Industrial drawing; comprising the description and uses of drawing instruments, the construction of plane figures, tinting ... mechanical and topographical drawing. For the use of high schools, academies, and scientific schools

Front matter

fornj nal

THE LIBRARY

OF

Preface

THIS revised edition has been enlarged by the addition of the chapters on Tinting, Shadows, Shading, Isometrical Drawing, Oblique Projection, and Perspective. The chapters on Drawing Instruments and their Uses have been rewritten and much new matter added ; while some changes and additions have been made in the chapters on Projections and Topography.

It is hoped that by these changes the book will prove more useful in the class-room, or as a guide for self -instruction.

The cuts of Drawing Instruments used in this work, marked K. & E. in the table of contents, have been kindly furnished by Keuffel & Esser, No. Ill Fulton St., New York.

D. F. T.

733392

Chapter I. Dra"wtnq Instruments And Materials

PAGE

Compasses (K. & E.} 1

Hair-spring dividers (K. & E.) 2

Bow compasses (K. & E.) 3

Proportional compasses (K. & E.) 3

Beam compasses (K. & E.) 4

Drawing pen (K. & E.) 5

Drawing1 board (K. & E.) 5

Tsquare(jST. & E.) 6

Triangles (JC & E.) 7

Irregular curves 7

India ink 8

Colors 8

Ink saucers 8

Pencils 8

Brushes 8

India rubber 8

Thumb-tacks 8

Horn centre 8

Drawing paper. 9

Tracing paper and cloth 9

Scales 9

A scale of equal parts 10

Manner of using the scale 11

Diagonal scale of equal parts 13

Duodecimally divided scales (K. & E.) 17

Chain scales 17

Protractor (K. <t E.) 18

Chapter II. Use And Cake Op Instruments

Compasses 19

Dividers 19

Drawing pen 20

Sharpening pen. 20

Vi CONTENTS.

FAGI

Drawing board < 21

T square 22

Triangles 23

Manner of using triangles, etc. 23

Irregular curves 25

Preparation of ink 25

Pencils 26

Stretching paper 26

Pencilling a drawing 27

Juicing a drawing • 27

Accuracy. 28

Cleaning a drawing 28

Cuttingoff adrawing 29

Tracing. 29

Accuracy of scales 29

Chapter III. Construction Op Problems Op Points And Straight Lines

Prob. 1. — To draw a straight line through two given points 31

44 2. — To set off a given distance along a straight line from a point

on it 33

44 3. — To set off along a straight line any number of equal dis-

4. — From a given point on a right line to set off any number of

unequal distances 34

5. — To divide a given line into equal parts 35

6. — To construct a perpendicular to a line from a point on it. . . 36

7. — To construct a perpendicular to a line at its extremity 38

8. — To construct a perpendicular to a line from a point not on it. 39 9. — To construct a perpendicular to a line from a point without

near its extremity 39

" 10.— To set off a given distance from a line 40

44 11.— To draw a parallel to a line 40

41 12. — To draw a parallel to a line at a given distance from it 41

" 13. — To transfer an angle 41

44 14.— To construct an angle of 60° 41

" 15. — To construct an angle of 45° 42

44 16.— To bisect an angle 42

44 17. — To bisect the angle between two lines that do not meet. ... 42

Construction of Ares of Circles, Straight Lines and Points.

Prob. 18. — To describe an arc with a given radius through two points . . 43

44 19. —To find the centre of a circle described through three points. 43

44 20. — To construct a tangent to an arc 44

" 21. — To construct an arc of a given radius tangent to a given arc. 45

CONTENfS. Vil

PAGE

Prob. 22. — To construct a tangent to an arc from a point without 45

" 23.— To draw a tangent to two circles 46

" 24. — To construct a circle with a given radius tangent to two lines. 46 " 25.— To construct any number of circles tangent to each other

and to two lines 47

" 26. — To construct a given circle tangent to another and to^a right

line .' 47

44 27. — To construct a circle tangent to another at a given point and

to a right line 48

44 28. — To construct a circle tangent to another and to a right line

at a given point. 48

" 29.— To construct a circle tangent to two others 49

" 30.— To construct a half oval of three centres 49

*' 81. — To construct a four centre curve 50

" 32.— To construct a half oval of five centres. 51

" 33.— To construct a quarter of a three centre oval tangent to two

lines 53

44 34. — To constrict a quarter five centre oval tangent to two lines. 53

" 35.— To construct an S curve tangent to two parallel lines 53

44 36. — To construct an S curve having its centres on two parallel

lines. 53

Construction of Problems of Circles and Rectilineal Figures.

