ENVIRONMENTAL 
 DESIGN 
 LIBRARY 
 
 GIFT OF 
 
 John Staley 
 
MECHANICAL DRAWING 
 
 TECHNIQUE AND WORKING METHODS 
 
 FOR TECHNICAL STUDENTS 
 
 BY 
 
 CHARLES L. ADAMS 
 
 PROFESSOR OF DRAWING AND DESCRIPTIVE GEOMETRY IN THE 
 MASSACHUSETTS INSTITUTE OF TECHNOLOGY 
 
 SIXTH EDITION 
 REVISED 
 
 BOSTON 
 
 PRESS OF GEO. H. ELLIS CO. 
 1913 
 
DESIGH LIBRARY 
 
 COPYRIGHT, IQOS, BY CHARLES L. ADAMS 
 
PREFACE. 
 
 A thorough preparation in drawing for a course in engineering or in archi- 
 tecture should include the study of descriptive geometry or the principles of rep- 
 resentation ; the training of the sense powers to give precision and facility 
 in the technique of drawing ; and instruction in practical freehand drawing. This 
 book, treating of the second of the requirements named and of technical methods 
 in execution, has been prepared for use in the first-year courses in drawing and 
 descriptive geometry at the Massachusetts Institute of Technology. It is not 
 intended as a prescribed set of exercises to be taken in the same form by all stu- 
 dents, but rather as a collection of material sufficient to enable the teacher, by 
 judicious selection, to lay out the work of a course, whether designed solely for 
 educational training, or as an introduction to a particular course in engineering or 
 architecture, or for a further specialization to meet the need of individual students. 
 
 To make up as far as possible for the inevitable loss, in large classes, of indi- 
 vidual instruction in details so necessary for the best results in technique a 
 large number of explanatory cuts has been introduced and minor processes have 
 been fully explained. This detailed presentation, together with the subjects con- 
 sidered briefly in the last chapter, should, it is believed, make the book useful for 
 reference in the student's future professional work. 
 
 The subject of projection, usually presented in text-books on mechanical 
 drawing has been here omitted in the belief that, when a course includes descrip- 
 tive geometry, it is unnecessary to give a portion of this subject under a different 
 name. Furthermore, drawing from actual objects appears to be the best educa- 
 tional and practical introduction to descriptive geometry. 
 
 Special care has been given to the originals for the plates, which were drawn 
 strictly in accordance with the directions in the practice exercises. The author 
 desires to express his thanks to Mr. H. C. Bradley and Mr. A. T. Robinson for 
 much valuable help with the text, and to other members of the Institute instruct- 
 ing staff for suggestions and criticism. 
 
CONTENTS. 
 
 CHAPTER PAGE 
 
 I. DRAWING INSTRUMENTS AND MATERIALS ; THEIR SELECTION i 
 
 II. USES AND CARE OF THE INSTRUMENTS AND MATERIALS; MANIPULATION. 14 
 
 III. RENDERING; CONVENTIONS; LETTERING AND DIMENSIONING; COMMON 
 
 WORKING METHODS 36 
 
 IV. STUDY PLATES ON INSTRUMENTAL RENDERING AND CONSTRUCTION . . 59 
 V. GEOMETRICAL CONSTRUCTION , 79 
 
 VI. SELECTION AND ARRANGEMENT 102 
 
 VII. OBJECT DRAWING 109 
 
 VIII. WORKING DRAWINGS 143 
 
 IX. PSEUDO-PICTORIAL REPRESENTATION; ISOMETRIC DRAWING 155 
 
 X. WASH DRAWING 166 
 
 XI. MECHANICAL COPYING; THE BLUE-PRINT PROCESS; PROCESS DRAWING; 
 
 PATENT OFFICE DRAWING 183 
 
MECHANICAL DRAWING 
 
 CHAPTER I. 
 
 DRAWING INSTRUMENTS AND MATERIALS THEIR SELECTION. 
 
 1. Mechanical Drawing the language of engineering, architecture, and the 
 mechanic arts is representation based on descriptive geometry and expressed 
 by means of drawing instruments. In the representation of objects, mechanical 
 drawing deals primarily with actual figure and measurement, and is not in general 
 concerned with the appearance of things. 
 
 2. The Instruments usually required for outline drawing are illustrated in 
 Plates i and 2. Several special instruments and materials for brush work are 
 shown in Plate 3. The following list represents the complete equipment for the 
 drawing exercises here given. In procuring the instruments, it is advisable for 
 the beginner to intrust their selection to an experienced draftsman ; but, if this 
 is impracticable, he should read Articles 3-13 before purchasing. 
 
 1 Set of Instruments. 
 
 2 Drawing Boards, 1 1^ x I5| in. and 17 x 22! in. 
 2 T-squares, 1 5-inch and 21 -inch, fixed head. 
 Rubber or Amber Triangles as follows : 
 
 i 45-45, 4-inch. 
 
 i 45-45, 8 
 
 i 30-6o, 5 " 
 
 i 30-6o, 10 " 
 
 2 Irregular Curves (of the shapes shown in Plate 2). 
 i 12-inch Architect's Triangular Scale (divided into sixteenths of an inch 
 
 and scales cf ^, T 3 g, J, J, f, J, f, i, i J, and 3 in. to a foot), 
 i Pricker. 
 
DRAWING INSTRUMENTS AND MATERIALS THEIR SELECTION. 
 
 Drawing Papers (in a strong envelope, 17 x 22^ in.), as follows : 
 
 3 Sheets Whatman's Half Imperial, cold pressed. 
 
 6 " " " " hot " 
 
 6 " Duplex Detail Paper (cut half imperial size). 
 
 6 " Tracing Cloth (cut half imperial size). 
 
 2 " Rowney's Roll Tracing Paper (cut half imperial size). 
 i Block of White Practice Drawing Paper, 1 1 x 15 in., 24 sheets. 
 i Dozen Thumb Tacks. 
 3 "Koh-i-noor" Pencils, H, 4.H, and 6H. 
 i 6H "Koh-i-noor" Lead (for the compasses). 
 i Fine File, or Sandpaper Pad (for sharpening pencils), 
 i Stick India Ink, super-super, half size, 
 i Slate Ink Slab, with cover, 
 i Emerald Rubber, 
 i Sand Rubber, T 3 g x i x i| in. 
 i Steel Eraser. 
 
 i Agate Burnisher (of the form shown in Plate 2). 
 i Piece Chamois Skin, size about lox 12 in. 
 i Fine Oil Stone, 3-inch (for sharpening ruling pens). 
 
 1 Penholder and Pens, \ doz. each of Gillott's 303, and D. Leonard & Co.'s 
 Ball Point, 521 F. 
 
 2 Camel-hair Brushes (of the sizes shown in Plate 3). 
 
 i Water Glass and Tumbler (of the size given in Plate 3). 
 
 i Medium Sized Sponge. 
 
 i 3-oz. Jar Drawing Board Paste. 
 
 i Sketch Book, 7x8^ in., ledger paper, 100 pages. 
 
 i 6-inch Calipers. 
 
 i 2-foot Folding Rule. 
 
DRAWING INSTRUMENTS AND MATERIALS THEIR SELECTION. 3 
 
 3. The Set of Instruments (Fig. i). The essential characteristic of a good 
 instrument is that, when put in satisfactory working order, it remains so for a 
 reasonable length of time, a condition dependent upon excellence of material and 
 
 Fig. i. 
 
 of workmanship in making the joints and tempering the points of the instrument. 
 The difference between a good and an inferior instrument may not be easily recog- 
 nized through inspection alone, as the appearance of the better grades is extensively 
 
DRAWING INSTRUMENTS AND MATERIALS THEIR SELECTION. 
 
 imitated. To the beginner a set at three dollars may appear quite as good as one 
 at twenty dollars. Hence his guide must be the selling price by a reputable dealer, 
 which is from eight to twenty-eight dollars a set according to quality. For the 
 best results in drawing, and for wear, the best instruments are necessary. A very 
 good set, but not the best, includes : the best imitation of the Alteneder pivot- 
 joint* compass ; Alteneder-style hair-spring dividers ; genuine Alteneder bow 
 instruments and ruling pens. The price for this set (1905) should be about fif- 
 teen dollars. If the student cares to pay the difference in price, it is advisable to 
 substitute a compass with hair-spring adjustment for that which comes with the 
 above set. 
 
 A substitute for a case, 
 Fig. 2, and better adapted 
 for carrying instruments 
 in the pocket, may be 
 made by the student. It 
 is of chamois leather 
 cloth-bound on the edges, 
 if desired and is fitted 
 with pockets of the same 
 material to hold the in- 
 struments. 
 
 4. The Drawing 
 Board (Plate 2) should be 
 of well-seasoned, straight- 
 grained white pine, free 
 from sap and knots and 
 neither shellacked nor var- 
 nished. The cleats should 
 be of the same wood, 
 tongued and grooved, and 
 screwed to the board 
 never glued. To provide 
 for the contraction and expansion of the board, due to atmospheric changes, the 
 screws should pass through slots in the cleat, having a width equal to the diameter 
 of the screw (see Plate 2). With this arrangement the board is less likely to 
 warp or split, since, while the heads of the screws have sufficient bearing to hold 
 the cleats in place, the slots permit the screws to move back and forth in the 
 
 *See section of the head of the Alteneder-style compass, Plate i. Not all compasses having the 
 handle attached to the head, as shown in the cut, are necessarily pivot-joint instruments. 
 
 Fig. 2. 
 
Plate 
 
 COMPASSES 
 
 ALTENEDER STYLE OLD STYLE 
 
 COMPASS PARTS 
 
 RULING 
 PEN 
 
 SOCKET FOR SOCKET FOR 
 NEEDLE. POINT LEAD 
 
 BOW SPACERS BOW PENCIL. 
 
 PRICKER 
 
 (5) 
 
Plate 2 
 
 TRIANGLES 
 
 DRAWING BOARD 
 
 
 
 SQUARE 
 
 FLAT SCALE 
 
 SANDPAPER PAD 
 
 PORTFOLIO 
 
 \\.Aw\vA.A \ ^ J i \ V . \ > . \ X V \ t > \\ 
 
 TRIANGULAR SCALE 
 
 / /./../,/ ,/ ,/ ,/ ,/ ,/,/ .1,1,1,1,1.1,1,1,1,1, 1,1,1,1,1: 1,1,1,1,1 ,1,1, 1,1,1, 1,1 ,1,1,1, 1,1, 1,1, 1:1, 1,1:1..,.] L 
 
 INK SLAB 
 
 STICK INDIA INK 
 
 READING GLASS 
 
 STEEL INK ERASER (SCALP 
 
 BURNISHER 
 
 IRREGULAR OR FRENCH CURVES 
 
 (7) 
 
DRAWING INSTRUMENTS AND MATERIALS -- THEIR SELECTION. 9 
 
 cleats with the expansion and contraction of the board. The outer edge of each 
 cleat should be perfectly straight, and the grain of the wood parallel to the edge of 
 the cleat. When purchasing ask the dealer for a steel straight-edge, and with 
 it test the straightness of the working edge of the board. Another method is 
 as follows : 
 
 (#) To test the straightness of the working edge of a drawing board: Place 
 the board on a sheet of paper laid flat, and upon it, using either cleat as a straight- 
 edge, rule a very narrow line the full length of the cleat. Now swing the board 
 around to reverse the ends of the same cleat with respect to the ruled line, and 
 to bring the same edge of the cleat on to the ruled line. Rule again, and, if 
 the two ruled lines coincide throughout, the edge of the cleat may be regarded 
 as practically straight. The two edges of each of the two cleats should be 
 tested. 
 
 The 'metal edge sometimes attached to small drawing boards is altogether 
 unsatisfactory. 
 
 5. The T-square (Plate 2). The usual T-square is made of pear wood. A 
 better one has the so-called ebony-lined blade. For greatest accuracy, a steel 
 T-square and a special steel edge for the drawing board are necessary, although 
 this T-square tends to soil the paper and to smear dry ink lines. In choosing a 
 T-square, see that the blade is wholly free from nicks and that the grain is straight 
 and parallel to the edges of the blade. The straightness of the blade and head 
 should be tested according to a, Art. 4, or by placing each against a steel straight- 
 edge held between the eye and the light ; if the contact is perfect throughout, no 
 light will be seen between the edges. 
 
 6. The Triangles (Plate 2) are made of wood, hard rubber, or amber. The rub- 
 ber and the amber triangles are more accurate than the wooden ones. The amber is 
 less likely to soil the drawing than the hard rubber, and also permits the lines of the 
 drawing to be seen through the 
 
 triangle often a decided con- 
 venience. In selecting a trian- 
 gle, sight across its surface to see 
 that it is not warped. To test the 
 straightness of the edges, proceed 
 according to a, Art. 4, or place 
 each edge against a steel straight- 
 edge held between the eye and 
 the light, as described in Art. 5. Fig. 3. 
 
 (a) To test the 90 angle : Place the triangle A, Fig. 3, against a straight- 
 edge, and with a very sharp pencil draw an accurate line along the edge ab. If, 
 
io DRAWING INSTRUMENTS AND MATERIALS THEIR SELECTION. 
 
 when the triangle is turned over, as at A', edge ab does not coincide with the 
 
 ruled line, the triangle is not " square." 
 
 (b) To test the 45 angles : After testing the T-square blade, the working 
 
 edge of the drawing board, and 
 the right angle of the triangle, 
 draw with the T-square two 
 parallel lines, ab and cd (Fig. 
 4). With the T-square as 
 shown and the triangle in posi- 
 tion A, draw line ef. Bring 
 the triangle to position A', 
 without turning it over, and 
 draw gh. With the dividers 
 compare the length of lines ef 
 and gh; if they are equal, the 
 45 angles are correct. 
 
 Fig. 4. 
 
 (c) To test the J0 and 6cP angles : After testing the T-square blade, the 
 working edge of the drawing board, and the right angle of the triangle, draw 
 with the T-square line ab (Fig. 
 5). Move the T-square down 
 about \ inch to the position 
 shown; place the triangle in 
 position A, and draw line cd. 
 Turn the triangle over to 
 position A', and draw de. 
 With the dividers, compare 
 the lengths of lines ce, cd, and 
 de ; if they are all equal, the 30 
 and 60 angles are correct. 
 
 7. The Scale (Plate 2) 
 should be perfectly straight 
 
 and free from nicks, all edges thin and sharp, and the graduations very narrow, 
 clear-cut lines. Blunt edges and blurred graduations seriously interfere with accu- 
 racy of measurement. 
 
 8. The Pricker (Plate i). A good substitute can easily be made thus: 
 Whittle out of soft, straight-grained wood a handle about 3! inches long and taper- 
 ing from inch to T 3 g inch in diameter. Break off the eye of a No. 9 sewing 
 needle, and with a pair of pincers push the point of the needle into the smaller end 
 of the handle, taking care to keep the needle accurately in line with the axis of the 
 
 Fig. 5- 
 
Plate 3 
 
 BEAM COMPASS 
 
 ADJUSTABLE 
 T SQUARE 
 
 SABLE BRUSH 
 
 CAMEL HAIR BRUSHES 
 
 ( A brush at both ends) 
 
DRAWING INSTRUMENTS AND MATERIALS THEIR SELECTION. 13 
 
 handle. When the needle has been pushed in about three-fourths of its length, 
 draw it out, reverse it, and force it broken end first into the hole. The needle 
 should project about | of an inch. 
 
 9. The Thumb Tacks. Tacks costing from five to twenty cents a dozen are 
 sufficiently good. Small copper tacks (not iron ones) are sometimes used. The 
 shank of a thumb tack should be slender, the point sharp, and the head shallow 
 and sloping to a sharp edge, that it may not catch the edge of the T-square blade. 
 The shank should be so fastened to the head that, when pressed into the drawing 
 board, it will not push through the head of the tack into the thumb. 
 
 10. The Pencils. The common writing pencil is wholly unfit for mechanical 
 drawing ; only the best hexagonal drawing pencils should be used. 
 
 11. The Pencil Sharpener (Plate 2). A small, fine-cut file is often used for 
 sharpening pencil and compass leads. A convenient and inexpensive substitute is 
 the sandpaper pad (Plate 2). A piece of fine sandpaper, or emery cloth fastened 
 to a strip of wood, say 6 x i.] x ^ in., will do very well. 
 
 12. The India Ink. The best stick ink gives a glistening, jet black line and 
 is satisfactory for brush work, while lines made with cheap inks are likely to look 
 dead, tend to smear easily, and are unsuitable for brush work. A stick, half size, 
 at fifty cents, is the cheapest that should be considered. 
 
 13. The Steel Ink Eraser. A surgeon's scalpel is recommended, as the steel 
 is far superior to that in ink erasers usually found at the stationer's. The length 
 should be about 5-*- in., and the shape as shown in Plate 2. 
 
CHAPTER II. 
 
 USES AND CARE OF THE INSTRUMENTS AND MATERIALS MANIPULATION. 
 
 14. The following pages deal with the technique and ^uork^ng methods of 
 mechanical drawing, independent of the principles of the subject, which are covered 
 by the descriptive geometry. 
 
 The study of technique is principally concerned with the training of the 
 several sense powers manual skill, correct observation, speed, judgment, and 
 taste which must underlie the operations of the expert all-around draftsman. 
 
 Working methods are those dependent upon knowledge rather than upon the 
 sense powers, and, especially, upon experience with the needs and necessities of 
 professional practice. The term also serves to distinguish directly effective and 
 practical methods from those which are purely educational. 
 
 The methods here presented are not set forth as the only ones of value. 
 Draftsmen often differ in their opinion of modes of procedure, influenced naturally 
 by their individual experience or by the traditions and character of the work of a 
 particular office. A beginner, however, should take pains to carry out instructions 
 literally until, having learned to work according to the methods indicated, he 
 reaches a point where he is competent to judge other methods. 
 
 Success in mechanical drawing rests largely on personal attention to many 
 details. The advantage of workmanlike habits should be kept in mind. Avoid 
 lounging on the drawing table, and other lazy habits. Quiet, brisk attention to 
 the work in hand is not only suggestive of one's personal quality, but is also con- 
 ducive to better results in drawing. Keep the instruments and materials in orderly 
 arrangement on the table, not only for the sake of appearance, but also to avoid 
 loss of time in searching for the thing needed. 
 
 The explanations and directions concerning the uses and care of the instru- 
 ments should receive close attention. It is not sufficient merely to read the text, 
 but this reading should be supplemented by an immediate examination of the in- 
 strument or article considered. The names of the instruments and their parts 
 (Plates i, 2, and 3) should be remembered. In the directions for manipulation, 
 the processes must not be deferred until the regular exercises are begun, but each 
 must be practiced at once and exactly as described. A great deal can be learned by 
 
 (14) 
 
THE CARE OF THE INSTRUMENTS AND MATERIALS. 15 
 
 experimenting with the instruments and materials, and through practice before be- 
 ginning to work on a finished drawing. 
 
 15. The Care of the Instruments and Materials. Keep the instruments 
 clean, free from moisture, and always in working order. The pens should be 
 sharpened properly, and must not become clogged with ink. The compass joints 
 should work freely without being either loose or stiff. A drop of oil may be used 
 on the regulating screws of the pens and bow instruments, should they not turn 
 easily. Do not use short leads or blunt needle points in the compass and bow 
 pencil. In opening and closing the bows, pinch the legs together to release the 
 pressure on the regulating nut (A, Fig. 6), then turn the 
 nut, and let the leg spring gently back. When not in use, 
 the bow instruments and the blades of the pens should be 
 left open (A, Fig. 7), and the instruments slightly oiled, 
 occasionally, with a soft cloth. 
 
 Wood is more likely to warp when one side only is ex- 
 
 posed to the air ; hence, the drawing board should be left 
 standing on edge, that air may circulate about it, or, if left 
 on the drawing table, it should be closely covered. When f| 
 not in use, the T-square and triangles should be hung up, 
 and away from heating apparatus and sunlight. 
 
 Test, from time to time, the working edge and surface 
 of the drawing board, and the edges of the T-square, and 
 
 Fie- 6 triangles (Arts. 4, 5, and 6) ; if found inaccurate, they A 
 
 should be sent to a cabinet or pattern maker to be trued. 
 
 If the drawing board is planed off to remove dents, it should be planed on both 
 sides, since it is more likely to warp if planed on one side only. 
 
 The best of care should be taken of drawing papers and of drawings, both 
 finished and unfinished, all of which should be kept flat in a portfolio or stiff paper 
 cover. The stick of ink should be nicely wrapped with paper, glued to the ink, to 
 prevent breaking. 
 
 16. Drawing Papers. The paper best suited for a drawing depends upon the 
 amount and character of the proposed rendering (Art. 34). In selecting a paper, it 
 may be necessary to take into account its surface whether hard or soft, smooth 
 or rough, and its interior quality whether comparatively soft, or hard and of 
 uniform texture. The Whatman papers are especially satisfactory for finished and 
 display drawing. This paper comes only in sheets, of various weights and sizes (see 
 the end of this paragraph), and is finished in three different styles of surface 
 hot pressed, cold pressed, and rough. In a line drawing which is to be inked, which 
 will require considerable time to finish, and which is likely to be subjected to fre- 
 quent erasure or hard usage, the paper should have a very smooth surface and be of 
 
16 DRAWING PAPERS TRACING PAPER TRACING CLOTH. 
 
 uniformly hard texture throughout qualities found in the "normal" paper. 
 For precise line drawing, in pencil or ink, without excessive erasure or very hard 
 usage, Whatman's hot pressed and linen record papers are suitable ; the former 
 stands erasure better than the latter, but the latter has the smoother surface. For 
 working drawings, and drawings to be traced, an inexpensive but fairly hard paper, 
 such as the " duplex," may be used. This paper is sold in sheets, by the yard, or in 
 ten-yard rolls, and in widths of 30, 36, 42, 56, and 62 inches. It comes in two tints, 
 cream and drab, which may be less trying to the eyes than a white paper. When 
 blue prints are to be made directly from the drawing, a hard bond paper (Crane's, 
 for example) is preferable. Wash drawings must be made on Whatman's cold 
 pressed or on a water-color paper. Useful for practice work and cheaper than the 
 preceding are the German papers, the American imitations, and Manila paper. 
 Besides the above-mentioned papers there are many others, for a description of 
 which the reader is referred to the dealer's catalogue. 
 
 Standard sizes of Whatman drawing papers : 
 
 Cap, 13x17 inches. Super Royal, 19 x 27 in. 
 
 Demy, 15 x 20 in. Imperial, 22 x 30 in. 
 
 Medium, 17 x 22 in. Atlas, 26 x 34 in. 
 
 Royal, 19 x 24 in. Double Elephant, 27 x 40 in. 
 
 Antiquarian, 31 x 53 in. 
 
 Whatman's extra heavy, normal, duplex, and bond papers come only in the 
 royal, imperial, and double elephant sizes. 
 
 The better side of a drawing paper is indicated by its water mark. Therefore, 
 in cutting up a sheet, keep track of the better side by putting some distinguishing 
 mark on the opposite side. 
 
 17. Tracing Paper ; Tracing Cloth. For temporary drawings, for transfers, and 
 in planning, tracing paper is well-nigh indispensable. Tracings for blue prints, and 
 tracings required to stand handling and ink erasure should be made on tracing cloth. 
 
 The dull surface of the cloth is better for pencil or pen. A wash of India ink 
 or color may be used on the dull surface, if sparingly applied, but the cloth will 
 cockle more or less. If a color wash is used, inking should be done on the opposite 
 or glazed side of the cloth. (Colored crayon works better on tracing cloth than a 
 wash, and is growing in favor ; the crayon should be evenly applied to the dull sur- 
 face, and, if preferred, may be worked flat with a stump.) The glazed surface of 
 the cloth is adapted only for inking, although many prefer the dull surface for this 
 work. When the surface does not take the ink satisfactorily, it should be cleansed 
 with soft paper or sprinkled with powdered chalk (scraped from blackboard 
 crayon) . Rub the chalk lightly into the surface, and dust off thoroughly. As 
 tracing cloth is very susceptible to moisture, which stretches it, the cloth should 
 not be used when permanent accuracy of drawing is required. 
 
DRAWING PENCILS. 
 
 1 8. Pencils. Ruled pencil lines should be legible, easy to erase, and unac- 
 companied by grooves in the paper. To satisfy these conditions, it is necessary 
 not only to manage the pencil properly, but to see that the grade of the pencil 
 is adapted to the surface and texture of the paper. 
 
 In precise drawing geometrical con- 
 struction, for example rendered in very 
 
 A 
 
 narrow, light lines on a paper hard through- 
 out and having either a smooth or a rough 
 surface, there should be used a 6H pencil 
 sharpened to a ruling point (a, Art. 19). If 
 greater distinctness of line is required 
 as, for example, when a drawing is to be 
 traced a 2H to 4H pencil is best. If a 
 surface grooves easily, as is the case with 
 Bristol board and bond paper, which have a 
 hard surface, but are soft beneath, it is best 
 to use an HB or F pencil. For sketching 
 (in mechanical drawing), for suggesting letter- 
 ing, and for lining in finished pencil drawings, 
 there should be used an H pencil with a some- 
 what blunt, conical point. 
 
 The following list gives a very general idea of the grades of pencil suitable 
 for the papers mentioned in Art. 16: 
 
 Whatman's Hot Pressed, H to 6H. 
 
 Whatman's Cold Pressed, for outline draw- 
 ing, 6H ; for wash drawing, HB to 3H. 
 
 Normal, H to 8H. 
 
 Water Color, HB to ^H. 
 
 Linen Record, H to 4H. 
 
 Duplex, sH to 6H. 
 
 Bond, HB to H. 
 
 Bristol Board, HB to H. 
 
 19. The Sharpening of Pencils and Compass 
 Leads. (a) The ruling point. Cut away 
 the wood of the pencil to expose at least half 
 an inch of the lead (A, Fig. 8). With the 
 file or sandpaper pad resting on something 
 solid, as the edge of the drawing table, and 
 
 with the forefinger on the wood where it meets the lead (Fig. 9), press the 
 lead lightly but firmly against the sandpaper, and with a steady back-and-forth 
 
 Fig. 8. 
 
 Fig. 9. 
 
i8 
 
 THE SHARPENING OF PENCILS AND COMPASS LEADS. 
 
 Fig. 10. 
 
 motion grind opposite sides of the lead to form an accurate wedge (see side view 
 B, Fig. 8, and edge view C). Next, holding the pencil as in Fig. 10, carry it very 
 
 lightly back and forth, and with 
 each separate stroke slightly rotate 
 the pencil about its axis in the op- 
 posite direction to that of the stroke. 
 This rocking motion forms the 
 finished point (D and E, Fig 8). 
 It will be noted that, seen side- 
 wise, the contour of the point is 
 elliptical (D, Fig. 8) ; a cross sec- 
 tion of the point gives the form 
 shown at ab, D, Fig. 8. The advantage of this ruling point is that, by slightly 
 changing the angle of the pencil, when ruling each new line, the pencil will rest 
 on a perfectly sharp portion of its point. 
 
 Another ruling point sometimes used, is formed by first making a conical point 
 (F, Fig. 8) and then grinding its opposite sides to form a wedge. 
 
 (b) The measuring point. This point, which is used to lay off measurements 
 from the scale, is formed by working the lead to a slender and extremely sharp 
 conical point (F, Fig. 8). When forming this point, carry the lead back and forth 
 on the sandpaper, meanwhile constantly rotating the pencil about its axis. 
 
 It is convenient to have the opposite ends of the same pencil sharpened 
 for ruling and measuring points, in which case the letter representing the 
 grade of the pencil should be scratched or cut at the middle of the pencil. 
 
 (c) The sketching point. This point is used for putting in an 
 occasional freehand line on the mechanical drawing, for sketching in 
 lettering, writing on the drawing, etc. It should be conical in form, 
 less slender than the point F, Fig. 8, and only fairly sharp. For 
 this purpose an H or HH pencil may be used. 
 
 (d) Compass leads. The leads for the compass and bow com- 
 pass should be placed in the sockets of these instruments and then 
 sharpened. Let the lead extend well beyond the socket of the in- 
 strument, that the latter may not come in contact with the sand- 
 paper. Form the point according to the directions for forming a 
 ruling point (see a). When sharpened, the lead should be adjusted 
 in the socket thus : Place the pen in the compass, set the needle 
 point of the compass to correspond with the point of the pen, and 
 then set the lead to correspond with the needle point. When 
 
 Fig. n. 
 
 the compass is closed (Fig. n), the needle should project slightly beyond the 
 tip of the lead or pen (see the distance in Fig. n). When the compass is 
 
. THE PRICKER THE T-SQUARE. 
 
 open (Fig. 12), the plane ab of the lead should be perpendicular to a plane pass- 
 ing through the axes cd and ef of the legs. 
 
 20. The Pricker ; its Use in Duplicating 
 Drawings. The pricker is used to define line 
 intersections, to lay off measurements from 
 the scale, and in duplicating drawings. A 
 fine needle should be used, and immediately 
 replaced when the point becomes at all 
 blunted. 
 
 (a) In using the pricker, hold it per- 
 pendicular to the paper (Fig. 13). When 
 defining a point in the drawing, do not force 
 the point of the needle through the paper, 
 but make an indentation which is barely 
 visible. In order that such a point may be 
 readily found again, enclose it in a small free- 
 hand circle. 
 
 (b] Diagrams, maps, photographs, etc., 
 are sometimes duplicated as follows : Place 
 the original over one or more fresh sheets 
 of paper, according to the number of dupli- 
 cates required. Prick the essential points 
 in the original through to the sheets beneath 
 it, and connect the points as in the original. 
 
 Take special care to hold the pricker perpen- & I2< 
 
 dicular to the paper. As a safeguard against connecting wrong points, before con- 
 necting the points draw a freehand circle about each point, and letter or number a 
 few of the more important ones. 
 
 21. The T-square ; Straight Line Ruling. The T-square is used in ruling 
 
 horizontal lines, and in combination with the triangles 
 (Art. 23). 
 
 (a) To rule a horizontal line. Hold the 
 T-square as shown in Fig. 14, press its head firmly 
 against the left-hand cleat of the drawing board, and 
 the blade flat against the paper. Incline the pencil 
 to the right (Fig. 15), and slightly away from the 
 T-square blade (Fig. 16), so that the surface of the 
 ruling point (D, Fig. 8) will bear against the blade, and the edge of the point lie 
 in the line of contact of the edge of the T-square blade and the paper. Let the 
 
 Fig. 13- 
 
20 
 
 THE STRAIGHT-EDGE THE TRIANGLES. 
 
 fingers rest on the T-square blade (Fig. 15), press the pencil firmly but lightly on 
 the paper, and carry it steadily from left to right, keeping the pressure uniform, 
 
 and do not change the 
 initial position of the 
 pencil. 
 
 22. The Straight- 
 edge. This is a special 
 ruler, similar to the T-- 
 square blade, and used 
 most, perhaps, in sur- 
 veying and engineering. 
 It is of wood, hard rub- 
 ber, or steel, and made 
 in various lengths from 
 12 inches to 120 inches. 
 () To draiv ac- 
 curately a line longer 
 than the straight-edge, 
 or any especially long 
 line : Stretch taut a fine silk thread between the points which mark the ends of 
 the required line ; prick off carefully one or more intermediate points in the thread, 
 and connect the points by means of a steel straight-edge. 
 
 Fig. 15. 
 
 b 
 Fig. 1 6. 
 
 23. The Triangles are used as rulers, to obtain parallel lines, and to draw 
 lines making certain angles, as shown in the following pages. 
 
USE OF THE T-SQUARE AND TRIANGLES. 
 
 21 
 
 TRIANGLE AND T-SQUARE COMBINATIONS. (a) To rule a vertical line. 
 Place the T-square as in drawing a horizontal line. With the left hand, hold 
 the head of the 
 T - square firmly 
 against the edge 
 of the drawing 
 board, and then 
 slide the hand 
 from the head of 
 the T-square along 
 the blade to keep 
 it in position. 
 Place the triangle 
 with the right hand 
 (Fig. 17), and hold 
 it in position with 
 two fingers of the 
 left hand which 
 also steadies the 
 T-square blade 
 that the right hand 
 
 shall be free to manage the pencil. Guide the pencil away from the T-square 
 rather than toward it. 
 
 (3) To draiv lines making angles of 15, 30, 45, 60, and 75 with the 
 
 Fig. 17- 
 
 Fig. 1 8. 
 
 Fig. 19. 
 
 horizontal. Place the T-square and triangles as shown in Figs. 18, 19, 20, 
 and 21. 
 
22 
 
 USE OF THE T-SQUARE AND TRIANGLES. 
 
 To draw a perpendicular to a line which makes an angle of 45, 30, or 60, 
 reverse the triangle, as shown in Fig. 20. It will be seen (Fig. 21) that the tri- 
 
 \ 
 
 Fig. 20. 
 
 Fig. 21. 
 
 angle which makes an angle of 75 with the horizontal A must make an angle of 
 15 with the vertical B. 
 
 In drawing a line from a given point in a line, as point C in line AC (Fig. 19), 
 do not fit the T-square to the line, as at A'C, and then attempt to place the 
 corner of the triangle at the given point, as shown at C f , but keep the T-square 
 blade away from the given line, A C, that the edge of the triangle shall pass through 
 the given point. 
 
 TRIANGLE COMBINATIONS, (c) To draw lines parallel or perpendicular to 
 an oblique line, or making with it angles of 15, 30, 45, 60, and 75. 
 
 Let it be required to draw through point C (Fig. 22) a line parallel to a 
 
 Fig. 22. 
 
 given line, as AB. Fit accurately to the given line an edge of either triangle, as 
 M, and place against it another triangle, as N. Hold N firmly in place with the 
 
USE OF THE TRIANGLES. 
 
 Fig- 23- 
 
 left hand, L, and slide the triangle M along N to position M' t with its edge pass- 
 ing through the given point C. Keep M' and N firmly in position with the left 
 hand, to free the right hand for drawing the required line, as from E through C to D. 
 Positions of the triangles for drawing a perpendicular to an oblique line, and for 
 
24 THE PROTRACTOR THE FRENCH CURVE. 
 
 drawing lines making with an oblique line any of the above-stated angles, are 
 shown in Fig. 23. The solid black represents a fixed triangle, and the dash-and- 
 dot, a movable triangle set upon the given line. The full line representing the 
 triangle which guides the pencil shows either a new position of the movable 
 triangle (A, B, D t E t F, G, and H}, or the position of a triangle substituted for it 
 (J, K, L t and M}. The method C, Fig. 23, which uses two movable triangles, 
 is occasionally more convenient, although less direct than the other methods that 
 give the same results. 
 
 24. The Protractor. This instrument, used for laying off angles, is a semi- 
 circular disc of metal, horn, or cardboard, divided into degrees, half and quarter 
 degrees. Metal protractors with a vernier attachment read to one minute. 
 
 25. The French Curve ; the Template ; Curved Line Ruling. Curved rulers 
 are made of hard rubber, wood, or celluloid, and include the French curve (Plate 
 
 Fig. 24. 
 
 2), the railroad curve, the ship curve, and the spline. There is also a patent ad- 
 justable curve made of rubber combined with soft lead. The spline and adjustable 
 curves may be bent to fit fairly flat curves up to 60 inches or more in length. 
 
 (a) The use of the French curve. Having located the points in a curve, con- 
 nect them by a freehand line sketched lightly with a 3H or 4H pencil. This line 
 should pass accurately through the located points and at the same time present 
 a curve as graceful as possible. The line should be sketched without excessive 
 erasure, because this tends to obscure or wholly to obliterate the located points 
 unless they have been defined with the pricker (a, Art. 20). The final line, whether 
 drawn in pencil or in ink, should be ruled by means of one or more French curves, 
 as follows : 
 
 Let BCD (Fig. 24) be a series of points connected freehand. Find by trial 
 the portion of a French curve which will coincide with or fit the sketched line, 
 
THE TEMPLATE SCALES. 
 
 and for as long a distance as possible. Rule the line ; find a curve which will fit 
 another succeeding portion of the sketched line, rule again, and continue the 
 process until the whole line is thus ruled in sections. In order to insure smooth- 
 ness of curvature in the line as a whole, in ruling each succeeding section the 
 French curve must be fitted back some distance on the preceding (inked) section. 
 For the same reason, in ruling each section, the line should stop a little short of 
 the full length of the section. These requirements are illustrated in Fig. 24. 
 Curve A fits section BG of the sketched curve BCD, but the ink line is carried 
 only from B to F. Curve A' fits section GK, and also fits back on section BG to 
 include portion EF already inked. The ink line is carried from F to J; that is, 
 distance JK short of the full length of section GK. Curve A" fits back on section 
 GK to H, which includes portion HJ already ruled, and forward to point M. The 
 inked line is carried from J to L. 
 
 In rilling a curve, the pen should be lie Id perpendicular to the paper (Fig. 2$), so 
 that, when carried around sharply curving portions of the French curve, it may 
 turn easily on its point. 
 
 (b] The template. This is a substitute 
 for the French curve made by the draftsman 
 and used either as a time-saving device or when 
 the French curve cannot be fitted to the given 
 points. It is made of thin sheet metal, wood, 
 rubber, or thick celluloid. If thin wood is used, 
 the required curve may be drawn directly on it. 
 In the case of rubber or celluloid, the curve should 
 be traced and then transferred to the rubber by 
 pricking through the points. The template 
 should be roughed out with a knife or hand fret- 
 saw, shaped more accurately with a coarse file, 
 and finished with a fine file. 
 
 26. Scales. If the measurements of a drawing are the same as those of 
 the object represented, it is said to be "full size." A drawing is said to be drawn 
 to a scale when, for convenience or from necessity, it is made smaller or larger 
 than the thing represented. For example, a map of the United States may be 
 drawn to a scale of i inch = 400 miles ; surveyors' plans, to scales of 50 feet to the 
 inch, 80 feet to the inch, and so forth. Drawings of objects are commonly made half 
 size ; quarter size, or 3 inches to the foot (written 3 in. = i ft.) ; eighth size, or i| 
 inches to the foot (i| in. = i ft.), etc. Of the various drawing scales manu- 
 factured, it is necessary to describe but two, the 1 2-inch architect's scale, divided 
 as stated in the list of materials (Art. 2), and the 1 2-inch engineers scale, divided 
 to 10, 20, 30, 40, 50, and 60 feet to the inch. 
 
 Fig. 25. 
 
26 
 
 READING THE SCALE. 
 
 (a) The architect's scale. One face of this scale is divided into inches and six- 
 teenths of an inch, like the common foot rule, and is used in making full-size draw- 
 ings. On each side of the other five faces there are two 
 scales, one being one-half of the other. To illustrate 
 the arrangement and reading of the several scales, 
 consider the scale of i in. = i ft. (Figs. 26 and 27). 
 The denomination of the scale is indicated by the 
 26. numeral " i " placed at its right-hand end. The scale 
 
 is divided into 12 equal parts, each representing i 
 foot, and the last one, CD, Fig. 27, is divided into 24 equal parts, representing inches 
 and half inches ; that is, this i inch, representing i foot, is divided proportionally 
 
 
 
 
 N O 
 
 > 1 
 
 
 
 C ; F H 
 
 c IDA 
 
 y* 
 
 "1" j"l"l 
 
 
 ; 
 
 
 
 
 20 
 
 3 A 9 
 
 1 
 
 '11 10 9 
 
 1 
 
 Fig. 27. 
 
 to a foot rule, except that the smaller divisions are omitted. Beginning at the zero 
 (under C} and reading to the right, groups of 3 inches each are indicated by the 
 numerals " 3," " 6," and " 9." Reading from the zero to the left, feet are indicated 
 by the numerals, as " i," " 9," " 10," and " 1 1," placed on the concave surface im- 
 mediately below the face of the scale. 
 
 To read a measurement. Let it be required to measure the line OP, Fig. 27. 
 The scale must be placed so that the feet and inches can be read continuously with- 
 out moving the scale. On applying the scale to the given line, it will be quickly 
 seen that the line contains feet and inches ; in this case, the graduation line " i " 
 (under L) must fall on the point O; the length of OP is i ft. 7| in. In the 
 scale 1 in. = i ft. (Fig. 27), it will be seen that the smallest divisions of EF (= i 
 inch) represent inches, and that these read from the zero (under F) to the left. 
 The feet are read from the zero to the right. The line MN, read from this scale, 
 measures 3 ft. 5 in. 
 
 (b] The engineers scale. The face (Fig. 28) selected to illustrate the several 
 
 A a 
 
 Fig. 28. 
 
 graduations of this scale is divided into 600 equal parts. Each inch is therefore 
 divided into 50 equal parts, each representing i foot, and the scale is said to be 50 
 
THE COMPASS. 
 
 27 
 
 feet to an inch, indicated by the " 50 " (under F) stamped on the scale. It will be 
 seen that groups of five divisions, as AB (Fig. 28), and of ten divisions, as DE, are 
 denoted by the greater length of the graduation lines, and that each group of 
 twenty divisions is indicated by a numeral stamped on the scale as the "2" oppo- 
 site C, which is read 20 feet. It will also be seen that inches are not distinguished 
 by number ; if required, these must be found by means of the group divisions and 
 numbers. Thus, for example, reading from the left-hand end of the scale, I in. is 
 obtained by taking the graduation line, E, midway between the "4" and the "6." 
 
 To find readily the face of the scale in use, a guard (see Fig. 26) is convenient. 
 
 The scale should never be used as a ruler. 
 
 27. The Compass Large circles and circular arcs are drawn, according to 
 length of radius, with the compass, the compass with the extension bar, or the 
 beam compass. 
 
 For small circles, of | inch radius or less, the bow compass should be used. 
 
 Fig. 29. 
 
 Fig. 30. 
 
 Fig. 31. 
 
 Use the shoulder tip of the needle point (Plate i), and have the lead of the com- 
 pass sharpened and adjusted in the socket according to d, Art. 19. For drawing 
 very small circles, the inside of the needle point should be beveled. 
 
 (a) To describe a circle. Set the compass to an approximate radius, with the 
 legs bent to bring each perpendicular to the paper (Fig. 12), and then set it to the 
 exact radius. Holding the head of the compass with the tips of the thumb and 
 first two fingers (Fig. 29), with the needle point merely resting on the paper, start 
 the circle at point A, under the inner edge of the wrist, and describe a circle with 
 one continuous sweep of the lead. In describing a circle, incline the head of the 
 compass slightly forward in the direction of its motion indicated by the arrows, 
 Figs. 29, 30, and 31, and guide the instrument by a combined finger, wrist, and 
 
28 
 
 THE COMPASS. 
 
 arm movement, during which the head of the instrument should roll between the 
 thumb and forefinger (Figs. 29-31). Do not acquire the habit of carrying the 
 lead back and forth over a circle ; once drawn, let the circle stand improvement 
 should come from practice, and not from going over or patching a line. If a darker 
 
 8 V 
 
 o 
 
 Fig. 34- 
 
 Fig. 32. Fig. 33. 
 
 line is required, change to a softer lead. Furthermore, do not thrust the needle 
 point into the paper, but give it only sufficient pressure to keep it from slipping. 
 
 The need of bending the needle-point leg and of inclining the compass but 
 slightly in describing a circle is shown in Figs. 32 and 33. When the needle point 
 is perpendicular to the paper (A, Fig. 32), if the paper is accidentally punctured, 
 the center thus made will have a diameter, a'b f , equal only to the diameter, ab, of 
 the needle point. If, however, the needle point is inclined, as in A, Fig. 33, the 
 
 Fig. 35. 
 
 swinging of the compass will cause the needle point to ream out the center, and 
 thus prohibit its further use for accurate work. 
 
