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A MANUAL 



OF 



ENGINEERING DRAWING 



FOR 



STUDENTS AND DKAFTSMEN; 



BY 



THOMAS E. FRENCH, M. E. 

PROFESSOR OP ENGINEERING DRAWING, THE OHIO STATE UNIVERSITY 



NEW YORK 

McGRAW-HILL BOOK COMPANY 

239 WEST 39TH STREET, NEW YORK 

1911 



COPYRIGHT, 1911 

BY THE 
MCGRAW-HILL BOOK COMPANY 



Printed and Electrotyped 

by The Maple Press 

York, Pa. 



PEEFACE 



There is a wide diversity of method in the teaching of engineer- 
ing drawing, and perhaps less uniformity in the courses in differ- 
ent schools than would be found in most subjects taught in 
technical schools and colleges. In some well-known instances 
the attempt is made to teach the subject by giving a series of 
plates to be copied by the student. Some give all the time to 
laboratory work, others depend principally upon recitations and 
home work. Some begin immediately on the theory of descrip- 
tive geometry, working in all the angles, others discard theory 
and commence with a course in machine detailing. Some 
advocate the extensive use of models, some condemn their use 
entirely. 

Different courses have been designed for different purposes, 
and criticism is not intended, but it would seem that better unity 
of method might result if there were a better recognition of the 
conception that drawing is a real language, to be studied and 
taught in the same way as any other language. With this 
conception it may be seen that except for the practice in the 
handling and use of instruments, and for showing certain stand- 
ards of execution, copying drawings does little more in the study 
as an art of expression of thought than copying paragraphs from 
a German book would do in beginning the study of the German 
language. 

And it would appear equally true that good pedagogy would 
not advise taking up composition in a new language before the 
simple structure of the sentence is understood and appreciated; 
that is, " working drawings" would not be considered until after 
the theory of projection has been explained. 

After a knowledge of the technic of expression, the "pen- 
manship and orthography/' the whole energy should be directed 
toward training in constructive imagination, the perceptive 
ability which enables one to think in three dimensions, to visual- 

v 

222476 



vi PREFACE 

ize quickly and accurately, to build up a clear mental image, a 
requirement absolutely necessary for the designer who is to 
represent his thoughts on paper. That this may be accomplished 
more readily by taking up solids before points and lines has been 
demonstrated beyond dispute. 

It is then upon this plan, regarding drawing as a language, the 
universal graphical language of the industrial world, with its 
varied forms of expression, its grammar and its style, that this 
book has been built. It is not a "course in drawing," but a 
text-book, with exercises and problems in some variety from 
which selections may be made. 

Machine parts furnish the best illustrations of principles, and 
have been used freely, but the book is intended for all engineering 
students. Chapters on architectural drawing and map drawing 
have been added, as in the interrelation of the professions every 
engineer should be able to read and work from such drawings. 

In teaching the subject, part of the time, at least one hour per 
week, may profitably be scheduled for class lectures, recitations, 
and blackboard work, at which time there may be distributed 
"study sheets" or home plates, of problems on the assigned 
lesson, to be drawn in pencil and returned at the next correspond- 
ing period. In the drawing-room period, specifications for plates, 
to be approved in pencil and some finished by inking or tracing, 
should be assigned, all to be done under the careful supervision 
of the instructor. 

The judicious use of models is of great aid, both in technical 
sketching and, particularly, in drawing to scale, in aiding the 
student to feel the sense of proportion between the drawing and 
the structure, so that in reading a drawing he may have the 
ability to visualize not only the shape, but the size of the object 
represented. 

In beginning drawing it is not advisable to use large plates. 
One set of commercial drafting-room sizes is based on the division 
of a 36"x48" sheet into 24"x36", 18"x24", 12"xl8" and 9"xl2". 
The size 12"xl8" is sufficiently large for first year work, while 
9"xl2" is not too small for earlier plates. 

Grateful acknowledgement is made of the assistance of Messrs. 
Robert Meiklejohn, O. E. Williams, A. C. Harper, Cree Sheets, 
F. W. Ives, W. D. Turnbull, and W. J. Norris of the staff of the 
Department of Engineering Drawing, Ohio State University, not 



PREFACE vii 

only in the preparation of the drawings, but in advice and 
suggestion on the text. Other members of the faculty of this 
University have aided by helpful criticism. 

The aim has been to conform to modern engineering practice, 
and it is hoped that the practical consideration of the draftsman's 
needs will give the book permanent value as a reference book in 
the student's library. 

The author will be glad to co-operate with teachers using it as 
a text-book. 

COLUMBUS, OHIO. 
May 6, 1911. 



CONTENTS 



PAGE 

PREFACE v 

CHAPTER I. INTRODUCTORY 1 

Engineering drawing as a language Its division into mechanical 
drawing and technical sketching Requirements in its study. - 

CHAPTER II. THE SELECTION OF INSTRUMENTS 4 

Quality List of instruments and materials for line drawing The 
pivot joint Points to observe in selecting instruments Com- 
passes Dividers Ruling pens Bow instruments Drawing 
boards T-squares Triangles Scales Inks Pens Curves 
Drawing papers etc. Description of special instruments and 
devices Railroad pen Curve pen Lettering pens Proportional 
dividers Beam compass Drop pen Protractor Section liners 
Drafting machines Vertical drawing boards Other instru- 
ments and appliances. 

CHAPTER III. THE USE OF INSTRUMENTS 23 

Good form in drawing Preparation for drawing The pencil The 
T-square Laying out the drawing Use of dividers To divide a 
line by trial Use of the triangles Use of the compasses Use 
of the scale Inking Faulty lines The alphabet of lines Use of 
the French curve Exercises A page of cautions. 

CHAPTER IV. APPLIED GEOMETRY 47 

Applications of the principles of geometry in mechanical drawing 
To divide a line into any number of parts To transfer a given 
polygon to a new base To inscribe a regular octagon in a square 
To draw a circular arc through three points To draw an arc tan- 
gent to two lines To draw an ogee curve To rectify an arc The 
conic sections Methods of drawing the ellipse Approximate ellip- 
ses The parabola The rectangular hyperbola The cycloid 
The epicycloid The hypocycloid Involutes The spiral of 
Archimedes. 

CHAPTER V. LETTERING 58 

Importance Should be done freehand Pens for lettering 
Single-stroke vertical caps Single-stroke inclined caps The 
Reinhardt letter Spacing and composition Titles. 

ix 



x CONTENTS 

CHAPTER VI. ORTHOGRAPHIC PROJECTION 65 

Definition The planes of projection Principles Writing the lan- 
guage and reading the language Auxiliary views Sectional views 
Section lining Revolution The true length of a line Shade 
lines Problems, in seven groups. 

CHAPTER VII.^ DEVELOPED SURFACES AND INTERSECTIONS . . . 100 
Classification of surfaces, ruled surfaces, double curved surfaces 
Developments Practical considerations To develop the hexag- 
onal prism The cylinder The hexagonal pyramid The rectan- 
gular pyramid The truncated cone Double curved surfaces 
Triangulation Development of the oblique cone Transition 
pieces The intersection of surfaces Two cylinders Cylinder 
and cone Cutting spheres Two cones Problems, in ten groups. 

CHAPTER VIII. PICTORIAL REPRESENTATION 122 

Use of conventional picture methods, their advantages, disad- 
vantages, and limitations Isometric drawing The isometric 
section Oblique projection Rules for placing the object The 
offset method Cabinet drawing The principle of axonometric 
projection Dimetric system Clinographic projection and its use 
in crystallography Problems Reading exercises, orthographic 
sketches to be translated into pictorial sketches. 

CHAPTER IX. WORKING DRAWINGS 145 

Definitions Classes of working drawings "Style" in drawing 
Order of penciling Order of inking Dimensioning, General 
rules for dimensioning Finish mark Notes and specifications 
Bill of material Title Contents of title Requirements in com- 
mercial drafting Fastenings Helix Screw threads Forms of 
threads Conventional threads Bolts and nuts Lock nuts 
Cap screws Studs Set screws Machine screws, etc. Pipe 
threads and fittings Gears Method of representation Con- 
ventional symbols and their use Commercial sizes Checking 
Structural drawing Rivets, Examples of structural drawing, 
Differences in practice Problems. 

CHAPTER X. TECHNICAL SKETCHING 201 

Its necessity to the engineer Sketching in orthographic pro- 
jection Dimensioning Cross-section paper Sketching by pic- 
torial methods, Axonometric, Oblique, Perspective Principles of 
perspective Exercises. 

CHAPTER XI... THE ELEMENTS OF ARCHITECTURAL DRAWING . . 214 
Characteristics of architectural drawing Kinds of drawings 
Display and competitive drawings Rendering Poohe* and 
Mosaic Preliminary sketching Use of tracing paper Working 
drawings Plans Elevations Sections Details Dimensioning 
Lettering Titles. 



CONTENTS xi 

CHAPTER XII. MAP AND TOPOGRAPHICAL DRAWING 229 

Classification of Maps Plats, A farm survey, Plats of subdivisions, 
City plats Topographical drawing, Contours, Hill shading, Water 
lining Topographic symbols, Culture,' Relief, Water features, 
Vegetation, Common faults Lettering Government Maps 
Profiles. 

CHAPTER XIII. DUPLICATION, AND DRAWING FOR REPRODUCTION. 248 
Tracing Tracing cloth Blue printing, Methods, Formulae Van 
Dyke prints Transparentizing Various suggestions Prepara- 
tion of drawings for reproduction Zinc etching Half tones 
Retouching The wax process Lithography. 

CHAPTER XIV. NOTES ON COMMERCIAL PRACTICE 257 

Suggestions and miscellaneous information To sharpen a pen 
To make a lettering pen Line shading, use, and methods Patent 
office drawings, rules, and suggestions Stretching paper and 
tinting Mounting tracing paper Mounting on cloth Methods of 
copying drawings Pricking Transfer by rubbing A transpar- 
ent drawing board The pantograph Proportional squares 
About tracings Preserving drawings Filing drawings Misel- 
laneous hints. 

CHAPTER XV. BIBLIOGRAPHY OF ALLIED SUBJECTS 274 

A short classified list of books on allied subjects, Architectural 
drawing Descriptive geometry Gears and gearing Handbooks 
Lettering Machine drawing and design Perspective Render- 
ing Shades and shadows Sheet metal Stereotomy Structural 
drawing Surveying Technic and standards Topographical 
drawing Miscellaneous. 

INDEX. 281 



ENGINEERING DRAWING 



ENGINEERING DRAWING 



CHAPTER I. 
INTRODUCTORY. 

By the term Engineering Drawing is meant drawing as used 
in the industrial world by engineers and designers, as the lan- 
guage in which is expressed and recorded the ideas and informa- 
tion necessary for the building of machines and structures; as 
distinguished from drawing as a fine art, as practised by artists 
in pictorial representation. 

The artist strives to produce, either from the model or land- 
scape before him, or through his creative imagination, a picture 
which will impart to the observer something as nearly as may be 
of the same mental impression as that produced by the object 
itself, or as that in the artist's mind. As there are no lines in 
nature, if he is limited in his medium to lines instead of color 
and light and shade, he is able only to suggest his meaning, and 
must depend upon the observer's imagination to supply the lack. 

The engineering draftsman has a greater task. Limited to 
outline alone, he may not simply suggest his meaning, but must 
give exact and positive information regarding every detail of the 
machine or structure existing in his imagination. Thus drawing 
to him is more than pictorial representation; it is a complete 
graphical language, by whose aid he may describe minutely every 
operation necessary, and may keep a complete record of the work 
for duplication or repairs. 

In the artist's case the result can be understood, in greater or 
less degree, by any one. The draftsman's result does not show 
the object as it would appear to the eye when finished, conse- 
quently his drawing can be read and understood only by one 
trained in the language. 

1 



2 ENGINEERING DRAWING 

Thus as the foundation upon which all designing is based, 
engineering drawing becomes, with perhaps the exception of 
mathematics, the most important single branch of study in a 
technical school. 

When this language is written exactly and accurately, it is 
done with the aid of mathematical instruments, and is called 
mechanical drawing.* When done with the unaided hand, 
without the assistance of instruments or appliances, it is known 
as freehand drawing, or technical sketching. Training in both 
these methods is necessary for the engineer, the first to develop 
accuracy of measurement and manual dexterity, the second 
to train in comprehensive observation, and to give control and 
mastery of form and proportion. 

Our object then is to study this language so that we may write 
it, express ourselves clearly to one familiar with it, and may 
read it readily when written by another. To do this we must 
know the alphabet, the grammar and the composition, and be 
familiar with the idioms, the accepted conventions and the 
abbreviations. 

This new language is entirely a graphical or written one. It 
cannot be read aloud, but is interpreted by forming a mental 
picture of the subject represented; and the student's success in 
it will be indicated not alone by his skill in execution, but by 
his ability to interpret his impressions, to visualize clearly in 
space. 

It is not a language to be learned only by a comparatively 
few draftsmen, who will be professional writers of it, but should 
be understood by all connected with or interested in technical 
industries, and the training its study gives in quick, accurate 
observation, and the power of reading description from lines, is 
of a value quite unappreciated by those not familiar with it. 

In this study we must first of all become familiar with the 
technic of expression, and as instruments are used for accurate 
work, the first requirement is the ability to use these instruments 
correctly. With continued practice will come a facility in their 
use which will free the mind from any thought of the means of 
expression. 

* The term "Mechanical Drawing" is often applied to all constructive 
graphics, and, although an unfortunate misnomer, has the sanction of long 
usage. 



INTRODUCTORY 3 

A knowledge of geometry is desirable as there will be frequent 
applications of geometrical principles. 

We recommend therefore, as preliminary, the drawing of one 
or two practice plates, and a few of the geometrical figures of 
Chapter IV which are often referred to, before the mind is 
occupied with the real principles or " grammar " of the language. 



CHAPTER II. 

THE SELECTION OF INSTRUMENTS. 

In the selection of instruments and material for drawing the 
only general advice that can be given is to secure the best that 
can be afforded. For one who expects to do work of professional 
grade it is a great mistake to buy inferior instruments. Some- 
times a beginner is tempted by the suggestion to get cheap 
instruments for learning, with the expectation of getting better 
ones later. With reasonable care a set of good instruments will 
last a lifetime, while poor ones will be an annoyance from the 
start, and will be worthless after short usage. As good and poor 
instruments look so much alike that an amateur is unable to 
distinguish them it is well to have the advice of a competent 
judge, or to buy only from a trustworthy and experienced dealer. 

This chapter will be devoted to a short description of the instru- 
ments usually necessary for drawing, and mention of some not 
in every-day use, but which are of convenience for special work. 
In this connection, valuable suggestions may be found in the 
catalogues of the large instrument houses, notably Theo. Alteneder 
& Sons, Philadelphia; the Keuffel & Esser Co., New York, and 
the Eugene Dietzgen Co., Chicago. With the exception of the 
Alteneder instruments, all drawing instruments are made abroad, 
principally in Germany. Scales, T-squares, surveying instru- 
ments, etc., are, however, made in this country. 

The following list includes the necessary instruments and 
materials for ordinary line drawing. The items are numbered 
for convenience in reference and assignment. 

List of Instruments and Materials. 

1. Set of, drawing instruments, in case or chamois roll, including at 
least: 5 1/2 in. compass, with fixed needle-point leg, pencil, 
pen, and lengthening bar. 
5-in. hairspring dividers. 
Two ruling pens. 
Three bow instruments. 
Box of hard leads. 

4 



THE SELECTION OF INSTRUMENTS 5 

y2. Drawing board. 

' 3. T-square. 

/4. 45 and 30-60 triangles. 

*r 5. 12-in. architects' scale (two flat or one triangular). 

x 6. One doz. thumb tacks. 

* 7. One 6 H and one 2 H drawing pencil. 

^ 8. Pencil pointer. 

y 9. Bottle of drawing ink. 

10. Penholder, assorted writing pens, and penwiper. 

-^ 11. French curves. 

^12. Pencil eraser. 

^ 13. Drawing paper, to suit. 

To these may added: 

14. Cleaning rubber. 

15. Hard Arkansas oil stone. 

16. Protractor. 

17. Bottle holder. 

18. Piece of soapstone. 

19. 2-ft. or 4-ft. rule.. 

20. Sketch book. 

21. Erasing shield. 

22. Dusting cloth. 

23. Lettering triangle. 

The student should mark all his instruments and materials plainly 
with initials or name, as soon as purchased and approved. 

(1) All modern high-grade instruments are made with some 
form of l 'pivot joint," originally invented by Theodore Alteneder 
in 1850 and again patented in 1871. Before this time, and by 





FIG. 1. Tongue joint. FIG. 2. Pivot joint (Alteneder). 

other makers during the life of the patent, the heads of compasses 
and dividers were made with tongue joints, as illustrated in 
Fig. 1, and many of these old instruments are still in existence. 



ENGINEERING DRAWING 



A modified form of this pin joint is still used for some of the 
cheap grades of instruments. The objection which led to the 
abandonment of this form was that the wear of the tongue on 
the pin gave a lost motion, which may be detected by holding a 
leg in each hand and moving them slowly back and forth. This 




A. B Co 

FIG. 3. Sections of pivot joints. 

jump or lost motion after a time increases to such an extent as 
to render the instrument unfit for use. The pivot joint, Fig. 2, 
overcomes this objection by putting the wear on the conical 
points instead of the through pin. 

Since the expiration of the patent all instrument makers have 
adopted this type of head, and several modifications of the 




FIG. 4. The three patterns. 

original have been introduced. Sectional views of the different 
pivot joints are shown in Fig. 3. 

The handle attached to the yoke while not essential to the 
working of the joint is of great convenience. Not all instruments 
with handles, however, are pivot-joint instruments. Several 



THE SELECTION OF INSTRUMENTS 7 

straightener devices for keeping the handle erect have been 
devised, but as they interfere somewhat with the smooth work- 
ing of the joint, they are not regarded with favor by experienced 
draftsmen. 

There are three different patterns or shapes in which modern 
compasses are made; the regular, the cylindrical and the Richter, 
Fig. 4. The choice of shapes is entirely a matter of personal 
preference. After one has^'become accustomed to the balance 




FIG. 5. Test for alignment. 

and feel of a certain instrument he will not wish to exchange it 
for another shape. 

A favorite instrument with draftsmen, not included in the 
usual college assortment, is the 3 1/2-inch compass with fixed 
pencil point, and its companion with fixed pen point. 

Compasses may be tested for accuracy by bending the knuckle 
joints and bringing the points together as illustrated in Fig. 5. 
If out of alignment they should not be accepted, 
-dividers are made either " plain, " as those in Fig. 4, or "hair- 
spring, " shown in Fig. 6. The latter form, which has one leg 
with screw adjustment, is occasionally of great convenience and 




FIG. 6. Hairspring dividers. 

should be preferred. Compasses may be had also with hair- 
spring attachment on the needle-point leg. 

Ruling pens (sometimes called right line pens) are made in a 
variety of forms. An old type has the upper blade hinged for 
convenience in cleaning. It is open to the serious objection 
that wear in the joint will throw the nib out of position, and the 
only remedy will be to solder the joint fast. The improved form 



8 



ENGINEERING DRAWING 



has a spring blade opening sufficiently wide to allow of cleaning, 
Fig. 7. A number are made for resetting after cleaning. Several 
of these are illustrated in Fig. 8. The form shown at (e) is 
known as a detail pen or Swede pen. For large work this is a 
very desirable instrument. Ivory or bone handles break easily 
and on this account should not be purchased. The nibs of the 



D 



FIG. 7. Ruling pen, with spring blade. 

pen should be shaped as shown in Fig. 434. Cheap pens often 
come from the factory with points too sharp for use, and must be 
dressed, as described on page 257, before they can be used. 

The set of three spring bow instruments includes bow points 
or spacers, bow pencil, and bow pen. There are two designs and 
several sizes. The standard shape is illustrated in Fig. 9, the 







FIG. 8. Various pens. 

hook spring bow in Fig. 10. Both these styles are made with 
a center screw, Fig. 11, but this form has not become popular 
among draftsmen. The springs of the side screw bows should 
be strong enough to open to the length of the screw, but not so 
stiff as to be difficult to pinch together. The hook spring bow 
has a softer spring than the regular. 



THE SELECTION OF INSTRUMENTS 9 

(2) Drawing boards are made of clear white pine (bass wood 
has been used as a substitute) cleated to prevent warping. 
Care should be taken in their selection. In drafting-rooms 




FIG. 9. Spring bow instruments. 





FIG. 10. Hook-spring bow instruments. 



FIG. 11. Center screw bow. 



drawing tables with pine tops are generally used instead of loose 
boards. 

(3) The T-square with fixed head, Fig. 12, is used for all 
ordinary work. It should be of hard wood, the blade perfectly 
straight, although it is not necessary that the head be absolutely 



10 



ENGINEERING DRAWING 



square with the blade. In a long square it is preferable to have 
the head shaped as at B. Fig. 13 is the English type, which is 
objectionable in that the lower edge is apt to disturb the eyes' 
sense of perpendicularity. In an office equipment there should 
always be one or more adjustable head squares, Fig. 14. The 



A 



M 

J\ 






FIG. 12. Fixed head T-squares. 



T-square blade may be tested for straightness by drawing a sharp 
line with it, then reversing the square. 

(4) Triangles (sometimes called set squares) are made of pear 
wood or cherry, mahogany with ebony edges> hard rubber, and 
transparent celluloid. The latter are much to be preferred for 



FIG. 13. English T-square. 

a variety of reasons, although they have a tendency to warp. 
Wooden triangles cannot be depended upon for accuracy, and 
hard rubber should not be tolerated. For ordinary work a 
6"- or 8"-45 degree and a 10"-60 degree are good sizes. A small 
triangle, 67 1/2 degrees to 70 degrees, will be of value for drawing 



THE SELECTION OF INSTRUMENTS 



11 



guide lines in slant lettering. Triangles may be tested for 
accuracy by drawing perpendicular lines as shown in Fig. 15. 
The angles may be- proven by constructing 45- and 60-degree 
angles geometrically. 





FIG. 14. Adjustable head T-squares. 




// 


IA\ 




O 








O 1 


1 







FIG. 15. To test a triangle. 



(5) Scales. 

There are two kinds of modern scales, the "engineers' scale" 
of decimal parts, Fig. 16, and the "architects' scale" of propor- 
tional feet and inches, Fig. 17. The former is used for plotting 



12 ENGINEERING DRAWING 

and map drawing, and in the graphic solution of problems, the 
latter for all machine and structural drawings. Scales are 
usually made of boxwood, sometimes of metal or paper, and of 
shapes shown in section in Fig. 18. The triangular form (a) is 
perhaps the commonest. Its only advantage is that it has more 

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\ 09 os M vs zs oc ev 9V W zv ov- B g ye V M 

^ XAAAAM^^^ 

FIG. 16. Engineers' scale. 

scales on one stick than the others, but this is offset by the delay 
in finding the scale wanted. Flat scales are much more con- 
venient, and should be chosen on this account. Three flat scales 
are the equivalent of one triangular scale. The " opposite bevel" 
scale (e) is easier to pick up than the regular form (d). Many 




v^Yvvv^vyvyvv^^ 

V~ V ] * 3 4 W-W " ^T 

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\ \ \ *\ \ x ? x 



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FIG. 17. Architects' scale. 

professional draftsmen use a set of 6 or 8 scales, each graduated 
in one division only, as Fig. 19. 

For the student two 12" flat scales, one graduated in inches 
and sixteenths, and 3" and 1 1/2", the other 1", 1/2", 1/4", 1/8", 
will serve for all ordinary work. The usual triangular scale 




contains in addition to these, 3/4", 3/8", 3/16" and 3/32", and 
third flat scale with these divisions may be added when needed. 
(6) The best thumb tacks are made with thin German silver 
head and steel point screwed into it (a) Fig. 20, and cost as high 
as seventy-five cents a dozen. The ordinary stamped tacks (b) 



THE SELECTION OF INSTRUMENTS 13 

thirty cents a hundred answer every purpose. Tacks with com- 
paratively short, tapering pins should be chosen. Instead of 
thumb tacks many draftsmen prefer 1/2- or 1-oz. copper tacks, 
but they are not recommended for students' use. 

(7) Drawing pencils are graded by letters from 6B (very soft 
and black) 5B, 4B, 3B, 2B, B, HB, F, H, 2H, 3H, 4H, 5H, 6H, 
to 8H (extremely hard). For line work 6H is generally used. 
A softer pencil (2H) should be used for lettering, sketching and 



\\ XX TT\ x \ 


N \ x 


\ v 


\ v 


\ v 


\ x \\ \ 

v \\ V\ 


I \\ 


i 




///////>///// / / 


/ 7 / 


; / 


7 / 


7 / 


7 LA 


7 7 


/ TJ 



FIG. 19. Single scale from a set. 

penciling not to be inked. Koh-i-noor or Faber are recom- 
mended. Many prefer a holder known as an "artists' pencil." 

(8) A sandpaper pencil pointer or flat file should always be at 
hand for sharpening the leads. 

(9) Drawing ink is finely ground carbon in suspension, with 
shellac added to render it waterproof. The non-waterproof ink 
flows more freely, but smudges very easily. 

Formerly all good drawings were made with stick ink, rubbed 
up for use with water in a slate slab, and for very fine line work 
this is still preferred as being superior to liquid ink. When 




FIG. 20. 

used in warm weather a few drops of acetic acid or oxgall should 
be added to prevent flies from eating it. A fly can eat up a line 
made of good Chinese ink as fast as it leaves the pen. 

(10) The penholder should have a cork grip small enough to 
enter the mouth of ink bottle. An assortment of pens for letter- 
ing, grading from coarse to fine may be chosen from the following: 

(Coarse) Leonardos ball points 506 F, 516 F, 516 EF, or Gillott 
1032, 1087, Spencerian No. 21, Esterbrook 788, 802, 805. 



14 ENGINEERING DRAWING 

(Medium) Spencerian No. 1, Gillott 604, 1050. 

(Fine) Gillott No. 1, 303, 170. 

(Very fine) For mapping and similar work, Gillott 431, 290, 
291 and tit quill. 

A penwiper of lintless cloth or thin chamois skin should always 
be at hand for both writing and ruling pens. 




FIG. 21. Curve. 



(11) Curved rulers, called irregular curves, or French curves, 
are used for curved lines other than circle arcs. Celluloid is the 
only material to be considered. The patterns for these curves 
are laid out in parts of ellipses and spirals or other mathematical 
curves in combinations which will give the closest approximation 
to curves likely to be met with in practice. For the student, one 
ellipse curve, of the general shape of Fig. 21, and one spiral, 




PIG. 22. Logarithmic spiral curve. 

either a log. spiral, Fig. 22, or one similar to the one used in Fig. 
65, will be sufficient. It has been found by experiments that 
the curve of the logarithmic spiral is a closer approximation to 
the cycloid and other mathematical curves than any other simple 
curve. 

Sometimes it is advisable for the draftsman to make his own 



THE SELECTION OF INSTRUMENTS 15 

templet for special or recurring curves. These may be cut out 
of thin holly or bass wood, sheet lead, celluloid, or even card- 
board or pressboard. 

Flexible curved rulers of different kinds are sold. A copper 
wire or piece of wire solder has been used as a home-made 
substitute. 

The curve illustrated in Fig. 23 has been found particularly 
useful for engineering diagrams, steam curves, etc. It is plotted 
on the polar equation r =A cos + K, in which A may be 
about 5 I/ 2" and K 8". 

(12) The ruby pencil eraser is the favorite at present. One 
of large size, with beveled end is preferred. This eraser is much 




FIG. 23. 

better for ink than a so-called ink eraser, as it will remove the 
ink perfectly without destroying the surface of paper or cloth. 
A piece of soft " H " rubber, or sponge rubber is useful f Or cleaning 
paper. 

(13) Drawing paper is made in a variety of qualities, white for 
finished drawings and cream or buff tint for detail drawings. 
It may be had either in sheets or rolls. In general, paper should 
have sufficient grain to " tooth" to take the pencil, be agreeable 
to the eye, and have good erasing qualities. In white paper the 
brands known as "Normal" and "Napoleon" have these 
qualities. For wash drawings Whatman's paper should be used, 
and for fine line work for reproduction Reynold's Bristol board. 
These are both English papers in sheets, whose sizes may be 
found listed in any dealer's catalogue. Whatman's is a hand- 
made paper in three finishes, H, C.P., and R, or hot pressed, 
cold pressed, and rough; the first for fine line drawings, the second 
for either ink or color, and the third for water color sketches. 
The paper in the larger sheets is heavier than in the smaller sizes, 
hence it is better to buy large sheets and cut them up. Bristol 
board is a very smooth paper, made in different thicknesses, 



16 



ENGINEERING DRAWING 



2-ply, 3-ply, 4-ply, etc.; 3-ply is generally used. For working 
drawings the cream or buff detail papers are much easier on the 
eyes than white papers. The cheap manilla papers should be 
avoided. A few cents more per yard is well spent in the increased 
comfort gained from working on good paper. In buying in 
quantity it is cheaper to buy roll paper by the pound. For maps 



FIG. 24. Railroad pen. FIG. 25. Double pen. FIG. 26. Curve pen. 

or other drawings which are to withstand hard usage, mounted 
papers, with cloth backing are used. Drawings to be duplicated 
by blue printing are made on bond or ledger papers, or traced on 
tracing paper or tracing cloth. Tracing and the duplicating 
processes are described in Chapter XIII. 

The foregoing instruments and materials are all that are needed 
in ordinary practice, and are as a rule, with the exception of 
paper, pencils, ink, erasers, etc., classed as supplies, what a 



THE SELECTION OF INSTRUMENTS 



17 



draftsman is expected to take with him into a commercial 
drafting room. 

There are many other special instruments and devices not 
necessary in ordinary work. With some of these the draftsman 




FIG. 27. Lettering pens. 

should be familiar, as they may be very convenient in some 
special cases, and are often found as part of a drafting room 
equipment. 

The railroad pen is used for double lines. In selecting this 




FIG. 28. Proportional dividers. 

pen notice that the pens are turned as illustrated in Fig. 24. 
Most forms have the pens in opposite directions. A much better 
pen for double lines up to 1/4" apart is the border pen, Fig. 25, 
as it can be held down to the paper more satisfactorily. It may 





FIG. 29. Beam compass. 

be used for very wide solid lines by inking the middle space as 
well as the two pens. 

The curve pen, Fig. 26, made with a swivel, for freehand curves, 
contours, etc., is of occasional value. 
2 



18 



ENGINEERING DRAWING 



Payzant pens, Fig. 27A, for large single stroke lettering save a 
great deal of time. They are made in sizes from \ to 6. Fig. 
27 B is the Shepard pen, made for the same purpose. 

Proportional dividers, for enlarging or reducing in any propor- 




FIG. 30. Drop pen. 



tion, Fig. 28, are used in map work, patent office drawings, etc. 
The divisions marked "lines" are linear proportions, those 
marked "circles" give the setting for dividing a circle whose 
diameter is measured by the large end into the desired number 
of equal parts. 




FIG. 31. Protractor. 



The beam compass is used for circles larger than the capacity 
of the compass and lengthening bar. A good form is illustrated 
in Fig. 29. The bar with shoulder prevents the parts from 
turning or falling off. 



THE SELECTION OF INSTRUMENTS 



19 



With the " drop pen " or rivet pen smaller circles can be made, 
and made much faster than with the bow pen. It is held as 
shown in Fig. 30, the needle point stationary and the pen revolving 
around it. It is of particular convenience in bridge and structural 
work, and in topographical drawing. 




FIG. 32. Section liner. 



A protractor is a necessity in map and topographical work. 
A semicircular brass or German silver one, 6" diameter, such as 
Fig. 31, will read to half degrees. They may be had with an arm 
and vernier reading to minutest 




D 




D 



FIG. 33. Section lining devices. 



Section lining or " cross hatching" is a difficult operation for 
the beginner, but is done almost automatically by the experienced 
draftsman. Several instruments for mechanical spacing have 
been devised. For ordinary work they are not worth the trouble 



20 



ENGINEERING DRAWING 



of setting up, and a draftsman should never become dependent 
upon them, but they are of limited value for careful drawing for 
reproduction. One form is shown in Fig. 32. 

A home-made device may be made of a piece of thin wood or 




FIG. 34. Universal drafting machine. 



celluloid cut in one of the shapes shown in Fig. 33, and used by 
slipping the block and holding the triangle, then holding the 
block and moving the triangle. 

There are several machines on the market designed to save time 




FIG. 35. Dotting pen. 



and trouble in drawing. The best known is the Universal 
Drafting Machine illustrated in Fig. 34. This machine, which 
combines the functions of T-square, triangle, scale and protractor, 
has had the test of ten years' use, and is used extensively in large 



THE SELECTION OF INSTRUMENTS 



21 



drafting rooms, and by practising engineers and architects. It 
has been estimated that 25% of time in machine drawing and 
over 50 % in civil engineering work is saved by its use. 

Vertical drawing boards with sliding parallel straight edges 
.are preferred by some for large work. 





FIG. 36. 



FIG. 37. 



Several kinds of dotting pens have been introduced. The 
one illustrated in Fig. 35 is perhaps the best. When carefully 
handled it works successfully, and will make five different kinds 
<of dotted and dashed lines. The length of the short dots may 





FIG. 38. 



FIG. 39. 



be varied by a slight inclination of the handle. For special work 
requiring a great many dotted lines it might prove to be a good 
investment. 

A number of different forms of patented combination "tri- 



22 



ENGINEERING DRAWING 



angles" have been devised. Of these the best known are the 

Kelsey, Fig. 36, the Rondinella, Fig. 37, and the Zange, Fig. 38. 

Bottle holders prevent the possibility of ruining the drawing, 

table or floor by the upsetting of the ink bottle. Fig. 39 is a 




FIG. 40. 



usual form, Fig. 40 a novelty by the Alteneder Co. by whose aid 
the pen may be filled with one hand and time saved thereby. 

Erasing shields of metal or celluloid, meant to protect the 
drawing while an erasure is being made, are sold. Slots for the 
purpose may be cut as needed from sheet celluloid or tough paper. 



CHAPTER III. 

THE USE OF INSTRUMENTS. 

In beginning the use of drawing instruments particular atten- 
tion should be paid to correct method in their handling. There 
are many instructions and cautions, whose reading may seem 
tiresome, and some of which may appear trivial, but the strict 
observance of all these details is really necessary, if one would 
become proficient in the art. 

Facility will come with continued practice, but from the outset 
good form must be insisted upon. One might learn to write 
fairly, holding the pen between the fingers or gripped in the closed 
hand, but it would be poor form. It is just as bad to draw in 
poor form as to write in poor form. Bad form in drawing is 
distressingly common, and may be traced in every instance to 
lack of care or knowledge at the beginning, and the consequent 
formation of bad habits. These habits when once formed are 
most difficult to overcome. 