Prob. 37. — To construct a triangle 54

44 38. — To construct a square 54

44 39. — To construct a parallelogram 54

44 40. — To circumscribe a triangle by a circle 55

41. — To inscribe a circle in a triangle 55

42. — To inscribe a square in a circle 55

43. — To inscribe an octagon in a circle 55

44, — To inscribe a hexagon in a circle 56

4 45. — To inscribe an equilateral triangle in a circle 56

" 46,— To inscribe a pentagon in a circle 56

44 47. — To construct a regular figure of a given side (two methods) . . 57

44 48. — To circumscribe a circle by a regular figure 58

44 49. — To inscribe a circle in a regular figure 58

44 50. — To inscribe equal circles in a given circle 58

44 51. — To circumscribe a circle by equal circles 69

Construction of Proportional Lines and Figures.

Prob. 52.— To divide a line into two proportional parts 60

44 53. — To divide a line into any number of parts proportional to each

other 60

44 54. — To construct a fourth proportional 60

i4 55. — To construct a mean proportional 61

44 56. — To divide a line into mean and extreme ratio 61

44 57. — To construct a figure proportional to another 62

Viii CONTENTS.

Construction of Equivalent Figures.

PAOB

Prob. 58 — To construct a triangle equivalent to a parallelogram 62

" 59. — To construct a triangle equivalent to a quadrilateral 62

" 60. — To construct a triangle equivalent to a polygon 63

" 61. — To construct a triangle equivalent to a regular polygon 63

'. Construction of Curved Lines by Points.

Prob. 62. — To construct an ellipse (two methods) 63

' 63. — To construct an ellipse with three points given 65

' 64. — To construct a tangent to an ellipse at a given point 66

' 65. — To construct a tangent to an ellipse from a point without. . . 66

' 66. — To copy a curve by points 67

* 67. — To make a copy greater or smaller than a given figure 67

' 68. — To describe an arc of a circle by points 68

' 69. — To construct a parabola by points 68

' 70. — To construct the circumference of a circle of given diameter. 69

Chapter IV. Tinting And Shading

Flat tints, line shading 70

Graduated tints, line shading 71

Flat tints, India ink. 71

Graduated tints, India ink 72

Dry shading. 73

Colors 74

Chapter V. Conventional Modes Op Representing Different Materials

Conventional tints 75

Wood , 75

Masonry 77

Metals 78

Earth, 78

Water 78

Chapter VI. Construction Of Regular Figures

To represent a pavement made up of squares , 79

To represent a pavement of equilateral triangles 79

To represent a pavement of hexagons 79

To represent a pavement made up of octagons and squares 79

To represent a pavement made up of isosceles triangles 80

Examples of architectural ornament .80

CONTENTS. U

CHAPTER VII. PBOJECTIOKa

PAGE

Principles. 82

Notation. 86

Shade lines 86

Profiles and sections 87

Projections of points and right lines 89

Prob. 71. — To construct the projections of a right pyramid 92

' ' 72. — To construct the parts of a right pyramid from its projections 93

" 73. — To construct the projections of an oblique pyramid 93

" 74. — To construct the projections of a right prism 94

Traces of planes on the planes of projection 95

Prob. 75. — To construct the projections and sections of a hollow cube. 96 " 76. — To construct the projections and sections of a hollow pyramid 98