 Never use the compass as shown in Fig. 34. 
 
 (b) The lengthening bar. When the lengthening bar (Fig. 35) is used, the 
 
THE BEAM COMPASS THE DIVIDERS - THE Bow SPACERS. 29 
 
 compass is likely to spring under pressure ; hence it must be handled lightly. 
 Bend the legs to bring them perpendicular to the paper, incline the instrument 
 slightly in the direction of its motion, and at the beginning and the end of the 
 line guide the describing leg with a finger of the left hand. 
 
 28. The Beam Compass. This instrument (Plate 3) is practically a compass 
 with a separated head (A and B, Plate 3) which slides on a wooden bar. Slight 
 corrections of distance between the legs of the compass may be made by means of 
 a spring which is regulated by the nut C. 
 
 29. The Hair-spring Dividers ; the Bow Spacers. The hair-spring dividers and 
 the bow spacers (Plate I ) are used to transfer distances, and to space or divide lines 
 into equal parts. The points of the instruments should be very sharp, of exactly 
 the same length, and, when closed, should come together accurately. If the points 
 are blunted or of unequal length, the defect should be remedied on the oil stone. 
 
 (a) Spacing. Before commencing to space, ascertain the range (BC, Fig. 
 36) of the hair-spring leg by turning the screw E, and then set the point of the leg 
 at A midway between B and C, so that the leg may be 
 moved by means of the hair spring in either direction ac- 
 cording to need. Let it be required, for example, to divide 
 line D' B' (Fig. 37) into 13 equal parts. Moving the legs 
 by means of the head joint, set the dividers approximately 
 equal to -Jg- D' B' ; then, starting with one leg of the di- 
 viders placed at D', step along the given line until the 
 1 3 spaces are laid off. If, on laying off the last, or 1 3th, 
 space, the leg of the dividers extends beyond the given 
 line, as distance B'A vii , the assumed distance in the di- 
 viders must be decreased by -jL- of the excess, B' A v ", de- 
 termined by judgment. If, however, on laying off the I3th space, the leg of the 
 dividers does not reach the end of the line, as at C, it is evident that the distance 
 
 in the dividers must be increased bv 
 
 ^t _ . /?~- * 
 
 rc/ y V^T V A ...'\ AM -j 1 ^ of the deficiency CB' . In making 
 
 N^-A^JLAJ^ either correction, if the error is a con- 
 
 Fig. 37. siderable one, the legs of the instrument 
 
 should be moved by means of the head- 
 joint, but for a slight error use the hair spring, which, as already stated, should be 
 set before beginning to space, so that the leg may at once be moved in either 
 direction. Until a close approximation to a required spacing unit is obtained, in- 
 stead of stepping the dividers along the given line, it is best to keep the points a 
 little to one side of the line in order not to mar it. In stepping off the spaces, 
 care should be taken not to spring the dividers, and thus change the distance be- 
 
i 
 
 30 SPACING WITH THE DIVIDERS. 
 
 tween the points of the instrument a result which will follow if the points are 
 pushed into the paper. When a close approximation to the required spacing unit 
 has been obtained, the trial spacing should be transferred to the given line ; 
 but the paper must not be punctured or perceptibly indented, since the points of 
 
 the dividers are very likely to slip back into the 
 holes, and thus to frustrate all efforts for a satis- 
 
 /" "/^"J" ~\ factory result. To minimize error from failure to 
 
 keep the points of the dividers exactly on the given 
 line, let the advancing leg swing in alternate direc- 
 tions, as indicated by the lettering and arrows 
 (Figs. 37 and 38). When indicating a final 
 38- spacing, the paper should be merely indented, not 
 
 directly, but by going over the given line several times, each time with just enough 
 pressure to indent the paper visibly after the several repetitions. 
 
 When stepping with the dividers, keep the plane of its legs perpendicular to the 
 paper. 
 
 (b) Setting the dividers (or compass) for a scale measurement. When setting 
 the dividers for a scale measurement, hold the scale in the left hand, with the face, 
 as ADC, Fig. 39, horizontal, meanwhile hold- 
 ing the dividers so that the plane of its legs !-'' 
 will be perpendicular to the face of the scale. <; 
 Or, place the scale on the drawing, with the it 
 wrists resting on the scale, to keep it in A) ' , , 7 .,. / .,.,.! > T, ., , ,. r , c).. y . 
 
 place, and to free both hands to manage /r/7TTr//7T7^r7fffry'77^rr77'Lr = d 
 
 t^(i i/ih iiiijii// ^/ii i[ji I, h L i^/, /,/, i ,1^,^,1,^ **( IT 
 
 the dividers. Never hold, with both hands, <c 
 
 the compass or dividers between the scale and 
 
 the body (see the lower side of Fig. 39), as 
 
 the position is an awkward one, the numbers 
 
 stamped on the scale are inverted, and the ,- 
 
 scale will slip. In taking a measurement 
 
 from the scale with the dividers, slight errors may readily be detected by stepping 
 
 the dividers along the scale for a considerable distance, and then noting whether 
 
 the total distance stepped off is an exact multiple of the required distance. 
 
 30. Proportional Dividers. This instrument (Plate 3) is occasionally very 
 convenient in making reduced or enlarged copies of drawings, photographs, etc. 
 A required ratio, as between distances ab and cd (Plate 3), is obtained by means 
 of the sliding joint A'. 
 
 31. India Ink. This medium in line drawing applied with the ruling and 
 compass pens is used to give finish to a pencil drawing, and for greater distinct- 
 
INDIA INK THE RULING PEN. 
 
 ness and durability. It is also used in wash drawing, as described in Chapter X. 
 The stick India ink gives the best results. Writing inks are wholly unsuitable for 
 drawing. The ready prepared drawing inks are not here recommended for 
 finished drawing ; they do not flow so well as the freshly ground ink, are not 
 always strictly black, and are likely to injure the paper sufficiently to cause fuzzy 
 lines. 
 
 (a) To prepare India ink for line drawing. Fill the ink slab (Plate 2) 
 with water just sufficient to overflow the ink well. Hold the stick of ink vertical, 
 and with a moderate pressure give it a rotary motion around the edge of the ink 
 well. Continue grinding until the ink is absolutely black, but not thick; this 
 will require perhaps five to ten minutes, according to the hardness of the ink and 
 the amount of water used. As the grinding proceeds, test the condition of the 
 ink by ruling lines on paper of the kind upon which the drawing is to be made. Do 
 not judge the ink before it is thoroughly dry. The stick of ink should be wrapped 
 as directed in Art. 15, and wiped perfectly dry after use; otherwise, it is likely 
 to crumble. Keep the liquid ink covered to prevent thickening and to keep 
 out dust. Do not set the ink slab on the drawing or the board, but keep it well 
 away from the work. 
 
 32. The Ruling Pen. () Manipulation of the pen. To fill the pen let it 
 rest in the ink a moment, then carefully wipe off the outside of the blades with a 
 rag or the chamois leather. A better way, is to fill between the blades with a 
 common writing pen or quill. Always, before beginning to ink, and on changing 
 the width of a line, the pen should be tried on the edge of the sheet, to see that 
 the ink flows freely and that the line is of a desired width. Avoid the habit of 
 touching the pen to the lips, to make the ink flow ; if two or three trials of the 
 pen on the paper, the finger, or the drawing board where the pen should follow 
 the grain of the wood will not cause the ink to flow, either the ink is too thick 
 or the pen needs cleaning. 
 
 When using the pen, hold it perpendicular to 
 the paper (Fig. 40), or nearly so, with the tip of the 
 forefinger resting on the head of the regulating 
 screw. If the pen is inclined in the direction of its 
 motion, it is difficult to keep a line uniform in width, 
 or to end a line accurately at a given point. Carry 
 the pen from left to right steadily, rather slowly, and 
 without the slightest rotation about its axis. To 
 satisfy this last condition, the position of the hand 
 
 relative to the T-square or to the ruler must not change ; there must be an arm 
 movement from shoulder and elbow, but no wrist motion. In drawing a long line 
 
3 2 
 
 CARE OF THE RULING PEN. 
 
 a slight movement of the wrist appears to be necessary, but this should not change 
 the position of the hand relatively to the ruler. If the handle of the pen is in- 
 clined outward, in order to bring the point into the line of contact of the ruler and 
 paper, the ruler, especially if made of rubber or steel, is likely to attract the ink and 
 thus blot the paper ; hence the blade should be kept slightly away from the lower 
 edge of the ruler, unless the latter is provided with a beveled edge. Blotting paper 
 should always be at hand in case of accident. 
 
 When filling the fen, do not hold it over the drawing. 
 
 (b) The care of the ruling pen. As the blades of a good pen are highly 
 tempered and therefore brittle, care must be taken, when filling the pen, not 
 to strike the points against the ink well ; also, in setting the pen, not to screw the 
 blades together too tightly. If a pen works badly, the blades should be slightly 
 separated and examined with a magnifying glass to see whether the pen is dull, 
 the blades of unequal length, or their points broken off. A blunted point may also 
 be detected by viewing the blades endwise ; if it is dull, a light spot, due to 
 reflected light, will be seen at the tip of the point. Every student should learn to 
 sharpen his own pen, since inability to do this may prove to be a serious handicap 
 if he chances in the future to be located at a point remote from an instrument re- 
 pair shop. 
 
 (c) To sharpen the ruling pen. Use a fine oil stone and plenty of oil. 
 With the blades closed, hold the pen perpendicular to the face of the oil stone, 
 
 Fig. 4 1 . 
 
 as indicated by views A and D, Fig. 41. Keeping the pen in a plane perpendicu- 
 lar to the surface and parallel to the long edges of the oil stone, carry the pen 
 
SHARPENING THE RULING PEN ERASURE. 
 
 33 
 
 Fig. 42. 
 
 back and forth, and at the same time rock the pen, as indicated by positions 
 B and C, Fig. 41. This grinding should bring the blades to the same length, and 
 so shape the point of the pen that, when seen as at A, Fig. 41, the outline of the 
 point will appear elliptical. Now grind separately the point of each blade as follows : 
 Hold the pen as shown at A, Fig. 42, making 
 an angle of about 10 or 12 with the surface of 
 the stone. Carry the pen back and forth as in- 
 dicated by the arrows, and, while so doing, rotate 
 it about the axis of its handle. In this rotation 
 the right-hand edge of the blade, in passing from 
 A to A', gradually approaches the surface of the 
 stone. At A' the pen is rotated to a position 
 corresponding to the initial position (see B}, 
 and in the stroke from B to B' the left-hand edge 
 of the blade gradually approaches the stone. 
 The pen is again rotated to the initial posi- 
 tion A, and the motions are continued. The 
 curved portion of a cross section of the point 
 should be approximately elliptical. As the 
 grinding proceeds, the point should be examined 
 from time to time with the reading glass (Plate 2), and the pen tested by lines 
 carefully ruled on drawing paper. When properly ground, the blades of a pen have 
 exactly the same length and sharpness ; if one blade is longer, or sharper than the 
 other it will be difficult to guide the pen, as it will persist in taking a course of its 
 own. As a rule, care, patience, and considerable time are necessary in order to 
 grind a pen properly. Never grind the inside of the blades. 
 
 (d) The point of the small pen (Plate i) should be as sharp as possible with- 
 out actually cutting the paper, and this pen should be used only for fine lines. The 
 larger pen, with its greater ink capacity, is better adapted for general work ; the 
 point should be only moderately sharp. 
 
 33. Erasure, (a) Pencil line. Use rubber which is clean and pliable. 
 When erasing on thin paper or tracing cloth, special care must be taken not to 
 crumple it; hold down firmly with the thumb and finger, and erase between. 
 For erasure within a small space, shave the rubber to a point or wedge, and 
 use a card to protect adjacent lines of the drawing. Sponge rubber is convenient 
 for large areas. 
 
 (b) To remove ink lines from drawing paper. In office practice, instead of 
 a new drawing, changes in design are frequently made on old drawings by means 
 of erasure and redrawing. In such work, and in ordinary corrections, removal 
 
34 
 
 ERASURE THE ERASING SHIELD. 
 
 N 
 
 of blots, and drawing over an erasure, the work should be so nicely done that it 
 will in nowise deface the drawing a matter requiring knowledge, care, and skill. 
 Every vestige of ink should be removed. Both the steel eraser and the sand rubber 
 (rubber ink eraser) may be used to advantage, and the first step toward 
 skilful erasure lies in keeping the steel eraser very sharp. The scalpel 
 (Plate 2), if a new one, should be reground, and afterwards kept to a 
 keen edge by frequent whetting on the oil stone. The form shown in Fig. 
 43 is recommended. This edge, but slightly convex, is best adapted for 
 erasing areas ; while the point, if kept sharp, is very satisfactory for 
 minor erasures and cleaning up ragged lines. 
 
 Before beginning to erase a line, note with the finger whether there 
 is a considerable deposit of ink. If so, first use the steel eraser to 
 remove as much of the ink as possible, but without scraping the 
 paper, and then apply the sand rubber. In using any eraser, the 
 principal thing is not to make grooves or ruts in the paper : hence 
 the eraser should be carried in the direction of the line to be erased, 
 not crosswise, and over the paper for some distance on all sides of the 
 line, so that the paper may be worn away uniformly. To the same end, 
 in converting a full line into dashes, carry the steel eraser back and forth 
 m ^ e direction of the line, not crosswise. To prevent ink from spread- 
 ing, when drawing over an erasure, the surface of the paper should be 
 thoroughly but lightly polished with the burnisher (Plate 2). If the burnisher is 
 applied too strongly, the drawing board will yield, and cause a rut in the paper. 
 To obtain the best result, place the paper on a hard surface, such as the rubber 
 triangle or a piece of glass. Excessive gloss due to burnishing .may be removed 
 with the soft rubber ; but, if lines are to be redrawn, the gloss should not be re- 
 moved until the lines have been put in. 
 
 (c) The erasing shield. This device is paper, cardboard, or celluloid, in which 
 are cut slits and holes of various shapes and sizes. The shield is placed over the 
 drawing, so that only the portion to be erased will be exposed to the rubber. While 
 shields may be procured of dealers in drawing supplies, it is usually more convenient 
 to keep a sheet of thin celluloid on hand, and to cut the apertures according to 
 immediate needs. 
 
 The use of the device is illustrated in Figs. 44, 45, 46, and 47. Fig. 44 
 shows a series of blots and mistakes at E, F, . . . M, supposed to have been 
 made in a drawing of the locomotive hand-rail stud, Plate 12. In Fig. 45 are given 
 the forms of the edges and of the apertures in the erasing shields appropriate in 
 this case. Fig. 46 represents the drawing after erasure, and Fig. 47 the drawing 
 with the lines restored. The edge M' (Fig. 45) is used in reducing the excess 
 
 Fie A. 3 
 
ERASURE USE OF THE ERASING SHIELD. 
 
 35 
 
 width of the lines M (Fig. 44). The full line lettered E, Figs. 44, 45, and 46, is 
 a mistake in inking, since, as this line represents an invisible edge of the object, it 
 should be composed of dashes (E, Fig. 47). The line lettered H (Figs. 44, 45, 
 
 L L^?*J /..._ 
 
 Fig. 44. Fig. 45. Fig. 46. Fig. 47. 
 
 and 46) represents a visible edge of the object, and therefore should be made a full 
 line as at H (Fig. 47). 
 
 (d) To remove ink lines from tracing cloth. Slip cardboard, glass, or a 
 triangle under the cloth, for a backing, and then remove accumulations of ink with 
 the steel eraser, which must not come in contact with the cloth. Complete the 
 erasing with a ruby or emerald rubber, using an erasing shield if necessary. Be- 
 fore redrawing, apply talc ("metal worker's crayon"), and polish with the bur- 
 nisher. Erasure with a soft rubber is easier on the glazed than on the dull surface 
 of the cloth ; but in no case should the sand rubber be used, as it will quickly 
 make a hole in the cloth. 
 
CHAPTER III. 
 
 RENDERING CONVENTIONS LETTERING AND DIMENSIONING COMMON WORKING 
 
 METHODS. 
 
 34. Rendering. This term signifies the material qualities of a drawing, and 
 the manner of its execution. The material qualities include the drawing surface 
 as wood, metal, or paper, and the medium employed as chalk, graver, pencil, or 
 ink. The manner of execution may rest wholly upon stated, definite methods as 
 in the manipulation of the instruments, Chapter II. or, besides this, may call for 
 individual ingenuity, judgment, or taste. 
 
 35. Precision and Speed. The degree of accuracy with which a drawing 
 should be rendered depends upon the purpose it is to serve. For example, the 
 plotting of surveys and the graphical solution of engineering problems often require 
 the greatest possible accuracy, to secure which it may be necessary to use a high- 
 power reading glass. Working sketches and architectural sketch rendering are 
 examples of the opposite extreme or free treatment ; here the principal considera- 
 tion is speed. The greater part of the practical requirement in drawing, however, 
 lies between these two extremes, and includes both accuracy and speed. 
 
 At the outset, whatever the character of his prospective work in drawing, the 
 student should learn to draw accurately. As he progresses, he should learn to 
 adapt himself to varied requirements, and should acquire the judgment necessary 
 to work to the best advantage. 
 
 Generally speaking, accuracy of rendering implies diminished speed. It does 
 not follow, however, that in order to obtain accuracy it is necessary to work slowly. 
 From the very start there should be a sustained effort to work accurately and 
 rapidly ; but fussiness must not be mistaken for the care necessary to secure 
 accuracy, nor mere bustle for speed. Speed depends upon quick judgment and 
 right methods rather than upon quickness of hand. 
 
 36. Refinements in Observation and Manipulation. The following methods 
 properly supplement the methods considered in Chapter II., when extreme accuracy 
 is required. 
 
 (a) The line of sight is an imaginary straight line drawn from the eye to any 
 observed point. It is important that the line of sight shall be perpendicular to 
 each observed portion of the drawing ; thus, in viewing the drawing paper in the 
 
 (36) 
 
REFINEMENTS IN OBSERVATION AND MANIPULATION. 37 
 
 vicinity of B, Fig. 48, the line of sight, AB, should be perpendicular to the paper. 
 This condition will be met best if the student stands, when drawing, so that he may 
 easily move about 
 as necessary to 
 bring the line of 
 sight to the posi- 
 tion indicated. A 
 block to incline the 
 drawing board is 
 convenient. 
 
 (^) When rul- 
 ing lines, the 
 draftsman's head 
 should move with 
 the ruling point. 
 If the head remains 
 in a fixed position 
 and only the eye 
 follows the ruling 
 
 point, it is evident ^. 
 
 Fig. 48. 
 that, as the point 
 
 moves away from the eye, the angle which the line of sight makes with the paper 
 constantly decreases, and, consequently, the chance of error increases. Also, in 
 ruling, the eye should see the line of contact of the ruler and paper ; hence the 
 line 'of sight, AD, cannot be exactly perpendicular to the paper, but the angle 
 BAD (Fig. 48) should be as small as possible. 
 
 In the case of a long line, the ruling should be done from a standing position 
 (Fig. 48). The draftsman should stand facing, and with the left side of the body 
 turned slightly toward, the drawing. Leaning over the drawing, the line of sight, 
 A C, should be directed slightly forward and inward from the perpendicular AB 
 forward, in order to see in advance of the moving point, D, and inward, to see dis- 
 tinctly the line of contact of the ruler and the paper. Standing as described, in 
 drawing a line the draftsman may walk forward, whereas, if he stands with the right- 
 hand side of the body turned toward the work, he is obliged to walk backward. 
 
 (c) In laying off a measurement from tJie scale, the line of sight must be 
 as nearly perpendicular as possible to the edge of the scale at each of the two 
 graduations which determine the measurement ; that is, in pricking off a gradua- 
 tion, as C, Fig. 49, the angle BAC (or BAD) between the perpendicular, AB, to 
 the edge of the scale, and the line of sight, A C, should be no greater than is neces- 
 sary to bring into view the point of the pricker, or pencil. 
 
REFINEMENTS IN OBSERVATION AND MANIPULATION. 
 
 (d] Precision in noting line intersections. In precise rendering it is not 
 sufficient, when noting an intersection, merely to glance at the point, but it must be 
 
 closely scrutinized in order that the point of the 
 pricker may be placed at the intersection of the 
 imaginary center lines of the lines of the draw- 
 ing. To illustrate, let the black lines, B, Figs. 
 50 and 5 i, represent an enlargement of the lines 
 ab and cd, A, Figs. 50 and 51, and the white 
 lines (B} represent the imaginary center lines of 
 lines ab and cd. The intersection of the white 
 lines represents the exact point at which the 
 point of the pricker must be placed when noting 
 the intersection, e, of the lines ab and cd. 
 
 In defining a tangent point, as g, Fig. 52, 
 
 Fig. 49. 
 
 the position of the point of the pricker should correspond to the intersection of 
 the vertical and horizontal white lines in B. 
 
 (e) Precision in laying off scale measurements. The point of the pricker 
 
 Fig. 50. Fig. 51. 
 
 must coincide exactly with the intersection of the center line of the graduation and 
 the edge of the scale. (See B, Fig. 53, where the black areas a', d', . . ./' rep- 
 resent enlargements of the graduations a, b, . . . f (A).) 
 
 (/) Precision in spacing witJi the dividers. It is not sufficient that the points 
 of the dividers fall somewhere near a given line, or even somewhere on this line, 
 
 Fig- 52. Fig. 53. 
 
 but they must be placed exactly on the imaginary center line of the given line, 
 using a reading glass (Plate 2), if necessary. To illustrate the importance of this, 
 
CONVENTIONS. 
 
 39 
 
 let it be supposed that the points of the dividers fall on opposite sides of the given 
 line, as at the intersection of the white lines with the edges of the black area in 
 C and F, Fig, 54. It is evident that the distance in the dividers will be laid off in 
 a zigzag line, and that, if the 
 points of the dividers fall several 
 times on one edge of the given 
 line, then several times on its 
 
 Fig. 54- 
 
 opposite edge, next on its imag- 
 inary center line, and so forth, a 
 very slight error will occur each time the dividers is advanced. This local error, 
 however trifling, will be multiplied in stepping the required distance, and may 
 result in a perceptible accumulated error. 
 
 (g) Precision in drawing circles. A compass setting taken from the scale 
 must be tested by drawing a trial circle and scaling its diameter. 
 
 In the case of a large number of equal circles the diameter must be carefully 
 tested from time to time, with the scale, to see if the resharpening of the compass 
 lead has changed the radius. 
 
 37. Conventions. (#) Line conventions commonly used in inking mechan- 
 ical drawings are given in Fig. 55. The cut shows the true width of line, length 
 
 For 
 
 Full line 
 
 problems | 
 and other { Dash line . . . . 
 fine-line j 
 work [_ Dash and dot line . 
 
 Visible lines . . . 
 Shade lines . . . 
 
 For Invisible lines . . 
 
 working ^ 
 
 drawings 
 
 Center lines . . 
 Extension lines . 
 Dimension lines 
 
 Fig- 55- 
 
 of dash, and space between dashes. The student should become familiar with 
 the relative line widths, lengths of dashes, and spaces by frequently comparing the 
 lines in the figure. Greater distinctions may be obtained by using colored inks, 
 which also saves time since lines in color are usually made full. 
 
 The conventions shown in Plate 4 are used more or less in practice, and, as an 
 exercise in rendering, afford excellent training. 
 
 (6) Breaks. When only a portion of an object is represented, this fact may 
 be indicated by an irregular line, as, for example, at F, Fig. A (Plate 4), and the 
 
4O CONVENTIONS. 
 
 drawing is said to be "broken off." To economize space, an object may be repre- 
 sented as broken and brought together, as in the first and last examples, Fig. A. A 
 break in a metal piece rectangular in section may be indicated according to E and 
 E' ; a break in a wooden piece, according to either of the two styles of treatment 
 //and H' . A cylindrical piece may be broken as shown in Fig. B, and the surface 
 of the break cross hatched or not, according to personal preference or the custom 
 of the office. 
 
 (c) Graining. A wooden piece seen lengthwise may be grained as shown in 
 F, Fig. A, an end view as shown at F' . 
 
 (d) Section lining or cross hatching. The conventions, Fig. ^indicate ma- 
 terial as follows : 
 
 J, Cast Iron. L, Wrought Iron. N, Composition. 
 
 K, Cast Steel. M, Wrought Steel. O, Babbitt. 
 
 The series P, Q, . . . U, is the same as the series J, K, ... O, except that the 
 areas are larger, which requires that the lines of the cross hatching shall be coarser 
 and more openly spaced. 
 
 (e) Conventional line shading (Fig. D), is used in drawings for cuts of me- 
 chanical objects and, to a very limited extent, in engineering drawing (see c, Art. 
 66). The number of lines, and their spacing and respective widths in a piece of 
 shading, depend upon the size of the shaded area and the effect desired. For 
 example, the effect of a highly polished surface might be suggested by means of a 
 shading lighter than that used on other surfaces. 
 
 38. Rendering of the Conventions, Plate 4. (a) Breaks and graining. 
 These conventions (Figs. A and B] should be rendered with a writing pen, of a 
 grade suited to the character and size of the drawing, wholly freehand, and in flexible 
 line. The outline of the break, Fig. B, should be of uniform width, curved through- 
 out its entire length, and be drawn tangent to the contour elements of the cylinder. 
 In general, these conventions should be rendered with regard to their general 
 effect ; but in first attempts the plate should be closely copied. 
 
 (b) Cross hatching (Fig. C}. The lines of the several cross hatchings should 
 be drawn at 45 with the horizontal, except in conventions O and U, where the lines 
 are drawn at 60. Place the proper triangle against the T-square, and space the 
 lines wholly by eye, or by touch that is, by sensing the amount the triangle 
 should be moved to obtain the required spacing. 
 
 Conventions L (R) and M (S) should be treated in the following manner : 
 Let R f represent the section lining at the upper left-hand corner of example R. 
 Set the pen for the narrow lines in R, and, keeping the same width of line, repre- 
 sent the wider lines in R by double lines, as at D and E (R'}. Cross hatch the 
 whole surface, and then fill in the narrower spaces to make the wide lines. Make 
 
Plate 4 
 
 CStudy Plate 3) 
 
 The dimensions and reference letters should not appear on the students drawing 
 
CONVENTIONS LETTERING . 43 
 
 the spaces, as A, B, and C (ft'), between the narrow lines and the edges of the 
 wide lines equal in width. 
 
 Some draftsmen insist that if a break is cross hatched (see Fig. B), it should 
 be done freehand. 
 
 The instrument known as a section liner may be convenient, or perhaps neces- 
 sary, in making fine drawings and cuts ; but this instrument must not be used in 
 the exercises here given. 
 
 (c) Conventional line sJiading (Fig. D]. The spacing and widths of line 
 must be determined wholly by eye. A preliminary penciling of a narrow strip 
 of the shading (as shown below V, V , and V", Fig. Z>), to establish the num- 
 ber of lines, spacing, and line widths, should be indicated ; but, with this exception, 
 the shading must be done directly with the ruling pen. Begin at the left-hand 
 border of a vertical piece and at the upper border of a horizontal piece. 
 
 In the case of a cylinder first set the pen for a very narrow line, and, while 
 changing the spacing, retain the same width of line until the wider lines at the 
 right-hand third of the cylinder are reached. Then, besides changing the spacing, 
 gradually increase the width of line by changing the setting of the pen. The 
 widest lines of the shading may need to be built up by going over each several 
 times, in which case let the lines dry frequently in order to avoid blots. When all of 
 the shading has been thus laid in, the narrower lines may be retouched, if necessary, 
 and the spacing and line widths of the right-hand third of the cylinder corrected. 
 
 Excellent examples of line shadings in great variety may be found in catalogues 
 of machinery, etc., illustrated with fine woodcuts. In first attempts, an example 
 should be closely copied, not line by line, but for its general effect. 
 
 39. Lettering. In connection with the study of mechanical drawing it is 
 important to have extended practice in lettering and dimensioning (Art. 42). 
 
 (a) Styles and sizes of letters. In Plate 5 are given vertical and inclined 
 Gothic letters and numerals in two sizes and widths of line, which should be used 
 in rendering data and dimensions on the practice drawings that follow. These 
 styles should also be used for titles, but the letters must be larger. 
 
 There should be lettered on the margin of each finished practice drawing the 
 word "Plate" the number of the plate, the student's name, and the date on which 
 the drawing is completed. The required heights of the letters, for two sizes of 
 border line, are given in Fig. 56. 
 
 The general effect of the lettering and dimensions of a drawing should cor- 
 respond with the general effect of the drawing. That is, if the drawing is strong 
 in appearance, a bold letter should be used ; but, if a drawing is light or weak in its 
 general effect as in a geometrical construction a lighter letter should be 
 selected (compare Figs. A and C, Plate 5). 
 
44 
 
 LETTER RENDERING. 
 
 40. Stroke Letters, (a) Rendering. In office practice it is commonly re- 
 quired that small titles, reference letters, and dimensions shall be rendered with 
 
 "* 
 
 4- 
 
 vf PILATE 5 
 
 1 t ^ 
 
 -/ "* /8" ru/ed border-line 
 
 -8"* 12" ruled border-fine 
 
 '. JOKTTicutL 
 
 -- 
 
 DATE: 
 
 
 Fig. 56. 
 
 direct strokes of the pen, rapidly, and without the use of guide lines. A system 
 of stroke letters is given in Fig. J (Plate 5) : the arrows show the direction in 
 which the pen should be carried ; and the numerals, the order in which the strokes 
 should be made. 
 
 The practice drawings here given must be lettered and dimensioned according 
 to this system, unless otherwise specified. To acquire proficiency, the student 
 should practice daily the alphabets, Plate 5, until he can make the letters and nu- 
 merals with a fair degree of speed and uniformity. For a line of letters or nu- 
 merals, one base or guide line, only, may be ruled. 
 
 (&) Lettering pens. For rendering dimensions and data when the letters 
 and numerals have a width of line corresponding to that of the letters in Fig. C or 
 D, Plate 5 a No. 303 Gillott's pen is recommended. Letters having a consider- 
 able width of line as wide as that in Figs. A and B may be rendered, according 
 to preference, with a coarse writing pen, a ball-point pen, a turned-point pen, or a 
 ruling pen specially ground for lettering. 
 
 (c) Letter rendering with the ruling pen. A reproduction of a piece of rapid 
 stroke lettering with the ruling pen is given in Fig. 57. The cut is half the 
 size of the original, which was taken from a large number of office drawings equally 
 well lettered, and in a like manner. 
 
Plate 5 
 
 ABCDEFGH U KLM NOPQRSTU VWXYZ 
 I234567890& abcdefghijklmnopqrstuvwxyz 
 
 Fig. A. ' 
 
 ABCDErGH/JKLMNOPQRSTUVWXYZ 
 
 Fig. B. 
 
 ABCDEFGHUKLJV1NOPORSTUVWXYZ 
 I2345678906c abcdefgh||klmnopqrstuvwxyz 
 
 Fig. C. 
 
 aobcde/gh/Jk/mnopqrstuvwxyz 
 
 Fig. D. 
 
 ABCDEFGHIJKLMNOPQRSrUVWXYZ 
 
 I2345678908t abcdefghijklmnopqrstuvwxyz 
 
 Fig. E. 
 
 Fig. F. 
 
 ABCDErGHUKLMNOPQRSTUVWXYZ 
 
 1234567890& abcdefghijklmnopqrstuvwxyz 
 
 Fig. G. 
 
 ABCDEFGHUKLMNOfJQnSTUVWXYZ 
 aobcdefyhfo/mnopqrstuvwxyz 
 Fig. H. 
 
 
 5*S 
 
 W^&/*^itWM1/g? 
 
 3VV^* T 
 
 Fig. J. 
 
 Fig. K. 
 
 (45) 
 
LETTER RENDERING. 
 
 47 
 
 The special advantage in lettering with the ruling pen is the increase obtain 
 able in the size of a letter and its width of line. An inexpensive pen, or one which 
 has proved unsatisfactory for ruling, is sufficiently good for the purpose. 
 
 (d) To grind a ruling pen for lettering. Hold the pen perpendicular to the 
 oil stone and grind until the point is very blunt. Next hold the pen as in Fig. 42, 
 
 r^\nJK--^B^Tr^^^ j^tr 
 
 Hours 
 
 Fig- 57- 
 
 and grind until the two blades, taken together, are conical in shape, except at the 
 point, which should remain blunt. To shape the point, start with the pen held 
 perpendicular to the stone, and carry its point in a circular path, meanwhile con- 
 stantly changing the direction of the pen to all angles from the perpendicular to 
 45 with the stone a movement which changes the roughly blunted point to one 
 having a spherical shape. 
 
 (e) Manipulation ; lettering with the ruling pen. Hold the pen at any angle 
 between 45 and 60 with the paper, with the regulating screw horizontal and the 
 thumb resting against the head of the screw. Render the letters according to J, 
 Plate 5. It is best to fill the pen with the common writing pen, or a quill, as wip- 
 ing is likely to absorb too much ink from between the blades. 
 
48 
 
 LETTER RENDERING. 
 
 41. Drawn Letters. When letters and numerals are gradually built up or de- 
 veloped by stages as is necessary for the most finished results in freehand letter- 
 ing they are said to be drawn. 
 
 (a) Rendering of drawn letters. Guide lines must be ruled as shown in Figs. 
 58 and 62. All letters and numerals throughout the drawing should be developed 
 
 A 4- B _,U 
 
 j .1 
 
 * I a '-> JL/I '' 3iE U^PF 
 
 gac 
 
 . g2 S >jl 
 
 -*', / 
 
 
 Fig. 58. 
 A B 
 
 ;"'>. Afrtt.K V\ -AM I-.'.-! 
 
 Fig- 59- 
 
 m 
 
 !*- . - y . -^. 
 
 T^./^M L-l J-3 
 
 -a- 
 
 := if i. UKAwK BY A.KL 
 
 Fig. 60. 
 
 
 X 
 
 / m 
 
 
 j r A 
 
 Xj f~I >*{ 
 
 ^ 
 
 / m 
 
 .*_.,! .!". 1?^=: f \- 
 
 !.KAVv'-; BY A. 
 
 
 ~ i *~ 
 
 
 !:. ij 
 
 . i '.-' '.' .S 
 
 
 
 Fig. 62. 
 
 Fig. 61. 
 
 wholly freehand, in the following order. (I.) Suggest in pencil (A, Fig. 59) the 
 letters and numerals for their sizes and position relatively to the drawing or its 
 parts. (II.) Correct the pencil suggestions, for the spacing, form, and verticality, or 
 slant, of the letters (B, Fig. 59). (III.) Without changing the treatment (A and B\ 
 ink in the suggestions throughout the drawing, but at the same time make, if nec- 
 essary, further corrections in the form and verticality, or slant, of the letters and 
 numerals (no figure). (IV.) Connect or pull together the blocks of the suggestions 
 
LETTER RENDERING DIMENSIONING. 
 
 49 
 
 (C, Fig. 59). (V.) Bring the lines to the required width and complete the letters, 
 making all edges sharp and true (D, Fig. 59). 
 
 (b) Balancing a title, or a line of letters. When one or more lines of letters 
 must be balanced on a given line, as XY, Fig. 61, proceed as follows : Lay off 
 
 Fig. 63. 
 
 accurately the heights of the letters, and rule the guide lines (Fig. 60) on a slip 
 of paper, but without regard to their position. Suggest each line of the title (Fig. 
 60). Find the middle point, as m, of each line of letters ; fit the middle point, m, 
 on the center line, XY, of the final title (Fig. 61) ; mark off the letter widths, and 
 develop the letters by stages as indicated in paragraph a. 
 
 42. Dimensioning. This term signifies the giving of measurements on draw- 
 ings (Fig. 63), and includes the rendering of the numerals, their arrangement on 
 the drawing, and the selection of their size and style. 
 
DIMENSIONING PRELIMINARIES TO DRAWING. 
 
 A dimension line is the broken line connecting the arrow heads which indicate 
 the points of a measurement. Extension lines (see the vertical lines composed of 
 short dashes, Fig. 63) are used, in case of interference or confusion, to carry points 
 of measurement to another part of the drawing. Line widths and length of dashes 
 for both dimension and extension lines are given in Fig. 5 5 . 
 
 Numerals of a size suitable for dimensioning average-sized drawings, and for 
 the study plates, together with the proper form of arrow heads, are given in Fig. 
 K, Plate 5. The sign ' means feet, and the sign " means inches: thus io'-6-|-" 
 is read ten feet, six and one-half inches. Inclined signs are always used by printers, 
 but in dimensioning a drawing vertical signs should be used with vertical numerals, 
 and inclined signs with inclined numerals. The quantities feet and inches must 
 always be separated by a dash (Fig. K, Plate 5). The numerator and the de- 
 nominator of a fraction should each be balanced on the center line of the fraction 
 taken as a whole (see the T 9 g, Fig. K, Plate 5). 
 
 43. Preliminaries to Drawing. A finished drawing is usually circumscribed 
 by a ruled border line, EEEE, Fig. 64, the dimensions of which may be given, 
 
 or which must be 
 determined from the 
 size and arrangement 
 of the drawings on 
 the sheet. Outside 
 of the ruled border 
 a margin, DDDD, 
 Fig. 64, should be 
 laid off, and lines, 
 CCCC, drawn for the 
 boundary of the fin- 
 ished plate when 
 trimmed. Therefore, 
 to ascertain the size 
 of the paper required 
 for a drawing, add to 
 the dimensions of the 
 
 A 
 
 Fig. 64. 
 
 ruled border line twice the width of the margin, together with an allowance of 
 extra paper for thumb-tack holes, which must fall outside the trimmed edge. 
 
 Never begin work on paper larger than the drawing board ; if the paper pro- 
 jects beyond the board, immediately trim the edges so that all shall lie at least ^ inch 
 inside the edges of the board. As the T-square is likely to work less accurately 
 near the lower edge of the board, the paper, when smaller than the board, should be 
 
PRELIMINARIES TO DRAWING. 
 
 JTl 
 
 Avoid 
 
 placed well above its lower edge (Fig. 66) . Smooth the paper flat, place it squarely 
 on the board, and start the thumb tacks at right angles to the board (A, Fig. 65), 
 
 so that, when the tack is pressed in, the head 
 will bear evenly on the paper (B, Fig. 65). 
 Never use the T-square to drive in thumb 
 tacks. 
 
 Provide a piece of clean cloth or paper 
 with which to protect the drawing ; when 
 not at work on the drawing, keep it covered. 
 Also, when working on a large or carefully 
 executed drawing, cover all parts not re- 
 ceiving immediate attention. 
 
 (a) To lay out a ruled border line. 
 Take, for example, a plate which shall have 
 an 8 in. x 12 in. ruled border line and a 
 
 margin i in. wide. Let A, A, Fig. 66, represent the edges of the paper cut for the 
 drawing, according to the preceding paragraph. With the aid of the T-square, place 
 the edges of the paper approximately parallel to the edges of the drawing board. 
 With the T-square and 
 triangle, draw horizon- 
 tal and vertical lines, 
 
 B, B, -- in. or more from 
 the edge of the paper, to 
 allow for the trimming, 
 and thumb tack holes. 
 Perpendicular to the 
 lines B, B, lay off i in., 
 the given width of the 
 margin. Draw lines, 
 
 C, C, of indefinite 
 lengths, and lay off 
 the dimensions of the 
 border line. Complete 
 the border line with the 
 
 Fig. 66. 
 
 T-square and triangle. Lay off the widths of the right-hand and lower margins, 
 and draw the remaining trimming lines. 
 
 When a strictly accurate border is necessary, it should be laid out by geomet- 
 rical construction (see Problem 4, Chapter V.). 
 
 (b) Trimming. A very sharp knife or scissors should be used for trimming 
 
52 WORKING METHODS. 
 
 drawings. When trimmed on a board, the drawing should be so placed that the 
 knife will be drawn across rather than with the grain of the wood ; otherwise the 
 knife is liable to follow the grain, and prevent a straight cut. The best cutting sur- 
 face is thick, smooth cardboard laid on the drawing board. The regular drawing 
 board and T-square should not be used in trimming drawings, but separate 
 ones should be kept for this purpose. If, as a last resort, the regular drawing 
 board and T-square are used, the cutting should be done on the back of the board 
 and along the lower edge of the T-square. 
 
 44. Common Working Methods, (a) Drawing by stages. For convenience 
 and to emphasize methodical procedure, the rendering of a drawing may be divided 
 into stages, as, for example: (I.) the constructive stage, represented by the laying 
 out of a drawing and all instrumental penciling ; and (II.) the finishing stage, repre- 
 sented by the inking, or by the final lining in of a finished pencil drawing. 
 Furthermore, a general stage may include any number of local stages, as described 
 in connection with Figs. 69-73. 
 
 The general stages of a drawing are illustrated in Fig. 67, which represents an 
 end of a marine engine connecting rod. The upper half of the cut shows the con- 
 
 Fig. 67. 
 
 structive stage ; the lower half shows the finishing stage, with the lines of the 
 constructive stage left in for the purpose of comparison. 
 
 () The constructive stage ; penciling. The penciling should invariably 
 represent the degree of accuracy required in the finished drawing ; that is, essen- 
 
\ 
 
 WORKING METHODS. 53 
 
 tials must never be slighted with the idea that they may be corrected when the 
 drawing is lined in, or inked. In the constructive stage all lines should be full, of 
 uniform width, light but firm, very narrow, and made with as hard a pencil as the 
 paper used will permit. Dash lines should not be used in this stage, as they can- 
 not be made so rapidly as full lines ; furthermore, as suggested in Fig. 68, desired 
 
 intersections, as at A, B, and C, are 
 N^'*' likely to be merely open spaces. 
 
 \ Lines upon which measurements 
 
 are to be laid off, as CD, Fig. 67, 
 must be drawn long enough to insure 
 ^'' \ the laying off of the measurement 
 
 x x^ x \ without patching out a line. The 
 
 ~x"^ -^ same is the case with lines required to 
 
 x be intersected by subsequent lines, as 
 AE, AB, and the other produced 
 
 lines in Fig. 67. To save time and to avoid patching, circles, as at FGH, which 
 are more or less broken up in the finished drawing, should be drawn complete in 
 the penciling. 
 
 There should be little or no erasure when a drawing is in progress, and it 
 should not be cleaned until finished, as the paper soils more quickly after the rub- 
 ber has been used. 
 
 (c) The finishing stage of a pencil drawing {finished rendering]. The use of 
 line conventions should be confined to this stage of the drawing, and rendered in 
 connection with the lining in. Use a rather soft pencil (F to 3H) and emphasize 
 all lines strongly. Dashes should be drawn with a deliberate stroke, not merely 
 touched in, and the ends of each dash should be clearly defined. All dashes of the 
 same convention should be equal in length, and the spaces between the dashes made 
 equal. The lines of the constructive stage need not be erased between the dashes, 
 as they become inconspicuous if the dashes are sufficiently emphasized. In a 
 carefully rendered drawing, dimension and extension lines (Art. 42) should first be 
 lightly ruled, in full line, in connection with the suggestion of the numerals, and 
 the dashes should be put in later along with other conventions. 
 
 (d) The finishing stage of an inked drawing {finished rendering). This 
 stage includes, besides inking, the rendering of dimensions and lettering (Arts. 39 
 and 42) which should not precede the inking together with any penciling 
 connected therewith. All line conventions should be rendered directly in ink ; 
 that is, without a preliminary penciling of the convention. Make all lines perfectly 
 smooth, and, except in the case of curved shade lines, keep all lines of the same 
 class uniform in width. Each dash should have the same width throughout, and 
 the ends should be made square or perpendicular to the direction of the dash. 
 
