  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. The Drawing Office.—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 circumstances 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 The drawing table should be placed under the window; it should have a breadth of about 2 feet 6 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 rounded over. 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. Instruments.—All drawing instruments should be of the best workmanship, for it is impossible to obtain accuracy with imperfect tools, and they must be kept in order 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 sufficiently 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 instrument 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 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 atmosphere 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 producing 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 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 HH is the best. The most suitable qualities of lead are those which are the most easily rubbed out; these qualities are sometimes gritty, but this defect is more than compensated 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 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:—
The sizes considered best, and almost universally used for engineering 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 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 cockling 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 3/8 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 adjoining 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 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 drawings, 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 × 20 inches, and 40 × 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 8s., or if extra stout, 16s. A much less expensive mode of obtaining tracing paper is to make it one’s self. Common silk or tissue paper may be purchased 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. 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 1/10, 1/8, 1/6, 1/5, and 1/4 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 subdividing 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 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 abrade 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 indiarubber 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 surface. 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 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. When 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. Whenever 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. When a point has to be determined by the intersection of circular arcs or straight lines, these should not meet at an angle less than 30°. In dividing a line into a number of parts, instead of setting off the part repeatedly 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 No. 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-paper, 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 drawing a line, or for trying a tint when colouring. Care should be taken not to leave too narrow a margin, for nothing detracts more from the appearance of a good drawing. 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 11/2 to “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 11/2 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 3/8 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 11/2 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 In joining sheets of tracing paper, the joint should never be made more than 1/4 inch broad. 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 7/8 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 1/8 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 downwards Some drawings, such as large plans of estates, have frequently to be varnished. This operation requires some skill, and can be satisfactorily 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 varnished, 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 drawing-board get accidentally dented, an application of water to the part will, within certain limits, bring it up to its proper level. Section II.—Geometrical Problems.To bisect a given Straight Line.—Let AB (Fig. 1) be the given line. From A and B, with any radius greater than 1/2 AB, draw arcs cutting each other in C and D; then the line joining CD will bisect the line AB as at E. Fig. 1. Fig. 2. Fig. 1. Fig. 2. To erect a Perpendicular to a given Straight Line.—Let it be required to erect a line perpendicular to the point B (Fig. 2) in the line AB. From any point C above the line, with radius BC, describe an arc as ABD; join AC and produce the line until it cuts the arc in D, and join DB; then will DB be perpendicular to AB. Fig. 3. To divide a Line into any number of equal parts.—Let it be required to divide the line AB (Fig. 3) into five equal parts. From B, at any angle, draw BC, and on the line BC 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 angle coincide with the points A and 5, and to the other side apply a straight-edge D; 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 AB, we shall have the line AB divided into five equal parts through the points 1', 2', 3', 4'. To draw a Line making, with another line, a given Angle.—Let it be required to draw a line making with the line AB (Fig. 4) an Fig. 4. Fig. 5. Fig. 4. Fig. 5. To bisect an Angle.—Let BAC (Fig. 5) be the angle which it is required to bisect. From A, with any radius, describe an arc cutting the lines AB and AC in D and E; from D and E, 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. 6. Fig. 7. Fig. 6. Fig. 7. To construct an Equilateral Triangle on a given base.—Let AB (Fig. 6) be the given base. From A and B, with radius AB, describe arcs cutting each other in C; join AC and CB, which will complete the required triangle. To 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 6, 5, and 4. Lay down the base AB (Fig. 7), making it equal to 6 divisions of the scale; from A with radius equal to 4 divisions, and from B with radius of 5 divisions of the scale Fig. 8. To construct an Angle equal to a given angle.—It is required to draw a line making with the line DE (Fig. 8) an angle equal to that contained by the lines BAC. From A, with any radius, draw an arc FG, and from D, with the same radius, draw the arc HI, and make HI equal FG; then a line drawn from D through I will make, with the line DE, an angle equal to the angle BAC. Fig. 9. 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 45° respectively. 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 G will complete the construction of the required triangle. Fig. 10. To describe a Circle which shall pass through three given points.—Let ABC (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 ABC as required. Fig. 11. 