing in circular details with the pencil, it will be well to place a small hand-drawn circle around the centre for reference when inking in; also, when a curve is struck from several centres, a temporary pencil line to represent the radii should be drawn from the centres to their respective arcs. When two or more views of the same objects are given, they should be worked upon simultaneously; because, having once drawn in the centre lines, one measurement may be applied to the corresponding part in each view, and so time and trouble saved. In copying maps and plans by this method of drawing from copy, both the copy and the fair sheets are divided up into small squares, by drawing a number of other lines parallel to the divisional lines de- scribed above. The intersection of detail with these lines may then be readily and correctly transferred from the copy to the fair sheet. Copying by T racing—Tracing furnishes the most expeditious means of multiplying drawings. When a tracing is required in outline only, the usual way is to fasten-the sheet of tracing paper with ordinary drawing pins over the drawing to be traced; the sheet of tracing paper should be sufficiently large to allow the pins to be clear of the drawing. If the sheet is not large enough for this, strips of thin paper, with one edge guinmed to the tracing paper and the other to the board, may be used. When this method is not practicable, the pin holes may be effaced to some extent by turning the drawing upside down, and pressing back the edges of the holes with the flat end of a pencil, after the tracing has been removed. If the tracing is to be coloured, it must be stretched on the board, or it will never lie flat after being moistened; and if the colouring is to be applied before the tracing is removed from the drawing, it is essential that the tracing paper be larger than the drawing, so that it may be cut off without injury to the latter. When there is not sufficient time to stretch the tracing paper, the tendency to buckle up when drying may be greatly lessened by placing weights around any part immediately after the colouring has been laid on. If the tracing is to be mounted, the APPLICATIONS. 1 29 colouring should be applied after mounting. When tracing cloth is used, a much better appearance will be produced by applying the colour to the back of the tracing. In performing the stretching process, the sponge must not be applied directly to the tracing paper, but to a piece of clean white paper laid over it; sufficient moisture will pass through to the tracing paper in a few seconds. Sometimes, when the sheet is small, merely breathing upon it will be found sufficiently effective. As tracing paper is thus greatly affected by the breath, it has been recommended to entirely finish both circles and lines within a small area at a time, when copying a drawing, as if all the circles were put in first, as on a drawing, many of them might be out of position before the lines could be drawn. This recommendation is, however, of doubtful value. When tracing from another tracing, a piece of white paper should be placed beneath the copy to render the lines distinct. A tracing may be made upon ordinary drawing paper by means of the glass drawing board. This consists of a sheet of plate glass let into a wooden frame about 3 inches wide flush with the face, the inner edges of the frame being rebated for this purpose. This copying board is placed on a table in front of a window, and supported at an angle of about 25°, so as to get a strong light beneath, which light may be increased by placing a sheet of white paper upon the table to reflect upwards. The original drawing being pinned down to this board with a sheet of drawing paper or parchment over it, the finest lines will be plainly visible, and the drawing may be traced in the same manner as upon tracing paper. To alter the light, the angle of the board may be changed. This method, which is coming extensively into use, is a very convenient one for copying plans and maps. Copying 63/ 731alzsfer.—Copying by transfer has superseded the method already described as “ drawing from copy.” Transfer paper, as employed for this purpose, may be made in the following manner. Take half an imperial sheet of very thin paper, such as tissue paper, and having stretched it upon a board, rub some common blacklead S 130 PLAN AND MAP DRAWING. powder well into it. Then, having removed the dust and superfluous blacklead, well rub the sheet with a cotton rag to prevent its soiling the paper when used for transferring a drawing. A sheet of trans- ferring paper prepared in this way will last for years. Red transfer paper, which is principally used by lithographers, is prepared in the same manner with red ochre. To transfer a drawing, the sheet of transfer paper is laid with its prepared face upon the paper which is to receive the drawing, and over this is placed a tracing of the drawing to be copied, carefully pinned down. The straight lines of the tracing may then be trans- ferred to the drawing paper below by going over them with a style or other pointed instrument that will not cut the tracing. For the regular curves and circles, it will be sufficient to mark the centres by a small cross, thus, >< , and the radii by short lines. Other curves may be transferred by means of the French curve. By this means a copy of the original drawing is obtained in black or red lines, which may be afterwards inked in. Though three distinct operations are re- quired in this process, making the tracing, transferring, and inking in, a drawing can be much more rapidly copied by means of it, than by measuring off with the dividers, as in drawing from copy. Reducing and Enlarging.——It is evident that in drawing from copy, the drawing may be reduced or enlarged at pleasure, since it is only necessary to take half or twice the dimensions as required. Usually proportional compasses are employed for this purpose. “Then reducing by scales, it is obviously not essential to use the same scale as that to which the original is made; the dimensions on one scale may be readily transferred to any other, and the student will do well to make himself familiar with the operation. For reducing or enlarging plans, several means are employed: one of these is known as the method of squares, and is illustrated on Plate 26. In the preceding remarks on drawing from copy, it was shown how in copying to the same scale, both the copy and the fair sheet were divided into squares of equal size, and how the intersections of the detail with the lines formng these squares on the copy were APPLICATIONS. 