54 
 
 WORKING METHODS. 
 
 Every line should be carried accurately to its destination, neither falling short of 
 nor extending beyond it ; special attention should be given to the rendering of cor- 
 ners, that all may be perfect. 
 
 (e) Inking by stages. To save time and also to minimize the chance of 
 smearing wet ink, similar operations should be grouped, as indicated in the follow- 
 ing model, which shows the steps actually taken in inking and dimensioning the 
 original drawing for Fig. 69. 
 
 Beginning at the upper left-hand corner of the drawing and to avoid wet ink 
 working downward and from left to right: (I.) Ink all circles and arcs of the 
 
 Fig. 70. 
 
 Fig. 71. 
 
 Fig. 72. 
 
 Fig- 73- 
 
 same radius, then all remaining circles and arcs (Fig. 70). (II.) Ink the vertical 
 lines (Fig. 71). (III.) Put in all the horizontals and other remaining full lines 
 (Fig. 72). (IV.) Draw the dash lines (Fig. 73). (V.) Render the shade lines 
 ( Fi g- 73)- (VI.) Render the dimensions (Fig. 73). (VII.) Draw the screw-thread 
 convention ; indicate the breaks ; and cross hatch the section (Fig. 69) . 
 
 (/) The inking of convergent lines. To prevent lines from running together 
 
 Fig. 74- 
 
 near their point of convergence, or intersection (A, B, and C, Fig. 74), let each 
 line dry before inking another, and carry the pen away from the point of conver- 
 gence rather than towards it ; or terminate the interior lines (D and E, Fig. 74) at 
 an arc described, in pencil, from the point of convergence taken as center. 
 
WORKING METHODS. 
 
 55 
 
 () Shade lines. When shade lines (Art. 58) are shown on a drawing, the 
 extra width of line, whenever practicable, should be added to the outer edges of 
 straight and curved lines so as not to encroach upon the sur- 
 face area bounded by the lines. In the case of a circle or a 
 circular arc, the shade line should be placed by shifting the 
 center. Thus, for example, in drawing shade lines mhk and 
 e gf* Fig. 75, the center was shifted from a to r, a point in 
 the line dg drawn at 45 to the horizontal, the distance ac 
 being determined by eye. It will be observed that the shade 
 lines, as thus drawn, do not encroach on the surface included 
 between the two circles. Likewise the shade line stnv, added 
 to the outer edge of line st, does not encroach upon the sur- 
 face, qrst, of the ring. 
 
 
 1 
 
 1 
 
 Fig- 75- 
 
 (//) Testing. The accuracy of a drawing should be frequently verified by check- 
 ing or testing ; in office practice, this is the only safeguard against costly mistakes. 
 
 45. Solution of Geometrical Problems by Practical Working Methods. It has 
 already been stated (Art. 23) that in practical drawing parallels, perpendiculars, 
 and angles of 15, 30, 45, 60, and 75 are obtained by means of the T-square 
 and triangles, or by the triangles alone. There are many other cases, however, 
 where exact geometrical construction (see Chapter V.), is unnecessarily laborious, 
 and where accurate results may be obtained by shorter methods, some of which are 
 given below. Apart from the value of the methods as such, it is intended that 
 they shall suggest to the student further possibilities in the use of the triangles 
 and compass. Speed, without the sacrifice of accuracy, often depends on a ready 
 application of some particular instrumental method. 
 
 (a) To draw a line perpendicular to a given line 
 at its middle point. Let A B be the given line. From 
 the ends, A and B, of the line, draw lines A C and BC, 
 making equal angles with AB. (Make these equal 
 angles either 30, 45, or 60; if the given line is 
 neither horizontal nor vertical, proceed according to D and E, Fig. 23.) From 
 the intersection C, draw the required line CD perpendicular to AB (see B, 
 Fig. 23). 
 
 (b} To draw a circular arc through three given 
 points. Let A, B, and C be the given points. Draw 
 AB and BC. Draw DO perpendicular to AB at its 
 middle point (see a}. Draw EO perpendicular to BC 
 at its middle point. The intersection, O, is the center 
 of the required arc. 
 
WORKING METHODS. 
 
 f 
 
 (c) To draw a tangent to a circular arc at a given 
 point on the arc. Let C be the given point on the arc, 
 center O. Draw the radius OC ; at C draw the re- 
 quired tangent AB perpendicular to OC (B, Fig. 23). 
 
 (d} To find the point of tangency of a given 
 
 straight line and circular arc. Let AB be the tangent to the arc, center O. From 
 O draw OC perpendicular to AB (B, Fig. 23) ; the intersection, C, is the required 
 point of tangency. 
 
 (e) To find the point of tangency of two given 
 circular arcs. Let A and B be the centers of the 
 given arcs. Draw AB ; the intersection, C, is the re- 
 quired point of tangency. 
 
 (/) To draw an arc of a given radius tangent to two given lines at right 
 angles. Let AB and BC be the given lines. Set the compasses to the given 
 radius; then, with B as center, intersect AB and BC A 
 at D and E. With the same radius, centers D and 
 E, draw arcs intersecting at O, the center of the 
 required arc. Points D and E are the points of 
 tangency. 
 
 (g) To draw a line parallel to a given line at a given distance from it. Let 
 AB be the given line. Set the compasses to a radius equal to the given dis- 
 tance, then, with any point on AB, as C, for a center, 
 draw an arc. Draw, tangent (by eye) to the arc, the 
 required line DE parallel to AB (A, Fig. 23). Note. 
 There are two solutions possible, one on each side of 
 the given line. 
 
 (//) To draw a circular arc parallel to a given circular arc, and at a given 
 distance from it. Let AB, center O, be the given arc. Draw any radius OC. 
 Make CD equal to the given distance. With radius A/ 
 
 DO, center O, draw the required arc DE. Note. \ *<> 
 
 There are two solutions possible, one on each side of 
 
 the given arc. 6 \ 
 
 (i) To draw an arc of a given radius tangent to two given intersecting^, 
 straight lines. Let AB and BC be the given lines. Draw DE parallel to AB 
 at a distance equal to the given radius (see g). Draw 
 FG parallel to BC at a distance equal to the given 
 radius. The intersection, O, is the center of the re- 
 quired arc ; the points of tangency may be found accord- 
 ing to d. Note. There are four solutions possible. 
 
WORKING METHODS. 
 
 57 
 
 (/) To draw an arc of a given radius tangent to a 
 given circular arc and to a given straight line. Let AB 
 be the given circular arc, and AC the given straight 
 line. Draw arc DE parallel to arc AB at a distance 
 equal to the given radius (see ti). Draw line FG parallel 
 to line A Cat a distance equal to the given radius (see g). The intersection, O, 
 is the centre of the required arc ; the points of tangency may be found according 
 to d and e. Note. There may be four solutions possible. 
 
 (k] To draw an arc of a given radius tangent to 
 two given circular arcs. Let AB and BC be the given 
 circular arcs. Draw arc EF parallel to arc AB at a dis- 
 tance equal to the given radius (see Ji). Draw arc GH 
 parallel to arc BC at a distance equal to the given 
 radius. The intersection, O, is the center of the required arc ; the points of 
 tangency may be found according to e. Note. There may be four solutions 
 possible. 
 
 (/) To bisect a given angle. Let ACB be the 
 given angle. Make CD and CE any equal distances. 
 Draw DE. From C draw CF, the bisector, perpendicular 
 to DE (B, Fig. 23). 
 
 (m) To draw an arc tangent to three given 
 straight lines. Let AB, BC, and CD be the given 
 lines. Bisect the angles ABC and BCD (see /). The 
 intersection, O, of the bisectors is the center of the 
 required arc. 
 
 () To draw an arc tangent to two given straight lines ; and to a circle the 
 center of which lies on the bisector of their angle. Let AB and BC be the given 
 lines, DB the bisector of the angle ABC, and F, lying 
 on DB, the center of the given circle. At E, in the 
 given circle, draw the tangent GH perpendicular to DB 
 (see c). Draw the required arc, center O, tangent to 
 lines AG, GH, and HC (see m). 
 
 (0) To draw an arc tangent to two equal circles, and passing through a 
 point equally distant from their centers. Let A and B be the centers of the given 
 circles, and P the given point. Draw, if not already 
 given, line PC perpendicular to AB at its middle point. 
 Make PC equal to the radius of either circle. Find 
 the center, O, of an arc which would pass through points 
 A, C, and B (see b). Point O is the center of the re- 
 quired arc EPF. 
 
WORKING METHODS. 
 
 To draw a scries of arcs of constant radius, 
 tangent to a series of equal circles. Find the center O 
 according to methods k or o. Since the given circles 
 are equal, AO equals BO. Using the constant radius 
 AO, find all the centers O', O", etc.; then, using the 
 constant radius CO, draw all the required tangent arcs. 
 
 (q) To draw a circular arc tangent to t^vo given straight lines, and passing 
 through a given point. Let AB and BC be the given lines, and P the given 
 point. Draw the bisector, BD, of the angle ABC 
 (see /). Find the required center, O, on the line BD> 
 by trial. Note. This is typical of cases where one 
 line through the required center may readily be drawn, 
 but the remainder of the geometrical construction is too 
 complicated to be easily remembered. 
 
 (r) To draw a circular arc tangent to two given circles, and passing through 
 a given point. Let the circles be described from the centers A and B, as shown, 
 and let P be the given point. Find the center, O, of the 
 required arc by trial. Note. This is typical of cases 
 where the entire geometrical construction is too com- 
 plicated to be easily remembered. 
 
 (s) To draw a regular hexagon, given its short diameter. Let AB be the 
 given diameter. On AB as a diameter draw a circle. Using the T-square and 
 3O-6o triangle, draw the sides of the required hexagon 
 tangent (by eye) to this circle. Note. A regular octa- 
 gon may be similarly constructed, using the T-square 
 and 45 triangle. 
 
 (f) In a scale drawing, to find the radius of a circle, given its diameter. Lay 
 off the length of the given diameter from the scale which is one-half the given 
 scale ; this will be the required radius. Note. This is a convenient method for 
 dividing any scale measurement by 2 without figuring ; thus, if a dimension be 
 laid out from the scale of 3" = i ft., then the same dimension taken from the scale 
 of \\" = i ft. will be one-half as long. 
 
CHAPTER IV. 
 
 STUDY PLATES ON INSTRUMENTAL RENDERING AND CONSTRUCTION. 
 
 46. In order to exercise good judgment in making a drawing, it is necessary 
 to grasp the leading points of the required work as a whole ; therefore in working 
 the following study plates the student should not proceed piecemeal merely 
 drawing as he reads but he should read all directions before beginning to draw. 
 Observe particularly the statement in the last paragraph of Art. 35. 
 
 STUDY PLATE 1. 
 
 For practice with the pencil, T-square, triangles, scale, pricker, and ruling pen; testing, 
 tracing; rendering of letters and numerals. 
 
 It is required to make a pencil drawing from Plate 6, and to trace this drawing. 
 The size of the finished tracing is to be 14" x 20". 
 
 I. THE PENCIL DRAWING. Read Art. 43. Use the detail paper and the 
 4H pencil sharpened as in a, Art. 19. Make all the lines fn II, very narrow and 
 light, but sufficiently distinct to be readily seen through the tracing cloth. 
 
 (a) Lay out the ruled border line. Draw the line PQ (KL, Fig. 76) and, 
 using the T-square, rule the lines in Fig. 
 A. Using the scale and the pricker (Art. 
 36, e), lay off accurately, as many times 
 as the length of each line will permit, the 
 following measurements : on line A, |" ; 
 on 7? i " - C 7 " D s " F 3 " F - 3 -" 
 
 uu u, y-g , u, ij2 > J -^) f > *"t ^ 16 
 
 G, ^". On line H lay off in succession 
 
 9_// 15_// _3_// _9_// S'f 2 I// anf ] _9_// T n 
 "^f & 9 ~^ *) ' 1 fi ' 1 fi 'IT ) "*T 9 I cm\-i I fi " -*!* 
 
 laying off the measurements on each line, do 
 not move the scale. Test. Using T-square 
 and triangle, drop a perpendicular, as ac, 
 Fig. 76, from each point of measurement 
 in line A. See whether each perpendicular 
 passes through the imaginary center of 
 
 e- 7 " 
 *~lg~ 
 
 H d 
 
 
 
 b 
 
 
 
 B 
 
 
 
 
 
 
 
 i"r 
 
 e 
 
 
 
 
 
 
 C 
 
 
 
 
 
 
 
 4 
 
 i~ 
 
 * 
 
 c 
 f 
 
 
 
 
 D 
 
 
 
 
 
 
 
 -i"- 
 
 n 
 
 
 9 
 
 
 
 
 E 
 
 
 
 
 
 
 
 S^ 
 
 
 
 
 h 
 
 
 
 
 F 
 
 
 
 
 
 
 
 \ k r$ 
 
 
 
 K 
 
 
 
 
 G 
 
 
 
 
 
 
 
 , 9 " ,' 
 
 5 I5 
 
 . 
 ' 
 
 ,3' 
 
 
 9' 
 
 
 
 " 
 
 
 2 
 
 
 
 9 "* 
 
 32 
 
 3^ 
 
 
 I6 
 
 
 16 
 
 
 na 
 
 
 
 3i 
 
 > 
 
 
 I6 
 
 Fig. 76. 
 
 each alternate point, as b, in line B ; also, whether each perpendicular from line A 
 passes through each fourth point, as c, in line C. Continue according to Fig. 76. 
 (/?) Using triangle and T-square, rule the lines in Fig. B. 
 
 (c] Fig. C. Draw the rectangles to the scales indicated. 
 
 (d) Figs. DJ. Draw the horizontal and vertical lines. Using triangle and 
 
 (59) 
 
60 STUDY PLATE i. 
 
 T-square, draw the lines lettered AB. Lay off the \" spaces and, using the 
 proper triangle and T-square, rule the parallel lines (see Fig. 20). 
 
 (e) Fig. K. Draw the line AB, and locate point C. Draw the equally spaced 
 lines parallel to AB (see A, Fig. 23). Rule the lines perpendicular to AB (see 
 B, Fig. 23), and lay off their length. Draw the lines from points E and F (see 
 Fig. 23) ; terminate the lines by circular arcs as shown. 
 
 (/) Using T-square and triangle, draw Figs. L and M. Test. In Fig. L, 
 with the 3O-6o triangle placed against the T-square, bisect the angles ; see if 
 the bisectors intersect in the same point. In Fig. M, with the 45 triangle placed 
 against the T-square, draw the diagonals of the square, upward from the ends of 
 the base ; see if each passes accurately through an upper corner of the square.* 
 
 (g) Figs. N and O. Begin by repeating Figs. L and M. Find, by scale 
 measurement, the middle point of each side of the triangle, Fig. N, and draw CD, 
 BD, and AD, respectively perpendicular to a side of the triangle. Lay off on 
 each perpendicular the measurements given on BD. Through these points, using 
 T-square and triangle, draw the sides of the interior triangles. Test. Produce CD, 
 BD, and AD, and see if the alignments of the corners of the triangles are accurate. 
 Fig. O. Find by scale measurement the centers C and B of two sides of the 
 square. Draw the diameters, CD and AB, of the square. On each semi-diameter 
 lay off the measurements given at C. Through these points draw the sides of the 
 interior squares. Test. Draw the diagonals of the outer square and see if they 
 pass through the center of the square, as located by the diameters, and also if they 
 pass through the corners of the inner squares. 
 
 (k) Fig. P. Construct the hexagon ; draw the sides in succession, and lay 
 off the length of each with the scale. Test. Connect the opposite angles ; see if 
 the diagonals thus obtained intersect in the same point. 
 
 (i) Fig. Q. Draw AB. Using T-square and triangle, complete the hexagon 
 without further scale measurement. Test. Measure with the scale each side of 
 the hexagon, and see if all have the same length. 
 
 (/) "Plate i," the student's name, the date, and all lettering and dimensions 
 on Plate 6 are to be given on the tracing, and rendered directly in ink. In an- 
 ticipation of this work, the position, judged by eye, of the lettering and dimensions 
 should be indicated on the preliminary drawing. Also suggest lightly and rapidly 
 the size, form, and spacing of the letters and numerals. For " Plate" students 
 name, date, and Fig. A, Fig. B, etc., draw two guide lines ; for all other lettering and 
 the dimensions use but one guide line. Suggest according to the general idea shown 
 in A and B, Fig. 58. Follow the forms of the letters and numerals in Figs. A 
 and F, Plate 5 ; but, when one guide line is used, determine sizes wholly by eye. 
 
 * If the results are not accurate, it should be found whether the fault lies in the triangle (see Art. 
 6, a, b, and c). 
 
(0 
 
 ~_nn:jm^nr- : co / 
 
 A . / 
 
STUDY PLATE i. 63 
 
 II. THE TRACING. Use tracing cloth; and work on the dull surface. 
 Smooth out the cloth so it will be as flat as possible, and fasten with four additional 
 thumb tacks placed midway between the corners. See that the ink is black. 
 If the cloth does not take the ink well, use chalk (Art. 17). The lines of the 
 tracing should cover the pencil lines accurately. Ink the lines drawn frCm E and 
 F, Fig. K, as shown (see Art. 44, /). 
 
 (k] Indicate the scale measurements laid off in the pencil drawing on lines 
 A H, Fig. A, by ruling through the center of each point of division a very narrow 
 line perpendicular to and extending about -jL" above and below the given line. 
 Make the lines A /, Fig. A, full, and of the width given in A, Fig. 55. Make the 
 lines K O, Fig. A, correspond to the lines B F, Fig. 55. Make the lines R W, 
 Fig. B, like the lines DJ, Fig. 55. Make incidental lines as AB, Fig. D, and 
 the arcs in Fig. K like A or B, Fig. 55. Ink all remaining lines according to 
 D, Fig. 55. The line width of the ruled border should be slightly greater than 
 that of the line D, Fig. 55. Test. Measure with the scale the divisions of lines 
 A H t Fig. A ; see if they correspond to the dimensions, Fig. 76. 
 
 (/) Read Art. 40, a; then stroke render, with the ball-point pen, the dimen- 
 sions and all letters including "Plate /," name of student, date, "Fig. A" "Fig. 
 B," etc. Rule the extension lines, then rule the dimension lines. Put in the arrow 
 heads, with the ball-point pen. Letter rapidly, but careftdly. 
 
 (m) Read Art. 33, b, c, and d. Erase the lines drawn from points E and F, 
 Fig. K ; the dimensions locating these points ; and the letters " E" and "F." Use 
 an erasing shield. Relocate the points E and .Fon the tracing at i-j 5 g" from AB. 
 Place the new points over the original ones on the pencil drawing, and retrace the 
 radiating lines. Change the dimensions to correspond to the new location of E and 
 F, and replace the letters. Restore any lines injured in making these alterations. 
 
 (;/) Hand in the pencil drawing and the tracing, each trimmed to size. Do 
 not roll or fold them,. 
 
 STUDY PLATE 2. 
 
 For accuracy and speed in the use of the compass, dividers, and French curve; testing; 
 tracing; the rendering of letters and numerals. 
 
 Read all of the following directions before beginning to draw. 
 
 It is required to make a drawing, from Plate 7, to be traced. The size of the 
 finished tracing is to be 14" x 20", the ruled border line 12" x 18". 
 
 I. THE PENCIL DRAWING. Use the detail paper and the 4H pencil. Make 
 lines full, narrow, and light, but so they can be readily seen when tracing. 
 
 (a) Fig. A. Describe circle A. Rule a line from the center to the circum- 
 
64 STUDY PLATE 2. 
 
 ference, and on this line lay off the spacing of the interior circles. Beginning 
 with the smallest, I" in diameter, describe the circles according to a, Art. 27. 
 From the same center, using the lengthening bar, draw the arcs, Fig. C (Art. 27, b\ 
 (b] Fig. B. Work the following steps very accurately. Draw AB, and locate 
 the center, C, by scale measurement. Using only the T-square and the 3O-6o 
 triangle placed against the T-square, draw the hexagon, its diameters, and its diag- 
 onals. Distant f" from A, locate point H, and, with C as center, describe the 
 circle OHK. With " radius, centers on circle OHK, describe the circles tangent 
 to the sides of the hexagon. Establish the points of tangency, as P, Q, and R, by 
 drawing, with C as center, the circle through point P, which is the intersection of 
 HK and CT. Tests. With C as center, radius CA, describe a circle; see if the im- 
 aginary center lines of the three tangent lines at A, G, E, B, F, and D, intersect in 
 a point (Fig. 52). With f" radius, Cas center, draw a circle; see if, in its intersec- 
 tion with each diameter of the hexagon, it is tangent to each of the six equal circles. 
 If the results in the foregoing constructions are found to be inaccurate, all lines 
 should be erased, the line AB moved I" to the left, and the construction repeated. 
 
 (c) Fig. D. Draw of indefinite length the line LH, and locate lines A F. 
 With the hair-spring dividers, and according to a, Art. 29, and f, Art. 36, space 
 the line D into 13 equal parts ; B into 9 ; and C, 7. With the bow spacers divide 
 equally as follows : A into 13 parts ; , 9 ; F, 7. Test. Produce JK to cut LH 
 in L. Pass an edge of a triangle successively through L and each point in the 
 line D. Draw short lines where the edge crosses line A, and note whether these 
 lines pass exactly through the points in A as obtained with the spacers. Test in 
 like manner the points in lines B and E, and in lines C and F. 
 
 (d) Fig. E. Draw the circles, circular arcs, and line EM. With the hair- 
 spring dividers, and starting at line EM, space the circles A and B each into 19 
 equal parts. With the bow spacers, starting at line EM, divide circles C and D each 
 into 19 equal parts. Test. Draw very accurately from center E to each point of 
 division in circle A ; see if each line passes through the centers of the correspond- 
 ing divisions in circles B, C, and D. 
 
 Draw EG through point 14., Fig. E. With the hair-spring dividers, divide 
 arc HN into 5 equal parts; JO and LQ each into 9; KP and MG each into 7 
 parts. Tests. Draw from center E, through points 75, 16, 77, and 18, circle A,\ 
 see if these lines produced pass through the centers of the points of division in arc 
 HN. From center E draw through the points of division in JO, and produce the 
 lines to intersect LQ; see if the lines pass through the centers of the points of 
 division in LQ. From center E draw through the points of division in MG; see 
 if the lines pass through the centers of the points of division in KP. 
 
 (e) Locate a point on the lower horizontal portion of the ruled border line, 
 
(65) 
 
64 STUDY PLATE 2. 
 
 ference, and on this line lay off the spacing of the interior circles. Beginning 
 with the smallest, |" in diameter, describe the circles according to a, Art. 27. 
 From the same center, using the lengthening bar, draw the arcs, Fig. C (Art. 27, ). 
 
 (b] Fig. B. Work the following steps very accurately. Draw AB, and locate 
 the center, C, by scale measurement. Using only the T-square and the 3O-6o 
 triangle placed against the T-square, draw the hexagon, its diameters, and its diag- 
 onals. Distant f" from A, locate point H, and, with C as center, describe the 
 circle OHK. With f " radius, centers on circle OHK, describe the circles tangent 
 to the sides of the hexagon. Establish the points of tangency, as P, Q, and R, by 
 drawing, with C as center, the circle through point P, which is the intersection of 
 HK and CT, Tests. With Cas center, radius CA, describe a circle; see if the im- 
 aginary center lines of the three tangent lines at A, G, E, B, F, and D, intersect in 
 a point (Fig. 52). With f" radius, C as center, draw a circle; see if, in its intersec- 
 tion with each diameter of the hexagon, it is tangent to each of the six equal circles. 
 If the results in the foregoing constructions are found to be inaccurate, all lines 
 should be erased, the line AB moved \" to the left, and the construction repeated. 
 
 (c) Fig. D. Draw of indefinite length the line LH, and locate lines A F. 
 With the hair-spring dividers, and according to a, Art. 29, and/, Art. 36, space 
 the line D into 1 3 equal parts ; B into 9 ; and C, 7. With the bow spacers divide 
 equally as follows : A into 13 parts; ,9; F, 7. Test. Produce JK to cut LH 
 in L. Pass an edge of a triangle successively through L and each point in the 
 line D. Draw short lines where the edge crosses line A, and note whether these 
 lines pass exactly through the points in A as obtained with the spacers. Test in 
 like manner the points in lines B and E, and in lines C and F. 
 
 (d} Fig. E. Draw the circles, circular arcs, and line EM. With the hair- 
 spring dividers, and starting at line EM, space the circles A and B each into 19 
 equal parts. With the bow spacers, starting at line EM, divide circles Cand D each 
 into 19 equal parts. Test. Draw very accurately from center E to each point of 
 division in circle A ; see if each line passes through the centers of the correspond- 
 ing divisions in circles B, C, and D. 
 
 Draw EG through point 14, Fig. E. With the hair-spring dividers, divide 
 arc HN into 5 equal parts; JO and LQ each into 9; KP and MG each into 7 
 parts. Tests. Draw from center E, through points 75, 16, 17, and 18, circle A,\ 
 see if these lines produced pass through the centers of the points of division in arc 
 HN. From center E draw through the points of division in JO, and produce the 
 lines to intersect LQ; see if the lines pass through the centers of the points of 
 division in LQ. From center E draw through the points of division in MG; see 
 if the lines pass through the centers of the points of division in KP. 
 
 (e) Locate a point on the lower horizontal portion of the ruled border line, 
 
(0 
 
CO 
 
 o 
 
o 
 
STUDY PLATE 2. 69 
 
 6" from the right-hand end. Cut small triangular holes in Plate 8, so that the 
 line AB can be placed accurately over the border line of the drawing, with the 
 point c at the located point. Read Art. 20, b. Lay the book on the drawing, 
 and place AB and c, as just described. Pricking through the plate, locate the axes 
 of the ellipses, and points in the curves, Fig. F. Locate as many of the latter as 
 are necessary to obtain smooth curves, but do not exaggerate the number. It is 
 evident that the points should be taken closer together for the more sharply curv- 
 ing portions of a line than for the flatter portions. It is suggested that the dis- 
 tances range from Jg" to \" according to the amount of curvature. Rule the 
 axes of the ellipses. Read Art. 25, a. In the ellipses, suggest the portions of 
 each at the extremities of the axes and then fill in the remaining portions. 
 
 (/) Suggest all lettering and dimensions according to Study Plate i,j. 
 
 II. THE TRACING. Use tracing cloth, and work on the dull surface. See 
 that the ink is black. Trace the drawing accurately. Proceed as follows : 
 
 (g) Fig. A . Ink, before the center is enlarged, circles N and O in line 
 similar to A, Fig. 55. Make the circles G M according to A F, Fig. 55; re- 
 peat for the circles A F. Fig. C. Ink A F according to D -J, Fig. 55. 
 Fig. B. The line of the hexagon and of the resultant circles should be the same 
 as D, Fig. 55. The other lines of this figure should correspond to line A, Fig,. 55, 
 and may be drawn with red or black ink. Figs. D and E. Rule (in red or black) 
 the division lines drawn in the tests, before inking the given lines. The division 
 lines should be very narrow, and extend ^", judged by eye, from each side of the 
 given line. Ink the remaining lines of the several figures according to D, Fig. 55. 
 Make the border line slightly heavier than line Z>, Fig. 55. 
 
 (//) Render the lettering, dimensions, dimension and extension lines, and 
 arrow heads according to /, Study Plate i . 
 
 (z) Erase and redraw the ellipse D, but place it I" to the left (Art. 33, d}. 
 
 (J] Hand in the pencil drawing and the tracing, each trimmed to size. Do 
 not roll or fold them. 
 
 STUDY PLATE 3. 
 
 For practice in rendering freehand lines, cross hatching, and line shading. 
 
 Read all of the follo^cving directions before beginning to dra^v. 
 
 It is required to make a preliminary drawing in pencil, and to render the con- 
 ventions, Plate 4, p. 41, directly in ink on tracing cloth. The tracing is to be 
 14" x 20" and the ruled border 13" x 19". 
 
 I. THE PENCIL DRAWING. Use the duplex detail paper and the 4H pencil. 
 Draw the outlines of Figs. A D. Read Art. 38, and then suggest the breaks and 
 graining, Fig. A. In the upper left-hand corner of each rectangle, Fig. C, rule four 
 or five lines representative of the cross hatching in the corresponding rectangle, 
 
yo STUDY PLATE 3. 
 
 to be used as a gage when cross hatching on the tracing. Make the line width 
 and spacing twice as great as in Fig. C. Obtain the widths thus : On a strip of 
 thin paper, with a very sharp pencil, and working under the reading glass, start a 
 line width with a short narrow line made freehand ; then gradually increase this 
 line until it is of the required width judged by eye. Lay off twice the space be- 
 tween the lines in Fig. C, and then indicate the required width for a second line 
 of the cross hatching. Transfer the widths from the strip to the drawing, making 
 the width of the lines of the gage exactly equal to them. 
 
 II. THE TRACING, (a) Use tracing cloth ; work on the dull surface. See 
 that the ink is black. Trace the ruled outlines of all of the figures except V- V" 
 and W- W" > Fig. D. Make the width of these lines the same as D, Fig. 55, 
 leaving the shade lines (Art. 58) to be added later on. Ink the breaks and the 
 cross hatching on the breaks of the cylinders freehand ; use a ball-point pen. Do 
 the graining ; use the Gillott's No. 303 pen. Proceeding strictly as directed in 
 Art. 38, b, cross hatch the rectangles. Trace the lines of the gage, and then keep 
 the line widths and spacing of the gage throughout, wholly by eye. As the 
 cross hatching proceeds, it should be frequently compared with the portion cover- 
 ing the gage. Read Art. 38, c. Pencil, on the tracing, the gages for the line 
 shading, Fig. D. It is best not to ink the contour elements before shading, as 
 the widths of these lines may need to be modified so as to preserve the gradation 
 of the shading. The rendering of each convention should be practiced on spare 
 tracing cloth before attempting it on the required drawing. Add the shade lines ; 
 make their width the same as line E, Fig. 5 5 . 
 
 (b) Lettering. Letter " Plate 3 " (drawn letters), your name, and the date 
 (stroke rendered). 
 
 (c) Hand in the pencil drawing and the tracing, each trimmed to size. Do 
 not roll or fold them. 
 
 STUDY PLATE 4. 
 For practice in strictly accurate pencil construction and finished rendering in ink. 
 
 Read all of the following directions before beginning to draw. 
 
 It is required to make a very accurate and finished drawing in ink, from 
 Plate 9. The size is to be 14" x 20", the ruled border 12" x 18". 
 
 I. THE PENCILING, (a) Use Whatman's hot-pressed paper, a 6H pencil, 
 and 6H leads in the compass and bow compass. Lay out the ruled border line. 
 Draw the center lines VWand XY, placing the sprockets ioi" apart instead of the 
 true distance, 18". Draw the center line of the chain, which should be broken as 
 shown. With radius 3^"* and P as a center, draw the pitch circle, J, of the front 
 
 *The diameters 6}^", Fig. A, and 2$J", Fig. B, are the nearest fractional equivalents of the true 
 (decimal) pitch diameters given on the plate (see table at the end of the book). 
 
STUDY PLATE 4. 73 
 
 sprocket, Fig. A. Draw line GH tangent to circle /. Tangent to GH, draw the 
 pitch circle, N, of the rear sprocket, Fig. B. (Lay off the diameter, 2f", on the 
 centre line XY, and find the centre by bisecting). 
 
 (b) To find the direction of the lower portions, TU arid RS, of the cJtain. 
 Tack a piece of paper over the drawing so as not to cover the lower half of the cir- 
 cles J and N. (Do not place the tacks inside the boundary of the finished plate.) 
 On this extra sheet make a half-size diagram of the center lines, similar to Fig. E, 
 placing line G'H' parallel to GH. Draw the common tangent, T'S' ; then, parallel 
 to T'S', draw the required tangents, TU and/? 5. (Do not draw this diagram di- 
 rectly on the finished drawing, as the necessary erasure will mar the paper.) 
 
 (c) The teeth of the sprockets and the links of the chain. It will be seen 
 (Figs. C and F) that the chain is composed of alternate closed and open links, and 
 that the teeth mesh into the latter. The inside length of an open link determines 
 the width, Y'Z, Fig. F t of the teeth, while the shape of the interior determines the 
 curves X', X', of the teeth. The spaces, ZY', between the teeth, must equal the 
 total length of a closed link. 
 
 Construction: the teeth of the front sprocket. Starting at point G, Fig. A, 
 with the hair-spring dividers space the pitch circle accurately into 21 equal parts 
 (a, Art. 29), and, to identify the points, enclose each point in a small freehand 
 circle. Let the first two spaces, G" V and V V", Fig. F, be typical of all of the 
 21 spaces. Take in the bow spacers the given distance between the centers of 
 an open link (that is, T 9 g"), and lay it off from points G" and V ; this establishes 
 the centers of the pins of all the links. With %" radius, centers G", W , V ', 
 W", and V", draw (all the way around the pitch circle) complete circles represent- 
 ing the ends of the links ; these circles determine the curves X', X' t of the teeth. 
 With radius if" ( T y minus one-half of ^g") describe, from the centers of the 
 pins, the curves Y' and Z of the teeth. The extremities of the teeth and the 
 bottoms of the spaces are portions of the circles abc and def, Fig. F, which are 
 drawn according to the measurements given in Fig. A. 
 
 The teeth of the rear sprocket. Starting at point H, Fig. B, divide the pitch 
 circle accurately into 8 equal parts. Draw the teeth according to the directions 
 given for the teeth of the front sprocket. 
 
 The chain. The pins and ends of the links for the portions of the chain in 
 contact with the sprockets are already drawn. Locate the centers of the pins for 
 the straight portions of the chain, and draw complete circl'es determining the ends 
 of the links. Find the radii for the sides of the links (o, Art. 45) ; find all the 
 centers for arcs that have the same radius, and draw all such arcs as one operation 
 (/, Art. 45). 
 
 (d) Draw the circles containing the centers of the holes in the webs of the 
 sprockets, and space each circle for the number of holes shown. 
 
74 STUDY PLATE 4. 
 
 (e) Locate Figs. C and D. The section, Fig. D, of the rear sprocket is a true 
 section taken on a line drawn through the center of Fig. B, downward to the right, 
 and just clearing the hole, in the web, which cuts KM. Otherwise, all lines in 
 Figs. C and D, not located by the given measurements, are to be projected from Figs. 
 A and B. The chain is projected from the horizontal portion. 
 
 (/) Complete the penciling. Look over the drawing, and see that no details 
 have been omitted. Do not indicate the dimensions and lettering before inking. 
 
 II. THE INKING, (g) Ink with special care. First make the width of all 
 lines equal to that of A, Fig. 55. Omit the cross-hatching for the present. 
 
 (/i) Shade lines. Read Arts. 44, g, and 58. Make the line width the same 
 as in D, Fig. 55. This width should be increased wherever a line may look weak, 
 and should be decreased if necessary to prevent lines from running together. 
 
 (2) Lettering and dimensions. All lettering and all dimensions given on Plate 
 9, except those marked *, should appear on the student's drawing. The letters and 
 numerals should be drawn (Art. 41), not stroke rendered. Rule guide lines ac- 
 cording to Figs. 58 and 62 ; make the size of the letters and numerals the same as 
 in Fig. E, Plate 5. Rule guide lines for the title, according to the measurements 
 given on the plate, and balance the title on the vertical center line of the plate 
 (b, Art. 41). Letter "Plate 4," your name, and the date. (See Art. 39.) 
 
 (/) Cross-hatch the sections, and erase pencil lines throughout the drawing. 
 
 Do not roll or fold the drawing. 
 
 STUDY PLATE 5. 
 
 For precise spacing with the dividers and bow spacers ; strictly accurate scale measurement 
 and penciling ; finished rendering in ink; lettering and dimensioning. 
 
 Read all the following directions before beginning to draw. 
 
 It is required to make a strictly accurate drawing of the spur gear, Plate 16. 
 The size of the drawing is to be 10" x 14", the ruled border line 8" x 12". The 
 " Scale Half Size" on the plate indicates the scale of the required drawing. As 
 dimensions on a drawing always indicate true measurement, it is evident that the 
 dimensions on the plate, except these marked*, must be divided by 2. The dia- 
 gram, Fig. C, is given to supplement the directions which follow, and should not 
 appear in the student's drawing ; note that corresponding lines in Figs. A and C are 
 similarly lettered. 
 
 I. THE PENCILING, (a) Use Whatman's hot-pressed paper, and the 6H 
 pencil. Make all lines full and very narrow. Lay out the border line, and draw 
 the center lines MO and DP, located as shown on the plate. With point N as 
 center, radius 3f" (equals 13!" divided by 4), draw the pitch circle G (G f , 
 Fig. C). 
 
 (b} Dividing the pitch circle. Starting at point a, Fig. C, lying in the 
 
STUDY PLATE 5. 77 
 
 center line D'P', divide with great precision (/, Art. 36) the pitch circle into 108 
 equal parts, each to contain one tooth and one space (between adjacent teeth). As 
 it is next to impossible to divide a circle directly into so great a number of equal 
 parts, first divide the circle very accurately into 6 equal parts (see points a, 
 R, S, P' , T, and U, Fig. C) ; for this, do not use the 3O-6o triangle, but lay off 
 the distances with the hair-spring dividers set to the radius of the pitch circle. To 
 see that the measurement is exact, test the division by stepping the dividers in an 
 opposite direction before indenting the points ; to identify the points, draw very 
 lightly a small freehand circle about each. Using the bow spacers, divide each of 
 the six divisions into 1 8 equal parts ; test the divisions by restepping in an opposite 
 direction ; draw a freehand circle about each point of division. 
 
 (c) The width of the teeth. Let ac and ce, Fig. C, represent the first two of 
 the 1 08 spaces. In the present drawing the widths of the teeth are made equal to 
 the spaces between them. Take one-half of ac in the bow spacers, and, starting at 
 point a, lay off this distance from each of the points marking the 108 spaces, as 
 shown for the teeth at ab, cd, and ef. In order that the space divisions may not 
 be mistaken for teeth divisions not an uncommon mistake each tooth division 
 should be identified by a very light freehand line, as shown between c and d, Fig. C. 
 
 (d) The outline of the teeth. The extremities of the teeth and the bottom 
 of the spaces are circular arcs ; in the present case the sides of the teeth are also 
 circular arcs. The centers of the sides of the teeth lie in the circle J. Draw 
 circles F, H, and J, according to the measurements in Fig. A. To complete the 
 teeth in pencil : With the same radius throughout (namely, one-half of 1 |-"), center 
 at the point marking a side of a tooth, as a, Fig. C, cut the circle .of centers, /', at 
 point //. With center h, draw the side of the tooth through point a. With center 
 at the point b, marking the opposite side of the tooth, cut the circle of centers at 
 point j. With center/, draw the side of the tooth. Draw each tooth in a similar 
 manner. 
 
 (<?) The arms of the gear. Draw circle K', and the center lines RT and SU 
 of the arms. The widths of each arm are measured in lines, perpendicular to the 
 center line of the arm, located from the center of the gear. With radii equal to one- 
 half of 5f", and one-half of i|", respectively, draw the circles Fand W. Tangent 
 to these circles, draw the lines upon which to lay off the widths of the arms. (Use 
 the 3O-6o triangle to draw the perpendiculars to the center lines RT and St7.) 
 Lay off the arm widths, and draw the sides of the arm produced, as kn and mo. 
 
 Make the circular arcs (fillets) connecting adjacent sides of the inner ends of 
 the arms, of T 3 g" radius (not given on the plate) ; draw them according to , Art. 45. 
 Make the fillets, at the outer ends of the arms, of \" radius (not given on the plate) ; 
 draw them according to/, Art. 45. 
 
78 STUDY PLATE 5. 
 
 (/) The section of the gear, Fig. B, is taken on line DP (Fig. A) . Locate 
 line EQ as shown on the plate. All parts not determined by the given dimensions 
 must be projected from Fig. A. Make the radius of the fillets T y (not given on 
 the plate) ; draw them according to/, Art. 45. 
 
 (g) Complete Fig. A ; the diameter of the hub must be taken from Fig. B. 
 Draw the cross section of the arm as shown, Fig. A, taking its width from the sec- 
 tion, Fig. B. 
 
 (li) Do not cross hatch the section, or indicate the measurements and letter- 
 ing before inking the drawing. 
 
 II. THE INKING. (?) Ink the drawing with special care ; make all lines at 
 first of the same width, and equal to that of the line A, Fig. 55. 
 
 (/) Shade lines. Add the shade lines; make their width equal to that of the 
 line D, Fig. 55 ; render them according to Art. 44,^. (Also see Art. 58.) 
 
 (k) Lettering and dimensions. All dimensions given on Plate 10, except 
 those marked *, should appear on the student's drawing. The letters and nu- 
 merals should be drawn (Art. 41), not stroke rendered. Rule guide lines 
 according to Figs. 58 and 62 ; make the size of the numerals the same as in Fig. 
 E t Plate 5. Rule guide lines for the title, according to the measurements given on 
 the plate, and balance the title on the vertical center line of the plate (b, Art. 41) 
 Letter " Plate 5," your name, and the date. 
 
 (/) Erase pencil lines throughout the drawing. 
 
 Do not roll or fold the drawing. 
 
CHAPTER V. 
 
 GEOMETRICAL CONSTRUCTION. 
 
 47- The following problems are given for further practice in precise rendering 
 and for their practical application. It should be understood that the use of such 
 problems is not necessarily confined to the drawing room or to drawings of the usual 
 sizes. A good example of this may be found in surveying, where problems are often 
 worked out on a large scale, the straight lines being run out with the transit, which 
 corresponds to the straight-edge in drawing, and the circular arcs swung with the 
 chain, or tape as a substitute for the drawing compass. Likewise, the landscape 
 gardener lays out geometrical figures directly on the ground, stretching the tape for 
 a straight-edge, and describing arcs with the aid of tape and measuring pins. In the 
 mechanic arts, the workman may need to lay out a construction to the actual size of 
 his work, on wood, metal, or the floor of the shop ; in large work substituting chalk 
 line for straight-edge, and striking the arcs with a piece of chalk held at the end of 
 a string or a strip of wood swung from a nail as center. 
 
 PENCILING. Use a 6H pencil, make all lines full, and draw with the greatest 
 accuracy possible. For appearance, intersecting arcs should be made of equal 
 length, and should be at right angles. 
 
 Instead of always following a geometrical method to its limit, it is better in 
 some cases to rely upon instrumental methods. For example, parallels (as in 
 Prob. 1 3) may be drawn by sliding the triangles (Art. 23) ; circular arcs may be 
 divided (as in the case of D5B, Prob. 27) with the bow spacers; and horizontals 
 and perpendiculars (as in Prob. 44) may be drawn with the T-square and triangle. 
 
 When practicable, final results should always be checked : for example, in 
 Prob. 1 3, see that AF= BE ; in Prob. 24, see whether AD = CE = CB. 
 
 INKING. Either of the following systems may be used : - 
 
 (a) All lines to be in black. Given lines, dash and dot ; construction lines, short 
 dashes ; result lines, solid. (See Fig. 55.) 
 
 (b) All lines to be in color and drawn full. Given lines, blue ; construction 
 lines, red ; result lines, black. 
 
 The French curve should be used in inking the irregular curves. 
 
 (79) 
 
8o 
 
 GEOMETRICAL CONSTRUCTION. 
 