" 77. — To construct the plans, elevations, &c., of a house 102

Cylinder 106

Prob. 85. — Projections of the cylinder 107

" 86.— The cone and its projections 108

" 87.— The sphere and its projections 109

" 88.— Oblique section of the cylinder (two methods) 109

" 89. — Oblique sections of the cone (three cases) Ill

" 90. — Oblique sections of the cone (two cases) 112

" 91.— Section of the sphere 112

" 92. — To construct the curves of section of the cylinder, cone and

sphere (1st method) 113

" 93. — Second method of preceding problem 114

Projections of cylinder and cones with axes oblique to the planes of

projection 115

Preliminary problems 94 and 95 115-117

Prob. 96.— Projections of cylinder with axis oblique to vertical plane. 118 " 97. — Projections of cylinder with axis oblique to horizontal plane. 119 " 98. — Projections of cylinder with axis oblique to both planes of

projection. 119

" 99. — Projections of cone with axis parallel to vertical plane 121

" 100. — Projections of cone with axis oblique to vertical plane 122

" 101. — Projections of cone with axis oblique to both planes of projection 122

" 102.— Projections of hollow cylinder with axis parallel to vertical

plane 122

" 103. — Projections of hollow cylinder with axis oblique to both

planes 123

" 104. — Projections of hollow hemisphere (1st case) 123

" 105. — Projections of hollow hemisphere (2d case) 124

Intersections of Cylinders, Cones, and Spheres.

Prob. 106..— Intersection of two right cylinders with axes parallel to

vertical plane 125

CONTENTS.

Prob. 107.— Intersection of two right cylinders, the axis of one oblique

to horizontal plane 127

" 108. — Intersection of two right cylinders, the axis of one oblique

to both planes. 128

" 109.— Intersection of cone and cylinder 128

" 110. — Intersection of cylinder and hemisphere 130

" 111.— Intersection of cone and sphere 131

Development of Cylindrical and Conical Surfaces.

Prob. 112.— Development of cylinder 133

" 113.— Development of cone 134

Chapter VIII. Shadows

Principles 1 36

Prob. .1.— To find the shadow of a cube , 137

" 2. — To find the shadow of the frustum of a square pyramid. . . . 137

" 3. — To find the shadow of a short hexagonal prism 137

" 4.— To find the shadow of a vertical cylinder 137

" 5. — Shadow of a cylindrical abacus upon an octagonal prism .... 138

" 6. — Shadow on interior of hollow semi-cylinder. 188

" 7.— Shadow on steps 139

" 8.— Shadow of framing 139

" 9. — Shadow of timber resting upon top of wall 140

" 10. — Shadow of inclined timber upon triangular prism 140

" 11. — To find the angle which a ray of light makes with . Jher

plane of projection 141

" 12. — Shadow on interior of hollow hemisphere 141

Line of shade 141

Prob. 13.— To find the line of shade upon a cone 142

" 14.— To find the line of shade upon a sphere 142

CHAPTEE IX.

SHADING.

Rules. 144

Application of rules to the shading of an hexagonal prism 144

«• " " " acylinder 145

" " " a cone and sphere 145

Chapter X. Isometrical Drawing

Principles of isometrical projection 146-148

Prob. 1. — To construct the isometrical drawing of a cube, with a block

upon one face and a recess in another 148

CONTENTS. XI

PAOB Prob. 2.— To construct the isometrical drawing of three pieces of

timber bolted together 149

* • 3. — To construct the isometrical drawing of a portion of framing. 149

*' 4. — To make the isometrical drawing of a circle 149

" 5. — To make an approximate construction of the isometrical

drawing of a circle 150

" 6. — To divide the isometrical drawing of a circle into equal parts. 150 ** 7. — To make the isometrical drawing of a cube, cylinder, and

sphere 150

•' 8. — Isometrical drawing of brackets supporting a shelf 151

" 9. — The isometrical drawing of a nut and washer. 151

" 10.— The isometrical drawing of letters. 153

Prob. 11. — The isometrical drawing of a cube with its shadow upon the

horizontal plane 153

" 12. — The isometrical drawing of an hexagonal prism with the

shadow 153

" 13.— The isometrical drawing of a beam, projecting from a vertical wall, with the shadow 153

" 14. — The isometrical drawing of a four-armed cross, with the

shadow 153

" 15. — The isomefcrical drawing of a vertical cylinder, passing

through an hexagonal block 154

Chapter XI. Oblique Projection

Principles of oblique projection 155

Prob. 1. — To make the oblique projection of a circle i 156

Chapter XII. Linear Perspective

Principles of perspective 158

Prob. 1. — To find the perspective of right lines in different positions by

means of visual rays 159

" 2. — To find the perspective of a cube when placed with a face

paralleltoV 159

" 3. — To find the perspective of a cube when placed with its faces

oblique to V 160

" 4. — To construct the perspective of a regular hexagon by means

of diagonals and perpendiculars 162

" 5. — To construct the perspective of a pavement made up of

6. — To find the perspective of a cube

7. — To find the perspective of a vertical hexagonal prism xii CONTENTS.