131 transferred by measurement to corresponding points on the fair sheet. It is obvious, therefore, that if the squares on the latter be larger or smaller than those on the former, as the intersections will be transferred to the same relative positions on the fair sheet as they occupy on the copy, the plan, or other drawing, will be enlarged or reduced accordingly. This is the principle upon which drawings are reduced by this method. Proportional compasses are required in the operations. Drawings may also be rapidly reduced or enlarged by means of instruments called the Pantogmplz and the Eidoglrap/i. Both of these instruments are shown on Plate 26. The following very complete description of the pantograph and the eidograph is given in an excel- lent work on ‘ Mathematical Drawing Instruments,’ by W. F. Stouley, of Holborn, London. “ The pantograph, as represented on the plate, consists of four rules of stout brass, which are jointed together in pairs, one pair of rules being about double the length of the other. The free ends of the shorter pair are again jointed to the longer in about the centre. It is important that the distance of the joints on each of the short rules should exactly correspond with the distance of the joints on the opposite longer rules, so that the inscribed space should be a true parallelogram. To enable the instrument to work freely and cor- rectly, all the joints should be perfectly vertical, and With double axes. Under the joints casters are placed to support the instrument, and to allow it to move lightly over the paper. One of the long rules has a socket fixed near the end, which carries a tracing point when the instrument is used for reducing. The other long rule, and one of the shorter rules, have each a sliding head fitted upon it, which is similar to one of the heads of a pair of beam compasses. Each head has a screw to clamp it in any part of the rule, and carries a perpen- dicular socket, which is placed over the edge of the rule in a true line with the joints. Each socket is adapted to hold either a pencil holder, tracing point, or fulcrum pin, as may be required. The rules upon which the heads slide are divided with a scale of proportions: 0 S4 132 PLAN AND MAP DRAWING. 1—2, 11—12, 9—10, &c., which indicate as one is to two, as eleven are to twelve, as nine are to ten, &c. “ A loaded brass weight, which firmly supports a pin that fits exactly into either of the sockets, forms the fulcrum upon which the whole instrument moves when in use. “ The pencil holder is constructed with a small cup at the top, which may be loaded with coin or shot to cause the pencil to mark with the required distinctness. “Arrangement is made to raise the pencil holder off the draw- ing. This is effected by a groove down one side of the pencil holder, in which a cord is fixed, passing from the pencil along the rules, turning the angles over small pulleys, and reaching the tracing point, where it may be readily pulled by the hand to raise the pencil. This will be found especially convenient when the pencil is required to pass over any part of the copy not intended to be reproduced. “The pantograph is set to reduce drawings in two ways, termed technically the erect manner and the reverse manner. It will be necessary to give full details of each manner, particularly in relation to the scales engraved upon the instrument, which are not very intelligible; indeed comparatively few professional men are sufficiently acquainted with them to avail themselves of their full value. “ By the erect manner of setting the pantograph, the reduced copy will appear erect; that is, the same way as in the original. The general position of the parts of the instrument set in this manner is shown in the plate, where it will be seen that the fulcrum pin is placed in the socket of the sliding head upon the outside long rule, and the pencil holder in the socket upon the short central rule. By this method of setting the instrument, it will reduce in any of the given proportions not exceeding half-size, technically from 1—2. The scales engraved upon the rules that accord with the erect manner of setting are those which have 1 for the first proportion; as 1—2, APPLICATIONS. 1 3 3 1—3, 1—4, 820. The other scales may be used, but will not accord with the reading, except through arithmetical deductions, the results of which may be given more clearly by the following complete Table than by rules with exceptions. TABLE OF REDUCTIONS BY THE PANTOGRAPII IN THE ERECT MANNER, THE FULCRUM BEING PLACED IN THE SOCKET UPON THE OUTSIDE RULE, AND THE PENCIL UPON THE CENTRAL RULE. 1 Reading glvon upon l Reduces in the Pro- , Reading given upon Reduces in the Pro- , the Scales. l portion of the Scales. portion of 3 1—2 ? 1 to 2 2—3 2 to 5 3 1—3 , 1 ,, 3 : 3—4 3 ,, 7 1 1—4 I 1 ,, 4 5 4—5 4 ,, 9 : 1—5 1 1 ,, 5 ; 5—6 5 ,, 11 I 1—6 ' 1 ,, 6 a 6—7 6 ,, 13 . 1—7 l 1 ,, 7 F 7—8 7 ,, 15 g 1—8 1 1 ,, 8 ; 8—9 8 ,, 17 a 1—9 1 1 ,, 9 9—10 9 ,, 19 1 1—10 I 1 ,, 10 : 10—11 10 ,, 21 l 1—11 l 1 ,, 11 a 11—12 11 ,, 23 I “ In the above Table the readings which are given with the proportions are given to show clearly which proportions agree with the erect scales; many of those that do not agree with the reading are very useful, as 2—3, which is often required to reduce a drawing from a scale of 20 to one of 50. “ In the reverse manner of setting the pantograph, the reduced copy appears reversed, or upside down, to the original. The fulcrum pin is placed in the socket upon the short central rule, and the pencil holder is placed in the socket upon the outside rule. This is gene- rally the most convenient way of using the pantograph for large drawings, as the original and copy come edge to edge, and need not overlap each other, which is often compulsory in the erect manner; the range of scale is also much greater, as the proportions include the unit proportions of the erect scale, and continue in ratios up to full size. “ The following Table will give the readings of the instrument 134 PLAN AND MAP DRAWING. which accord with the reverse setting, and those which may be used to this setting, obtained by calculation. TABLE OF REDUCTIONS BY THE PANTOGRAPH IN THE REVERSE MANNER, TIIE FULCRUM BEING PLACED IN THE SOCKET ON THE CENTRAL RULE, AND THE PENCIL IN THE SocKET UPON THE OUTSIDE RULE. Reading given upon Reduces in the Pro- Reading given upon Reduces in the Pro- thc Scales. portion of the Scales. portion of 1 1—2 1 to lfull size' 2—3 2 t0 3 1—3 1 ,, 2 3—4 3 ,, 4 1—4 1 ,, 3 4—5 4 ,, 5 1—5 1 ,, 4 5—6 5 ,, 6 1—6 1 ,, 5 6—7 6 ,, 7 1—7 1 ,, 6 7—8 7 ,, 8 1—8 1 ,, 7 8—9 8 ,, 9 1—9 1 ,, 8 9—10 9 ,,10 1—10 1 ,, 9 10—11 10 ,, 11 1—11 1 ,, 10 11—12 11 ,, 12 “ The above Table and the previous one give the proportions for reductions, the tracing point being in every instance considered upon the outside rule. If it were required to produce an enlarged copy, which the pantograph will do but very imperfectly, the pencil and tracer would have to change places; the proportions of course would read the same. “ In using the pantograph some care is required in setting the fulcrum weight in the best position to allow easy action of the instru- ment over the space required. It should always be roughly tried over the boundary before commencing the copy. “ The ordinary pantograph will in no instance work over a large drawing at one operation, but it may be shifted about as required, using care, and testing the copy after the fulcrum is moved, to see that the tracer and pencil correspond in those parts already produced, that the pantograph will reach in its shifted position. The fulcrum weight being generally made with needle points to attach it to the drawing will be found very difficult to shift so short a distance as is frequently required. This may be easily remedied by attaching with gum a piece of indiarubber over each of the sharp points, when it is APPLICATIONS. 