 Problem i. To bisect a straight line or a circu- 
 lar arc. 
 
 Let AB or AE'B be the given line. With any 
 appropriate radius, centers A and B, describe arcs inter- 
 secting in points C and D. Draw CD intersecting AB 
 and AE' B in E and E' ', the required middle points. 
 
 Problem 2. To draw a line perpendicular to a 
 given line at a given point in the line. 
 
 Let AB be the given line, and C the given point. 
 With any radius, C as center, draw arcs intersecting 
 AB in D and E. With any appropriate radius, centers 
 D and E, describe arcs intersecting in point F. Draw 
 FC, the required perpendicular. 
 
 Problem 3. To draw a perpendicular to a line at or 
 near its extremity. First Method. 
 
 Let AB\>z the given line, and A the given point. 
 With any appropriate radius, center A, draw the arc 
 CDE. With the same radius, center E, intersect arc 
 CDE in the point D. With the same radius, center D, 
 intersect arc CDE in C. With the same or any appro- 
 priate radius, centers C and D, draw arcs intersecting 
 in F. Draw FA, the required perpendicular. 
 
 Problem 4. To draw a perpendicular to a line at or 
 near its extremity. Second Method. 
 
 Let AB be the given line, and A the given point. 
 Assume any point D. With radius AD, center D, draw 
 the arc CAB, intersecting AB at B. Draw from B 
 through point D, to intersect arc CAB in C. Draw 
 AC, the required perpendicular. 
 
 Problem 5. To draw a perpendicular to a line from 
 a point outside the line. 
 
 Let AB be the given line, and Tthe given point. 
 With any appropriate radius, center C, draw an arc 
 intersecting AB in points D and E. With any appro- 
 priate radius, centers D and E, draw arcs intersecting in 
 point F. Draw CF, the required perpendicular. 
 
 /\ 
 
GEOMETRICAL CONSTRUCTION. 
 
 81 
 
 Problem 6. To draw a perpendicular to a given 
 line from a point opposite to the end of the line. 
 
 Let AB be the given line, and Cthe given point. 
 Draw a line from C to any point, as B, in AB. Bisect 
 CB at D (Prob. i). With CD as radius, center D, 
 draw arc CAB, intersecting the given line at A. Draw 
 CA, the required perpendicular. 
 
 Problem 7. To draiv a line at a given distance 
 from and parallel to a given line. 
 
 Let AB be the given line, and CD the given dis- 
 tance. With radius CD, any two assumed points E 
 and F on the line as centers, draw arcs GH and JK. 
 Erect perpendiculars to AB at points E and /''(Prob. 
 3), intersecting arcs GH and JK in points H and J. 
 Through points ffandj draw HJ, the required line. 
 
 Problem 8. To draiv a line parallel to a given 
 line and passing through a given point. 
 
 Let AB be the given line, and D the given point. 
 With any appropriate radius, center D, draw arc EC. 
 With the same radius, center E, describe arc DF. With 
 chord DF as radius, center E, intersect arc CE in point 
 C. Draw CD, the required line. 
 
 Problem 9. To bisect an angle. 
 
 Let JSACbe the given angle. With any appropri- 
 ate radius, center A, describe an arc intersecting AB 
 and A Cm points B and C. With any radius, centers 
 B and C, describe arcs intersecting in point D. Draw 
 AD, the bisector of the given angle. 
 
 Problem 10. To trisect a right angle. 
 
 Let ABC be the given right angle. With any ap- 
 propriate radius, center B, describe an arc intersecting 
 AB and BC in points A and C. With the same radius, 
 centers A and C, intersect arc A Cm points E and D. 
 Draw BD and BE, the trisectors of the given right 
 angle. 
 
 \o 
 
82 
 
 GEOMETRICAL CONSTRUCTION. 
 To construct an angle equal to a 
 
 Problem n. 
 
 given angle. 
 
 Let CAB be the given angle. Draw A'B' of indefi- 
 nite length. With any equal radii, centers A and A' ' , 
 draw arcs CB and C'B'. With the chord BC as radius, 
 center B', intersect arc B'C' in C '. Draw A' C' ; then 
 angle C'A'B' is equal to the given angle CAB. 
 
 Problem 12. To divide a given line into any num- 
 ber of equal parts. First Method. 
 
 Let AB be the given line, and the required number 
 of parts five. Through point A draw AC, making any 
 angle with AB. Draw BC 1 ', making angle ABC' equal 
 to CAB (Prob. n). Take any distance as a unit, and 
 lay it off on A C and BC' as many times as the required 
 number of parts less one. Draw lines 1-4', 2-j' ', J-2 f , 
 4-1', dividing AB into the required number of equal 
 parts. 
 
 Problem 13. To divide a given line into any num- 
 ber of equal parts. Second Method. 
 
 Let AB be the given line, and the required number 
 of parts five. Draw AC, making any angle with AB. 
 Lay off on AC any distance taken as a unit, as many 
 times as the required number of parts. Connect the 
 last point of division, 5, with point B. Parallel to 5 B 
 draw lines through points 4, j, 2, I, intersecting AB in 
 points /, J', 2', i', dividing AB into the required num- 
 ber of parts. 
 
 Problem 14. To divide a given line proportionally 
 to a given divided line. First Method. 
 
 Let AE, divided into the parts AB, BC, CD, and 
 DE t be given, and let FG be the line required to be 
 divided proportionally to AE. Draw F' G' , equal to FG, 
 parallel to AE, and at any convenient distance from it. 
 Draw AF' and EG' produced to intersect in point H. 
 Draw BH, CH, and DH, intersecting F'G' in points B 1 , 
 C' t and D', marking the required divisions. 
 
GEOMETRICAL CONSTRUCTION. 
 
 Problem 15. To divide a given line proportionally 
 to a given divided line. Second Method. 
 
 Let AB, divided by the points E, F, G, H, J, be 
 given, and CD the line required to be divided propor- 
 tionally to AB. Draw A K at any convenient angle 
 with AB, and make AD' equal to CD. Draw BD > ', and 
 parallel to it draw EE' ', FF , etc., giving the points E' ', 
 F', G', H' , J' , which mark the required divisions. 
 
 Problem 16. To fend the distance which is the 
 fourth proportional to three given distances. 
 
 Let AB, CD, and EF be the given distances. 
 Draw GJ of indefinite length, and lay off GH equal to 
 AB, and HJ equal to EF. Draw GL of indefinite 
 length, and making any convenient angle with GJ. On 
 GL lay off GK equal to CD, and draw KH. Through 
 J, and parallel to KH, draw LJ intersecting GL in point 
 L. Distance KL is the required fourth proportional ; 
 that is, AB is to CD as EFis to KL. 
 
 Problem 17. To find the distance which is the 
 mean proportional between two given distances. 
 
 Let AB and CD be the given distances. Draw 
 EH of indefinite length, and lay off EG equal to AB, 
 and GH equal to CD. Bisect EH (Prob. i) in point F. 
 With radius EF, center F, draw the semicircle EJH. 
 At point G erect a perpendicular to EH (Prob. 2), inter- 
 secting the semicircle in point J. Distance JG is the 
 required mean proportional ; that is, AB is to JG as JG 
 is to CD. 
 
 Problem 18. To draw a circle through three points 
 not in the same straight line, or to circumscribe a circle 
 about a triangle. 
 
 Let A, B, and D be the given points or ABD the 
 given triangle. Bisect AB and AD by lines EG and FH, 
 intersecting in point C, the center of the required circle. 
 
 Note. To find the center of a circle, assume any 
 three points in its circumference and use the same 
 construction. 
 
84 
 
 GEOMETRICAL CONSTRUCTION. 
 
 Problem 19. To draiv a circular arc through three 
 points not in the same straight line, when the center is 
 not accessible. 
 
 Let A, E, and J be the given points. Draw AJ. 
 With AJas radius, centers A and/, draw the arcs AMP 
 and RNJ. Draw AE produced to intersect arc RNJ 
 in point N, zndJJE produced to intersect arc AMP in 
 M. Above and below points M and N lay off on arcs 
 AMP and RNJ, with any convenient unit, equal spaces as M I, M i", N /', A" 
 /'", etc. Draw J I and A /' intersecting in F, a point in the required arc. 
 Draw J 2 and A 2' intersecting in G, a second point in the required arc. 
 Locate in like manner, aided by inspection of the figure B, C, D, K, L, the rest of 
 the points determining the required arc. 
 
 Problem 20. Through a given point to draw a line 
 which shall pass through the inaccessible intersection of 
 two given lines. 
 
 Let AB and CD be the given lines, P the given 
 point. Assume any two points E and E' on AB, and 
 any point F on CD ; draw PE, PF, and EF. Through 
 E' draw E' F' parallel to EF ' ; draw E' P' parallel to 
 EP, and F 1 P' parallel to FP, intersecting in point P' . 
 Draw PP', the required line. 
 
 Problem 21. To construct a triangle, the lengths 
 of its three sides being given. 
 
 Let AB, CD, and EF be the given sides, and AB 
 be the base. With CD as radius, center A, describe 
 an arc at G. With EF as radius, center B, intersect 
 the preceding arc in point G. Draw AG and GB, 
 completing the required triangle AGB. 
 
 Problem 22. To construct a rectangle, the lengths 
 of its sides being given. 
 
 Let AB and CD be the given sides. At either end 
 of AB, as A, draw a perpendicular (Prob. 4) of indefinite 
 length, and upon it lay off EA equal to CD. With AB 
 as radius, center E, describe an arc at F. With CD as 
 radius, center B, intersect the preceding arc in point F. Draw EF and FB, com 
 pleting the required rectangle. 
 
GEOMETRICAL CONSTRUCTION. 
 
 Problem 23. To construct a polygon equal to a 
 given irregular polygon. 
 
 Let ABCDFE be the given polygon. Draw lines 
 dividing the given polygon into triangles, as ABE, EEC, 
 etc. Draw E' F 1 equal to EF, and on E' F' construct 
 triangle C' E'F' , equal to triangle CEF (Prob. 21). On 
 E' C' construct triangle E' B' C' , equal to triangle EEC. 
 By similar construction draw the triangles E' A' B' and 
 C'D'F' , completing the required polygon. 
 
 Problem 24. To construct a regular pentagon, the 
 length of one side being given. 
 
 Let AB be the given side. Bisect AB by the per- 
 pendicular FH. Make GH equal to GB. With radius 
 GB, centers B and H, draw arcs intersecting at J. 
 Draw AJ produced, and make JK equal to GB. With 
 radius KB, center B, intersect FH at F; with the same 
 radius, center F, draw the circle ABD. With AB as 
 radius, start at A, and cut the circle in points C, D, and 
 E. Draw AC, CD, DE, and EB, completing the re- 
 quired pentagon. 
 
 Problem 25. To construct a regular hexagon, the 
 lengtJi of one side being given. 
 
 Let AB be the given side. With radius AB, centers 
 A and B, describe arcs intersecting in point C. With 
 radius AB, center C, draw the circle AEB. With the same 
 radius, starting at point A, cut the circle in points D, E, F, 
 G, locating the remaining sides of the required hexagon. 
 
 Problem 26. To construct a regular pentagon, the 
 circumscribing circle being given. 
 
 Let AEB be the given circle. Draw any diameter, 
 AB, of the circle, and at its center, C, draw EC perpen- 
 dicular to AB. Bisect CB in K, and with EK as radius, 
 center K, draw arc EJ. With chord JE as radius, center 
 E, intersect the given circle in D. DE is one side of the 
 required pentagon. 
 
86 
 
 GEOMETRICAL CONSTRUCTION. 
 
 Problem 27. To construct a regiilar polygon of any 
 number of sides, the length of one side being given. 
 
 Let AB be the given side, and the number of sides 
 seven. With radius AB, A as center, draw the semi- 
 circle I4-B. Divide the semicircle into as many equal 
 parts as there are sides in the required polygon. Draw 
 AD, which is a side of the required polygon, connecting 
 point A with the second point of division in the semi- 
 circle. Bisect AB and AD (Prob. i), and produce the 
 bisectors to intersect in point C, the center of the required polygon. With radius 
 AC, center C, draw the circle AFH. With AB as radius, start at D, and cut the 
 circle in points E, F, G, and H, the remaining corners of the polygon. 
 
 Problem 28. To find the point of tangency of a 
 straight line and a circle. 
 
 Let AB be the given straight line, and DF the 
 given circle, described from C. From C draw CE per- 
 pendicular to AB (Prob. 6), intersecting AB at E, 
 the required point of tangency. 
 
 Problem 29. To draw a circular arc tangent to a 
 straight line and to a circle at a given point. 
 
 Let AB be the given straight line and E the given 
 point on circle DE described from point C. Draw CE 
 produced. Draw EF perpendicular to CE (Prob. 2). 
 Bisect angle EFA (Prob. 9). Point G, the intersection 
 of the bisector and of CE produced, is the center of the 
 required arc. 
 
 Problem 30. To connect two given lines by a re- 
 versed curve, given one point of tangency and the radii 
 of the two curves. 
 
 Let AB and CD be the given lines, and B the 
 given point of tangency. At B draw; the indefinite line 
 EF perpendicular to AB (Prob. 4) . Make BE equal to one given radius, and BF 
 equal to the other given radius. Draw the indefinite line HJ parallel to CD and at 
 a distance equal to EB from CD (Prob. 7). With radius EF, center F, draw arc 
 EJ to intersect HJ in point J. From J draw JC perpendicular to CD, intersecting 
 CD at C. With radius BF, center F, draw arc BK. With radius CJ, center J, 
 draw arc KC. BKC is the required curve. 
 
GEOMETRICAL CONSTRUCTION. 
 
 87 
 
 Problem 31. To connect two given parallel lines 
 by a reversed curve, given one point of tangency and the 
 point of reversed curvature. 
 
 Let AB and CD be the given lines, A the given 
 point of tangency, and K the given point of reversed c 6 
 curvature. Draw AK produced to meet CD at D. At points A and D, draw the 
 indefinite lines AE and DF, perpendicular to AB and CD. Bisect A K and pro- 
 duce the bisector to meet AE at E. Bisect KD and produce the bisector to meet 
 DFat F. With radius AE, center E, draw arc AK. With radius DF, center F, 
 draw arc KD. AKD is the required curve. 
 
 Problem 32. To connect two given parallel lines 
 by a reversed curve, given the points of tangency and the 
 ratio of the radii. 
 
 Let AB and CD be the given parallel lines, B and 
 C the given points of tangency, and let the required 
 radii be in the ratio of HJ to JK. At the points of 
 tangency B and C, draw the indefinite lines BE and CF, perpendicular to the given 
 lines. Connect B and C and find point G, so that BG is to GC as HJ is to JK 
 (Prob. 15). Bisect BG and produce the bisector to meet BE at E. Bisect GC 
 and produce the bisector to meet CF at F. With radius BE, center E, draw arc 
 BG. With radius CF, center F, draw arc CG. BGC'is the required curve. 
 
 Problem 33. To connect two given non-parallel 
 lines by a reversed curve, given the points of tangency 
 and the ratio of the radii. 
 
 Let AB and CD be the given lines, B and C the given 
 points of tangency. At points B and C, draw the indefi- 
 nite lines BE and CF, perpendicular to AB and CD. 
 Connect B and C. Bisect BC at G and with radius 
 BG, center G, draw the indefinite arc BH. On BC find point J, so that the ratio 
 of ZT/toyCis the given ratio of the radii (Prob. 15). From J draw JK perpen- 
 dicular to AB, andyZ, perpendicular to CD. Make LM equal to B K. With radius 
 MC, center C, describe an arc intersecting arc BH in H. Draw BH of indefinite 
 length, and make BP equal to BC. From P draw PQ perpendicular to CD, make 
 PQ equal to CJ, and draw BQ. From C draw " parallel to BQ, intersecting BE 
 in E. From . draw ZTjF parallel to BP, intersecting CF at F. With radius Z?.Zi, 
 center E, draw arc .Z?Af. With radius CF, center F, draw arc NC. BNC is the 
 required curve. 
 
88 
 
 GEOMETRICAL CONSTRUCTION. 
 
 Problem 34. To draw a circle tangent to 
 two given circles and at a given point in one of 
 them (tzvo solutions). First Method. 
 
 Let ABD and EFH be the given circles, 
 and B the given point. Draw from point B 
 through C, the center of circle ABD, and pro- 
 duce the line indefinitely. 
 
 First solution. Make BJ equal to the 
 radius of circle EFH. Draw JG, bisect it, and 
 produce the bisector to intersect CB produced 
 in point L. With BL as radius, center L, draw 
 arc BO of the required circle. 
 
 Second solution. Make BM equal to the 
 radius of circle EFH. Draw MG, bisect it, and 
 produce the bisector to intersect CL in N. 
 With BN as radius, center N, draw BP, the re- 
 quired circle. 
 
 Problem 35. To draw a circle tangent to 
 two given circles and at a given point in one of 
 them (two solutions] . Second Method. 
 
 Let ABD and MEJ be the given circles, 
 and B the given point. Draw from point B 
 through C, the center of circle ABD, and pro- 
 duce the line indefinitely. Through G, the cen- 
 ter of circle MEJ, draw a line parallel to BC, 
 cutting the circle MEJ in points E and F. 
 
 First solution. Draw BE produced to meet 
 the circle MEJ in point J. Draw JG produced 
 to meet BC at L. With BL as radius, center 
 L, draw arc BOJ oi the required circle. 
 
 Second solution. Draw BF intersecting 
 circle MEJ in point M. Draw GM produced 
 to meet BC at N. With BN as radius, center 
 N, draw BMP, the required circle. 
 
 F\ 
 
89 
 
 GEOMETRICAL CONSTRUCTION. 
 
 Problem 36. To inscribe a circle within a triangle. 
 
 Let ABD be the given triangle. Bisect any two 
 angles of the triangle (Prob. 9) . The intersection C of 
 the bisectors is the center of the required circle. 
 
 Note. If adjacent exterior angles, as EAB and 
 ABF, be bisected, the bisectors will intersect in a point, 
 C', which is the center of a circular arc tangent to one 
 side of the triangle and to two of its sides produced. 
 
 Problem 37. Witliin an equilateral triangle to in- 
 scribe three equal circles, each tangent to the otliers and 
 to two sides of the triangle, 
 
 Let ABC be the given equilateral triangle. Bisect 
 the sides in points D, E, and F. Draw FA, DC, and 
 BE. With radius DE, centers D, E, and F, draw arcs 
 EF, FD, and DE. The intersections G, J, and H are 
 the centers of the required circles. 
 
 Problem 38. Within an equilateral triangle to 
 inscribe six equal circles, tangent to each other. 
 
 Let ABC be the given equilateral triangle. Bisect 
 the sides in points D, E, and F. Draw BE, DC, and 
 FA. Bisect the angle EBC by line BG, intersecting AF 
 in point G. Make DJ and EK each equal to FG, and 
 through points /, K, and G, draw L M, LH, and HM, 
 parallel to the sides BC, BA, and AC of the triangle. 
 With GF as radius, centers L,J, H, K, M, and G, de- 
 scribe the required circles. 
 
 Problem 39. Within a given circle to inscribe 
 three equal circles tangent to each other. 
 
 Let BDG be the given circle, center C. Divide 
 the circumference into six equal parts by making the 
 chords AD, DF, etc., each equal to the radius CA of the 
 circle. Draw the diameters AG, BF, and ED. Pro- 
 duce any diameter, as BF, and make FH equal to CF. 
 Draw GH and bisect the angle CHG by the line HJ, in- 
 tersecting CG in point /. With radius JC, center C, draw the circle MKL, 
 intersecting the diameters in points M, K, and L, the centers of the required 
 circles. 
 
9 o 
 
 GEOMETRICAL CONSTRUCTION. 
 
 Problem 40. Within a given circle to inscribe any 
 given number of equal circles tangent to each other. 
 
 Let DAE be the given circle, and the required 
 number of inscribed circles five. Divide the circle DAE 
 into ten equal parts (Prob. 26), and draw the diameters 
 AB, DE, etc. At the extremity of any diameter, as B, 
 draw the tangent FG perpendicular to AB, and produce 
 the adjacent diameters to intersect the tangent at Fand 
 G. In the triangle CFG find the center H of the 
 inscribed circle (Prob. 36). With radius HC, center C, 
 giving the remaining required centers, L, J, K, and M. 
 
 draw the circle LJK, 
 
 Problem 41. 7!? draw an ellipse, 
 given the rectangular axes. First MetJi- 
 od. 
 
 Let AB be the major axis, and DE the 
 minor axis. With radius equal to one-half 
 the major axis, centers D and E, intersect 
 AB in. points F and F' ', the foci of the 
 required curve. Divide by eye, FC and CF' into any number of parts, decreasing 
 from Cto Fand from Cto F' . To locate the points of the curve : With A$ as radius, 
 center F, describe an arc at L. With B$ as radius, center F , intersect the pre- 
 ceding arc in L, a point in the required curve. With radii A$, Aj, A2,and Ai, 
 center F, describe arcs at K, /, H, and G. With radii Bj, j, B2, and Bl, center 
 F', intersect in the same order the arcs at K t J, H, and G, four additional points 
 in the required curve. Repeat in each of the remaining quadrants. 
 
 Problem 42. To draw a tangent to an ellipse at a given point in the curve. 
 First Method. 
 
 Let Q be the given point. Find the foci F and F' (Prob. 41). Draw F'Q 
 and FQ produced. Bisect angle F 1 QR (Prob. 9). The bisector ST is the required 
 tangent. 
 
 = 
 Problem 43. To draw a tangent to an ellipse from a given point outside the 
 
 curve. First Method. 
 
 Let J/be the given point. Find the foci F and F' (Prob. 41). With FJ/as 
 radius, center M, draw arc FN. With AB as radius, center F', intersect arc FN 
 in point N. Draw NF 1 . Bisect the angle FMN (Prob. 9) and draw the bisector, 
 intersecting F'TVat P. MP is tangent to the ellipse at point P. 
 
GEOMETRICAL CONSTRUCTION. 
 
 Problem 44. To draw an ellipse, given 
 the rectangular axes. Second Method. 
 
 Let AB and DE be the axes. With 
 A C and DC as radii, center C, describe the 
 major and minor auxiliary circles AGQ and 
 DJ' E. Assume points in the outer circle, 
 as G, H,J. Draw radii CG, CH, and CJ. 
 Draw lines parallel to AB from points G f , 
 H', and J' , intersected by lines parallel to 
 DC from G, H, and / in ", H", and /", 
 points in the required curve. Repeat in each of the remaining quadrants. 
 
 Problem 45. 71? draw a tangent to an ellipse at a given point in the curve. 
 Second Method. 
 
 Let K be the given point on the ellipse. At K 1 ', the corresponding point on 
 the major auxiliary circle (see Prob. 44), draw the tangent LK 1 ', perpendicular to 
 the radius K' C, meeting the major axis at L. Draw LK, the required tangent. 
 
 Note. The minor auxiliary circle and minor axis may be similarly used. 
 
 Problem 46. 7<? draw a tangent to an ellipse from a given point outside the 
 curve. Second Method. 
 
 Let M be the given point. Find either focus, as F (Prob. 41). On MF as 
 diameter, draw a circle intersecting the major auxiliary circle in points TV and O, 
 through which draw MN and MO, the required tangents. 
 
 To find the exact point of tangency, as of MP. Take the point P where the 
 tangent MO intersects the major axis. On CP as diameter draw a semicircle, 
 intersecting the major auxiliary circle at Q. Find Q" , the point on the ellipse 
 corresponding to Q (Prob. 44). Point Q" is the point of tangency. 
 
 Note. The minor axis and minor auxiliary circle may be similarly used. 
 
 Problem 47. To draw an ellipse, 
 given the oblique axes. 
 
 Let AB be the major axis, and DE 
 the minor axis. Through point E draw 
 HJ parallel to AB, and through point A, 
 HF parallel to ED ; complete the parallelogram HFGJ, containing the points D and 
 B. Divide CB and GB into any number of similarly spaced parts, as shown by 
 /, 2, 3, and /', 2', 3'. Draw Dl' , D2' , Df, and El, E2, Ej produced. The 
 intersections K, L, and M, are points in the required curve. 
 
 Note. The same construction applies when the axes are at right angles. 
 
GEOMETRICAL CONSTRUCTION. 
 
 Problem 48. To find the axes of symmetry 
 (rectangular axes] of an ellipse. 
 
 Let AC and CB be the oblique semi-axes. 
 Draw AD perpendicular to CB, and make AD 
 and AE each equal to CB. Draw DC and 
 CE, and produce both indefinitely. Bisect the 
 angles DCE and ECF; the bisectors CM and 
 CP are the major and minor axes respectively. 
 
 To find the extremities of the rectangular 
 axes. Make CX and CY each equal to CE. 
 Bisect Z>Fand lay off CL and CM, each equal 
 to one-half of DY ; bisect DX and lay off CN 
 and CP, each equal to one-half of DX. Points 
 L, M, N, and P are the extremities of the rec- 
 tangular axes. 
 
 Problem 49. To draw a parabola, given 
 the focus and the directrix. 
 
 Let AR' be the directrix of the parabola, 
 BC its axis, and F the focus. Bisect BF in 
 point Z>, the vertex of the parabola. Assume 
 on the axis BC, any points, as G, H, . . . M, and 
 through these points draw the indefinite lines 
 G'G", H'H", etc., parallel to AR' . With BG 
 as radius, center F, intersect G'G" in points G' 
 and G" ; with radius BH, center F, intersect 
 H'H" in H' and H" ', and so on. 
 
 First 
 
 Problem 50. 71? draw a tangent at a given point on a parabola. 
 Method. 
 
 Let L' be the given point. Draw from L' to the focus F. Through L' draw 
 L'N parallel to BC. Bisect the angle JVL'Fby L'O, the required tangent. 
 
 Problem 51. To draw a tangent to a parabola from a given point outside the 
 curve. First Method. 
 
 Let P be the given point. Connect P with the focus F. With FP as radius, 
 center P, draw an arc intersecting the directrix AR' in points R and R' . Bisect 
 the angles RPF&nd FPR' ; the bisectors PS and PS' are the required tangents. 
 
 To find the exact points of tangency. From R and R' draw lines parallel to 
 BC, intersecting the tangents PS and PS' in 5 and S' , the required points. 
 
GEOMETRICAL CONSTRUCTION. 
 
 93 
 
 Problem 52. To draw a parabola, 
 given the axis, the vertex, and a point on 
 the curve. 
 
 Let AB be the axis of the parabola, 
 A its vertex, and D a point on the curve. 
 Complete the rectangle ABDC. Divide 
 AC into any number of equal parts, say 
 five, by points /, 2, J, 4. Divide CD into 
 the same number of equal parts by points 
 i', 2', 3', 4' . Through points /, 2, J, 4, 
 draw lines parallel to AB. Draw Al' , A2', 
 Aj', A 4', intersecting the parallels from 
 /, 2, 3, 4, in G, H,J, K, points in the required curve. 
 ABD'O. 
 
 To find the focus. From point 7 draw a line perpendicular to A 4' 
 produced to intersect the axis AB in F, the required point. 
 
 Problem 53. To drazv a tangent at a given point on a parabola. Second 
 Method. 
 
 Let D be the given point. Draw CD parallel to AB, intersecting AC in point 
 C. Bisect AC in. point L. Draw LD, the required tangent. 
 
 Problem 54. To draw a tangent to a parabola from a given point outside the 
 curve. Second Method. 
 
 Let .A^be the given point. Connect TV with the focus .F(Prob. 52). On NF 
 as diameter draw a circle intersecting CC' in points O and O' . Through O and 
 O' draw NP and NP' , the required tangents. 
 
 To find the exact point of tangency. Make O' T equal to O' A . Through T 
 draw TP' parallel to AB, intersecting NP' in P' , the required point of tangency. 
 
 Problem 55. To dra^v a hyperbola, 
 given tJie major axis and one point on the 
 curve. 
 
 Let AB be the major axis, and D the 
 given point. Draw the rectangle BCDE. 
 Divide CD and ED each into any number 
 of equal parts, in this case four. Draw Bl, 
 B2, B$, and Al' , A2 1 , Aj f , intersecting in 
 F, G, and H, points in the required curve. Draw the rest of this branch and the 
 opposite branch of the curve by the same construction. 
 
94 
 
 GEOMETRICAL CONSTRUCTION. 
 
 Problem 56. To find the asymptotes 
 and foci of a Jiyperbola. 
 
 Let AB\>z the major axis of the hy- 
 perbola, and G a known point on the curve. 
 Bisect AB by the perpendicular DH (Prob. 
 i). With radius AC, center C, draw the 
 circle ABH. 
 
 To find the asymptotes. At H draw 
 the tangent HJ parallel to AB. Through 
 the known point of the curve, G, draw DG parallel to AB. With DG as radius, 
 center C, draw an arc intersecting HJ in point J. Make DE equal to HJ and 
 draw CE, one required asymptote. Make angle KCL equal to angle LCM 
 (Prob. 1 1), and draw KC, the other required asymptote. 
 
 To find the foci. At the points of intersection, TV and N', of ME with the 
 circle ABH, draw NF and N' F' perpendicular to ME, intersecting the major 
 axis AB in points /''and F', the required foci. 
 
 Note. The circle ABH'vs> known as the major auxiliary circle. 
 
 Problem 57. To draw a tangent to 
 a hyperbola at a given point in the curve. 
 
 Let D be the given point. Draw the 
 major auxiliary circle on AB as diameter. 
 From D draw DE perpendicular to AB 
 (Prob. 5). On EC as diameter, draw the 
 semicircle EGC, intersecting the major 
 auxiliary circle in point G. From G draw 
 GH perpendicular to AB. Draw DH, the 
 required tangent. 
 
 Problem 58. To draiu a tangent to a hyperbola from a given point outside 
 the curve. 
 
 Let / be the given point. Connect / with either focus, as F' . On JF' as 
 diameter, draw a circle intersecting the major auxiliary circle at points K and 
 K' . Draw KJzn&JK', the required tangents. 
 
 To find the exact point of tangency. Tangent JK' intersects the major axis 
 AB in point L. At L draw LM perpendicular to AB and intersecting the major 
 auxiliary circle at M. Draw CM, and perpendicular to CM draw MN. Draw NO 
 perpendicular to AB, intersecting the tangent JK' in point O, the required point 
 of tangency. 
 
GEOMETRICAL CONSTRUCTION. 
 
 Problem 59. To draw an ellipse with a 
 trammel, given the rectangular axes. 
 
 Let AB and CD be the given axes. On 
 the edge of a strip of paper or cardboard, mark 
 the distance A' E' equal to the semi-major axis 
 AE. Mark the distance E' F equal to the 
 semi-minor axis CE. Place the trammel so that 
 point A' falls on the axis CD, produced if 
 necessary, and point F on the axis AB ; then 
 point E' will be a point of the required ellipse. 
 Find as many points as desired, and draw the 
 curve. 
 
 Problem 60. To draw a curve approximat- 
 ing an ellipse, composed of circular arcs, given 
 the major axis. 
 
 Let AB be the given major axis. Make 
 AC and C'B each equal to five-sixteenths of AB 
 (Prob. 15). With AC as radius, centers 7 and 
 O ', draw the circles ADE' and DBF', intersect- 
 ing in D and D' . Draw DC, DC', D' C, and 
 D'C, all produced. With radius E' D, centers 
 D and D 1 , draw arcs E'F' and EF, completing 
 the required curve. 
 
 Note. The minor axis of this curve is three- 
 quarters of the major axis. 
 
 Problem 61. To draw a curve approximat- 
 ing an ellipse, composed of circular arcs, given 
 the major and minor axes. First Method. 
 
 Let AB be the major axis and DE the 
 minor axis. Draw DB. Make CG equal to CD 
 and make DH equal to GB. Bisect HB by line 
 f K, intersecting CB in L' ' , and CE produced in 
 J' . Make CJ equal to CJ' , and CL equal to 
 CL' . Draw J' L, JL' , and JL, all produced. 
 To draw the curve : With radius f D, centers 
 /' and /, draw the arcs MDN and M' EN' . 
 With radius LA, centers L and L', draw the 
 arcs MAM' and NBN' . 
 
 95 
 
96 
 
 GEOMETRICAL CONSTRUCTION. 
 
 Problem 62. To draiv a curve ap- 
 proximating an ellipse, composed of circu- 
 lar arcs, given the major and minor 
 axes. Second Method. 
 
 Let AB be the major axis, and DE 
 the minor axis. Produce DE indefi- 
 nitely in both directions. Through E, 
 draw HJ parallel to AB, and complete 
 the rectangle HFGJ, its sides pass- 
 ing through points A, D, and B. Draw 
 AD. From point jpdraw a perpendicular 
 to AD (Prob. 5), intersecting AB in Z 
 and produced to intersect DE produced 
 in K' . Make CK equal to CK' , and 
 CL' equal to CL. With radius DC, 
 center C, draw an arc intersecting AB 
 in point N. On AN as a diameter draw the semicircle AMN. Make CO and CO' 
 each equal to MD, and with radius OK, centers K and K' , draw arcs through 
 points O and O' . Make ^/^ and P',5 each equal to MC, and with radius LP, 
 centers Z and Z', intersect the arcs drawn through O and 0' in points Q, Q', 
 R, and R' . Draw, of indefinite length, LQ, LR, L' Q' , and L' R' . Draw, of 
 indefinite length, K' R, K'R', KQ, and KQ'. To draw the required curve: 
 With radius DK' , centers K 1 and K, describe arcs SDTand S'ET'. With radius 
 SR, centers R, R' , Q, and Q ', draw arcs S/, S'U' t TV, and T' F'. With radius 
 AL, centers Z and Z', draw arcs UAU' and VBV . 
 
 Problem 63. To draiv an oval, given its width. 
 
 Let AB be the width of the oval. On AB as di- 
 ameter draw the circle AEB. With radius AB, centers 
 A and B, draw arcs intersecting in D. Draw DC. 
 Bisect arcs AE and EB in points Fand F' . Draw ^l/ 7 ' 
 and BF produced to intersect arcs AGD and DG'B in 
 and G' . Bisect AC and CB in Zf and ZT. Draw 
 HD and //'Z>, intersecting ^4G' and GZ? in Z and Z'. 
 Bisect *jy in K and draw ZAT and L' K produced. 
 With raums GZ', centers L' and Z, draw arcs GM and 
 J/'G'. Bisect HC and #' in ^V and N' . Draw A^Z> and 
 N'D, intersecting LM' and J/Z' in O and <9'. Draw 
 
 and O' E produced. With radius MO' , centers O' and O, draw arcs MP and 
 !/'. With radius EP, center E, draw arc PP' , completing the required curve. 
 
GEOMETRICAL CONSTRUCTION. 
 
 97 
 
 Problem 64. Given the short diameter, to draw 
 an oval the long diameter of which shall be iy 2 times 
 the short diameter. 
 
 Let AB represent the short diameter. Bisect 
 AB and draw the perpendicular DE produced. 
 With center C, draw the circle ADE. Produce AB 
 in each direction, and make AF, BF' ', and EG, each 
 equal to AC. Bisect EG in H. Draw /7/and F'H 
 produced. With radius FB, centers Fand F', draw 
 arcs BJ' and AJ. With radius GH, center H, draw arc JGJ 1 ', completing the 
 required curve ADBJ'GJ. 
 
 Problem 65. To draw a variable 
 spiral. 
 
 Let CD be the measure of the re- 
 quired curve. Divide CD into eight 
 equal parts, as indicated by the points /, 
 2, . . . /. Upon division 4-$ as diameter 
 draw a circle, the eye of the spiral. 
 (See also the enlargement, Fig. /?.) On 
 4-5 as a diagonal draw the square E^F^, 
 its diameters GK and JH t and the 
 square GHKJ. Divide GL into two 
 equal parts, and through the point of 
 division draw $ 4' . Divide LM into six 
 equal parts, and through the points of 
 division draw 8'f , 4' 3' , i' 2' , and $6'. 
 Divide MK into tJiree equal parts, and 
 through the points of division draw 3' 2' 
 and f 6' . To draw the curve : With 4-1' 
 as radius, center /', draw the arc ^N, 
 carried to the line 2' l' produced. With 
 radius N2 r , center 2' ' , draw the arc from 
 point N to O, lying in 3' 2 1 produced. 
 With radius Oj f , center J', carry the arc 
 to 4 '3' produced, and so on. Take for 
 successive centers the points 4* ', $', 6' , 
 /, 8',J, K, H, and G, and draw the arc 
 described from each center to the line drawn through the center used and the 
 next one in advance. 
 
9 8 
 
 GEOMETRICAL CONSTRUCTION. 
 
 Problem 66. To draw an Ionic 
 volute. 
 
 Let AB, Fig. A, be the measure 
 of the required curve. Divide AB into 
 seven equal parts. Through the fourth 
 point of division from A draw CD, in- 
 definite in length and perpendicular to 
 AB. Take for the center of the spiral 
 any point on CD, and from this point, 
 with radius equal to one-half of a division 
 of AB, describe circle FGHJ, the eye of 
 the volute. (See also its enlargement, 
 Fig. B.} Draw the diameter of the eye, 
 GJ, perpendicular to FH. On Fffas a 
 diagonal draw the square FGHJ, its 
 diameters KNand ML, and the square 
 KLNM. Divide KM into six equal 
 parts. Draw l"2" parallel to and dis- 
 tant from FH one-half of 3' 4'. Draw 
 9"IO" parallel to and distant from MN 
 one-half of 5' ' M. Project points /' and 
 2' to GO, and through the points thus 
 obtained draw 8"f and /'j" parallel to 
 KL. Draw $"6" parallel to and mid- 
 way between i"2" and (}"lo". Draw 
 8' '0", 4" 5", 3" 2", and 7" 6" parallel to 
 
 KM and separated by spaces each equal to a division of KM. To draw the outer 
 spiral TUV (Fig. A) : Take Gl" as radius, center /", and draw arc GE 
 tangent to the eye of the volute at G, and carried to the line 2" l" produced. 
 With radius 2" ', center 2" , draw from E to Q, lying in 3" '2" produced. With 
 radius <2j" center j", describe an arc from Q to 4" 3" produced, and so on. Take 
 for successive centers the points 4"5"6"f'8"c)"lO", L, and K, and draw the arc 
 described from each center to a line drawn through the center used and the next 
 one in advance. To draw the inner spiral WXY (Fig. A) : Locate the point P in 
 OH, midway between point O and line 3" 2" . Locate the point 5 midway between 
 P and 2" . With radius FS, center S, draw an arc from F to Z, lying in 3" 2" 
 produced. Locate point R, making, by eye, distance 3" R equal to 2" S. With 
 radius ZR, center R, draw an arc from Z to Z' ', lying in 4" 3" produced. The 
 dot placed between 4" and O indicates the next center, and is placed a distance 
 from 4" equal to 3" R. Continue in like manner. 
 
GEOMETRICAL CONSTRUCTION. oo 
 
 Problem 67. To draw an Archimedean 
 spiral. 
 
 Let AN be the measure of the spiral. 
 With NA as radius, center A, describe the 
 circle ^Nj f . Divide line AN and the circle 
 y 'Nf' into the same number of equal parts, as 
 twelve. Draw Ai' , A2 1 , . . . An'. With A as 
 center, draw arcs from each numbered point in 
 AN, to intersect the correspondingly numbered 
 line drawn from center A to the circle p'N}', 
 giving A,>, C, . . . N, which are points in the required curve. 
 
 Note. To obtain a spiral of two turns, divide AN into twice as many parts as 
 the circle p'Nj'. 
 
 Problem 68. To draw the involute of a 
 circle. 
 
 Let Ajffbe the given circle. Lay off on 
 the circle equal spaces as indicated by the points 
 I, 2, . . . 5, and at each point draw a tangent to 
 the circle. Lay off the chord lA, once on 
 tangent IB, twice on 2C, three times on jD, 
 etc., giving A, B, C, . . . G, points in the re- 
 quired curve. 
 
 Note. In this and the succeeding problems a more accurate result is ob- 
 tained by using the true length of the circular arc instead of its chord (Prob. 73). 
 
 Problem 69. To draw a cycloid. 
 
 Let the required curve, AA'" A v \ be generated by point A lying in the circle 
 BDA, which rolls on the straight line AE. 
 Divide the semi-circumference Aj6 into six or 
 more equal parts as indicated by the points 
 A, I, . . . 6. Starting at point A, lay off the chord 
 A I along AE, giving points /', 2' , . . . 6' . Draw 
 the path, CC vi , of the center of the rolling circle. 
 From i', 2', . . . 6' erect perpendiculars to intersect CC vi in points C', C", . . . C. 
 With CA as radius, centers C, C", . . . >", draw arcs tangent to AE at points 
 l', 2' , . . . 6' . To find points, as A', A", . . . A"\ in the required curve. First 
 method. Make the chord i'A' equal to the chord Ai ; make chord 2' A" equal to 
 chord A2, etc. Second method. Intersect arcs A'l', A"2 r , . . . A vi 6' by lines 
 drawn parallel to AE, and passing through points j, 2, . . . 6. 
 
IOO 
 
 GEOMETRICAL CONSTRUCTION. 
 
 Problem 70. To draw art extetior epicycloid. 
 
 Let the required curve, A A'" A, be generated by point A, lying in the circle 
 BCA, which rolls on the circular arc DAE. Divide the semi-circumference Aj6 
 into six or more equal parts as indicated by the points A, i, ... 6. Starting at 
 point A, lay off the chord Ai along the arc AE, giving the points j', 2' , . . . 6' . 
 With the center, K, of arc AE draw arc HGJ y the path of the center of the rolling 
 circle. From K draw straight lines through /', 2' , . . . 6' , intersecting HGJ in 
 points G', G", . . . G vi . With radius GA, centers G 1 ', G", . . . G vi , draw arcs tangent 
 to the directing circle at points /', 2' , . . . 6' '. To find points A' , A", . . . A vi in the 
 required curve. First method. Lay off on arc l'A' the chord l'A' equal to the 
 chord Ai ; make chord 2' A" equal to chord A2 ; etc. Second method. With 
 K as center, draw arcs, as J 'A'" and jA, from the points of division in the 
 rolling circle BCA to intersect, as at A'" and A"', each of its successive positions. 
 
 Problem 71. To draw a Jiypocycloid. 
 
 Let the required curve, FF'"F V \ be generated by point F, lying in the circle 
 MLF, which rolls on the circular arc DAE. Divide the semi-circumference Fj6 
 into six or more equal parts as indicated by the points /%/,... 6- Starting at F, lay 
 off the chord Fi along arc AE, giving the points /', 2', . . . 6' '. With K as center, 
 draw arc NOP, the path of the center of the rolling circle. From K draw straight 
 lines through /', 2', . . . 6', intersecting NOP in points O', O", . . . CK With FO 
 as radius, centers O r , O", . . . O 7 "', describe arcs tangent to the directing circle at 
 /', 2 f ,...6 f . To find points, as F' , F", . . . F v *, in the required curve. First 
 method. Lay off on arc i'F' the chord i' F' equal to the chord Fi ; make chord 
 
GEOMETRICAL CONSTRUCTION. 
 
 101 
 
 2'F" equal to chord F2; etc. Second method. With K as center, draw arcs, as 
 F' i and F"2, from the points of division in the rolling circle MLF to intersect, as 
 at F' and F", each of its successive positions. 
 
 Problem 72. To draw an interior 
 epicycloid. 
 