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 OB, Fig. 12. To find the Centre of a circle.—From any point in the circumference, as B, (Fig. 12), describe an arc cutting the circumference in A and C, and from A and C, with the same radius, describe arcs cutting the first arc in two points; through the points of intersection draw lines to the interior of the circle, and the point O where these lines intersect will be the centre of the circle. Fig. 13. To draw lines which shall be Radii of a circle, the centre being inaccessible.—Having laid off on the circumference of the arc, the distances apart of the radii, as A, B, C, &c. (Fig. 13), from each of these points, with radius greater than a division, describe arcs cutting each other as at a, b, c, &c., join A a, B b, C c, &c., and the lines so drawn will be radii of the circle as required. Fig. 14. To construct an Oval, the width being given.—Draw the line AB (Fig. 14) equal to the width, and bisect AB by CD (see Fig. 1). From the point of intersection E, with radius EA or EB, describe the circle ACBF, and from A and B through F, draw the lines AG Fig. 15. 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 AB, describe an arc cutting the perpendicular in C; also from B and C, with the same radius, describe arcs cutting each other in D; join CD and BD, which will complete the required square. Fig. 16. To construct a square that shall be a Multiple of any given square.—Let ABCD (Fig. 16) be the given square, and let it be required to construct a square that shall contain 2, 3, 4, &c., times its surface. Draw the diagonal BC, then the square described on BC will be double the square ABCD. Lay off DE, equal to BC, and draw CE; then the square described on CE will be three times the square ABCD. In the same manner lay off DF, equal to CE, and the square described on CF will be four times the square ABCD; and so for any multiple of the square ABCD. Fig. 17. To construct a square that shall be equal to 1/2, 1/4, &c., of any given square.—Let ABCD (Fig. 17) be the given square. On AB, as a diameter, describe the semicircle AGB, and erect at the centre E the perpendicular EG. Draw GB, 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 Fig. 18. To construct a square that shall be in any Proportion to a given square.—Let ABCD (Fig. 18) be the given square. It is required to construct a square which shall be to ABCD as 2 is to 5. Upon the side AB as a diameter describe the semicircle AFB, and divide the line AB into five equal parts. At the second point of division erect the perpendicular EF and join AF; the square described upon AF will be to the given square ABCD as 2 is to 5. Fig. 19. 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 AB, one that shall be similar to AEFG. Produce AE and lay off the given base from A to B; draw the diagonal AG and produce it indefinitely. Erect a perpendicular to AB at B, and from the point D where it intersects the diagonal produced, draw DC perpendicular to AF produced. Then ABCD will be similar to AEFG. All rectangles having their diagonals in the same line are similar. Fig. 20. To describe a regular Pentagon on a given line.—Let AB (Fig. 20) be the given line. Bisect AB at C, draw CF perpendicular to AB, and make CD equal to AB. Draw AD and produce it Fig. 21. To 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 ABCDEF. Fig. 22. To draw a Parabola, the base and height being given.—Let CA (Fig. 22) equal half the base, and CD the height. From the point D draw DE parallel and equal to AC, and from the point A draw AE parallel and equal to CD. Divide DE and AE similarly, making the end E of AE correspond to the end D of ED. Through 1, 2, &c., in DE draw 1, 1; 2, 2, &c., parallel to DC. 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 CA. Fig. 23. Fig. 24. Fig. 25 a. Fig. 25 b. Fig. 23. Fig. 24. Fig. 25 a. Fig. 25 b. To draw an Ellipse.—I. By means of a piece of string and pins. Place the diameters AB and CD (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 EFC and pass it round the pins, stretch the string with For this last method, which in practice is by far the best, we are indebted to Binns’ ‘Orthographic Projection.’ Fig. 26. To construct a Semi-Elliptical Arch.—The span AB (Fig. 26) and rise CD being given, divide CA and CB into any number of equal parts. Through the point D, draw EF parallel to AB, and from the points A and B erect the perpendiculars AE and BF. Divide AE and BF similarly to CA and CB. Produce CD and make CG equal CD. From D draw lines to the points 1, 2, 3, &c., in the lines AE and BF; also from G draw lines through the points 1, 2, 3, &c., in the line AB, and produce these lines until they cut those drawn from D to the corresponding numbers in AE and BF. Through the points thus obtained draw the curve of the ellipse. Fig. 27. To draw the Gothic Equilateral Arch.—From the points A and B (Fig. 27), with radius AB equal to the span, describe the arcs BC and AC. By joining C to A and B we obtain an equilateral triangle from which this arch derives its name. Fig. 28. 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. 29. To draw the Gothic Obtuse 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. Fig. 30. To draw the Gothic Tudor Arch.—On the line of springing AB (Fig. 30), take any two points as F and G, so that AF is equal to GB. Draw FE and GD cutting each other on the bisecting line through C; from F and G, with radius FA or GB, describe the short arcs, and from E and D, with radius EC or DC, describe the arcs meeting in C. Fig. 31. To draw the Moorish 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 Fig. 32. To draw the Gothic Ogee Arch.—The most pleasing form of this arch is that constructed on an equilateral triangle, in the following manner. Having drawn the equilateral triangle AB C (Fig. 32), draw FG parallel to AB. Bisect the sides AC and CB and produce the bisecting lines to FG and H, which will complete the triangle FGH similar and equal to the triangle ABC. From H, with radius HA or HB, describe the arcs AE and BD, and from F and G, with the same radius, describe the arcs EC and CD. Fig. 33. Fig. 34. Fig. 33. Fig. 34. To draw the Roman Cyma Recta and Cyma Reversa.—Join AB (Fig. 33) and bisect AB in C. From the points C and B, with the distance BC, describe arcs cutting each other in E; and from A and C, with the same radius, describe arcs cutting each other in D; from D, with the same radius, describe the arc AC, and from E describe the arc CB. The projection of the upper end of the curve over the under, as FB, is generally equal to the height, AF, of the moulding. The same description applies to the Cyma Reversa (Fig. 34) letter for letter. Fig. 35. To draw the Gothic Trefoil.—Having drawn the equilateral triangle ABC (Fig. 35), bisect the angles and produce the bisecting Fig. 36. To draw the Gothic Quatrefoil.