All the mechanical drawing we do serves incidentally for 
practice in the use of instruments, but it is best for the beginner 
to learn the functions and become familiar with the handling and 
feel of each of his instruments by drawing two or three plates 
designed solely for that purpose, so that when real drawing 
problems are assigned the use of the instruments will be easy and 
natural, and there need be no distraction nor loss of time on 
account of correction for faulty manipulation. 

Thus while the drawings are worth nothing when finished 
except to show the student's proficiency and skill, some such 
figures as those on pages 42 and 45 should be practised until he 
feels a degree of ability and assurance, and is no^ afraid of his 
instruments. 

As these figures are for discipline and drill, the instructor should 
not accept a plate with the least inaccuracy, blot, blemish, or 
indication of ink erasure. It is a mistaken kindness to the 
beginner to accept faulty or careless work. The standard set at 
this time will be carried through his professional life, and he 

23 



24 



ENGINEERING DRAWING 



should learn that a good drawing can be made just as quickly 
as a poor one. Erasing is expensive and mostly preventable, 
and the student allowed to continue in a careless way will grow 
to regard his eraser and jack knife as the most important tools 
in his kit. The draftsman of course erases an occasional mistake, 
and instructions in making corrections may be given later in 
the course, but these first plates must not be erased. 

Preparation for Drawing. 

The drawing table should be set so that the light comes from 
the left, and adjusted to a convenient height for standing, that 
is, from 36 to 40 inches, with the board inclined at a slope of 
about 1 to 8. One may draw with more freedom standing than 
sitting. 

The Pencil. 

The pencil must be selected with reference to the kind of paper 
used. For line drawing on paper of such texture as " Normal " 
a pencil as hard as 6H may be used, while on Bristol, for example, 
a softer one would be preferred. Sharpen it to a long point as 
in Fig. 41 removing the wood with the penknife and sharpening 
the lead by rubbing it on the sand paper pad. A flat or wedge 




FIG. 41. A wedge point. 

point will not wear away in use as fast as a conical point, and on 
that account is preferred for straight line work by most drafts- 
men. By oscillating the pencil slightly while rubbing the lead 
on two opposite sides, an elliptical section is obtained. A softer 
pencil (2H) should be at hand, sharpened to a long conical point 
for sketching and lettering. Have the sand paper pad within 
reach and keep the pencils sharp. Pencil lines should be made 
lightly, but sufficiently firm and sharp to be seen distinctly 
without eye strain, for inking or tracing. The beginner's usual 
mistake in using a hard pencil is to cut tracks in the paper. Too 



THE USE OF INSTRUMENTS 



25 



much emphasis cannot be given to the importance of clean, 
careful, accurate penciling. Never permit the thought that poor 
penciling may be corrected in inking. 

The T-Square. 

The T-square is used only on the left edge of the drawing 
board (an exception to this is made in the case of a left-handed 
person, whose table should be arranged with the light coming 
from the right and the T-square used on the right edge). 

Since the T-square blade is more rigid near the head than 
toward the outer end, the paper, if much smaller than the size 
of the board, should be placed close to the left edge of the board 
(within an inch or so) with its lower edge several inches from the 
bottom. With the T-square against the left edge of the board, 




FIG. 42. 

square the top of the paper approximately, hold in this position, 
slipping the T-square down from the edge, and put a thumb tack 
in each upper corner, pushing it in up to the head; move the 
T-square down over the paper to smooth out possible wrinkles 
and put thumb tacks in the other two corners. 

The T-square is used manifestly for drawing parallel horizontal 
lines. These lines should always be drawn from left to right, 
consequently points for their location should be marked on the 
left side; vertical lines are drawn with the triangle set against 
the T-square, always with the perpendicular edge nearest the 



26 



ENGINEERING DRAWING 



head of the square and toward the light. These lines are always 
drawn up from bottom to top, consequently their location points 
should be made at the bottom. 

In drawing lines great care must be exercised in keeping them 
accurately parallel to the T-square or triangle, holding the pencil 
point lightly, but close against the edge, and not varying the 
angle during the progress of the line. 

The T-square is adjusted by holding it in the position either 
of Fig. 42 the thumb up, and fingers touching the board under 




FIG. 43. 

the head, or of Fig. 43, the fingers on the blade and the thumb on 
the board. In drawing vertical lines the T-square is held in 
position against the left edge of the board, the thumb on the 
blade, while the fingers of the left hand adjust the triangle, as 
illustrated in Fig. 44. One may be sure the T-square is in contact 
with the board by hearing the little double click as it comes 
against it. 

Laying off the Drawing. 

The paper is usually cut somewhat larger than the desired 
size of the drawing, and is trimmed to size after the work is 
finished. Suppose the plate is to be 9" x 12" with a half-inch 



THE USE OF INSTRUMENTS 



27 



border. Near the lower edge of the paper draw a horizontal line, 
and near the left edge a vertical line. If the lower left-hand 
corner of the board is known to be square these long vertical 
lines may be drawn with the T-square thrown around against 
the lower edge. With the scale flat on the paper mark off on 
these lines the length and width of the finished plate, and points 




FIG. 44. 

for the border 1/2" inside these marks. Draw lines through these 
points giving the trimming line and the border line. These 
" points " should not be dots, or holes bored with the pencil, but 
short, light dashes. 

Use of Dividers. 

Suppose the space inside the border is to be divided into six 
equal parts by bisecting the left border line and dividing the 
lower border line into three parts. These divisions are made not 
with the scale but with the dividers. Facility in the use of this 



28 ENGINEERING DRAWING 

instrument is most essential, and quick and absolute control of 
its manipulation must be gained. It should be opened with one 
hand by pinching in the chamfer with the thumb and second 
finger. This will throw it into correct position with the thumb 
and forefinger on the outside of the legs and the second and third 
finger on the inside, with the head resting just above the second 
joint of the forefinger, Fig. 45. It is thus under perfect control, 




FIG. 45. 

with the thumb and forefinger to close it and the other two to 
open it. This motion should be practised until an adjustment 
to the smallest fraction can be made. In coming down to small 
divisions the second and third fingers must be gradually slipped 
out from between the legs while they are closed down upon them. 

To Divide a Line, by Trial. 

In bisecting a line the dividers are opened roughly at a guess 
to one-half the length. This distance is stepped off on the line, 
holding the instrument by the handle with the thumb and fore- 
finger. If the division be short the leg should be thrown out to 
one-half the remainder, estimated by the eye, without removing 
the other leg from its position on the paper, and the line spaced 
again with this setting, Fig. 46. If this should not come out 
exactly the operation may be repeated. With a little experience 
a line may be divided in this way very rapidly. Similarly a line 
may be divided into any number of equal parts, say five, by 
estimating the first division, stepping this lightly along the 
line, with the dividers held vertically by the handle, turning the 
instrument first in one direction and then in the other. If the 
last division fall short, one-fifth of the remainder should be added 



THE USE OF INSTRUMENTS 29 

by opening the dividers, keeping the one point on the paper. 
If the last division be over, one fifth of the excess should be taken 
off and the line respaced. If it is found difficult to make this 
small adjustment accurately with the fingers, the hairspring 
may be used. It will be found more convenient to use the bow 




FIG. 46. Bisecting a line. 

spacers instead of the dividers for small or numerous divisions. 
Avoid pricking unsightly holes in the paper. The position of a 
small prick point may be preserved if necessary by drawing a 
little ring around it with the pencil. 

Use of the Triangles. 

We have seen that vertical lines are drawn with the triangle 
set against the T-square, Fig. 44. Usually the 60-degree triangle 
is used, as it has the longer perpendicular. In both penciling and 
inking, the triangles should always be used in contact with a 
guiding straight-edge. 

With the T-square against the edge of the board, lines at 30 
degrees, 45 degrees and 60 degrees may be drawn as shown in 
Fig. 47, the arrows showing the direction of motion. The two 
triangles may be used in combination for angles of 15, 75, 105 



30 



ENGINEERING DRAWING 



degrees, etc., Fig. 48. Thus any multiple of 15 degrees may be 
drawn directly, and a circle may be divided with the 45-degree 




FIG. 47. 



triangle into 4 or 8 parts, with the 60-degree triangle into 6 or 
12 parts, and with both into 24 parts. 
To draw a parallel to any line, Fig. 49, adjust to it a triangle 




FIG. 48. 



held against the T-square or other triangle, hold the guiding edge 

in position and slip the first triangle on it to the required position. 

To draw a perpendicular to any line, Fig. 50, fit the hypothenuse 



THE USE OF INSTRUMENTS 



31 



of a triangle to it, with one edge against the T-square or other 
triangle, hold the T-square in position and turn the triangle until 
its other side is against the edge, the hypothenuse will then be 
perpendicular to the line. Move it to the required position. 




FIG. 49. To draw parallel lines. 



Never attempt to draw a perpendicular to a line by merely 
placing one leg of the triangle against it. Never work to the 
extreme corner of a triangle, but keep the T-square away from 
the line. 




Fi G. 50. To draw perpendicular lines. 



Use of the Compasses. 

The compass has the same general shape as the dividers and 
is manipulated in a similar way. Its needle point should first 
of all be adjusted by turning it with the shoulder point out, 



32 



ENGINEERING DRAWING 



inserting the pen in the place of the pencil leg and setting the 
needle a trifle longer than the pen. The needle point should be 
kept in this position so as to be always ready for the pen, and the 
lead adjusted to it. The lead should be sharpened on the sand 




FIG. 51. 



paper to a fine wedge or long bevel point. Radii should be 
pricked off or marked on the paper and the pencil leg adjusted to 
the points. The needle point may be guided to the center with 
the little finger of the left hand, Fig. 51. When the lead is 




FIG. 52. 



FIG. 53. 



adjusted to pass exactly through the mark the right hand should 
be raised to the handle and the circle drawn (clockwise) in one 
sweep by turning the compass, rolling the handle with the thumb 
and forefinger, inclining it slightly in the direction of the line, 



THE USE OF INSTRUMENTS 



33 



Fig. 52. The position of the fingers after the revolution is illus- 
trated in Fig. 53. Circles up to perhaps three inches in 
diameter may be - drawn with the legs straight but for larger 
sizes both the needle-point leg and the pencil leg should be turned 




FIG. 54. 



at the knuckle joints so as to be perpendicular to the paper, 
Fig. 54. The 5 1/2-inch compass may be used in this way for 
circles up to perhaps ten inches in diameter; larger circles are 
made by using the lengthening bar, as illustrated in Fig. 55. In 




FIG. 55. Use of lengthening bar. 



drawing concentric circles the smallest should always be drawn 
first. 

The bow instruments are us^L for small circles, particularly 
when a number are to be macto^Mhe same diameter. In chang- 
3 -*4fl[ 



34 



ENGINEERING DRAWING 



ing the setting, to avoid wear and final stripping of the thread, 
the pressure of the spring against the nut should be relieved by 
holding the points in the left hand and spinning the nut in or out 
with the ringer. Small adjustments should be made with one 
hand, with the needle point in position on the paper, Fig. 56. 




FIG. 56. 

Use of the Scale. 

In representing objects which are larger than can be drawn to 
their natural or full size it is necessary to reduce the dimensions 
on the drawing proportionately, and for this purpose the archi- 
tects' scale is used. The first reduction is to what is commonly 
called half size or correctly speaking, to the scale of 6" = 1'; that 
is, each dimension is reduced one-half. This scale is used in 
working drawings even if the object be only slightly larger than 
could be drawn full size, and is generally worked with the full- 
size scale, halving the dimensions mentally. If this scale is too 

-*--74'. 



FIG. 57. 

large for the paper the drawing is made to the scale of three 
inches to the foot, often called "quarter size," that is, three inches 
measured on the drawing is equal to one foot on the object. 
This is the first scale of the usual commercial set, on it the 
distance of three inches is divided into twelve equal parts and 
each of these subdivided into eighths. This distance should 



THE USE OF INSTRUMENTS 35 

be thought of not as three inches but as a foot divided into inches 
and eighths of inches. It is noticed that this foot is divided with 
the zero on the inside, the inches running to the left and the feet 
to the right, so that dimensions given in feet and inches may be 
read directly, as 2 ft. 7 1/8", Fig. 57. On the other end will be 
found the scale of 11/2 inches equals one foot, or eighth size, 
with the distance of one and one-half inches divided on the right 
of the zero into twelve parts and subdivided into quarter inches, 
and the foot divisions to the left of the zero, coinciding with the 
marks of the 3" scale. 

, If the 1 1/2" scale is too large for the object, the next commer- 
cial size is to the scale of one inch equals one foot, and so on 
down as shown in the following table. 

Full size 3/4" = 1' 

Scale 6" =1' 1/2" = 1' 

4" =1' (rarely used) 3/8"=!' 

3" = 1' 1/4" =1' 

2" =1' (rarely used) 3/16" -I/ 

11 /2" = 1' 1/8" =1' 

1" =1' 3/32"- 1' 

The scale 1/4" equals 1 ft. is the usual one for ordinary house 
plans and is often called by architects the "quarter scale." 
This term should not be confused with the term "quarter size," 
as the former means 1/4" to 1 ft. and the latter 1/4" to 1 inch. 

A circle is generally given in terms of its diameter. To draw 
it the radius is necessary. In drawing to half size it is thus often 
convenient to lay off the amount of the diameter with a 3-in. 
scale and to use this distance as the radius. 

As far as possible successive measurements on the same line 
should be made without shifting the scale. 

For plotting and map drawing the " engineers' scale " of deci- 
mal parts 10, 20, 30, 40, 50, 60, 80, 100 to the inch, is used. 
This scale should never be used for machine or structural work. 
Inking. 

After being penciled, drawings are finished either by inking 
on the paper, or in the great majority of work, by tracing in ink 
on tracing cloth. The beginner should become proficient in 
inking both on paper and cloth. 

The ruling pen is never used freehand, but always in connec- 



36 



ENGINEERING DRAWING 



tion with a guiding edge, either T-square, triangle, straight-edge 
or curve. The T-square and triangle should be held in the same 
positions as for penciling. It is bad practice to ink with the 
triangle alone. 

To fill the pen take it to the bottle and touch the quill filler 
between the nibs, being careful not to get any ink on the outside 
of the blades. Not more than three-sixteenths of an inch should 
be put in or the weight of the ink will cause it to drop out in a 
blot. The pen should be held as illustrated in Fig. 58, with the 
thumb and second finger in such position that they may be used 
in turning the adjusting screw, and the handle resting on the 




FIG. 58. Holding the pen. 

forefinger. This position should be observed carefully, as the 
tendency will be to bend the second finger to the position in 
which a pencil or writing pen is held, which is obviously conveni- 
ent in writing to give the up stroke, but as this motion is not 
required with the ruling pen the position illustrated is preferable. 

For full lines the screw should be adjusted to give a strong line, 
of the size of the first line of Fig. 62. A fine drawing does not 
mean a drawing made with fine lines, but with uniform lines, 
and accurate joints and tangents. 

The pen should be held against the straight edge with the 
blades parallel to it, the handle inclined slightly to the right and 
always kept in a plane through the line perpendicular to the 
paper. The pen is thus guided by the upper edge of the ruler, 
whose distance from the pencil line will therefore vary with its 



THE USE OF INSTRUMENTS 



37 



thickness, and with the shape of the under blade of the pen, as 
illustrated in enlarged scale in Fig. 59. If the pen is thrown out 
from the perpendicular as at B it will run on one blade and a line 
ragged on one side will result. If turned in from the perpendicu- 
lar as at C the ink is very apt to run under the edge and cause a 
blot. 

A line is drawn with a whole arm movement, the hand resting 
on the tips of the third and fourth fingers, keeping the angle of 
inclination constant. Just before reaching the end of the line 
the two guiding fingers on the straight edge should be stopped, 




FIG. 59. Correct position at A. 

and, without stopping the motion of the pen, the line finished 
with a finger movement. Short lines are drawn with this finger 
movement alone. When the end of the line is reached lift the 
pen quickly and move the straight edge away from the line. 
The pressure on the paper should be light, but sufficient to give 
a clean cut line, and will vary with the kind of paper and the 
sharpness of the pen, but the pressure against the T-square should 
be only enough to guide the direction. 

If the ink refuses to flow it is because it has dried and clogged 
in the extreme point of the pen. This clot or obstruction may 
be removed by touching the pen on the finger, or by pinching the 
blade slightly, breaking it up. If it still refuses to start it should 
be wiped out and fresh ink added. The pens must be wiped clean 
after using or the ink will corrode the steel and finally destroy 
them. 



38 ENGINEERING DRAWING 

Instructions in regard to the ruling pen apply also to the com- 
pass pen. It should be kept perpendicular by using the knuckle 
joint, and the compass inclined slightly in the direction of the 
line. In adjusting the compass for an arc which is to connect 
other lines the pen point should be brought down very close to 
the paper without touching it to be sure that the setting is exactly 
right. 

It is a universal rule in inking that circles and circle arcs must 
be drawn first. It is much easier to connect a straight line to a 
curve than a curve to a straight line. 




FIG. 60. 

It should be noted particularly that two lines are tangent to 
each other when their centers are tangent, and not when the 
lines simply touch each other, thus at the point of tangency the 
width will be equal to the width of a single line, Fig. 60 A. 

After reading these paragraphs the beginner had best take a 
blank sheet of paper and cover it with ink lines of varying lengths 
and weights, practising starting and stopping on penciled limits, 
until he feels acquainted with the pens. If in his set there are 
two pens of different sizes the larger one should be used, as it fits 
the hand of the average man better than the smaller one, holds 
more ink, and will do just as fine work. 

Faulty Lines. 

If inked lines appear imperfect in any way the reason should 
be ascertained immediately. It may be the fault of the pen, the 
ink, the paper, or the draftsman, but with the probabilities 
greatly in favor of the last. Fig. 61 illustrates the characteristic 
appearance of several kinds of faulty lines. The correction in 
each case will suggest itself. 



THE USE OF INSTRUMENTS 39 

High-grade pens usually come from the makers well sharpened. 
Cheaper ones often need dressing before they can be used satis- 
factorily. If the pen is not working properly it must be sharp- 
ened as described in Chapter XIV, page 257. 



. ... i . . .,..,.,,. Pesifoo faraway frv/7? edge ofTsgva/e 

- * !-^ -gnaBBHWB^i^HHB^^^B^* ^ en ^ C/OS ^ e ^ e ^ raf? (/ff( ^ er 
^^ mtf * m ^ mmm - m ^ m ^ m B mmmm n^^~^i**~ fak on oufe/de 0f6/ade, nyr? i/fider 
___ _ -~ Penb/ades nof kepf para//e/ fo T*?. 

^rrr, i n WJK\ m iPPi^pPiPii Tsgvasif s///petf//7fo tref///?e 

*"' "i^"' ~ i Wl T" 

- /4^?/ enough //?/ ^ //y?/>^ ^ />7tf 

FIG. 61. Faulty lines. 

The Alphabet of Lines. 

As the basis of the drawing is the line, a set of conventional 
symbols covering all the lines needed for different purposes may 
properly be called an alphabet of lines. There is as yet no 
universally adopted standard, but the following set is adequate, 
and represents the practice of a majority of the larger concerns 
of this country. 

( 1 ) Visible outline . 

(2) Invisible outline. 

(3) Center line. 

(3a) Center line, in pencil. 

(4) Dimension line. 

(5) Extension line. 

(6) Alternate position. 

(7) Line of motion. 

(8) Cutting plane. 




(9) "Ditto" or repeat line. 

(10) Broken material. 

(11) Limiting break. 



(12) Cross-hatching line. 



FIG. 62. The alphabet of lines. 



40 



ENGINEERING DRAWING 



It is of course not possible to set an absolute standard of weight 
for lines, as the proper size to use will vary with different kinds 




FIG. 63. The alphabet illustrated. 

and sizes of drawings, but it is possible to maintain a given 
proportion. 

Visible outlines should be strong full lines, at least one-sixty- 
fourth of an inch on paper drawings, and even as wide as one- 




FIG. 64. The alphabet illustrated. 



thirty-second of an inch on tracings. The other lines should 
contrast with this line in about the proportion of Fig. 62. 

Dash lines, as (2) and (7), should always have the space between 



THE USE OF INSTRUMENTS 



41 



dashes much shorter than the length of the dash. Figs. 63 and 
64 illustrate the use of the alphabet of lines. 

The Use of the French Curve. 

The French curve, as has been stated on page 14, is a ruler for 
non-circular curves. When sufficient points have been deter- 
mined it is best to sketch in the line lightly in pencil freehand, 
without losing the points, until it is clean, smooth, continuous, 
and satisfactory to the eye. The curve should then be applied 
to it, selecting a part that will fit a portion of the line most nearly, 
and noting particularly that the curve is so laid that the direction 
of its increase in curvature is in the direction of increasing curv- 
ature of the line, Fig. 65. In drawing the part of the line matched 




FIG. 65. Use of the curve. 

by the curve, always stop a little short of the distance that seems 
to coincide. After drawing this portion the curve is shifted to 
find another part that will coincide with the continuation of the 
line. In shifting the curve care should be taken to preserve the 
smoothness and continuity and to avoid breaks or cusps. This 
may be done if in its successive positions the curve is always 
adjusted so that it conincides for a little distance with the part 
already drawn. Thus at each joint the tangents must coincide. 
If the curved line is symmetrical about an axis, after it has 
been matched accurately on one side, marks locating the axes 
may be made in pencil on the curve and the curve reversed. In 
such a case exceptional care must be taken to avoid a "hump " at 
the joint. It is often better to stop a line short of the axis on 
each side and to close the gap afterwards with another setting of 
the curve. 



42 



ENGINEERING DRAWING 



When inking with the curve the pen should be held perpen- 
dicularly and the blades kept parallel to the edge. Inking curves 
will be found to be excellent practice. 

Sometimes, particularly at sharp turns, a combination of 
circle arcs and curve may be used, as for example in inking an 
eccentric ellipse, the sharp curves may be inked by selecting a 
center on the major axis by trial, and drawing as much of an arc 
as will practically coincide \vith the ends of the ellipse, then 
finishing the ellipse with the curve. 

The experienced draftsman will sometimes ink a curve that 
cannot be matched accurately, by varying the distance of the 
pen point from the ruling edge as the line progresses, but the 
beginner should not attempt it. 

Exercises in the Use of Instruments. 

The twelve following figures are given simply as a typical set 
of progressive exercises for practice in the use of the instruments. 
More or fewer may be used according to the student's evidence 
of ability. The geometrical figures of Chapter IV may be used 
for the same purpose. 






FIG. 66. 



FIG. 67. 



FIG. 68. 



Lay off a 9" x 12" plate, with 1/2" border. Divide the space 
inside the border into six equal parts, with the dividers. Locate 
the center of each space by drawing short intersecting portions 
of its diagonals. 
Fig. 66. An Exercise for the T-square, Triangle and Scale. 

Through the center of the space draw a horizontal and a 
vertical line, measuring on these lines as diameters lay off 
a three-inch square. Along the lower side and the upper 
half of the left side measure 3 / 8" spaces with the scale. Draw 



THE USE OF INSTRUMENTS 



43 



all horizontal lines with the T-square and all vertical lines 
with the T-square and triangle. 

Fig. 67. A "Swastika." For T-square, triangle and dividers. 
Draw three-inch square. Divide left side and lower side 
into five equal parts with the dividers. Draw horizontal 
and vertical lines across the square through these points. 
Erase the parts not needed. 

Fig. 68. Converging Lines. Draw three-inch square. Draw 
lines AB, BC, DE and EF at 30 degrees. Divide lower side 
into seven equal parts, with the dividers. Draw the vertical 
lines, and mark divisions on AC with the pencil as each line 






FIG. 70. 



FIG. 71. 



is drawn. Through the division points on top and bottom 
draw the converging lines using the triangle alone as a 
straight-edge. 

Fig. 69. A Hexagonal Figure. For 30-60 triangle and bow 

points (spacers). 

Through the center of the space draw the three construction 
lines, AB vertical, DE and FG at 30 degrees. Measure CA 
and CB 1 1/2" long. Draw AE, AF, DB, and BG at 30 
degrees. Complete hexagon by drawing DF and GE 
vertical. Set spacers to 3/32". Step off 3/32" on each side 
of the center lines, and 3/16" from each side of hexagon. 
Complete figure as shown, with triangle against T-square. 

Fig. 70. A Street Paving Intersection. For 45-degree triangle and 
scale. 

An exercise in starting and stopping short lines. Draw 
three-inch square. Draw diagonals with 45-degree triangle. 
With scale lay off 3/8" spaces along the diagonals, from 



44 



ENGINEERING DRAWING 



their intersection. With 45-degree triangle complete figure, 
finishing one-quarter at a time. 

Fig. 71. A Maltese Cross. For T-square, spacers, and both 
triangles. 

Draw three-inch square and one-inch square. From the 
corners of inner square draw lines to outer square at 15 
degrees and 75 degrees, with the two triangles in combina- 
tion. Mark points with spacers 3/16" inside of each line of 
this outside cross, and complete figure with triangles in 
combination. 






I 
\ 


\ 


\ 

\ 
\ 

\ 


\ 


\ 
\ 

\ 


\ 




\ 




























i 














1 












y 


1 








1 






1 


1 


1 




1 





FIG. 72. 



FIG. 73. 



FIG. 74. 



Fig. 72. Concentric Circles. For compass (legs straight) and 
scale. 

Draw horizontal line through center of space. On it mark 
off radii for six concentric circles 1/4" apart. In drawing 
concentric circles always draw the smallest first. The 
dotted circles are drawn in pencil with long dashes, and 
inked as shown. 

Fig. 73. Concentric Arcs. For compass (knuckle joints bent). 
On horizontal center line mark off eleven points I'/ 4" apart, 
beginning at left side of space. Draw horizontal limiting 
lines (in pencil only) 1 1/2" above and below center line. 

Fig. 74. Concentric Arcs. For compass and lengthening bar. 
On horizontal center line mark off eight points 3/8" apart, 
beginning at right side of space Center of arcs is center of 
Fig. 72. 

Fig. 75. Tangent Arcs. For accuracy with compass and dividers. 
Draw a circle three inches in diameter. Divide the circum- 
ference into five equal parts by trial with dividers. From 
these points draw radial lines and divide each into four 



THE USE OF INSTRUMENTS 



45 



equal parts with spacers. With these points as centers 
draw the semicircles as shown. The radial lines are not to 
be inked. 

Fig. 76. Tangent Circles and Lines. For accuracy with compass 
and triangles. 

On base A B, 31/2" long construct an equilateral tri- 
angle, using the 60-degree triangle. Bisect the angles 
with the 30-degree angle, extending the bisectors to the 
opposite sides. With these middle points of the sides as 
centers and radius equal to 1/2 the side, draw arcs cutting 
the bisectors. These intersections will be centers for the 




FIG. 75. 



FIG. 76. 



FIG. 77. 



inscribed circles. With centers on the intersection of 
these circles and the bisectors, round off the points of the 
triangle as shown. 

Remember the rule that circles are inked before straight 
lines. Construction lines are not to be inked. 
Fig. 77. Tangents to Circle Arcs. For bow compasses. 

Draw one and one-half inch square about center of space. 
Divide AE into four 3/16" spaces, with scale. With bow 
pencil and centers A, B, C, D draw four semicircles with 
3/8" radius and so on. Complete figure by drawing the 
horizontal and vertical tangents as shown. 



46 ENGINEERING DRAWING 

A PAGE OF CAUTIONS. 

Never use the scale as a ruler. 

Never draw with the lower edge of the T-square. 

Never cut paper with a knife and the edge of the T-square as a 

guide. 

Never use the T-square as a hammer. 
Never put either end of a pencil in the mouth. 
Never jab the dividers into the drawing board. 
Never oil the Joints of compasses. 
Never use the dividers as reamers or pincers or picks. 
Never take dimensions by setting the dividers on the scale. 
Never lay a weight on the T-square to hold it in position. 
Never use a blotter on inked lines. 
Never screw the nibs of the pen too tight. 
Never run backward over a line either with pencil or pen. 
Never leave the ink bottle uncorked. 
Never hold the pen over the drawing while filling. 
Never dilute ink with water. If too thick throw it away. (Ink 

once frozen is worthless afterward.) 
Never try to use the same thumb tack holes when putting paper 

down a second time. 
Never scrub a drawing all over with the eraser after finishing. 

It takes the life out of the inked lines. 

Never begin work without wiping off table and instruments. 
Never put instruments away without cleaning. This applies 

with particular force to pens. 
Never put bow instruments away without opening to relieve the 

spring. 

Never fold a drawing '6r tracing. 
Never use cheap materials of any kind. 



CHAPTER IV. 

APPLIED GEOMETRY. 

With the aid of a straight-edge and compass all pure geo- 
metrical problems may be solved. The principles of geometry 
are constantly used in mechanical drawing, but as the geometrical 
solution of problems and construction of figures differs in ma-ny 
cases from the draftsman's method, equipped as he is with 
instruments for gaining time and accuracy, such problems are 
not included here. For example, there are several geometrical 
methods of erecting a perpendicular to a given line, in his ordinary 
practice the draftsman equipped with T-square and triangles 
uses none of them. The application of these geometrical methods 
might be necessary occasionally in work where the usual drafting 
instruments could not be used, as for example in laying out full 
size sheet metal patterns on the floor. It is assumed that 
students using this book are familiar with the elements of plane 
geometry and will be able to apply their knowledge. If a par- 
ticular problem is not remembered, it may readily be referred to 




in any of the standard hand-books. There are some construc- 
tions however with which the draftsman should be familiar as 
they will occur more or less frequently in his work. The few 
problems in this chapter are given on this account, and for the 
excellent practice they afford in the accurate use of instruments 
as well. 

The "trial method" of dividing a line was explained in the 
previous chapter. A convenient geometrical method is illus- 
trated in Fig. 78. To divide the line AB into (say) five equal 

47 



48 



ENGINEERING DRAWING 



parts, draw any line AC indefinitely, 6n it step off five divisions 
of convenient length, connect the last point with B, draw lines 
through the points parallel to CB intersecting A B, using triangle 
and straight-edge. 

To transfer a given polygon ABCD to a new base A'B', Fig. 79. 
With radii AC and BC describe intersecting arcs from centers 
A'B', locating the point C' '. Similarly with radii AD and BD 





FIG. 79. 

locate the point D'. Connect BC and CD, and continue the 
operation. 

To inscribe a regular octagon in a given square, Fig. 80. Draw 
the diagonals of the square. With the corners of the square as 
centers and radius of half the diagonal draw arcs intersecting 
the sides of the square and connect these points. 

To draw a circular arc through three given points A, B, and C, 





FIG. ,80. 

Fig 81. Join AB and BC, bisect AB and BC by perpendiculars. 
Their intersection will be the center of the required circle. 

To draw an arc of a given radius R tangent to two given lines 
AB and CD, Fig. 82. Draw lines parallel to AB and CD at 
distance R from them. The intersection of these lines will be 
the center of the required arc. 

To draw a reverse or "ogee" curve connecting two parallel 
lines AB and CD, Fig. 83. Erect perpendiculars at B and C. 



APPLIED GEOMETRY ' 



49 



Any arcs tangent to the lines must have their centers on these 
perpendiculars. Join B and C by a straight line. Assume point 
E on this line through which the curve is desired to pass, and 
bisect BE and EC by perpendiculars. Any arc to pass through 
B and E must have its center on a perpendicular at the middle 
point. The intersection therefore of these perpendiculars with 
the two first perpendiculars will be the centers for arcs BE and 





FIG. 83. 

EC. This line might be the center line for a curved road or pipe. 
To lay off on a straight line the approximate length of a circle - 
arc, Fig. 84. Let A B be the given arc. At A draw the tangent 
AD and chord AB produced. Lay off AC equal to half the chord 
AB. With center C and radius CB draw an arc intersecting A% 
at E, then AE will be equal in length be to the arc AB (very 





FIG. 84. 

nearly). If the given arc is greater than 60 degrees it should be 
subdivided.* 

In ordinary work the usual way of rectifying an arc is to step 
around it with the dividers, in spaces small enough as practically 
to coincide with the arc, and to step off the same number on the 
right line, as in Fig. 85. 

* In this (Professor Rankine's) solution, the error varies as the fourth 
power of the subtended angle. At 60 degrees the line will be 1/900 part 
short. 
4 



50 



ENGINEERING DRAWING 



In cutting a right circular cone by planes at different angles 
four curves called the conic sections are obtained, Fig. 86. These 
are the circle, cut by a plane perpendicular to the axis; the ellipse, 
cut by a plane making a greater angle with the axis than the 
elements do; the parabola, cut by a plane making the same angle 
with the axis as the elements do; the hyperbola, cut by a plane 




FIG. 86. The conic sections. 

making a smaller angle than the elements do. These curves are 
studied mathematically in analytic geometry but may be drawn 
without a knowledge of their equations by knowing something of 
their characteristics. 

As an ellipse is the projection of a circle viewed obliquely it 
is met with in practice oftener than the other conies, aside from 
the circle, and draftsmen should be able to construct it readily, 
hence several methods are given for its construction, both as a 
true ellipse and as an approximate curve made by circle-arcs. 
In the great majority of cases when this curve is required its 
long and short diameters, i.e., its major and minor axes are known. 

Ellipse First Method. 

The most accurate method for determining points on the 
curve is shown in Fig. 87. With C as center describe circles on 
the two diameters. From a number of points on the outer circle 
as P and Q draw radii CP, CQ, etc., intersecting the inner circle 
at P f , Q f , etc. From P and Q draw lines parallel to CD, and from 
P' and Q' lines parallel to CB. The intersection of the lines 
through P and P f gives one point on the ellipse. The intersection 
of the lines through Q and Q' another point, and so on. For 
accuracy the points should be taken closer together toward the 
major axis. The process may be repeated in the four quadrants 
and the curve sketched in lightly freehand, or one quadrant only 



APPLIED GEOMETRY 



51 



may be constructed and the remaining three repeated by marking 
the French curve. A tangent at any point H may be drawn by 
projecting the point to the outer circle at K and drawing the 
auxiliary tangent KL cutting the major axis at L. From L 
draw the required tangent LH. 




FIG. 88. 



Ellipse Trammel Method. Fig. 88. 

On the straight edge of a strip of paper, thin cardboard or 
sheet celluloid mark the distance PQ equal to one-half the major 
axis and PR equal to one-half the minor axis. If the strip be 
moved keeping Q on the minor axis and R on the major axis, P 




FIG. 89. An Ellipsograph. 

will give points on the ellipse. This method will be found very 
convenient, as no construction is required, but for accurate 
results great care should be taken to keep the points P and Q 
exactly on the axes. The ellipsograph, Fig. 89, is constructed 
on the principle of this method. 



52 



ENGINEERING DRAWING 



Ellipse Pin and String Method. Fig. 90. 

This well-known method sometimes called the "gardener's 
ellipse" is often used for large work, and is based on the mathe- 
matical principle of the ellipse that the sum of the distances 
from any point on the curve to two fixed points called the foci 
is a constant, and is equal to the major axis. The foci may thus 
be determined by making DF and DF' equal to AC. Drive pins 




FIG. 90. 

at the points D, F, and F f and tie an inelastic thread or cord 
tightly around the three pins. If the pin D be removed and a 
marking point moved in the loop, keeping the cord taut, it will 
describe a true ellipse. The bisector of the angle between the 
focal lines will be normal to the curve, hence a tangent at any 
point L may be drawn by bisecting the exterior angle MLF. 