 Let point A, lying in circle BAC 
 which rolls on circle ADE, be the genera- 
 trix. From F, the center of the directing 
 circle, draw a circle HJG, passing through 
 the center G of the rolling circle. Start- 
 ing at point A, lay off on the directing 
 circle any equal distances, as indicated by 
 the points I, 2, . . .6. Draw iF, 2F, . . .$F, 
 produced to intersect the path of the center 
 of the rolling circle in points G f , G", . . . G vi . With each of these points as a center, 
 radius A G, draw arcs tangent to the directing circle at /, 2, . . . 6. From the tangent 
 point of each arc, lay off the chord of arc A I once on arc I A', twice on arc 2 A", 
 three times on jA" f , etc., giving A', A", . . . A vi , points in the required curve. 
 
 Problem 73. To lay off on a straight line the 
 length of a given circular arc. An approximate method. 
 
 Let ABC be the given arc. Draw AD tangent to 
 arc ABC. Draw chord CA produced. Bisect AC at E 
 and lay off AF equal to AE. With CFas radius, center F, intersect AD in point 
 G ; then AG is equal to arc ABC, very nearly. 
 
 Note. If the arc subtends more than about 60, it should be subdivided 
 before using this construction, which becomes more accurate the smaller the sub- 
 tended angle. Thus, if the arc subtends 60, the length obtained is about one part 
 in 900 too short ; if 30, about one part in 15,000. 
 
 Problem 74. To lay off on a circular arc of given 
 radius the length of a given straight line. An approxi- 
 mate method. ^ 
 
 Let AB be the given straight line. With the 
 given radius, draw arc ACD tangent to AB. Make AE equal to \ AB. 
 
 With 
 
 radius BE, center E, intersect arc ACD in point F; then arc ACF is equal to 
 AB, very nearly. 
 
 Note. The result is more accurate the smaller the angle subtended by the 
 arc, substantially as in Prob. 73. 
 
CHAPTER VI. 
 
 SELECTION AND ARRANGEMENT. 
 
 48. The Layout. This is a freehand or instrumental sketch in which is 
 planned the general scheme of a proposed drawing. The principal requirements in 
 making a layout are taste and good judgment in the selection and arrangement of 
 the matter to appear in the drawing. 
 
 While in office practice selection and arrangement are likely to be restricted, 
 more or less, on account of the fixed character of such work, yet, when opportunity 
 offers, especially in architectural practice, taste and good judgment may be of 
 decided value.* As these are personal qualities, it is evident that no hard-and-fast 
 rules can be given for the guidance of the beginner ; he must depend largely upon 
 observation, criticism, and experience. 
 
 In order to emphasize the difference between good and bad selection and 
 arrangement, first take a case illustrating the latter, as follows : Let it be required 
 
 to select eight or ten geometri- 
 cal constructions from the pre- 
 ceding chapter, and to arrange 
 them on a sheet of some given 
 size. 
 
 It is evident that the selec- 
 tion shown in Fig. 77 is bad, 
 because the problems are not all 
 of the same general character, 
 the last two problems being 
 wholly out of keeping with the 
 remaining simple ones. As to 
 Fig. 77- the arrangement, the term does 
 
 not apply to such haphazard placing there is no semblance here of either order 
 or taste. 
 
 * Sooner or later, from one source or another, the student is sure to hear it said that matters of 
 taste have no place in engineering ; that time spent, for example, in making well-formed letters, or an 
 effective title, or in attempting to make a design agreeable to the eye, as well as structurally correct, is 
 time wasted. From a strictly commercial and utilitarian standpoint this may be true ; but, on the other hand, 
 some engineers recognize the fact that beauty in engineering works, even in machinery, is possible, and 
 that, with a growing public appreciation, the element of beauty will not only be demanded, but paid for. 
 Already in the building of several important bridges the question of beauty has been recognized by the 
 engineer and architect working in conjunction. Apart from practical considerations, however, a student 
 cannot afford, as a matter of education, to remain blind to the difference between good and bad taste, 
 
 (102) 
 
SELECTION AND ARRANGEMENT. 
 
 103 
 
 APPLIED GEOMETRY 
 
 Fig. 78. 
 
 As the question of selection is inseparable from the requirements of each par- 
 ticular drawing, no definite rules can be given other than the one general rule that 
 the selection should be consistent with the purpose of a drawing. In the subject 
 of arrangement, the following methods are important. 
 
 (a) In designing an arrangement, quicker and better results will be obtained if, 
 instead of clinging to mechanical methods, the broader methods of freehand draw- 
 ing be adopted. Use a rather 
 soft pencil, and start with the 
 intention of spoiling several 
 sheets of paper, if necessary, to 
 secure a satisfactory result 
 a good result is always worth 
 more than the paper. When 
 sketching in the views, let the 
 pencil swing freely over the 
 surface of the paper, in all di- 
 rections, as suggested by the 
 arrows, Fig. 78. Let the mo- 
 tion be from the arm rather 
 than from the wrist or fingers ; 
 the freedom of motion thus obtained tends, in itself, to prevent one from see- 
 ing things in a detailed, constrained way. Do not begin by placing a problem 
 up in one corner of the sheet, then another beside it, then a third one close to the 
 second, and so on until the sheet is filled ; but strike out boldly, and with the ob- 
 ject of indicating roughly the shapes and quantity of the more important figures, 
 in order to gain quickly a first impression of the (tentative) arrangement as 
 a whole. 
 
 In working for an arrangement, it is necessary to take into account not only 
 the shape and quantity of the problems, but also the shape and quantity of the 
 spaces between problems, and between problems and the border line of the sheet. 
 First place the dominant or most important problem, as A, Fig. 78, thereby 
 breaking up the regular (rectangular) figure of the sheet into an irregular shape. 
 Next place an important problem, as B and C, in a manner best calculated to fill 
 the irregular space satisfactorily, thereby breaking up the surface into new irreg- 
 ular spaces, the shape and size of each of which must be considered in placing ad- 
 ditional problems, as, for example, those shown in Fig. 79. 
 
 When a rough basis for what appears to be a satisfactory arrangement is se- 
 cured, as in Fig. 79, then work out the problems with more care freehand, or with 
 ruler and compass, but only to the extent necessary to serve as a basis for the fin- 
 
104 
 
 SELECTION AND ARRANGEMENT. 
 
 APPUE.O GEOMETRY 
 
 Fig- 79- 
 
 ished sheet. In rearrangements it is convenient to make changes on tracing paper 
 placed over the first layout, and for succeeding changes to use a fresh sheet of trac- 
 ing paper placed over the pre- 
 ceding one. In some cases it is 
 convenient to cut up the sheet 
 so that the problems or views 
 of an object may be moved 
 about until the desired arrange- 
 ment is obtained, after which 
 the loose pieces may be pasted 
 in position. 
 
 (^) Forms of arrangement. 
 A layout should be begun with 
 some definite scheme or form of 
 arrangement in mind. If it is 
 found that the subject matter 
 does not lend itself to a proposed scheme, other forms may be experimented with 
 until a form is obtained which proves satisfactory. 
 
 Symmetrical lateral arrangements ; balance. If the problems or views on 
 a sheet be regarded as so many actual zveights, then, in viewing the sheet, it may be 
 considered whether the weights on opposite sides of the center lines of the sheet 
 counterbalance. In an arrangement symmetrical with respect to the vertical center 
 line of a sheet, an appearance of stability may be obtained by making the problems 
 placed on the center line larger than those placed on either side. 
 
 Symmetry with respect to a central draiving. The central drawing should be 
 the largest on the sheet, and the other drawings should balance, both laterally and 
 vertically, with respect to the central drawing. 
 
 Abstract arrangement. In this form the problems may be placed irregularly, 
 but exaggerated and grotesque effects should be avoided. An effect of stability 
 may be secured by making the weights of the problems placed low on the sheet 
 somewhat heavier than of those placed high on the sheet or by giving the ar- 
 rangement, as a whole, the form of a truncated pyramid with slightly sloping sides. 
 The problems should fill the sheet ; that is, an arrangement should appear 
 neither crowded nor scant. 
 
 In Figs. 80, 8 1, 82, 83, and 84 are given as examples and for criticism 
 specimens of students' work in selection and arrangement, reproduced from draw- 
 ings 1 8" x 26". Criticisms : 
 
 Fig. 80. The sheet is sparsely filled. The left-hand two problems of the lower 
 line are too small ; the title is too large compared with the size of the problems. 
 Fig. 81. The sheet is crowded. 
 
EXAMPLES OF SELECTION AND ARRANGEMENT. 
 
 Avoid 
 
 105 
 
 APPLIED GEOMETRY 
 
 
 Avoid 
 
 Fig. 80. 
 
 APPLIED GEOMETRY 
 
 Fig. 8 1 
 
io6 
 
 EXAMPLES OF SELECTION AND ARRANGEMENT. 
 
 
 APPLIED 
 GEOMETRY 
 
 Fig. 82. 
 
 APPLIED 
 GEOMETRY 
 
 , , J ,, -. 
 
 k-i r ... 
 
 Fig. 83. 
 
SELECTION AND ARRANGEMENT STUDY PLATE 6. 
 
 107 
 
 Fig. 82. The arrangement is slightly top-heavy, the two problems at the top 
 of the sheet being too large. If these problems were smaller, the remaining six 
 problems would appear too low on the sheet. 
 
 Fig. 83. The side problems of the middle horizontal line are rather small for 
 the central problem ; the two problems on the top line are somewhat large ; and 
 the spacing of the side lines of problems is a trifle close compared with the spacing 
 of the problems in the horizontal lines. 
 
 APPLIED 
 GEOMETRY 
 
 
 Fig. 84. 
 
 Fig. 84. The lower left-hand problem appears farther from the bottom border 
 line than does the lower right-hand problem. This is due to not allowing for the 
 emptiness of the lower portion of the larger circle ; it is the group of construction 
 lines which here attracts the eye. 
 
 STUDY PLATE 6. 
 
 For selection, arrangement, and precise rendering. 
 
 It is required to make a finished drawing, which shall contain problems selected 
 from Problems I to 18, Chapter V., and also include one of the following titles, to 
 be designed by the student : " Geometrical Construction" ; " Selection and Arrange- 
 ment "; "Applied Geometry." Use Whatman's hot-pressed paper; the sheet is 
 
io8 STUDY PLATES 6, 7, AND 8. 
 
 to be 10" x 14", with a ruled border line 8" x 12". Make the layout on any spare 
 paper, and do not begin the finished drawing until the arrangement has been fully 
 decided. 
 
 PENCILING. The final sheet should be drawn very accurately ; make the lines 
 full. 
 
 INKING. Ink according to either a or b, Art. 47, and make the width of line 
 the same as that of the lines A, B, and C, Fig. 55. Letter the title; also "Plate 
 6," your name, and the date. The letters must be drawn (Art. 41). 
 
 STUDY PLATE 7. 
 
 For selection, arrangement, and precise rendering. 
 
 It is required to make a finished drawing, which shall contain problems selected 
 from Problems 19 to 40, Chapter V., and a title. Use Whatman's hot-pressed paper; 
 the sheet is to be 14" x 20", with a ruled border line 12" x 18". Proceed accord- 
 ing to the directions for Study Plate 6. 
 
 STUDY PLATE 8. 
 
 For selection, arrangement, and precise rendering. 
 
 It is required to make a finished drawing, which shall contain problems selected 
 from Problems 41 to 74, Chapter V., and a title. The drawing is to be 20" x 26", 
 with a ruled border line 18" x 24". Use Whatman's hot-pressed paper. Proceed 
 according to the directions for Study Plate 6. 
 
CHAPTER VII. 
 
 OBJECT DRAWING. 
 
 49. In engineering, architectural, and shop construction, objects are com- 
 monly represented by means of geometrical views called projections. For the 
 complete representation of any object two or more projections are necessary, each 
 being a different view of the object. In order to comprehend or read a. projection 
 drawing, it is necessary to combine the several views in imagination, thereby form- 
 ing a mental picture of the object as a whole. The ability to read projections 
 easily, usually requires extended practice, which is best obtained through the study 
 of descriptive geometry and a considerable amount of drawing from objects. 
 
 50. Sketching and Measuring, (a) The sketches. As, in practice, objects 
 from which drawings are to be made are usually not near 
 
 by, it is necessary to make the final drawings from 
 sketches showing the character and measurements of the 
 object. The same procedure should be adopted when 
 drawing from class-room models ; that is, the model should 
 be sketched and measured, and then put aside, so that the 
 subsequent work shall be wholly from the sketches. 
 
 (b) Character of the sketch rendering. The sketches 
 must not be loosely rendered, as when experimenting for 
 an arrangement (a, Art. 48), but must be rendered in single 
 line, carefully and directly thus giving the sketch a 
 somewhat set appearance and with little or no erasure, 
 or preliminary suggestion. The lines should be firm, crisp, 
 and accurately placed with respect to the vertical and the 
 horizontal. 
 
 (c) The measurements. Take the measurements 
 with the two-foot rule and the calipers (see materials, p. 2). 
 Care should be taken to make well-formed and legible numer- 
 als, signs, and arrow heads. The dimensions, other data, 
 and remarks may be stroke rendered or neatly written. 
 Center, extension, and dimension lines may be ruled. 
 
 All sketches made in connection with the exercises in object drawing should 
 be placed in the note book (see materials, p. 2), and this book should be used for 
 no other purpose. 
 
 (109) 
 
I IO 
 
 OBJECT DRAWING SKETCHING AND MEASURING. 
 
 (d} As a first example of sketching and measuring, take the sketch, Fig. 86, 
 made from a wooden model of a locomotive hand-rail stud. The stud, A (Fig. 85), 
 
 through which passes the hand rail B, rests on 
 the horizontal portion, C\ of a bracket riveted 
 ITM / ^ -v \ to the boiler. The necessary sketches of this 
 
 /I *tL P] It \\ 
 
 u oj> W I If \\ object include : a front view or front elevation 
 
 V^.*- 2 $' D -&\ | \V_X/ (A, Fig. 86); a side view or side elevation 
 
 (B), as seen in the direction of the arrow X, 
 Fig. 85 ; and a lower end or bottom view (in- 
 verted plan}, C, as seen in the direction of 
 the arrow Y, Fig. 85. The necessary meas- 
 urements of the hand-rail stud are given in 
 Fig. 86. 
 
 (e) Sketches of another drawing room 
 model, Fig. 87, are given in Fig. 88. The ob- 
 ject is a cabinet maker's clamp (see also Plates 
 13 and 14). The parts of the clamp, A and 
 B (Fig. 87), which compress the glued pieces, 
 C, C, C, C, are attached to a wooden bar, F. 
 The block, A, is attached to the bar by the 
 binder, G. The head of the clamp, B, is at- 
 tached to the bar by the iron strap, H, which 
 bears against the plate, J. In order that the 
 sketches might be of a size adapted to the page 
 of the sketch book, parts of the object were 
 broken and brought together as shown (Fig. 
 88). The order in which the sketches were made is as follows : B (projection 
 in the direction Z t Fig. 87), B' (projection in the direction Y, Fig. 87), B" (pro- 
 jection in the direction X}\ A, A', D, D', etc. It should be noted that the 
 same letter is used in Figs. 87 and 88 to indicate corresponding parts of the 
 clamp. 
 
 51. Selection and Arrangement ; the Layout. To illustrate further methods 
 in object drawing, let it be supposed that it is required to make a finished trac- 
 ing on cloth of a mechanical drawing to be made from the sketches of the 
 hand-rail stud, Fig. 86, and also that the tracing shall be a satisfactory example of 
 symmetrical arrangement.* The size of the tracing is to be 14" x 20", with a ruled 
 border line I3"x 19" (i" margin). The first step is to decide upon an arrangement. 
 
 * A symmetrical arrangement is chosen merely as an example ; more often an abstract arrangement 
 (b, Art. 48) appears to be necessary (see Plates 13, 14, and 15). 
 
 Fig. 86. 
 
OBJECT DRAWING THE LAYOUT. 
 
 in 
 
 For this purpose any spare paper is suitable ; a border line of the required size 
 should be ruled, a soft pencil used, and the procedure should be in accordance with 
 a, Art. 48. 
 
 NOTE. On account of the small size of this cut, some of the 
 dimensions are omitted. 
 
 Fig. 88. 
 
 A glance at the overall measurements, Fig. 86, will show that, if the projec- 
 tions of the stud are not to appear lost on the sheet, the drawing cannot be made 
 to a reduced scale, but must be full size. It will also be seen that the number of 
 
ii2 OBJECT DRAWING THE LAYOUT COLLECTIVE RENDERING. 
 
 views, Fig. 86, necessary to represent the stud are not sufficient to fill the sheet. 
 But in view of the requirement that, besides representing the stud, the drawing 
 shall be a satisfactory example of arrangement, the number of projections need not 
 be restricted, as in the case of a working drawing (b, Art. 64), to those projections 
 which are actually necessary ; hence a section may be added and a title introduced. 
 A first arrangement is illustrated in Fig. 89. In this sketch the views fill the sheet 
 
 Fig. 89. Fig. 90. 
 
 satisfactorily, but the elevation at the right-hand side of the sheet does not balance 
 the section at the left-hand side ; the title hardly balances the lower left-hand 
 section, and the lower views are crowded. A second scheme of arrangement is 
 shown in Fig. 90. Here the projections on either side of the central figure bal- 
 ance each other, but the eye is attracted to the right-hand side of the sheet on 
 account of the heavier effect due to the cross hatching. The title and the views 
 on either side of the title are crowded ; if the size of the title is reduced to give 
 a satisfactory spacing, it will appear too small. The third scheme, Fig. 91, the^ 
 one finally adopted (see Plate 12), appears to be the best of the examples given. 
 The stronger black-and-white value, due to the cross hatching, is kept central ; and 
 the space in the lower right-hand corner is filled by the additional section. 
 
 52. The Drawing for Tracing ; Collective Rendering. (Methods continued.) 
 The locations of the views in the pencil drawing for the tracing are taken from the 
 layout. Of special importance is the treatment of the projections, which should 
 
OBJECT DRAWING COPYING SCREW THREADS. 
 
 be drawn in combination ; that is, in penciling, no one projection should ever be 
 carried to completion, then another completed, then another, and so on, but at each 
 stage of the drawing each projection should shoiv that it lias received equal attention. 
 
 Tlie projections of an object should always 
 be laid out with reference to their center lines. 
 (See b, Study Plate 9.) 
 
 53. Copying as a Preliminary to Object 
 Drawing. A great deal can be learned by 
 copying good examples of drawing, from 
 the originals, or from prints of the same. 
 Mere automatic imitation, however, of a draw- 
 ing or print, unaccompanied by thought of 
 the meaning and application of the construc- 
 tion and technique there represented, is of 
 little value ; but if the copying serves to im- 
 press correct methods of rendering, to culti- 
 vate taste and good judgment, and to afford 
 practice in reading drawings, then there is no 
 question that a reasonable amount of time 
 given to copying is well spent. Students 
 appear to be particularly weak in making 
 neat and rapid sketches, in rendering dimen- 
 sions on sketches, and in sketching layouts. 
 
 When this is the case, the student should not expect to correct his deficiency 
 through the sketching connected with a required amount of object draw- 
 ing, as the time here spent in sketching is relatively small compared with the 
 time necessary for making the mechanical drawings. He should give special 
 attention to sketching, and to sketch dimensioning as such, making it a practice 
 to sketch any object at hand at every opportunity, though it be for only five 
 minutes at a time. In this connection the preliminary exercises in sketching 
 indicated in Study Plates 9-13 are important. 
 
 54. Screw Threads, (a] Single and double threads ; pitch. If a point were 
 carried along an edge, as EFGHJ, of the actual thread represented in A, Fig. 92, 
 it would be seen that, in passing from point E to point J t vertically over E, the thread 
 makes one turn about the axis of the screw, and that the screw has but one thread. 
 The rise or advance, EJ, of the thread in making one turn is termed its pitch, and, 
 in a single threaded screw, the pitch is equal to the combined widths of the thread 
 and the groove (see EJ, A, Fig. 92). 
 
 If, in following a thread, as at EFGHJ, B, Fig. 92, an intervening thread is 
 
OBJECT DRAWING SCREW THREADS. 
 
 seen between points E andy, the screw evidently has two threads, and is said to be 
 double threaded. In this case the pitch, EJ, is equal to the combined widths of the 
 A B two threads and the two grooves. 
 
 If the front of a thread ascends from 
 left to right, as from E toy in Fig. 92, the 
 screw is said to be right-handed ; if the front 
 of the thread ascends from right to left, the 
 screw is left-handed. 
 
 (b) The shape and size of a screw 
 thread. The actual shape and size of a 
 thread are determined by the shape and size 
 of its cross section (Fig. 93) taken in a 
 plane passing through the axis of the screw. 
 The size of a thread, while determined by 
 the size of its section, is commonly expressed 
 by stating the number of sections in one inch, 
 measured parallel to the axis of the screw, 
 thus : i o threads to an inch (usually given 
 in the form IO Th. or IO Thds.}. 
 
 (c\ Measuring a screw. When familiar 
 
 9 2 - 
 
 V-THREAD WHITWORTH 
 
 with the various thread sections, Fig. 93, the shape of a particular thread can be 
 easily identified from inspection. There should be recorded in the sketch : the 
 shape of the thread ; the number of threads to an inch ; and whether the thread 
 is single or double. The necessary measurements of a 
 threaded bolt are as follows : total length, including the 
 head ; length of body, including threaded portion ; length of 
 the threaded portion ; diameter of body ; height and short 
 diameter of the head. 
 
 (d) Drawing a screw thread. The drawing must be 
 begun by making a longitudinal section A, Fig. 94, taken 
 through the axis of the screw. For a complete representa- 
 tion, it is necessary to show the curvature of the thread (see 
 helix, descriptive geometry) ; but ordinarily, in object drawing, 
 straight lines, as FH, HM, JK, and KL, B, Fig. 94, are sub- 
 stituted for the curves. 
 
 In each of Figs. 94-97 are illustrated four things, 
 namely : at A, the pencil construction ; B, the directions of 
 
 I 
 SQUARE 
 
 U.S. STANDARD 
 
 SECTIONS OF 
 SCREW THREADS 
 
 Fig- 93- 
 
 the front and back edges of the thread ; C, the front of the completed thread ; 
 and D, the completed thread as seen in a section of a tapped hole or nut. 
 
OBJECT DRAWING SCREW THREADS. 
 
 (e) Construction of a single, right-hand, V thread, 4 threads to an inch. (Fig. 
 94.) Lay off EG equal to the given diameter of the screw, and draw the contour 
 elements, JSFand GH the entire length of the threaded portion. Set the scale to 
 the element EF, and, starting at point E, lay off \" distances, as 1-2, 2-3, the 
 entire length of the threaded portion. With the 30 triangle, draw the section, 
 iR2, of the groove, and through point R draw the line RS parallel to EF. Com- 
 plete the sections of the groove and thread along the left-hand side of the screw, 
 and, as a check, see that the roots, as R and S, of the thread fall accurately in the 
 line RS. From point R, draw RP perpendicular to line EF, intersecting element 
 
 Fig. 94- 
 
 Fig- 95- 
 
 Fig. 9 6 
 
 Fig. 97. 
 
 GH in point P, thus locating since the thread is single a point of the 
 thread. Starting at point P, draw one triangle representing a section of the 
 thread, and also the line TU containing the roots of the thread. Lay off from the 
 scale the positions of the points of the threads, and complete the sections at the 
 right-hand side of the screw. Having thus drawn the sections of the thread, 
 note (at /?), the one turn FHM, zndJKL, of the point and root edges respectively ; 
 then draw the visible edges of the screw, and of the nut, as shown at C and D. 
 The end of the screw in the drawing is usually finished by an arc of a circle, as X, 
 Fig. 94, described from any appropriate point, as O, lying in the axis of the screw. 
 
 (/) Construction of a double , left-hand, V thread, 2 threads to an inch. 
 (Fig. 95.) Observe that the pitch is i inch, and that, since the thread is double, 
 the points of the sections on opposite sides of the screw fall opposite each other ; 
 otherwise the construction is the same as in Fig. 94. 
 
 (g) Construction of a U.S. standard thread, 4 threads to an inch. (Fig. 
 96.) Draw the contour elements, Z TV and OV, of the screw. Outside of LN ', and 
 O V, at a distance equal to | of the pitch of the screw, draw EF and PH. Using 
 
n6 
 
 OBJECT DRAWING CONVENTIONAL SCREW THREADS. 
 
 EFand Pffas corresponding to EFand PH in Fig. 94, construct the sections of 
 a V thread of the given pitch (see e). Outside of RS, and 777, at a distance equal 
 to | the pitch of the screw, draw L' N' and O' V . Connect the points of the sec- 
 tions as shown at C and 1), Fig. 96. 
 
 (//) Construction of a single, square thread, 4 threads to an inch. The con- 
 struction is evident from Fig. 97. 
 
 55. Conventional Screw Threads. Any of the conventions shown in Figs. 98 
 and 99 may be used according to preference or requirement. The constructions are 
 as follows : 
 
 (a) Convention A, Fig. 98. Starting at point D, lay off, for the entire length 
 of the left-hand contour element, any assumed distance, as DF ; at E, opposite D, 
 
 Fig. 98. 
 
 Fig. 99. 
 
 lay off the same distance, EG, on the right-hand contour element. Connect the 
 points F and E ; then, by sliding the triangle, draw lines parallel to FE, passing 
 through the points laid off on the left-hand element. 
 
 The distance laid off on the elements need not be the actual pitch of the 
 thread, but any convenient distance which gives a satisfactory spacing for the 
 parallel lines. 
 
 (&) Convention B, Fig. 98. First draw the thread in pencil according to A, 
 Fig. 98. Make the distances JK and LM each equal to the unit, as /A 7 , of the* 
 vertical spacing, and draw KK' and LL' . When inking the convention, begin -and 
 end the lines representing the thread, alternately, at the lines KK' and LL' . Thus, 
 for example, draw from point N to line LL' , and from point P' , in KK' , to line 
 MQ (see the lower portion of the figure). 
 
 (c] Convention C, Fig. 98. First draw the thread according to the pencil 
 construction in B, Fig. 98. Ink the convention as shown in the figure. The 
 
OBJECT DRAWING CHAMFER OF NUTS AND BOLT HEADS. 117 
 
 wide lines should be first represented by two narrow lines, and afterward filled in 
 as described for the wider lines in section lining (b, Art. 38). 
 
 (d] Convention A, Fig. 99. The pencil construction is the same as for con- 
 vention B, Fig. 98. Make DE and FG each equal to | of CE, and draw lines 
 DH and GJ. Ink the convention as shown in the figure. 
 
 (e) Convention B, Fig. 99. The thread should be drawn according to e, Art. 
 54. The black areas represent conventional shadows, the curved edges of which 
 may be located as follows : Lay off distance KL equal to | of KN, and draw line 
 LU. Make MN equal to \ of LN, and draw MV. Through the points, as P 
 and Q, in which L U and MV intersect the root of a thread, draw a circular arc, 
 center found by trial, tangent to the point of the thread, as at O, Through the 
 center, R, of .this arc, draw line OT. With the same radius, and keeping the 
 center always in line OT, draw the arcs for all the shadows, as indicated by the 
 arrows. Fill in the shadows with India ink applied with a brush or a writing pen. 
 
 56. Chamfer of Nuts and Bolt Heads. Let Fig. TOO represent the head of a 
 bolt supposed to revolve about its axis ad, while the 
 tool, Z, cuts off or chamfers the edges, JQ, QX, XR, 
 etc. The surface BFNUWTP, etc., of the chamfer 
 is a portion of the surface of the imaginary cone, 
 def : the right-hand edge, FNU, of the chamfer is a 
 circle, since it is the boundary of a right section of 
 the cone def ; and the left-hand boundary BEHMW, 
 etc., is a series of six equal hyperbolic arcs, being the 
 intersection of the cone def, by the six faces of the 
 bolt head. Since the base of the head is perpendicular 
 to the axis, ab, the edges AB, GH, OP, and VW are 
 cut off the same length ; likewise the distances DE, 
 LM, and ST are equal. In practical drawing, the 
 hyperbolic curves are always represented by arcs of 
 circles; the position of the arcs may be determined 
 as follows : 
 
 Fig. 100. 
 
 (a) Construction. Through the lowest point, A, Fig. 101, in the chamfer 
 (located by measuring the edge AB), draw the line AD making, in this case, 45 
 with the top surface of the bolt head. With radius CD, draw the circle D'G', rep- 
 resenting the top edge of the chamfer. The lowest points in the chamfer, as E, A, 
 and E", lie in the vertical edges of the head. The highest points in the chamfer, as 
 H, N, and N", lie in the center lines of the vertical faces. Pass the plane C K'f , 
 containing the axis of the head and bisecting its front face ; this plane, revolved, 
 corresponds to the half side view C"K" J". Layoff C"G" equal to C' G' , and 
 
u8 OBJECT DRAWING CHAMFER OF NUTS AND BOLT HEADS. 
 
 through point G" draw the line G"H", at 45, thus determining point H", which is 
 the highest point of the chamfer, lying in the center line HJ of the front face of 
 
 YI VIP I ir.y/' ' * |c" ii 
 
 - -'- A- - lj?,I Z^Sl 
 
 Fig. 101. 
 
 102. 
 
 the head. Project the highest and lowest points in the curves as shown. Find 
 
 each center, as P, from which to describe the circular arcs, according to b, Art. 45. 
 
 A 30 conical chamfer on a square head is shown in Fig. 102. A spherical 
 
 chamfer is shown in Fig. 103. It will be seen that the chamfer is made only deep 
 
 t 
 
 Fig. 103. 
 
 enough to complete the curve on each face of the nut ; the lower edges of the 
 chamfer are therefore tangent to its upper edge. 
 
 57. Doubtful Lines. In object drawing it frequently happens that, on account 
 of rounded corners or other curved surfaces, a part of an object shows no definite' 
 line boundary ; hence, theoretically, the part cannot be expressed by an outline. 
 When, in such cases, the question arises whether a line should be put in or omitted, 
 it is best to ignore geometrical truth, if the drawing will be made clearer thereby. 
 Examples : 
 
 (a) Detail of the clamp, A, B, and C, Fig. 104. (See also Plate 7J.) The 
 strictly correct projection, B, can show no interior lines, since all corners of the 
 
OBJECT DRAWING DOUBTFUL LINES SHADE LINES. 119 
 
 object are slightly rounded, as shown in the boundaries of A and B. The more 
 satisfactory drawing, C, is obtained by putting in the doubtful lines. 
 
 (b} The angle iron, D, , F, Fig. 104. The projection D is correct ; but the 
 addition of the doubtful lines in the projection E makes this view the clearer. 
 
 ~~LT 
 
 Fig. 104. 
 
 (c) The ornamental terminations of a hand-rail stud, G, H,J, K, Fig. 104, 
 (See also Plate 12.) In the form G, it is clear that there should be no line drawn 
 from L to M ' ; in the form J t it is equally clear that there should be a line from P 
 to Q. Forms //and K are the same ; the former, without a line drawn from JVto 
 O, is correct ; but the latter, showing the doubtful line, RS, seems preferable. 
 
 58. Shade Lines. If rays of light from any source be supposed to fall on an 
 object, some of its faces will be in the light, the rest in shadow. The edges of the 
 object that separate its light from its dark surfaces are called shade lines. These 
 lines are indicated in a drawing by their width, which is greater than that of any 
 other lines in the same drawing. Shade lines may be used to make a drawing 
 more effective in appearance, and, to a limited extent, to explain form. 
 
 (a) Theory of shade lines ; rectangular objects. Let B, Fig. 105, represent 
 a cube with its base horizontal. The cube is supposed to be lighted by parallel 
 rays, the direction of which is represented by the diagonal, ed, of the cube (arrow 
 X), which makes the angle, /3, of 35 15' 52" with all faces of the cube. It will 
 be seen that the faces abfe, efhg, and aegc receive the light, while the remaining 
 faces are in shadow ; hence the shade edges of the cube are those forming the 
 boundary abfhgc. Next, let the cube be represented by the projections A and C 
 (elevation and plan). To determine the shade lines of the projections, it is nec- 
 essary also to represent the light by means of projections of its rays. The eleva- 
 
I2O 
 
 OBJECT DRAWING SHADE LINES. 
 
 tion X v (B} of the ray X, coincides with the diagonal, ad, of the back face of the 
 cube, and therefore takes a direction downward and to the right at 45 with the hori- 
 zontal, and is so represented in the elevation, A, of the cube. The plan, X h (B) of 
 the ray X, coincides with the diagonal,^/, of the base of the cube, and therefore takes 
 a direction backward and to the right at 45 with the horizontal, and is so repre- 
 sented in the plan, C, of the cube. Now, by reading in combination the elevation 
 and plan of both object and rays, the shade lines may be determined. Thus, for 
 example, the elevation (A) shows that the top surface, abfe, of the plan (C) is in 
 light ; the plan shows that the back surface, abdc, is in shadow ; hence the line ab, 
 representing the (shade) edge separating the two surfaces in question, is a shade line. 
 
 Fig. 105. 
 
 A cylinder. Let J, Fig. 105, represent a cylinder, with its base horizontal, 
 inscribed in a half cube, as indicated by the diagonals ^ and X h . The upper base, 
 ad, is in the light ; the lower base is in shadow. The ray of light, X, is tangent to 
 the curved lateral surface at point b ; therefore, the element ac, passing through 
 point b, separates the light from the dark portion of the curved surface, and is a 
 shade line. The element de, diametrically opposite ac, must also be a shade line ; 
 hence, the entire shade-line boundary of the cylinder is the broken line afdegca. 
 
 As a preliminary to object drawing, further consideration of the theory -of 
 shade lines is unnecessary. To determine all shade lines, in all cases, requires an 
 extensive knowledge of the theory of shades and shadows a subject useful in 
 certain architectural drawing and for the training it affords, but of no practical use 
 in construction drawing, since the process requires much time, and in many cases 
 the shade lines become so complicated that they are more likely to obscure than to 
 explain the form of an object. 
 
OBJECT DRAWING SHADE LINES. 121 
 
 In practice there is no general understanding in regard to shade lines ; the 
 architect shades his drawings in one way, the engineer in another. Then, drafts- 
 men differ in opinion as to whether particular lines should be shaded or not, and 
 this is an ever-present theme for discussion. In any case, the question to be de- 
 cided is at what point the theory shall be ignored in the interest of clearness and 
 utility. In some offices, shade lines are omitted altogether. The following ex- 
 amples represent the more general practice : - 
 
 (b) Architect's method of shade lines. Figs. D, E, H, and K, Fig. 105, are 
 shaded according to the architect's method. The rectangular objects, Figs. D and 
 E, are shaded strictly in accordance with the shading of the cube (A and C). In Z>, 
 the shade lines on the elevation show that the rectangle, A, represents a recess, and 
 the rectangle, B, a projecting block. In E, the shade lines on the plan indicate the 
 same facts. The elevation of the cylinder (//), is not shaded wholly in accordance 
 with theory : The shade elements, ac and de, do not coincide with the contour 
 (outside) elements of the cylinder ; they are therefore omitted, and no element is 
 shaded. The shade line of the lower base, by theory extending only from // to c, 
 is carried clear across the base, and no part of the upper base is shaded. The 
 shade line of the plan (K}, agrees with the theory. 
 
 (c) Engineer s method of shade lines. In this method, the direction of the 
 light is taken the same for all views and sections of an object. The direction as- 
 sumed is downward to the right, and all views are shaded similarly to the elevation 
 in the architect's method. The shading is generally done by some arbitrary rule, 
 such as the following : Shade the lower and right-hand (sharp) edges of objects, and 
 the upper and left-hand (sharp) edges of holes on all views and sections. A " sharp " 
 edge is usually taken to mean, besides an actual angle, a rounded corner where 
 the rounding is very slight, and intended only for a finish. Examples : 
 
 In Figs, /''and G, Fig. 105, the same objects as in D and E are shaded accord- 
 ing to the engineer's method. A comparison will show the difference between the 
 two methods of shading. 
 
 An elevation, a section, and two plans of a hollow cylinder are given in L. The 
 right-hand contour element of the full cylinder is not shaded because it is not a 
 "sharp" edge; but, where the section is taken, both the right-hand edge of the 
 cylinder and the left-hand edge of the hollow are shaded. 
 
 The object, N, as it is bounded entirely by curved surfaces, can have no shade 
 lines, since none of its edges is " sharp." 
 
 The object, O, is bounded by flat surfaces; but the corners are slightly 
 rounded for a finish. In this and similar cases, by theory, the shade lines would 
 be represented by the fine dash-and-dot lines shown in the figure, and hence the 
 contour would not be shaded ; in practice, however, in order to indicate the general 
 (rectangular) form of the object, the edges might be shaded. 
 
122 
 
 OBJECT DRAWING SHADE LINES IRREGULAR OBJECTS. 
 
 (d ) The following rules apply to both systems. 
 
 Details which fall within the shadow of an object of which they are parts 
 should be shaded with respect to their own light and shade, unaffected by that of 
 the larger object. Thus, for example, each link of the bicycle chain, Fig. 106, is 
 
 Fig. 1 06. 
 
 Fig. 107. 
 
 shaded according to the arrows shown, whether or not the sprocket wheel is in 
 place. The rim of the sprocket, Fig. 107, casts a shadow on some of the teeth; 
 but all of the teeth are shaded individually according to the arrows. 
 
 Dotted lines, representing invisible edges of an object, are never shaded. 
 
 Finally, if there is any question as to whether a line should be shaded or not 
 it is usually best to leave it unshaded. 
 
 59. Representation of Irregular Objects; Mixed Rendering. An object is 
 said to be irregular when it cannot be readily resolved into the common geometri- 
 cal forms, such as prisms, cylinders, spheres, etc. To represent an irregular object, 
 it is necessary to locate geometrically its essential points, which are then connected 
 by lines rendered, according to convenience, with the instruments, by means of the 
 French curve, freehand, or by a combination of these methods (mixed rendering). 
 
 (a) Methods of measuring irregular objects. Either of the following methods 
 may be used in locating points in an object. (I.) By base lines and offsets (rec- 
 tangular co-ordinates). Assume or locate a base line, such as the line AB of the 
 hook, Fig. G, Plate 1 1 . From the point required to be located, as X, let fall a per- 
 pendicular or offset, as KH, to the base line. Locate the position of the foot of 
 the offset by measuring along the base line, and then measure the length of the 
 offset. (II.) By triangulation. To locate a point, as D, Fig. E, Plate n, meas- 
 ure the distances, as AD and BD, from each end of any line, as AB, already de- 
 termined. 
 
Plate II 
 
 (Study Plate 14) 
 
 -4 -^Fiq?H MS 
 ~ ..^Tff^^^-T-zk 
 
 T KiiiiSE^ * W- 
 
 TTlTf^-^r-r^ 7 i &Bk 
 
 IUVW4 'f^ 
 ^^f^-- 1 - 1 -^ 
 
 The dimensions and reference letters should nof appear on the student's drawing. 
 
 ("3) 
 
OBJECT DRAWING IRREGULAR OBJECTS. 
 
 125 
 
 If an object is quite irregular, the measuring may require considerable judg- 
 ment and ingenuity. 
 
 (b) A three-pronged hook. To illustrate modes of procedure, take the three- 
 pronged hook, Fig. H, Plate n, also shown pictorially in Fig. 108. The hook is 
 symmetrical with respect to an imaginary plane (central plane) which passes through 
 the highest point, D, of the hook, and 
 contains the center line of the upper 
 prong, EGD. The imaginary plane 
 RSZ' Y' is parallel to the central 
 plane; and the imaginary plane 
 QRY'X', representing the flat sur- 
 face of the hook, Z, produced, is per- 
 pendicular to plane RSZ 1 Y' . 
 
 The left-hand vieiv, Fig. H, Plate 
 II. This is a view seen in the direc- 
 tion of the arrow X y Fig. 108, per- 
 pendicular to the imaginary plane 
 RSZ' Y' ; hence all measurements 
 for this view must be taken in direc- 
 tions parallel to the plane RSZ' Y'. 
 In Fig. 1 08 the central plane of the 
 hook is represented by the triangles 
 /', 2', and J. The total height of the 
 hook is equal to the distance CA', 
 measured along the edge of the tri- 
 angle /', between the edge CD of the 
 triangle J, which passes through the 
 highest point, D, of the hook, and the 
 edge A' B' of the triangle 2> ', which 
 passes through a point midway be- Fig. 108. 
 
 tween the lowest points A'" and A' v 
 
 of the hook. Point A'" is located by the base line obtained with the triangle /, 
 and the offset A A'" established with the triangle 2. 
 
 The upper prong, since it is parallel to plane RSZ' Y', can be wholly located by 
 means of points, such as D, determined by base lines and offsets. For the lower 
 prongs, K, K', a different method must be adopted, as the center line of each 
 prong lies in a plane oblique to both RSZ' Y' and QR Y'X ' . The upper ends of 
 the prongs, being comparatively straight, may be referred to the center lines KL 
 and K' L' . Viewed in the direction of the arrow X, the nearer prong hides the 
 
 J 
 
126 
 
 OBJECT DRAWING IRREGULAR OBJECTS. 
 
 further one, and, therefore, only the nearer one need be considered. In order to 
 locate two points in the center line, GP, a means must be found for projecting the 
 points on lines which are parallel to the plane RSZ' Y' . The following method 
 is usually sufficiently accurate. Looking in the direction of the arrow X, hold any 
 straight-edge parallel to plane RSZ' V, between the eye and the hook, so that the 
 edge will cover the center line. Without changing the position of the eye or of the 
 straight-edge, note carefully, either by sighting or by squaring out with the triangle 
 held perpendicular to the edge, the points where the straight-edge appears to cross 
 any two lines which are parallel to the plane RSZ' Y' . For example, points so 
 located are point G in the upper prong, and point H in the offset AB. 
 
 The curved portion of the prongs may be determined by measuring diameters, 
 as ^-|-" and -3-^", Fig. H, Plate 1 1, and then locating the position of these diameters 
 by base lines and offsets as shown. 
 
 The right-hand view, Fig. H, Plate II. This is a view seen in the direction 
 of the arrow Y, Fig. 108, perpendicular to the imaginary plane QRY'X ' ; hence 
 all measurements must be taken in lines parallel to this plane. No dimensions, 
 however, should be taken which can be projected from the left-hand view, Fig. H. 
 For example, the measurement i^V', Fig. 108, giving the vertical height of the 
 lower prong, is wholly unnecessary, as this height is already determined by means of 
 the center line JH, in the left-hand view of Fig. H. The projection of the angle, 
 
 KPK' , Fig. 108, made by the center lines 
 of the straight portions of the lower 
 prongs, is readily determined by measuring 
 the lines KK' and LL' parallel to the 
 plane, QRY'X', the heights of which are 
 projected from the left-hand view, Fig. H. 
 (c) Turned handles. (Figs. A, B, C, 
 and D, Plate n). Use the center line, 
 AB, of the handle as an axis. Measure 
 diameters at a sufficient number of points 
 to determine the curvature fully, and locate 
 the positions of these diameters by meas- 
 urements taken parallel to the axis. En- 
 deavor, as far as possible, to find places 
 where the measurements will come some 
 even division on the scale, for both the dia- 
 Fig. 109. meters and the distances along the axis. 
 
 In addition to the measurements the dis- 
 tinctive characteristics of the cmves should be sketched as accurately as possible. 
 