135 required to be used for large drawings. The rubber will hold the paper sufficiently if the pantograph work freely in the joints and casters, as it should do. “In copying the buildings which frequently occur in plans of estates, &c., a straight slip of transparent horn will be found very convenient to guide the tracing point. Some draughtsmen have the horn cut with an internal angle, by which one side and one end of a building may be traced without shifting the horn. “ Architects and mechanical engineers seldom use the panto- graph; however, it may perhaps be sometimes used with advantage for tracing in the most difficult and tedious parts of a drawing with a precision impossible by hand. This applies particularly to such parts as are frequently repeated, as capitals, trusses, bosses, tracery, &c., upon drawings to very small scales. In these instances it is only necessary to make a detail sketch, say six times the size required, and to place the fulcrum weight in such position that the pencil will pass over the parts required to be filled in, the tracer at the same time resting on a corresponding part of the detail sketch, which may be placed in position under the tracing point, and be held sufficiently by two lead weights. For a second ornament on the same drawing, the detail may be shifted without moving the fulcrum. “ To follow the outline of any object of the ornamental class, or for the reduction of mechanical drawings to a size suitable for wood or other engravings, the strip of horn will be found particularly useful ; indeed, to obtain any degree of precision, it will. be better, generally, to let the tracer follow a guiding edge placed over the original for that purpose. French curves are particularly useful, although perhaps only a small piece may be available at once. The tracer may rest on the surface until another part of the curve is found to correspond with the continuation of the line. “In some old pantographs a guide is fixed to the tracing point. The guide is a kind of handle similar to a drawing pencil, the point of which is hinged to the point of the tracer. This gives a convenient and firm hold of the point, and appears to the author a useful appendage. 136 PLAN AND MAP DRAWING. “Pantographs have been made in many shapes‘unnecessary to describe, as they are all of one principle—that of a parallelogram jointed at the four corners; the principal difference being in the position of the points and fulcrum in relation to the parallelogram. One thing is essential in every construction,—-that is, that the fulcrum, tracer, and pencil should alwaystbe in a true line when the instrument is set for use. The parallelogram may be in any position on the instrument, to the fancy of the maker. “The Eidograp/z was invented by Professor Willis in 1821. It is a most ingenious and exact instrument, for many purposes superior to the pantograph, within the range of its working powers, which, however, may be considered to be limited to reducing or copying off, between the full size of the original and one-third of the size; for greater reductions, the balance of the various parts is thrown so far out that it appears clumsy to use, and is really inferior to the pantograph. The great merit of the eidograph is, that within its range it reduces conveniently and exactly in all proportions; for instance, we may reduce in the proportion of 9 to 25 as readily as 1 to 2. It is also in every way superior to the pantograph in freedom of action, there being no sensible friction on the single fulcrum of support, and in its movement it covers a greater surface of reduction. “It is somewhat curious that an instrument of such great merit should be little known in the profession, where its uses would be so constantly convenient. This may partly be attributed to the very few published descriptions which are to be found in works treating 011 mathematical instruments. It is not intended, however, to infer that there are not many eidographs in use, but that the writer presumes they are comparatively little known, from his personal acquaintance with professional men, and from the number of large pantographs that are made and sold to perform work that could be done so much more exactly and conveniently by the eidograph. This remark will not apply to the small pantograph, which is less expensive than a small eidograph, and answers perfectly for the reduction of small plans for instance, those frequently attached to leases and conveyances. as, APPLICATIONS. 1 3 7 “ The details of the construction of the eidograph are as follows :—-— The point of support is a heavy, solid, leaden weight, which is entirely covered with brass; from the under side of the weight three or four needle points project, to keep it in firm contact with the drawing. Upon the upper side of the weight a pin, termed a fulcrum, is erected, upon which the whole instrument moves. A socket is ground accurately to fit the fulcrum, and attached to a sliding box, which fits and slides upon the centre beam of the instrument. The sliding box may be clamped to any part of the beam by a clamping screw attached. Under the ends of the beam are placed a pair of pulley wheels, which should be of exactly equal diameter; the centre pins of these revolve in deep socket fittings upon the ends of the beam. The action of the two wheels is so connected as to give them exact and simultaneous motion. This is effected by means of two steel bands, which are attached to the wheels. The bands have screw adjustment to shorten or lengthen them, or to bring them to any degree of tension. Upon the under side of each of the pulley wheels is fixed a box, through which one of the arms of the instrument slides, and is clamped where required. At the end of one of the arms a socket is fixed to carry a tracing point, at the end of the other arm a similar socket is fixed for a pencil. The pencil socket may be raised by a lever attached to a cord, which passes over the centres of the instrument to the tracing