FIG. 91. 

Ellipse Parallelogram Method. Fig. 91. 

This method may be used with either the major -and minor 
axes or with any pair of conjugate diameters. On 'the diameters 
construct the parallelogram ABDE. Divide AC into any number 
of equal parts and AG into the same number of equal parts, 
numbering the points from A. Through these points draw lines 
from D and E as shown. Their intersections will be points on 
the curve. 



APPLIED GEOMETRY 



53 



To determine the major and minor axes of an ellipse, the conjugate 
axes being given. The property of conjugate diameters is that 
each is parallel to the tangent to the curve at the extremities of 
the other. At C draw a semicircle with radius CE. Connect 
the point of inte*rsection P of this circle and the ellipse with D 
and E. The major and minor axes will be parallel to the chords 
DP and EP. 

Approximate Ellipse with Four Centers. Fig. 92. 

Join A and D. Lay off DF equal to AC -DC. Bisect AF by 
a perpendicular crossing AC at G and intersecting DE produced, 
at H. Make CG' equal to CG and CH' equal to CE. Then Q, 





FIG. 93. 

G', H, and H' will be centers for four arcs approximating the 
ellipse. The half of this ellipse when used in masonry construc- 
tion is known as the three-centered arch. 

When a closer approximation is desired, the five-centered arch 
(eight-centered ellipse) may be constructed as in Fig. 93. Draw 
the rectangle AFDC, connect AD and draw FH perpendicular 
to it. Make CM equal to DL. With center H and radius HM 
draw the arc MN. With A as center and radius CL intersect 
A B at 0. With P as center, and radius PO intersect the arc 
MN at N, then P, N and H are centers for one-half of the 
semi-ellipse or " five centered oval." This method is based on 
the principle that the radius of curvature at the end of the minor 
axis is the third proportional to the semi-minor and semi-major 
axes, and similarly at the end of the major axis is the third 
proportional to the semi-major and semi-minor axes. The 
intermediate radius found is the mean proportional between 
these two radii. 



54 



ENGINEERING DRAWING 



Approximate Ellipse. Fig. 94. 

When the minor axis is at least two-thirds the major, the 
following method may be used: 

Make CF and CG equal to AB-DE. 

Make CH and CI equal to 3/4 CF. 

F, G, H, I will be centers for arcs E } D, A, and B. 




FIG. 95. Curve inked with circle arcs. 



It should be noted that an ellipse is changing its radius of 
curvature at every point, and that these approximations are 
not ellipses but simply curves of the same general shape. 

Any non-circular curve may be approxiamted by tangent 
circle arcs, selecting a center by trial, drawing as much of an arc 
as will practically coincide with the curve, then changing the 
center and radius for the next portion, remembering always that 





FIG. 96. Parabola. 



FIG. 97. Hyperbola. 



if arcs are to be tangent, their centers must lie on the common 
normal at the point of tangency. Many draftsmen prefer to ink 
curves in this way rather than to use irregular curves. Fig. 95 
illustrates the construction. 

A parabola may be drawn in a manner analogous to the paral- 
lelogram method of the ellipse, as shown in Fig. 96. 



APPLIED GEOMETRY 



55 



One of the commercial uses of the parabola is in parabolic 
reflectors and search lights. 

The only case of the hyperbola of practical interest to us is 
the equilateral or rectangular hyperbola on its asymptotes, as 
representing the. relation between the pressure and volume of 
steam or gas expanding under the law pv equals c. 




FIG. 98. Cycloid. 

To draw the rectangular hyperbola. Fig. 97. 

Let OA and OB be the asymptotes and P a point on the curve 
(this might be the point of cut off on an indicator diagram). 
Draw PC and PD. Mark any points on PC; through these points 
draw ordinates parallel to OA and through the same points lines 
to 0. At the intersection of these lines with PD draw abscissae. 
The intersections of these abscissae with the ordinates give points 
on the curve. 




FIG. 99. Epicycloid and hypocycloid. 

A cycloid is the curve generated by the motion of a point on 
the circumference of a circle rolled along a straight line. If the 
circle be rolled on the outside of another circle the curve is called 
an epicycloid; when rolled inside it is called a hypocycloid. - These 
curves are used in drawing gear teeth. To draw a cycloid, Fig. 
98, divide the rolling circle into a convenient number of parts 
(say 12), lay off the rectified length of the circumference with 
these divisions on the tangent AB. Draw through C the line of 



56 



ENGINEERING DRAWING 



centers CD and project the division points up to this line by 
perpendiculars. On these points as centers draw circles repre- 
senting different positions of the rolling circle, and project across 
on these circles in order, the division points of the original circle. 





FIG. 100. Involute of a pentagon. 



FIG. 101. Involute of a circle. 



These intersections will be points on the curve. The epicycloid 

incl .vj> -'..ycloid may be drawn similarly as illustrated in Fig. 99. 

"v :e is a curve generated by unwrapping an inflexible 

froiu around a polygon. Thus the involute of any polygon 

may be drawn by extending its sides, as in Fig. 100, and with the 





FIG. 102. 



FIG. 103. 



corners of the polygon as successive centers drawing the tangent 



arcs. 



A circle may be conceived as a polygon of an infinite number of 
sides. Thus to draw the involute of a circle, Fig. 101, divide it 
into a convenient number of parts, draw tangents at these points, 



APPLIED GEOMETRY 57 

lay off on these tangents the rectified lengths of the arcs from the 
point of tangency to the starting point, and connect the points 
by a smooth curve. It is evident that the involute of a circle 
is the limiting case of the epicycloid, the rolling circle becoming 
of infinite diameter. It is the basis for the involute system of 
gearing. 

To Draw the Spiral of Archimedes making one turn in a given 
circle, Fig. 102. 

Divide the circumference into a number of equal parts, drawing 
the radii and numbering the points. Divide the radius N9- 1 
into the same number of equal parts, numbering from the center. 
With C as center draw concentric arcs intersecting the radii of 
corresponding numbers, and draw a smooth curve through these 
intersections. This is the curve of 'the heart cam, Fig. 103, for 
converting uniform rotary motion into uniform reciprocal 
motion 



CHAPTER V. 
LETTERING. 

To give all the information necessary for the complete con- 
struction of a machine or structure, there must be added to the 
"graphical language" of lines describing its shape, the figured 
dimensions, notes on materials and finish, and a descriptive title, 
all of which must be lettered, freehand, in a style that is perfectly 
legible, uniform, and capable of rapid execution. So far as its 
appearance is concerned there is no part of a drawing so impor- 
tant as the lettering. A good drawing may be ruined in appear- 
ance by lettering done ignorantly or carelessly. 

Lettering is not mechanical drawing. The persistent use by 
some draftsmen of kinds of mechanical caricatures known as 
geometrical letters, block letters, etc., made up of straight lines 
and ruled in with T-square and triangles, is to be condemned 
entirely. Lettering should be done freehand, in a style suited 
to the class of the drawing.* On working drawings the lettering 
is done in a rapid single-stroke letter, either vertical or inclined, 
the inclined form being preferred. The ability to letter well in 
this style can be acquired only by continued and careful practice, 
but it can be acquired by any one with normal muscular control 
of his fingers, who will take the trouble to observe carefully the 
shapes of the letters, the sequence of strokes composing them, 
and the rules for composition; and will practice faithfully and 
intelligently. It is not a matter of artistic talent, nor even of 
dexterity in handwriting. Many draftsmen letter well who 
write very poorly. 

The term " single-stroke " or " one-stroke " does not mean that 
the entire letter is made without lifting the pen, but that the 
width of the stroke of the pen is the width of the stem of the 
letter. For the desired height, therefore, a pen must be selected 

* A more complete study of the subject of lettering than is given in this 
chapter is necessary for draftsmen who will have any variety of work, 
especially civil engineers and architects, who should give particular atten- 
tion to the different forms of Roman letter. Several books on the subject 
are mentioned in Chapter XV. 

58 



LETTERING 59 

which will give the necessary width, and for what are known as 
"gothic" letters one which will make the same width of line 
when drawn horizontally, obliquely, or vertically. 

The coarse pens mentioned on page 13 are particularly 
adapted to this purpose. Leonardt's ball point 506 F will make 
a line of sufficient width for letters 1/4" high, which is as large as 
would be used on any ordinary working drawing. 516 EF or 
Gillott's 1032 might be used for letters 3/16" high For small 
letters Hunt's shot point, Gillott's 1050, 604 or Spencerian No. 1 
may be used. Some draftsmen prepare a new pen by dropping 
it in alcohol, or by holding it in a match flame for two or three 
seconds. 

Single -stroke Vertical Caps. 

The upright single-stroke " commercial gothic" letter shown 
in Fig. 104 is a standard for titles, reference letters, etc. In the 
proportion of width to height the general rule is that the smaller 
the letters the more extended their width should be. A low 
extended letter is more legible than a high compressed one and 
at the same time makes a better appearance. This letter is 

IHLFETNKMAV 

WXYZ4OOCGDUJP 

RBS83206957& 

FIG. 104. Upright single stroke capitals. 

seldom used in compressed form. Before commencing the prac- 
tice of this alphabet some time should be spent in preliminary 
practice to gain control of the pen. It should be held easily, in 
the position illustrated in Fig. 105, the strokes drawn with a 
steady, even motion and a slight uniform pressure on the paper, 
not enough to spread the nibs of the pen. 

For the first practice draw in pencil top and bottom guide 
lines for. 3/16" letters and with a 516 F or similar pen make 
directly in ink a series of vertical lines, drawing the pen down 
with a finger movement. This one stroke must be practised 
until the beginner can get lines vertical and of equal weight. 
Remember this is drawing, not writing, and that all the flourish 



60 



ENGINEERING DRAWING 



movements of the penman must be avoided. It may be found 
difficult to keep the lines vertical; if so, direction lines may be 
drawn, as in Fig. 105, an inch or so apart to aid the eye. 




FIG. 105. Position for lettering. 

It is ruinous to the appearance of upright letters to allow them 
to slant forward. A slight backward slant is not so objectionable, 
but the aim should be to have them vertical. When this stroke 

M 111^ ///// \\\\\ OOP 

FIG. 106. Practice strokes. 

has been mastered, the succeeding strokes of Fig. 106 should be 
taken up. These strokes are the elements of which the single 
stroke letters are composed. After sufficient practice with them, 




FIG. 107. Order and direction of strokes. 



they should be combined into letters in the order of Fig. 107, 
penciling in one pattern letter and numbering its strokes, then 
drawing directly in ink several beside it. Care must be taken 



LETTERING 61 

to keep all angles and intersections clean and sharp. Getting too 
much ink on the pen is responsible for appearances of the kind 
shown in Fig. 108. 

EHMNWTZ 

FIG. 108. Too much ink. 

Single -stroke Inclined Caps. 

The single stroke inclined letter made to a slope of between 
60 and 70 degrees, Fig. 109, is preferred by perhaps a majority of 
draftsmen. The order and direction of strokes for the capitals 
of this form will be the same as in the upright form, but these 
letters are usually not extended. If a rectangle containing a 

IHLFETNKMAV 

WX YZ4 OQCGDUJP 

RBS83 2O6957& 

FIG. 109. Inclined capitals. 

flexible O should be inclined the curve would take the form 
illustrated in Fig. 110, sharp in the upper right-hand and lower 
left-hand corners, and stretched flat in the other two corners. 
This characteristic should be observed in all curved letters. A 
convenient and pleasing slope for these letters is in the proportion 
of 2 to 5, which angle may be made by laying off 2 units on the 




horizontal line and 5 units on the vertical line. Triangles of 
about this angle are sold by the dealers. 

The first requirement is to learn the form and peculiarity of 
each of the letters. Too many persons think that lettering is 
simply printing in the childish way learned in the primary grades. 
(Fig. Ill is from actual examples of men's work.) There is an 
individuality in lettering often nearly as marked as in handwrit- 



62 ENGINEERING DRAWING 

ing, but it must be based on a careful regard for the fundamental 
letter forms. 

In our practice we must first learn the individual letters, then 
compose them into words and groups of words. The inclined 
letter is used in capitals for titles and headings, and in capitals 




FIG. 111. Inexcusable faults. 

and small letters for less important captions, and for notes and 
descriptions. In all lettering there should always be drawn 
guide lines for both the tops and bottoms. In the inclined style 
the 2 to 5 direction lines should be drawn until one has become 
very proficient in keeping the lines to a uniform slant. The snap 
and swing of professional work is due largely to two things; 




FIG. 112. Practice strokes. 

keeping the letters full, and close together, and of uniform slope. 
The beginner's invariable mistake is to cramp the letters and 
space them too far apart. 

It will be noticed that the letters are arranged in family groups 
instead of in the usual alphabetical order. After practising a 
few preliminary strokes Fig. 112, the letters should be taken up 

r/ 






FIG. 113. Order and direction of strokes. 



in the order given in Fig. 113, and each one practised. The rule 
of stability requires that such letters as B, E, K, S, X, Z, with 
the figures 3 and 8 be smaller on the top than on the bottom, and 
that the cross lines in E, F, H, be slightly above the middle. 
The bridge of the A is up about 1/3 of the height. Particular 



LETTERING 



63 



care should be given to the accurate formation of numerals, 
making them round and full bodied and of the same heightf as 
the capitals. 

Single -stroke Inclined Lower Case. 

The lower case or small letters of this style are drawn with 
bodies two-thirds the height of the capitals. This letter is 

/////-/// /. / / 




7 T~7 T 
FIG. 114. Basis of Reinhardt letter. 

generally known as the Reinhardt letter, in honor of Mr. Charles 
W. Reinhardt, Chief of the Drafting Department of the "En- 
gineering News," who has used it so successfully in the illustra- 
tions for that periodical, and who published' it as a system in his 
admirable little book " Lettering for Engineers." It is the minu- 
scule or lower case letter reduced to its lowest terms, omitting all 
unnecessary hooks and appendages. It - is very legible and 











' I I 



FIG. 115. Analysis of Reinhardt letter. 

effective, and after its swing has been mastered can be made very 
rapidly. This lower case letter should be used in all notes and 
statements on drawings, for the two reasons given above, it is 
read much more easily than all capitals, as we read words by their 
shapes and are familiar with these shapes in the lower case letters ; 
and it can be done fast. 



64 ENGINEERING DRAWING 

All the letters of this alphabet are based on two strokes, the 
straight line, and the partial ellipse whose conjugate axes are 
the slope line and the horizontal line, and consequently whose 
major axis is about 45, Fig. 114. The general direction of 
strokes is always downward or from left to right, and in the 
order given in the analyzed letters in Fig. 115. 

In the composition of letters into words three general rules 
must be remembered. 1, Keep the letters close together; 2, 
have the areas of white spaces, the back grounds between the 
letters, approximately equal; 3, keep words well separated, to a 
space at least equal to the height of the letter. Paragraphs are 
always indented. Fig. 116 is an example of spacing of letters, 
words, and lines. 

As soon as the letter forms have been mastered all the practice 
should be directed to composition, which is fully as important as 
the individual shapes. Titles on working drawings are usually 
boxed in the lower right hand corner. The question of dimen- 
sioning and the contents of the title are fully discussed in Chapter 
IX on working drawings. 

The spac//70 ef Setters in words, fhe spac/na 
of words, and fhe s/?ac//?a 0f//n0s 0se a// des/grt 
prop /ems in fhe d/sjt?0s/f/0/? ofwh/fe 0/xf frfacfc. 
and /he/r success ft// so/vf/0/7 depends or? fhe 
artistic perception of fhe draffs/nan more fftar? 
on ariyrc'/es which m/ghf be a/Ve/7. 

FIG. 116. Composition. 



CHAPTER VI. 
ORTHOGRAPHIC PROJECTION. 

The previous chapters have been preparatory to the real sub- 
ject of engineering drawing as a language. In Chapter I was 
pointed out the difference between the representation of an object 
by the artist to convey certain impressions or emotions, and the 
representation by the engineer to convey information. 

If an ordinary object be looked at from some particular station 
point, one may usually get a good idea of its shape, because (1) 
generally more than one side is seen, (2) the light and shadow 
on it tell something of its configuration, (3) looked at with both 




FIG. 117. Perspective projection. 

eyes there is a stereoscopic effect to aid in judging dimensions. 
In technical drawing the third point is never considered, but the 
object is drawn as if seen with one eye; and only in special cases 
is the effect of light and shadow rendered. In general we have 
to do with outline alone. 

If a transparent plane P, Fig. 117, be imagined as set up between 
the object and the station point S of the observer's eye, the 
5 65 



66 



ENGINEERING DRAWING 



intersection with this plane, of the cone of rays formed by lines 
from the eye to all points of the object, will give a picture of the 
object, which will be practically the same as the picture formed 
on the retina of the eye by the intersection of the other end 
(nappe) of the cone. 

Drawing made on this principle is known as perspective drawing 
and is the basis of all the artist's work. In a technical way it is 
used chiefly by architects in making preliminary sketches for 
their own use in studying problems in design, and for showing 
their clients the finished appearance of a proposed building. It is 
entirely unsuited for working drawings, as it shows the object as 
it appears and not as it really is. In this book we shall take up 





FIG. 118. Orthographic projection. 



FIG. 119. The H plane. 



only the general principles of perspective as applied in freehand 
sketching, Chapter X. The titles of several books which ex- 
plain in detail the methods of perspective are given in Chap- 
ter XV. 

Orthographic Projection. 

The problem in engineering drawing is to represent accurately 
on the paper having only two dimensions, length and breadth, 
the three dimensions of the structure.* 

* The whole subject of graphic representation of solids on reference 
planes comes under the general name of descriptive geometry. That term, 
however, has by common acceptance been restricted to a somewhat more 
theoretical treatment of the subject as a branch of mathematics. This 
book maybe considered as an ample preparation for that fascinating subject, 
with whose aid many difficult problem's may be solved graphically. 



ORTHOGRAPHIC PROJECTION 



67 



If the station point S be conceived as moved back theoretically 
to an infinite distance, the cone of rays would become a cylinder 
with its elements perpendicular to the picture plane 7, Fig. 
118, and its intersection with it will give a picture known as the 



\ 




FIG. 120. The H plane revolved. 



orthographic projection. If we then discard the part of the cylin- 
der between the picture plane and the eye we may say that the 
orthographic projection of an object on a plane would be found 
by dropping perpendiculars from the object to the plane. 




FIG. 121. 



Evidently, then, a line or surface of the object parallel to the 
plane would be shown in its true size (abed), a line perpendicular 
would be projected as a point (ce) 7 and a plane surface perpen- 
dicular to the picture plane would be projected as a line 



68 



ENGINEERING DRAWING 



(beef). Thus the height and width of the object would be 
shown on the projection in their true size. 

If now another plane be placed horizontally above the object 
and perpendicular to the first plane, Fig. 119, the projection on 
this plane will give its appearance as if viewed from directly 
above, showing its width and thickness. If this plane be re- 
volved about its intersection with the first plane until they 




FIG. 122. "The transparent box." 

coincide, Fig. 120, they will represent the plane of the paper 
and the two views together will show exactly the three dimensions 
of the object. Similarly any other side may be represented by 
imagining it to be projected to a plane and the plane afterward 
revolved away from the object into the plane of the paper. 

Thus the object, Fig. 121, may be thought of as surrounded by a 
box with transparent sides, Fig. 122. The projections on these 
sides would be practically what would be seen by looking straight 
at the object from positions directly in front, above, and at both 
sides. These " planes of projection" when revolved into one 
plane, Fig. 123, and represented on the paper as in Fig. 124 give 
what are known as the different ''views" of the object. The 
projection on the front or vertical plane is known as the front 






ORTHOGRAPHIC PROJECTION 



69 



\ 




FIG. 123. The box opened. 












5 


_,, n 


nn H mi 


Coiil'! 



FIG. 124. The three projections. 



70 



ENGINEERING DRAWING 



view, vertical projection, or front elevation; that on the horizontal 
plane as the top view, horizontal projection, or plan; that on 
the side or profile plane as the side view, profile projection, or 
side elevation. When necessary the bottom view and back 
view may be made in a similar way, by projecting to their planes 
and opening them up to coincide with the vertical plane. 

Three principles are evident, first, the top view is directly over 
the front view, second, the side views are in the same horizontal 
line as the front view, third, the width of the side views are ex- 
actly the same as the width of the top view. For brevity we 
shall call the vertical plane V, the horizontal plane H and the 
profile plane P. The intersection of H and V is called the ground 
line, GL, and the intersections of P with H and V called the H 
trace of P, and the V trace of P. P is generally revolved about 
its V trace as in the illustration in Fig. 124, but may be revolved 
about its H trace as in Fig. 126. Evidently the side view of any 
point as Q would be as far from the V trace of P as its top view 
is from the ground line. 




FIG. 125. First angle projection. 

Note.^ If the horizontal and vertical planes are extended beyond their 
ntersection, 'four dihedral angles will be formed, which are numbered as 
illustrated in Fig. 125. If the object be placed in the first angle, projected 
to the planes and the planes opened as before, the top view would evidently 
fall below the front view, and if the profile plane were added the view of 
the left side of the figure would be to the right of the front view. This 
system, known as first angle projection, was formerly in universal use, but 
was generally abandoned in this country more than twenty years ago and 
is now almost obsolete. The student should understand it, however, as it 
may be encountered occasionally in old drawings, in some book illustrations, 
and in foreign drawings. In England some attempt is being made to 
introduce true (third angle) projection, but as yet it has not been accepted 
to any extent. 



ORTHOGRAPHIC PROJECTION 



71 



The monument Fig. 127 is shown in orthographic projection in 
Fig. 128. On the top view the H tr. of P is OA. Evidently in 
the revolution of P about its V tr. ? the H tr. would revolve to 
OB and the points projected to it from the top view would re- 
volve with it. These, if projected down from OB to meet hori- 




O 



FIG. 126. 



zontal projectors from corresponding points on the! front view, 
would locate the points on the side view. Fig. 129 illustrates the 
principle pictorially. 

In practice only as many views are made as are necessary to 
describe the object, and the ground line and P traces are not 





FIG. 127. 



FIG. 128. 



represented, but center lines or other lines of the views are used 
for reference or datum lines as in Fig. 130. Thus the center 
line of the side view may be regarded as the edge of a reference 
plane whose H trace is the center line on the top view. In our 
theoretical study we shall make the three views of a number of 



72 



ENGINEERING DRAWING 



simple objects, at first working from the GL and V trace of P 
as datum lines, afterward using center lines; developing the 
ability to write the language, and exercising the imagination in 
seeing the object itself in space by reading the three projections. 




FIG. 129. 



Fig. 131 shows successive cuts made on a block, and the cor- 
responding projections of the block in the different stages. The 
effort should be made to visualize the object from these pro- 
jections until the projection can be read as easily as the picture. 
A drawing as simple as A' or B' can be read, and the mental 






















\ 








1 


f 






_] 






















1 










1 


i 
i 

L, 














1 






1 










F 


EG. 130. 









picture formed, at a glance; one with more lines as E' will re- 
quire a little time for study and comparison of the different 
views. One cannot expect to read a whole drawing at once any 
more than he would think of reading a whole page of print at a 
glance. 



ORTHOGRAPHIC PROJECTION 



73 



Fig. 132 is another progressive series, illustrating the necessary 
use of hidden lines. 

The objects in Fig. 133 are to be "written" in orthographic 



n 



C3H 

FIG.. 131. 




projection by sketching their three views. Similar practice 
may be gained by sketching the projections of any simple models, 




FIG. 132. 



or objects with geometrical outlines, such as those illustrated in 
Fig. 390. 




FIG. 133. 



After a study of the methods of pictorial representation (Chap- 
ter VIII) we shall reverse this operation and practise reading, by 
making the pictures of objects drawn in orthographic projection. 



74 



ENGINEERING DRAWING 



Auxiliary Views. 

Sometimes a view taken from another direction will aid in show- 
ing the shape or construction of an object to better advantage 
than can be done on the three reference planes alone, and often 
such a view may save making one or more of the regular views. 
For example, the three views of Fig. 134 do not show the face A 
clearly. A projection on a plane whose edge (H trace) is S-S, 
parallel to the face A, Fig. 135, would show the true size of the 
face, and the position of the hole, and would obviate the necessity 
for a side view. The projection is imagined as made by dropping 
perpendiculars to the plane, and revolving the plane about S-S 








V*.. 

VL 


fe 

\J 





^^ 



1 1 


'l 

\J 


i 

i 


1 /~ 



FIG. 134. 



FIG. 135. Auxiliary projection. 



into the plane of the top view, as illustrated pictorially in Fig. 
136. Since this plane is perpendicular to H, the width W of 
this view would evidently be the same as the width of the front 
view. 

Such a plane as S is called an auxiliary plane, and the projec- 
tion on it an auxiliary projection or auxiliary view. 

These planes may be set up anywhere perpendicular to one of 
the planes of projection, and revolved into the plane of the paper. 
In practical work extensive use is made of auxiliary views in 
showing the true size of sections and inclined surfaces. 

The plane S in Fig. 136 was taken perpendicular to H and re- 
volved into H. It might as readily have been revolved about 
its V trace into V. Fig. 137 is the picture of an object with the 
H and V planes, and an auxiliary plane parallel to one of the 



ORTHOGRAPHIC PROJECTION 



75 





76 



ENGINEERING DRAWING 



faces of the object and perpendicular to V. F.ig. 138 shows the 
position of the planes and the projections when opened up, the 
auxiliary plane being revolved about its V trace to coincide 





FIG. 138. Auxiliary projection. 



FIG. 139. Auxiliary projection. 



with V. These figures illustrate clearly that the dimensions of 

the auxiliary view are obtainable directly from the other views. 

In practice the auxiliary plane trace is not actually drawn, 

but, like the ground line, after use has been made of it in explain- 




FIG. 140. 



ing the principle, its position is simply imagined, and the views 
are worked from center lines. Thus in Fig. 139 the center line 
on the auxiliary view is really the projection of the center line 
of the top view or, more accurately, the edge of a plane whose H 



ORTHOGRAPHIC PROJECTION 



77 



trace is the center line of the top view, and the perpendicular 
distance of any point as p or q from the center line on the top 
view is laid off perpendicular to the center line on the auxiliary 
view. 

Often it is not necessary to project the whole figure on the 
auxiliary plane, but only the part to be shown in true shape, as 
the lug or pad in Fig. 140 or the cut face of Fig. 141. 

An auxiliary plane may be imagined as detached from its 
trace and may be set off anywhere at a convenient place on the 
paper. 




FIG. 141. 



FIG. 142. Section on A-B. 



Sectional Views. 

Often it is not possible to show clearly the interior construction 
or arrangement of an object by outside views, using dotted lines 
for the invisible parts. In such case the object is drawn as if a 
part of it were cut or broken away and removed. A projection 
of this kind is known as a sectional view, or section, and the ex- 
posed cut surface of the material is indicated by " section lining." 
It should be understood that in thus removing an obstructing 
portion so as to show the interior on one view, the same portion 
is not removed from the other views; but on the view to which 



78 



ENGINEERING DRAWING 



the cut surface is perpendicular the trace of the cutting plane is 
indicated by a line. Thus in Fig. 142 the top view shows the 
trace of the cutting plane A-B, and the front view is a section 





FIG. 143. 



showing the bearing as it would appear if the part in front of the 
plane A-B were removed. Fig. 143 is a pictorial illustration. 
This figure also illustrates the fact that the cutting plane need not 




FIG. 144. Half section. 



be continuous, but may be taken so as to show the construction 
to the best advantage. 

When a figure is symmetrical about an axis, it is a common 



ORTHOGRAPHIC PROJECTION 



79 



practice to show half in section and the other half in full. Figs. 
144 and 145 are examples. Fig. 146, an illustration of a broken 
section, is self-explanatory. 




FIG. 145. Half section. 



Little auxiliary views known as turned sections, or revolved 
sections, are of great convenience in showing the shape of some 
particular part. They may be drawn directly on the view, as 




FIG. 146. Broken section. 



in Fig. 147, or the piece may be broken to admit of placing the 
section, as in Fig. 148. 

It is not assumed that the cutting plane cuts everything 




FIG. 147. Revolved sections. 



through which it* passes. It is a practical rule in drawing that 
if in a sectional view a part can be shown more clearly by leaving 



80 



ENGINEERING DRAWING 



it in position full, it is so left. This is true of shafts, bolts, rods, 
keys, etc., which are never sectioned, but are drawn as in Figs. 
149 and 150. A combination full and sectional view, known as a 
"dotted section" will sometimes show the construction of an 
object economically. Fig. 151 A is an illustration. 




FIG. 148. Revolved section. 

Section lining is done with a fine line, generally at 45 degrees, 
and spaced uniformly, to give an even tint, the spacing being 
governed by the size of the surface, but except in very small 
drawings not less than 1/16 of an inch. On drawings to be 
inked or traced the section lining is only indicated freehand in 





FIG. 149. 



FIG. 150. 



pencil, and is done directly in ink. The spacing is done entirely 
by the eye. Care should be exercised in setting the pitch by the 
first two or three lines, and one should glance back at the first 
lines often in order that the pitch may not gradually change to 
wider or narrower. 



ORTHOGRAPHIC PROJECTION 



81 



Large surfaces in section are sometimes shown as in Fig. 152. 
This both saves time and improves the appearance. Adjacent 
pieces are section lined in opposite directions, and are often 





FIG. 151. A dotted section. 



brought out more clearly by varying the pitch, using lines closer 
together for smaller pieces. 

Different materials are sometimes indicated by conventional 
symbols. The use of those symbols is discussed in Chapter IX. 




FIG. 152. 



Revolution. 

The natural way to place an object would be in the simplest 
position, with one face or edge parallel to a plane of projection. 
6 



82 



ENGINEERING DRAWING 



It is sometimes necessary, however, to represent it in a position 
oblique to the planes. In such a case it may be necessary to 
draw the object first in a simpler position, and revolve it about an 
axis perpendicular to a plane of projection to the required 
position. 








FIG. 153. Revolution about axis perpendicular to H. 

Rule: If an object be revolved about an axis perpendicular to 
a plane, its projection on that plane will remain unchanged in 
size and shape, and the dimensions parallel to this axis on other 
planes will be unchanged. 

Thus if the pyramid Fig. 153 be revolved through 30 degrees about 
an axis perpendicular to the H plane, its H projection will take the 








FIG. 154. Revolution about axis perpendicular to V. 

position shown at B. The height of the pyramid has not been 
changed in the revolution, hence the front and side views are 
the same height as the original front view. If, instead/ the pyra- 
mid be revolved about an axis perpendicular to V, the front view 
will be unchanged and may be copied in the new position. The 



ORTHOGRAPHIC PROJECTION 



83 



distance from the ground line to any point in the top view would 
be unchanged, hence the new top view may be found by pro- 
jecting up from the front view and across from the original top 
view, Fig. 154. 

Similarly in the revolution forward or back, about an axis 
perpendicular to P, the side view is unchanged and the dimensions 
(widths) on the top and front are the same as in the original 
position, Fig. 155. 









FIG. 155. Revolution about axis perpendicular to P. 

Successive revolutions may be made under the same rules. 
Fig. 156 is a block revolved from its first position about an axis 
perpendicular to H through 45 degees, then about an axis per- 
pendicular to P through 45 degrees until the cut face MNO is 
parallel to the vertical plane. To avoid confusion it is well to 
letter or number the corresponding points as the views are car- 
ried along. 

Evidently the only difference in principle between revolutions 



84 



ENGINEERING DRAWING 



and auxiliary planes is that in the former the object is moved 
and in the latter the plane is moved. 

Although objects in practical drawing would never be placed 
in these complicated positions, unless unavoidable, problems 
in revolution are an excellent aid in the understanding of the 
theory of projection. 




FIG. 156. Successive revolutions. 

The True Length of a Line. 

These principles are evident : If a line is parallel to a plane 
its projection on that plane will be equal in length to the line 
itself. 

If a line is perpendicular to a plane its projection on the plane 
will be a point. 



ORTHOGRAPHIC PROJECTION 



85 



If a line is inclined to a plane its projection will be shorter 
than the line. 

If a line is parallel to H or V its projection on the other plane 
will be parallel to the ground line. 

A line inclined to both H and V will not show its true length 





FIG. 158. 



in either projection. If it be revolved until it is parallel to one 
of the planes its projection on that plane will be its true length. 
In Fig. 157 the line AB is revolved about an axis perpendicular 
to H until it is parallel to V and its true length is A v B v r . 
Fig. 158 is a similar construction with the axis perpendicular to V. 





159. 



FIG. 160. 



Or by a second method the line may be revolved about its 
projection, into the plane. This is illustrated pictorially in Fig. 
159. The H projection of the line AB in space is a line con- 
necting the feet of all the perpendiculars from A B to the plane. 
These perpendiculars form what is known as the projecting plane. 



86 ENGINEERING DRAWING 

If this projecting plane be revolved about its H trace, which is the 
H projection of the line, until it coincides with H, the line will be 
seen in its true length. 

Construction. Fig. 160. The distance of A and B below H 
is indicated on the V projection. Thus if to A h B h the perpendic- 
ulars A h A r and B h B r be drawn, A r B r will be the true length of 
AB. 

Shade Lines. 

In the alphabet of lines the visible outline was indicated as a 
uniform, bold, full line. This is the general practice for working 
drawings. 

It is possible by using two weights of lines, to add something 
to the clearness and legibility of a drawing, and at the same 




FIG. 161. Shading a circle. 

time to give to its appearance a relief and finish very effective 
and desirable in some classes of work. Shade lines are required 
on patent office drawings, and are used in a few shops on assem- 
bly drawings, but for ordinary shop drawings the advantage 
gained is overbalanced by the increased cost. It is correct to 
use them whenever the gain in legibility and appearance is of 
sufficient importance to warrant the expenditure of the added 
time necessary. 

Theoretically the shade line system is based on the principle 
that the object is illuminated from one source of light at an in- 
finite distance, the rays coming from the left in the direction of 
the body diagonal of a cube, so that the two projections of any 
ray each make an angle of 45 degrees with the GL. Part of the 
object would thus be illuminated and part in shade, and a shade 



ORTHOGRAPHIC PROJECTION 



87 



line is a line separating a light face from a dark face. The strict 
application of this theory would involve some trouble, and it is 
never done in practice, but the simple rule is followed of shading 
the lower and right hand lines of all figures. 

The light lines should be comparatively fine and the shade 
lines about three times their width. The width of the shade 
line is added outside the surface of the piece. They are never 
drawn in pencil, but their location may be indicated, if desired, 
by a mark on the line. In inking a shaded drawing all light lines 
alone should be inked first, then the shade lines. 





FIG. 162. Shade lines. 