 (d) Oblique curves. In locating the points of a curve which takes a diagonal 
 
OBJECT DRAWING IRREGULAR OBJECTS STUDY PLATE 9. 127 
 
 direction, a carpenter's square may be used to advantage. Let the curves, Fig. 
 109, represent the edges of the legs of a lathe or other machine, which are oblique 
 to a vertical surface of the bed or table portion of the machine. Place one edge of 
 the square on the floor, with the other edge passing through the highest point of 
 the left-hand curve, Fig. 109. On the floor draw a line passing through the foot 
 of the vertical edge of the square and perpendicular to the front vertical surface of 
 the bed of the machine. Keeping the lower end of the vertical edge of the square 
 always in the line on the floor, move the square forward so that each horizontal 
 measurement, as B and C, D and E, etc., taken at convenient heights, A, A.. ..A, on 
 the square, will lie in a vertical plane containing the face of the square. Also, if a 
 plan of the curve is required, measure on the floor line the distance the square is 
 moved forward for each horizontal measurement. 
 
 (e) It is sometimes convenient to duplicate a given curve by cutting out a 
 template, or by fitting a strip of sheet lead to the curve ; the curve is plotted from 
 the template or lead instead of measuring the original. 
 
 (/) In concluding this subject, it should be pointed out that the drawing of 
 irregular objects is a final test of skill in rendering, especially when the represen- 
 tation depends largely on freehand methods. The common objects given in Plate 
 1 1 are typical of the more important cases which are likely to arise, and afford 
 excellent practice in mixed rendering and in the management of complicated di- 
 mensions. Although objects requiring treatment similar to those on Plate 1 1 may 
 be met with only occasionally in engineering drawing, yet, when such occur, they 
 should be as well rendered as the purely instrumental work ; otherwise the ap- 
 pearance of the whole drawing will be ruined. 
 
 STUDY PLATE 9. 
 
 For sketching; the rendering of dimensions on sketches; collective rendering; reading 
 drawings ; lettering and dimensioning ; speed. 
 
 (a) Sketching. Place Plate 12 from 20" to 30" from the eye and perpen- 
 dicular to the line of sight. On a single page of the sketch book (see materials, 
 page 2) make freehand sketches of Figs. A, B, C, Z>, and E, Plate 12 ; the sketches 
 must not be the same size as the views on the plate. Use an H to 3H pencil, and 
 let the sketches fill the page. Read Art. 50 ; plan the general position of the sev- 
 eral views on the page ; lay in the masses of each projection, and then add the de- 
 tails. Place on the sketch all measurements and data given on Plate 12, except 
 when marked * ; render the numerals neatly and rapidly, and without the aid of 
 guide lines. 
 
 (b) Collective rendering. It is required to make a pencil drawing of the hand- 
 rail stud, on duplex detail paper, for a tracing the size of which is to be 1 4" x 20", with 
 a ruled border line 1 3" x 19" (-i" margin). Make this pencil drawing from the above 
 
128 
 
 STUDY PLATE 9. 
 
 sketches and measurements, but locate the views according to the measurements 
 given on the Plate 1 2. Lay out the projections as follows : Draw the center lines, 
 NO, PQ, RS, 777, and VW, Fig. 1 10. Do not complete one projection inde- 
 pendently of the other projections, but, within practical limits, let each stage of the 
 
 drawing show that each projection 
 has received equal attention. Thus, 
 for example, draw the circle A (K, 
 Fig. no), and project the width 
 of the parts A' (Fig. /) and A" 
 (Fig. H) from this circle. With 
 the compass as set for circle A, lay 
 off the widths of the part A'" (L) 
 and A iv (M). Take in the di- 
 viders one-half the length of part 
 A', Fig. J, and with this setting, 
 measuring from the center lines, 
 lay off the lengths of A', A", A'", 
 and A iv . Draw the circle B (Fig. 
 Z,) ; from B project B 1 ', B' , and 
 with the compass lay off the width 
 of B' at B", B", and B'", B'". 
 Draw the nut E (Fig. Z), accord- 
 ing to s, Art. 45 ; project E' (Fig. 
 H] ; make E" equal to E' . Make 
 the width of the nut at F equal 
 to FG (Fig. L). From this point 
 the several views may be treated 
 more in detail. 
 
 Draw the screw threads ac- 
 cording to c, Art. 55. 
 
 Fig. 1 10. 
 
 (c) The tracing ; the lettering and dimensioning. Trace the drawing accord- 
 ing to the general directions for tracing, Study Plate i (also see e, Art. 44). Make 
 the widths of line according to those of the lines D -J, Fig. 5 5 . Take particular 
 notice of the arrangement, on Plate 1 2, of the dimensions and data relative to each 
 view of the object ; then stroke render all dimensions and data, not marked *, 
 given on the plate ; make the style and size of the numerals and letters accord- 
 ing to Fig. F, Plate 5. Balance the title (b, Art. 41) on the vertical center line of 
 the sheet ; make the letters of the title according to the style and heights given on 
 Plate 12 ; the letters should be drawn (a, Art. 41). 
 
 Hand in the sketch book, the pencil drawing, and the tracing. 
 
Plate 12 
 
 (Study Plate 9) 
 
 D/mens/ons and fettering mar /fed * snou/d not appear on f/?e s/uden/j 
 
 (129) 
 
STUDY PLATES 10 AND u. 
 
 STUDY PLATE 10. 
 
 For sketching; the rendering of dimensions on sketches ; arrangement; collective render- 
 ing; reading drawings; lettering and dimensioning; speed. 
 
 (a) Sketching. Sketch the several projections, Plate 1 3 f ; proceed strictly 
 in accordance with a, Study Plate 9, but let the sketches fill two (or three) pages 
 of the sketch book ; the sketches must be larger than the views on Plate 13. Break 
 the screw and bring the parts together (b, Art. 37). Place on the sketches all 
 measurements and data given on the plate, except when marked *. 
 
 (b) Arrangement. On any spare paper, rule a border line i$"xig", and 
 design an arrangement different from that of Plate 1 3, but which shall include all of 
 the views there given. (See Art. 51.) 
 
 (c) Collective rendering. Use duplex detail paper ; rule a border line 1 3" x 
 19"; and make, from the sketches (see a), a drawing which is to be traced. The 
 views must be located according to the student's layout (see ft). Draw the views 
 with respect to their center lines, and according to the method suggested in b, 
 Study Plate 9. Draw the square threaded screw according to Fig. 97. 
 
 (d) The tracing ; the lettering and dimensioning. The size of the tracing is 
 to be 14" x 20", with a ruled border line 13" x 19". Proceed according to the gen- 
 eral directions for tracing Study Plate i (also see e , Art. 44) . Make the widths of 
 line according to those of the lines DJ, Fig. 5 5 . Take particular notice of the 
 arrangement, on Plate 1 3, of the dimensions and data relative to each view of the 
 object ; then stroke render all dimensions and data, not marked *, given on the 
 plate ; make the style and size of the letters and numerals according to Fig. F, 
 Plate 5. Balance the title on the vertical center line of the sheet ; make the letters 
 of the title according to the styles and heights given on Plate 13 ; the letters 
 should be drawn (a, Art. 41). 
 
 Hand in the sketch book, the layout, the pencil drawing, and the tracing. 
 
 STUDY PLATE 11. 
 
 For the assembling of details ; speed. 
 
 Make an assembly drawing of the head of the clamp, from the sketches, a f 
 Study Plate 10. Locate all views, and draw the projections of the block of the 
 clamp according to the measurements given on Plate 14. 
 
 Use Whatman's cold-pressed paper. The finished sheet is to be 14" x 20", 
 with a ruled border line 13" x 19". 
 
 Ink the drawing carefully, according to e, Art. 44 ; make the widths of line 
 correspond to those of the lines D, E, F and G, Fig. 55. The dimensions and data, 
 not marked *, should be stroke rendered ; make the style and size of the letters and 
 
 t The clamp and the wrench are from non-related objects. 
 
132 STUDY PLATES n, 12 AND 13. 
 
 numerals according to Fig. F, Plate 5. Balance the title on the vertical center "line 
 of the sheet ; make the letters of the title according to the styles and heights given 
 on Plate 14 ; the letters should be drawn (a, Art. 41). 
 
 STUDY PLATE 12. 
 
 For sketching ; the rendering of dimensions on sketches ; arrangement ; collective render- 
 ing ; reading drawings ; lettering and dimensioning ; speed. 
 
 (a) Sketching. Sketch the details of the hanger, Plate 1 5 ; proceed strictly 
 in accordance with a, Study Plate 9, but let the sketches fill three (or four) pages 
 of the sketch book ; the sketches mtist be larger than the views on Plate 1$. Place 
 on the sketches all measurements and data given on the plate, except when 
 marked *. 
 
 (b) Arrangement. On any spare paper rule a border line i 3" x 19", and de- 
 sign an arrangement different from that of Plate 15, but which shall include all of 
 the views there given. (See Art. 5 1 .) 
 
 (c) Collective rendering. Use duplex detail paper; rule a border line I3"x 
 19". Make, from the sketches (see a), a drawing which is to be traced. The 
 views must be located according to the student's layout (see b}. Draw the views 
 with respect to their center lines, and according to the method suggested in b, 
 Study Plate 9. Draw the large V-threaded screw according to e, Art. 54. 
 
 (d) The tracing ; the lettering and dimensioning. The size of the tracing 
 is to be I4"x 20", with a ruled border line I3"x 19". Proceed according to the 
 general directions for tracing Study Plate i (also see e, Art. 44). Make the widths 
 of line according to those of the lines D -J, Fig. 5 5 . Take particular notice of the 
 arrangement, on Plate 15, of the dimensions and data relative to each view of the 
 object ; then stroke render all dimensions and data, not marked *, given on the 
 plate ; make the style and size of the letters and numerals according to Fig. E, 
 Plate 5. Locate, vertically, the lines of the title according to the measurements 
 given on the plate, but center the title between the edge of the drawing and the 
 ruled border line. The letters of the title should be drawn (a, Art. 41), and their 
 style copied from Plate 15. 
 
 Hand in the sketch book, the layout, the pencil drawing, and the tracing. 
 
 STUDY PLATE 13. 
 
 For the assembling of details ; speed. 
 
 Use Whatman's cold-pressed paper; the finished sheet is to be I4"x2o", 
 with a ruled border line I3"x 19". 
 
 Make an assembly drawing of the hanger from the sketches, a, Study Plate 
 12. Locate the drawings according to the measurements given on Plate 16. 
 
Plate 13 
 
 (Study Plate 10) 
 
 or CLAMP 
 
 > ***:$. 
 
 ON 
 
 >'r /fto/v, ROUGH 
 
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 4 SQUARE THREADS TO /" 
 
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 ^HiS_I 
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 j. / 
 
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 ^ 
 
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 J 
 
 
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 H / H 
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 TAP f 
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 r~i 
 
 
 
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 T 
 
 ^ *j+\ Oft/LL * \ 
 
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 ^3: 
 
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 T ' " 
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 t-+ 
 
 *-^Z 
 
 %&~~\ 
 
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 s * r 
 
 SL 
 
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 h-J'f^C45r 
 
 /f?OM 
 
 : *> 
 
 AMD GftOLWD 
 
 Dim ens/o/75 /narked sfiou/d nof crojoear on Me s/t/tfe/t/s dratr/tig 
 
 (i33) 
 
Plate 14 
 
 (Study Plate 1 1) 
 
 or CLAMP 
 
 &$c53aa& Fu// Size 
 
 /'ons marked * sfiov/c/ not appear on //>e s/ude#/!s 
 
 (US) 
 
Plate 15 
 
 (Study Plate 12) 
 
 '13' 
 
 ~|2 
 
 4f 
 
 o 
 
 a- 
 
 4 , 
 
 
 
 X 
 
 
 
 
 1 
 
 1 
 
 i 
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 rolool 
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 1 ' 
 
 i 
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 ! 
 
 ! J 
 
 BC 
 
 ie" 
 
 <O 
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 / 
 
 r/ 
 
 </* , 
 
 \ 
 
 *' 
 
 .5" 
 16* 
 
 
 
 
 (0 
 
 ' 
 
 ! 
 
 5'' 
 
 16 
 
 |3" > 
 
 / 
 
 ;-KEETAILS-_. 
 
 3SHANGEB.1 
 
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 ^ 
 
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 1 
 
 r ~ 
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 I 
 
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 = = 
 
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 vO 
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 <1 
 
 ^4- 
 
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 00 
 
 
 rCt 
 
 3? 
 
 > 
 
 1 '"Si 
 
 1ITULLSIZE T 
 
 "WJi,! 
 
 7 
 
 \ 
 
 > 
 
 C 8 
 
 
 
 HH?*- 
 
 Dimensions marked should not appear on the student's drawing 
 
 (37) 
 
Plate 16 
 
 (Study Plate 13) 
 
 Dimensions marked * should nof appear on the students drawing 
 
 039) 
 
STUDY PLATES 13 AND 14. 141 
 
 Ink the drawing carefully according to e, Art. 44 ; make the widths of line corre- 
 spond to those of the lines D, E, F, and G, Fig. 5 5 . Balance the title on the verti- 
 cal center line of the sheet ; make the letters of the title according to the style and 
 heights given on Plate 16; the letters should be drawn (a, Art. 41). 
 
 STUDY PLATE 14. 
 
 For practice in managing complicated measurements ; mixed rendering in pencil and in ink. 
 
 Use Whatman's hot-pressed paper ; the finished sheet is to be 14" x 20", with 
 a ruled border line I3"x 19". 
 
 I. PENCILING. Lay out the border line, and draw the several figures full 
 size, according to the dimensions given on Plate 1 1 . 
 
 (a) The turned handles (Figs. A, B, C, and D}. Locate and draw, of in- 
 definite length, the center lines AB. Locate the lower end, and lay off the height 
 of the handle. On the center or base line lay off the distances which locate the 
 positions of the diameters ; lay off the diameters on lines drawn perpendicular to 
 the base line. After all the points in the contour of the handle have been located, 
 connect them by a lightly rendered freehand line. To test the symmetry of the 
 contour of each handle, place tracing paper over the drawing, rule the center line, 
 and carefully trace one side of the contour. Turn the tracing paper over, make 
 the two center lines coincide, and compare the semi-contour on the tracing paper 
 with the underlying semi-contour of the original. The original may be corrected 
 by means of the tracing paper, but the points located by scale measurement must 
 not be changed. 
 
 (b) The plane handle (Fig. E}. Locate AB, and, using this line as a base, 
 triangulate for point D thus : With radius 4^", center B, describe an arc ; with 
 radius 4|", center A, intersect the preceding arc in point D. Draw BD and AD. 
 With A> as a. base, in a similar manner triangulate for point C. Locate pointy, 
 lying in AB, \" from point A. Draw the base line CJ ' ; locate the offsets EF and 
 GH ' ; measure the offsets, and connect the points C, F, and H. Draw a horizontal 
 line T y above AJ. With radius ^", center in a line drawn parallel to, and ^" 
 distant from the base line CJ, draw a circular arc tangent to the preceding horizon- 
 tal line above AJ. Produce, freehand, the line already drawn through points F and 
 H, to give a smooth curve tangent to the circular arc. Proceed in a similar 
 manner, and, in general, consider the longer distances first. 
 
 (c) The saw handle (Fig. F). Locate and draw the vertical line AB. Draw 
 AC perpendicular to AB ; locate point C, and draw CB. With CB as a base 
 line, triangulate for point D. With DC as a base line, locate points G and H by 
 means of the offsets FG and EH. Locate point R, lying in GH produced ; locate 
 point S in line CB, and draw RS. Draw base line DB, and locate point / by 
 
STUDY PLATE 14. 
 
 means of the offset KJ. Locate point P on line DG, point Q on line BC, and draw 
 base line PQ. Locate points Fand X on line PQ, point Fby means of the offset 
 WY, and draw VY and YX. Then, proceeding as thus suggested, finish the 
 traverse or generalized boundary of the handle as a whole ; locate, by means of 
 base lines and offsets, the more important points in the boundary ; and finally, lo- 
 cate and draw the curves in detail. 
 
 (d) The hooks and the cam (Figs. G, H, and J). The drawings of these 
 objects should be plotted according to the preceding methods. 
 
 II. INKING. Make the width of line equal to that of line D, Fig. 55. All 
 freehand lines and lines ruled by means of the French curve should be so skillfully 
 rendered that they will be uniform in appearance with the straight lines made with 
 the ruling pen. 
 
 (e) Lettering. Letter " Plate 14," your name, and the date. The dimen- 
 sions and all other lettering may be omitted. 
 
CHAPTER VIII. 
 
 WORKING DRAWINGS. 
 
 60. A Working Drawing is a drawing, made in accordance with engineering 
 or architectural practice,* which presents such views and measurements of an 
 object as will enable a mechanic to make the object wholly from the drawing. For 
 complicated structures, such as buildings, bridges, and machines, two kinds of 
 drawings are required, namely: (I.) the assembly drawing (see Plate 16), which 
 shows the relative positions of the parts in the completed structure, together with 
 its most general dimensions; and (II.) the detail drawings (see Plate 15), which 
 give the form, arrangement, and dimensions of the parts of an object taken sepa- 
 rately. 
 
 If a drawing is made from an existing object, the data consists of sketches and 
 measurements from the object. When a new design is required to be expressed, 
 the drawing is usually worked out from explanatory sketches, calculations, and 
 previous drawings. The making of drawings involving data of the latter kind, be- 
 longs to some one of the various branches of engineering or architectural construc- 
 tion, and therefore lies outside the scope of this book. 
 
 In the duplication of objects, requiring no engineering or architectural experi- 
 ence, the following practice should be adopted. 
 
 61. Sketching the Object. (See also Art. 50.) Sketch only such views of 
 an object, or a part, and only as much of each view, as are necessary to make the 
 working drawing. Supplement the freehand sketching by the use of straight-edge 
 and compass whenever this will save time. Cultivate the habit of rendering neatly 
 and legibly all sketches and dimensions, as frequently in office practice one man 
 makes the sketches, while another makes the drawing from the sketches. 
 
 62. Measuring the Object. (See also Art. 50.) Be careful not to omit any 
 essential measurements ; if the object is not near by, an omission may mean both 
 trouble and expense. 
 
 (a) Small, nicely machined pieces should be measured with a micrometer 
 caliper. For ordinary work a two-foot rule and machinist's calipers are sufficient. 
 Whenever practicable, take as the base lines for measurements finished edges (as 
 
 * The drawings reproduced in Plates 12 to 1 6 were made primarily to illustrate arrangement and 
 to give practice in reading and rendering. Though in each case the object might readily be made from 
 them, they are not, in a strictly technical sense, working drawings, since their form, as will presently be 
 seen, is not wholly in accordance with office practice. 
 
 ('43) 
 
144 
 
 WORKING DRAWINGS MEASURING THE OBJECT. 
 
 ft f> Fig. J 35) f tne object, and, if possible, take all measurements from the 
 same base lines (compare Figs. 135 and 136). 
 
 (b] Circular holes. In locating a hole, do not attempt to measure to its 
 center, but take measurements as shown in the following examples. Place on the 
 sketch the measurements just as they are taken, although 
 in many cases this is not the way they should appear on 
 the working drawing (see e, Art. 65). 
 
 A single hole. (Fig. 1 1 1 .) From edge A, measure 
 distances AB and BC. When making the working draw- 
 ing, give the position of the center of the hole, found by 
 adding to the distance AB one-half of the diameter BC. 
 Equally spaced holes in a straight line. (Fig. 112.) 
 
 JL. 
 
 4- 
 
 Fig. iii. 
 
 Lay the rule along the center line AB, measure the distance between correspond- 
 ing edges, as A and B, of two holes at a considerable distance apart, and state the 
 
 Fig. 112. 
 
 number of spaces between the holes in question in this case 6. To find the 
 distance between the centers of adjacent holes, when making the working draw- 
 ing, divide AB by the number of spaces between the holes. 
 
 Equally spaced holes in a circle, as, for example, a series of bolt holes. When 
 the number of holes is even (Fig. 1 1 3), measure between corresponding points, as 
 A and B, in opposite holes. Re- 
 cord the number of holes ; if nec- 
 essary, one hole may be located 
 with respect to the vertical or 
 the horizontal axis of the piece. 
 In making the working drawing, 
 draw the circle of centers (bolt 
 
 circle) with a radius equal to one- ^ 
 
 half of AB. and space the circle 
 
 T^ * T "* * 
 
 for the required number of holes. r ' * X 3- 
 
 When the number of holes is odd (Fig. 1 14), the measurements must be taken 
 from the inner or outer edge of the piece, according to which is the smoother. In 
 the case shown in Fig. 114 the inner edge of the piece is threaded, and therefore 
 the holes are located from the outer edge. Measure the outside diameter D, the 
 distance AB, and the diameter BC of a hole. When making the working draw- 
 
WORKING DRAWINGS PLANNING THE DRAWING. 145 
 
 ing, draw the bolt circle with a radius equal to one-half of D, minus the sum 
 of AB and one-half of BC, and space the circle for the required number of holes. 
 
 If the holes are not equally spaced, each hole may need to be located sepa- 
 rately. No general rule can be given. 
 
 63. Making the Drawing ; General Directions. Ordinarily, a working draw- 
 ing may be said to include the layout and preliminary drawing, a tracing, and a blue 
 print. Both the tracing and the blue print are called working drawings. The 
 tracing is usually retained in the office, while the blue print is sent away for shop 
 or other outside use. 
 
 (a) The layout should be made directly on duplex detail or a similar paper. 
 After the scale of the drawing, the number and arrangement of the views, and the 
 spaces for dimensions and title have been decided upon, the pencil drawing for the 
 tracing should be continued on the layout. (See Art. 52.) 
 
 (b) The tracing. (See also Art. 52.) For most working drawings of ma- 
 chine construction the line widths D, E J, Fig. 55, are appropriate. In draw- 
 ings for steel construction, since many of the lines come close together, it may be 
 necessary to make the lines somewhat narrower, both for clearness and to prevent 
 them from running together. It must be borne in mind, however, that, if the lines 
 on the tracing are made much narrower than lines D J, Fig. 5 5, they are very 
 likely to be weak in the blue print, and hence, except for dimension and extension 
 lines, they are unsatisfactory. 
 
 (c) The blue prints. The process of obtaining copies by blue printing is 
 explained in Chapter XI. 
 
 64. Planning the Drawing, (a) The scale. In order that a working draw- 
 ing may best serve its purpose, it is necessary, when planning it, to take into account 
 not only the immediate facts concerning the making of the drawing as such, but 
 also the facts connected with its ultimate use. Thus, for example, if the drawing 
 is to be used at the bench or lathe, it should not be of a size which will be un- 
 wieldy, or which cannot be easily scanned by the mechanic. On the other hand, 
 the drawing must be of a sufficiently large scale to enable the workman to read 
 easily all of its parts and dimensions. 
 
 () The number of vieivs. In the interest of both convenience and economy 
 the number of sheets should be as small as possible ; that is, as many views of an 
 object should be placed on the same sheet as there is room for without overcrowd- 
 ing. Do not give views, or parts of vietvs, which are unnecessary. The views se- 
 lected should be such as will best set forth the essential characteristics of the 
 object. Thus, the interior of an object is usually represented best by one or more 
 sectio?ial views rather than by dotted lines, which are more likely to confuse than 
 to explain. For example, compare the projection, Fig. 115, having all invisible 
 
146 
 
 WORKING DRAWINGS ARRANGEMENT OF THE VIEWS,, 
 
 lines shown, with the corresponding projection, Plate 16, in which most of the in- 
 visible lines are omitted. 
 
 (c) The arrangement of the views. In planning an arrangement, endeavor to 
 anticipate the probable space that will be required for dimensions placed outside of 
 
 Avoid 
 
 Fig. 115. 
 
 the views, so that dimensions belonging to different views shall not conflict. (See 
 Art. 65.) In all drawings of machinery place the views according to third angle 
 projection* This gives the following arrangement : 
 
 Top view. 
 
 Left-hand side or end view. Front view. Right-hand side or end view. 
 
 Bottom view. 
 
 * The system of projection most generally adopted in mechanical engineering is that of the third 
 angle of descriptive geometry, although first angle projection is also followed to some extent. In archi- 
 tecture and civil engineering, first angle projection appears to be generally adopted; that is, the top 
 view is placed below the front view, the left-hand side view to the right of the front view, and the right- 
 hand side view to the left of the front view. 
 
 That two systems of projection are used in practice is unfortunate, for several reasons. When a 
 person becomes accustomed to one angle, it is more or less confusing to read drawings made in the other 
 angle. Then, besides this inconvenience, there is always the chance for costly mistakes in the shop, result- 
 ing from reading the drawing in the angle other than the one intended by the draftsman. To illustrate, 
 take a case which occurred just at the time of writing. A former student in architecture, having patented 
 an electric street railway signal, made a drawing from which to have the device manufactured. Naturally, 
 as an architect, he made his drawing in the first angle. When the lot of castings was delivered, he found 
 that certain parts which should be on particular faces of certain pieces had been made on opposite faces, 
 and that the castings were useless. The pattern makers read his drawing in the third angle instead of 
 in the first; hence the mistakes. 
 
WORKING DRAWINGS DIMENSIONING. 147 
 
 65. Dimensioning, (a) Necessary dimensions. In order to dimension a 
 working drawing properly, it is evidently necessary to know what dimensions should 
 be given. This requires not only the ability to discriminate between necessary and 
 unnecessary measurements, but also some practical knowledge of shop construction, 
 in order to know when, and what, particular measurements may be needed by the 
 mechanic. As a simple example, take the case of a hexagonal bolt head. In 
 forging the hexagonal figure of the head, the mechanic can easily work with refer- 
 ence to its short diameter, or " distance between the flats " ; whereas, if the meas- 
 urement of the diagonal (long diameter), or distance between corners, is given, 
 he must figure out the short diameter, or work at a disadvantage. As a further 
 illustration, if a drilled hole is dimensioned according to the directions for measur- 
 ing (Art. 62), that is, by giving its diameter and the distance to the edge of the 
 hole, the workman must figure for the center, since he must know at what point 
 to set the point of the drill. 
 
 If unfamiliar with shop requirements, it is best, when dimensioning a working 
 drawing, to give all essential measurements used in making the drawing. 
 
 (b) Forms of dimensions. The general form of a dimension which in- 
 cludes the numerals expressing the measurement, the dimension and extension 
 lines, and the arrow heads is described in Art. 42. 
 
 Because of the general use in shop work of the two-foot rule, dimensions less 
 than two feet should be given in inches ; if greater than two feet, in feet and 
 inches. 
 
 (c) General system of placing dimensions. No dimension should appear 
 upside down, when a drawing is read from the bottom or the right-hand side. A 
 satisfactory system of placing is illustrated by the several 
 
 positions of the diameter dimension shown in Fig. 1 1 6, 
 which will be found convenient for reference in doubtful 
 cases. It will be seen that, in this system, all dimensions 
 read from the bottom of the sheet, except those on the verti- 
 cal line AB, which read from the right-hand side of the sheet. 
 
 (d) Position of dimensions ; clearness. It is always 
 important to place a dimension in such a position that it may 
 readily be seen ; its connection with the part of the drawing 
 to which it refers must at once be evident ; and it must not 
 conflict with or obscure the drawing. To secure these results 
 
 may require considerable ingenuity and judgment, as varying conditions must be 
 met in different ways, but always in conformity with the following practice, which 
 must be regarded, by the beginner, as invariable. 
 
 On assembly drawings give only the most general dimensions, such as overall 
 
148 
 
 WORKING DRAWINGS DIMENSIONING. 
 
 B 
 
 Avoid 
 
 JT - 
 
 1 
 
 T.T 
 
 1 1 
 
 i._ 
 
 :-- 
 
 dimensions and distances between centers. Do not give unnecessary dimensions 
 nor repeat a dimension on the same drawing, and do not leave any calculating, 
 
 however simple, to be done by the 
 workman. Do not fail to give the 
 totals (overall measurements) of inter- 
 mediate measurements. 
 
 Whenever a dimension tends to 
 obscure the drawing, or if the actual 
 place of measurement will be more 
 clearly shown thereby, place the dimen- 
 sion outside of the view by means of 
 extension lines (B, Fig. 117); do not, 
 however, place the dimension so far 
 from the place to which it refers that 
 it shall appear detached. In the example of placing, Fig. 1 18, the distance, a, be- 
 tween dimensions, and between a dimension and an edge of the drawing, is made 
 equal to the distance, b, 
 used for the height of 
 the numerator and the de- 
 nominator. It should be 
 understood, however, that 
 the distances a and b are 
 not to be measured ; all 
 placing should be deter- 
 mined by eye. 
 
 Fig. 117. 
 
 Fig. 1 1 8. 
 
 Avoid 
 
 Extension lines must always be drawn parallel (see error, Fig. 119), and at 
 right angles (B, Fig. 120) to the direction in which the measurement is taken. 
 (See error, A, Fig. 120.) A dimension line must 
 always be drawn parallel to the line of measurement. 
 H j I r 1 Never place a dimension on a line of the draw- 
 
 ing, on a center line (A, Fig. 117), on an extension 
 /' ,\ / ,)\ line, or on a dimension line of another dimension (B, 
 Fig. 121). 
 
 Place overall dimensions outside of detail di- 
 mensions, and place a longer dimension outside of a 
 
 Fie:. 1 20. 
 
 Avoid 
 Fig. 119. 
 
 shorter one (B, Fig. 117). If a long measurement is placed between the drawing 
 and a shorter measurement (A, Fig. 117), it is necessary to cross the dimension 
 line of the longer measurement by the extension lines of the shorter, an arrange- 
 ment which may cause confusion. 
 
WORKING DRAWINGS DIMENSIONING. 
 
 149 
 
 In some cases greater clearness may be obtained by staggering the dimensions. 
 This consists, A, Fig. 122, in breaking each continuous line of dimensions (compare 
 A with B, Fig. 122) or in breaking up symmetrical columns 
 of dimensions, as the diameters in Fig. 117, by placing the 
 dimensions in a diagonal column, or by placing alternate di- 
 mensions in separate columns. Note. As the system A, Fig. 
 122, is not in common use, it should not be adopted unless au- 
 thorized. 
 
 (^) Special forms of dimensions. When the space in 
 which a dimension should be placed is too small to take the 
 
 Fig. 121. 
 
 dimension without interference or crowding, the following forms may be used : 
 If space permits, place the arrow heads as usual, but place the dimension at 
 
 13-4'V- -H 4'-0"l- \ 4'-0"l- 
 
 l k 8' 0- j J 6' 0" > l 6' 0"- 
 
 rre 
 
 Fig. 122. 
 
 Fig. 123. 
 
 one side and connected with the dimension line by a narrow freehand line (see the 
 left-hand example, A, Fig. 123). When there is no room for the arrowheads, 
 reverse them and place the dimension and freehand line as in the preceding case 
 
 (see middle example, A, Fig. 123). Or reverse 
 the arrow heads and place the dimension in line 
 with the arrow heads, omitting or using dimen- 
 sion lines extending outward from the points of 
 the arrows according to preference (see the 
 right-hand example, A, Fig. 123). A combina- 
 tion of the last two forms is shown in B, Fig. 
 123. 
 
 A comparison of confused and clear dimen- 
 sioning is given in Fig. 124. The dimensions given in A, Fig. 124, are intended for 
 the widths of the projections,, but are so placed that they give the widths of the 
 spaces between the projections a result due to the position of the measurement 
 relatively to the arrow heads, and the omission of a freehand line drawn from the 
 
 ? r ^r N2 ii >* 
 
 Avoid 
 
 (III 
 
 Correct 
 
 Fig. 124. 
 
WORKING DRAWINGS DIMENSIONING. 
 
 numerals to the arrow heads. Compare the confused arrangement, A, with the 
 clear one, B, Fig. 1 24. 
 
 Radii of circles. If there is sufficient room, a radius measurement should be 
 placed between the arc and its center, Fig. 125, and the center enclosed in a free- 
 
 Fig. 125. Fig. 126. Fig. 127. Fig. 128. 
 
 hand circle of about -Jg-" diameter. If there is not room for this, the center should 
 be ignored, the dimensions placed according to Fig. 126, and the letter " R" or 
 " Rad" invariably added. In the case of concentric arcs, the larger radius may be 
 reversed (Fig. 126), or either of the forms shown in Fig. 127 may be used. (The 
 second example includes the radii f and g.) Do 
 not distort the form, Fig. 126, by placing the 
 quantities too far from the arrow heads (see Fig. 
 128). 
 
 Do not give the radii of non-essential curves 
 such as those representing corners rounded for a 
 finish. 
 
 Diameters of circles. When a diameter di- 
 mension is given with one arrow head and only a 
 portion of its dimension line, Fig. 1 29, whether the 
 
 W 
 
 V 
 
 Fig. 130. 
 
 Fig. 129. 
 
 whole or only a part of the circle be shown, the dimension must invariably be fol- 
 lowed by " D " or " Dia." 
 
 Angle measurements should be given as shown in Fig. 1 30. 
 
 Diameters of solids. When a diameter is given on a side view of a solid 
 which is unaccompanied by a view showing the shape of the cross section of the 
 
 DIA 
 
 " SQ 
 
 *-l"HEX > 
 
 " OCT *{ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 i 
 
 
 ^ 1 
 
 
 
 
 
 : ) 
 
 
 
 
 
 
 3 
 
 Fig. 131. 
 
 solid, the dimension should include an abbreviation descriptive of the cross section, 
 as follows: " D." or " Dia." (diameter); " Sq" (square); "Hex" (hexagonal); 
 "Oct." (octagonal). (See Fig. 131.) 
 
WORKING DRAWINGS DIMENSIONING. 
 
 In a composite view, where a partial section is combined with an outside view, 
 the dimension line on one side of a dimension may be drawn of indefinite length 
 and its arrow head omitted, Fig. 132, which shows 
 that the measurement reads to a point corresponding 
 to that at which the one arrow head is placed. 
 
 Hollow cylindrical pieces, of material which is 
 
 Fig. 132. 
 
 Fig. 133- 
 
 Circular holes. 
 
 thin relatively to the diameter of the piece, as the 
 shell of an engine boiler, should be dimensioned according to Fig. 133; that is, 
 give the thickness of the material and both the inside and the outside diameters 
 of the piece. 
 
 A hole must be dimensioned by giving its diameter (B, Fig. 
 1 34) and the distance of its center from a finished edge 
 of the piece (A, Fig. 134). The dimensions taken in 
 measuring the object (b, Art. 62) must be reduced to 
 bring them to this form. When there are several holes, 
 their centers should be located as shown in Fig. 135, using 
 the same two edges of the piece as base lines (see error, 
 Fig. 136). 
 
 When the holes are all of the same diameter and 
 
 te B * 
 
 Fig. 134- 
 
 Holes in a straight line. 
 equally spaced, they may be dimensioned as follows : Locate the centers of the 
 first and last holes in the line, and give the overall dimension between these 
 centers. At each end of the line, dimension, two or three times, the distance 
 
 3"- 
 
 Avoid 
 
 Fig. 135- 
 
 Fig. 136. 
 
 from center to center of adjacent holes, also two or three diameters of the holes ; 
 but omit the intermediate dimensions the omission will indicate that the spacing 
 and diameters, respectively, are uniform throughout. 
 
 Holes in a circle. When holes are equally spaced around a circle, give the 
 diameter of the circle passing through the centers of the holes, as shown at A, 
 
152 
 
 WORKING DRAWINGS CONVENTIONS. 
 
 Figs. 137 and 138, or as shown at B, Fig. 138. Calculate the diameter according 
 to b, Art. 62. Give also the diameter of one or two of the holes ; this will indicate 
 that the others are of the same size. No other dimensions are usually necessary, 
 
 since equal spacing is understood 
 unless otherwise stated, and the 
 number of holes, unless very nu- 
 merous, may be counted from the 
 drawing. 
 
 When holes in a circle are ir- 
 regularly spaced, or not all of the 
 same size, all necessary measure- 
 ments must be given. 
 
 66. Conventions. (a) Line 
 conventions are given in Fig 55. 
 When a sectional and an outside view are combined (composite view or projection), 
 the two views should be separated by a dash-and-dot line (see Plate 15). 
 
 (b) Shade lines, if indicated, should be treated according to Art. 58. 
 
 (c) Shading is rarely seen in working drawings. If it is used, the light, 
 
 Fig. 137- 
 
 Fig. 138. 
 
 Fig- 139- 
 
 rapidly rendered examples shown in Fig. 1 39 should be taken as a guide, rather 
 than the examples given in Fig. D, Plate 4. 
 
 (d) Materials. The conventions shown on Plate 4 may be used (see Art. 
 38). The graining, Fig. A, Plate 4, should be used sparingly, and only in cases 
 where wood might be mistaken for a metal. 
 
WORKING DRAWINGS CONVENTIONS. 
 
 '53 
 
 
 (e) Finished surfaces. When a surface of an object is required to be finished 
 in the shop, the fact is indicated by means of a lower-case italic /(Fig. 140). The 
 letter should never be placed on a surface, as view B, Fig. 140, 
 but it should be placed on a line, straight or curved, which is an 
 edge view of the surface. Thus the three f's in A, Fig. 140, 
 indicate that the front, top, and back surfaces of the block are 
 to be finished, since the three lines on which the letters are 
 placed are edge views of the surfaces in question. Let the 
 cross stroke of the / intersect the line on which the letter is 
 
 /' 
 
 -r- 
 
 Fig. 140. 
 
 placed ; if the line is horizontal, the cross stroke should incline at 45. When all 
 the surfaces of an object are to be finished, the / should not be used, but instead 
 place on the drawing the note, " Finish all over'' 
 
 (/) Screws and tapped Jioles. Any of the con- 
 ventions given in Figs. 98 and 99 is appropriate. In 
 addition to the convention the number of threads to an 
 inch, as " 16 THD." (A, Fig. 141), must always be stated. 
 To save time, the inclination and spacing of the lines of 
 a screw thread convention should be determined by eye ; 
 care should be taken that the opposite ends of the 
 longer lines shall have the same relative positions as the 
 points of a thread, Fig. 94, but do not attempt to repre- 
 sent the number of threads to an inch. 
 
 Additional conventions are shown in Fig. 141. 
 The dotted lines, A, indicate that a piece is threaded for 
 the distance covered by the lines in question. The con- 
 vention B is used to represent a longitudinal projection 
 of an invisible threaded or tapped hole ; the same con- 
 vention is also used for the screw when in position. 
 The dotted circle, C, shows that the hole is threaded ; if 
 the hole is invisible, both circles should be dotted. In 
 the last two cases, besides the thread convention, always 
 give the diameter of the tap and the number of threads 
 to an inch, as "f" 16 TAP" (B and C, Fig. 141), 
 unless already given in the immediate vicinity. At D 
 is shown a section through the tapped hole which re- 
 ceives the screw A ; it should be noticed that the lines 
 of the thread convention are drawn in the opposite di- 
 rection to those of convention A. 
 
 When a section is taken through a screw and the tapped hole into which it 
 
 i 
 
 
 
 - f 16 TAP 
 
 f 16 TAP 
 
 SECTION 
 
 Fig. 141. 
 
154 
 
 WORKING DRAWINGS LETTERING. 
 
 fits, none of the thread conventions can be used ; it is therefore necessary to draw 
 
 the sections of the threads (see Fig. 142). 
 
 67. Letters and Numerals. Plain letters and nu- 
 merals, such as those given in Plate 5, should be used. 
 They must be perfectly legible, and for speed, if under 
 I" in height, should be stroke rendered (Art. 40). All 
 letters and numerals should be sufficiently large to be 
 easily read by the workman, but they should not be more 
 conspicuous than the drawings. 
 
 As vertical numerals take less space laterally than 
 inclined ones, if there is any probability of crowding, 
 only vertical numerals should be used. Comparing A 
 and B, Fig. 143, it will be seen that the dimensions in B 
 are the clearer; even when the size of the inclined 
 numerals is materially reduced, they still appear more 
 
 Fig. 142. 
 
 crowded in the narrower spaces than the vertical (compare B and C}. 
 
 Do not omit the dash between feet and inches, Fig. 144. Do not make 
 straight top 3*3; if carelessly made, they may be taken for 5*5, Fig. 
 144. Do not make open-top 4's ; if carelessly made, they may be 
 taken for 7's. Always make the dividing line of a fraction hori- 
 zontal ; if inclined, it may lead to an error in reading : thus, for 
 example, the i yg" (Fig. 144) might easily be taken for \\" . 
 
 68. Titles. Office drawings are usually filed away in drawers ; 
 hence, for easy reference, the title must be placed in the lower 
 right-hand corner of the drawing. An expert draftsman can 
 render excellent letters up to |" in height by means of the ruling 
 pen sharpened for lettering (c, Art. 40). Several pens should be kept, each 
 sharpened for different line widths. In larger letters the edges of the outlines 
 
 ,,,.| r ,,| 
 -. -+-/<? - 
 
 Avoid Avoid 
 
 5 " / " 
 
 f^ * f^ ij ^7 / L^. t^^ 
 
 & 0.4 ->->*-) *+ / '/$ 
 
 Fig. 144. 
 
 should be stroke rendered, the spaces filled in with the pen, and the letters rapidly 
 finished freehand. 
 
CHAPTER IX. 
 
 PSEUDO-PICTORIAL REPRESENTATION ISOMETRIC DRAWING. 
 
 69. Pseudo-pictorial Representation. This form of drawing includes two 
 general systems : axonometric projection, which includes isometric projection ; and 
 oblique projection, which includes cavalier or cabinet projection. In either of these 
 systems an object is represented by a single view having a more or less pictorial 
 effect a fact which makes these methods occasionally convenient in describ- 
 ing a construction to persons not familiar with representation by plan and ele- 
 vation. 
 
 In axonometric projection an object is supposed to be projected on a plane, 
 usually vertical, by projectors at right angles to the plane ; its special case of iso- 
 metric projection results from a particular position of the object. In oblique pro- 
 jection an object is supposed to be projected on a plane, usually vertical, by 
 parallel projectors not at right angles to the plane ; its special case of cavalier or 
 cabinet projection results when the projectors make an angle of 45 with the 
 plane. 
 
 Isometric drawing is a practical modification of isometric projection, and because 
 of its greater simplicity and more general usefulness will be considered first. 
 
 70. Isometric Drawing. All rectangular objects are bounded by three sys- 
 tems of parallel edges. In isometric drawing, lines belonging to these systems are 
 drawn parallel, respectively, to three lines, as HK, HJ, and HD, Fig. B, Plate 17, 
 known as the isometric axes. One axis is usually taken vertical, the other two at 
 30 with the horizontal. 
 
 Isometric drawings are usually made either from the actual object or from 
 plans and elevations. Let Fig. A, Plate 17, represent the plan (C) and elevation 
 (B) of a cube supposed to be viewed in the direction of the arrow 5. It will be 
 seen that, in the isometric (Fig. B) all edges of the object which make 45 with 
 the vertical plane X (Fig. A) are drawn parallel and at 30 with the horizontal, 
 and that the vertical edges are drawn vertical. The lengths of the edges in the 
 isometric drawing are made equal to the edges in the object, as shown by the 
 measurements given on both drawings. 
 
 71. Isometric of Rectangular Solids, (a) A cube (Figs. A and B, Plate If). 
 Construction : From any assumed point, D, Fig. B, draw, of indefinite lengths, the 
 vertical line DH, and the lines DE and DF, making angles of 30 with the hori- 
 
 (155) 
 
156 ISOMETRIC DRAWING. 
 
 zontal. From point D lay off on DH, DE, and DF the measurement (|") given 
 in Fig. A. Draw, at 30 with the horizontal, the back edges EG and FG of the 
 base ; put in the vertical edges, and draw the top of the cube. 
 