point. The two arms and beam are generally made of square brass tubes, and are divided exactly alike into 200 equal parts, which are figured so as to read 100 each way from the centre, or by the vernier cut in the boxes through which the arms and beam slide they may be read to 1000. “ There is a loose leaden weight which fits upon any part of the centre beam, packed in the box with the instrument. The weight is used to keep the instrument in pleasant balance when it is set to proportions which would otherwise tend to overbalance the fulcrum weight. “ In the above details it will be particularly observed that the pulley wheels must be of exactly equal diameters. It is upon this that '1‘ 138 PLAN AND MAP DRAWING. chiefly depends the accuracy of the instrument, the periphery of these wheels being the equivalent to the parallelogram, which has been already described as the essential feature of the pantograph. The adjustment of the wheels to size, by turning in the lathe, is, perhaps, the reason the results of the eidograph are more exact than those of the pantograph, which has no equivalent compensation for the always possible inaccuracy of workmanship. “From the details just given, the general principle of the eido- graph may be easily comprehended. Thus, the wheels at each end of the beam being of equal size, the steel bands connecting them being adjustable, so as to bring the wheels into any required relative position, it follows, that if the arms fixed to the wheels be brought into exact parallelism, they will remain parallel through all the evolutions or movements of the wheels upon their centres; consequently, if the ends of the arms be set at similar distances from the centres of the wheels, any motion or figure traced by the end of one arm will be communicated-to the end of the other, provided the fulcrum of support be placed also at a similar distance from the centre of one of the wheels. “ To adjust, or ascertain if the eidograph is in adjustment, is very simple, from the reason that when. the arms are parallel the adjustment is perfect for all proportions. The manner of ascertaining this is as follows: place all the verniers at zero, which will bring them to the exact centres of the arms and the beam, place the arms at about right angles with the beam, then mark simultaneously with the tracer and pencil point, turn the instrument round upon its fulcrum, so that the pencil point be brought into the mark made by the tracer; then, if the tracer fall into the mark made by the pencil the instrument is in adjustment. If it should not fall into the same mark, the difference should be bisected, and the adjusting screws on the bands should be moved until the tracer fall exactly into the bisection, which will be perfect adjustment. “When the eidograph is in adjustment, if the three verniers be set to the same reading on any part of their scale, the pencil point, APPLICATIONS. 1 3 9 fulcrum, and tracer will be in a true line. If it should not be so, it will show the dividing of the instrument to be inaccurate. Thus we have a simple way of testing the eidograph in every important particular. “ The divisions upon the eidograph do not positively indicate the reductions required to be performed by the instrument, but merely give a scale, which, with the assistance of the vernier, divides the beam and arms into 1000 parts. To obtain the quantity to which the verniers are to be set, it is necessary either to apply to a table of pro- portions relative to divisions, or to simple arithmetic, as will be shown. A printed table is very generally placed inside the lid of the box in which the instrument is packed, which contains part of the following proportions : TABLE FOR REDUCING OR ENLARGING PnoronTroxs. Proportions. l Divisions on Bars. l Proportions. Divisions on Bars. As 1 is to 2 : 33‘333 i As 2 is to 3 20 ” 1 n 3 i 50 n 2 n 5 42'857 ,, 1 ,, 4 i 60 ,, 3 ,, 4 14-285 ,, 1 ,, 5 5 66'666 ,, 3 ,, 5 25 ,, 1 ,, 6 l 71-428 ,, 4 ,, 5 11-111 ,, 1 ,, 7 1 75 ,, 5 ,, G 9-09 ,, 1 ,, 8 77.777 ,, 1 ,, 9 l 80 ,, 1 ,, 10 l 81-818 1 “The table here given answers for the general purposes of reducing, such as the bringing of a plan from one chain scale to another, the quantities of which are found by the following rule : “ T 0 find the quantity equal to any given proportion for the setting of the eidograplz.——Subtract one sum of the proportion from the other, and multiply this difference by 100 for a dividend; add the two sums of the proportion together for a divisor : the quotient from the working of this will give the number to which the arms and beam are to be set. '1‘ 2 140 PLAN AND MAP DRAWING. “For instance, let it be required to reduce a drawing in‘ the proportion of 3 to 5. 5-3=2 X100 5+3=8) 200 (25 “ The centre beam is to be set to 25 on the side nearest the pencil point, the pencil arm is also set to the 25 nearest the pencil point, and the tracer arm is set to the 25 farthest from the trace. If it were required to enlarge in the same proportion, each side would have to be set at the opposite 25. “ To clearly illustrate the subject, it may be well to give another example. Let it be required to reduce an ordnance plan of five feet to the mile to a scale of three chains to the inch. First, we must have like terms, therefore to reduce both proportions to feet to the inch will, in this instance, be the most simple way ; thus: 5 feet to the mile 2 88 feet to the inch. 3 chains to the inch = 198 198 - 88 = 110 100 2’ 198 + 88 = 280) 11000 (38-401 “If the slides of the instrument be set to 38'46, it will be, prac- tically, sufficiently near.” Photography is also frequently resorted to for the purpose of re- ducing and enlarging drawings. The results are satisfactory within certain limits of size; for it is obvious that when the drawing is large, the parallel lines will converge in the photograph, for reasons which will be understood from the laws of perspective. For enlarging small and intricate drawings, photography is very useful. In preparing drawings for reduction by this process, all lines and shadows should be put in in Indian ink only. For optical reasons, colour cannot be reproduced by photography, and as certain colours produce an effect which might not be anticipated by the inexperienced, it will be well to warn such against these effects, to prevent disap- pointment at the results obtained. Thus blue, for instance, shows APPLICATIONS. 141 very indistinctly, and yellow surfaces in coloured drawings come out very dark. Drawings for Lithographers and Engravers.