A circle may be shaded by shifting the center on a 45-degree 
line toward the lower right hand corner, to an amount equal to 
the thickness of the shade line, >and drawing another semicircular 
arc with the same radius, or it may be done much more quickly, 
particularly with small circles, after the "knack" has been 
acquired, by keeping the needle in the center after drawing the 
circle and springing the compass out and back gradually by 
pressing with the middle finger in the position of Fig. 161. 
Never shade a circle arc heavier than the straight lines. 

Fig. 162 is an example of a shade line drawing. The aid in 
reading given by the shade lines will be noted. 



88 



ENGINEERING DRAWING 



Line shading is a method of representing the effect of light 
and shade by ruled lines, used on patent drawings, "show plans," 
drawings for illustration, and the like-. To execute it effectively 





FIG. 163. 



FIG. 164. 



and 'rapidly requires practice and is an accomplishment not 
usual among ordinary draftsmen. An explanation of the 
methods, a'nd several examples illustrating its application are 
given in Chapter XIV, page 259. 





FIG. 165. 



FIG. 166. 



PROBLEMS. 

If drawn to the dimensions and scales given, these problems 
will each occupy a space not to exceed 4" x 5". 
Group I. Orthographic from pictorial views. 
Prob. 1. Draw three views of block, Fig. 163, using G.L. 

2. Draw three views of core box, Fig. 164, using center 
lines (without G.L.}. 



ORTHOGRAPHIC PROJECTION 



89 



3. Draw three views of box, Fig. 165, using center lines. 

4. Draw three views of block, Fig. 166, using G.L. 

5. Draw three views of support, Fig. 167, using center lines. 

6. Draw three views, of block, Fig. 168, using G.L. 





FIG. 167. 



FIG. 168. 



7. Draw three views of block, Fig. 169, using G.L. 

8. Draw three views of piece, Fig. 170, using center lines. 
When three views are specified, the top view, front 

view, and right side view are understood. 




FIG. 169. 



FIG. 170. 



Group II. Views to be completed. 

Prob. 9. Draw the top and front views given, Fig. 171, and add 
side view. Scale Q" = l ft. 

10. Draw three views of clamp, Fig. 172. Scale 6" = 1 ft. 

11. Complete the top and front views and draw side view 
of block, Fig. 173.. Scale 3" - 1 ft. 

12. Draw three views of block, Fig. 174. Scale 3" = 1 ft. 



90 



ENGINEERING DRAWING 




FIG. 171. 



FIG. 172. 



*>!> .1 

FnJi 



T 

^ 





H% ' 
j i 
HT 'i 



Jl 



FIG. 173. 



FIG. 174. 





1 

pf-f 



W 



FIG. 175. 



FIG. 176. 



ORTHOGRAPHIC PROJECTION 



91 



13. Draw three views of circular block, Fig. 175. Scale 
3" = 1 ft. 

14. Draw three views of block, Fig. 176. Scale 3" = 1 ft. 
For further practice the bottom and left side views 

of problems 12, 13, and 14 may be drawn. 




FIG. 177. 




15. Draw front view, complete top view, and draw left 
side view of frame, Fig. 177. Scale 3"=^1 ft. 

16. Draw front view, top view, and complete left side 
view given, of the standard, Fig. 178. Scale 6" = 1 ft. 




FIG. 179. 



FIG. 180. 



Group III. Auxiliary projections. 

Prob. 17. Draw the front view given, complete the top view and 

draw auxiliary view on the given C.L. of truncated 

pyramid, Fig. 179. Full size. 
18. Draw auxiliary view of cylinder, Fig. 180. 



92 



ENGINEERING DRAWING 




FIG. 181. 




FIG. 182. 




FIG. 183. 



ORTHOGRAPHIC PROJECTION 



93 



19. Draw auxiliary view of square prism, Fig. 181. 

20. Draw auxiliary view of cylinder, Fig. 182. 

21. Draw auxiliary view of block, Fig. 183. 




FIG. 184. 



22. Draw auxiliary view of cone cut by plane, Fig. 184. 

23. Draw auxiliary view of pentagonal pyramid, Fig. 185. 

24. Draw auxiliary view of bearing, Fig. 186. Scale 3" = 
1ft. 





FIG. 186. 

Group IV. Sectional views. 

Prob. 25. Draw front view and sectional side view of ring, Fig. 

187. Full size. 
26. Draw front view and sectional top view of eccentric, 

Fig. 188. Scale 6" = 1 ft. 



94 



ENGINEERING DRAWING 





FIG. 188. 




FIG. 189. 




FIG. 191. 




ORTHOGRAPHIC PROJECTION 



95 



27. Draw top view and sectional front view of casting, 
Fig. 189. Scale 6" = 1 ft. 

28. Draw top view, side view, and sectional front view of 
body, Fig. 190. Scale 6" = 1 ft. 




FIG. 193. 

Half sections. 

29. Draw top view and half-section front view of flanged 
piece, Fig. 191. Scale 3" = 1 ft. 

30. Draw top view and half-section front view of sleeve 
Fig. 192. Scale 6" = 1 ft. 




FIG. 194. 



31. Draw end view in section, and front view with lower 
half in section, of piston, Fig. 193. Scale 6" = 1 ft. 

32. Draw top view, front view in half -section, and end view 
of tool-rest holder, Fig. 194. Scale 6" = 1 ft. 



96 



ENGINEERING DRAWING 



Group V. Revolution. 

Prob. 33. (1) Draw three views of Fig. 195 in simplest position, 
(2) Revolve from position (1) about an axis perpendic- 
ular to H through 15 degrees. 




FIG. 195. 



(3) Revolve from position (2) about an axis perpendic- 
ular to V through 45 degrees. 

(4) Revolve from position (1) about an axis perpendic- 
ular to P forward through 30 degrees. 




r-^H r-'f-*\ 

[HE! VO 




o 

o 



5 6 

FIG. 195 A. 



(5) Revolve from position (2) about an axis perpendic- 
ular to P forward through 30 degrees. 

(6) Revolve from position (3) about an axis perpendic- 
ular to P forward through 30 degrees. 





FIG. 197. 



(4), (5), (6) may be placed to advantage under 
(1), (2), and (3) so that the widths of front and top 
views may be projected down directly. 



ORTHOGRAPHIC PROJECTION 



97 



In problem 33 any of the objects in Fig. 195 A 
may be used instead of Fig. 195. 

34. (1) Draw three views of Fig. 196. 

(2) Revolve from position (1) about an axis perpendic- 
ular to V through 30 degrees. 

(3) Revolve from position (2) about an axis perpendic- 
ular to H through 45 degrees. 

35. (1) Draw three views of Fig. 197. 




1 

1 


H] 



1 



FIG. 198. 



(2) Revolve from position (1) about an axis perpendic- 
ular to P through 30 degrees. 

36. Complete top and front views, and draw side view of 
box in position as shown in Fig. 198, using auxiliary 
view shown at A to obtain projections of lid. Scale 
6" = 1ft. 

Group VI. True length of lines. 

Prob. 37. Find true length of the body diagonal of a 1 1/2" cube. 

38. Find true length of the brace AB in tower diagram, 
Fig. 199. 

39. Find true length of any element, as A B, of oblique 
cone, Fig. 200. Scale 6" = 1 ft. 

40. Find true length of line AB of pier, Fig. 201. Scale 
6" = 1 ft. 

41. Find true length of line AB on brace, Fig. 202. Scale 
3/4" = 1ft. 

7 



98 



ENGINEERING DRAWING 



Group VII. Drawing from description. 

Prob. 42. Draw three views of a pentagonal prism, axis V long 
and perpendicular to H, circumscribing circle of base 
1 1/8" diam., surmounted by a cylindrical abacus 
(cap) 1 1/2" diam., 1/2" thick. 





FIG. 199. 



FIG. 200. 



43. Draw three views of a triangular card each edge of 
which is 1 3/4" long. One edge is perpendicular to P, 
and the card makes an angle of 30 degrees with H. 

44. Draw three views of a circular card 1 3/4" diam., in- 





FIG. 201. 



FIG. 202. 



45. 



clined 30 to H, and perpendicular to V. (Find 8 
points on the curve). 

Draw three views of a cylinder 1" diam., 2" long, with 
hexagonal hole, 3/4" long diam., through it. Axis of 
cylinder parallel to H and inclined 30 degrees to V. 



ORTHOGRAPHIC PROJECTION 99 

46. Draw top and front views of a hexagonal plinth whose 
faces are 5/8" square and two of which are parallel 
to H, pierced by a square prism 2 3/4" long, base 1/2" 
square. The axes coincide, are parallel to H, and 
make an angle of 30 degrees with V. The middle 
point of the axis of the prism is at the center of the 
plinth. 

47. Draw the two projections of a line 2" long, making an 
angle of 30 degrees with V, and whose V projection 
makes 45 degrees with G.L., the line sloping down- 
ward and backward to the left. 

48. Draw three views of a square pyramid whose faces are 
isosceles triangles 1 1/4" base and 2" alt., lying with 
one face horizontal, the H projection of its axis at an 
angle of 30 degrees with G.L. 

49. Draw three views of a triangular pyramid formed of 
four equilateral triangles whose sides are 1 3/4". 
,The base makes an angle of 45 degrees with H, and 
one of the edges of the base is perpendicular to V. 

50. Draw top and front views of a rectangular prism, 
base 5/8" x 1 1/4" whose body diagonal is 13/4" long. 
Find projection of prism on an auxiliary plane per- 
pendicular to the body diagonal. 



CHAPTER VII. 

DEVELOPED SURFACES AND INTERSECTIONS.* 

A surface may be considered as generated by the motion of a 
line. Surfaces may thus be divided into two general classes, (1) 
those which can be generated by a moving straight line, (2) those 
which can be generated only by a moving curved line. The 
first are called ruled surfaces, the second, double curved surfaces. 
Any position of the moving line is called an element. 

Ruled surfaces may be divided into (a) planes, (b) single curved 
surfaces, (c) warped surfaces. 

A plane may be generated by a straight line moving so as to 
touch two other intersecting or parallel straight lines. 

Single curved surfaces have their elements either parallel or 
intersecting. These are the cylinder and the cone; and a third 
surface, which we shall not consider, known as the convolute, in 
which the consecutive elements intersect two and two. 

Warped surfaces have no two consecutive elements either 
parallel or intersecting. There is a great variety of warped 
surfaces. The surface of a screw thread and of the pilot of a 
locomotive are two examples. 

Double curved surfaces are generated by a curved line moving 
according to some law. The commonest forms are surfaces of 
revolution, made by the revolution of a curve about an axis in 
the same plane, as the sphere, torus, or ring, ellipsoid, paraboloid, 
hyperboloid, etc. 

In some kinds of construction full sized patterns of different 
faces, or of the entire surface of an object are required; as for 
example in stone cutting, a templet or pattern giving the shape 
of an irregular face, or in sheet metal work, a pattern to which a 
sheet may be cut that when rolled, folded, or formed will make 
the object. 

* The full theoretical discussion of surfaces, their classification, proper- 
ties, intersections, and development may be found in any good descriptive 
geometry. 

100 



DEVELOPED SURFACES AND INTERSECTIONS 101 

The operation of laying out the complete surface on one plane 
is called the development of the surface. 

Surfaces about which a thin sheet of flexible material (as paper 
or tin) could be wrapped smoothly are said to be developable; 
these would include figures made up of planes and single curved 
surfaces only. Warped and double curved surfaces are non- 
developable, and when patterns are required for their construction 
they can be made only by some method of approximation, 
which assisted by the pliability of the material will give the re- 
quired form. Thus, while a ball cannot be wrapped smoothly, a 
two-piece pattern developed approximately and cut from leather 
may be stretched and sewed on in a smooth cover, or a flat disc 
of metal may be die-stamped, formed, or spun to a hemispherical 
or other required shape. 

We have learned (page 74) the method of finding the true 
size of a plane surface by projecting it on an auxiliary plane. 




FIG. 203. FIG. 204. 

If the true. size of all the faces of an object made of planes be 
found and joined in order, at their common edges, the result 
will be the developed surface. This may be done usually to the 
best advantage by finding the true lengths of the edges. 

The development of a right cylinder would evidently be a 
rectangle whose width would be the altitude, and length the 
rectified circumference, Fig. 203; and the development of a 
right cone with circular base would be a sector with a radius 
equal to the slant height, and arc equal in length to the circum- 
ference of the base, Fig. 204. 

In the laying out of real sheet metal problems an allowance 
must be made for seams and lap, and in heavy sheets for the 
thickness and for crowding of the metal; there is also the con- 
sideration of the commercial sizes of material, and of economy 
in cutting, in all of which some practical shop knowledge is 



102 ENGINEERING DRAWING 

necessary. In this chapter we will be confined to the principles 

alone. 

In the development of any object we must first have its pro- 
jections, drawing only such views or parts of views as are neces- 
sary to give the lengths of elements and true size of cut surfaces. 

To develop the hexagonal prism, Fig. 205. 

Since the base is perpendicular to the axis it will roll out into 
the straight line AB. This line is called by sheet metal workers 
the "stretchout." Lay off on AB the length of the perimeter 
of the base, and at the points 1, 2, 3, etc., erect perpendiculars, 




FIG. 205. Development of hexagonal prism. 

called "measuring lines," representing the edges. Measure on 
each of these its length as given on the front view, and connect 
the points. Attach to one of the top lines the true size of the 
cut face C, and to one of the bottom lines the size of the base. 
The figure will then be the development of the entire surface of 
the prism. It is customary to make the seam on the shortest 
edge. 

To develop the cylinder, Fig. 206. 

In rolling the cylinder out on a tangent plane the base, being 
perpendicular to the axis, will develop into a straight line. 
Divide the base, here shown as a bottom view, into a number of 
equal parts, representing elements. Project these elements up 
to the front view. Draw the stretchout and measuring lines as 
before. Transfer the lengths of the elements in order, either by 



DEVELOPED SURFACES AND INTERSECTIONS 



103 



projection or with dividers, and connect the points by a smooth 
curve. This might be one-half of a two-piece elbow. Three- 
piece, four-piece, or five-piece elbows may be drawn similarly, as 




FIG. 206. Development of cylinder. 




FIG. 207. Five-piece elbow. 



illustrated in Fig. 207. As the base is symmetrical, one-half 
only need be drawn. In these cases the sections as B will de- 
velop on their center lines as stretchouts, and measurements will 



104 



ENGINEERING DRAWING 



J_J_iUJ 




FIG. 208. Development of five-piece elbow. 




FIG. 209. Development of octagonal dome. 



DEVELOPED SURFACES AND INTERSECTIONS 



105 



be taken on each side of the center line, since the center line repre- 
sents a "right section," i.e. the section cut by a plane perpen- 
dicular to the axis. 

Evidently any elbow could be cut from a single sheet without 
waste if the seams were made alternately on the long and short 
sides. Fig. 208. 

The development of the octagonal dome Fig. 209 illustrates an 
application of the development of cylinders. 




FIG. 210. Development of hexagonal pyramid. 

To develop the hexagonal pyramid, Fig. 210. 

The edge GA is shown on the front view in its true length. As 
the edges are all of equal length, an arc may be drawn with the 
radius GA and the perimeter of the base stepped off on it. The 
cutting plane intersects the edges at the points HJKL. Revolve 
these points to GA to find the true length of the intercepts and 
measure these distances on the corresponding lines of the develop- 
ment. Find the true size of the cut face and attach it to the 
development. 

The rectangular pyramid Fig. 211 is develped in a similar way, 
but as the edge EA is not parallel to the plane of projection it 
must be revolved to EA' to obtain its true length. 

To develop the truncated cone, Fig. 212. 

Divide the base into a convenient number of equal parts, 
project these points on the front view and draw the elements 



106 



ENGINEERING DRAWING 



through them. With a radius equal to the slant height of the 
cone, i.e. the true length of the element OA, draw an arc and lay 
off on it the circumference of the base; draw the developed posi- 




FIG. 211. Development of rectangular pyramid. 




FIG. 212. Development of cone. 

tions of the elements and on them measure the true lengths 
from the vertex to the cutting plane, found by revolving each 
point over to the extreme element OA. 



DEVELOPED SURFACES AND INTERSECTIONS 



107 



Double -curved surfaces are developed approximately by 
assuming them to be made up of parts of developable surfaces. 
Thus the sphere may be made of sections of cylinders whose 




FIG. 213. Sphere, gore method 



diameter is equal to the diameter of the sphere, and developed 
as in Fig. 213, or it may be made up of frustra of cones and 
developed as in Fig. 214. 




FIG. 214. Sphere, zone method. 



Triangulation. 

The commonest and best method for approximate develop- 
ment is by triangulation, i.e., assuming the surface to be made 
up of a large number of triangular strips, or plane triangles with 



108 



ENGINEERING DRAWING 



very short bases. This is used for all warped surfaces, and for 
oblique cones, which, although single-curved surfaces, and capable 
of true theoretical development, can be done much more easily 
and accurately by triangulation. 

The method is extremely simple. It consists merely in divid- 
ing the surface into triangles, finding the true lengths of the sides 
of each, and constructing the triangles one at a time, joining 
them on their common sides. A study of Fig. 215, the develop- 
ment of an oblique cone, will explain the method completely. 




FIG. 215. Development of oblique cone by triangulation. 

In this case the triangles all have a common vertex, the apex of 
the cone, their sides are elements, and their bases the chords of 
short arcs of the base of the cone. 

Divide the base into a number of equal parts 1, 2, 3, etc. (as 
the plan is symmetrical about the axis A h C h one-half only need 
be constructed). If the seam is to be on the short side, the line 
AC will be the center line of the development and may be drawn 
directly at A'C' as its true length is given. Find the true lengths 
of the elements 1A, 2A, etc., by revolving them until parallel to 1 
V. This may be done without confusing the H and V projections, 



DEVELOPED SURFACES AND INTERSECTIONS 



109 



by constructing the triangles for the true lengths in an auxiliary 
figure as shown, laying off the lengths of the H projections as 
bases on the line DC' and connecting with the point A" '. With 
A' as center and radius A'V draw an arc on each side of A'C'. 
With C' as center and radius C h l intersect these arcs at 1'. 
Then A'V will be the developed position of the element Al. 
With 1' as center and arc 1, 2, intersect A'2' and continue the 
operation. 




FIG. 216. Development of oblique cone by triangulation. 

Fig. 216 is an oblique cone connecting two parallel pipes of 
different diameters. This is developed in the same way as Fig. 
215, except that the true size of the base is not given in the top 
view and must be revolved until parallel to H, as shown. 

Transition Pieces. 

Transition pieces are used to connect pipes or openings of 
different shapes of cross-section. Fig. 217, for connecting a 
round pipe and a square pipe on the same axis, is typical. These 
are always developed by triangulation. 

The piece shown in Fig. 217 is evidently made up of four 
isosceles triangles whose bases are the sides of the square, and 
four parts of oblique cones. As the top view is symmetrical 



110 



ENGINEERING DRAWING 



about both center lines, one-fourth only need be divided. The 
construction is illustrated clearly in the figure. 




FIG. 217. Transition piece. 





FIG. 218. Transition piece. 



Fig. 218 is another transition piece from rectangular to round. 
By using the turned sections of one-half the round opening, the 
need of the full side view is avoided. 



DEVELOPED SURFACES AND INTERSECTIONS 



111 



The Intersection of Surfaces.* 

The habit should be formed of thinking of surfaces as made up 
of elements, the successive positions of the generating line. 
When two surfaces intersect, their common line, the line of 
intersection, would be found by connecting the points at which 
the elements of one surface pierce the other. 

Two reasons make it necessary for the draftsman to be familiar 
with the methods of finding the intersections of surfaces, first, 
intersections are constantly occurring on working drawings, and 
must be represented, second, in sheet metal combinations the 
intersections must be found before the pieces can be developed. 
In the first case it is only necessary to find a few points usually, 
and "guess in" the curve; in the second case enough points 
must be determined to enable the development to be laid out 
accurately. 

Intersection of Two Cylinders. 

Any practical problem resolves itself into some combination of 
the geometrical type forms of solids. 

In Fig. 219 the intersection of two cylinders might represent a 
dome on a boiler. If the top view of the cylinder A is divided 






LI 

I i 

i i 


< 

i i 




rjSs 
B 


41. j 




FIG. 219. Intersection of two cylinders. 

into a number of equal parts the points will represent the top 
views of elements. Draw the side views of these elements, which 
will pierce the cylinder B as shown. If these points be projected 
across to meet the corresponding elements on the front view the 
intersections will be points on the curve. Since the axes inter- 

* Often called "penetrations" or "interpenetrations." 



112 



ENGINEERING DRAWING 



sect, the projection of the invisible part of the curve will coincide 
with the visible part. 

The method of development of the cylinder A is evident from 
the figure. 

In general, the method of finding the line of intersection of any 
two surfaces is to pass a series of planes through them in such a 
way as to cut from each the simplest lines. The intersection of 
these lines will be points on the curve. 

In Fig. 219 the plane T may be assumed as cutting out two 
elements from the cylinder A whose intersections with the ele- 
ment cut from the cylinder B, being points common to both, 
cylinders, will be points on the curve, as shown in the sketch. 




FIG. 220. Two cylinders, axes not intersecting. 

This principle is illustrated in Fig. 220 with two cylinders whose 
axes do not intersect. If the cylinder A were to be developed a 
right section as at &-/S would have to be taken, whose stretchout 
would be a straight line. If the cutting planes were taken at 
uniform distances apart, or at random, the elements would not 
be spaced uniformly on the stretchout but would be found as 
they project on the turned section of $-/S. 

Intersection of Cylinder and Cone. 

To find the intersection of a cylinder and a cone the cutting 
planes may be taken so as to pass through the vertex of the cone 
and parallel to the elements of the cylinder, thus cutting ele- 
ments from both cylinder and cone; or with a right cone they may 
be taken perpendicular to the axes, so as to cut circles from the 



DEVELOPED SURFACES AND INTERSECTIONS 



113 



cone. Both these methods are illustrated in Fig. 221. Some 
judgment is necessary in the selection both of the direction and 
number of the cutting planes. More points need be found at the 




FIG. 221. Intersection of cylinder and cone. 

places of sudden curvature or change of direction of the line of 
intersection. 

Cutting spheres instead of planes may be used to advantage in 
some cases. If any surface of revolution be cut by a sphere whose 





FIG. 222. 



FIG. 223. 



center is on the axis of revolution, the intersection will be a 
circle. This principle may be employed in finding the inter- 
section of a cylinder and cone of revolution, whose axes intersect, 
8 



114 



ENGINEERING DRAWING 



as in Fig. 222. If spheres be drawn with, center at the intersec- 
tion of the axes they will cut circles from each, whose intersection 
will be points on the curve. 

The intersection of two cones of revolution may be found in the 
same way, Fig. 223. The cone B would be developed by cutting 
a right section as S-S whose stretchout will be a circle arc, locat- 
ing the elements on it and finding the true length of each from 
the vertex to the line of intersection 




FIG. 224. Intersection of a surface of revolution and a plane. 

It is often necessary on a drawing to represent the line of inter- 
section of a plane and a surface of revolution, such as is shown 
in Fig. 224. The method is clearly illustrated in the figure. A 
series of planes as S-S are passed perpendicular to the axis of 
revolution, cutting out the circles shown on the end view. The 
points at which these circles cut the "flat" are projected back 
as points on the curve. 

PROBLEMS. 

Selections from the following problems may be constructed 
accurately in pencil, without inking. Any practical problem can 
be resolved into some combination of the "type solids," and the 
exercises given illustrate the principles involved in the various 
combinations. 

When time permits, an added interest in developments may 



DEVELOPED SURFACES AND INTERSECTIONS 



115 



be found by working the problems on suitable paper, allowing for 
lap, and cutting them out. 

In the sheet metal shops, development problems, unless very 
complicated, are usually laid out directly on the iron. 

Except when noted, the following problems may be drawn in a 
space 4"x5". 




Group I. Prisms, Fig. 225. 

Prob. 1. Develop entire surf ace of triangu- 
lar prism (A) 
2. Develop entire surface of pentag- 
onal prism (B) 





FIG. 226. 

3. Develop entire surface of oblique 
square prism (C) 

4. Develop entire surface of triangu- 
lar prism (D) 



116 ENGINEERING DRAWING 

Group II. Cylinders, Fig. 226. 

Prob. 5. Develop entire surface of cylinder (A) 

6. Develop three-piece elbow (B) 

7. Develop one section of octagonal 




FIG. 227. 



roof and find true shape of a hip 
rafter (C) 

8. Develop one section of dome, and 
find true shape of hip (D) 




FIG. 228. 

Group III. Pyramids, Fig. 227. 

Prob. 9. Develop entire surface of triangu- 
lar pyramid (A) 

10. Develop pattern for octagonal 
lamp shade (B) 

11. Complete top view, and develop 
surface of pentagonal pyramid (C) 



DEVELOPED SURFACES AND INTERSECTIONS 

12. Complete top view and develop 
surface of oblique hexagonal 
pyramid (D) 

Group IV. Cones, Fig. 228. 

Prob. 13. Complete top view, and develop 

cone (A) 

14. Complete top view, and develop 
flange and hood cones of (B) 

15. Complete top view, and develop 
cone (C) 

16. Complete top view, and develop 
cone (P) 



117 




FIG. 229. 



Group V. Triangulation, Fig. 229 (space 5"x 8"). 

Prob. 17. Develop conical connector (A) 

18. Develop connnector (B) 

19. Develop transition piece (C) 

20. Develop transition piece (D) 

21. Develop offset boot (E) 

22. Develop three-way pipe (F) 



118 ENGINEERING DRAWING 

Group VI. Intersection of Prisms, Fig. 230 (space 5"x 8") 
Prob. 23. Find the line of intersection of 

two prisms (A) 

24. Find the line of intersection of 
two prisms (B) 

25. Find the line of intersection of 
two prisms (C) 




26. Find the line of intersection of 

two prisms (D) 

Develop the surface of the larger prism in Probs. 23, 24, 25, 26. 

Group. VII. Intersection of Cylinders, Fig. 231. 
Prob. 27. Find the line of intersection of 

two cylinders (A) 

28. Find the line of intersection of 
two cylinders (B) 



DEVELOPED SURFACES AND INTERSECTIONS 

29. Find the line of intersection of 
two cylinders (C) 

30. Find the line of intersection of 
two cylinders (D) 



119 




FIG. 231. 

Group VIII. Intersection of Cylinder and Cone, Fig. 232. 
Prob. 31. Find the line of intersection of 

cylinder and cone (A) 

32. Find the line of intersection of 
cylinder and cone (B) 

33. Find the line of intersection of 
cylinder and cone (C) 

34. Find the line of intersection of 
cylinder and cone (D) 

35. Find the line of intersection of 
cylinder and cone (E) 

36. Find the line of intersection of 
cylinders and cone (F) 



120 



ENGINEERING DRAWING 




FIG 232. 




FIG. 233. 



DEVELOPED SURFACES AND INTERSECTIONS 



121 



Group IX. Intersection of Two Cones, Fig. 233. 
Prob. 37. Find line of intersection of two 

cones (A) 

38. Find line of intersection of two 

cones (B) 

If desired, any of the figures in Groups VII, VIII and IX may 
be developed, in a space 4" x 5". 




FIG. 234. 

Group X. Intersection of Surfaces by Planes, Fig. 234, 
Prob. 39. Find line of intersection of (A) 

40. Find line of intersection of (B) 

41. Find line of intersection of (C) 

42. Find line of intersection cut by 
planes R and S from cast-iron 
transition piece (D) 

43. Find line of intersection cut by 
planes R S and T from cast-iron 
transition elbow (E) 



CHAPTER VIII. 
PICTORIAL REPRESENTATION. 

We have noted the difference between perspective drawing and 
orthographic projection. Perspective drawing shows the object 
as it appears to the eye, but its lines cannot be measured directly. 
Orthographic projection shows it as it really is in form and 
dimensions, but to represent the object completely we have 
found that at least two projections were necessary, and that an 
effort of the geometrical imagination was required to visualize 
.it from these views. To combine the pictorial effect of perspec- 
tive drawing with the possibility of measuring the principal 
lines directly, several kinds of one plane projection or conven- 
tional picture methods have been devised, in which the third 
dimension is taken care of by turning the object in such a way 
that three of its faces are visible. With the combined advan- 
tages will be found some serious disadvantages which limit their 
usefulness. They are distorted until the appearance is often 
unreal and unpleasant; only certain lines can be measured; the 
execution requires more time, particularly if curved lines occur, 
and it is difficult to add many figured dimensions, but with all 
this, the knowledge of these methods is extremely desirable and 
they can often be used to great advantage. Structural details 
not clear in orthographic projection may be drawn pictorially, 
or illustrated by supplementary pictorial views. Technical 
illustrations, patent office drawings and the like are made 
advantageously in one plane projection; layouts and piping plans 
may be shown, and many other applications will occur to drafts- 
men who can use these methods with facility. One of the uses to 
which we shall apply them is in testing the ability to read^ortho- 
graphic projections bv translating into pictorial representation. 

Isometric Drawing. 

The simplest of these systems is isometric drawing. 
If a cube in orthographic projection, Fig. 235, be conceived as 
revolved about a vertical axis through 45 degrees, then tilted 

122 ' 



PICTORIAL REPRESENTATION 



123 



forward until the edge AD is foreshortened equally with A B and 
AC, the front view in this position is said to be in isometric 
(equal measure) projection. The three lines A B, AC and AD 
make equal angles with each other and are called the isometric 
axes. Since parallel lines have their projections parallel, the 
other edges of the cube will be respectively parallel to these axes. 
Any line parallel to an isometric axis is an isometric line, and the 
planes of these axes and all planes parallel to them are called 
isometric planes. It will thus be noticed that any line or plane 





FIG. 235. Revolution to isometric position. 

which in its orthographic projection is perpendicular to either of 
the reference planes, will be an isometric line or plane. 

In this isometric projection the lines have been foreshortened 
to approximately 81/100 of their length and an isometric scale 
to this proportion might be made as drawn in Fig. 236. If the 
amount of foreshortening be disregarded and the full lengths 
laid off on the axes, a figure slightly larger but of exactly the 
same shape would result. This is known as isometric drawingt 
As the effect of increased size is usually of no consequence, and 
the advantage of measuring the lines directly with an ordinary 
scale is a great convenience, isometric drawing is used almost 
exclusively instead of isometric projection. 

To make an isometric drawing of a rectangular object start 
with the three axes 120 degrees apart, drawing one vertical, the 
other two with the 30-degree triangle. Let this represent the 
front corner of the object and measure on the three lines its 
length, breadth and thickness, Fig. 237. To draw intelligently in 
isometric it is only necessary to remember the direction of the 
three principal isometric planes. Hidden lines are always 
omitted except when necessary for the description of the piece. 



124 



ENGINEERING DRAWING 



Lines not parallel to one of the isometric axes are called non- 
isometric lines. The first rule is, measurements can be made only 
on isometric lines; and conversely, measurements cannot be made 
on non-isometric lines. Thus the diagonals of the face of the 
cube, Fig. 235, are non-isometric lines, and although equal in 





FIG. 236. An isometric scale. 



FIG. 237. The isometric axes. 



length, are evidently of very unequal length on the isometric 
drawing. 

To draw an object composed of non-isometric lines, an iso- 
metric construction must be built up and the points located by 





FIG. 238. Isometric construction lines. 



isometric coordinates. Thus the hexagonal prism, Fig. 238, 
may be enclosed in the rectangular box and the corners located 
on these isometric lines by measuring the orthographic projection. 
It is not at all necessary actually to enclose the object in rec- 
tangular construction. In many instances it is better to get the 



PICTORIAL REPRESENTATION 



125 



isometric coordinates by offsets. Figs. 239 and 240 are self- 
explanatory. 

Of course angles in isometric drawing cannot be measured in 
degrees. In general to represent any angles, or combination of 
non-isometric lines, their orthographic view must be drawn first, 




FIG. 239. Offset construction. 

adding construction lines which can be drawn isometrically, and 
transferring the measurements from the orthographic to these 
isometric lines. 

A circle on any isometric plane would be projected as an 
ellipse. It may be constructed from the orthographic projection 
by coordinates, or by the method of conjugate diameters. A 




FIG. 240. Offset construction. 

four-centered circle-arc approximation sufficiently accurate for 
all ordinary work is made by drawing a perpendicular from the 
point of tangency, that is, the middle point of each side of the 
square. As the center of any arc tangent to the line at this point 
must lie on the perpendicular, the intersections of these perpen- 



126 



ENGINEERING DRAWING 



diculars would be centers for arcs tangent to two sides, Fig. 241. 
Two of these intersections will evidently fall in the corners of the 
square, as the lines are altitudes of equilateral triangles. The 
construction of Fig. 241 may thus be made by simply drawing 




FIG. 241. Approximate isometric circle. 

60-degree lines from the corners A and B. To draw any circle- 
arc, the isometric square of its diameter should be drawn in the 
plane of the face, with as much of this construction as is necessary 
to find centers for the part of the circle needed. Fig. 242 shows 
arcs on the three visible faces with the construction indicated. 




FIG. 242. Construction of isometric circles. 



If a true ellipse be plotted in the same square as this four- 
centered approximation it will be a little longer and narrower, 
and of more pleasing shape, but in the great majority of drawings 
the difference is not sufficient to warrant the extra expenditure 



PICTORIAL REPRESENTATION 



127 



of time required in execution. The construction of a closer 
approximation with eight centers as illustrated in Fig. 243. This 
might be used when a more accurate drawing of an inscribed 
circle is required. 

It is evident that the isometric drawing of a sphere would 





FIG. 243. 



FIG. 244. Reversed axes. 



have a diameter equal to the long axis of the ellipse inscribed in 
the isometric square of the real diameter of the sphere, as this 
ellipse would be the isometric of a great circle of the sphere. 

It is often desirable to show the lower face of an object by 
tilting it back instead of forward, thus reversing the axes to the 




FIG. 245. Construction with reversed axes. 

position of Fig. 244. The construction is just the same but the 
direction of the principal isometric planes must be remembered. 
Figs. 245 and 246 are applications. Sometimes a piece may be 
shown to better advantage with the main axis horizontal as in 
Fig. 247. 



128 



ENGINEERING DRAWING 




FIG. 246. Architectural detail on reversed axes. 




FIG. 247. Main axis horizontal. 





FIG. 248. Isometric section. 



FIG. 249. Isometric half section. 



PICTORIAL REPRESENTATION 



129 



The isometric section and half section may sometimes be 
employed to good advantage. The cutting planes are taken as 
isometric planes, and the section lining done in a direction to give 
the best effect. Figs. 248 and 249 are examples. 

Shade lines in isometric drawings have no value so far as aiding 
in the reading is concerned, but they may by their contrast add 




FIG. 250. 



FIG. 251. 



some attractiveness to the appearance. Assuming the light as 
coming from the left in the direction of body diagonal of a cube, 
and disregarding shadows, shade lines separating light from dark 
faces would be added as in Fig. 250. 