—Draw the square ABC D (Fig. 36); bisect the sides of the square at IKLM and produce the bisecting lines to EFGH. From the angles ABCD of the square as centres, with radius AI or AM equal to half the side of the square, describe the arcs PNRS, and draw the outer concentric arcs. The circles, completing the figure, are drawn from the centre O of the square. Fig. 37. To construct the Gothic Cinquefoil.—Having drawn the regular pentagon ABCDE (Fig. 37), bisect the angles and produce the bisecting lines to FGHIK, which will cut the sides of the pentagon in a, b, c, d, e. From ABCD and E as centres, with radius A a or A b, equal to one-half of the side of the pentagon, describe the arcs LMNPR, and draw the outer concentric arcs and those concentric with them. The circles are drawn from the centre O of the pentagon, as in the preceding example. Section III.—Lines, Dots, and their Combinations.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 representation 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 Lines.—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 difficult 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 difficulties in ruling a straight line with 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 lakes, horizontal straight lines are drawn parallel to each other and at equal distances apart over the surface, as shown in Fig. 39. Fig. 38. 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 Fig. 40. Lines of uneven thickness.—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 increased 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. 41. Fig. 42. Fig. 41. Fig. 42. Fig. 43. The Broken Line.—The broken line, shown in Fig. 41, 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 considerably 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 Fig. 44. The Dotted Line.—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 architectural 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 different 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 difficulty 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 abandoned by draughtsmen. But if the instrument were better constructed and carefully handled, it might be made to do good service. Fig. 45. Fig. 46. Fig. 45. Fig. 46. Fig. 47. Fig. 48. Fig. 49. Fig. 48. Fig. 49. Combinations of Straight, Broken, and Dotted Lines.—Combinations of the foregoing lines are used for various purposes. Some Fig. 50. 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 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 The Wavy Line.—The wavy line is very important in topographical drawings, as it is employed to represent running water, and frequently large bodies of standing water to which motion is communicated 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. Fig. 51 shows the manner of employing these lines. In representing 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 distance from it. This gradual diminution of the thickness of the lines, and increase of the spaces, must be continued to the middle of the 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 inadmissible. 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. Fig. 52. Grass-land.—Various combinations of lines and dots are used, conventionally, to represent certain natural features of common occurrence. As far as convenient execution will allow, these signs are made to resemble the objects denoted. Thus the sign for grass-land consists of groups of short lines, arranged like tufts of herbage, as shown in Fig. 52. Each tuft is composed of five or seven lines converging 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, Fig. 53. Swamps and Marshy 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 interspersed 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 otherwise an offensive appearance will be produced. This caution applies equally to all signs. Fig. 54. 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 Fig. 55. Fig. 56. Fig. 55. Fig. 56. Woodland.—Trees are generally shown in plan (as in Fig. 55). The outline is circular in character, and, to have a good effect, it 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 cast by parallel rays of light inclined 45° 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. 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 Fig. 57. 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. Fig. 58. Contour Lines.—Suppose a cone AB C (Fig. 58) cut at regular vertical intervals apart by a series of horizontal planes 1, 2, 3. The intersections of these planes with the surface of the cone will give lines upon that surface; and it is obvious that the cone may be represented in plan by the projection of these lines, as shown in the figure. To obtain this projection, draw the horizontal line DE, and from the apex of 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 DE as a centre, with radii equal to the distances from this point to those where the lines from the sections meet DE, 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 elevation, we have only to draw horizontal lines at the given distance apart, and from the points in DE 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 b, a portion of the normal DE, as a base, erect a perpendicular b c, equal in height to the distance of the sections apart, and join a c. The hypothenuse a c then represents that portion of the surface of the cone which is included between the two contour lines, and of which 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 projections 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 representation in plan by contour lines of an irregularly shaped object, and the latter an elevation of the same object projected from the plan. Fig. 59. Fig. 60. 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 Section IV.—Colours.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 topographical 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 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 immediately 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. While the paper is drying, the tints may be prepared. To ensure satisfactory results, care must be taken in the preparation 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 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 The alternate or double tint consists of two colours applied alternately, their edges being made to blend into each other. The application 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 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. White 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 surfaces which are parallel to the plane of the picture, and therefore equally distant from the eye, should receive a tint of uniform intensity; (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 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.