—The drawings re- quired by the lithographic draughtsman are simply outline drawings or tracings, with the shaded drawing for reference when such is required. The shaded drawing should be traced when in outline only with a fine-pointed pencil, not too hard. The engraver prefers such a tracing to the drawing itself, unless he can have the latter before it is shaded. He will, however, require the shaded drawing as a guide in copying in the shadows. As the drawing always gets soiled under such circumstances, unless protected, it is prudent to place it upon a board of the exact size, with a glass over it to fit, the glass being kept in its place by a strip of paper pasted round the edge. The drawing will not be required at all if only an outline engraving is to be made. In that case, the lines that are to be shade lines must be indicated on the pencil tracing; a dot in red ink on each of such lines will be suflicient. A scale should always be put upon lithographs and engravings, instead of merely stating that it is drawn to some particular scale, because the paper just before receiving the impression is damped, and consequently expands. For this reason, no engraving is of the same size as the original drawing; and as the degree of moisture varies, no two engravings from the same plate ever are exactly equal in size. Hence the necessity for drawing the scale is obvious. The Plate relating to this Section is No. 26. (142) TRIGONOMETRICAL FORMULAZ. To compute the Sides of Triangles—Let A B C be the angles of a plane triangle, and who the sides opposite. Then, for right-angled triangles, we have b=usin.B =ctan.B b ccotC c=acos.B or c b tB c=btan.C and for oblique-angled triangles we have _ a sin. B — sin. A i a sin. 0 _ sin. A To compute the Areas of Triangles—“When two sides and the included angle are known, a and 1) representing the two sides and 6 the included angle, absin.6 A———~2 - To find by logarithms the area in acres and decimals of an acre, Log. A = log. a + log. I) + log. sin. 0 — 15'30103. When two angles and the included side are known, B and 0 being the angles and a the included side, _ a? sin. [‘3 sir_1_._(_9 _ 2 sin. ([3 + 6). To find b -10 arithms the area in acres and decimals of an acre Y g , Log. A = 2 log. a + log. sin. [3 + log. sin. 6 — log. sin. ([3 + 6) — 15-30103, When the three sides are known, who being the three sides and 3 their half sum, A = «/ si(957)791--77(7-7). To find by logarithms the area in acres and decimals of an acre, log. 5 + log. (3 —- a) + log. (3 — b) + log. (3 — c) F 2 -— i). Log. A 2 (143) INCLINED MEASURE. TABLE SHOWING THE REDUCTION IN LINKS AND DECIMALS or A LINK TO BE MADE PER CHAIN FOR EVERY HALF DEGREE 0F INCLINATION FROM 3° T0 30°. (100 x versed sine of the inclination.) Angle } Reduction. Anglo. Reduction. P Angie. Reduction. 0 I O l O I i 3 O 0'15 12 30 2'37 22 0 7'28 3 30 0'19 13 0 2'56 22 30 7'61 4 0 0'24 13 30 2'76 23 0 7'95 4 30 0'31 ‘ 14 0 2'97 23 30 8'29 5 0 0'38 14 30 3'19 24 0 8'65 5 30 0'46 15 O 3'41 24 30 9'01 6 0 0'55 15 30 3'64 25 O 9'37 6 30 0'64 16 0 3'87 25 30 9'74 7 0 0'75 1 16 30 4'12 26 0 10'13 7 30 0'86 17 O 4'37 26 3O 10'51 8 0 0'97 1 17 30 4'63 27 0 10'90 8 30 1'10 18 0 4'89 27 3O 11'30 9 0 1'23 I 18 30 5'17 28 0 11'71 9 30 1'37 1 19 O 5'45 28 30 12'11 10 0 1'53 | 19 30 5'74 29 0 12'53 10 30 1'67 1 20 0 6'03 29 30 1296 11 0 1'84 | 20 30 6'33 1 30 0 13'40 11 30 2'01 1 21 0 6'64 i 12 O 2'19 21 30 6'96 CURVATURE AND REFRACTION. TABLE OF CORRECTIONS IN FEET AND DECIMALS OF A Poor. Dishince Curvature Refraction (93:52:32 5:16 2 Distance Curvature Refraction ggrrecttion {03' in 911105. ' ' Refraction. ill “liles' ' . i éégugi‘ieolal? 1k '04 '01 '03 5 16'67 2'38 14'29 4 '17 '02 '15 i 5;— 20'18 2'88 17'30 % '37 '05 '32 i 6 24'01 3'43 20'58 1 '67 '09 '58 6% 28'18 4'03 24'15 1;- 1'50 '21 1'29 7 32'68 4'67 28'01 2 2'67 '38 2'29 7% 37'52 5'36 32'16 2% 4'17 '60 3'57 8 42'69 6'10 36'59 3 6'00 '86 5'14 1 8% 48'19 6'88 41'31 ; 8'17 1'17 7'00 3 9 54'02 7'72 46'30 4 10'67 1'52 9'15 1 9% 6020 8'60 51'60 4; 1355 1'93 11'62 i 10 66'70 9'53 57'17 (144) INDEX“. -—o-o;o::oo— A. ANGLE, to bisect, 16 , to construct, equal to a given angle, 17 , to draw a line making a given, 15 —— of light in mechanical drawings, 48 in topographical drawings, 54 Arch, Gothic, equilateral, to draw, 23 ———_ , lancet, to draw, 24 —, —-——- obtuse, to draw, 24 —, ogee, to draw, 25 —, — Tudor, to draw, 24 —-, Moorish horse-shoe, to draw, 24 , semi-elliptical, to construct, 23 Architectural drawings, 121 Arcs, centres of, to be marked, 10 Areas to triangles, to compute, 142 B. BISECTING an angle, 16 Blacklead paper, 8 Book of reference, 97, 101 Books for field sketching, 115 Borders and corners, 69 Borings, 104 Bottle indiarubber, 9 Boundary maps, 104 Bows, 2 , spring, 2 Broken lines, 30 Brushes for tinting, 41 Buildings—plans, sections, and elevations, posi- tion of, on drawing, 125 C. CAnnomc paper, 8 Cartridge paper, 6 Centre lines, 10 , care to be taken in placing correctly, 10 Centre of circle, to find the, 18 Centres of arcs to be marked, 10 Cinquefoil, Gothic, to draw, 26 Circle, to describe, through three given points, 17 , to draw a tangent to, 17 , to draw radii of, the centre being inac- cessible, 18 —, to find the centre of, 18 Circles, concentric drawing, 10 Cities, to represent size of, 112 Civil engineers” plans, 96 Cleaning drawing pen, 3 Cleaning 011' drawings, 9 Cleanliness, importance of, 9 , precautions to be taken to ensure, 9 Cloth, tracing, 7 --———, , Sager’s vellum, 7 —-—, , sizes of, 7 Colour for buildings, 47 —— for cultivated land, 47 for fences, 47 for grass-land, 45 for gravel, 46 for marsh, 45 —— for mud, 46 for roads, 47 for sand, 46 for streets, 47 for water, 45 ——- for woodland, 46 for uncultivated land, 47 Colouring cylindrical objects, 124 drawings, 11, 122 rivers and streams, 110 Colours, 39 , conventional, Table of, 44 for sections, 44 Compasses, 2 , manner of using, 2 INDEX. 1 45 Compasses, pencil leg of, 2 ——., points of, 2 , removing movable leg, 2 Competition drawings, paper for, 6 Concentric circles, drawing, 10 Construction of scales, 11 Continuous cartridge paper, 6 ~— tracing paper, 7 Contour lines, 37 Contours, to plot, 90 Conventional colours, Table of, 44 Copying by tracing, 128 — by transfer, 129 drawings, 11, 126 ' from tracing, 11 Corners and borders, 69 Cross sections, 98, 102 Cultivated land, to represent, 32 Curvature and refraction, Table for correction of, 143 Curved lines, 29 , to draw, 29 Cutting off drawings, 7, 11, 12 Cylinders, various methods of shading, 61 Cylindrical objects, to colour, 1241 —— surfaces, shade lines, 50 , shading lines, 51 C ynia recta, to draw, 25 reversa, to draw, 25 D. DENTED drawing-board, to remedy, 14 Detail plotting, 89 Dimensions of drawing table, 2 to be written on drawings, 122 Distances, scales of, 70 Dividing a line into equal parts, 10 Dotted lines, 31 Dotting pen, 31 , regular, to produce, 111 Drawing, copying and reducing, 12G , inking in to commence from top of, 10 , stretching paper for, 6 Drawing concentric circles, 10 from copy, 127 lines, 10 . Drawing board, dented, to remedy, 14 office, essentials of, 1 , gaslights, 2 ~— —, position