Another method popular among patent draftsmen and others 
using this kind of drawing for illustration, is to bring out the 
nearest corner with heavy lines, as Fig. 251. 




FIG. 252. Illustration of first rule. 

Oblique projection, sometimes called cavalier projection, is 
based on the theoretical principle that with one face of the object 
parallel to the picture plane, if the projectors instead of being 
perpendicular to it as in orthographic and isometric, make an 
angle of 45 degrees with it in any direction, lines perpendicular 
9 



130 



ENGINEERING DRAWING 



to the plane would be projected in their true length. It ,would 
thus be similar to isometric in having three axes, representing 
three mutually perpendicular lines, upon which measurements 
could be made. Two of th axes would always be at right angles 
to each other, being in the plane parallel to the picture plane, 




FIG. 253. Illustration of second rule. 



and the cross axis might be at any angle, 30 degrees being gener- 
ally used. Thus any face parallel to the picture plane will be 
projected without distortion, an advantage over isometric of 
particular value in the representation of objects with circular or 




FIG. 254. (A) not (B). 



irregular outline, and the first rule for oblique projection would 
be, place the object with the irregular outline or contour parallel 
to the picture plane. Fig. 252 A instead of B or C. 

One of the greatest disadvantages in the use of either isometric 
or oblique drawing isthe effect of distortion produced by the lack 



PICTORIAL REPRESENTATION 



131 



of convergence in the receding lines, the violation of perspective. 
This in some cases, particularly with large objects, becomes so 
painful as practically to prohibit the use of these methods. It 
is perhaps even more noticeable in oblique than in isometric, 
and of course increases with the length of the cross axis. Hence 




FIG. 255. 

the second rule, always have the longest dimension parallel to 
the picture plane. A not B in Fig. 253. 

In case of conflict between these two rules the first should 
have precedence, as the advantage of having the irregular face 
without distortion is greater than is gained by the second rule. 
Fig. 254. 




FIG. 256. Offsets from right section. 

It will be noted that so long as the front of the object is in one 
plane parallel to the plane of projection, the front face of the 
oblique projection is exactly the same as the orthographic. 
When the front is made up of more than one plane, particular 
care must be exercised in preserving the relationship by selecting 
one as the starting plane and working from it. In such a figure 
as the link, Fig. 255, the front bosses may be imagined as cut off 



132 



ENGINEERING DRAWING 



on the plane A-A, and the front view, i.e., the section on A-A 
drawn as the front of the oblique projection. On axes through 
the centers C and D the distances CE behind and CF in front may 
be laid off. When an object has no face perpendicular to its 




FIG. 257. Piping system in oblique drawing. 

base it may be drawn in a similar way by cutting a right section 
and measuring offsets from it as in Fig. 256. 

This offset method, previously illustrated in the isometric 
drawings, Figs. 239 and 240, will be found to be a most rapid and 
convenient way for drawing almost any figure, and it should be 
studied carefully. 





FIG. 258. Circle construction. 



FIG. 259. "Cabinet" drawing. 



Fig. 257 is an illustration of a piping lay-out, showing the value 
of oblique drawing in explaining clearly what would be very 
difficult to represent in orthographic. 

Circles in oblique drawing may either be plotted, or may be 
drawn approximately, on the same principle as Fig. 241, by 
erecting perpendiculars at the middle points of the containing 
square. In isometric it happens that one intersection falls in 



PICTORIAL REPRESENTATION 



133 



the corner of the square, and advantage is taken of the fact. 
In oblique its position depends on the angle of the cross axis. 
Fig. 258 shows three oblique squares at different angles and their 
inscribed circles. 

Cabinet drawing is a modification of oblique projection in 
which all the measurements parallel to the cross axis are reduced 
one-half, in an attempt to overcome the appearance of excessive 
thickness produced in oblique drawing. The cabinet drawing 
Fig. 259 may be compared with the oblique drawing Fig. 255. 

Axonometric Projection. 

The principle of isometric projection was shown in the double 
revolution of the cube. A cube might be revolved into any 
position showing three of its faces, and the angles and proportion- 
ate foreshortening of the axes used as the basis for a system of 




rr=Uk5--. 
FIG. 260. Dimetric projection. 

pictorial representation, known in general as axonometric (or 
axometric) projection. Isometric projection is therefore simply 
a special case in which the axes are foreshortened equally. 

Other positions which would show less distortion may be 
chosen, but on account of the added time and special angles 
necessary for their execution, are not often used. 

When two axes are equal, and the third unequal, the system 
is sometimes called "dimetric" projection. A simple dimetric 
projection in which the ratios are 1:1:1/2 is shown in Fig. 260. 
In this position the tangents of the angles are 1/8 and 7/8, 
making the angles approximately 7 and 41 degrees. 



134 



ENGINEERING DRAWING 



A simple and pleasing system known as clinographic projection 
is used in the drawing of crystal figures in mineralogy. It is a 
form of oblique projection in which the figure is imagined as 
revolved about a vertical axis through an angle whose tangent 
is 1/3, then the eye (at an infinite distance) elevated through an 
angle whose tangent is 1/6. Fig. 261 is a graphic explanation. 



(1) 
cube. 

(2) 
(3) 



represents the top and front views of the three axes of a 



1/3. 



is the top view revolved through tan- 
is .the side view of (2) . 
(4) is a front view projected from (2) and (3), the projectors 
from (3) being at tan" 1 1/6. 




FIG. 261. Analysis of clinographic axes. 

When used in crystallography a diagram of the axes is usually 
constructed very accurately on card board, and used as a templet 
or^stencil, transferring the center and terminal points by pricking- 
through to the sheet on which the drawing is to be made. Fig. 
262 shows, in stages, a method of constructing this diagram, 
which as will be seen is simply a combination in one view of 2 
3, and 4 of Fig. 261. Take MON of convenient length, divide 
it into three equal parts, at G and H, and draw perpendiculars as 
shown. Make MS = 1/2 MO and draw SVD. Then CD will be 
one horizontal axis. 

Make ML =1/2 OG and draw LO. Project the point of inter- 
section of LO and GC back horizontally to LM at A, then AOB 
will be the other horizontal axis. 



PICTORIAL REPRESENTATION 135 

To obtain length of vertical axis make ME' = OG, and lay off 
OE and OF = OE'. 




_^4^S$fe 



f J^ 
^' 



FIG. 262. Stages of construction of clinographic axes. 

The axial planes, and some crystals drawn on these axes, are 
shown in Fig. 263. 




FIG. 263. Crystals in clinographic projection. 

These axes are for the isometric system of crystals. Axes for 
the other crystal systems may be constructed graphically in the 









T 


V* 





p* 



FIG. 264. 



FIG. 265. 



same way, by drawing their orthographic projections, revolving, 
and projecting to the vertical plane with oblique projectors as 
was done in Fig. 261. 



136 



ENGINEERING DRAWING 



PROBLEMS. 

The following problems are intended to serve two purposes; 
they are given first, for practice in the various methods of pictor- 



hh 




*<M 

J 



I 



m 



FIG. 266. 



FIG. 267. 



ial representation, second, for practice in reading and translating 
orthographic projections. 




FIG. 268. 



They may be drawn in a space not to exceed 4x5 inches, and 
are arranged in groups for convenience in selection and assign- 





I 








- ?z~- 




1 





FIG. 269. 



FIG. 270. 



ment; but any of the figures may, if desired, be drawn in one of 
the other methods. Some of the figures in Chapter VI may be 
used for a still further variety of problems in this connection. 



PICTORIAL REPRESENTATION 



137 



Do not show invisible lines, except when necessary to explain 
construction. 

Group I. Isometric Drawing : 

Prob. 1. Isometric drawing of the oil-stone, Fig. 264. 
Full size. 



I 





FIG. 271. 



FIG. 272. 



2. Isometric drawing of truncated pyramid, Fig. 265. 
Full size. 

3. Isometric drawing of steps, Fig. 266. Full size. 

4. Isometric drawing of a 1 1/2" cube with circles on 
the three visible faces (approx. method) . 





Bottom 



FIG. 273. 



FIG. 274. 



5. Isometric drawing of brass, Fig. 267. Scale 
6"=!'. 

6. Isometric drawing of bracket, Fig. 268. Full size. 
Prob. 7. Isometric drawing of brick, Fig. 269. Full size. 

8. Isometric drawing of brick, Fig. 270. Full size. 



138 



ENGINEERING DRAWING 



9. Isometric drawing of core box, Fig. 271. Full size. 

10. Isometric drawing of block, Fig. 272. Full size. 

11. Isometric drawing of knee brace, Fig. 273. Scale 
1/2"=!'. 




Boffom ^/ens 



FIG. 275. 

12. Isometric drawing of mitered corner (face return), 
Fig. 274; axes reversed to show under side. Scale 
6"=!'. 

13. Isometric drawing of stone (springing stone of 
plate band, or flat arch) Fig. 275, axes reversed. 
Full size. 





FIG. 276. 



FIG. 277. 



Group II. Isometric Sections : 

Prob. 14. Isometric section of cap, Fig. 276. Scale 3"=!'. 
15. Isometric section of pulley, Fig. 277. Scale 
6"=!'. 



PICTORIAL REPRESENTATION 



139 



16. Isometric half-section of cone, Fig. 278. Scale 
6"=!'. 

17. Isometric half-section of gland, Fig. 279. Scale 
6"=!'. 





FIG. 278. 

Group III. Oblique Drawing: 

Prob. 18. Oblique drawing of block, Fig. 280, 30 degrees to 
the left. Full size. 

19. Oblique drawing of block, Fig. 281, 30 degrees to 
the right, full size. 

20. Oblique drawing of grindstone, Fig. 282, 45 de- 
grees to the right. Scale 1"=!'. 








FIG. 280. 

21. Oblique drawing of 1 1/2" cube, 30 degrees to the 
right, with circles on the three visible faces 
(approximate) . 

22. Oblique drawing of 1 1/2" cube, 45 degrees to the 
left, with circles on three visible faces (approxi- 
mate) . 

23. Oblique drawing of column section, Fig. 283, 30 
degrees to the left. Scale 1 1/2"= I'. 

24. Oblique drawing of monument, Fig. 284, 30 
degrees to the right. Scale 1/2"=!'. . 



140 



ENGINEERING DRAWING 



25. Oblique drawing of gland, Fig. 285, 45 degrees 
to the right. Full size. 

26. Oblique drawing of angle brace, Fig. 286, 30 
degrees to the left. Scale 6"= I'. 





FIG. 282. 



FIG. 283. 





FIG. 285. 



FIG. 284. 



Ttr Hfrai 




tl^g 



FIG. 286. 



27. Oblique drawing of slotted link, Fig. 287, 30 
degrees to the left. Scale 1 1/2"= 1'. 

28. Oblique drawing of bell-crank, Fig. 288, 45 
degrees to the left. Scale 6"=!'. 



PICTORIAL REPRESENTATION 



141 



29. Oblique drawing of link, Fig. 289, 30 degrees to 
the right. Full size. 

30. Oblique drawing of cap, Fig. 290, 45 degrees to 
the left. Scale 6"=!'. 




FIG. 287. 





FIG. 291. 




FIG. 290. 




FIG. 292. 



31. Oblique drawing of cam, Fig. 291, 30 degrees to 
the right. Scale 3"= V . 

32. Oblique drawing of bearing. Fig. 292, 30 degrees 
to the right. Scale 6"=!'. 



142 



ENGINEERING DRAWING 



33. Oblique drawing of moulded brick and face 
return, Fig. 293, 45 degrees to the right, axes 
reversed to show under side. Scale 3" = !'. 

34. Oblique drawing of culvert arch, Fig. 294, 30 
degrees to the left, draw by offsets from right 
section. Full size. 



s- 



I-*"' 




T 

*o 

L 



FIG. 293. 



i 



i 




1 



==$ 






FIG. 295. 



FIG. 294. 



ftf" 



//* 



S-4-'- 
-a-7- 






FIG. 296. 




FIG. 297. 



FIG. 298. 



Group IV. Cabinet and Dimetric Projection. 

Prob. 35. Cabinet projection of frame, Fig. 295. Scale 
3/4"=!'. 



PICTORIAL REPRESENTATION 



143 




144 



ENGINEERING DRAWING 



36. Cabinet projection of desk, Fig. 296. Scale 
1" = !'. 

37. Dimetric Projection of table, Fig. 297. Scale 
3/4"=!'. 

38. Dimetric projection of Roman chair, Fig. 298. 
Scale 1"=!'. 








J L 





FIG. 300. Reading exercises. 

Group V. Reading Exercises. 

Assuming that the student is now familiar with the methods 
of pictorial representation, the objects in Fig. 299 and 300 are 
given to test further the ability to read orthographic projec- 
tions, by sketching the figures shown, in any one of the pictorial 
systems. 

Some may be read at a glance, others will require careful com- 
parison of the different views before the mental image of the 
object is clearly defined.' 



CHAPTER IX. 
WORKING DRAWINGS. 

A working drawing is a drawing that gives all the information 
necessary for the complete construction of the object represented. 

It will thus include: (1) The full graphical representation of 
the shape of every part of the object. (2) The figured dimen- 
sions of all parts. (3) Explanatory notes giving specifications 
in regard to material, finish, etc. (4) A descriptive title. 

Although isometric, oblique and cabinet drawing are used to 
some extent in special cases, the basis of practically all working 
drawing is orthographic projection. To represent an object 
completely, at least two views would be necessary, often more. 
The only general rule would be, make as many views as are 
necessary to describe the object, and no more. 

Instances may occur in which the third dimension is so well 
understood as to make one view sufficient, as for example in the 
drawing of a shaft or bolt. In other cases perhaps a half dozen 
views might be required to show the piece completely. Some 
thought will be involved as to what views will show the object 
to the best advantage; whether an auxiliary view will save one 
or more other views, or whether a section will better explain the 
construction than an exterior view. One statement may be 
.made with the force of a rule If anything in clearness may be 
gained by the violation of any one of the strict principles of 
projection, violate it. 

This statement is of sufficient importance to warrant several 
examples, although there is no guide but the draftsman's judg- 
ment as to when added clearness might result by disregarding a 
theoretical principle. 

If a six-arm wheel, Fig. 301, be shown in section as if cut by a 

plane A- A, the true projection would be as A; if cut by a plane 

B-B the true projection would be as B. Neither of these would 

be good practical working drawings, the first does not show the 

10 145 



146 



ENGINEERING DRAWING 



true size of the arm, the second is misleading. The sectional 
view whether taken on A-A or B-B would be better if made as C. 




(NOT) 



FIG. 302. Section through a rib. 



Similarly, if a section taken through a rib, as the section S-S 
of the piston, Fig. 302, is cross-hatched as in A the effect is mis- 
leading. Its character may be indicated much better by 



WORKING DRAWINGS 



147 



omitting the lining on the rib, as if the section were just in front 
of it, as at B, or by running every other line across the rib 
section, as at C. 

Often a true section would give an unsymmetrical appearance 
to the drawing of a symmetrical piece. In such cases principle 
should be violated to preserve the effect of symmetry. Fig. 303 
is an illustration. 




(NOT) B 



FIG. 303. A symmetrical section. 



Classes of Working Drawings. 

Working drawings may be divided into two general classes, 
assembly drawings and detail drawings. 

An assembly drawing or general drawing is, as its name implies, 
a drawing of the machine or structure showing the relative 
positions of the different parts. 

A detail drawing is the drawing of a separate piece or group of 
pieces, giving the complete description for the making of each 
piece. In a very simple machine the assembly drawing may be 
made to serve as a detail drawing by showing fully the form and 
dimensions of each part composing it. 

Under the general term assembly drawing would be included 
preliminary design drawings and layouts, piping plans, and final 
complete drawings used for assembling or erecting the machine 
or structure. 

The design drawing is the preliminary layout, full size if 
possible, on which the scheming, inventing, and designing is 
worked out accurately after freehand sketches have determined 
the general ideas. From it the detail drawings of each piece are 
made. The design drawing may be finished and traced to form 
the assembly drawing, or the assembly drawing may be drawn 
from it, perhaps to smaller scale to fit a standard sheet. 



148 ENGINEERING DRAWING 

The assembly drawing would give the over-all dimensions, the 
distances from center to center or from part to part of the 
different pieces, indicating their location and relation so that the 
machine could be erected by reference to it. 

The grouping of the details is entirely dependent upon the 
requirements of the shop system. In a very simple machine 
and if only one or two are to be built, all the details may perhaps 
be grouped on a single sheet. If many are to be built from the 
same design, each piece may have a separate sheet. In general, 
it is a good plan to group the parts of the same material or 
character. Thus forgings may be grouped on one sheet, bolts 
and screws on another. 

A complete set of working drawings therefore consists of 
assembly sheets, and detail sheets for each of the classes of work- 
men, as the patternmaker, blacksmith, machinist, etc. These 
special drawings need not include dimensions not needed by 
those trades. The set may include also drawings for the 
purchaser. 

There is a "style" in drawing, just as there is in literature, 
which in one way indicates itself by the ease of reading. Some 
drawings " stand out," while others which may contain all the 
information are difficult to decipher. Although dealing with 
"mechanical thought," there is a place for some artistic sense in 
mechanical drawing. The number, selection, and disposition of 
views, the omission of anything unnecessary, ambiguous, or 
misleading, the size and placing of dimensions and lettering, and 
the contrast of lines are all elements concerned in the style. 
Order of Penciling. 

In penciling a working drawing the order should be as follows : 
first, lay off the sheet to standard size, with border (1/2 inch), 
and block out space for the title; second, plan the arrangement 
by making a little preliminary freehand sketch, guessing roughly 
at the space each figure will occupy, and placing the views to the 
best advantage for preserving if possible a balance in the appear- 
ance of the sheet; third, draw the center lines for each view, and 
on these lay off the principal dimensions. In Chapter VI the 
general principle was given that the view showing the character- 
istic shape should be made first. The different projections should 
however be carried on together and no attempt made to finish 
one view before drawing another. Fourth, finish the projections, 



WORKING DRAWINGS 



149 



putting in minor details last; fifth, draw the necessary dimension 
lines and add the dimensions; sixth, lay off the title; seventh, 
check the drawing carefully. 

Fig. 304 illustrates the stages of penciling a drawing. Over- 
lapping and overextending pencil marks should not be erased 




FIG. 304. Stages of penciling. 

until after the drawing has been inked. These extensions are 
often convenient in preventing the overrunning of ink lines. All 
unnecessary erasing should be avoided as it abrades the surface, 
of the paper so that dirt catches more readily. 




FIG. 305. Stages of inking. 

Order of Inking. 

First, ink all circles, then circle arcs; second, ink the straight 
lines in the order, horizontal, vertical, inclined; third, ink center 
lines; extension and dimension lines; fourth, ink the dimensions; 
fifth, section line all cut surfaces; sixth, ink notes, title, and 
border line; seventh, check the tracing. Figure 305 shows the 
stages of inking. 



150 ENGINEERING DRAWING 

DIMENSIONING. 

After the correct representation of the object by its projec- 
tions, the entire value of the drawing as a working drawing lies 
in the dimensioning. Here our study of drawing as a language 
must be supplemented by a knowledge. of the shop methods 
which will enter into the construction. The draftsman to be 
successful must have an intimate knowledge of pattern making, 
forging, sheet metal working and machine shop practice. 

The dimensions put on a drawing are not those which were 
used in making it, but those necessary and most convenient for 
the workman who is to make the piece. The draftsman must 
thus put himself in the place of the pattern maker, blacksmith or 
machinist, and mentally construct the object represented, to 
see if it can be cast or forged or machined practically and eco- 
nomically, and what dimensions would give the required infor- 
mation in the best way. In brief, the drawing must be made 
with careful thought of its purpose. 
General Rules for Dimensioning. 

In the alphabet of lines in Fig. 62 the dimension line was shown 
as a fine full line, with long arrow heads whose extremities 
indicate exactly the points to which the dimension is taken, and 
having a space left for the figure. 

Some practice uses a long dash line, and some a red line for 
dimension lines. It is common practice among structural 
draftsmen to place the dimension above the continuous line as 
in Fig. 346, but it is not recommended for machine or architec- 
tural work. 

Dimensions of course always indicate the finished size of the 
piece, without any reference to the scale of the drawing. 

Dimensions should read from the bottom and right side of the 
sheet, no matter what part of the sheet they are on. 

Dimensions up to 24" should always be given in inches. An 
exception is again noted in structural practice. Over 24" 
practice varies, but the majority use feet and inches. The sizes 
of wheels, gears, pulleys and cylinder bores, the stroke of pistons, 
and the length of wheel bases are always given in inches; and 
sheet metal work is usually dimensioned in inches. 

Feet and inches are indicated thus 5'-6" or 5 ft.-6". When 
there are no inches, it should be indicated as 5'-0", 5'-(H". 



WORKING DRAWINGS 



151 



Fractions must be made with a horizontal line as 2J", 

The diameter of a circle should be given, not the radius. 

In general give dimensions from center lines, never from the 
edge of a rough casting. 

Have figures large enough to be easily legible. In an effort 
for neatness the beginner often gets them too small. 

Radii of arcs should be marked It or Had. 

Dimensions should generally be placed between views. 









~j 

<Vj 

t, 


J^ 


i 

u 


f- 

t 


'* p 




v v 








3" 








// 


H & 






FIG. 306. Example of dimensioning. 

In general do not repeat dimensions on adjacent views. 

Preferably keep dimensions outside the figure unless added 
clearness, simplicity, and ease of reading the drawing will result 
from placing them in the figure. See Fig. 306. Keep them off 
sectioned surfaces if possible. 

Extension lines should not touch the outline. 

Always give an over-all dimension. Never require the work- 
man to add or subtract figures. 

Never use any center line as a dimension line. 

Never put a dimension on a line of the drawing. 

A dimension not agreeing with the scaled distance, or which 
has been changed after the drawing has been made should be 
heavily underscored as in Fig. 307 (2) , or marked as in (3) . 



152 



ENGINEERING DRAWING 



Dimensions must never be crowded. If the space is small, 
methods as illustrated in Fig. 307 (4) (5) (6) (9), etc., may be used. 

The direction in which a section is taken should be indicated 
by arrows on the line representing the cutting plane, as in (29). 

If it is possible to locate a point by dimensions from two center 
lines, do not give an angular dimension. 



NOT THUS 







"/H h*H -UTI- Hh/ 

(D 








@ 



FHl-fHl J ^ 



FIG. 307. Dimensions. 



The Finish Mark. 

Several methods are used for indicating that certain parts are 
to be machined, and that allowance must therefore be made on 
the casting or forging for finish. The symbol in common use is 
a small "f" placed on the surface, on the view which shows the 
surface as a line, Fig. 307 (26). If the piece is to be finished all 
over, the note "f. all over" is placed under it, and the marks 
on the drawing omitted. 

Another finish mark, proposed by Professor Follows for 
adoption as a standard, is shown at (27). It has a distinct 
individuality, and, by pointing to the line instead of crossing it, 
does not mar the appearance of the drawing as the "f " does. 
The symbol as used in (28) indicates that the entire surface 
between the extension lines is to be finished. 

Some elaborate symbols for different kinds of finish have been 
devised, but it is much better to specify these in words. 

Notes and Specifications. 

Some necessary information cannot be drawn, and hence 
must be added in the form of notes. This would include the 



WORKING DRAWINGS 153 

number required of each piece, the kind of material, kind of 
finish, kind of fit (as force fit, drive fit, etc.), and any other 
specifications as to its construction or use. 

Do not be afraid of putting notes on drawings. Supplement 
the graphic language by the English language whenever added 
information can be conveyed, but be careful to word it so clearly 
that the meaning cannot possibly be misunderstood. 

If a note as to the shape of a piece will save making a view, 
use it. 

If two pieces are alike, but one " right-hand" and the 'other 
"left-hand," one only is drawn and a note added 1-R. H., 1-L. H. 

Standard bolts and screws are never detailed, but are specified 
in the bill of material. 

The bill of material is a tabulated statement placed on a draw- 
ing, or in some cases, for convenience, on a separate sheet, which 
gives the mark, name, number wanted, size, material, pattern 
number, and sometimes the weight, of each piece. A column 
giving the over-all dimensions of the piece when crated or boxed 
for shipping is sometimes added, particularly in manufactures 
for foreign shipment. A final column is usually left for 
" remarks." 

Fig. 308 is a detail drawing illustrating the use of the bill of 
material. 

Title.* 

The title to a working drawing is usually boxed in the lower 
right hand corner, the size of the space varying of course with 
the size of the drawing. For 12"xl8" sheets the space reserved 
may be about three inches long. For 18"x24" sheets four or 
four and a half, and for 24"x36" sheets five or five and a half 
inches. 

A form of title which is growing in favor is the record strip, 
a narrow strip marked off entirely across the lower part of the 
sheet, containing the information required in the title, and 
ample space for the record of orders, changes, etc. Fig. 309 
illustrates this form. 

It is sometimes desired to keep records of orders and other 
private information on the tracing, but not have them appear 

*For a full discussion of titles for different classes of drawings see "The 
Essentials of Lettering/' from which this paragraph is condensed. 



154 



ENGINEERING DRAWING 




WORKING DRAWINGS 



155 



on the print. In such case both the corner title and record 
strip are used, and the record strip trimmed off the print before 
sending it out. 

Contents of Title. 

In general the title of a machine or structural drawing should 
contain: 

(1) Name of machine or structure. 

(2) General name of parts (or simply " details"). 



B895/ 


THE THOMPSON A UTOMOB/LE CO., DETffO/T. M/CH. \ Sca/e 6*/ ' 


<Zi&t<*ur^ 


_/J S. a J<42S 
Chonyeet from /O* 
Change* from /" 


2} 


3J 


CAR A-6-6O-// 

DT^li- 

C.YLJMDE.F3S 

5gX5~ 


T "^ji^^L. 


CH gS&^ 



FIG. 309. A record strip. 

(3) Name of purchaser, if special machine. - 

(4) Manufacturer; company or firm name and address, 

(5) Date; usually date of completion of tracing. 

(6) Scale or scales; desirable on general drawings, often 
omitted from fully dimensioned detail drawings. 

(7) Drafting room record; names, initials or marks of the 
draftsman, tracer, checker, approval of chief draftsman, 
engineer or superintendent. 











The Jeffrey Mfg. Co. 

COLUMBUS, OHIO. U. S. A. 

Engineering Department. 

CONVEYING AND ELEVATING MACHINERY. 


SCALE 


DIRECTED 




APPROVED .. . 


TRACED " 






CHECKED " 
CORRECT " _ 





FIG. 310. A printed title form. 

(8) Numbers; of the drawing, of the order. The filing 
number is often repeated in the upper left hand corner 
upside down, for convenience in case the drawing should 
be reversed in the drawer. 



15G ENGINEERING DRAWING 

The title should be lettered freehand in single stroke capitals, 
either upright or inclined, but never both styles in the same title. 

Any revision or change in the drawing should be noted, with 
date, in the title or record strip. 

Every drafting room has its own standard form for titles. 
In large offices this is often printed in type on the tracing cloth. 
Figs. 310 and 311 are characteristic, examples. 

Sometimes a title is put on with a rubber stamp, and inked 
over while wet. 



GENERAL NOTES. 



WORKMANSHIP- 
MATERIAL 



CONTRACT. 

SHEET No, 



ASSEMBLING PAINT- 
SHOP PAINT 

FIELD PAINT 



BUILT BY 

KING BRIDGE COMPANY 



FIELD CONNECTION* CLEVELAND, OHIO 

F.O. B 

SHIP __^ DRAWINGS FINISHED 



o 



FIG. 311. A printed title form. 

In commercial drafting, accuracy and speed are the two require- 
ments. The drafting room is an expensive department, and 
time is an important element. The draftsmen must therefore 
have a ready knowledge not only of the principles of drawing, 
but of the conventional methods and abbreviations, and any 
device or system that will save time without sacrificing effective- 
ness, is desirable. 



FASTENINGS. 

In every working drawing will occur the necessity of repre- 
senting the methods of fastening parts together, either with 
permanent fastenings (rivets) or with removable ones (bolts, 
screws and keys), and the draftsman must be thoroughly familiar 
with the conventional methods of their representation. 



WORKING DRAWINGS 



157 



The Helix. 

A helix is the line of double curvature generated by a point 
moving uniformly along a straight line while the line revolves 
uniformly about another line, as an axis. 

The distance advanced parallel to the axis in one revolution is 
called the pitch. If the moving line is parallel to the axis it will 
generate a cylinder, and the word "helix" alone always means 
a cylindrical helix. If the moving line intersects the axis (at an 
angle less than 90 degrees) it will generate a cone and the curve 
made by the moving point will be a conical helix. When the 
angle becomes 90 degrees the helix degenerates into a spiral. 



f 2 3 4 5 6 7 S 9 /O///2/ 




FIG. 312. Construction of the helix. 

To Draw a Helix. Divide the circle of the base of the cylinder 
into a number of equal parts, and the pitch into the same number. 
As the point revolves through one division it will advance one 
division of the pitch, when half way around the cylinder it will have 
advanced one-half the pitch. Thus the curve may be found by 
projecting the elements represented by the divisions of the Circle, 
to intersect lines drawn through the corresponding divisions of 
the pitch, as in Fig. 312. 

The conical helix is drawn similarly, the pitch being measured 
on the axis. 

Screw Threads. 

The helix is the curve of the screw thread, but is not often 
drawn, and only with screws of large diameter. Fig. 313 
illustrates its application on a square thread screw and section of 



158 



ENGINEERING DRAWING 



nut. Two helices of the same pitch but different diameters are 
required, one for the tip and one for the root of the thread. If 
many threads are to be drawn, a templet may be made, by laying 
off the projection of the helix on a piece of cardboard, and cutting 
out with a sharp knife. 

Fig. 314 shows the method of drawing a helical spring with 
round section, by constructing the helix of the center line of the 




FIG. 313. Construction of square thread. 

section, drawing on it a number of circles of the diameter of the 
stock, and" drawing an envelope curve tangent to the circles. 

Forms of Threads. 

Screws are used for fastenings, for adjustment, and for trans- 
mitting power or motion. For these different purposes several 
different forms of thread are in use. The United States Standard 




FIG. 314. 

(sometimes called the Franklin Institute, and Sellers standard), 
Fig. 315, A, is the commonest, and in this country is the form 
intended when not otherwise specified. It is a V thread at 
60 degrees with the tip flattened one-eighth of its height, which 
lessens the liability of its being injured, and the root filled the 
same amount, thus increasing the strength of the bolt. In 
drawing, these flats need not be represented. 



WORKING DRAWINGS 



159 



The sharp V at 60 degrees is still used, although it has little^to 
recommend it. The square thread and the Acme or Powell 
thread are used mainly to transmit motion. Other forms shown 
are the buttress, knuckle, and Whitworth, the English standard. 




fA) U. S. STANDARD 
-P 



SHARP V 



SQUARE 




KNUCKLE WH/TWOGTH 

FIG. 315. Forms of screw threads. 

Threads are always understood to be single and right hand 
unless otherwise specified. 

A right hand thread advances away from the body when turned 
clockwise. A left hand thread is always marked plainly "L H," 
and is quickly recognized also by the direction of slant. 




FIG. 316. Conventional threads. 



A single thread has one thread, of whatever section, winding 
around the cylinder. When it is desired to give a more rapid 
advance without using a coarser thread, two or more threads are 
wound together, side by side, giving double and triple threads, as 
illustrated in Fig. 316, C and D. 



160 



ENGINEERING DRAWING 



Conventional Representation of Threads. 

For ordinary practice the labor of drawing the exact curves of 
threads is altogether unnecessary, and the helix is conventional- 
ized into a straight line. The square thread screw would thus 



WfiMffi 



.-V- 



M 4/T/l/l/j/M/Vl - ^W^^^ fjTWK'^i^ 

"" UU- 4^-n- iuU-Sm 4|%Wi% 

ill /U/llllvl 4/1^474^AiA4/ ^H^lMWJ> 



Hiwk- 

FIG. 317. Stages in drawing V threads. 

be drawn as in Fig. 316 (A) or (B), which while not so realistic 
or pleasing as Fig. 313, requires very much less time. 

The V thread would be drawn, both in pencil and ink, in the 
stages shown in Fig. 317. 




For screws less than perhaps one inch in diameter, the thread 
shapes are omitted and one of the conventional forms of Fig. 318 
used.. A is a very common convention. The lines are drawn 
with a slight slant (one-half the pitch), and spaced by eye. The 




FIG. 319. Tapped hoi 



spacing need not be to the correct pitch, but to look well should 
somewhat approximate it. 

The root lines are usually made heavier, for effect. The 
beginner's usual mistake of exaggerating the slant must be care- 
fully guarded against. It is a question as to whether there is 



WORKING DRAWINGS 



161 



any necessity of slanting the lines at all, and in much good 
practice they are drawn straight across. 

B is a simpler convention, in that it requires no pencil lines 
for limiting the root lines, as there is always a center line already 
drawn. In this the root lines are always placed on the shade 
side. 

C is a convention that does not look like a thread, but that can 
be made rapidly, and is understood by all workmen. 

Fig. 319 shows the conventional representation of' tapped 
holes in plan, section and elevation. In showing a tapped hole 




FIG. 320. 



in section the slant of the thread lines would evidently be reversed 
as the part represented fits the invisible side of the screw. In 
tapped holes not extending through the piece, the "drill point," 
or shape of the bottom of the hole should always be shown. 

When two pieces fitted together are shown in section the 
threads must be drawn, as in Fig. 320. The same is true for a 
male thread in section. 

It is not necessary to draw the threads on the whole length of 
a long threaded shaft. They may be started at each end, and 
" ditto" lines used in the space between. 
11 



162 



ENGINEERING DRAWING 



Dimensioning Threads. 

If a thread is U. S. Standard the only dimensions given are 
the outside diameter and the length. When these dimen- 
sions are given the thread is always assumed to be U. S. 
Standard right hand, and the machinist knows the pitch, drill 
sizes, etc. The word "pitch" has been defined as the distance 
between threads. A commonly accepted meaning among 
machinists is the number of threads per inch, thus "8 pitch" 
would mean eight threads per inch. There is very little danger 
of misunderstanding in these two meanings, but it may be safer, 

particularly in screws of large diameter, to say " threads 

per in." 




FIG. 321. U. S. Standard bolts (unfinished). 

With double and triple threads "pitch" is generally accepted 
to mean the distance between adjacent threads, and the distance 
advanced in one revolution is called the "lead." 

A distinction in designation should be made between tapped 
holes and threaded holes. 

Bolts and Nuts. 

There are adopted sizes for standard hexagonal and square 
bolt heads and nuts, hence on a standard bolt no dimensions are 
placed except the diameter, length (under the head to tip of 
point), and length of threaded part. As there is so frequent 
necessity for the representation of bolts and screws the drafts- 
man must be able to draw them without reference to tables or 
measurement. 



WORKING DRAWINGS 



163 



Fig. 321 shows the U. S. Standard hex. head, and the stand- 
ard square head bolt and nut. In drawing a hex. head three 
faces are shown, and in a square head, one face. 