 (b} An object composed of rectangular solids. In Fig. C is given the plan 
 (B} and elevation (A) of a model. Consider, as in the projections of the cube 
 (Fig. A], that the object is placed so that its horizontal edges make 45 with 
 the imaginary vertical plane X, Fig. C. Construction : Starting at any assumed 
 point, D, Fig. D, and reading all measurements from Fig. C, draw the part FGE. 
 A projecting piece, as dbg, must be built up from its surface of contact ; that is, 
 from the surface, abcF, common to both pieces. The left-hand piece : Starting at 
 the corner F, Fig. D, draw the surface of contact Fabc, its edges equal to Fabc, 
 Fig. C ; draw the edges ad, be, eg, and Ff, and connect for the end degf. The 
 right-hand piece : Lay off Gm, Fig. D, equal to Gm (\"}> Fig. C. Draw the sur- 
 face of contact mk/ij, Fig. D, its edges equal to mkhj, Fig. C. Draw the vertical 
 edges and connect for the top. 
 
 (c) A rectangular recess. The method of drawing a recess is illustrated by 
 the mortise in the piece D, Figs./" and K. The construction is begun with the 
 rectangle oprq, and completed as shown. (Compare the similarly lettered lines in 
 Figs. /and K.) 
 
 72. Non-isometric Lines. Curves and straight lines oblique to either of the 
 three systems of a rectangular object must be located by means of rectangular 
 co-ordinates taken parallel to two (or all three) of the systems. Let A and B, 
 Fig. E, be two vertical faces of a cube, and C a horizontal face, upon which are 
 drawn oblique straight lines and curves as shown. The method by which these 
 oblique lines and curves would be drawn in isometric is illustrated in Fig. G. 
 
 (a) The lines M and N, Fig. E. As the line M intersects the two edges, 
 KH and FD, of the cube, make Ka and Fb, Fig. G, equal to the distances Ka and 
 Fb, Fig. F, and connect the points a and b. The line N. The extremity d of the 
 line, Fig. E, is located by the co-ordinates He and cd ; the extremity f, by He and 
 ef. The isometric of these co-ordinates gives the position of the points d and /, 
 Fig. G. 
 
 (b) Polygons. The isometric should be made from a preliminary drawing 
 showing the true shape of the given polygon. Circumscribe a rectangle, as kmqp, 
 C, Fig. E, about the polygon ; draw the isometric of the circumscribing rectangle, 
 and locate the corners of the polygon (see Fig. ). 
 
 (c) Plane curves. In drawing the isometric of a curve, first make a drawing 
 showing the true shape of the curve, and draw rectangular co-ordinates locating a 
 number of its points. In the case of a circle it is convenient to inscribe and cir- 
 cumscribe parallel squares, the sides of which establish the co-ordinates of eight 
 
ISOMETRIC DRAWING. 157 
 
 points in the circle ; namely, at the middle points of the outer square and at the 
 corners of the inner square. 
 
 Construction of the vertical circle, B, Fig. E. Draw the diagonals and diam- 
 eters of the face HJED, Fig. G. On a diameter, as OP, lay off the distance, as 
 Od, Fig. E, between the inscribed and circumscribed squares. Construct the 
 inscribed square, and draw the curve as indicated by the lettering in Figs. E and G. 
 
 The horizontal circle, C, Fig. E. The construction is the same as the preced- 
 ing, as indicated by the corresponding letters in Figs. E and G. 
 
 (d) Planes and solids. The faces of the cube, and the lines drawn on them, 
 Fig. E, are repeated in Fig. F. It will be seen, however, that by means of the 
 additional projections D, E, and G, the lines drawn on the faces, Fig. E, become in 
 Fig. F the projections of planes and solids. An isometric drawing of the planes 
 (A], cylinders (B and C), and the prism (C) would be begun by making a drawing 
 precisely the same as Fig. G. The lines and figures drawn on the surface of the 
 cube, Fig. G, are the lines and surfaces of contact of the planes and solids, Fig. F, 
 which would be completed in the isometric as follows : 
 
 The planes, A, Fig. F. The edges a'g', h'f , d'k' , and f'm' of the planes M 
 and N are perpendicular to the surface of the cube, and hence are represented in 
 the isometric, Fig. H, by lines drawn at 30 and equal to the lengths shown in D, 
 Fig. F. 
 
 The cylinders. Each cylinder is supposed to be circumscribed by a square 
 prism ; the base of the prism circumscribed about the horizontal cylinder (B, Fig. 
 F) is represented by the isometric square, acrp, Fig. H. From the corner a of the 
 square, Fig. H, draw the edge aj of the prism equal to the height, g't' , of the cylin- 
 der, Fig. F. Draw the isometric of the outer base of the prism ; inscribe the 
 isometric circles, and draw the elements of the cylinder tangent to them. The 
 construction is similar for the vertical cylinder, C, Fig. F. 
 
 The inclined brace F, Fig. K. The inclined edges of the brace should be 
 obtained by connecting the ends of the brace (surfaces of contact), which are 
 drawn first because they are bounded by isometric lines. 
 
 (e) Spheres ; double curved surfaces of revolution. Make a preliminary draw- 
 ing, showing the true size and figure of the given solid. Take a series of parallel 
 sections, and find the isometric of each. A line tangent to these sections is the 
 required curve. An isometric drawing of a sphere is a circle, but its diameter is 
 about two-ninths greater than the diameter of the given sphere. 
 
 (/) An approximate method for drawing the isometric of a circle, by the use 
 of circular arcs, is given in Fig. 145. As all the oblique lines are drawn at either 
 30 or 60, the construction should become clear by inspection of the figure. 
 Turning the figure so as to bring either diameter, 2 2, vertical, will give the 
 
158 
 
 ISOMETRIC DRAWING AXONOMETRIC DRAWING. 
 
 correct positions of the construction lines for circles lying in vertical planes. This 
 method is usually sufficiently accurate, except in the case of very large circles. 
 
 Fig. 145- 
 
 Fig. 146. 
 
 The application of the method to rounded corners is shown in Fig. 146. 
 When AC does not exceed ^ inch, however, the construction at A becomes so 
 small that it is better to proceed as follows : Make distance A' B' , Fig. 146, equal 
 to distance C'D', and sketch a freehand curve through points C', B' , and '. 
 
 73. Shade Lines in Isometric Drawing. The light is supposed to take the 
 direction V, Fig. B, Plate 1 7, parallel to the diagonal KE of the cube ; the 
 shadow of line ab is represented by the line da', parallel to the diagonal KJ. The 
 shade lines of the cube comprise the boundary LJHDF ; the practical shade lines 
 of an isometric drawing are those which can be determined by eye. Another 
 method is to shade all lower and right-hand (sharp) edges (see c, Art. 58). 
 
 74. Applications of Isometric Drawing. In Figs. J P, Plate 17, are shown 
 practical uses of isometric drawing. The detail, Fig. M, is drawn from its plan and 
 elevation A and B, Fig. L. The detail of framing, Figs. O and P, is taken from 
 an old-time working drawing of a bridge across the Saco River at Hiram, Me. 
 While the type of construction is obsolete, the drawing suggests the value of 
 isometric in representing a construction not easily shown in plan and elevation (see 
 A and B, Fig. N). 
 
 Perhaps the most useful and general application of isometric is to describe 
 details of building construction (see Plate 18). 
 
 75. Axonometric Drawing. Isometric drawing is a special case of axono- 
 metric drawing, resulting from a particular choice of the axes (see Art. 70) taken 
 to represent the three systems of parallel edges of a rectangular object. The 
 general case of axonometric drawing is illustrated by the cube shown in Fig. 147. 
 The lines AB, AC, and AD are the axonometric axes. One axis, AD, is usually 
 
Plate 17 
 
 Fig-N 
 
 (159) 
 
AXONOMETRIC DRAWING OBLIQUE PROJECTION. 
 
 161 
 
 Fig. 147. 
 
 drawn vertical, and made equal to the true length of the edge of the object ; the 
 other axes, AB and AC, are drawn at any convenient angles, and their lengths 
 determined by descriptive geometry. In general, the lengths of AB and AC will 
 not be equal to the true lengths of the lines of the ob- 
 ject, as in isometric drawing, but will be proportional to 
 these lengths ; these proportions, when determined, are 
 known as the scales of the axes. For example, if AC 
 were found to equal one-half the length of the line in 
 the object, then all lines in the system parallel to AC 
 must be drawn one-half of their true lengths. 
 
 For practical purposes the axes may be arbitrarily 
 assumed in such positions, and. of such lengths, as will 
 give a desirable representation. The following system 
 agrees closely with the results derived by descriptive geom- 
 etry, and gives a satisfactory appearance. In Fig. 147 draw AD vertical, AB at 
 12 with the horizontal, and AC at 45 with the horizontal. Make AD and AB 
 each equal to the lines of the object, and A C equal to two-thirds the length of the 
 line of the object, or in these proportions : for example, if AD and AB are laid off 
 from the scale of i^" = i foot, then AC should be laid off from the scale of 
 i"= i ft. For drawing the lines at 12 with the horizontal, a special triangle is 
 convenient. 
 
 Curves, and straight lines not parallel to the axonometric axes must be de- 
 termined by means of co-ordinates parallel to the axes. The methods are similar 
 to those of isometric drawing, except that the scales of the axes must always be 
 applied to the co-ordinates. 
 
 76. Oblique Projection. A cube drawn in oblique projection is shown in 
 Figs. 148 and 149. In this system one axis, AD, is taken vertical, another axis, 
 
 Fig. 148. 
 
 Fig. 149. 
 
 Fig. 150. 
 
 AB, is taken horizontal, and both these axes are laid off in their true lengths. 
 The third axis, AC, may be drawn at any oblique angle, and laid off to any desired 
 
162 
 
 OBLIQUE PROJECTION STUDY PLATE 15. 
 
 proportion of its true length. In Figs. 148 and 149 the line ACis made equal to 
 its true length, giving the special case of oblique projection known as cavalier or 
 cabinet projection. 
 
 An idea of the general effect obtained by oblique projection may be gained 
 from Fig. 150. (Compare with the same object drawn in isometric, Fig. M, Plate 
 17.) It will be seen that the drawing, Fig. 150, shows the true shape of the front 
 and back faces of the object. The lines connecting these faces are drawn at 45, 
 and their lengths are laid off to a scale one-half of that used for the front and back 
 faces. 
 
 Oblique projection may occasionally be useful ; but, as the principles and 
 methods are similar to those of isometric drawing, further explanation is unnec- 
 essary. 
 
 r 
 
 rt 
 
 I/I ft] 
 
 f*M K 
 
 1 
 
 
 I 
 
 
 
 
 
 
 .9 
 
 
 
 
 
 
 *p 
 1 
 
 1 
 
 
 
 
 
 <P 
 
 * r 
 
 t f 
 
 
 
 = 
 
 i_ 
 
 
 & I U 
 
 ll w 
 
 LW \f 
 
 i =* 
 
 
 40'-0" Span 
 
 Fig. 151. 
 
 STUDY PLATE 15. 
 
 Isometric drawing. 
 
 Use Whatman's hot-pressed paper. The size of the sheet is to be io"x 14", 
 with a ruled border line 9" x 1 3". Make a finished isometric drawing, in ink, 
 scale \" ' = i ft., of the roof truss, rafters, etc., given in Fig. 151. Place the point 
 B, Fig. 151, !" from the lower, and 3" from the right-hand line of the border; 
 draw the line AB upward to the left. 
 
Detail of Framing 
 
 Plate 18 
 
 Scale %-\nch - I fool"* 
 
 IsomelTic View 
 
 Spike Furring 
 
 Snjd 
 
 corner poat* ro 
 
 nail end of larti 
 
 re- 
 
 Raised girr 4-" 8%-^ 
 
 Spike plank 
 againsr girf 
 hasten ceiling 
 Furring ro. 
 
 /I furring strip 
 2."" 4-" is aer on in- 
 ner edge of sill 
 for secure nailing 
 of upper Floor. 
 
 ElevarTon-oF Corner 
 
 Copyr^bl- I9,o by 
 
 From Chandler's Building Construction by permission 
 Size of the Original I4"x20!! 
 
 (163) 
 
STUDY PLATES 15 AND 16. 165 
 
 Omit invisible lines, and the bolts. Put in shade lines. Do not give the 
 dimensions (Fig. 151). 
 
 Design and letter on the drawing the title "Roof Truss, Scale \" =i ft."; 
 also letter "Plate 15," your name and the date; all of the letters are to be drawn. 
 
 STUDY PLATE 16. 
 
 Isometric drawing. 
 
 Use Whatman's hot-pressed paper. The size of the sheet is to be io"x 14", 
 with a ruled border line g" x 1 3". Make an isometric drawing, in ink, of an as- 
 sembly of the clamp, Fig. 87. Take with the dividers the distances directly from 
 Plates 13 and 14. 
 
 Before beginning the drawing, make a layout to determine the position of the 
 drawing on the sheet. Show the bar F, and the glued pieces C, C, C, C, Fig. 87. 
 Break the bar and the piece K, in order that each shall fall within the ruled border 
 line. Represent the thread of the screw according to convention C, Fig. 98, but 
 draw the lines of the convention curved, and parallel to the edge of the hole through 
 the part B, Fig. 87.* 
 
 In the binder, G, first draw it as if square in cross section, and then shape it 
 freehand. Treat the knobs on the part K according to e, Art. 72. Omit all in- 
 visible edges ; put in shade lines. 
 
 Design and letter on the drawing the title " Cabinet Maker's Clamp" ; letter 
 also " Plate 16," your name and the date ; all of the letters are to be drawn. 
 
 * A template may be made having one edge straight, and the curve so inclined that the template 
 may be moved along the edge of the T-square. 
 
CHAPTER X. 
 
 WASH DRAWING. 
 
 77. A Wash is a mixture of India ink or a water color and water, applied 
 with a brush. 
 
 (a) The materials for wash drawing. Apart from the considerable skill 
 necessary to manage washes successfully, the quality of a result depends largely 
 upon the quality of the materials used. For a brief course of study, intended merely 
 to give the practice necessary for a fairly presentable coloring of small areas 
 as on maps and surveyor's plans the materials given on page 2 may be used. 
 
 If, however, the subject of wash drawing is approached with view to elaborate 
 rendering as in architectural drawing, see Plate 22 only the best materials 
 should be used. Get the best quality of Japanese ink ; select a stick which dis- 
 solves readily under the moistened finger, and in which the dissolved ink tends to 
 a brown shade rather than to a blue. The brown sable brushes made by Winsor and 
 Newton, while expensive, are the best ; the red sable of the same make are the 
 next best. Satisfactory sizes are the Nos. 6 and n, and No. 4 of the extra large 
 series. In purchasing a brush, selection should be made from half a dozen or 
 more after trying each, as follows : Thoroughly saturate the brush ; then, with only 
 enough water to bring the hairs to a point, test the brush by drawing it briskly 
 downward and across the finger or the edge of a water glass. Select the brush in 
 which the hairs show the most life, and, in springing to place, form the sharpest and 
 straightest point. 
 
 If a wash is applied to a free or unstretched light-weight paper (as 72 Ib. 
 Whatman), it causes the paper to expand ; and, when dry, the paper will be more 
 or less uneven or wrinkled. Hence there should be used a very heavy paper (not 
 lighter than 140 Ib. Whatman) ; a Whatman or a water-color paper mounted on 
 cardboard ; or any of these papers made into a water-color block. The best results 
 are obtained on stretched paper. % 
 
 (b) To stretch paper. Place the paper on the drawing board, with the better 
 side of the paper uppermost. Rule a pencil line parallel to and i inch from each 
 edge of the sheet. At each corner of the paper, outside of the ruled line, cut out 
 a triangular slip of the paper, as shown at C, D, E, and F, Fig. 152 (A). Lay 
 a straight-edge along each pencil line, and bend the paper until it stands perpen- 
 dicular to the drawing board. With a sponge well filled with water, moisten 
 
 (i 66) 
 
WASH DRAWING FLAT WASHES. 167 
 
 the surface, L, taking care to keep the upturned margin dry and not to abrade the 
 paper. When the paper has become quite limp, apply to the outer surface of the 
 margin, G', H',J',K> (B), a 
 liquid glue, strong paste, or 
 mucilage ; * turn down the mar- 
 gin, A, Fig. 152, and at the 
 same time pull each portion -p. 
 
 of the margin, G, H, J, and K, 
 
 toward the edge of the board. If the stretching is properly done, the paper will dry 
 out perfectly flat. It is necessary, however, to watch the work until the adhesive has 
 set. If the paper dries out faster than the adhesive, the contraction of the paper 
 will cause the glued margin to slide away from the edges of the board, and the 
 paper will dry slack ; hence, if the adhesive dries but slowly, the pulling out of the 
 glued margin should be repeated, and the paper again moistened, if necessary. On 
 the other hand, if the paper is very wet and is pulled too tight, the contraction may 
 cause the paper to tear, or may warp or even split the drawing board. 
 
 (c) To prepare an India ink ^vasJl. Never use stale ink, but grind it fresh at 
 each exercise. The prepared waterproof liquid inks are wholly unsuitable for wash 
 drawing. As the ink should be free from sediment, it is best to grind it on a china 
 slab. See that the slab and the nest of saucers are clean and free from dust. 
 Grind a reasonable quantity of ink which need not be so thick as for line draw- 
 ing to be used as a first supply in mixing the washes. In order that the ink 
 may be as " smooth " as possible, bear down but lightly on the stick, and, before mix- 
 ing a wash, let the ink stand a few minutes, so that the sediment may settle. If it 
 is required that a wash shall match a given wash or printed area (Plate 20), the 
 wash must be tried on-spare paper from time to time, when preparing it ; the shade 
 or value must not be judged until the wash is thoroughly dry. To mix a wash, 
 half fill three or four of the saucers with clear water ; add to the water in each 
 saucer a varying quantity of ink, taken from the slab, so as to produce several 
 washes of different values. The final wash should then be obtained by modifying 
 any one of the preceding washes by admixture from the others, or by addition of 
 clear water, until the required value is obtained. It is difficult to obtain a required 
 light value by a direct mixture of dark ink and water. 
 
 78. A Flat Wash. A wash is said to be fiat when it dries out to a uniform 
 value, and is free from a clouded appearance, streaks, and spots. A direct wash 
 signifies one obtained by a single application of the liquid wash. A built up wash 
 is obtained by repeated washes. 
 
 * The liquid glue is the best, but it softens very slowly when the glued paper is soaked in cleaning 
 the board. 
 
1 68 
 
 WASH DRAWING FLAT WASHES. 
 
 As a means of stating, very roughly, the amount of wash a brush should con- 
 tain for different results, let the expressions a " full brush " mean one holding as 
 much of the wash as is possible without dripping, and a " dry brush " indicate one 
 holding the least amount which will permit the brush to transmit wash to the 
 paper. 
 
 (a) To lay a direct fiat wash on an unbroken surface. With an H to 3H 
 pencil, rule lightly a boundary for the wash, as KADM, Fig. 153. Have ready a 
 
 generous supply of wash and 
 also some blotting paper. In- 
 cline the drawing at an angle of 
 from 10 to 15 with the hori- 
 zontal. With the largest brush 
 half -full, starting near the upper 
 right-hand corner, C, Fig. 153, 
 and carrying the brush firmly 
 and accurately along the ruled 
 line, DA, lay a broad strip of 
 the wash, C to B. The inclina- 
 tion of the paper causes the 
 wash to settle or form a pool (a 
 
 portion of which is shown at GH} along the lower edge of the strip, and the man- 
 agement of this pool (" flowing the wash ") is the principal consideration in laying 
 flat washes. Working very rapidly, and using a full brush, so as to keep the pool 
 as full as possible without overflowing, guide the pool from its first position, FH, to 
 a second position, a portion of which is shown at KL ; this should be done with 
 strokes of the brush perpendicular to the line FH. The pool must now be left for 
 an instant in order to carry the wash, 
 before it has begun to dry, accurately 
 into the corners A and D, and to the ruled 
 border at AE and DJ ' ; for this use a dry 
 brush, either a small one, or the one al- 
 ready in use, dried on the blotting paper. 
 After the edges of the wash have thus 
 been attended to, the pool must be ad- 
 vanced with the full brush, the edges 
 again managed with the dry brush, and 
 the process repeated until the bottom 
 ruled line is reached. As this line is 
 
 Fig. 154. 
 
 approached, the wash should be gradually exhausted from the brush and the finish- 
 ing strokes should be made with the dry brush. 
 
WASH DRAWING FLAT WASHES. 169 
 
 (b] To lay a flat wash on a broken surface. Let Fig. 154 represent a sur- 
 face broken up by the rectangles X X, which are not to receive the wash. The 
 process is the same as that described in the preceding paragraph, except that the 
 single pool, as AB, is broken up, as it advances, into three pools, as at C, D, and E, 
 when the wash must be treated as three simultaneous washes. Along the line, 
 FG, of the lower edges of the rectangles, the pools C, D, and E are again joined to 
 form a single pool, as HJ. With the attention divided between the alternate use 
 of the wet and the dry brush, the keeping of all advancing edges wet, and the 
 accurate following of the ruled lines, it is evident that considerable dexterity is 
 necessary, and that the draftsman must work rapidly. 
 
 (c) Precautions necessary to secure aflat wash. In order that a wash shall 
 dry out flat, it is necessary that the value of the wash shall not vary ; therefore, as 
 a wash quickly settles in the saucer, it must be remembered to stir up the wash 
 each time it is applied to the drawing. Moreover, it is necessary that the wash 
 shall be fed uniformly into the pool ; that is, in floating a wash, the brush must 
 hold the same amount each time it is applied to the paper. The results of a non- 
 observance of the latter requirement, and of working too slowly, are shown in Fig. 
 F, Plate 19. In making the drawing for this cut, the wash lay flat while handled 
 at a proper speed ; but on slower working the slight cloudiness, at DE, appeared. 
 At FG the wash was allowed to become almost dry, hence the streak. The 
 streak at HJ resulted from an excessive pool at KL t which caused the wash to 
 flow back into the partially dried portion between FG and KL. The spot at the 
 corner N resulted from carrying the pool into the corner, instead of exhausting the 
 wash, as described above. 
 
 A wash tends to dry out in a hard edge, as at BC and CE ; and hardness is 
 increased if the wash collects in a groove made by using too hard a pencil or by 
 bearing down on the pencil. Hard edges may be avoided, as at GJ t by slightly 
 thinning the wash, at its very edge, with clear water, used in a dry brush. A soft 
 edge may also be obtained by building up a wash with two washes, and keeping the 
 boundary of the second wash without the aid of a ruled line a trifle inside 
 the boundary of the first (see the edges AB and AD}. 
 
 Before laying a wash, see that the paper is clean ; if at all soiled, it should be 
 washed with clean water applied with a soft sponge. The use of a rubber is likely 
 to injure the surface. A direct wash is likely to work better if the surface is first 
 gone over with a very light wash of the India ink, or with water containing a trace 
 of yellow ochre. A wash is more likely to be flat if the paper can be kept slightly 
 damp (not moist). 
 
 In laying in a narrow stripe (see Plate 20), the wash should be managed as 
 described for a flat wash, but the pool should contain less of the wash. For very 
 
170 WASH DRAWING GRADED WASHES. 
 
 large areas, a foot square or more, a camel-hair sky brush may be used, but the 
 edges should be managed with the sable brush. 
 
 79. Graded Values. The light and shade of a surface may be expressed by 
 means of a series of graded flat washes, or by grading a direct wash. 
 
 (a) To lay a wash of uniform gradation, by means of fiat washes. 
 Let it be required to obtain a gradation with four washes, as shown by A D, Fig. 
 
 A, Plate 19. Rule, lightly, pencil lines representing the edges of the several 
 washes, D, Fig. A. Repeat these lines several times on spare paper to be used 
 in the trials necessary to determine the value of the dry washes. Prepare a 
 wash which shall give the lightest value, Fig. A ; then a second wash which, 
 when applied over the first one, will give the next value, Fig. B ; and so on. Lay 
 the washes in the order of the values, beginning with the lightest, as shown in 
 A D, Fig. A . The edges will be somewhat softer if the washes are laid in the 
 reverse order ; that is, beginning with the darkest value, and overlapping the 
 subsequent washes. Each wash should be thoroughly dry before the next one is 
 applied. 
 
 The modeling of a cylinder by using four flat washes is shown in A D, Fig 
 
 B, Plate 19. The shading of a sphere, by the same method, is given in B E, 
 Fig. C ; the outlines for the washes may be drawn as indicated in A. 
 
 A water line (see Plate 21) should be begun with the lightest wash, A, Fig. D, 
 Plate 19. As the width of the wash must not vary, the edges may merge in the 
 narrow places, thus giving a continuous wash, as between the shore lines on the right- 
 hand side of A. In the second wash, B t Fig. D, the edges merge only between the 
 island and the shore line. 
 
 The drawing of the hook, Fig. G, was built up with a considerable number of 
 flat washes applied without the aid of pencil outlines. 
 
 (b) To lay a graded, direct wash. This gradation, E, Fig. A, Plate 19, may 
 be effected by beginning the wash with the darkest value, and then gradually dilut- 
 ing the pool of wash, as it advances, by adding clear water. A better way is to 
 prepare several washes of graded values ; begin with the darkest, and lighten the 
 advancing pool with the prepared washes taken in the order of their values. Clear 
 water should also be at hand to modify the advancing pool, if necessary. 
 
 (c) A built-up graded wash. Proceed as in the previous paragraph, but use 
 much lighter washes. In H, Fig. B, is shown a cylinder shaded by this method ; 
 the several stages are indicated in E, F, and G. 
 
 80. Methods of Correcting a Wash Drawing, (a) Washing. Minor spots 
 and streaks may be partially eliminated by washing with clean water applied with 
 the brush. The part should be thoroughly soaked and scrubbed with the brush, 
 and the water then removed with blotting paper ; in medium to light washes a 
 
Plate 19 
 
 Fig. A. 
 
 Fig. D. 
 
 Avoid 
 
 Fig. F. 
 
 Fig. G. 
 
 (170 
 
WASH DRAWING METHODS OF CORRECTION. 173 
 
 result may not be perceptible until the process has been repeated several times. 
 In order to make radical corrections, it is necessary to sponge the whole drawing, 
 although a part of the drawing, if isolated by clear paper, may be so treated. All 
 traces of the wash must be removed from the paper by repeated applications of 
 clean water, as the slightest discoloration of the water will stain the paper. If the 
 whole drawing is to be washed, it may be placed directly under the water faucet. 
 The sponge must be a soft one, and used lightly, so as not to rub up the surface of 
 the paper. 
 
 () Stippling. This is the modifying of a dry wash by the placing of small 
 spots of liquid wash applied with the point of a dry brush. To illustrate the proc- 
 ess, let it be required to build up a value EF, Fig. E, Plate 19, wholly by stip- 
 pling. The paper is first spotted with the point of the dry brush, as shown at AB. 
 The spots of clear paper at AB are broken up by additional touches, as at CD, 
 but without overlapping the first spots. The clear paper is further eliminated by 
 a third spotting, as at GH t with smaller touches of the wash, and the process con- 
 tinued until a required value, EF, is produced. Stippling consumes much time, 
 and considerable practice is necessary in order to judge correctly the value of the 
 liquid wash used in the spotting. 
 
 Stippling is permissible only when it may be the means of saving considerable 
 time in redrawing. Brush washing with pure water and stippling may be alter- 
 nated. 
 
 81. Miscellaneous Notes, (a) Ink lines. In a wash drawing proper such 
 as the architectural drawing. Plate 22 all edges which would be represented by 
 lines in an outline drawing are represented by the value differences of the washes. 
 Such edges must never be further defined by ruled lines in black ink, although an 
 edge may be accented, occasionally, by a line of wash applied with the ruling pen. 
 In elaborate engineering drawings, maps, and plans, on which flat washes are used, 
 the inking should follow the laying of the washes ; but, in working drawings and 
 rush work, washes may be applied after the inking, providing the lines are drawn 
 with waterproof ink. 
 
 Chinese white, a pigment of value in making pictorial illustrations, should not 
 be used on washes in architectural or engineering drawing. 
 
 An ink line should never be drawn around the edge of a cast shadow. 
 
 (b) Care of the brushes. The brushes should be washed out thoroughly after 
 use, the hairs brought to a straight point, and the brushes kept in a brush holder. 
 If a brush is laid in a drawer, care must be taken that the point does not come in 
 contact with anything ; a point which dries bent is usually spoiled. India ink 
 ground black for line work should never be used in a wash brush, as it is difficult 
 to remove all traces of the ink. 
 
174 
 
 STUDY PLATE 17. 
 
 STUDY PLATE 17. 
 
 Flat and graded washes. 
 
 Use Whatman's cold-pressed paper. The size of the finished plate is to be 
 io"x 14", with a ruled border line 8" x 12". Stretch the paper (b, Art. 77), and 
 rule lightly with an H pencil the boundaries of the washes, Plate 20, according to 
 the measurements given in Fig. 155. Any erasure in connection with the pencil- 
 ing should be done lightly with a velvet rubber, so as not to injure the surface of 
 the paper. 
 
 It is required to lay flat and graded India ink washes (Arts. 78 and 79) 
 of the values shown on the plate. Take the areas in the order of their ar- 
 
 (0100 
 
 Fig. B 
 
 Fig.A 
 
 
 
 
 -too 
 
 
 
 ( 
 
 j 
 
 _ 
 
 
 1 I J fc 
 
 * 
 
 * 
 
 Fig.C 
 
 Fig. D 
 
 Fig. K 
 
 Fig- 155- 
 
 rangement. The values, Figs. A, B, E, F, H, and K, must be obtained with a* 
 single wash ; not more than two washes may be used for Fig. D, and not more than 
 three washes for Fig. C ' ; the number of washes for Figs. G and J is not limited. 
 Stippling must not be used. 
 
 Ink only the ruled border line of the plate, and the lettering "Plate 17," your 
 name, and the date (drawn letters). 
 
o ^ 
 
 CVJ 4) 
 
 "15 
 E 
 
 2 f 
 
 0- 
 
 075) 
 

STUDY PLATES 18, 19, 20, AND 21. 177 
 
 STUDY PLATE 18. 
 
 Modeling by graded washes. 
 
 Use Whatman's cold-pressed paper, stretched. The finished plate is to be 
 10" x 14", with a ruled border line 8" x 12" '. 
 
 It is required to arrange and shade six figures similar to B, D, F, H,J t and L, 
 Fig. 156 (also see Plate 21), changing the sizes and the proportions so as to fill the 
 sheet satisfactorily. Make a layout for the arrangement, and then lightly draw the 
 figures with an H pencil. Model the forms with graded washes; take Plate 21 as 
 a general guide, but keep the darkest value in each figure lighter than that on the 
 plate. 
 
 Ink only the ruled border line of the plate, and the lettering " Plate 18," your 
 name, and the date (drawn letters). 
 
 STUDY PLATE 19. 
 
 Modeling by flat washes. 
 
 Pi-oceed as in Study Plate 1 8, but let the modeling be done with graded fiat 
 washes (see Figs. A, C, E, G, and K}. 
 
 STUDY PLATE 20. 
 
 Modeling and water lines by graded washes. 
 
 Use Whatman's cold-pressed paper, stretched. The finished plate is to be 
 10" x 14", with a ruled border line 8" x 12". 
 
 It is required to arrange and shade three figures similar to M, O, and Q, 
 Fig. 156 (also see Plate 21), changing the sizes and proportions so as to fill the 
 sheet satisfactorily. Make a layout for the arrangement, and then lightly draw 
 the figures with an H pencil. Render the pipe and the water lines with graded 
 washes; take Plate 21 as a general guide, but keep the darkest value in each 
 figure lighter than that on the plate. 
 
 Ink only the ruled border line of the plate, and the lettering " Plate 20," your 
 name, and the date (drawn letters). 
 
 STUDY PLATE 21. 
 
 Modeling and water lines by flat washes. 
 
 Proceed as in Study Plate 20, but let the pipe and the water lines be ren- 
 dered vaflat instead of graded washes (see Figs. TV and />). 
 
I 7 8 
 
 STUDY PLATE 22. 
 
 STUDY PLATE 22. 
 
 Modeling and water lines by flat and graded washes. 
 
 Use Whatman's cold-pressed paper. The size of the finished plate is to be 
 io"x 14", with a ruled border line 8" x 12". Stretch the paper, and lay out the 
 figures, Plate 21, according to the measurements given in Fig. 156. 
 
 Fig. 156. 
 
 It is required to make an accurate copy of Plate 21, for values, and treatment 
 (see Arts. 78 and 79). 
 
 Ink only the ruled border line of the plate, and the lettering " Plate 22," your 
 name, and the date (drawn letters). 
 

Plate 22 
 
 ROME 
 
 FORVM 
 
 DE-TRAlAN 
 
 ENTABLEMENT 
 DE-LA-BASEIOVE * 
 
 JBL JB ^mr .jg .j../jBr..jBt'.3it\ja JH jg ;?! .JH.:JH..JH a 
 
 FROM THE WASH DRAWING BY A. TOURNAIRE. 
 
 The size of the original is 24 x 38 inches. 
 
 (181) 
 
CHAPTER XL 
 
 MECHANICAL COPYING THE BLUE-PRINT PROCESS PROCESS DRAWING 
 
 PATENT OFFICE DRAWING. 
 
 82. Mechanical Copying, (a) A tracing-paper transfer. Place, tracing paper 
 over the outline required to be copied. Trace the outline; turn the paper over; 
 go over the traced line with a soft pencil, and rub down the lead. Reverse the 
 tracing paper, place it on the drawing and go over the traced line with a 3H pencil. 
 Instead of rubbing lead on the back of the traced line, a transfer paper pre- 
 pared by rubbing powdered lead uniformly on tissue paper may be placed be- 
 tween the tracing and the drawing paper. 
 
 () A celluloid transfer. A sharper and narrower line than by the preceding 
 methods may be obtained by making the tracing on thin celluloid, with a sharp steel 
 point. Go over the back of the traced line with a steel point, and then rub into 
 the line the lead of a black or a blue pencil. Dust off the superfluous lead, place 
 the celluloid with the lead-filled line next to the paper, and then rub the line 
 briskly with the burnisher. 
 
 (c) A rubbing. The outlines of forms in relief, such as ornament and letter- 
 ing, may be obtained, if their edges are fairly sharp, by placing thin paper over the 
 forms, and then rubbing over their edges. 
 
 83. Enlargement and Reduction, (a) By pantograph. Irregular figures, 
 such as maps and diagrams, may be enlarged or reduced with a fair degree of accu- 
 racy by means of an inexpensive pantograph. An expensive form of this instrument 
 is necessary for accurate engineering work. 
 
 (b] By triangulation, base lines, and offsets. First establish the principal 
 points of the given outline by a series of triangles, built up from a base line connect- 
 ing any two important points in the given outline, and then tie in additional points 
 by means of offsets from the sides of the triangles taken as additional base lines. 
 Begin the enlargement or reduction by drawing a line proportional to the prin- 
 cipal base line in the original, and, starting from this base line, draw triangles and 
 offsets proportional to those on the original. Having thus determined the position 
 of the principal points, the outline must be sketched in by eye. The proportional 
 distances used in constructing the triangles may be obtained by the use of two 
 scales, or with the proportional dividers. If the size of the original and of the 
 
 (183) 
 
1 84 
 
 ENLARGEMENT AND REDUCTION. 
 
 reduction or enlargement will permit, place the paper on which the copy is to be 
 made close to the original, and obtain the triangles for the copy by means of lines 
 drawn by sliding'the triangle (Art. 23) parallel to the sides of the triangles in 
 the original. 
 
 Fig. 157. 
 
 (c) By proportional squares. Let it be supposed that it is required to make 
 from a photograph or a cut, Fig. 157, a large wall diagram to illustrate this machine. 
 
 Fig. 158. 
 
 Circumscribe a rectangle about the photograph, and rule lines, as i, 2, 43, Fig. 
 158, dividing the rectangle into squares. Begin the diagram, Fig. 159, by drawing 
 a rectangle of the size required, and having the sides proportional to those of the 
 
ENLARGEMENT AND REDUCTION. 
 
 rectangle, Fig. 158. Divide the sides i 25 and 25 43, Fig. 159, into the 
 number of parts used on the original, Fig. 158, and draw the horizontal and vertical 
 lines as shown. Find the vanishing points VP Z and VP 3 (the latter is at the inter- 
 section of the lines A, B, L, Fig. 159; also see note on the cut of the original, 
 Fig. 158) by producing several of the convergent lines, and draw the horizon. 
 
 i '' /. a it- if '* / 
 
 / i * + If I 7 r 
 
 Fig. 159. 
 
 Draw the horizon, Fig. 159, and locate the vanishing points by laying off on the 
 horizon the necessary (proportional) distances. Note the point where a line crosses 
 the edge of a square in the original, Fig. 158, and sketch the line through the cor- 
 responding point (judged by eye) in the corresponding square on the diagram, Fig. 
 159. The convergent lines should be ruled with the aid of a long straight-edge 
 passed through the proper vanishing point. 
 
 If there is objection to drawing directly lines on an original, the squares may 
 be drawn on tracing paper placed over the original. 
 
 In making a copy directly from a flat (actual) object, it is sometimes con- 
 venient, first, to obtain its outline by running a pencil around the object laid on 
 paper, after which the outline may be enlarged or reduced by any of the methods 
 described. 
 
1 86 THE BLUE-PRINT PROCESS. 
 
 84. The Blue-print Process. Blue-print paper is a white paper with a coating 
 which is sensitive to light. So long as the paper is protected from light, the coat- 
 ing can be easily removed by washing ; but on exposure to sunlight the coating 
 turns blue, and becomes insoluble in water. 
 
 A print is obtained by means of a wooden frame set with glass, and having a 
 removable back lined with felt. The drawing, preferably a tracing, is placed with 
 the ink lines next to the glass ; the blue-print paper with the sensitized surface next 
 to the tracing. The frame is then exposed to direct sunlight, which, passing through 
 the portion of the tracing cloth not covered by the ink lines, acts on the sensitized 
 surface, while the portions of this surface protected by the lines of the tracing are 
 not affected. After an exposure varying from twenty seconds to five minutes, de- 
 pendent upon the "speed" of the paper, the print is thoroughly washed in a tank 
 of running water or by means of a hose. The print is then hung up, that it may 
 drain properly and dry flat. A good print shows clear white lines on a uniform 
 blue ground. 
 
 When the back of the printing frame is in position, the blue-print paper, the 
 tracing, and the glass should be in close contact. If the contact is imperfect, it 
 should be corrected by means of a felt pad ; otherwise more or less light will pass 
 under the lines, with the result that edges of the white lines in the print will be 
 blurred, or the lines tinged with blue. 
 
 If a print is under-exposed, it washes out to a pale greenish blue, giving a 
 weak contrast with the white lines. If a print is over-exposed, the light is likely to 
 work through the lines of the tracing, in which case the lines on the print wash out 
 to a pale blue instead of white, and the ground becomes too dark or turns gray. 
 
 Special care must be taken to exclude all light from quick papers a covered 
 case or can is convenient and to open them only in a subdued light or a dark 
 room. Quick papers may be printed by electric light. 
 
 As excellent prepared blue-print papers, of different speeds, can be purchased 
 at a moderate price, it is usually not worth while for the draftsman to coat his own 
 paper. The process, however, is as follows : 
 
 For a paper requiring an exposure of about five minutes, mix separately, 
 
 (1) Red Prussiate of Potash (recrystalized) i part (by weight) 
 Water 5 parts " " 
 
 (2) Citrate of Iron and Ammonia i part " " 
 Water 5 parts " " 
 
 Working in a subdued light, mix equal parts of these solutions, and apply to 
 the paper with a sponge, or a flat 3-inch camel-hair brush. (For a quicker paper 
 more of the citrate of iron solution must be used, but the color of the print will not 
 be so good.) A good quality, hard surface paper should be used. As the solutions 
 / and 2 are not affected by light, they may be kept on hand ready for use. 
 
THE BLUE-PRINT PROCESS PROCESS DRAWING. 187 
 
 Blue lines on a ivhite ground (positive prints) . Make a preliminary negative 
 on thin brown-print paper obtained of dealers in drawing supplies with the 
 tracing reversed ; that is, with the ink lines next to the sensitized surface. Substi- 
 tute the brown-print negative, which shows white lines on a brown ground, for the 
 tracing, and proceed as described for the prints on a blue ground. 
 
 Good blue prints can be made from drawings on thin, or on bond paper. When 
 a blue print is to be made from a drawing on thick paper, the drawing may be made 
 more transparent by wetting with naphtha or gasolene, which dries out without 
 injury to the drawing. For a sharp print it is necessary, in order to exclude the 
 oblique rays which will pass under the lines, to lay the drawing face down, but 
 with the disadvantage that the print is reversed. 
 
 When a part of a drawing is not wanted in a print, the part may be covered 
 with thick paper placed between the tracing and the glass of the printing frame. 
 Pencil lines and spots may be removed from a tracing by sponging with naphtha or 
 gasolene, which does not injure the cloth or the ink lines. 
 
 For making alterations on a blue print, white lines may be made with soda, 
 or any alkali, dissolved in water, with a small quantity of gum arabic added to pre- 
 vent the mixture from spreading on the blue print ; or black drawing ink may be 
 used on light blue prints, and red ink on dark ones. 
 
 Blue prints required to stand much handling, if the size permits, may be 
 mounted on binder's board and then shellacked. 
 
 85. Process Drawing. A drawing made to be reproduced by any of the photo- 
 mechanical processes, such as photo-engraving and photo-lithography, is termed a 
 process drawing. 
 
 The practical bearing of the special requirements in this kind of drawing will 
 be better understood from a brief description of the processes of photo-engraving. 
 
 86. Line Plates. A line plate is one which reproduces an outline drawing. 
 The photographic negative. A negative of the drawing is made by means 
 
 of a wet plate, so prepared that the film or negative can be pulled ("stripped") 
 from the glass. After exposure in the camera, the negative is developed, sub- 
 jected to various chemical processes, and then stripped. 
 
 The zinc transfer. When dry, the film is reversed, placed on a thick plate 
 of glass, and a print is made on a sheet of highly polished zinc or copper, coated 
 with a mixture of glue sensitized with bichromate of ammonia. The mounted 
 film and the sheet of metal are placed in a heavy printing frame, and exposed to 
 light, as in blue printing ; the light causes the sensitized glue to become insoluble 
 in water. The print is washed, to remove the portions of the coating not affected 
 by the light, and then " burned in " by exposure to an intense heat, which car- 
 bonizes the insoluble glue remaining on the plate. 
 
1 88 PROCESS DRAWING LINE PLATES. 
 
 Etching. The plate is placed in a solution of nitric acid, which eats out 
 the surface not covered by the carbonized glue. After a short exposure to the 
 acid (" first bite ") the plate is dried and brushed over with powdered dragons- 
 blood, to protect the sides of the lines from the acid, which would otherwise attack 
 the lines beneath the carbonized surface, and thus produce what is technically called 
 " undercutting." The etching and the application of the dragons-blood are done 
 three times (four times for extra deep etching). 
 
 Finishing. The plate now goes to the engraver, to be cleaned up by 
 hand ; after which the relief of the lines is increased by cutting the ground of the 
 plate deeper with the "routing 1 " machine. The plate is then proved on a printing 
 press ; finally it is nailed to a block to bring it to the height .of printer's type. 
 
 87. Drawings for Line Plates. The first step toward securing excellence in 
 a line plate is attention to details in making the original drawing. 
 