of windows, 1 Drawing office, skylights unsuitable, 1 paper, sectional, 8 , to join sheets of, 12 papers, 5 , sizes of, 5 pen, 3 -—-—— —-—, cleaning, 3 — —, more than one required, 3 , setting, 3 , supplying with ink, 3 table, dimensions of, 2 , position of, 2 Drawings, cleaning off, 9 —, competition, paper for, 6 , colouring, 11 ———-, cutting oil“, 7, 11, 12 —, ink for, 8 , margin to be left, 11 —, mechanical and architectural, 121 -—-, parchment for, 8 —-, to colour, 122 , to preserve rolled, 12 —, to reduce or enlarge, 130 —, to remove grease spots from, 10 —, to varnish, 14: for lithographers and engravers, 141 for specifications for letters patent, 8 Dusters, 2 E. EIDOGRAPH, 136 —, method of setting, 139 , table for setting, 139 , to adjust, 138 Elevation of trees, 36 Ellipse, to draw, 21 Elliptical arch, to construct a semi—, 23 Encamping grounds, 112 Engravers, drawings for, 141 Enlarging by instruments, 131 by scales, 130 by squares, 130 Equal parts, to divide a line into, 15 Equidistant and parallel lines, to draw, 28 Equilateral arch, to draw, 23 triangle, to construct, on a given base, 16 Erasure of ink lines, 11 of pencil marks, 9 Error-sheets, 91 , examples of, 92 Errors, 91 14G Essentials of drawing office, 1 Estate plans, 107 Examination of maps and plans, 117 F. FERRIHS, 111 Field-book, example of, 80 Field sketching, 114; Fir-graining, 32 Flat-tints, 40 Formula‘, trigonometrical, 112 ~ GI GASLIGHTS in drawing office, 2 Glass—paper to erase ink lines, 11 Glue for mounting paper, 6 lothie cinquefeil, to draw, 26 equilateral arch, to draw, 23 lancet arch, to draw, 241 -— obtuse arch, to draw, 24 ogec arch, to draw, 25 —— quatrefoil, to draw, 26 trefoil, to draw, 25 Tudor arch, to draw, 24: Gradients, to lay down, 95 Graining, fir, 32 , oak, 32 , wood, 32 Grass-land, to represent, 34: Gravel, to represent, 35 Grease spot, to remove from drawing, 10 H. HEXAGON, to describe a regular, 21 Hills, representation of, 38 , sand, to represent, 36 , shading, horizontal system, 53 , , vertical system, 57 , sketching, shading, and copyin Horizontal zones, 33 Horse-shoe arch, to draw, 24 —. W 113 ‘07 I. IMPORTANCE of cleanliness, 9 Inclined measure, Table for correction of, 143 Indian ink, 8 , preparation of, for drawing, 9 -——- -—-, quality of, 9 INDEX. Indiarubber, native or bottle, 9 —, vulcanized, 9 Ink for drawings, 8 ——-—, Indian, 8 , preparation of, 9 —, quality of, 9 ._ lines, erasure of, 11 , to avoid smearing, 10 — slab or saucer, position of, when in use, 10 Inking in to commence at top of the drawing, 10 Instruments, 2 , quality of, 2 Islands, 110 —_ J. JOINING sheets of paper, 12, 13 Jungle, 112 L. LAKES, outline of, 30 Lancet arch, to draw, 24 Land, cultivated, to represent, 32 , uncultivated, to represent, 37 Lead—pencil marks, erasure of, 9 Lettering, 66, 122 , position of, on plans and maps, 69 Letters, arrangement of, in titles, &c., 68 , kinds to employ, G7 , mechanical construction of, 66 , size of, G7 Level—book, example of, 91 Line, dividing into equal parts, 10 , regular pentagon on a given, 20 , to bisect a given straight, 15 , to construct a square on a given, 19 , to divide a, into equal parts, 15 , to draw a, making a given angle, 15 , to erect a perpendicular to, 15 Lines, drawing, 10 , broken, 30 , centre, 10, 122 , combinations of, 31 , curved, to draw, 29 —, curved and straight, 27 , contour, 37 , dotted, 31 , ink, to avoid smearing, 10 -—, parallel and equidistant, to draw, 28 Lines, reference, 7 8 , section, 29 —-, —, to draw, 28 —, shade, application of, 48 ———-, shading, 50 —, , in topographical drawings, 52 —, straight, difficulties in ruling, 27 —, , to draw, 27 , wavy, 33 -— of greatest descent, 57 of uneven thickness, 30 Litlrograplrers, drawings for, 141 Local Government Board, regulations of, 104 M. MACHINE-MADE paper, 6 Machinery, rough sketches of, 121 Manner of using compasses, 2 Map drawing, 109 Maps, boundary, 104 , field, examination of, 118 ——-—, signs used in, 120 for division into wards, 101- Margin to drawings, width of, 11 Marshy ground, to represent, 35 Mechanical drawings, 121 Mile stones, 112 Mining plans, 106 Moorish horse—shoe arch, to draw, 24 More than one drawing pen required, 3 Mountain passes, 111 Mounting paper, glue for, G on stretchers, 13 -—— tracings, 129 Mud in rivers, to represent, 36 N. NATIVE irrdiarubber, 9 Needle to erase ink lines, 11 North points, 69 Northings and soutlrings, 87 0. OAK-GRAINING, 32 Obtuse arch, to draw, 24 Ogee arch, to draw, 25 Orchards, to represent, 36 Outline of lakes, 30 rxnnx. 147 ' Outline of ponds, 30 —- of rivers, 3O Oval, to construct, the width being given, 18 P. l‘AXTOGRAPH, 131 -—-, methods of setting, 132 , tables for setting, 133, 134- , to use, 134 Paper, blacklead, 8 , carbonic, 8 —, cartridge, (5 —-——, continuous cartridge, (5 —, drawing, 5 —, —, to join, 12 —, , sizes of, 5 —, glue for mounting, G —, machine—made, 6 , sectional, 8 , stretching for drawing, 6 —, tracrng, 7 —, , continuous, 7 —, —, preparation of, 7 —, , sizes of, 7 , , to join, 13 , transfer, 8 —, , preparation of, 129 , to join sheets of, 12 —, to mount on stretchers, 13 for competition drawings, 6 for large plans, 6 Parabola, to draw, base and height being given, 21 Parallel and equidistant lines, to draw, 28 Parchment for drawings, 8 Parliamentary plans and sections, 100 standing orders, 98 Paste, 14: Patent, drawings for specifications, 8 Pathways, 111 Pen, dotting 01' wheel, 31 Pencil marks, erasure of, 9 —— leg of compasses, 2 Pencils, 4: , pointing, 4 —— for field sketching, 115 Pentagon, to describe, on a given line, 20 Perpendicular, to erect a, 15 Plan of trees, 36 Plans, civil engineers’ and surveyors’, 96 U2 148 Plans, estate and town, 107 ,large, paper for, G —, mining, 106 —, railway, 97 —, parliamentary, 100 Plotting, 77 -———- angular surveys, 81 -— contours, 90 —— detail, 89 ——-—- sounded points in submerged districts, 90 --—- traverse reference lines, 84 vertical sections, 92 Pointing pencils, 4 Points of compasses, 2 Ponds, outline of, 30 Position of drawing table, 2 of ink slab or saucer when in use, 10 of windows in drawing office, 1 Precautions to be taken to ensure cleanliness, 9 Preparation of colours for tinting, 4O -— of ink for drawing, 9 — of stretchers, 13 —— of tracing paper, 7 —-—— of transfer paper, 129 Preserving drawings, rolled, 12 Q. QUALITY of Indian ink, 9 —— of instruments, 2 Quatrefoil, Gothic, to draw, 26 R. RADII of circle, to draw, the centre being inac- cessible, 18 Railway plans, 97 sections, 102 stations and termini, 112 Railways, 112 Rectangle, to construct, similar to a given rect- angle, 20 Rectangular ce-ordinates, to plot by, 87 Reducing and enlarging drawings, 126, 130 ——-— by instruments, 131 —— by scales, 130 by squares, 130 icference, book of, 97, 101 lines and points, 78 lines, secondary, 7 9 Refraction and