DIMENSIONS OF U. S. STANDARD BOLTS AND NUTS. 



Diam. 
of 
bolt 


Thrd's 
per 
inch 


Distance 
across 

flats 


Distance 
across corners 


Thickness 


Area at 
root of 
thread 


Hexagon 


Square 


Nut 


Head 


F 


20 


I" 


tr 


ir 


r 


F 


.026 


iV 


18 


w 


H* 


w 


TV 


if 


.045 


t" 


16 


w 


ir 


w 


r 


H" 


.068 


T y 


14 


tr 


tr 


w 


7 '/ 
TV 


ir 


.093 


F 


13 


r 


W 


ir 


F 


TV" 


.126 


iV 


12 


tr 


ir 


ir 


T 9 / 


IF 


.162 


r 


11 


W 


nr 


if 


r 


IF. 


.202 


f 


10 


IF 


iff 


itr 


r 


F 


.302 


F 


9 


W 


' itr 


2^/ 


F 


IF 


.420 


i" 


8 


ir 


if" 


2H* 


i r/ 


if 


.550 


IF 


7 


iir 


S// 


2 T 9 / 


IF 


IF 


.693 


IF 


7 


2* 


2 T 5 / 


2ff" 


H" 


1* 


.889 


ir 


6 


2A" 


2ir 


33 3 / 


if 


1A" 


1.054 


IF 


6 


2f 


2f 


3ff 


IF 


1 T 3 F 


1.293 


ir 


5 


2f 


3 T 3 / 


sir 


if 


if 


1.744 


2" 


4i 


sr 


3ir 


4r 


2" 


1 T 9 F 


2.302 



164 



ENGINEERING DRAWING 



A quick method of penciling a standard hex. head or nut is 
shown in stages in Fig. 322. Mark a point on the center line at 




LLTJ 

I ~ezz& * 



FIG. 322. A method of drawing a hexagonal head. 

a distance 1 1/2D + 1/8". Sixty-degree lines drawn from this 
point to the base will give points for the outside corners. The 
remainder of the construction is evident from the figure. 



CTTJ 



LCD 



r 



m 







FIG. 323. Locknuts. 

It is evident from geometry that the projected width of the 
inclined face is one half that of the front face. 

For the conventional representation of the smaller sizes it is 
sufficient to draw the long diameter of the head twice the diam- 
eter of the shaft, and the thickness of both head and nut equal 
to the diameter of the shaft. 

Many different lock-nut devices to prevent nuts from working 
loose, are used in machine design. The jam nut or check nut is 
a common method, Fig. 323, using either two "three-quarters" 
or standard nuts, or one full and one thin nut. Theoretically 
the thin nut should be under, but it is sometimes placed outside. 
D is another application. In automobile work the "castle" nut 
shown in Fig. 324 with pin through the bolt is universally used. 
These are made on the A. L. A. M. (Assn. of Licensed Automobile 
Manufacturers) standard, which has finer threads and smaller 
heads and nuts than the U. S. Standard. A table of sizes of 
A. L. A. M. bolts is given under the figure. 



WORKING DRAWINGS 



165 



Cap screws differ from bolts in that they are used for fastening 
two pieces together by passing through a clear hole in one and 




FIG. 324. A. L. A. M. Standard bolt and castle nut. 



D 


Threads 


A 


B 


c 


E 


F 


H 


K 


L 


i 


28 


I 


$ 


A 


3 9 2 


A 


A 


A 


t 


A 


24 


1 


A 


A 


H 


if 


A 


A 


H 


I 


24 


T 9 <r 


i 


i 


H 


3 9 * 


i 


A 


T^ 


TV 


20 


tt 


1 


i 


H 


H 


i 


A 


H 


* 


20 


t 


i 


A 


A 


1 


i 


A 


f 


T 9 * 


18 


1 


A 


A 


If 


H 


i 


A 


H 


5 




18 


H 


A 


i 


If 


H 


i 


A 


H 


tt 


16 


i 


A 


i 


fi 


If 


i. 


A 


1A 


f 


16 


11 


A 


i 


H 


A 


i- 


A 


H 


1 


14 


H 


A 


i 


If 


H 


1 


A 


1A 


1 


14 


1* 


A 


i 


i 


t 


i 


A 


H 



screwing into a tapped hole in the other. The heads are the 
same thickness as the diameter of the bolt, but are usually 
somewhat smaller in diameter than bolt heads. Some cap screw 



166 



ENGINEERING DRAWING 



heads are made, however, to U. S. Standard. Fig. 325 shows 
six different forms with an accompanying table of sizes. 




SQUAP 



OVAL FILLISTER FLAT FILL/STEP BUTTON 

FIG. 325. Cap screws. 



COUNTERSUNK 



D 


A 


B 


c 


E 


F 


G 


H 


i 


J 


K 


L 


M 


N 





P 


R 


S 


1 












A 


if 


A 


A 


.032 


3V 


A 


.035 


i 


A 


.040 


A 


A 












i 


A 


A 


A 


.040 


A 


A 


.051 


1 


A 


.064 


A 


1 


I 


A 


ft 


I 


f 


t 


H 


A 


A 


.064 


A 


i 


.072 


if 


A 


.072 


A 


A 


A 


i 


1 


A 


1 


A 


If 


A 


i 


.072 


& 


A' 


.091 


f 


A 


.102 


A 


I 


1 


A 


H 


1 


1 


T 9 <5 


If 


A 


& 


.091 


f 


A 


.102 


f 


A 


.114 


if 


A 


TV 


f 


if 


T 9 * 


li 


f 


II 


A 


H 


.102 


1 


3^ 


.114 


if 


A 


.114 


i! 


\ 


i 


I 


U 


f 


li 


f 


it 


i 


T 3 * 


.114 


if 


i 


.114 


1 


& 


.128 


if 


& 


T 9 6 


if 


i* 


ii 


If 


11 


i* 


6\ 


sV 


.114 


if 


A 


.114 


1 


A 


.133 


A 


1 


I 


i 


IT S <T 


f 


li 


1 


1A 


A 


if 


.128 


i 


T 5 <r 


.133 


li 


i 


.133 


1! 


1 


I 


i 


H 


1 


if 


1 


li 


T 3 * 


A 


.133 


U 


t. 


.133 


If 


A 


.133 


A 


1 


I 


li 


Hi 


H 


2i 


H 


1H 


aV 


ft 


.133 
















i 


1 


n 


H 


H 


2i 


H 


1A 


i 


t 


.165 
















H 


H 


it 


2A 


if 


2f 














* 












H 


H 


li 


2i 


li 


3 



























Studs. Threaded studs are bolts having a thread on each end, 
one end to screw into a tapped hole, the other for a nut, Fig. 326. 
The screwed end should be 11/4 to 1 1/2 D long. 



WORKING DRAWINGS 



167 



Set screws are used for holding two parts in relative position, 
being screwed through one part and having the point set against 
the other. They are made with square and hex. heads, whose 
thickness and short diameter are equal to the diameter of the 





FIG. 326. Studs. 



REGULAR LOW HEAD HEADLESS 

FIG. 327. Set screws. 



screw, with low head, and headless, as shown in Fig. 327; and 
with points of different shapes for different purposes, Fig. 328. 
The Allen headless set screw, patented in 1910, with countersunk 




POUND FLAT 



CUP 

FIG. 328. Set screw points. 



CONr 



hexagonal socket, shown in Fig. 330, is approved by factory 
inspectors as safe, and is used where there might be danger of 
clothing being caught in moving parts. 




FLAT POUND FILLISTER FRENCH 
FIG. 329. Machine screws. 



Machine screws are specified by gage number, not by sizes in 
fractions of an inch. Fig. 329 shows the various forms of 
machine screw heads. 



168 



ENGINEERING DRAWING 



A new standard for machine screws was proposed in 1907 by 
the American Society of Mechanical Engineers but has not yet 
come into general use. Tables of these sizes, as well as for other 



ALLEN HEADLESS 
5ET SCREW 




WOOD SCREWS 



COLLAR SCREW 



DRIVE SCREW. 



LAG SCREW 




SHOULDER SCREW 



EXPANSION BOLT 



HANGER BOLT 



CARRIAGE BOLT 




EYE BOLT 





TURN BUCKLES 
FIG. 330. Various bolts and screws. 



WING NUT 



standard screws, may be found in Kent, American Machinist's 

and other handbooks. 

Various other types of bolts and screws are illustrated in Fig. 330. 



F/at Tops 
F/at Bottoms 



\F/af Tops\ 



Complete Threads 



Pound Round Tops and Bottoms 
Bottoms tin* *T~~ ^ J." na - /" 



Bottoms 



f Taper 32 per f of Length 




.8 outside cf/'am. + <4.8 
Threads V~ Number o , Threads per /"' 



FIG. 331. Section of Briggs pipe thread. 



Pipe Threads and Fittings. 

Pipe threads are cut on a taper, known as the Briggs Standard, 
illustrated in enlarged scale in Fig. 331. In drawing pipes the 
taper of the threaded portion is usually slightly exaggerated. 



WORKING DRAWINGS 169 

DIMENSIONS OF STANDARD STEEL AND WROUGHT IRON PIPE. 



Nominal 
inside 
diameter 


Actual 
outside 
diameter 


Actual 
inside 
diameter 


Internal 
area 


Thds. 
per 
inch 


Dist. 
pipe 
enters 


Actual inside diam. 


Extra 
heavy 


Double 

extra 


* 


.405 


.270 


.057 


27 


A 


.205 




I 


.540 


.364 


.104 


18 


A 


.294 




1 


.675 


.494 


.191 


18 


U 


.421 




| 


.840 


.623 


.304 


14 


1 


.542 


.244 


I 


1.05 


.824 


533 


14 


H 


.736 


.422 


1 


1.315 


1.048 


.861 


ill 


1 


.951 


.587 


H 


1.66 


1.38 


1.496 


1U 


If 


1.272 


.885 


H 


1.9 


1.61 


2.036 


m 


A 


1.494 


1.088 


2 


2.375 


2.067 


3.356 


111 


11 


1.933 


1.491 


2| 


2.875 


2.468 


4.78 


8 


! 


2.315 


1.755 


3 


3.5 


3.067 


7.383 


8 


i-f 


2.892 


2.284 


3| 


4 


3.548 


9.887 


8 


i 


3.358 


2.716 


4 


4.5 


4.026 


12.73 


8 


1 T V 


3.818 


3.136 


4J 


5 


4.508 


15.961 


8 


1A 


4.28 


3.564 


5 


5.563 


5.045 


19.986 


8 


iA 


4.813 


4.063 


6 


6.625 


6.065 


28.89 


8 


H 


5.751 


4.875 


7 


7.625 


7.023 


38.738 


8 


if 


6.625 


5.875 


8 


8.625 


7.982 


50.027 


8 


i* 


7.625 


6.875 


9 


9.625 


8.937 


62.72 


8 


IrV 


8.625 




10 


10.75 


10.019 


78.823 


8 


Itt 


9.75 





170 



ENGINEERING DRAWING 



Pipe is designated by the nominal inside diameter, which 
differs slightly from the actual inside diameter, as will be noted 
from the table on page 169. " Extra" and "double extra" heavy 
pipe has the same outside diameter as standard weight pipe of 
the 'same nominal size, the added thickness being on the inside. 
Thus the outside diameter of V r pipe is 1.315, the inside diameter 




S/ZE OF 

PIPE: 



'A 



73 



I 



M 






' 



*t 






'A 



' 



/O 






4 



a 



FIG. 332. Cast iron fittings. 



of standard I" pipe 1.05, of 1" extra strong .951, and of XX, 
.587". 

The dimensions of fittings vary somewhat with the different 
manufacturers. In dimensioning piping the best practice is to 
give figures from center to center of fittings. 

Fig. 332 illustrates some of the ordinary cast iron fittings. 
The dimensions indicated are given in the accompanying table. 

Fig. 333 shows malleable fittings. 



WORKING DRAWINGS 



171 




deducing Union 

Coup/mg / gfa. 




L-A/Cap A ^_ 



A' 



Ji 



I 



~w 



'76 









/xl 



*JL 



FIG. 333. Malleable fittings. 




3O TEETH - CAST Iff ON - FULL SIZE 
FIG. 334. Cast spur gear. 



172 



ENGINEERING DRAWING 




/O P., 48 r. 

DEPTH OF CUT. 3/6 " 

FIG. 335. Cut spur gear. 




FIG. 336. Cast bevel gear. 



WORKING DRAWINGS 173 

Gears. 

While it is not within our scope to take up any machine design, 
it is important that designers know the correct methods for the 
representation of designed parts. In the working drawings of 




5 P/TCfi - 3S TEETH 

Finish a// o\ser 

FIG. 337 Cut bevel gear. 




Ang/e for gashing cuf 5g 

5. 72 "f?D.. "C. P. 36 TEETH 
HARDENED STEEL 

FIG. 338. Worm and gear. 



N( <> Finish a// over 
"c.P. S/NGLE THBEAO 
HARDENED STEEL 



gears and toothed wheels the teeth are never drawn on the wheel. 
For cast gears the pitch circle, addendum circle and root circle 
are drawn, and the full sized outline of one tooth, Fig. 334. 



174 



ENGINEERING DRAWING 



For cut gears the blank is drawn, and notes added for full 
information regarding pitch, cutters, etc., Fig. 335. 

Fig. 336 is a drawing of a cast bevel gear, showing the 
method of complete dimensioning for the construction of the 
pattern. Fig. 337 is a cut bevel gear and Fig. 338 is a worm 
gear. 

On assembly drawings gears are represented as in Fig. 339. 




FIG. 339. 



CONVENTIONAL SYMBOLS. 

The methods of drawing screw-threads and gears just con- 
sidered would be called conventional, as they do not represent 
real outlines of the objects. Other conventions are used for 
electrical apparatus, for materials, etc. 

In specifying the materials of which objects are to be made, 
the safest rule to follow is to add the name of the material as a 
note. There are cases however in which when the piece is shown 
in section, adjacent parts made of different materials can be 
indicated to good advantage by using different characters of 
cross-hatching. 

The commonest example of this is in distinguishing a bearing 
or lining metal poured into place hot, such as babbitt metal. 
It is universal practice to show such metals by the conventional 
symbol of crossed lines shown in Fig. 340. An example of this 
is the lead lined valve, Fig. 144. 



WORKING DRAWINGS 



175 



The quickest way to make this symbol is to section over both 
the lining metal and the adjacent cast iron at once, then cross 
the lining metal in the other direction. 

There have been a number of different codes of symbols pro- 
posed and published for the representation on working drawings 
of different metals and materials. Aside from their doubtful 
value on account of the lack of agreement, they are all open to 
the same objection, that of the added time necessary for their 
execution. 

With the variety of materials used in modern construction it 
is entirely impracticable to have symbols for all. 




LEATHER 

(OTHER FLEXIBLE MATERIALS) 



GLASS LIQUID 

FIG. 340. Symbols for materials in section. 



INSULATING 
MATERIAL 



Fig. 340 gives conventions for a number of different mate- 
rials. Those in the first line are accepted by practically all who 
use conventional cross-hatching. There is much variation in 
the symbols proposed for the other materials shown. Those 
given are part of the ,codes of government standards of the 
Bureau of Steam Engineering and the Bureau of Construction 
U. S. N., who require their use on assembly drawings submitted 
by firms estimating on government work. 

Until a standard is adopted universally it would seem necessary 
to add to a drawing made with symbolical section lining, a key 
to materials, as is done in architectural drawing, or else to letter 
the name of the material on each piece, in which case the fancy 
section-lining would appear to be unnecessary. 



176 



ENGINEERING DRAWING 




SQUARE SECTION 



FIG. 341. Conventional breaks and other symbols. 



(6) (M) |(M) 

} ' re nL2Z ref7f O.C.5hut. 

e ^ij e orM %%* 

lerafor or Motor 

6-6 A 



31 



_j4- 

Crossings 



D. C. Ser/es >.C. Compound 
Dynamo 



-0- 



Pnase TwoPnase 

Alternator 



n TT 



C[ R 

Orcv/t Breaker 



AAAAAAA ^AAA^V 
Resistance Vanaffi/e 



Converter 



Transformer /nsfrvment 
I Transformer 

1 



Jl Jl 

i n 11 R;I 

5.^ &/? ^./? 

^ST: 7: 5.^- 




Sw/fches 



FIG. 342. 



' *Yor5tor . 

Connection Connect/on Connection 



WORKING DRAWINGS 177 

Fig. 341 shows a number of conventional breaks and other 
useful symbols. 

In making a detail of a long bar of uniform section there is 
evidently no necessity for drawing its whole length. It may be 
shown much better by breaking out a piece and giving the length 
in a dimension. 

The crossed diagonals are used for two distinct purposes, to 
indicate position or finish for a bearing, and to indicate a piece 
square in section, but are not apt to be confused. 

Sheet metal and structural shapes in section to small scale may 
be shown most effectively in solid black with white spaces between 
parts. 

Very short section-lines are best made freehand. 

Fig. 342 gives a set of electrical diagrammatic symbols. 
There is no universal standard, but of those proposed here a 
number are in general use. The standard wiring symbols of the 
National Electrical Contractors Association is given on page 221. 

COMMERCIAL SIZES. 

The following notes give the commercial methods of specifying 
sizes of the items in the list. The material must, of course, 
always be specified. 

Chain. Give diameter of rod used. 

Electrical Conduit. Same as pipe. 

Pipe. Give nominal inside diameter. 

R. R. Rails. Give height of section and weight per yard. 

Rolled Steel Shapes; Give name, essential dimensions and 
weight per foot. 

Rope. Give largest diameter. 

Shafting. The best practice is to give the actual diameter. 

Sheet Metal. Give thickness by gage number, or in thou- 
sandths of an inch (for 3/ 16" and over, give thickness in fractions). 

Springs. Helical, give outside diameter, gage of wire, and 
coils per inch when free. 

Tapered Pieces. Give size at small end, and taper per foot. 

Tubing. Give outside diameter and thickness. 

Wire. Give diameter by gage number or in thousandths of 
an inch. 

Wire Cloth. Give number of meshes per lineal inch, and gage 
of wire. 
12 



178 ENGINEERING DRAWING 

Wood Screws. Give length, diameter by number, and kind of 
head. 

Special. Manufactured articles or fittings, give manufacturer's 
name and catalogue number. 

CHECKING. 

Before being sent to the shop, a working drawing must be 
checked for errors and omissions by an experienced checker, who 
in signing his name to it becomes responsible for any inaccuracy. 
This is the final "proof-reading" and cannot be done by the one 
who has made the drawing nearly so well as by another person. 
In small offices all the work is checked by the chief draftsman, 
and draftsmen sometimes check each other's work; in large 
drafting rooms one or more checkers who devote all their time 
to this kind of work are employed. 

Students may gain experience in this work by being assigned 
to check other students' work. 

To be effective, checking must be done in an absolutely 
systematic way, and with thorough concentration. 

Professor Follows in his "Dictionary of Mechanical Drawing" 
has specified admirably the work of checking, in twelve items, 
which are given with his permission. Each of these should be 
followed through separately, allowing nothing to distract the 
attention from it. As each dimension or feature is verified a 
checkmark should be placed above it. 

1. Put yourself in the position of those who are to read the 
drawing and find out if it is easy to read and tells a 
straight story. Always do this before checking any 
individual features; in other words, before you have 
had time to become accustomed to the contents. 

2. See that each piece is correctly illustrated and that all 

necessary views are shown, but none that are not 
necessary. 

3. Check all the dimensions by scaling, and, where advisable, 

by calculation also. 

4. See that dimensions for the shop are given as required by 

the shop, that is, that the shop is not left to do any 
adding or subtracting in order to get a needed dimension. 



WORKING DRAWINGS 179 

5. Go over each piece and see that finishes are properly 

specified. 

6. See that every specification of material is correct and that 

all necessary ones are given. 

7. Look out for " interferences." This means check each 

detail with the parts that will be adjacent to it in the 
assembled machine and see that proper clearances have 
been allowed. 

8. When checking for clearances in connection with a mechan- 

ical movement, lay out the movement to scale, figure 
the principal angles of motion and see that proper 
clearances are maintained in all positions. 

9. See that all the small details, as screws, bolts, pins, keys, 

rivets, etc., are standard and that, where possible, stock 
sizes have been used. 

10. Check every feature of the record strip. 

11. Review the drawing in its entirety in connection with any 

points that rj/ave suggested themselves during the above 
checking, f 

12. Bearing in mind the value of explanatory notes, do not 

fail to add such notes as your experience tells you will 
increase the efficiency of the drawing. 



STRUCTURAL DRAWING. 

The term "structural drawing" is always understood to mean 
working drawings and details for steel construction, such as 
bridges, roof trusses, skeletons of tall buildings, etc. 

Structural work differs from machine work in that it is made 
up of rolled shapes and put together permanently with rivets. 
The function of the drawing is to show the shapes and sizes of 
the steel used in the design, and the spacing of the rivets. 

Some of the parts are put together in the shop and some at 
the place of erection, and a distinction must be shown between 
"shop rivets" and "field rivets." The holes left for field con- 
nection are always made solid black. 

Fig. 343 shows the Osborn symbols for riveting, which are 
so universally used that no key on the drawing is necessary; and 
Fig. 344 shows rivets in larger scale. 



180 



ENGINEERING DRAWING 



In drawing rivets the drop pen, Fig. 30, is a favorite instrument 
with structural draftsmen. 

The general rules for working drawings are of course applicable 
to this branch, but there are some minor differences in common 
practice that should be noticed. 



Srtopff/wte 




FIG. 343. Standard symbols for riveting. 



Structural drawings are necessarily made with finer outlines 
than machine drawings, and shade lines are never used. 

To prevent confusion on the tracing, center lines and gage 
lines are very often drawn in red. 




FIG. 344. 



On account of the limited space for successive dimensions, the 
figures are set over continuous dimension lines, instead of in 
spaces left in the lines. 

Dimensions ovbr one foot are given in feet and inches. 



WORKING DRAWINGS 181 

Care should be taken that dimensions are given to commercial 
sizes of materials. 

Angles, as for gussets, are indicated by their tangent, on a 12" 
base line. 

The stress diagram is often added to the drawing. 

Bent plates should be developed, and the " stretchout" length 
of bent forged bars given. 

When showing only part of a given piece, always draw it from 
the left end toward the right. 

A bill of material always accompanies a structural drawing. 
This may be put on the drawing, but the best practice now 
attaches it as a separate "bill sheet." 

Figs. 345 and 346 are given to illustrate the general make-up 
of structural drawings. The original drawings were 24"x36". 
When a view is given under a front view, as in Fig. 345, it is not 
a bottom view, but a section taken through the web, above the 
lower flange. 

PROBLEMS. 

The first part of any working drawing problem consists of 
the selection of views, the choice of suitable scales, and the 
arrangement of the sheet. In class work the preliminary sketch 
layout should be submitted for approval before the drawing is 
commenced. 

All views of an object must be drawn to the same scale, but 
different objects on the same sheet may be drawn to different 
scales. 

The problems here given may be drawn on 12"xl8" or 18"x24" 
sheets. Their division into groups is suggestive rather than 
arbitrary, and the selections made from them will depend 
upon the kind and length of course. 

Group I. Bolts, Screws, Pipes, etc. 

Prob. 1. Draw helical screw threads and springs as indi- 
cated in Fig. 347. 

Prob. 2. Draw a bolt sheet containing: 3/4"x3" bolt with 
hex. head and nut; 3/4"x3" square head bolt; 7/8" 
x3 1/2" stud, with hex. nut; l/2"x2" hex. head 
cap screw; 5/8"xl 1/2" cup point set screw; 



182 



ENGINEERING DRAWING 







WORKING DRAWINGS 



183 




184 



ENGINEERING DRAWING 
Prob. 2. l/4"xl 1/2" oval fillister head machine screw; 

(Continued.) 



l/2"x2 1/2" low head, round point set screw, with 
jam nut; 5/16"x3/4" headless set screw, with. 
hanger point; 3/8"xl 1/2" countersunk head cap 
screw; l/4"xl 3/4" round head machine screw; 
3 1/2" lag screw (1/2" diam,); 2 1/2" flat head 




FIG. 347. 

wood screw (3/16" diam.); l/2"x4" hanger bolt, 
with lock nut; 5/8" Allen set screw; 1/4" wing 
nut. 

Prob. 3. Pipe Fittings. In the upper left-hand corner of 
sheet draw a 2" T. Plug one outlet, in another 
place a 1 l/2"x2" bushing, in remaining outlet 
use a 2" close nipple and on it screw a 1 l/2"x2" 
reducing bushing. Lay out remainder of sheet so 
as to include the following 1 1/2" fittings: coup- 
ling, globe valve, R. & L. coupling, angle valve, 45- 
degree ell, 90-degree ell, 45-degree Y, cross, cap, 3 
part union, flange union. 

Add extra pipe, nipples and fittings so that the 
system will close at the reducing fitting first 
drawn. 






WORKING DRAWINGS 



185 



Prob. 4. A Piping Problem. Given two sources of pres- 
sure supply a city main and a steam pump. A 
sprinkler system must have pressure on at all 
times, and is to be connected so as to have city 
pressure, pump pressure, or pressure from -an 
overhead tank. A battery of boilers is also to be 
connected to these three sources. The tank is to 
be capable of supply from either pump or main. 




FIG. 348. 



Design a pipe layout in elevation, so that each 
system can be operated independently, and be 
perfectly interchangeable, using the fewest 
fittings and simplest connections. Fig. 348 is a 
sketch showing the position of the outlets. 

Group II. Study Sheets in Dimensioning. 

(All to be in orthographic projection, with 
necessary views.) 

Prob. 1. Make a freehand working sketch of the casting, 
Fig. 349, showing the location of all dimensions, 
according to the rules for dimensioning, thus 

Prob. 2. Same for Fig. 350. 



186 ENGINEERING DRAWING 

Prob. 3. Freehand sketch of yoke (A) Fig. 351, indicating 
dimensions for the blacksmith. The holes to be 
punched. 

Prob. 4. Same for equalizing bar (B) Fig. 351. 




FIG. 340. 



FIG. 350. 



Prob. 5. Freehand sketch of casting, Fig. 352, giving 

necessary machine shop dimensions in blank. 
Prob. 6. Same for Fig. 353. 

Additional practice may be had by applying the rules for 
dimensioning to Figs. 130, 140, 294, 295, 296, etc. 




FIG. 351. 



Group III. Drawing from Sketches. 

Models, furnished by the Department, are to be sketched 
and measured; drawings are to be made from the sketches 




FIG. 352. 



without further reference to the model or machine; sketches 
to be submitted along with finished tracings. 
Reference, Chapter X, Technical Sketching. 



WORKING DRAWINGS 



187 



Group IV. Machine Parts, etc. 

Prob. 1. Make working drawing of crank shaft from dimen- 
sioned sketch, Fig. 354. 

Prob. 2. Working drawing of cross-head, Fig. 355. 

(Notice the occurrence of a curve of intersection.) 




FIG. 354. 




FIG. 355. 



Prob. 3. Working drawing of a flange coupling, size to be 
assigned, and dimensions taken from the table 
accompanying Fig. 356. 

Prob. 4. Working drawing of bearing, from Fig. 357. 



188 



ENGINEERING DRAWING 

D 




ABC 



UL 



It 



9 4. 



E 



a? 



ZF 









A' 









7J 



FIG. 356. 




ABC 



//f 



3% 4- 8 



M. 



7J 7 



FIG. 357. 



WORKING DRAWINGS 



189 





FIG. 359. 



190 



ENGINEERING DRAWING 



T sis 




Section on A A 
FIG. 360. 




Column 5ecf ion ABC D E F~ O 



H 



L 



22" 



jj. 

/6 



22" 



26 



7" 



24" 



28 



7" 



/P 







28" 33" 8" /e" 



* 



20 






FIG. 361. 



WORKING DRAWINGS 



191 




FIG. 362. 




FIG. 363. 



192 



ENGINEERING DRAWING 







WORKING DRAWINGS 



193 



Prob. 5. Working drawing of fly-wheel. Outside diameter 
60"; hub 6" diameter, bore 3", keyway l/2"x7/8". 
Arms at rim to be 3/4 the size at the hub. Sec- 
tions of rim, arm, and hub are shown in the 
sketch, Fig. 358. 

Prob. 6. Working drawing of eccentric, from Fig. 359. 

Prob. 7. Working drawing of pulley, figuring dimensions 
from formulae given, Fig. 360. 




FIG. 366. 



Suggested sizes (a) 24" dia. 6" face 2" bore. 

(b) 42" dia. 14" face 3 7/16" bore. 

(c) 20" dia. 10" face 2 3/16" bore. 

(d) 12" dia. 16" face 2 7/16" bore. 

(e) 60" dia. 8" face 3 15/16" bore. 

(f) 36" dia. 4" face 1 7/16" bore. 

Prob. 8. Working drawing of column base, from Fig. 361. 
Prob. 9. Working drawing of a column base with G = 

71/2" and H = 10", to carry 137,000 Ibs., assuming 
13 



194 



ENGINEERING DRAWING 




WORKING DRAWINGS 



195 



the bearing value of foundation to be 300 Ibs. 

per sq. in. Ribs 45 degrees. 
Prob. 10. Working drawing of roof truss from sketch, Fig. 

362. 
Prob. 11. Working drawing of cast iron manhole cover, 

from sketch, Fig. 363. 
Prob. 12. Working drawing of timber trestle, height, 12, 14, 

16, 18, or 20 feet, Fig. 364, using timbers of 

sizes given. 




FIG. 368. 

Group V. -Assembly and Detail Drawings. 

Prob. 1. Make detail drawings of screw jack, Fig. 365. 
Prob. 2. Make detail drawings of wrought iron hanger, 

Fig. 366. 
Prob. 3. Make assembly drawing of milling machine vise 

from details in Fig. 367. The sketch is not a 

part of the detail drawing but is given to show 

the arrangement of parts. 
Prob. 4. Make assembly and detail drawings of pop safety 

valve from the sketch details of Fig. 368. 



196 



ENGINEERING DRAWING 




IS 



rt.rw =5 ^^ > v . c\ ^0 S* I - f f/M^ 



gj^||i^^j|to 



;/^_j 





WORKING DRAWINGS 



197 



Prob. 5. Make assembly drawing of center grinder, from 

detail drawing, Fig. 369. 
Prob. 6. Make assembly drawing of friction clutch shifter, 

from detail drawing, Fig. 308. Its arrangement 

is shown in sketch, Fig. 370. 




FIG. 370. 

Prob. 7. Make detail drawings of grinder, from assembly 

drawing, Fig. 371. 
Prob. 8. Make assembly drawing of gas engine mixer from 

details of Fig. 372. 

Group VI. Checking. 

Prob. 1. Fig. 373 is incorrect in several places both in 
drawing and dimensions. Check it for errors, 
following the system given on page 178, and re- 
port the errors and corrections on a separate 
sheet. 

Prob. 2. Check Fig. 374 in the same way. 

Group VIII. Miscellaneous. 

Prob. 1. A patent office drawing, on Bristol board, from an 
assigned model or sketch. Reference, Chapter 
XIV. 



198 



ENGINEERING DRAWING 




WORKING DRAWINGS 



199 




M/xer /eeve 
C0sf/rv/i 



FIG. 372. 




FIG. 373. An incorrect drawing to be checked for errors. 



200 ENGINEERING DRAWING 

Prob. 2. A sheet metal problem, to be drawn, developed 
and dimensioned, from specifications assigned. 

Prob. 3. A plan of building or room, to be measured and 
drawn. Reference, Chapter XI. 

Prob. 4. A problem in furniture designing. 

Prob. 5. A problem in structural drawing. 




FIG. 374. An incorrect drawing to be checked for errors. 



CHAPTER X. 

TECHNICAL SKETCHING. 

From its long use in connection with art the word "sketch" 
has come to suggest the impression of a free or incomplete or 
careless rendering of some idea, or some mere note or suggestion 
for future use. This meaning is entirely misleading and wrong 
in the technical use of the word. A sketch is simply a working 
drawing made freehand, without instruments, the quick expres- 
sion of graphic language, but in information adequate and 
complete. 

So necessary to the engineer is the training in freehand sketch- 
ing, it might almost be said in regard to its importance that the 
preceding nine chapters have all been in preparation for this one. 
Such routine men as tracers and detailers may get along with 
skin and speed in mechanical drawing, but the designer must -be 
able to sketch his ideas with a sure hand and clear judgment. 
In all mechanical thinking in invention, all preliminary designing, 
all explanation and instructions to draftsmen freehand sketching 
is the mode of expression. 

It represents the mastery of the language, gained, only after 
full proficiency in mechanical execution, and is the mastery which 
the engineer, and inventor, designer, chief draftsman, and contrac- 
tor, with all of whom time is too valuable to spend in mechanical 
execution, must have. 

It may be necessary to go a long distance from the drawing 
room to get some preliminary information and the record thus 
obtained would be valueless if any detail were missing or obscure. 
Mistakes or omissions that would be discovered quickly in making 
an accurate scale drawing may easily be overlooked in a freehand 
sketch, and constant care must be observed to prevent their 
occurrence. 

Sometimes, if a piece is to be made but once a sketch is used 
as a working drawing and afterward filed. 

The best preliminary training for' this work is the drawing in 

201 



202 



ENGINEERING DRAWING 



the public schools, training the hand and eye to see and represent 
form and proportion. Those who have not had this preparation 
should practice drawing lines with the pencil, until the hand 
obeys the eye to a reasonable extent. 

The pencil should be held with freedom, not close to the point, 




FIG. 375. Sketching a vertical line. 




FIG. 376. Sketching a horizontal line. 

vertical lines drawn downward, Fig. 375, and horizontal lines 
from left to right, Fig. 376. 

An H or 2H pencil sharpened to a long conical point, not too 
sharp, a pencil eraser, to be used sparingly, and paper, either in 
note book, pad, or single sheet clipped on a board, are all, the 
materials needed. 



TECHNICAL SKETCHING 203 

In making working sketches from objects a two-foot rule and 
calipers are necessary. Other machinists' tools, a try square, 
surface gauge, depth gauge, thread gauge, etc., are very con- 
venient. The draftsman's triangle may often be used in place of 
a square. Sometimes a plumb line is of service. Much ingenuity 
is often required to get dimensions from an existing machine. 

Sketches are made in orthographic, axonometric, or perspective 
drawing, depending upon the use which is to be made of them. 
Sketches of machine parts to be used in making working drawings, 
etc., would be made in orthographic; explanatory, or illustrative 
sketches might be made in axonometric or perspective. 

The best practice is obtained by sketching from castings, 
machine parts, or simple machines, and making working draw- 
ings from the sketches without further reference to the ob j ect . In 
class work a variation may be introduced by exchanging the 
sketches so that the working drawing is made by another student. 
This emphasizes the necessity of putting down all the information 
necessary, and not relying on memory to supply that missing; and 
working with the idea that the object is not to be seen after the 
sketch is made. A most valuable training in the observation of 
details is the sketching from memory a piece previously studied. 
It is an excellent training in sureness of touch to make sketches 
directly in ink, perhaps with fountain pen. 