MM

Prob. 8.— To find the perspective of a square pillar resting upon a

pedestal 163

« 9.— To find the perspective of a square pyramid 164

««« 10.— To find the perspective of a square pyramid resting upon a

pedestal 164

•* 11. — To find the perspective of an hexagonal prism, whose axis is

parallel to H and inclined to V 164

" 12.— To find the perspective of a circle 165

•* 13. — To find the perspective of a circle when it is perpendicular

«« 14 — To find the perspective of a vertical cylinder 165

" 15.— To find the perspective of a cylinder whose axis is perpendicular to V 1!vS

" 16.— To find the perspective of a rectangular block with a semicircular top 166

CHAPTER Xin.

ARCHITECTURAL ELEMENTS.

Roof truss 168

Columns and entablatures 169

Arches... 171

Chapter XIV. Mechanism

Prob. 114. — Projections of cylindrical spur wheel 175

" 115. — Projections of cylindrical spur wheel with axis oblique to

vertical plane 177

" 116.— Projections of mitre wheel. 177

" 117.— Projections of mitre wheel with axis oblique to vertical plane. 180

" 118.— Projections of a helix on a cylinder 180

" 119.— Projections of screw with square fillet. 182

" 120. — Projections and sections of the mechanism of a part of a

steam engine 183

" 121.— Sketches and finished drawings of the crab engine. 184

Chapter XV. Topographical Drawing

Preliminary remarks on the manner of representing irregular surfaces. 187

Plane of comparison 191

References 192

Projections of horizontal curves 192

Pi-ob. 123.— To construct the horizontal curves from a survey 194

CONTENTS. X1U

Conventional Methods of representing the Natural and Artificial Features of a Locality.

PAGE

Slopes of ground. 197

Scale of spaces 200

Surfaces of water 201

Shores. 201

Meadows, marshy grounds, trees, rivulets, rocks, artificial objects 202

Practical methods. 203

Colored topography 203

Scales of distances 206

Table of scales ... 207

Copying maps 208

Chapter 1. Dba Wing Instruments And Materials

1 Good instruments are necessary for good work, and the beginner who desires to excel should procure the best. These can be purchased by the case, or by the piece. The latter being the best way, as there are sometimes pieces in the case which are seldom, if ever, used. After selecting the pieces a case can be made for them, or, if one does not wish to incur that expense, roll them up in a piece of chamois skin, arranging so that they do not touch each other. By folding over one edge of the skin, and stitching together, little pockets may be formed for each piece.

The following instruments will be necessary : a compass with pen, pencil and needle points, and lengthening bar ; hair-spring dividers ; bow compass with pen and pencil points ; and one or two drawing pens. These with a drawing board, T square, triangles, etc., will make a sufficient outfit.

2. Compasses. These instruments are so well known as hardly to require description here. They consist of two legs, which are connected by a joint or hinge. The extremities of the legs are finished with fine steel points, the upper portions are of brass, German silver, or some other metal that does not readily rust. The joint is generally made partly of steel, as the wear will be more equal. The joint should be accurate and firm, but admit of easy play without any sudden jerks in opening and closing the legs. If by use the joint becomes loose, it can be tightened with the small screw-driver which accompanies the instruments. The points should come accurately together when the legs are closed.

3. Compass with movable parts. Fig. 1. represents a good form of this instrument, with its furniture, the pen, pencil,

INDUSTRIAL DRAWING.

and needle points, and lengthening bar. This form of needle point is much the best ; the shoulder of the needle should be large enough to prevent making a hole in the paper when used. This style of pencil point is also very convenient, being made for the use of leads. The lengthening bar is used in describing larger circles than the compasses would otherwise admit of. With some of these instruments there is a dotting pen, but this is not recommended as it cannot be depended upon. In selecting, see that the parts all fit well together.

Fio. 1

FIG. a

4. Hair-spring dividers. These are so constructed, that by means of a spring and screw, the distance between the points may be changed without any motion at the joint. By turning the screw, Fig. 2, the point may be moved a very fine distance, thus making it very convenient for taking measure-

DRAWING INSTRUMENTS AND MATERIALS. 3

ments from scales, or dividing distances into equal j>arts. The spring should be pretty stiff.