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 Water.—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. Marsh.—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 Sand and Gravel.—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 flat-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 Cultivated Land.—Cultivated land is represented by a flat-tint of burnt sienna. Uncultivated Land.—Uncultivated land or brushwood is represented 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 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. Fig. 61. Fig. 62. Fig. 61. Fig. 62. Application of Shade Lines.—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 definitions 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 Fig. 63. Fig. 64. Fig. 63. Fig. 64. The same principles are observed in the end elevation of the hollow cylinder, shown in Fig. 63. The extreme rays meet the circumference in the points a and b; consequently the surface a c b is in light, and the surface a d b is in shade. The middle ray meets the surface perpendicularly at the point c, 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 d. The shading of the inner circle will be the converse of the outer. Fig. 64 shows a plan of the same object. Fig. 65. Cylindrical Surfaces.—Let a b c d, Fig. 65, be a plan, and k l n m an elevation of a cylinder. The portion a c b is in light, and the portion a d b is in shade, of which latter portion a and b are the edges. From the points a and c draw vertical lines e f, g h. Then will e f be that part of the cylinder upon which the light falls perpendicularly, or the lightest part, and g h the edge of the surface in shade, or that portion of the surface 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 k l 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. Fig. 66. Shading Lines.—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 hexagon, the surface c is in shade, and to represent this 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 b is in light, but the rays fall upon it obliquely; 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 Fig. 67. 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 present 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 preceding. 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 on the other side. The thickening 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. Fig. 68. Fig. 69. Fig. 70. Fig. 71. Fig. 68. Fig. 69. Fig. 70. Fig. 71. 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. 68, 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 Fig. 72. Shading Lines in Topographical Drawings.—The shading lines put upon mechanical drawings are merely accessories used for purposes 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 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 1/20, corresponding to a vertical interval of 25 feet, will be 20 × 25 = 500 feet, which, on a scale of six inches to a mile, will be represented by a length equal to 500/5280 × 6 = 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 1/20, continued over a space of 0·566 inch. Fig. 73. 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 45° will not reflect any. The drawing of the hachures presents certain difficulties of execution 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 hachures 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 1/4 inch to 3/4 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, b, 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 approximated 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 Fig. 74. 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 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 declivity 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 5°, from a level up to a slope of 45°, which is the steepest Fig. 75. Larger illustration (48 kB). To find the proportion of black to white in the foregoing scale for any given slope:—Subtract the given inclination from 45° for a denominator, and put the given inclination for a numerator. In the scale, as drawn in the figure, the variations are by 5°; but it is obvious that a scale may be drawn in the same manner to mark smaller variations, if thought desirable. 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:—
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:—
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 221/2°, which thickness must be suited to the scale, and to the degree of fineness and finish it is intended to give the drawing. Generally, 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, 1/1 or 45° for the greatest and 1/64 or 0° 53' 43 for the smallest. The largest scale that will admit of conveniently drawing the lines of greatest descent is 1/600 full size, or about 83/4 feet to a mile. The vertical distance between the horizontal sections is generally taken as 1 yard. Hence to a scale of 1/600 the least width of zone will be 6/100 inch, and the greatest 6/100 × 64 = 384/100 inches. The distance between the shading lines is 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 3/10 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 1/60 and the scale 1/600, the width of zone will be ·06 × 60 = 3·60 inches, and by the rule we have 3·60 + ·316 = 3·916 = 0·244 inch. Another rule is:—To a fourth of the distance between the upper and the lower curves of any zone, add 75/1000 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 1/1 the thickness of the shading lines is equal to 2/3 of the distance between their centres, 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 hillside. 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 1/6 of an inch on the steepest slopes, and 3/4 of an inch on the gentlest. Fig. 76. 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 sufficient 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 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 Fig. 77, it would give rise to an error in principle; for soon after leaving the summit we should have too few lines of descent. When the hill has been covered with shading lines, the base and the summit must be 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. Fig. 77. When the curves are parallel or nearly so, the shading lines are Fig. 78. 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 Colours.—Frequently in topographical drawings, and still more frequently in mechanical drawings, colour is resorted to to produce the effect 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. Hill Slopes.—In representing slopes, the tint employed to give the effect of that produced by the ink lines already described is composed 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 accomplish Cylindrical Surfaces in Mechanical Drawings.—In shading cylindrical surfaces and drawings generally, three methods are employed. One of these is known as softening off, 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 preceding one is quite dry, as the colour will spread more evenly over a damp surface. The previously applied coat must, however, have been 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 polygon 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. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
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