,*! 



rv^ 



FIG. 377. 

Sketching in Orthographic Projection. 

The principles of projection and all the rules for working 
drawings are to be remembered and applied here. 

The object should be studied and the necessary views decided 
upon. In some cases fewer views would be made in the sketch 
than in the working drawing, as a note in regard to thickness or 
shape of section might save a view, Fig. 377. In other cases 



204 ENGINEERING DRAWING 

additional views may be sketched rather than complicate the 
figures by added lines which would confuse a sketch, although 
the same lines might be perfectly legible in a scale drawing. 

In beginning a sketch always start with center lines or datum 
lines, and remember that the view showing the contour or charac- 
teristic shape is to be drawn first. This is generally the view 
showing circles if there are any. 

In drawing on plain paper, the location of the principal points, 
centers, etc., should be marked so that the sketches will fit the 
sheet, and the whole sketch with as many views, sections and 
auxiliary views as are necessary to describe the piece, drawn 
without taking any measurements, but in as nearly correct propor- 
tion as the eye can determine. 

An object should of course be represented right side up, i.e., 
in its natural working position. If symmetrical about an axis, 
often one-half only need be sketched. Circles may be drawn 
with some accuracy by marking on the center lines points equi- 
distant from the center. 

Often fragmentary auxiliary views or sections aid in explaining 
construction. The rules of projection are to be broken if any 
advantage may be gained. 

If a whole view cannot be made on one page it may be put on 
two, each being drawn up to a break line used as a datum line. 

Sketches should be made entirely freehand, no ruled lines being 
used. 

Dimension Lines. 

After the sketching of the piece is entirely finished it should be 
gone over and dimension lines for all the dimensions needed for 
the construction added, drawing extension lines and arrow heads 
carefully and checking to see that none are omitted, but still 
making no measurements. 

Dimensions. 

Up to this stage the object has not been handled and the 
drawing has been kept clean. The measurements for the 
dimensions indicated on the drawing may now be added. The 
two-foot rule will serve for most dimensions. Never use the 
draftsman's scale for measuring castings. Its edge will be 
marred and it will be soiled. The diameters of holes may be 
measured with the inside calipers. It is often necessary to lay 



TECHNICAL SKETCHING 



205 



a straight edge across a surface as in Fig. 378. In measuring the 
distance between centers of two holes of the same size measure 
from edge to corresponding edge. Always measure from finished 
surfaces if possible. Judgment must be exercised in measuring 
rough castings so as not to record inequalities due to the foundry. 
Fig. 379 illustrates measuring a curve by offsets. 




FIG. 378. 



It is better to have too many dimensions rather than too few. 
It is a traditional mistake of the beginner to omit a vital figure. 

Add all remarks and notes that may seem to be of any value 
at all. 




FIG. 379. Measurements by offsets. 

The title should be written on the sketch, and for class sketches 
the amount of time spent. 

Always date every sketch. Valuable inventions have been lost 
through the inability to prove priority, because the first sketches 
had not been dated. In commercial work the draftsman's note- 
book with its sketches and calculations is preserved as a permanent 



206 



ENGINEERING DRAWING 



record, and sketches should be made so as to stand the test of 

time, and be legible after the details of their making have been 

forgotten. 

Cross Section Paper. 

Sketches are often made on coordinate paper ruled faintly in 
sixteenths, eighths or quarter inches, either simply as an aid in 
drawing straight lines and judging proportions; or assigning 




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FIG. 380. Sketch on coordinate paper. 

suitable values to the unit spaces, and drawing to approximate 
scale. In the latter case a sufficient number of measurements 
must be taken while the sketch is being made, to permit of its 
being laid off on the coordinate paper. Fig. 380 is an illustration. 

Sketching by Pictorial Methods. 

An axonometric, oblique or perspective sketch of an object or 
of some detail of construction will often explain it when the 
orthographic projection cannot be read intelligently by a work- 
man. Often again a pictorial sketch may be made more quickly 
and serve as a better record than orthographic views of the same 
piece would do, and the draftsman who can make a pictorial 
sketch with facility will find abundant opportunity for its 
advantageous use. 



TECHNICAL SKETCHING 207 

Axonometric Sketching. 

Since measurements are not made on sketches there is abso- 
lutely no advantage in sketching on isometric axes 120 degrees 
apart and making an unnecessary distortion. A much better 
effect is gained and the distortion greatly lessened by drawing 
the cross axes at a much smaller angle with the horizontal, Fig. 
381, and foreshortening them until satisfactory to the eye. It 
is legitimate in such an isometric sketch still further to decrease 
the effect of distortion by slightly converging the receding lines. 
Objects of rectangular outline are best adapted to sketching in 
axonometric projection. 




FIG. 381. 120 axes and flattened axes compared. 

When it is important to show the top surface the axes may be 
drawn at greater angles to the horizontal, and the vertical axis 
foreshortened, thus tipping the object forward as in Fig. 382. 

Some care must be exercised in adding dimensions to a pic- 
torial sketch. The extension lines must always be either in or 
perpendicular to the plane on which the dimension is being given. 

Oblique Sketching. 

The advantage of oblique projection in preserving one face 
without distortion is of particular value in sketching, and the 
painful effect of this kind of drawing done mechanically may be 
greatly lessened in sketching, by foreshortening the cross axis 
to a pleasing proportion, Fig. 383. By converging the lines 
parallel to the cross axes, the effect of parallel perspective is 
obtained. This converging in either isometric or oblique is 
sometimes called "fake perspective." 

Perspective Sketching. 

A sketch made in perspective will of course give the best 
effect pictorially. As we do not in this book take up the subject 



208 



ENGINEERING DRAWING 



of mechanical perspective, with its rules and methods, only the 
phenomena of perspective and their application in freehand 
sketching can be considered in this connection. 

Perspective has already been defined as being the representa- 
tion of an object as seen by the eye from some particular station 
point. Geometrically, it is the intersection of the cone of rays 




FIG. 382. 

from the eye to the object, with the vertical plane, or "picture 
plane." There is a distinction between "artist's perspective" 
and "geometrical perspective/' in that the artist draws the 
object as he sees it projected on the spherical surface of the 
retina of his eye, while geometrical, or mechanical perspective is 




FIG. 383. Oblique, with and without foreshortening. 

projected on a plane, as in a photograph, but except in wide 
angles of vision the difference is not very noticeable. 

The ordinary phenomena of perspective, affecting everything 
we see, the fact of objects appearing smaller in proportion to 
their distance from the eye, and of parallel lines appearing to 
converge as they recede, are of course well known. 

The outline of the object in Fig. 384 is drawn from a photo- 



TECHNICAL SKETCHING 



209 



graph. It will be noted that the vertical lines remain vertical 
in the picture, and that the two sets of horizontal lines each 
appear to converge toward a point called the " vanishing point. " 
These two vanishing points will lie on a horizontal line drawn 
at the level of the eye, called the " horizon"; and the first rule is, 
all horizontal lines vanish on the horizon. 

When the object is turned as in Fig. 384, with its vertical faces 
at an angle with the picture plane, the drawing is said to be in 
angular perspective. It is sometimes called "two-point" per- 
spective because of having two vanishing points. 




FIG. 384. Perspective (from photograph). 

If the object is turned so that one face is parallel to the picture 
plane, the horizontal lines on that face and all lines parallel to 
them would remain horizontal in the picture and would thus 
have no vanishing point. The object drawn in this position is 
said to be in parallel, or "one-point" perspective. 

In sketching in perspective from the model the drawing is 
made simply by observation, the directions and proportionate 
lengths of lines being estimated by sighting and measuring on the 
pencil held at arm's length; and knowledge of the geometrical 
rules and principles used only as a check. 

With the drawing board or sketch pad held perpendicular to 
the "line of sight" from the eye to the object, the direction of a 
line is tested by holding the pencil at arm's length parallel to 
the board, rotating the arm until the pencil appears to coincide 
with the line on the model, then moving it parallel to this position, 
back to the board. 

The apparent lengths of lines are estimated in the same way, 
holding the pencil in a plane perpendicular to the line of sight, 
14 



210 ENGINEERING DRAWING 

marking with the thumb the length of pencil which covers a line 
of the model, rotating the arm, with the thumb held in position, 
until the pencil coincides with another line, and estimating the 
proportion of this measurement to the second line, Fig. 385. 

The sketch should be made lightly, with free sketchy lines, and 
no lines erased until the whole sketch has been blocked in. 

Have the drawing as large as the paper will admit. 

In constructing a perspective from an orthographic or other 
drawing, use may be made of the plan and cone of rays, and the 
vanishing points. Imagining the eye as located at the station 




FIG. 385. 

point, a little thought will show that the vanishing point of any 
system of parallel lines is the projection on the picture plane of 
their infinite ends, the eye looking farther and farther out, till 
the line of vision is parallel to the lines. Hence, the vanishing 
point of any system of parallel lines is found by drawing from the 
station point a line parallel to the given lines and finding where it 
pierces the picture plane. 

A line drawn from the station point perpendicular to the 
picture plane pierces it in a point called the "center of vision." 
Evidently all lines perpendicular to the picture plane will vanish 
in the center of vision. This is the basis of parallel perspective. 

An object in parallel perspective with one face in the picture 
plane is shown at A, Fig. 386. At B is shown the top view of A 



TECNHICAL SKETCHING 



211 



with the cone of rays. C shows the picture plane detached and 
set forward in order that it may not interfere with the plan when 
revolved. D is the top view of C after the picture plane has been 
revolved. 




FIG. 386. Parallel perspective. 




FIG. 387. Angular perspective. 

It will be noticed that the edges perpendicular to the picture 
plane vanish in the center of vision, and that their perspective 
lengths are found by dropping to them points the of intersection 
of the cone of rays with the picture plane. 

Direct measurements can be made only in the picture plane. 



212 



ENGINEERING DRAWING 



The station point should be taken at a distance at least twice 
the length of the longest side. 

Fig. 387 is a series illustrating an object in angular perspective. 
A the object, with one corner in the picture plane; B the plan, 




FIG. 388. 



showing the finding of the vanishing points for the two series of 
horizontal lines by drawing lines through the station point paral- 
lel to them; C the picture plane moved forward bringing with it 




FIG. 389. A perspective sketch. 

the horizon and vanishing points; D the picture plane revolved. 
The figure illustrates the general case. It is usual, in practice, 
to take the S. P. directly in front of the corner that is in the 
P.P. 



TECHNICAL SKETCHING 



213 



Fig. 388 shows that the vanishing point of a system of oblique 
lines is on a perpendicular from the vanishing point of their 
projections. 

Fig. 389 gives an application of perspective sketching, showing 
construction. 

Fig. 390 contains a selection of perspective sketches to be 
sketched in orthographic. 





FIG. 390. Perspective sketches. 



CHAPTER XI. 

THE ELEMENTS OF ARCHITECTURAL DRAWING. 

It is entirely beyond the scope of this book to take up archi- 
tectural designing. But in the application by the architect, of 
engineering drawing as a language, there are idioms and peculi- 
arities of expression, with which all engineers should be familiar, 
as in the interrelation of the professions they are often required 
to read or work from architects' drawings, or to make the draw- 
ings for special structures. 
Characteristics of Architectural Drawing. 

The general principles of drawing are the same for all kinds of 
technical work. Each profession requires its own special appli- 
bation of these principles, and the employment of particular 
methods, symbols and conventions. 

In architectural drawing the necessary smallness of scale 
makes it impossible to represent the different parts exactly, and 
the drawings thus become largely conventional. The necessary 
notes for their explanation, and the information regarding the 
details of material and finish are too extensive to be included on 
the drawings so are written separately, and are called the speci- 
fications. These specifications have equal importance and 
weight with the drawings. 

Architecture is one of the fine arts, and in an architect's draw- 
ings there is an evidence of artistic feeling in their make up, 
produced in part by the freehand work and lettering upon them, 
that gives them an entirely different appearance from a set of 
machine drawings. 

The present day fad of over running corners is however a 
rather senseless affectation. 
Kinds of Drawings. 

Architectural drawings may be divided into three general 
classes : 

(1) Display and competitive drawings. 

(2) Preliminary sketches. 

(3) Working Drawings. 

214 



THE ELEMENTS OF ARCHITECTURAL DRAWING 215 




216 



ENGINEERING DRAWING 




THE ELEMENTS OF ARCHITECTURAL DRAWING 217 




FIG. 393. Perspective in ruled outline. 







FIG. 394. A pencil rendering. 



218 



ENGINEERING DRAWING 




FIG. 395. A pen drawing. 




FIG. 396. A wash drawing. 



THE ELEMENTS OF ARCHITECTURAL DRAWING 219 

Display Drawings. 

The object of display drawings is to give a realistic or effective 
representation of the arrangement and appearance of a proposed 
building, for illustrative or competitive purposes. They may be 
either plans and elevations, or may include perspective drawings; 
and contain little or no structural information. For legibility 
and attractiveness they are "rendered/' generally on Whatman, 
eggshell, tracing, or other white paper, in some medium, giving 
the effect of light and shade. Fig. 391 illustrates an elevation 
rendered in wash, in which a certain perspective effect is added 
by extending the foreground. 

Figures, trees, other buildings, etc., are sometimes introduced 
on such drawings, not so much for pictorial effect, but to give an 
idea of the relative size of the buildings. 

In rendering plans for display or competitive purposes, tints 
and shadows are often used to show the plan in relief and to 
express the ideas of the architect more fully. Fig. 392 illustrates 
a plan of this kind, employing poche and mosaic; "poche" 
meaning simply the blackening of the walls to indicate their 
relative importance in the composition, and " mosaic " the 
rendering, in light lines and tints, of the floor design, furniture, 
etc., on the interior, and the walks, drives and gardening of the 
exterior. 

The architect must be familiar with perspective drawing, as 
he uses it both in the preliminary study of his problem and to 
show the client the finished appearance of the proposed structure. 
Perspectives are rendered according to the purpose of the draw- 
ing. Four different methods are illustrated. Fig. 393 is a ruled 
outline, Fig. 394 a pencil drawing, usually done on tracing paper; 
Fig. 395 a pen drawing, and Fig. 396 awash drawing, done either 
in monochrome or in color. In rendering a perspective in water 
color it is best to transfer it by rubbing, as described on page 
268, in order to preserve the surface of the paper. 

Preliminary Sketching. 

The architects' designing problems present so many solutions 
that a great amount of preliminary sketching is necessary, and 
the architectural draftsman must be facile with the pencil. 
These schemes are carried on first in very small sketches, not to 
scale, and afterward worked up enlarging them in sketches to 



220 



ENGINEERING DRAWING 



scale. Tracing paper is very desirable for this work as one sketch 
can be made over another, thus saving time in laying out, and 
enabling the preservation of all the different solutions. The 
final preliminary sketches are submitted to the client, and should 
give all the general dimensions. In preparing these sketches 
the important consideration to be kept in mind is that the client 
is usually a person not accustomed to reading a drawing, and that 
they must therefore be particularly clear and free from ambiguity. 
Tracing paper drawings are often mounted for display either 
by " tipping" or " floating," as described on page 267. 

' AILCH1TECTV1LAL SYMBOLS - 






EAfcTHMM'SECTlOrt' 'COflCRETE-lH-SECTIOrt- >TA6E5WMAKIN6>CONCRCfE*yM80l 

FIG. 397. Symbols for building materials. 

Working Drawings. 

All the general principles in Chapter IX regarding working 
drawings are applicable to architectural working drawings. 
The assembly drawings are plans, elevations and sections. The 
plans of a building of the size of an ordinary house would be 
drawn to the scale of 1/4"= 1', larger buildings to 1/8"= 1'. 
In order to keep the drawings to convenient working size, only 
one view, usually, is drawn on a sheet. 
Plans. 

A floor plan is a horizontal section at a distance above the floor 
varying so as to cut the walls at a height which will best show 



THE ELEMENTS OF ARCHITECTURAL DRAWING 221 



STANDARD SYMBOLS FO& WIRING PLANS 

OS adopted and recommended by 
THE NATIONAL ELECTRICAL CONTRACTORS ASSOCIATION of the UNITED STATES and THE AMERICAN. INSTITUTE of ARCHITECTS 



Celling Outlet; Electric only. Numeral 
in center indicates number of 
Standard 16 C.R Incandescent Lamps. 

Bracket Outlet; Electric only. Numeral^ 
in center indicates number of 
Standard 16 C.R Incandescent Lamps. 

Ceiling Outlet; Gas only. 



m 



Wall or Baseboard Receptacle. Numeral > 

in center indicates number of 

Standard 16 C.P. Incandescent Lamps. < 

f Outlet for Outdoor Standard or 

)6 Pedestal; Electric only. Numeral indicates 

* number of Stand. 16 C.P. Incan . Lamps. 

\ Drop Cord Outlet. 
| Arc Lamp Outlet. 



Ceiling Outlet. Combination .| indicate* 

4- 16 C.P. Standard Incandescent 
Lamps and 2 Gas Burners . 

Bracket Outlet ; Combination . 
^ indicates 4-16 C P. Standard Incan- 
descent Lamps and 2 Gas Burners. 

Bracket Outlet; Gas only. 

Tloor Outlet Numeral irt 
center indicates number of 
Standard 16 C P Incandescent Lamps. 

Outlet for Outdoor Standard or Pedestal. 

Combination ^-indicates 6-16 C P 
Stand . Incan. Lamps and 6 6as Burners. 

One Light Outlet for Lamp Receptacle. 



Special Outlet, for Lighting , Heating 
and Power Current, as described in Spec. 



S 1 S.P. Switch Outlet. 
S 2 - D.P. Switch Outlet. 
S 3 3- Way Switch Outlet. 
S* 4- Way Switch Outlef 

Automatic Door Switch Outlet. 
Electrolier Switch Outlet. 
Meter Outlef. 
Junction or Pull Box 
Cx3 Motor Control Outlet . 

' Main or Feeder run concealed under floor. 

- Main or Feeder run exposed. 



Ceiling Fan Outlet. 
\ 



S 
S E 



Show as many symbols as there are 
switches, or , in case of a- very larg* 
group of switches, indicate number 
of switches by a Roman Numeral , 
thus : S 1 XII , meaning 12 Single ' Pole 
switches. Describe type of switch 
in specifications, that is, Flush or 
Surface , Push Button or Snap. 

Distribution Panel . 

Motor Outlet: Mumeral .o center indicates H.R 

Transformer . 

Mam or Feeder run concealed under flooroboe. 

Branch Circuit run concealed under floor. 



Branch Circuit run concealed under floor above. Branch Circuit Run Exposed 

- " Pole Line. Riser. 

fa Telephone Outlet, Private Service . M Telephone Outlet; Public Service H Bell Outlet. 
f~"V Buzzer Outlet. ] |g Push Button Outlet; Numeral Indicates number- of Pushes. 
____/B\ Annunciator: Humeral indicates number of Points. ^ Spa)ting Tub*. 

(S) Watchman Clock Outlet . J Watchman Station Outlet. - Master Time Clock Outlet. 

[[) Secondary Ti'me Clock Outlet. GO Door Opener 

JXJ Special Outlet; for Signal Systems.as described in Specifications. |l|l|| Battery Outlet. 

f Circuit-for Clock, Telephone , Bell or other Service, run under floor , conccolad. 

"" \ Kind of Service wanted ascertained by Symbol to which line connects 

- ( Circuit for Clock, Tele phone. Bell or other Service, run under floor above concealed. 

\ Kind of Service wanted ascertained by Symbol to which line, connects. 

Note If other than Standard 16 C.R Incandescent Lamps ore. desired, 
Specifications should describe capacity of Lamp to be used 

SUGGESTIONS IK COMHECTIOtt WITH , STANDARD SYMBOLS TOR. WllEING PLANS 

It i* important that ample space bt allowed for the installation of mains, feeders, branches and distribution 
panels . It is da.sirable that a key to the symbols used accompany oil plans. 

If mains , feeders , branches and distribution panels ore shown on the plan* , .it i* desirable that they 
be designated by letters or numbers. 

' Living Rooroa S'-6" 

S'-O" 
6'-0" 
6'- 3' 

4 1 -0 - 

F THE UNITED 5TATCS- 



Me.ghts of center of W ( 
Outlets (unless otherwis 



specified j 
Height of switches (unless otherwise 



, ( Living Roo 
Chambers 
} Off.ce* 
\ Corridor* 



COPYRIGHT -l0 -I9O7 BY THE NAT 



FIG. 398. Standard wiring symbols. 



222 



ENGINEERING DRAWING 



the construction. The cut would thus evidently cross all 
openings no atmter at what height they were from the floor. 
The joist system or construction of the floor, and also any infor- 
mation regarding the ceiling above, as beams, gas and electric 
outlets, etc., may be shown on the same drawing. 



; - Ilfadr 

:::-:;;::." 5 - ^"TT^ I- 




FIR.3 7 FLOOR.. PLAM 

' C A L E ' 4-0* 



HESIDETtCE 


/^ ' 


MR.-A-F- BR.OOKS 


MEDIA OHIO 




X'Y'Z. AR.CHI 


TECT 


DF CATVR- ILL 


I ' 



FIG. 399. A residence floor plan. 

The different details such as windows, doors, etc., must be 
indicated by conventional representation, using symbols, which 
are readily understood by the contractors who have to read the 
drawings, A wall, of whatever material, is shown by two lines 
giving its thickness, with the space between generally section- 
lined (or tinted) to indicate the material. A code of conventional 



THE ELEMENTS OF ARCHITECTURAL DRAWING 223 



symbols, representing good practice, is given in Fig. 397. As 
there is no universally accepted standard of symbols, a key to 
materials represented in section should always be shown on the 
drawing. 

Fig. 398 contains the standard symbols for wiring plans. 




5E COM D FLOO R_ - PUAN 

s CA L e r- 4-0" 



RESIDE MCE /. 
MR.-A-F.-BR.OOKS 

MEDIA OHIO 
X-Y-Z ARCHITECT 
DE CATVR. ILL 



FIG. 400. A residence floor plan. 

Figs. 399 and 400 are representative residence floor plans, 
showing the application of a number of conventions, and Fig. 401 
is the plan of an engineering structure. 

Elevations. 

An elevation is a vertical projection showing the front, side or 
rear view of a structure, giving the heights and exterior treat- 



224 



ENGINEERING DRAWING 




FIG. 401. Floor plan of sub-station. 




FIG. 402. An elevation, with wall section. 



THE ELEMENTS OF ARCHITECTURAL DRAWING 225 

ment. The visualizing power must be exercised to imagine the 
actual appearance or perspective of a building from its elevations. 
Roofs in elevation are thus often misleading to persons unfamiliar 
with drawing, as their appearance in projection is so different 
from the real appearance of the building when finished. 

Only those dimensions should be put on elevations as are not 
possible to show on the other drawings. 

Fig. 402 is an elevation, with wall section of the house whose 
plans are shown in Figs. 399 and 400. 




FIG. 403. Section of sub-station. 

Sections. 

A section is an interior view on a vertical cutting plane and is 
used primarily to indicate the heights of the floors and different 
parts, and to show the construction and architectural treatment 
of the interior. In a simple structure a part section or "wall 



226 



ENGINEERING DRAWING 



section/' shown with the elevation, as in Fig. 402, is often suffi- 
cient. This cutting plane, as the horizontal, need not be continu- 
ous, but may be broken so as to include as much information as 
possible. Fig. 403 is a full section, or sectional elevation of the 
sub-station shown in plan in Fig. 401. 
Details. 

Architectural details are made to explain peculiar construc- 
tions or to give a full graphic description of any part. Often 




DETAIL -OF- FRAMING 'AR.QVND BASE MEMT' WIHDOW5 
SCALE "=i-o" 

FIG. 404. An isometric detail. 

some peculiarity of framing may be explained easily by an iso- 
metric detail, as Fig. 404. Stair details and the like may be 
shown with sufficient clearness, as in Fig. 405, to the scales of 
3/4" or I". Mouldings and other mill work details are generally 
made full size. The turned or revolved section is often of use 
in showing moulding sections in position. 

Dimensioning. 

As in machine drawing, the correct dimensioning of an archi- 
tectural drawing requires a knowledge of the methods of building 



THE ELEMENTS OF ARCHITECTURAL DRAWING 227 

construction. The dimensions should be placed so as to be the 
most convenient for the workman, should be given from and to 
accessible points, and chosen so that commercial variation in the 
sizes of materials will not affect the general dimensions. 

A study of the dimensioning on the figures of this chapter will 
be of value. 

The statement that the notes were put in the specifications 
does not at all imply that no notes are to be placed on the 




FIG 405. A stair detail. 

drawings. On the other hand, there should be on architectural 
working drawings clear, explicit notes in regard to material, 
construction and finish. The builders are apt to overlook a 
point mentioned only in the specifications, but as they are using 
the drawings constantly, will be sure to see a reference or note 
on the drawing of the part in question. 

Lettering. 

There are two distinct divisions in the use of lettering by the 
architect, the first, Office Lettering, including all the titles and 
notes put on drawings for information; the second, Design 
Lettering, covering drawings of letters to be executed in stone or 
bronze or other material in connection with design. 



228 ENGINEERING DRAWING 

The Old Roman is the architect's one general purpose letter 
which serves him with few exceptions for all his work in both 
divisions. It is a difficult letter to execute properly and the 
draftsman should make himself thoroughly familiar with its 
construction, character, and beauty, through a text-book on 
the subject, before attempting to design inscriptions for perma- 
nent structures, or even titles. 

Titles on display drawings are usually made in careful Old 
Roman, and on working drawing, in a rapid single stroke based 
on Old Roman. For notes the Reinhardt letter is best adapted. 

An architectural title should contain part or all of the following 
items: 

(1) Name and location of structure. 

(2) Kind of view, as roof plan, elevation (sometimes put on 
different part of sheet). 

(3) Name and address of owner or client. 

(4) Date. 

(5) Scale. 

(6) Name and address of architect. 

(7) Number (in the set). 

(8) Key to materials. 

(9) Office record. 



CHAPTER XII. 
MAP AND TOPOGRAPHICAL DRAWING. 

Thus far in our consideration of drawing as a graphic language 
we have had to represent the three dimensions of an object, 
either pictorially or, in the usual case, by drawing two or more 
views of it. In map drawing, the representation of features on 
parts of the earth's surface, there is the distinct difference that 
the drawing is complete in one view, the third dimension (the 
height) either being represented on this view, or in some cases 
omitted as not required for the particular purpose for which the 
map was made. 

The surveying and mapping of the site is the first preliminary 
work in improvements and engineering projects, and it is desira- 
ble that all engineers should be familiar with the methods and 
symbols used in this branch of drawing. Here again, as in our 
discussion of architectural drawing, we cannot consider the prac- 
tice of surveying and plotting, or go into detail as to the work of 
the civil engineer, but we are interested in his use of drawing as 
a language, and in the method of commercial execution of plats 
and topographical maps. The titles of several books on plane 
and topographic surveying are given in Chapter XV. 

Maps in general may be classified as follows: 

(1) Those on which the lines drawn represent imaginary or 
unreal lines, such as divisions between areas subject to different 
authority or ownership, either public or private; or lines indicating 
geometrical measurements on the ground. In this division may 
be included plats or land maps, farm surveys, city subdivisions, 
plats of mineral claims. 

(2) Those on which lines are drawn to represent real or 
material objects within the limits of the tract, showing their 
relative location, or size and location, depending upon the purpose 
of the map. When relative location only is required the scale 
may be small, and symbols employed to represent objects, as 
houses, bridges or even towns. When the size of the object is an 

15 229 



230 ENGINEERING DRAWING 

important consideration the scale must be large and the map 
becomes a real orthographic top view. 

(3) Those on which lines or symbols are drawn to tell the 
relative elevation of the surface of the ground. These would be 
called relief maps, or if contours are used with elevations marked 
on them, contour maps. 

Various combinations of these divisions may be required for 
different purposes. A topographic map, being a complete 
description of an area, would include 1, 2 and 3, although the 
term may be used for a combination of any two. 

Plats. 

A map plotted from a plane survey, and having the third 
dimension omitted, is called a "plat" or "land map." It is 
used in the description of any tract of land w r hen it is not neces- 
sary to show relief, as in such typical examples as a farm survey 
or a city plat. 

The first principle to be observed in the execution of this kind 
of drawings is simplicity. Its information should be clear, con- 
cise and direct. The lettering should be done in single stroke, 
and the north point and border of the simplest character. The 
day of the intricate border corner, elaborate north point, and 
ornamental title is, happily, past, and all such embellishments 
are rightly considered not only as a waste of time, but as being 
in extremely bad taste. 

A Farm Survey. 

The plat of a farm survey should give clearly all the informa- 
tion necessary for the legal description of the parcel of land. It 
should contain: 

(1) Lengths and bearings of the several sides. 

(2) Acreage. 

(3) Location and description of monuments found and set. 

(4) Location of highways, streams, etc. 

(5) Official division lines within the tract. 

(6) Names of owners of abutting property. 

(7) Title and north point. 

(8) Certification. 

Fig. 406 illustrates the general treatment of this kind of 
drawing. It is almost always traced and blue printed, and no 



MAP AND TOPOGRAPHICAL DRAWING 



231 



water lining of streams or other elaboration should be attempted. 
It is important to observe that the size of the lettering used for 
the several features must be in proportion to their importance 



/ 



/ ' frereby certify ffre atove p/0f /{? be correct 




PLAT 
OF svxYfr of 

THJ. C.WARD FARM 

Z.OT6 TffACTfZ Oit.OT-9- TKACT8 

MAD/SOM THSf>. 
LAK CO. 

o. 



SCALE /''ZOO' 



* S, 



ff3/p29c/ r 



Co. Sur 



FIG. 406. A farm plat. 



Plats of Subdivisions. 

The plats of subdivisions and allotments in cities are filed with 
the county recorder for record, and must be very complete in 
their information concerning the location and size of the various 



232 



ENGINEERING DRAWING 



lots and parcels composing the subdivisions, Fig. 407. All 
monuments set should be shown and all measurements of lines 
and angles given, so that it will be possible to locate any lot with 
precision. 

Sometimes landowners desire to use these maps in display to 
prospective buyers, and some degree of embellishment is allowable, 





c 










Sffi 


TwT? 


60 


35 




' 








S3 


r 


^ 















3E^ 20 




V 


86 


85 


84 


83 


<?.? 


tfA 




''80 


73 


78 


77 


76 


7S 


7<f s 




h 


7? 


7/ 


7<i7 


5^ 


5<? 


4 


| 


















































/Jftj \ 




40 


. 




,. 


- 


.. 


40 




40 














10 




^ 















M'J ( ) \ 




' SUBDI V/5 r ION 

^ 3 "** CF TH 

^-&Ffi&-^ r- R DOT y ESTATE 

' COLUMBUS. O. 



FIG. 407. A city subdivision. 



but care must be taken not to overdo the ornamentation. These 
drawings are usually finished as blue prints. Fig. 408 is an 
example showing an acceptable style of execution and finish. 

When required for reproduction to small size for illustrative 
purposes a rendering such as shown in Fig. 409 is sometimes 
effective. 



MAP AND TOPOGRAPHICAL DRAWING 



233 




FIG. 408. A real estate display map. 



- MM 

-I =! J J J J J 



J J _l _J J 5 ] -J -I _l -J _J 

JJJJJ=! s ^J-iZSJS_l 



J J r! J _J =! =r: =! zd =J 
J d d 

J _JJ S^l =i =; 




FIG. 409. A shade line map. 



234 



ENGINEERING DRAWING 



City Plats. 

Under this head is included chiefly maps or plats drawn from 
subdivision plats or other sources for the record of city improve- 
ments These plats are used for the record of a variety of infor- 
mation, such as, for example, the location of sewers,water mains, 
street railways, and street improvements. One valuable use is 




rr 



FIG. 410. A sewer map. 



in the levying of assessments for street paving, sewers, etc. As 
they are made for a definite purpose they should not contain 
unnecessary information, and hence will not include all the 
details as to sizes of lots, location of monuments, etc., which are 
given on subdivision plats. 

They are usually made on mounted paper and should be to a 



MAP AND TOPOGRAPHICAL DRAWING 235 

scale large enough to show clearly the features required, 100' 
and 200' to the inch are frequent scales, and as large as 50' is 
sometimes used. For smaller cities the entire area may be 
covered by one map; in larger cities the maps are made in con- 
venient sections so as to be filed readily. 

A study of Fig. 410, a sewer map, will show the general treat- 
ment of such plats. The appearance of the drawing is improved 
by adding shade lines on the lower and right hand side of the 
blocks, i.e., treating the streets and water features as depressions. 

A few of the more important public buildings are shown, to 
facilitate reading. The various wards, subdivisions or districts 
may be shown by large outline letters or numerals as illustrated 
in the figure. 

Topographical Drawing. 

As before defined, a complete topographical map would contain: 

(1) The imaginary lines indicating the divisions of authority 
or ownership. 

(2) The geographical position of both the natural features and 
the works of man. They may also include information in regard 
to the vegetation. 




FIG. 411. 

(3) The relief, or indication of the relative elevations and 
depressions. 

The relief, which is the third dimension, is represented in 
general either by contours or by hill shading. 

A contour is a line on the surface of the ground which at every 
point passes through the same elevation, thus the shore line of a 
body of water represents a contour. If the water should rise 
one foot the new shore line would be another contour, with one 
foot "contour interval." A series of contours may thus be 
illustrated approximately by Fig. 411. 



236 



ENGINEERING DRAWING 



Fig. 412 is a perspective view of a tract of land. Fig. 413 is a 
contour map of this area, and Fig. 414 is the same surface shown 
with hill shading by hachures. Contours are drawn as fine, full 
lines, with every fifth one of heavier weight, and the elevations in 




FIG. 412. 



feet marked on them at intervals, usually with the sea level as 
datum. They may be drawn with a swivel pen, Fig. 26, or with 
a fine pen such as Gillott's 303. On paper drawings they are 
usually made in brown. 




FIG. 413. 



The showing of relief by means of hill shading gives a pleasing 
effect but is very difficult of execution, does not give exact eleva- 
tions and would not be applied on maps to be used for engineering 
purposes. They may sometimes be used to advantage in re- 



MAP AND TOPOGRAPHICAL DRAWING 



237 



connoissance maps, or in small scale maps for illustration. 
There are several systems, of which hachuring is the commonest. 
Fig. 415 illustrates the method of execution. The contours are 
sketched lightly in pencil and the hachures drawn perpendicular 




FIG. 414. 



to them, starting at the summit and making heavier strokes for 
steeper slopes. The rows of strokes should touch the pencil line, 
to avoid white streaks along the contours. 

Fig. 416 is a topographic map of the site of a proposed filtra- 




FIG. 415. 



tion plant, and illustrates the use of the contour map as the 
necessary preliminary drawing in engineering projects. Often 
on the same drawing there is shown, by lines of different character, 
both the existing contours and the required finished grades. 



238 



ENGINEERING DRAWING 



Water Lining. 