5. Bow compasses. These are for drawing small circles both in pencil and ink. There are some forms made, where the pen and pencil points can be exchanged as in the larger compasses. It is more convenient, however, to have ,«> separate instruments, one for the pen, and the other foi che pencil, as shown in Fig. 3. See that the springs are stroig.

There are other forms of compasses, which are convenient at times, but not necessary to buy at first. Among thei,e are the proportional and beam compasses.

6. Proportional compasses. These are useful for en" urging or reducing drawings. The simplest form, shown ifc Fig. 4, is called halves and wholes ; where the shorter legs .*re half the length of the others, so that the distance between the points of the shorter legs will be one half of that bet tveen the points at the other end.

Fig. 5 shows another form of these compasses, & tmilar in principle to the last, but constructed so that the position of the joint can be changed, thus giving different p. ©portions between the extremities at either end. To adjust the instrument, close it, and after unscrewing the nut, move the slide

INDUSTRIAL DRAWING.

along until the mark across it coincides with the required number, then clamp the nut.

Four scales are sometimes engraved upon these compasses, called lines, circles, planes, and solids. The last two are omitted upon many of the instruments, as they are of little use.

If the mark is brought to £ in the scale of lines, the distance ab will be one-third of cd. If the mark is brought to 8 in the scale of circles, ab will be the chord of the eighth part of the circumference of a circle whose radius is cd.

Place the mark at 4 in the scale of planes, and ab will be the side of a square, or radius of a oircle whose area is one-fourth that of the square or circle formed with cd. In the scale of solids, with the mark at 4, ab will be the diameter of a sphere or edge of a cube whose solidity is one-fourth that of a sphere or cube whose diameter or edge is cd.

The graduation of these instruments cannot always be relied upon, and the accuracy of the proportions is also affected by any change in the length of the legs, occasioned by use or breaking.

It would be well to test their accuracy before purchasing.

7. Beam compasses. These are for describing larger arcs than would be possible with the other compasses. There are different forms of these. In all of them there is a beam of wood, or metal, with two collars, one carrying a pen or pencil point, and the other a needle point. Fig. 6 shows a convenient form of this instrument. In this the tops of the collars are left open so that they can be used on any straight edge,

DRAWING INSTRUMENTS AND MATERIALS. 5

being damped to it by means of screws. The needle point is clamped at one end, while the other collar can be clamped at any distance from it. By turning the screw a the point b can be moved slightly, thus enabling one to adjust nicely the distance between 5 and c. In some forms there is a scale upon the beam, but ihis is not necessary and makes it more expensive.

8. Drawing pen. Fig. 7. This is made of two flat pointed steel blades, one of which has a hinge-joint at its base, thus allowing the blades to be sufficiently separated for cleaning or sharpening. The distance between the points is regulated by means of a screw connecting the two blades. This distance determines the width of the lines. Do not select one in which the blades are much curved.

9. Drawing board. This is an indispensable part of the draughtsman's outfit. It should be made of a thoroughly seasoned light wood; pine is generally used. A board twenty -eight inches long, twenty inches wide, and about one inch thick is a convenient size. Each end should be finished

INDUSTRIAL DRAWING.

with a cleat, as shown in Fig. 8, to prevent warping. Each side should be rubbed to a smooth plane surface, with fine sand-paper. The edges should be straight and at right angles to each other.

10. J square. This consists of a long thin blade, with a head at right angles to it ; fig. 9 is a good pattern, where the blade is simply laid upon the head and screwed to it. Any fine-grained hard wood will do for material, pear-wood is very

DRAWING INSTRUMENTS AND MATERIALS. 7

good. Sometimes metal is used, and for accuracy it would be the best ; but as it rusts and tarnishes easily, the paper is liable to be soiled. The blade should be about the same length as the board. For a blade thirty inches in length, in order to be sufficiently stiff, the width should be at least two and a half inches, and the thickness one-eighth of an inch. The head is generally made of one piece, although sometimes of two, one on either side of the blade, as shown in fig. 10. One of these pieces is fixed while the other can be clamped at any angle with the blade ; so that, if the square is turned over and used with this side of the head against the edge of the board, parallel lines may be drawn making a corresponding angle with the sides of the board. This is not used very much, as it cannot be clamped sufficiently tight to prevent displacement by a slight rap, or any great pressure upon the blade.