curvature, Table for correction of, 143 INDEX. Regulations of Local Government Board, 104 Removing movable leg of compasses, 2 Rivers, beds of, 110 - -——-, mud in, to represent, 36 —, outline of, 30 — and streams, colouring, 110 -— —, inking in, 109 Reads, 111 Rolled drawings, to preserve, 12 Roman cyma recta and cyma reversa, to draw, 25 Roofs, to draw, 30 Rough sketches of machinery, 121 Ruling straight lines, difficulties in, 27 Running water, to represent, 33 So SAGER’s vellum tracing cloth, 7 Sand, to represent, 35 banks, 110 -—-—- hills, to represent, 36 Scales, 70 ——-—, choice of, 72 ———-, construction of, 11, 70, 75, 76 —-—-—, diagonal, 7 5 , vernier, 75 —, Tables of, 73, 74 ——-— of construction, 74: — of distances, 70 -———- of shade, English, 59 , Lehmann’s, 57 , standard, 53 —— ——-, United States’, 59 Sectional drawing paper, 8 Section lines, 29 of water, to represent, 30 Sections, colours for, 44 -——, cross, 98, 102 —, parliamentary, 101 —, railway, 102 ———-, to plot, from contour map, 96 , working, 94, 103 —— of wood, 32 , vertical, to plot, 92 Semi-elliptical arch, to construct, 23 Setting drawing pen, 3 Shade lines, application of, 48 , cylindrical surfaces, 50 Shading, 48 cylinders, various methods, 64: —— hills, horizontal system, 53 _— .— INDEX. Shading hills, vertical system, 57 ’ , rounding curves, 55 —-— lines, 50 ——- —-—, cylindrical surfaces, 51 in topographical drawings, 52 ——- in colours, 63 , cylindrical surfaces, 64 , hill slopes, 63 Sides of triangles, to compute, 142 Sizes of drawing papers, 5 of tracing cloth, 7 of tracing paper, 7 Sketches, rough, of machinery, 121 Sketching, field, 114 Skylights unsuitable for drawing office, 1 Sounded points, to plot, 90 Specifications for letters patent, drawings for, 8 Spring bows, 2 Springs, 112 Square, to construct, equal to %, 5:, &c., of a given square, 19 , to construct, in any proportion to a given square, 20 —, to construct, on a given line, 19 , to construct, which shall be a multiple of a given square, 19 Standing orders of Parliament, 98 water, to represent, 29 Stations, railway, 112 , telegraph, 112 Straight-edge, thickness of, 5 Straight line, to bisect a, 15 lines, difficulties in ruling, 27 , to draw, 27 and curved lines, 27 Stretchers, mounting paper on, 13 —, preparation of, 13 Stretching paper for drawing, 6 , glue for, 6 Supplying drawing pen with ink, 3 Surveyors’ plans, 96 Swamps, to represent, 35 _ T. TABLE, drawing, position of, 1 , , size of, 1 Table for correction of curvature and refraction, 143 for correction of inclined measure, 143 —-— for setting eidograph, 139 149 Table of conventional colours, 44 Tables for setting pantograph, 133, 134 Tangent, to draw, to a circle, 17 Telegraph lines and stations, 112 Thickness of straight-edge, 5 Tinting, 39 ‘ Tints, art of applying, 40, 41, 43 ——-, brushes for applying, 41 —, double or alternate, 42 —, flat, 40 , preparation of, 40 Toll-gates, 111 Topographical drawings, shading lines in, 52 To remove grease spots from drawings, 10 Town plans, 107 Towns, to represent size of, 112 Tracing, copying from, 11 —, to copy by, 128 —— cloth, 7 —— —, Sager’s vellum, 7 , sizes of, 7 — paper, 7 , continuous, 7 —— —-—, preparation of, 7 , sizes of, 7 , to join sheets of, 13 Tracings, to mount, 129 Transfer paper, 8 , preparation of, 129 Transferring, to copy by, 129 Traverse plotting by rectangular co-ordinates, 87 —-— reference lines, to plot, 84 Trees in plan, 36 in elevation, 36 , to represent, 36 Trefoil, Gothic, to draw, 25 Triangle, equilateral, to construct, 16 , to construct, the length of base and angles at base being given, 17 , to construct, the lengths of the sides being given, 16 Triangles, primary and secondary, 78 ,- to compute the areas of, 142 , to compute the sides of, 142 Trigonometrical formulae, 142 Tudor arch, to draw, 24 U. UNCULTIVATED land, to represent, 37 150 V. VARNISHING drawings, 14 Vellum tracing cloth, Snger’s, 7 Vertical sections, to plot, 92 Villages, to represent size of, 112 Vulcanized indiarubber, 9 W. WASIIES, art of applying, 40, 41, 43 —, brushes for, 41 , double or alternate, 42 Water, running, to represent, 33 , standing, to represent, 29, 33 THE LONDON 2 INDEX. Water in section, to represent, 30 Wavy lines, 33 Wells, 112 Whatman’s drawing papers, 6 Wheel pen, 31 Width of margin to drawings, 11 \Vindows, position of, in drawing ofliee, 1 \Vood-graining, 32 Wood sections, 32 Woodland, to represent, 36 Working sections, 103 Z. ZONES, horizontal, 38 END. PRINTED BY WILLIAM CLOWES AND SONS, STAMFORD STREET AND CHARING CROSS. PLAN SENT TO BE COPIED Mitsws.,,’ 31:4: 5 MM” ___LA ,4. ___n__.. _L-_. LnflJ PLAN SHEWING WRITING? GAUGED f? ff 7:11; '7 L. A E (9: INSPon Tondcm kit-4w York PLAN TRACED BY JUNIOR HAND. PLATE 2. . J— I; PLAN FINISHED. {A “ PLAN Rafi’n'e’d to : \\ / /wa IVaod/Fbeld? 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Hmiwntal/ Jada sz‘ (71L .YmIna a I 2 3 4 .5 6’ 7 8151411471153 50min a) In 0 50 101‘ 150 200 .950 .7047 350 m‘r‘n'rtrrm'rrn‘rTrn— x r x J L .1 nnnnnn L 1 n x L l u 'IZ ELLV'Iél JAInnmdm L'n'h. E 82 FIN .Spon. London 8:. New Ycrk PIECE OF MARINE ENGINE OF H.M.S.S. “RESEARCH? '38 ':I_I.‘r"Id .P L“ ‘EQ. SKEW BRIDGE. PERMANENT WAY. R A]: r n I vl(:}4 i. »‘r F. \7 Sp-‘Jnlondon &New York /./1/nmmu7./M/I , rt "Mt [A \\\ . 11%)!qu ,v/l I/r‘lv ”VII/10117] I! ~ W23” ‘ "tz‘fltiimpwfi v I WM 7;: .(...".'.'.':::;‘.‘.".':.ma. smzmmzmxw é :mmmmuu PLATE 25. MT‘KE'FN Afiofl 1.75531 x-fxiriflcuigw H H PLATE 26 . METHODS OF REDUCING OR ENLARGING. BY SQUARES Q\ \ ( /\ ( BY ENGLISH PEN TA GRAPH, \0 BY FRENCH PENTAGRAPH. ‘ 0 K E 0 °\ and (A Phtwqqlvlp/W E k YN .Spon. Landon 34c New York. i ll _ _—~i’1i%5g:aé’_—Jfiv “"i 1-5 #5571; PLATE 27. EXTERIO . 1». E ME spECLonaon 2e New Yuri" 48;.Alaflaéyi 31.x”: 28. Depositary Rodks. 1.5g] ("my Mum .asunam I @141»de Qty. #1353 (7mm- zeamm- Mark 75% I.(.::',l}6‘1uwd'rmd&(hnlll . HgfiaId/(Xlgy, Emmi/sfiuni L! Malawi, ”filial: Sand _ ' . 13%(51111 [(115 If: diff-77L {7:1} 'I] I:_ 7677111! (’nidchFIlllmlz'uIfl ’0 @4114!" gzilh‘ J7mlc. .9 Mmymu Smubdmu? V :D‘lllylzmiarl..fmll(mum . (ball 1mm 01-. 11mm" ‘01: (; Cmilk‘tvntv (in? with 122111 . 5 maninfiMI .r Lunmlmw , {bul (I1 4!?”(111’d5mulo1umz mmidé 070w» 3 ”Ealmdlpw RockarfiLimmt/rm‘ . 2 -fuudntvmafllysfi .Vlzmn'. (aria/(£11111: 07411:, Idncous Rocks. napalm/law.“ s— » »-~._.4,r,, __ [:11 M11311 L and; «fanfi. iimwm "J‘u‘u' [IF .lU-‘iux. , E911 “WV. é YorE ‘ at FN Span‘london It» ew E PLATE 29. .8. .1 SIGNS usao m INDIAN & COLONIAL PLANS. IéIrgI-aph, _I-_I. ~~_T_ funk Road MM) :: le'h'l'd D? D? Hammad ........................................ MIIILIII/ (7" Wm fill/Id, orEmIIwflrmmt W Half/es with Few M River with [shuuic‘zg/fi-R Ihn/er m7. 51ml Bank Sit/III Sluice (£ch \_ laid: or Ttmk k Salt Pam; Scott/l. ‘Hdls Rulge pr Hills “ \ '\ Hills wit/L Hairs Bax/(me Garden Palm, Garden Wllage/ Fer/1f Flying Bridge, 1&5 " .