 To obtain a greater sharpness of line when the drawing is photographed, also 
 to eliminate imperfections as far as possible, the drawing should be made larger than 
 the plate. Over-reduction, however, may result in broken or ragged lines in the 
 plate, a weak-looking cut, or one so small that its details may not easily be seen. 
 The best results are obtained from a drawing made from one-third to one-half larger 
 than the plate. Make the drawing on smooth, white bristol board,* and keep it 
 clean. See that all lines of the drawing have sharp, smooth edges, and that the 
 lines are black. If the plate is to be considerably smaller than the drawing, ample 
 allowance must be made for the reduction in line widths, in order that the lines on 
 the plate may not come so fine that, unless retouched on the zinc not always 
 skilfully done there will be danger of the lines breaking down from undercutting. 
 In " forcing " the line widths in a drawing, as necessary for a considerable reduc- 
 tion, the beginner must not be misled by the difference between the appearance of 
 his process drawing and that of an engineering drawing, since, as compared with 
 the latter, the former may appear altogether too heavy. In dimensioning and letter- 
 ing a drawing, it is specially important to allow for the reduction, as a reduction 
 satisfactory for the drawing may bring the letters to a size not easily read. A 
 reducing glass will give some idea of the appearance of a reduction, the approximate 
 size of which may be obtained by measuring the image on the glass. 
 
 When very narrow lines on the plate are desired, it should be remembered 
 that ragged lines tend to thicken in the photographic negative. A perfectly smooth 
 line on the drawing will give a narrower line on the plate than will a ragged line 
 of the same or even less width. 
 
 A rubber must be used with caution on a process drawing, as its use will 
 quickly make black lines gray. 
 
 * Drawings on tracing cloth give excellent results, but correction is more difficult. 
 
PROCESS DRAWING HALF-TONE PLATES. 189 
 
 Special methods. White lines ruled or freehand on a black ground 
 may be obtained by laying in the ground and then drawing the lines in Chinese 
 white. The white (Plate 3) must be diluted with water, and the proper thickness 
 must be judged from trial lines, which must be allowed to dry, as the dry pigment 
 is whiter than the liquid. The black ground must be laid in with waterproof ink. 
 
 Dash lines may be ruled solid in waterproof ink, and the dashes may be 
 obtained by cutting the line with the white, applied with a brush. 
 
 Methods of correction. Minor corrections can be made to advantage with 
 Chinese white. For example, the width of a line may be reduced and ragged edges 
 removed by ruling a line with the white, applied with the ruling pen. Letters may 
 be cleaned up and their outlines corrected by means of the white, applied with 
 a small, sharp-pointed brush. It is necessary, however, to use the white with cau- 
 tion ; as the pigment accumulates rapidly, several applications of it may be suf- 
 ficient to cast a shadow when the drawing is photographed. If a correction is not 
 satisfactory, scrape off the white and correct again. As a slight film of the white 
 over black will prevent the black from photographing, it is a good plan to look over 
 all Chinese white corrections with a magnifying glass before sending the drawing 
 away. Lines should never be cleaned up with a steel eraser, as furred edges in the 
 drawing are exaggerated by the camera. 
 
 When necessary to redraw a line, it is better to draw the line on thin, smooth 
 paper pasted over the line than on a surface furred up by erasure. The edges of 
 a patch however, cast a shadow which must be removed by the engraver ; hence 
 the edges of the patch must be kept as far away as possible from lines of the 
 drawing, in order that the engraver may have sufficient space in which to work. 
 
 If any considerable portion of a drawing must be corrected, the place may be 
 patched as just described, or the place may be cut out and fresh piece of card- 
 board inserted. If the latter method is adopted, the inserted cardboard must 
 match that on which the drawing is made, since a difference in the shade and 
 cleanliness of the two pieces may show in the negative, and thereby affect the 
 quality of the line plate. 
 
 88. Half-tone Plates. The reproduction, by a plate, of light and shade 
 drawings must be done by the half-tone process, which is similar to that of the line 
 plate with the following exceptions : The drawing is photographed through a 
 screen composed of lines ruled on glass placed close to the sensitized plate. 
 The image of the screen appears on the negative, breaking up the image of the 
 drawing into minute points of varying character; and the duplication of these 
 points on copper constitutes the half-tone plate. The etching of the plate done 
 with perchloride of iron instead of with nitric acid takes considerably more time 
 than the etching of a line plate. 
 
190 DRAWINGS FOR HALF-TONE PLATES PATENT OFFICE DRAWING. 
 
 The coarseness of the screen is measured by the number of its lines to an 
 inch, and the particular screen used depends upon the character of the printing in 
 which the plate will be used. For the coarsest newspaper work a screen of 65 
 lines is used, and for fine book work a screen of 200 lines, although as high as 
 400 lines has been used. (The screen for Plate 22 was one of 175 lines.) The 
 finer finish of half-tone plates is the work of skilled (hand) engravers, and finishers 
 who re-etch locally with a brush. A plate is darkened by burnishing and lightened 
 by re- etching. 
 
 89. Drawings for Half-tone Plates. Black and white drawings for half-tone 
 plates are made in the usual manner. Lamp black is perhaps the best medium to 
 use, although good results attend the use of India ink, charcoal gray, etc. Unless 
 it is desired to have the grain of the paper show in a print, very smooth paper must 
 be used. The whitest of paper is reproduced by a tint in the plate (see Fig. G, 
 Plate 19, showing the tint of the paper on which the hook was drawn) ; hence, for 
 a reproduction on a white ground, the tint must be removed by the engraver and 
 the routing machine (see Plate 22). When the tint is to be removed, the engraver 
 will be materially assisted, in mechanical subjects, if the boundary of the drawing 
 is defined by a line in Chinese white. 
 
 Fig. 1 60. 
 
 90. Patent Office Drawing. An application for a patent must be accom- 
 panied by a drawing made in accordance with the requirements contained in the 
 extract from the " Rules of Practice of the United States Patent Office " which 
 follows. Any system of drawing, such as orthographic projection, perspective, iso- 
 
PATENT OFFICE DRAWING. 191 
 
 metric, etc., may be used, and the one selected should be that which will show the 
 invention to the best advantage. 
 
 The cuts, Figs. A and B, Plate 23, reproduced from the "Rules of Practice," 
 indicate the character of patent-office drawings. It will be seen that the upper 
 left-hand view, Fig. B, is in isometric, while the other views are orthographic pro- 
 jections. In the case of a drawing such as is shown in Fig. A, considerable line 
 shading is permissible, but it should be used sparingly in drawings of machinery. 
 For example, the drawing, Fig. 160, is overshaded ; other objections to this draw- 
 ing are the placing of letters, as N, K, and Q, on shaded surfaces and the unneces- 
 sary representations of wood and stone. 
 
 A plate giving the conventions to be used in drawings of electrical apparatus 
 will be found opposite page 86 of the " Rules of Practice." 
 
 Extract from the "Rules of Practice of the United States Patent Office" : 
 
 "... The applicant for a patent is required by law to furnish a drawing of his 
 invention whenever the nature of the case admits of it. 
 
 . . . The drawing may be signed by the inventor, or the name of the inventor 
 may be signed on the drawing by his attorney in fact, and must be attested by two 
 witnesses. The drawing must show every feature of the invention covered by the 
 claims, and the figures should be consecutively numbered if possible. When the 
 invention consists of an improvement on an old machine the drawing must exhibit, 
 in one or more views, the invention itself, disconnected from the old structure, and 
 also in another view so much only of the old structure as will suffice to show the 
 connection of the invention therewith. 
 
 . . . Three several editions of patent drawings are printed and published, 
 one for office use, certified copies, etc., of- the size and character of those attached 
 to patents, the work being about 6 by Q|- inches ; one reduced to half that scale, 
 or one-fourth the surface, of which four are printed on a page to illustrate the 
 volumes distributed to the courts ; and one reduction to about the same scale 
 of a selected portion of each drawing for the Official Gazette. 
 
 This work is done by the photolithographic process, and therefore the char- 
 acter of each original drawing must be brought as nearly as possible to a uniform 
 standard of excellence, suited to the requirements of the process, and calculated to 
 give the best results, in the interests of inventors, of the office, and of the public. 
 The following rules will therefore be rigidly enforced, and any departure from them 
 will be certain to cause delay in the examination of an application for letters patent : 
 (i) Drawings must be made upon pure white paper of a thickness cor- 
 responding to three-sheet Bristol board. The surface of the paper must be 
 calendered and smooth. India ink alone must be used, to secure perfectly 
 black and solid lines. 
 
192 PATENT OFFICE DRAWING. 
 
 (2) The size of a sheet on which a drawing is made must be exactly 10 
 by 15 inches. One inch from its edges a single marginal line is to be drawn, 
 leaving the "sight" precisely 8 by 13 inches. Within this margin all work 
 and signatures must be included. One of the shorter sides of the sheet is 
 regarded as its top, and, measuring downwardly from the marginal line, a 
 space of not less than i^ inches is to be left blank for the heading of title, 
 name, number, and date. 
 
 (3) All drawings must be made with the pen only. Every line and 
 letter (signatures included) must be absolutely black. This direction applies 
 to all lines, however fine, to shading, and to lines representing cut surfaces in 
 sectional views. All lines must be clean, sharp, and solid, and they must not 
 be too fine or crowded. Surface shading, when used, should be open. Sec- 
 tional shading should be made by oblique parallel lines, which may be about 
 one-twentieth of an inch apart. Solid black should not be used for sectional 
 or surface shading. 
 
 (4) Drawings should be made with the fewest lines possible consistent 
 with clearness. By the observance of this rule the effectiveness of the work 
 after reduction will be much increased. Shading (except on sectional views) 
 should be used only on convex and concave surfaces, where it should be used 
 sparingly, and may even there be dispensed with if the drawing is otherwise 
 well executed. The plane upon which a sectional view is taken should be 
 indicated on the general view by a broken or dotted line. Heavy lines on the 
 shade sides of objects should be used, except where they tend to thicken the 
 work and obscure letters of reference. The light is always supposed to come 
 from the upper left-hand corner at an angle of forty-five degrees. Imitations 
 of wood or surface graining should not be attempted. 
 
 (5) The scale to which a drawing is made ought to be large enough to 
 show the mechanism without crowding, and two or more sheets should be 
 used if one does not give sufficient room to accomplish this end ; but the 
 number of sheets must never be more than is absolutely necessary. 
 
 (6) The different views should be consecutively numbered. Letters 
 and figures of reference must be carefully formed. They should, if possible, 
 measure at least one-eighth of an inch in height, so that they may bear re^luc- 
 tion to one twenty-fourth of an inch ; and they may be much larger when 
 there is sufficient room. They must be so placed in the close and complex 
 parts of drawings as not to interfere with a thorough comprehension of the 
 same, and therefore should rarely cross or mingle with the lines. When 
 necessarily grouped around a certain part, they should be placed at a little 
 distance, where there is available space, and connected by short broken lines 
 
ffi 
 
 bJD 
 LL 
 
 (i93) 
 
PATENT OFFICE DRAWING. 195 
 
 with the parts to which they refer. They must never appear upon shaded 
 surfaces, and, when it is difficult to avoid this, a blank space must be left in 
 the shading where the letter occurs, so that it shall appear perfectly distinct 
 and separate from the work. If the same part of an invention appear in more 
 than one view of the drawing, it must always be represented by the same 
 character, and the same character must never be used to designate different 
 parts. 
 
 (7) The signature of the inventor should be placed at the lower right- 
 hand corner of each sheet, and the signatures of the witnesses at the lower 
 left-hand corner, all within the marginal line, but in no instance should they 
 trespass upon the drawings. (See specimen drawing. . . .) The title should 
 be written with pencil on the back of the sheet. The permanent names and 
 title will be supplied subsequently by the office in uniform style. 
 
 When views are longer than the width of the sheet, the sheet should be 
 turned on its side and the heading will be placed at the right and the sig- 
 natures at the left, occupying the same space and position as in the upright 
 views, and being horizontal when the sheet is held in an upright position ; and 
 all views on the same sheet must stand in the same direction. One figure 
 must not be placed upon another or within the outline of another. 
 
 (8) As a rule, one view only of each invention can be shown in the 
 Gazette illustrations. The selection of that portion of a drawing best calcu- 
 lated to explain the nature of the specific improvement would be facilitated 
 and the final result improved by the judicious execution of a figure with 
 express reference to the Gazette, but which might at the same time serve as 
 one of the figures referred to in the specification. For this purpose the figure 
 may be a plan, elevation, section, or perspective view, according to the judg- 
 ment of the draftsman. It must not cover a space exceeding 16 square 
 inches. All its parts should be especially open and distinct, with very little 
 or no shading, and it must illustrate the invention claimed only, to the exclu- 
 sion of all other details. (See specimen drawing.) When well executed, it 
 will be used without curtailment or change, but any excessive fineness, or 
 crowding, or unnecessary elaborateness of detail will necessitate its exclusion 
 from the Gazette. 
 
 (9) Drawings should be rolled for transmission to the office, not 
 folded." 
 
DECIMAL EQUIVALENTS OF FRACTIONS OF AN INCH. 
 
 *V -0156 
 
 & -*4o6 
 
 H - 26 56 
 
 M .3906 
 
 If - -5' 56 
 
 n -6406 
 
 II -7656 
 
 Ji -8906 
 
 A -0313 
 
 A -'563 
 
 A - 28l 3 
 
 if -4063 
 
 il -5313 
 
 n -6563 
 
 1! -7813 
 
 M -9063 
 
 s 3 ? -0469 
 
 U -'719 
 
 H -2969 
 
 H -4*19 
 
 M -5469 
 
 1! -6719 
 
 M -7969 
 
 if -9219 
 
 A - 62 5 
 
 A -1875 
 
 A -3 I2 5 
 
 T 7 * -4375 
 
 A -5625 
 
 tt -6875 
 
 it -8125 
 
 H -9375 
 
 ft .0781 
 
 if -2031 
 
 *1 -3281 
 
 II -453' 
 
 Si -5781 
 
 II -7031 
 
 H -8281 
 
 tt -9531 
 
 A -0938 
 
 A - 2l88 
 
 H -3438 
 
 M -4688 
 
 if -5938 
 
 II .7188 
 
 i .8438 
 
 n -9688 
 
 & -1094 
 
 il -2344 
 
 II -3594 
 
 H .4844 
 
 II -6094 
 
 1} -7344 
 
 H -8594 
 
 II .9844 
 
 i .1250 
 
 j .2500 
 
 1 -375 
 
 | .5000 
 
 .6250 
 
 * .7500 
 
 * .8750 
 
 I 1 .0000 
 
 INCHES AND FRACTIONS REDUCED TO DECIMALS OF A FOOT. 
 
 Inch 
 
 
 1" 
 
 2" 
 
 3" 
 
 4" 
 
 5" 
 
 6" 
 
 1" 
 
 8" 
 
 9" 
 
 10" 
 
 11" 
 
 Inch 
 
 
 .000 
 
 .083 
 
 .167 
 
 250 
 
 333 
 
 .417 
 
 .500 
 
 583 
 
 .667 
 
 .750 
 
 833 
 
 .917 
 
 
 A" 
 
 .005 
 
 .089 
 
 .172 
 
 255 
 
 339 
 
 .422 
 
 .505 
 
 589 
 
 .672 
 
 755 
 
 839 
 
 .922 
 
 A* 
 
 r 
 
 .010 
 
 .094 
 
 .177 
 
 .260 
 
 344 
 
 .427 
 
 .510 
 
 594 
 
 .677 
 
 .760 
 
 .844 
 
 .927 
 
 Y 
 
 T v 
 
 .016 
 
 .099 
 
 .182 
 
 .266 
 
 349 
 
 43 2 
 
 516 
 
 599 
 
 .682 
 
 .766 
 
 .849 
 
 93 2 
 
 A" 
 
 r 
 
 .021 
 
 .104 
 
 .188 
 
 .271 
 
 354 
 
 438 
 
 5 21 
 
 .604 
 
 .688 
 
 77i 
 
 .854 
 
 938 
 
 P 
 
 A" 
 
 .026 
 
 .IO9 
 
 193 
 
 .276 
 
 359 
 
 443 
 
 .526 
 
 .609 
 
 693 
 
 .776 
 
 859 
 
 943 
 
 5 
 T 
 
 i" 
 
 .031 
 
 "5 
 
 .198 
 
 .281 
 
 365 
 
 448 
 
 531 
 
 .615 
 
 .698 
 
 .781 
 
 .865 
 
 .948 
 
 r 
 
 A" 
 
 .036 
 
 .120 
 
 .203 
 
 .286 
 
 37 
 
 453 
 
 536 
 
 .620 
 
 703 
 
 .786 
 
 .870 
 
 953 
 
 A* 
 
 V 
 
 .042 
 
 125 
 
 .208 
 
 .292 
 
 375 
 
 .458 
 
 .542 
 
 .625 
 
 .708 
 
 .792 
 
 .875 
 
 958 
 
 V 
 
 A* 
 
 .047 
 
 .130 
 
 .214 
 
 297 
 
 .380 
 
 .464 
 
 547 
 
 .630 
 
 .714 
 
 797 
 
 .880 
 
 .964 
 
 9 H 
 TS 
 
 r 
 
 .052 
 
 35 
 
 .219 
 
 .302 
 
 385 
 
 .469 
 
 55 2 
 
 635 
 
 .719 
 
 .802 
 
 .885 
 
 .969 
 
 K 
 
 
 
 057 
 
 .141 
 
 .224 
 
 37 
 
 39i 
 
 474 
 
 557 
 
 .641 
 
 .724 
 
 .807 
 
 .891 
 
 974 
 
 Hf 
 
 r 
 
 .063 
 
 .146 
 
 .229 
 
 3 J 3 
 
 396 
 
 479 
 
 563 
 
 .646 
 
 729 
 
 813 
 
 .896 
 
 979 
 
 r 
 
 ir 
 
 .068 
 
 .151 
 
 234 
 
 318 
 
 .401 
 
 .484 
 
 .568 
 
 .651 
 
 734 
 
 .818 
 
 .901 
 
 .984 
 
 ir 
 
 r 
 
 73 
 
 .156 
 
 .240 
 
 3 2 3 
 
 .406 
 
 .490 
 
 573 
 
 .656 
 
 .740 
 
 .823 
 
 .906 
 
 .990 
 
 r 
 
 tr 
 
 .078 
 
 .161 
 
 .245 
 
 3 2 8 
 
 .411 
 
 495 
 
 578 
 
 .661 
 
 745 
 
 .828 
 
 .911 
 
 995 
 
 H* 
 
 (196) 
 
INDEX. 
 
 Abstract Arrangement, 104. 
 
 Angles, of 15, 30, 45, 60, 75, to obtain, 21, 22. 
 
 To dimension, 150. 
 
 Applications of Isometric Drawing, 158. 
 Architect's Method of Shade Lines, 121. 
 Architect's Scale, 26. 
 Arrangement, 102. 
 
 Abstract, 104. 
 
 Examples of, 104. 
 
 Forms of, 104. 
 
 In Object Drawing, no. 
 
 Of Views in Working Drawings, 146. 
 
 Study Plates for, 131, 132. 
 
 Symmetrical, 104. 
 
 To balance, 104. 
 
 To design, 103. 
 Arrow Heads, 50. 
 
 Assembling of Details, Study Plates for, 131, 132. 
 Assembly Drawings, 143. 
 Axes, Axonometric, 158. 
 
 Isometric, 155. 
 
 Oblique, 161. 
 Axonometric, Axes, 158. 
 
 Co-ordinates, 161. 
 
 Drawing, 158. 
 
 Projection, 155. 
 
 Balancing, a Fraction, 50. 
 
 An Arrangement, 104. 
 
 A Title or Line of Letters, 49. 
 Beam Compass, 29. 
 Bicycle Chain and Sprockets, Shade Lines, 122. 
 
 Study Plate, 70. 
 Blue Print, Process, 186. 
 
 To correct a, 187. 
 Bolt Heads, Chamber of, 117. 
 
 Dimensioning, 147, 150. 
 Border Line, 50. 
 
 Ruled, to lay out, 51. 
 Bow Compass, 4. 
 
 Care of, 15. 
 
 Use of, 27. 
 
 Bow Spacers, Care of, 15. 
 
 Use of, 29. 
 Breaks, 40. 
 
 Rendering of, 40. 
 Brushes for Wash Drawing, 166. 
 
 Care of, 173. 
 Built-up Wash, 170. 
 
 Cabinet Maker's Clamp, no. 
 
 Doubtful Lines on, 118. 
 
 Measurements for, no. 
 
 Sketches for, no. 
 
 Study Plates on, 131. 
 Cabinet Projection, 155, 161. 
 Cavalier Projection, 155, 161. 
 Celluloid, Erasing Shield, 34. 
 
 Template, 25. 
 
 Transfer, 183. 
 Center Lines, 39. 
 
 Use of in Object Drawing, 113. 
 Chain, Bicycle, see Bicycle Chain and Sprockets. 
 Chamfer of Nuts and Bolt Heads, 117. 
 Circle, to describe, 27. 
 Circles, Precision in Drawing, 39. 
 
 Radii of, to dimension, 150. 
 
 Diameters of, to dimension, 150. 
 
 Approximate Construction in Isometric, 157 
 Circular Holes, to measure, 144. 
 
 To dimension, 151. 
 Clearness in Dimensioning, 147. 
 Cloth, Tracing, see Tracing Cloth. 
 Collective Rendering, 112. 
 
 Example of, 127. 
 Common Working Methods, 52. 
 Compass, 4. 
 
 Beam, 29. 
 
 Bow, see Bow Compass. 
 
 Care of, 15. 
 
 Setting for Scale Measurement, 30. 
 
 Use of, 27. 
 Compass Leads, to Adjust, 18. 
 
 To Sharpen, 18. 
 
 (197) 
 
198 
 
 INDEX. 
 
 Composite View, to dimension, 151. 
 Construction, Geometrical, 79. 
 
 Instrumental, Study Plates on, 59. 
 
 Of Chamfer, 117. 
 
 Of Isometric Circles, 157. 
 
 Of Screw Threads, 115. 
 Constructive Stage, 52. 
 Conventions, 39 
 
 Breaks, 40. 
 
 Cross Hatching, 40. 
 
 Finished Surfaces, 153. 
 
 Graining, 40. 
 
 Line, 39. 
 
 Line Shading, 40, 152. 
 
 Materials, 40. 
 
 On Working Drawings, 152. 
 
 Rendering of, 40. 
 
 Screw Threads, 116, 153. 
 
 Study Plate of, 69. 
 
 Tapped Holes, 153. 
 Convergent Lines, Inking of, 54 
 Co-ordinates, Axonometric, 161. 
 
 Isometric, 157. 
 Copying, Mechanical, 183. 
 
 Preliminary to Object Drawing, 113. 
 Correcting, a Blue Print, 187. 
 
 A Process Drawing, 189. 
 
 A Wash Drawing, 170. 
 Cross Hatching, 40. 
 
 Rendering of, 40. 
 Curve, French, 24. 
 
 Use of, 24. 
 
 Curved Line Ruling, 24. 
 Curved Solids, Isometric of, 157. 
 
 Modeling by Washes, 170. 
 Curves, Oblique, to measure, 126. 
 
 Duplication by Template, 127. 
 Cylinders, Isometric of, 157. 
 
 Modeling by Washes, 170. 
 
 Dash Lines, 39. 
 
 Abuse of, 53. 
 
 Rendering in Ink, 53. 
 
 Rendering in Pencil, 53. 
 
 Decimal Equivalents, Fractions of an Inch, 196. 
 Decimals of a Foot, Inches and Fractions Re- 
 duced to, 196. 
 
 Designing an Arrangement, 103. 
 
 Detail Drawings, 143. 
 
 Details, Assembling of, Study Plates for, 131, 132 
 
 Diameters, of Circles, to dimension, 150. 
 
 Of Solids, to dimension, 150. 
 Dimension Line, 50. 
 Dimensioning, 49. 
 
 A Composite View, 151. 
 
 Angles, 150. 
 
 A Working Drawing, 147. 
 
 Circular Holes, 151. 
 
 Clearness in, 147. 
 
 Diameters of Circles, 150 
 
 Radii of Circles, 150. 
 Dimensions, 49. 
 
 Form of, 50, 147. 
 
 Necessary, 147. 
 
 Position of, 147. 
 
 Special Forms of, 149. 
 
 Staggering of, 149. 
 
 System of Placing, 147. 
 Dividers, Hair-spring, 29. 
 
 Precision in Spacing with, 38. 
 
 Proportional, 30. 
 
 Setting for Scale Measurement, 30. 
 
 Spacing with, 29. 
 Dotted Lines, 39. 
 
 Never Shaded, 122. 
 Double-threaded Screw, 113. 
 
 Construction of, 115. 
 Doubtful Lines, 118. 
 Drawing, A Screw Thread, 114. 
 
 Assembly, 143. 
 
 Axonometric, 158. 
 
 By Stages, 52. 
 
 Detail, 143. 
 
 For Half-tone Plates, 190. 
 
 For Line Plates, 188. 
 
 For Tracing, 112. 
 
 Inked, Finishing an, 53. 
 
 Isometric, see Isometric Drawing. 
 
 Object, see Object Drawing. 
 
 Patent Office, 190. 
 
 Pencil, Finishing a, 53, 
 
 Preliminaries to, 50. 
 
 Process, 187. 
 
INDEX. 
 
 Drawing, to protect, 51. 
 
 To trim, 51. 
 
 Wash, see Wash Drawing. 
 
 Working, see Working Drawings. 
 Drawing Board, 4. 
 
 Care of, 15. 
 
 To Test, 9. 
 Drawing Paper, 15. 
 
 Care of, 15. 
 
 Selection of, 15. 
 
 Sizes of, 16. 
 
 To stretch, 166. 
 Drawn Letters, 48. 
 
 Rendering of, 48. 
 Duplication, by Use of Pricker, 19. 
 
 By Use of Template, 127. 
 
 Mechanical Copying, 183. 
 
 Of Objects, Working Drawings, 143. 
 
 Engineer's Method of Shade Lines, 121. 
 Engineer's Scale, 26. 
 Enlargement, 183. 
 
 By Pantograph, 183. 
 
 By Proportional Squares, 184. 
 
 By Triangulation, 183. 
 Erasing Shield, 34. 
 Erasure, 33. 
 
 Pencil Line, 33. 
 
 Ink Line, 33. 
 
 Use of Erasing Shield, 34. 
 
 From Tracing Cloth, 35. 
 Examples of Selection and Arrangement, 104. 
 
 Of Sketching and Measuring an Object, no. 
 Extension Lines, 50, 148. 
 
 Finished Rendering, in Ink, 53. 
 
 In Pencil, 53. 
 Finished Surfaces, 153. 
 Finishing an Inked Drawing, 53. 
 
 A Pencil Drawing, 53. 
 Finishing Stage, 53. 
 Flat Wash, 167. 
 
 Precautions to secure, 169. 
 Foot, Decimals of, 196. 
 Forms, of Arrangement, 104. 
 
 Of Dimensions, 50, 147. 
 
 Fractions, Balancing, 50. 
 
 Of an Inch, Decimal Equivalents of, 196. 
 
 On Working Drawings, 154. 
 French Curve, 24. 
 
 Use of, 24. 
 
 Geometrical Construction, 59. 
 Geometrical Problems, 79. 
 
 Solution by Working Methods, 55. 
 Graining, 40. 
 
 Rendering of, 40. 
 
 Hair-spring Dividers, 4. 
 
 Use of, 29. 
 Half-tone Plates, 189. 
 
 Drawing for, 190. 
 Hand-rail Stud, 109. 
 
 Designing the Layout, no. 
 
 Doubtful Lines on, 119. 
 
 Measurements of, no. 
 
 Sketches of, no 
 
 Study Plate on, 127. 
 Hanger, Study Plates on, 132. 
 Holes, Circular, to dimension, 151. 
 
 Circular, to measure, 144. 
 
 Tapped, 153. 
 Horizontal Line, to rule, 19. 
 
 Inch, Fractions of, Decimal Equivalents, 196. 
 Inches and Fractions Reduced to Decimals of 
 
 a Foot, 196. 
 India Ink, 13. 
 
 Care of, 15. 
 
 To prepare for Line Drawing, 31. 
 
 To prepare for Wash Drawing, 167. 
 
 Use of, 30. 
 Ink, Drawing, 31. 
 
 Finished Rendering in, 53. 
 
 India, see India Ink. 
 Inked Drawing, Finishing an, 53. 
 Ink Eraser, Steel, 13, 34. 
 Inking, by Stages, 54. 
 
 Of Convergent Lines, 54. 
 Ink Lines, on Wash Drawings, 173. 
 
 To erase, 33. 
 
 Instrumental Rendering and Construction, Study 
 Plates on, 59. 
 
2OO 
 
 INDEX. 
 
 Instruments, Care of, 15. 
 
 Case for, 4. 
 
 Set of, 3. 
 
 Intersections, Precision in Noting, 38. 
 Irregular Objects, 122. 
 
 Methods of Measuring, 122. 
 
 Study Plate of, 141. 
 Isometric, Axes, 155. 
 
 Co-ordinates, 156. 
 Isometric Drawing, 155. 
 
 Applications of, 158. 
 
 Approximate Construction of Circles, 157. 
 
 Curved Solids, 157. 
 
 Non-isometric Lines, 156. 
 
 Planes, 157. 
 
 Rectangular Solids, 155. 
 
 Shade Lines, 158. 
 
 Spheres, 157. 
 
 Study Plates on, 162. 
 
 Layout, for Object Drawing, no. 
 
 For Selection and Arrangement, 102. 
 
 For Working Drawings, 145. 
 Leads, Compass, see Compass Leads. 
 Lengthening Bar, 28. 
 Lettering, 43. 
 
 Pens, 44. 
 
 To grind a Ruling Pen for, 47. 
 
 With Ruling Pen, 44, 47. 
 Letters, Drawn, 48. 
 
 For Working Drawings, 154. 
 
 Line of, to balance, 49. 
 
 Sizes of, 45. 
 
 Stroke, 44. 
 
 Styles of, 45. 
 Line, Border, 50. 
 
 Conventions, 39. 
 
 Conventions on Working Drawings, 152. 
 
 Curved, to rule, 24. 
 
 Dash, 39, 53. 
 
 Dimension, 50. 
 
 Extension, 50. 
 
 Horizontal, to rule, 20. 
 
 Ink, to erase, 33. 
 
 Intersections, 38. 
 
 Of Letters, to balance, 49. 
 
 Line, of Sight, 36. 
 
 Parallel, to draw, 22. 
 - Pencil, to erase, 33. 
 
 Perpendicular, to draw, 22. 
 
 Plates, 187. 
 
 Plates, Drawing for, 188. 
 
 Shading, 40. 
 
 Vertical, to rule, 21. 
 
 Water, 170. 
 
 Widths for Working Drawings, 39, 145. 
 Lines, Convergent, to ink, 54. 
 
 Doubtful, 118. 
 
 Ink, on Wash Drawings, 173. 
 
 Non-isometric, 156. 
 
 Shade, Rendering of, 55. 
 
 Shade, see Shade Lines. 
 
 Materials, Care of, 15. 
 
 Conventions for, 40. 
 
 For Wash Drawing, 166. 
 
 List of, i. 
 
 On Working Drawings, 152. 
 Measurements, of an Object, 109. 
 
 Of Cabinet Maker's Clamp, no. 
 
 Of Hand-rail Stud, no. 
 Measuring, a Screw, 114. 
 
 A Three-pronged Hook, 125. 
 
 An Irregular Object, 122. 
 
 An Object, 109. 
 
 Circular Holes, 144. 
 
 Examples of, no. 
 
 For Working Drawings, 143. 
 
 Oblique Curves, 126. 
 
 Turned Handles, 126. 
 Measuring Point, 18. 
 Mechanical Copying, 183. 
 Method of Shade Lines, Architect's, 121. 
 
 Engineer's, 121. 
 
 Methods, Common Working, 52. 
 Mixed Rendering, 122. 
 
 Study Plate for, 141. 
 Modeling by Washes, 170. 
 
 Study Plates on, 177. 
 
 Necessary Dimensions, 147. 
 Non-isometric Lines, 156. 
 
INDEX. 201 
 
 Numerals for Working Drawings, 154. Plate 2, 7. 
 
 Nuts, Chamfer of, 117. 3, n. 
 
 Dimensioning, 150. 4, 41. 
 
 5 45- 
 
 Object, Measuring for Working Drawings, 143. 6, 61. 
 
 Sketching for Working Drawings, 143. 7, 65. 
 
 Object Drawing, 109. 8, 67. 
 
 Collective Rendering, 112. 9, 71. 
 
 Copying as a Preliminary to, 113. 10, 75. 
 
 Doubtful Lines, 118. n, 123. 
 
 Selection and Arrangement of Views, no. 12, 129. 
 
 Shade Lines, 119. 13, 133. 
 
 Sketching and Measuring the Object, 109. 14, 135. 
 
 Study Plates on, 127. 15, 137. 
 
 The Drawing for Tracing, 112. 16, 139. 
 
 The Layout, no. 17, 159. 
 
 Objects, Irregular, see Irregular Objects. 18, 163. 
 
 Oblique, Axes, 161. 19, 171. 
 
 Projection, 155, 161. 20, 175. 
 
 Oblique Curves, Measuring, 126. 21, 179. 
 
 22, 181. 
 
 Pantograph, Use in Enlargement and Reduc- 23, 193. 
 
 tion, 183. Plates, Line, 187. 
 
 Paper, Drawing, see Drawing Paper. Line, Drawing for, 188. 
 
 To stretch, 166. Half-tone, 189. 
 
 Tracing, 16. Half-tone, Drawing for, 190. 
 
 Parallel Line, to draw, 22. Study, see Study Plate. 
 
 Patent-office Drawing, 190. Position of Dimensions, 147. 
 
 Penciling, 52. Precision, 36. 
 
 Pencil Drawing, to finish, 53. In Drawing Circles, 39. 
 
 Pencil Line, to erase, 33. In Noting Line Intersections, 38. 
 
 Pencil Point, Measuring, 18. In Scale Measurement, 38. 
 
 Ruling, 17. In Spacing, 38. 
 
 Sketching, 18. Preliminaries, to Drawing, 50. 
 
 Pencils, 13. To Object Drawing, 113. 
 
 Selection of, 17. Preparation of an India Ink Wash, 167. 
 
 To sharpen, 17. Pricker, 10. 
 
 Use of, 17. Use in Duplication, 19. 
 
 Pencil Sharpener, 13. Use of, 19. 
 
 Pen, Ruling, see Ruling Pen. Prints, Blue, 184. 
 
 Pens, Lettering, 44. Problems, Geometrical, 79. 
 
 Perpendicular Line, to draw, 22. Solution by Working Methods, 55. 
 
 Pitch of Screw Threads, 113. Process, Blue Print, 186. 
 
 Planes, Isometric of, 157. Process Drawing, 187. 
 
 Planning a Working Drawing, 145. To Correct, 189. 
 
 Plate i, 5. Projection, Axonometric, 155. 
 
202 
 
 INDEX. 
 
 Projection, Cabinet, 155, 161. 
 
 Cavalier, 155, 161. 
 
 Isometric, 155. 
 
 Oblique, 155, 161 
 
 Systems of, 146. 
 Projections, 109. 
 
 Treatment in Object Drawing, 112. 
 Proportional Squares, Enlargement and Re- 
 duction by, 184. 
 Protecting a Drawing, 51. 
 Protractor, 24. 
 Pseudo-pictorial Representation, 155. 
 
 Radii of Circles, to dimension, 150. 
 Rectangular Solids, Isometric of, 155. 
 Reduction, 183. 
 
 By Pantograph, 183. 
 
 By Proportional Squares, 184. 
 
 By Triangulation, 183. 
 Refinements, in Observation, 36. 
 
 In Ruling Lines, 37. 
 
 In Scale Measurement, 37. 
 Rendering, 36. 
 
 Collective, 112. 
 
 Finished in Ink, 53. 
 
 Finished in Pencil, 53. 
 
 Instrumental, Study Plates on, 59. 
 
 Mixed, 122. 
 
 Of Breaks, 40. 
 
 Of Conventions, 40. 
 
 Of Cross Hatching, 40. 
 
 Of Drawn Letters, 48. 
 
 Of Graining, 40. 
 
 Of Letters with Ruling Pen, 44. 
 
 Of Line Shading, 43. 
 
 Of Shade Lines, 55. 
 
 Of Stroke Letters, 44. 
 
 Sketch, for Object Drawing, 109. 
 Representation, Pseudo-pictorial, 155. 
 Rubbing, A, 183. 
 Ruled Border Line, 50. 
 
 To lay out, 51. 
 Ruling, Curved Line, 24. 
 
 Refinements in, 37. 
 
 Straight Line, 19. 
 Ruling Pen, 4. 
 
 Care of, 15, 32. 
 
 Ruling Pen, Lettering with, 44, 47. 
 
 To grind for Lettering, 47. 
 
 To sharpen, 32. 
 
 Use of, 31. 
 Ruling Point, 17. 
 
 Scale, 10. 
 
 Architect's, 26. 
 
 Engineer's, 26. 
 
 For Working Drawings, 145. 
 Scale Measurement, Precision in, 38. 
 
 Refinements in, 37. 
 
 Setting Dividers for, 30. 
 Scales, 25. 
 Screw Threads, 113. 
 
 Conventional, 116. 
 
 Drawing of, 114. 
 
 Measuring of, 114. 
 
 On Working Drawings, 153. 
 
 Sections of, 114. 
 Selection and Arrangement, 102. 
 
 Examples of, 104. 
 
 For Object Drawing. 
 
 Study Plates on, 107, no. 
 Shade Lines, Architect's Method of, 121 
 
 Engineer's Method of, 121. 
 
 In Isometric Drawing, 158. 
 
 On Working Drawings, 152. 
 
 Rendering of, 55, 119. 
 
 Theory of, 119. 
 Shading, Line, 40. 
 
 On Working Drawings, 152. 
 
 Rendering of Line, 43. 
 Single threaded Screw, 113. 
 
 Construction of, 115. 
 
 Conventional, 116. 
 Sketches, of Cabinet Maker's Clamp, no. 
 
 Of Hand-rail Stud, no. 
 Sketching Point, 18. 
 
 An Object, 109. 
 
 And Measuring, Examples of, no. 
 
 For Working Drawings, 143. 
 Solids, Curved Isometric of, 157. 
 
 Diameters of, to dimension, 150. 
 
 Modeling by Washes, 170. 
 
 Rectangular, Isometric of, 155. 
 Spacers, Bow, 29. 
 
INDEX. 
 
 203 
 
 Spacing, 29. 
 
 Precision in, 38. 
 Speed, 36. 
 Spheres, Isometric of, 157. 
 
 Modeling by Washes, 170. 
 Sprockets, Bicycle, see Bicycle Chain and 
 
 Sprockets. 
 
 Squares, Proportional, Enlargement and Re- 
 duction by, 184. 
 
 Square-threaded Screw, Construction of, 116. 
 Stage, Constructive, 52. 
 
 Finishing, 53. 
 Stages, Drawing by, 52. 
 
 Inking by, 54. 
 
 Staggering of Dimensions, 149. 
 Stippling, 173. 
 Straight-edge, 20. 
 Straight Line, Especially Long, to rule, 20. 
 
 Horizontal, to rule, 19. 
 
 Parallel, to draw, 22. 
 
 Perpendicular, to draw, 22. 
 
 Ruling, 19. 
 
 Vertical, to rule, 21. 
 Stretching Paper, 166. 
 Stroke Letters, 44. 
 
 Rendering of, 44. 
 Study Plate i, 59. 
 
 2, 63. 
 
 3, 69. 
 
 4, 70. 
 
 5, 74- 
 
 6, 107. 
 
 7, 108. 
 
 8, 108. 
 
 9, 127. 
 10, 131. 
 u, 131. 
 12, 132. 
 
 J 3> X 3 2 - 
 
 14, 141. 
 
 15, 162. 
 
 16, 165. 
 
 i7 174- 
 18, 177. 
 
 iQ. 177- 
 
 20, 177. 
 
 Study Plate 21, 177. 
 22, 178. 
 
 Surfaces, Finished, 153. 
 Symmetrical Arrangement, 104. 
 System of Placing Dimensions, 147. 
 Systems of Projection, 146. 
 
 Tapped Holes, 153. 
 Taste, 102. 
 Template, 25. 
 
 Use in Duplication, 127. 
 Testing, 55. 
 Tests, for Drawing Board, 9. 
 
 For Triangles, 9. 
 
 For T-square, 9. 
 
 Threads, Screw, see Screw Threads. 
 Three-pronged Hook, Measuring a, 125 
 Thumb Tacks, 13. 
 
 Allowance for, 50. 
 Title, to balance, 49. 
 Titles on Working Drawings, 154. 
 Tracing Cloth, 16. 
 
 Erasure from, 35. 
 Tracing, Drawing for, 112. 
 
 For Working Drawings, 145. 
 
 To clean, 187. 
 Tracing Paper, 16. 
 
 Transfer, 183. 
 Transfer, Celluloid, 183. 
 
 Tracing Paper, 183. 
 Triangles, 9. 
 
 Care of, 15. 
 
 Combinations of, 22. 
 
 To test, 9. 
 
 Use of, 20. 
 
 Use with T-square, 21. 
 
 Triangulation, in Measuring Irregular Objects, 
 122. 
 
 In Enlargement and Reduction, 183. 
 Trimming a Drawing, 51. 
 T-square, 9. 
 
 Abuse of, 51. 
 
 Care of, 15. 
 
 To test, 9. 
 
 Use of, 19. 
 
 Use with Triangles, 21. 
 
204 
 
 INDEX. 
 
 Turned Handles, Measuring, 126. 
 To draw, 141. 
 
 United States Standard Screw Thread, Con 
 struction of, 115. 
 
 Vertical Line, to rule, 21. 
 
 View, Composite, to dimension, 151. 
 
 Views, Arrangement in Working Drawings, 146. 
 
 Number for Working Drawings, 145. 
 
 Of Objects, 109. 
 V-threaded Screw, Construction of, 115. 
 
 Wash, 166. 
 
 Built up, 170. 
 
 Flat, 167. 
 
 Graded, 170. 
 
 India Ink, to prepare, 167. 
 Wash Drawing, 166. 
 
 Care of the Brushes, 173. 
 
 Materials for, 166. 
 
 Stippling, 173. 
 
 Study Plates on, 174. 
 
 To correct, 170. 
 Water Lines, 170. 
 Widths of Line, 39. 
 
 For Working Drawings, 39, 145. 
 
 Working Drawings, 143. 
 
 Arrangement of Views, 146. 
 
 Blue Prints, 145. 
 
 Conventions for, 152. 
 
 Dimensioning, 147. 
 
 Finished Surfaces, 153. 
 
 General Directions for Making, 145. 
 
 Layout for, 145. 
 
 Letters and Numerals, 154. 
 
 Line Conventions, 152. 
 
 Line Widths for, 39, 145. 
 
 Materials, 152. 
 
 Measuring for, 143. 
 
 Number of Views, 145. 
 
 Planning, 145. 
 
 Scale for, 145. 
 
 Screw Threads, 153. 
 
 Shade Lines, 152. 
 
 Shading, 152. 
 
 Sketching for, 143. 
 
 Tapped Holes, 153. 
 
 Titles, 154. 
 
 Tracing, 145. 
 Working Methods, 14. 
 
 Common, 52. 
 
 Solution of Geometrical Problems by, 55. 
 
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