11. Triangles. These are made of different materials, as wood, metal, rubber, etc., the last being the best ; metal triangles are open to the same objection that metal squares are. Triangles are made solid or open, as shown in fig. 11, the open ones being the most convenient to handle. The draughtsman requires two of these, one having angles of 90°, 45°, 45°, while the other has angles of 90°, 60°, 30°. A convenient size is from six to ten inches on side.

12. Irregular curves. These are for tracing curves, other than arcs of circles, which are determined by points. Those made of thin pear-wood will be found to answer well. They have a great variety of shapes, so that one is at a loss which to select. Choose one with curves of both small and large radius.

13. India ink. It is important to have this material of the best quality, as it is used exclusively for all black lines. Good India ink, when broken across, should have a shining and somewhat golden lustre. If an end of it is wetted and rubbed on the thumb-nail, it should have a pasty feel, free from grains, and exhale an odor of musk ; when dried the end should present a shiny and golden-hued surface. Ink of inferior quality is of a dull bluish color, and when wetted and rubbed on the nail feels granular ; also when rubbed up in water it settles ; whereas good ink remains thoroughly diffused through the water.

14. Colors. Windsor and Newton's water colors are considered the best. There are two sizes of cakes, called the whole and half cakes. The moist colors which come in porcelain dishes are equally good, and are preferred by some, as the cakes are liable to crack and crumble.

15. Ink saucers. These come in nests of four or six, and are very convenient for preserving the colors after they are prepared. One forms a cover for another and thus keeps out the dust, besides keeping the colors moist for some time.

16. Pencils. These should be of the hardest and best quality. A. W. Faber's hexagonal pencils are the best. HH and HHH 9xv good numbers for mechanical drawing.

17. Brushes. The best brushes are made of sable hair, of which there are two varieties, the red and black. The red is somewhat the cheapest, but is about as good as the black. Camel's-hair brushes will answer very well, if one does not want to afford the sable. In selecting brushes see that they come to a point when moistened with water ; they should keep this point when used.

18. India rubber. Fine vulcanized rubber is the best for removing pencil marks. Sponge rubber is good for cleaning drawings.

19. Thumb tacks. These are for fastening the paper to the drawing board, when it is not necessary to stretch it. The best have the steel point riveted into the head. The top of the head should be slightly rounded, the edges being thin, so as to allow the J square to pass over readily.

20. Horn centre. This is used in case many circles are to

DRAWING INSTRUMENTS AND MATERIALS.

Elephant

Columbier

23 '

Atlas, Double Elephant . . .

Antiquarian.

... 26 '

...27 * ...31 '

Emperor . . .

.. 48 '

be drawn from the same centre. The needle point rests upon this instead of the paper, to prevent the wearing of a large hole. It is made of a piece of transparent horn, with three little steel points to prevent slipping.

21. Drawing paper. — Watmau's drawing paper is considered the best. It comes in sheets of standard sizes, as follows :

Cap 13 in. by 17

Demy 15

Medium 17

Eoyal 19

Super Royal 19

Imperial 22

There are two kinds of this paper, the rough- or cold-pressed, and the smooth- or hot-pressed ; the smooth paper is better for finished line drawings, while the rough surface takes color better ; does not show erasures, and is better for general work. On holding the paper up to the light the maker's name is seen in water lines, and when it can be read, the nearest surface is considered the right side. If there is any difference between the two, it is supposed to be in favor of this side. The double elephant sheet is of a good weight and size for general work. For smaller sizes cut it in halves or quarters.

22. Tracing paper. This is a thin paper prepared so as to be sufficiently transparent to allow the lines of a drawing to show through, for the purpose of copying. It comes in sheets or by the roll. The best paper is tough, transparent, and without any greasiness.

23. Tracing cloth. This is for the same purpose as tracing paper. It is better than paper for preserving copies, or for those that are to be subjected to any wear, as in the case of working drawings. It comes in rolls of twenty-four yards, and of different widths. That which has a dull surface on one side is better for pencil marks or for tinting.