} HmdmxBa/wr WW Md Fort fiwka Fart Daverwd leaye Hmmmt Survey Stalin/w Secoizdar'y 1).” flag 7?)!“ SLU'VQ/mg (5 Q X A A F ,B.,A1zazznda- lit/L: LI E 5; F N SPOILLOHdOY‘. 5:.NOW bek, T'LATEWQQ; [—1 3011 GUZUIL SIGNS uszo m INDIAN & COLONiAL PLANS. fir Salt Clunvlagy 51H; Fara/1y Indigo Factory Sugar Emmy Pm, Office,- Dalc Bungalvw P (711?? 0r 77“”qu 8m? J/agiab'atek .Eafdzmy {3 Sicily ,7. .thfl’d Ikuscsi’ifi [3] Q QMIhmm’dan,’ Mosqulj f f j i fflndno 123"ka Q .1. Sig/m1 Stuff A Telegrvwh wagr ,Boundwy I‘fllw‘ _ i; Wmdtn Boundary Pbst fl- Paola, Well 161th WEZL Ion’ szglgs Grass Jungles Jhmv Jungle *1: .g:& Jllfld J I: ’ Tamaruzd flees i 2G": :“lfi if ff m Bamboo Wit} kff {WE 45¢? Salt Waste Salt Waste with Junglr Mimgoe fipe/ Cocoa Ml; Yi'ees Bezel Nab Trees Swim? @953 {g flees gateway Date fives W T I 1' ,Palm/ or Tar Twas * Rail Road EAIAIMLde: ‘15—:1/1; E W <__A_ E &F.N,Spon ,Lonclon 8: New York. PLATE _: . L: L] Te'lc (11L Punt Vrdrw‘s Aft/duty Pits Afiliea‘ 51531117554 Encmnpm/I ”198 Burnt .Barr’icr’ Fltld .Plktcr anr] Limba- MILITARY aliaul: ("agility \ v SIGNS AND A .‘ ( Air/[1‘90 n- 0mm Rd A- I 7;?"(3/“15‘ x" ”(33ch {Ar 77"!!(7).>‘ ""2? [HII‘lN/ILV Engaywi Cb (I‘ll filly En (HINIIIPIZ 5% is? 21,,,c/'...(?:t!!_l_t.u' ! i Hmmunitjcn "599m and Lllfllle‘l’ FORTIFICATIONS. v‘v; mr{ Bur/x In {I '1-7urlnru'rlf ('mmm (hm/11V Engur/C/l Par/r T 1; III a]; 1; (runs on,- A/orc/I .| n ; a Gun 13an ImpamNt {hr 17:54121/3: Baggage Wzgqmns i r ['Irr'ufisd Castles \ (Kasai \_ L BASTIONED FORT wum LUNETTES. m ““3 I. 8¢F,N. SponV London & New York. 15' AlaamJa', Lu]: . J PLATE 33. IL -I L As SHEWN BY HAND ON PAPER, PORTION OF MINING PLAN‘SHEWING PILLAR WORKINGS. [~ ‘17—’71 6 l '1 r . AS SHEWN BY ENGRAV/NG OR LITHOGRAPHY~ n. JL H [-r m..- #1” W”) w—wn ““ 1 7 \ I. I \\ a 4. v, l .4 7,7 —. ~ 4— ~r 57/31 . , a"; ,4‘{/// x2/Airei.” .x‘ ¢//§{: rl/ 727/277. ‘— 1.2 gm / ’47,, /// nu // A 3 _\“.\ \ \\‘ \ ~ \~Z~‘ ‘ ‘~.\\ \:~‘ U. HH References . 77w Downcast/ «Shaft. Alr SW. Air Doom: “.2 ‘ E &'F.N.Spon 1.01110an Nevaork. CM \ 9‘3 . ‘Q ~-{‘\\ \3 \\\\\\1 »——» Dz'reatl'on/ 0/" Vandal/y Gamma Rx . Parditm/ of Regulators ("n/Air Curran / E. a F. N. SPer’PSAREQENTPUBLIGATIONS. ' SHORT LOGARITHMS. SHORT LOGARITHMIC AND OTHER TABLES, intended to facilitate Practical Calculations, and for solving Arithmetical Problems in class. 8220, Cloth, ls. 6d. ; sewed, 15. GAS WORliS. Instructions for the Management of Gas Works. By W. C. HOLMES, Engineer and Contractor for Gas \Vorks, Whitestone Ironworks, Huddersfield. Demy 800, Cloth, 48. DICTIONARY OF ENGINEERING. SPONS’ DICTIONARY OF ENGINEERING, CIVIL, MECHANICAL, MILITARY, AND NAVAL, with Technical Terms in French, German, Italian, and Spanish. 3100 pp., and nearly 8000 Engravings, super-royal 8V0, in 8 divisions, cloth, 13s. 6d. each .. .. .. 5?. 8s. ’ ,, half morocco . . . . . . . . . . Gl. 83. 8 ,, French morocco . . .. .. .. .. Tl. 43. Complete in 3 vols, cloth .. .. .. .. .. .. 5l. 5s. Bound in a superior manner, half morocco, top edge gilt, 3 vols. Gl. 12$. Imperial 4250, Cloth, 2l. 2s. IRON AND TIMBER BRIDGES. Iron and Timber Railway Superstructurcs and General \Vorks; giving Dimensions and Quantities for the Standard 4 ft. 8% in. gauge, and the Metre 3 ft. 3% in. gauge, with some Earthwork Tables and Outlines of a Specification and requirements. By J. \V. GROVER, M. Inst. C.E. STEEP GRADIENTS ON RAILWAYS. A Treatise on the Improved Method for overcoming Steep Gradients on Railways, whereby an ordinary locomotive capable of hauling a given load up a gradient of 1 in 80, can take the same up 1 in 8. By HENRY HANDYSIDE. 8110, 15. ECONOMY IN THE USE OF STEAM. A Statement of the Principles on which a Saving of Steam can best be effected. By FRANK SALTER, BSO. Crown 8120, Cloth, 33. 6d. Crown 8210, Cloth, 53. COM PENSATION S : A TEXT-BOOK FOR SURVEYORS, In 'l'alnulatcd Form. By BANISTER FLETCHER, Associate of the Royal Institute of British Architects. Inzperz'dlILItoJIOs. Gd. THE ORNAMENTATION OF THE TRANSITIONAL PERIOD OF BRITISH ARCHITECTURE. 20 Photo—lithographic Plates. No. 2, Part I. By EDMUND SHARPE, M.A. Imperial 4to, 218. THE MOULDINGS OF THE SIX PERIODS OF BRITISH ARCHITECTURE. No. 3. By EDMUND SHARPE, M.A. 8vo, sewed, 25. RAILIVAY SIGNALS. A Treatise upon Railway Signals and Accidents. By ARCHIBALD D. DAWN AY, Assoc. Inst. CE. THE JOURNAL OF THE IRON AND STEEL INSTITUTE. No. l. 1874. 8170, sewed, 73. 6d. London: E. & F. N. SPON, 48, eating Cross. Ne}; York: 446, Broome Street. JustPublished, in crown 8vo, cloth, with Illustrations, 5s. WORKSHOP RECEIPTS, FOR THE USE OF MANUFACTURERS, MECHANICS, AND SCIENTIFIC AMATEURS. BY ERNEST SPON. THIS WORK CONTAINS RECEIPTS FOR Bookbinding. Bronzes and Bronzing. Candles. Cements. Cleaning. Colourwashing. Concretes. Dipping Acids. Drawing Office Details. Drying Oils. Dyeing. Dynamite. Electro-Metallurgy—(Cleaning, Dipping, Scratch - brushing, Batteries, Baths, and Deposits of every description). Enamels. Engraving on Wood, Copper, . Gold, Silver, Steel, and Stone. ' Etching and Aqua Tint. Firework Making — (Rockets, Stars, Turbillons, Candles, balloons, and minor Fireworks. Fluxes. Foundry hIixtures. Freezing. Rains, Gerbes, Jets, 1 Fires, I Lances, Lights, Wheels, Fire- -, Fulminates. Furniture Creams, Oils, Polishes, Lacquers, and Pastes. Gilding. Glass Making. , Glass Cutting, Cleaning, Frost- ing, Drilling, Darkening, Bend- ing, Staining, and Painting. Gold. Glues. Graining. Gums. Gun Cotton. Gunpowder. . Horn Working. Indiarubber. Inks—(Writing and Printing). J apans, J apanning, and kinder I processes. I Lacquers. Lathing. Leather. Lubricants. Matches. Marble Working. ‘ Mortars. Nitro-Glycerine. I Oils. Paper. Painting in Oils, in Water Colours, as well as Fresco, House, Transparency, Sign, and Carriage Painting. Paper Hanging. Pigments. Photography. Plastering. I Pottery—(Clays, Bodies, Glazes, Colours, Oils, Stains, Fluxes, Enamels, and Lustres. Polishes. Scouring. Silvering. Soap. Solders. Tanning. Taxidermy. Tompering Metals. Treating Horn, Mother-o’-Pearl, and like substances. [of. Varnishes, Manufacture and Use Veneering. Washing. 1 Waterproofing. I Welding. VVhitewashing. Besides Receipts relating to the lesser technological matters and processes, such as the manufacture and use of Stencil Plates, Blacking, Crayons, Paste, Putty, Wax, Size, Alloys, Catgut, Tun- bridge Ware, Picture Frames and Architectural Mouldings, Compos., Cameos, and others too numerous to mention. London: E. & F. N. SPON, 48, Charing Cross. New York: 446, Broome Street. 13 v; ‘ 3'33“? M‘ U.C. BERKELEY LIBRARIES . mm\mIlglglglgwlml“mum "‘A_-r,fir'mll . 3-5m..;q. g... rm .m.» : x? .. Swan .. 7,. .. .z . . , _. :1; . f __ r u 5 n .5 y ‘ w. : i J .. _ . 5.. w 4 \ . 5 , . ~ , . ‘ / , , , , 4 , a mu. $32. . pH .r..9r.:1 .5..r.v.1...i£ ...\...A,...:. . , ,:..v....v£v.l.vx. .