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 A B, C D, one half being on A B 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 finallythe 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 22shows a piece of marine engine carefully coloured to indicate the material of which the several parts are made, andPlate 23contains 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, isometrical, 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. ThusPlate 24is a perspective drawing, such as are frequently made by architects, requiring a high degree of skill and taste on the part of the colourist. AndPlate 27contains 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, and27.
Duplicates of drawings are very frequently required; so frequently, indeed, and in such numbers, that their production constitutes a large portion of the work executed in every drawing office. Generally, 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,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 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 centre 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 incorrect 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, andcompletely 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 described above. The intersection of detail with these lines may then be readily and correctly transferred from the copy to the fair sheet.
—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 gummed 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, thecolouring 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 theglass 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 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 blackleadpowder 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 transferring 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 transferred 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 required in this process,making the tracing,transferring, andinking 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.
—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. When 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 onPlate 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 forming these squares on the copy weretransferred 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 thePantographand theEidograph. Both of these instruments are shown onPlate 26. The following very complete description of the pantograph and the eidograph is given in an excellent work on ‘Mathematical Drawing Instruments,’ by W. F. Stouley, of Holborn, London.
“The pantograph, as represented on theplate, 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 correctly, 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 perpendicular 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: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 drawing. 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 theerect mannerand thereverse 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 theerectmanner 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 theplate, 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—2,1—3, 1—4, &c. 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 Pantograph in the Erect Manner, the Fulcrum being placed in the Socket upon the Outside Rule, and the Pencil upon the Central Rule.
Table of Reductions by the Pantograph in the Erect Manner, the Fulcrum being placed in the Socket upon the Outside Rule, and the Pencil upon the Central Rule.
“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 thereversemanner 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 generally 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 instrumentwhich 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, the Fulcrum being placed in the Socket on the Central Rule, and the Pencil in the Socket upon the Outside Rule.
Table of Reductions by the Pantograph in the Reverse manner, the Fulcrum being placed in the Socket on the Central Rule, and the Pencil in the Socket upon the Outside Rule.
“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 instrument 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 isrequired 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 pantograph; 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.
“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 always be 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.
“TheEidographwas 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 on 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—as, for instance, those frequently attached to leases and conveyances.
“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 thatchiefly 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 eidograph 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,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 proportions 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 Proportions.
“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:
—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.
“For instance, let it be required to reduce a drawing in the proportion of 3 to 5.
“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:
“If the slides of the instrument be set to 38·46, it will be, practically, sufficiently near.”
Photography is also frequently resorted to for the purpose of reducing 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 disappointment at the results obtained. Thus blue, for instance, showsvery indistinctly, and yellow surfaces in coloured drawings come out very dark.
—The drawings required 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 sufficient.
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.
To compute the Sides of Triangles.—Let A B C be the angles of a plane triangle, andabcthe sides opposite. Then, for right-angled triangles, we have
and for oblique-angled triangles we have