On topographic maps made for display or reproduction the 
water features are usually finished by water-lining," running a 
system of fine lines parallel to the shore lines, either in black or 
in blue (it must be remembered that blue will not photograph 
for reproduction nor print from a tracing). Poor water-lining 
will ruin the appearance of an otherwise well executed map, and it 



Je/fersor? Zo//ir?gers fairs 




Saraft J Potre/f 



C/ara3 Me Comb 



FIG. 416. Contour map for engineering project. 

is better to omit it rather than do it hastily or carelessly. The 
shore line is drawn first, and the water-lining done with a fine 
mapping pen, as Gillott's 170 or 290, always drawing toward the 
body and having the preceding line to the left. The first line 
should follow the shore line very closely, and the distances between 
the succeeding lines gradually increased and the irregularities 
lessened. Sometimes the weight of lines is graded as well as the 
intervals but this is a very difficult operation and is not necessary 
for the effect. 



MAP AND TOPOGRAPHICAL DRAWING 239 

A common mistake is to make the lines excessively wavy^or 
rippled. 

In water-lining a stream of varying width, the lines are not to 
be crowded so as to be carried through the narrow portions, but 
corresponding lines should be brought together in the middle of 
the stream as illustrated in Fig. 417. Care should be taken to 
avoid any spots of sudden increase or decrease in spacing. 




FIG. 417. Water lining. 

Topographic Symbols. 

The various symbols used in topographic drawing may be 
grouped under four heads : 

(1) Culture, or the works of man. 

(2) Relief relative elevations and depressions. 

(3) Water features. 

(4) Vegetation. 

When color is used the culture is done in black, the relief in 
brown, the water features in blue, and the vegetation in black 
or green. 

These symbols, used to represent characteristics on the earth's 
surface, are made when possible to resemble somewhat the 
features or object represented as it would appear either in plan 
or elevation. We cannot attempt to give symbols for all the 
features that might occur in a map, indeed one may have to 
invent symbols for some particular locality. 

Fig. 418 illustrates a few of the conventional symbols used for 
cultures or the works of man, and no suggestion is needed as to 
the method of their execution. When the scale used is large, 
houses, bridges, roads and even tree trunks can be plotted so 



240 



ENGINEERING DRAWING 




E/ectric Railway 

-7/^v7f#~)^. ~*Tvnn~ei*~ 

City ortt/lage 



Bridge 




, Jill 

nfifflr 

Fet 

^' 1 
I 



Privafe ffoads 



Ferry 



Sing/e Track 



Dot/b/e Track 
ffai/roads 



Foraf 



Dam 



State Line 

County Line 

Township L/ne 

C/ry or 



T T T T T 
Te/egrap/? or 
Te/epnor/e 




Hedge 

AA/WNA/VW 
ffai/ or Worm fence 



'w 

*, 

Levees ' 

x B.M. ^ 
Bench Mark M/fJeor 
& Quarry 

Triangu/ofiorr B 
5 fa f /'on 



SfoneSence 
W/re Fence 



frvflerfy iris nof/ittced 



t 

Church 

F mL.S.5. 

. Life-sav/na 
Sc/?ot?/ Station 



FIG. 418. Culture. 



Location, n'a or t/r/////?? we//.. .O 

O// We//. 

Smaf/ O/'/ We//. 

Dry Ho/e.... -cj>- 

Symtio/ of abandonment. . V, thus, ...)& 

A/umber of we//s, thus, > /g 

Show vo/vmes, thus -- 



ryr/o/e M//? shomagrefo//. 
Gas 



*; 



-?- 



FIG. 419. Oil and gas symbols. 




Determined 
E/evafion 



Sand 



Mud flat 



FIG. 420. Relief. 



MAP AND TOPOGRAPHICAL DRAWING 



241 



that their principal dimensions can be scaled. A small scale 
map can give by its symbols only the relative locations. 

Fig. 419 gives the standard symbols used in the development 
of oil and gas fields. 

Fig. 420 contains symbols used to show relief. 

Water features are illustrated in Fig. 421. 

In Fig. 422 is shown some of the commoner symbols for vege- 
tation and cultivation. 

Draftsmen should keep in mind the purpose of the map, and 
the relative importance of features should be in some measure 
indicated by their prominence or strength, gained principally 



Lock 




Jrjfermiftenf Streams 



Dry Lake 



Submarine Cortfot/rs 




Fresh Marsh Sa/t Marsh Submerged Marsh T/ata/ F/at 



FIG. 421. Water features. 



by the amount of ink used. For instance, in a map made for 
military maneuvering a cornfield might be an important feature, 
or in maps made to show the location of special features, such as 
fire hydrants, etc., these objects would be indicated very plainly. 
This principle calls for some originality to meet varying cases. 

A common fault of the beginner is to make symbols too large. 
The symbols for grass, shown under "meadow," Fig. 422, if not 
made and spaced correctly will spoil the entire map. This 
symbol is composed of from five to seven short strokes radiating 
from a common center and starting along a horizontal line, as 



242 



ENGINEERING DRAWING 



shown in the enlarged form, each tuft beginning and ending 
with a mere dot. Always place the tufts with the bottom parallel 
to the border and distribute them uniformly over the space, 
but not in rows. A few incomplete tufts, or rows of dots improve 
the appearance. Grass tufts should never be as heavy as tree 
symbols. 

In drawing the symbol for deciduous trees the sequence of 
strokes shown should be followed. 



Meadow 



t, ft r * t 

i t f { f f 

Willows 



O (5 Q O f j) O 
'> O O Q O 0> 
O O> O C> C? Q 



Orchard 



, 

*--^ > * & c?o frisS *s<x --ovi ***V* **-:< 

Evergreen Trees 



Deciduous Trees^ 



Oak Trees 



Pine, Willow& Brush Cleared Land Cultivated Land 

tttuu . rr^vrrur y^y^Vi 

.t, ,i, ^- a, ^, .u i f I i i i i i 
*>i^ iiii 



Corn 



Tobacco 



Vineyard 



FIG. 422. Vegetation. 

The topographic map, Fig. 423, is given to illustrate the general 
execution and placing of symbols. 

Fig. 424 is a type of map made by landscape architects in the 
study of improvements for parks, additions, and estates. Shadows 
are often employed on these maps to show the comparative 
heights of tall trees, low trees, and shrubs. 
Lettering. 

The style of lettering on a topographic map will of course 
depend upon the purpose for which the map is made. If for 
construction purposes, such as a contour map for the study of 
municipal problems, street grades, plants, or railroads, the single- 
stroke gothic and Reinhardt is to be preferred. For a finished 
map vertical Roman letters for land features, and inclined 



MAP AND TOPOGRAPHICAL DRAWING 



243 







244 



ENGINEERING DRAWING 




MAP AND TOPOGRAPHICAL DRAWING 245 

Roman and stump letters for water features should be used. 
The scale should always be drawn as well as stated. 

The well known maps of the Coast Survey and Geological 
Survey are good examples of this kind of map. The quadrangle 
sheets issued by the topographic branch of the U. S. Geological 
Survey are excellent examples and so easily available that every 
draftsman should be familiar with them. These sheets represent 
15 min. of latitude and 15 min. of longitude, and the entire 
United States is being mapped by the department. In 1911 about 
81 per cent, of New York state, 50% of Pennsylvania, and 67% 
of Ohio, and other states in somewhat the same percentages 
are already completed. These maps may be secured for 5 
cents each (not stamps) by addressing The Director, U. S. Geo- 
logical Survey, Washington, D. C., from whom information as to 
the completion of any particular locality or the progress in any 
state may be had. The scale of these maps is approximately 
1 inch to the mile. Some territory in the West has been mapped 
to 1/2 inch to the mile. On the back of each sheet will be 
found a code of the conventional symbols used by the depart- 
ment. 
Profiles. 

Perhaps no kind of drawing is used more by civil engineers than 
the ordinary profile, which is simply a vertical section taken 
along a given line either straight or curved. Such drawings are 
indispensable in problems of railroad construction, highway and 
street improvements, sewer construction, and many other prob- 
lems where a study of the surface of the ground is required. 
Very frequently engineers other than civil engineers are called 
upon to make these drawings. Several different types of pro- 
file and cross-section paper are in use and may be found in the 
catalogues of the various firms dealing in drawing materials. 
One type of profile paper in common use is known as " Plate A" 
in which there are four divisions to the inch horizontally and 
twenty to the inch vertically. Other divisions which are used 
are 4 X 30 to the inch and 5 X 25 to the inch. At intervals 
both horizontally and vertically somewhat heavier lines are 
made in order to facilitate reading. 

Horizontal distances are plotted as abscisses and elevations as 
ordinates. The vertical distances representing elevations, be- 
ing plotted to larger scale, a vertical exaggeration is obtained 
16 



246 



ENGINEERING DRAWING 



which is very useful in studying the profile for the establishing 
of grades. The vertical exaggeration is sometimes confusing to 
the layman or inexperienced engineer, but ordinarily a profile 
will fail in the purpose for which it was intended if the horizontal 
and vertical scale are the same. Again the profile unless so 

H/gbest /b/rtf of Excavation 
6o/d M// /. 34.0 / \ 



Proposed Bottom ofCario/ /. +40 

Mean Sta JLere/ Q 




33 34 35 36 37 38 

Miles 
FIG. 425. Profile. (Vert, scale 50 times hor.) 

distorted would be a very long and unwieldy affair, if not entirely 
impossible to make. The difference between profiles with and 
without vertical exaggeration is shown in Figs. 425 and 426. 
Fig. 427 is a profile together with the alignment which is drawn 



1 



o 


Q. 


o 

c 


1 


% a PP 


<s> 


8 

CO 


3 


3 


Q. 

e 


^T&c^ d ^ 


n Q T3 
?' <? (SjcJ 










Mean Sea Leve/-*^ 




\ 




\ 


\ 


\ \ 


1 | 


1 1 



33 



34 



37 



35 36 

Miles 
FIG. 426. Profile. (Vert, and hor. scales equal.) 

just below the profile proper. This figure represents a common 
method employed by draftsmen in railroad offices. Attention 
is called to the method of straightening out the alignment. 
Such a method is also used on surveys for improvement of high- 
ways and the like. 



MAP AND TOPOGRAPHICAL DRAWING 



247 




CHAPTER XIII. 
DUPLICATION AND DRAWING FOR REPRODUCTION. 

As has been stated, working drawings or any drawings which 
are to be duplicated are traced. Sometimes drawings of a tem- 
porary character are, for economy, traced on white tracing 
paper, but tracing cloth is more transparent, much more durable, 
prints better, and is easier to work on. 

Drawings intended for blue printing are sometimes penciled 
and inked on bond or ledger paper. A print from these papers 
requires more exposure and has a mottled appearance, showing 
plainly the texture and watermarks. 

Tracing cloth is a fine thread fabric, sized and transparentized 
with a starch preparation. The three brands Excelsior, Imperial, 
and Kohinoor are recommended. The smooth side is considered 
by the makers as the right side, but most draftsmen prefer to 
work on the dull side, principally because it will take a pencil 
mark. The cloth should be tacked down smoothly over the 
pencil drawing and its selvage torn off. It should then be dusted 
with chalk or prepared pounce and rubbed off with a cloth, to 
remove traces of grease which sometimes prevents the flow of 
ink (a blackboard eraser serves very well for this purpose) . 

To insure good printing the ink should be perfectly black, 
and the outline should be made with a bolder line than would 
be used on paper, as the contrast of a white line on the blue 
ground is not so strong as the black line on a white ground. 
Red ink should not be used unless it is desired to have some lines 
very inconspicuous. Blue ink will not print. Sometimes, in 
maps, diagrams, etc., to avoid confusion of lines, it is desired to 
use colored inks on the tracing; if so a little Chinese white added 
will render them opaque enough to print. 

Sometimes, instead of section lining, sections are indicated by 
rubbing a pencil tint over the surface on the dull side, or by 
putting a wash of color on the tracing either on the smooth side 
or on the dull side. These tints will print in lighter Hue than 
the background. 

248 



DUPLICATION AND DRAWING FOR REPRODUCTION 249 

Ink lines may be removed from tracing cloth by rubbing with 
a pencil eraser. A triangle should be slipped under the tracing 
to give a harder surface. The rubbed surface should afterward 
be burnished with an ivory or bone burnisher, or with a piece of 
talc (tailor's chalk) or, in the absence of other means, with the 
thumb nail. In tracing a part that has been section lined, a 
piece of white paper should be slipped under the cloth and the 
section lining done without reference to the drawing underneath. 

For an unimportant piece of work it is possible to make a 
freehand tracing from an accurate pencil drawing in perhaps 
one-half the time required for a mechanical drawing. 

Tracing cloth is very sensitive to atmospheric changes, often 
expanding over night so as to require restretching. If the com- 
plete tracing cannot be finished during the day some views 
should be finished, and no figure left with only part of its lines 
traced. 

Water will ruin a tracing, and moist hands or arms should not 
come in contact with the cloth. The habit should be formed of 
keeping the hands off drawings. It is a good plan, in both drawing 
and tracing on large sheets, to cut a mask of drawing paper to 
cover all but the view being worked on. Unfinished drawings 
should always be covered over night. 

Tracings may be cleaned of pencil marks and dirt by rubbing 
over with a rag or waste dipped in benzine or gasolene. 

The starch may be washed from scrap tracing cloth to make 
penwipers or cloths. 

The tracing is a " master drawing" and should never be allowed 
to .be taken out of the office, but prints may be made from it by 
one of the processes described below. Any number of prints 
may be taken from one tracing. 

Blue Printing. 

The simplest of the printing processes is blue printing, made by 
exposing a piece of sensitized paper in contact with the tracing to 
sunlight or electric light in a printing frame made for the purpose. 
The blue print paper is a white paper free from sulphites, coated 
with a solution of citrate of iron and ammonia, and ferricyanide of 
potassium. On exposure to the light a chemical action takes 
place, which when fixed by washing in water gives a strong blue 
color. The parts protected from the light by the black lines 



250 ENGINEERING DRAWING 

of the tracing wash out, leaving the white paper. Blue-print 
paper is usually bought ready sensitized, and may be had in dif- 
ferent weights and different degrees of rapidity. When fresh it 
is of a yellowish green color, and an unexposed piece should wash, 
out perfectly white. With age or exposure to light or air, it 
turns to a darker gray-blue color, and spoils altogether in a 
comparatively short time. In some emergency, it may be neces- 
sary to prepare blue-print paper. The following formula will 
give a paper requiring about three minutes' exposure in bright 
sun-light. 

(1) Citrate of iron and ammonia (brown scales) 2 oz., water 
8 oz. 

(2) Red prussiate of potash 11/2 oz., water 8 oz. 
Keep in separate bottles away from the light. 

To prepare paper take equal parts of (1) and (2) and apply 
evenly to the paper with a sponge or camel's-hair brush, by 
subdued light. 

To make a blue print. 

Lay the tracing in the frame with the inked side toward the 
glass, and place the paper on it with its sensitized surface against 
the tracing. Lock up in the frame so there is a perfect contact 




FIG. 428. A blue print frame. 

between paper and cloth. See that no corners are turned under. 
Expose to the sunlight or electric light. If a frame having a 
hinged back is used, Fig. 428, one side may be opened for ex- 
amination. When the paper is taken from the frame it will be a 
bluish gray color with the heavier lines lighter than the back- 
ground, the lighter lines perhaps not being distinguishable. Put 



DUPLICATION AND DRAWING FOR REPRODUCTION 251 

the print for about five minutes in a bath of running water, 
taking care that air bubbles do not collect on the surface, and 
hang up to dry. An overexposed print may often be saved by 
prolonged washing. The blue color may be intensified and the 
whites cleared by dipping the print for a moment into a bath 
containing a solution of potassium bichromate (1 to 2 oz. of 
crystals to a gallon of water), and rinsing thoroughly. This 
treatment will bring back a hopelessly *' burned " print. 

To be independent of the weather, most concerns use electric 
printing machines, either cylindrical, in which a lamp is lowered 
automatically inside a glass cylinder about which the tracing and 
paper are held, or continuous, in which the tracing and paper 
are fed through rolls, and in some machines, printed, washed 
and dried in one operation. 

Prints too large for a frame may be made in sections and 
pasted together. 

In an emergency it is possible to make a fair print by holding 
tracing and paper to the sunlight against a window pane. 

A clear blue print may be made from a typewritten sheet 
which has been written with a sheet of carbon paper back of it, 
so that it is printed on both sides. 

Van Dyke paper is a thin sensitized paper which turns dark 
brown on exposure and fixing, which is done by first washing in 
water, then in a bath of hyposulphite of soda, and washing 
again thoroughly. A reversed negative of a tracing may be 
made on it by exposing with the inked side of the tracing next 
to the sensitized side of the paper. This negative, if printed on 
blue-print paper will give a blue-line print with white back- 
ground. 

The Van Dyke negative may be " transparentized " so as to 
print in one-half to one-third the time, by a solution sold by the 
dealers, or by a solution of paraffin cut in benzine. 

A direct black paper is made by the Carlton Supply Co., 
Brooklyn, N. Y., which is printed and washed the same as a 
blue print and gives permanent black lines on white ground. 

White ground prints have the advantage that additions or 
notes may be made in ink or pencil, and that tints may be added. 

Changes are made on blue prints by writing or drawing with 
any alkaline solution, such as of soda or potash, which bleaches 
the blue. A little gum arable will prevent spreading. A tint 



252 ENGINEERING DRAWING 

may be given by adding a few drops of red or other colored ink 
to the solution.- Chinese white is sometimes used for white- 
line changes on a blue print. 

A blue print may be made from a drawing made in pencil or 
ink on bond paper or tracing paper, but with thick drawing 
paper the light will get under the lines and destroy the sharpness. 
A print may be made from Bristol or other heavy white paper 
by turning it with the ink side against the paper, thereby revers- 
ing the print, or by making a Van Dyke negative, with a long 
exposure; or it may be soaked in benzine and printed while wet. 
The benzine will evaporate and leave no trace. 

A blue-line print may be taken from a blue print by fading the 
blue of the first print in weak ammonia water, washing thor- 
oughly, then turning it red in a weak solution of tannic acid, 
and washing again. Transparentizing at this stage will assist. 

In printing a number of small tracings they may be fastened 
together at their edges with gummed stickers and handled as a 
single sheet. 

Any white paper may be rendered sufficiently translucent to 
give a good blue print, with the " transparentizing solutions" 
mentioned before, and a machine called the " mechanigraph " 
is now on the market which does this commercially, enabling 
drawings to be made on white paper in pencil, from which 
finished prints can be made without inking or tracing. 

The methods of the hectograph or gelatine pad, neostyle, 
mimeograph, etc., often used for duplicating small drawings, are 
too well known to need description here. 

Large drawings or drawings in sets are often photographed to 
reduced size and blue prints or other prints made from the 
negatives giving convenient prints for reference. 
Drawing for Reproduction. 

By this term is meant the preparation of drawings for repro- 
duction by one of the photo-mechanical processes used for 
making plates, or "cuts," as they are often called, for printing 
purposes. Such drawings will be required in the preparation 
of illustrations for books and periodicals, for catalogues or other 
advertising, and incidentally for patent office drawings, which 
are reproduced by photo-lithography. 

Line drawings are usually reproduced by the process known as 
zinc etching, in which the drawing is photographed on a process 



DUPLICATION AND DRAWING FOR REPRODUCTION 253 

plate, generally with some reduction, the negative film reversed 
and printed so as to give a positive on a sensitized zinc plate 
(when a particularly fine result is desired, a copper plate is used) 




zMMvmmmz^ 



FIG. 429. Drawing for one-half reduction. 




FIG. 430. 



which is etched with acid, leaving the lines in relief and giving, 
when mounted type-high on a wood base, a block which can 
be printed along with type in an ordinary printing press. 



254 



ENGINEERING DRAWING 



Drawings for zinc etching should be made on smooth white 
paper or tracing cloth in black drawing ink and preferably 
larger than the required reproduction. 

If it is desired to preserve the hand-draw T n character of the 




FIG. 431. Drawing for "two- thirds" reduction. 

original, the reduction should be slight; but if a very smooth 
effect is wanted, the drawing may be as much as 3 or 4 times as 
large as the cut. The best general size is one and one-half 
times linear. Fig. 429 illustrates the appearance of an original 




FIG. 432. 

drawing and Fig. 430 the same drawing reduced one-half. Fig. 
431 is another original which has been reduced two-thirds, Fig. 
432. The coarse appearance of these originals and the open 
shading should be noticed. 

A reducing glass, a concave lens mounted like a reading glass 



DUPLICATION AND DRAWING FOR REPRODUCTION 255 

is sometimes used to aid in judging the appearance of a drawing 
on reduction. If lines are drawn too close together the space 
between them will choke in the reproduction and mar the effect. 

One very convenient thing not permissible in other work may 
be done on drawings for reproduction any irregularities may 
be corrected by simply painting out with Chinese white. If it is 
desired to shift a figure after it has been inked it may be cut out 
and pasted on in the required position. The edges thus left 
will not trouble the engraver, as they will be tooled out when 
the etching is finished. 

Wash drawings and photographs are reproduced in a similar 
w T ay on copper by what is known as the half-tone process in 
which the negative is made through a ruled " screen" in front of 
the plate, which breaks up the tints into a series of dots of varying 
size. Screens of different fineness are used for different kinds of 
paper, from the coarse screen newspaper half-tone of 80 to 100 
lines to the inch, the ordinary commercial and magazine half- 
tone of 133 lines, to the fine 150 and 175 line half-tones for print- 
ing on very smooth coated paper. 

Photographic prints for reproduction are often retouched and 
worked over, shadows being strengthened with water color, 
high-lights accented with Chinese white, and details brought 
out that would otherwise be lost. In catalogue illustration of 
machinery, etc., objectionable backgrounds or other features can 
be removed entirely. Commercial retouchers use the air-brush 
as an aid in this kind of work, spraying on color with it very 
rapidly and smoothly and securing results not possible in hand- 
work. 

Half tones cost from ten to fifteen cents per sq. in. with a 
minimum price of $1.00, and zinc etching from five to seven 
cents per sq. in. with a minimum of sixty cents. 

Line illustrations are sometimes made by the "wax process" 
in which a blackened copper plate is covered with a very thin 
film of wax, on which a drawing may be photographed and its 
outline scratched through the wax by hand with different sized 
gravers. The lettering is set up in type and pressed into the 
wax; more wax is then piled up in the wider spaces between the 
lines and an electrotype taken. Drawings for this process need 
not be specially prepared, as the work may be done even from a 
pencil sketch or blue print. Wax plates print very clean and 



256 



ENGINEERING DRAWING 



sharp and the type-lettering gives them a finished appearance, 
but they lack the character of a drawing, are more expensive than 
zinc etching and often show mistakes due to the lack of famili- 
arity of the engraver with the subject. Fig. 433 shows the 
characteristic appearance of a wax plate. 



Gear Bracket Bearing, 1 O.I. 




FIG. 433. A wax plate. 



Maps and large drawings are usually reproduced by lithog- 
raphy, in which the drawing is either photographed or engraved 
on a lithographic stone, and transferred from this either to another 
stone from which it is printed or in the offset process to a thin 
sheet of zinc which is wrapped around a cylinder, and prints to 
a rubber blanket which in turn prints on the paper. 



CHAPTER XIV. 



NOTES ON COMMERCIAL PRACTICE. 

Under this heading there is included a number of suggestions 
and items of miscellaneous information for student and drafts- 
man. 

To Sharpen a Pen. 

Pens that are in constant use require frequent sharpening 
and every draftsman should be able to keep his own pens in 
fine condition. The points of a ruling pen should have an oval 
or elliptical shape as (a) Fig. 434, with the nibs exactly the same 
length, (b) is a worn pen and (c) (d) and (e) incorrect shapes* 








B C D 

FIG. 434. Corrected ruling pen points. 

sometimes found. The best stone to use is a hard Arkansas 
knife piece or knife edge. It is best to soak a new stone in oil 
for several days before using. The ordinary carpenter's oil 
stone is too coarse to be used for instruments. 

The nibs must first be brought to the correct shape as (a) and 
as indicated on the dotted lines of (b), (c) and (d). This is 
done by screwing the nibs together until they touch and, hold- 
ing the pen as in drawing a line, drawing it back and forth on the 
stone, starting the stroke with the handle at perhaps 30 degrees 
with the stone, and swinging it up past the perpendicular as the 

257 



258 ENGINEERING DRAWING 

line across the stone progresses. This will bring the nibs to 
exactly equal shape and length, leaving them very dull. They 
should then be opened slightly and each blade sharpened in 
turn until the bright spot on the end has just disappeared, 
holding the. pen as in Fig. 435 at a small angle with the stone 
and rubbing it back and forth with a slight oscillating or rocking 
motion to conform to the shape of the blade. The pen should 
be examined frequently and the operation stopped just when the 
reflecting spot has vanished. A pocket magnifying glass may 
be of aid in examining the points. The blades should not be 
sharp enough to cut the paper when tested by drawing a line, 
without ink, across it. If over-sharpened the blades should 




FIG. 435. 



again be brought to touch and a line drawn very lightly across 
the stone as in the first operation. When tested with ink the 
pen should be capable of drawing clean sharp lines down to the 
finest hair line. If these finest lines are ragged or broken the pen 
is not perfectly sharpened. It should not be necessary to touch 
the inside of the blades unless a bur has been formed, which 
might occur with very soft metal or by using too coarse a stone. 
In such cases the blades should be opened wide and the bur 
removed by a very light touch, with the entire inner surface of 
the blade in contact with the stone, which of course must be 
sufficiently thin to be inserted between the blades. The beginner 
had best practise by sharpening several old pens before attempt- 
ing to sharpen a good instrument. After using, the stone should 
be wiped clean and a drop of oil rubbed over it to prevent 
hardening and glazing. 

To Make a Lettering Pen.* 

Lettering should never be done with the ruling pen, but some 
draftsmen make a lettering pen for coarse single-stroke letters, 
* Described by Prof. C. L. Adams. 



NOTES ON COMMERCIAL PRACTICE 



259 



out of an old ruling pen by first rubbing the point very blunt, 
then grinding the blades together to a conical shape, and finally 
shaping a ball end on the blunted point. This pen will make a 
line somewhat similar to that made by the Payzant and Shepard 
pens. Its handle should be plainly cut or marked to distinguish 
it from a ruling pen. 

Line Shading. 

Line shading, the rendering of the effect of light and shade by 
ruled lines, was referred to in Chapter VI as " an accomplishment 
not usual among ordinary draftsmen." The reason for this is 
that it is not used at all on working drawings and the drafts- 
man engaged in that work does not have occasion to apply it. 
It is used, however, on display drawings, illustrations, patent 
office drawings, and the like, and is worthy of study if one is 
interested in this class of finished work. 




FIG. 436. Flat and graded tints. 



To execute line shading rapidly and effectively requires con- 
tinued practice and some artistic ability, and, as much as any- 
thing else, good judgment in knowing when to stop. Often the 
simple shading of a shaft or other round member will add greatly 
to the effectiveness of a drawing, and may even save making 
another view, or a few lines of " surface shading " on a flat surface 
will show its position and character. The pen must be in per- 
fect condition, with its screw working very freely. 

Fig. 436 shows three preliminary exercises in flat and graded 
tints in which the pitch or distance from center to center of lines 
is equal. In wide graded tints as (b) and (c) the setting of the 
pen is not changed for every line, but several .lines are drawn, 



260 



ENGINEERING DRAWING 



then the pen changed slightly and several more drawn. Fig. 
437 is an application, illustrating the rule that an inclined 
illuminated surface is lightest nearest the eye and an inclined sur- 
face in shade is darkest nearest the eye. 

With the light coming in the conventional direction a cylinder 
would be illuminated as in Fig. 438. Theoretically the darkest 





^ Shade Snt 



FIG. 437. 



FIG. 438. 



line 'is at the tangent or shade line and the lightest part at the 
"brilliant line" where the light is reflected directly to the eye. 
Cylinders shaded according to this theory are the most effective, 
but often in practice the dark side is carried out to the edge, and 
in small cylinders the light side is left unshaded. 




ABC D 3" 

FIG. 439. Cylinder shading. 



Fig. 439 is a row of cylinders of different sizes. The effect of 
polish is given by leaving several brilliant lines, as might occur 
if the light came in through several windows. 

A conical surface may be shaded by driving a fine needle at 
the apex and swinging a triangle about it, as in (A) Fig. 440. 



NOTES ON COMMERCIAL PRACTICE 



261 



To avoid a blot at the apex of a complete cone the needle may 
be driven on the extension of the side as in (B), or it may be 
shaded by parallel lines as in (C). 
Fig. 441 illustrates several applications of these principles. 




A B C 

FIG. 440. Cone shading. 





FIG. 441. Shaded single curved surfaces. 




FIG. 442. Spheres. 

It is in the attempt to represent double curved surfaces that 
the line-shader meets his principal troubles. The brilliant line 
becomes a brilliant point and the tangent shade line a curve, 
and to represent the gradation between them by mechanical 
lines is a difficult proposition. 
17 



262 



ENGINEERING DRAWING 



Fig. 442 shows three methods of shading a sphere. The bril- 
liant point and shade line may be found by revolving the pro- 
jecting plane of the ray passing through the center, about its 





FIG. 443. 






FIG. 444. Shaded double curved surfaces. 

vertical trace as in Fig. 443, but in practice these are usually 
"guessed in." The first method (a) is the commonest. Con- 
centric circles are drawn from the center, with varying pitch, 



NOTES ON COMMERCIAL PRACTICE 263 

and shaded on the lower side by springing the point of the com- 
pass. In (b) the brilliant point is used as center. In (c), the 
"wood cut" method, the taper on the horizontal lines is made 
by starting with the pen out of perpendicular and turning the 
handle up as the line progresses. 

Fig. 444 shows several applications with double curved surfaces 
of different kinds. 

Patent Office Drawings. 

In the application for letters patent on an invention or dis- 
covery there is required a written description called the specifi- 
cation, and in case of a machine, manufactured article, or device 
for making it, a drawing, showing every feature of the invention. 
If it is an improvement, the drawing must show the invention 
separately, and in another view a part of the old structure with 
the invention attached. A high standard of execution, and con- 
formity to the rules of the Patent Office must be observed. A 
pamphlet called the "Rules of Practice," giving full information 
and rules governing patent office procedure in reference to appli- 
cation for patents may be had gratuitously by addressing the 
Commissioner of Patents, Washington, D. C. 

The drawings are made on smooth white paper specified to be 
of a thickness equal to three-sheet Bristol-board. Two-ply 
Reynolds board is the best paper for the purpose, as prints may 
be made from it readily, and it is preferred by the Office. The 
sheets must be exactly 10 by 15 inches, with a border line one 
inch from the edges. Sheets with border and lettering printed, 
as Fig. 445, are sold by the dealers, but are not required to be used. 

A space of not less than 11/4 inches inside of the top border 
must be left blank for the printed title added by the Office. 

Drawings must be in black ink, and drawn for a reproduction 
to reduced scale. As many sheets as are necessary may be used. 
In the case of large views any sheet may be turned on its side 
so that the heading is at the right and the signatures at the left, 
but all views on the same sheet must stand in the same direction. 

Patent Office drawings are not working drawings. They are 
descriptive and pictorial rather than structural, hence will have 
no center lines, no dimension lines nor figured dimensions, no 
notes nor names of views. The scale chosen should be large 
enough to show the mechanism without crowding. Unessential 



264 



ENGINEERING DRAWING 



details or shapes need not be represented with constructional 
accuracy, and parts need not be drawn strictly to scale. For 
example, the section of a thin sheet of metal drawn to scale 
might be a very, thin single line, but it should be drawn with a 
double line, and section-lined between. 

Section lining must not be too fine. One-twentieth of an 
inch pitch is a good limit. Solid black should not be used 
excepting to represent insulation or rubber. 





3 

T 






'xj 77?/5 space /eft fr/anA; fo be /?//&& 
~Y in a/ We f&fefff <?fifce 




* 




\ 




ATTORNEY 






T 






. _ 






FIG. 445. 





Shade lines are always added, except in special cases where 
they might confuse or obscure instead of aid in the reading. 

Surface shading by line shading is used whenever it will add 
to the legibility, but it should not be thrown in indiscriminately 
or lavishly simply to please the client. 

Gears and toothed wheels must have all their teeth shown, 
and the same is true of chains, sprockets, etc., but screw threads 
may be represented by the conventional symbols. The Rules 
of Practice gives a chart of electrical symbols, symbols for colors, 
etc., which should be followed. 

The drawings may be made in orthographic, axonometric, 



NOTES ON COMMERCIAL PRACTICE 265 

oblique, or perspective. The pictorial system is used extensively, 
for either all or part of the views. The examiner is of course ex- 
pert in reading drawings, but the client, and sometimes the attor- 
ney, .may not be, and the drawing should be clear to them. In 
checking the drawing for completeness it should be remembered 
that in case of litigation it may be an important exhibit in the 
courts. 

Only in rare cases is a model of an invention required by the 
Office. 

The views are lettered "Fig. 1," "Fig. 2" etc., and the parts 
designated by reference numbers though which the invention is 
described in the specifications. One view, generally "Fig. 1," 
is made as a comprehensive view that may be used in the Official 
Gazette as an illustration to accompany the "claims." 




FIG. 446. 

The draftsman usually signs the Hrawing as the first witness. 
The inventor signs the drawing in the lower right-hand corner. 
In case an attorney prepares the application and drawing, the 
attorney writes or letters the name of the inventor, signing his 
own name underneath as his attorney. 

To avoid making tack holes in the paper it should be held to 
the board by the heads of the thumb tacks only. 

Fig. 446 is a clamp drawing board used by some patent drafts- 
men. 

The requirements for drawings for foreign patents vary in 
different countries, most countries requiring drawings and several 
tracings of each sheet. 

Fig. 447 is an example of a patent office drawing, reduced to 
1/2 size. 

Stretching Paper and Tinting. 

If a drawing is to be tinted the paper should be stretched on 
the board. First, dampen it thoroughly until limp, either with 



266 



ENGINEERING DRAWING 




WITNESSES: 




Duqizesne Sprague INVENTOR. 




FIG. 447. A patent office drawing. 



NOTES ON COMMERCIAL PRACTICE 267 

a sponge or under the faucet, then lay it on the drawing board 
face down, take up the excess water from the edges with a 
blotter, brush glue or paste about one-half inch wide around the 
edge, turn over and rub the edges down on the board until set, 
and allow to dry horizontally. 

Drawings or maps on which much work is to be done, even 
though not to be tinted, may be made advantageously on 
stretched paper; but Bristol or calendered paper should not be 
stretched. 

Tinting is done with washes made with moist water colors. 
The drawing may be inked (with waterproof ink) either before, 
or preferably after tinting. 

The drawing should be cleaned and the unnecessary pencil 
marks removed with a very soft rubber, the tint mixed in a 
saucer and applied with a camePs-hair or sable brush, inclining 
the board and flowing the color with horizontal strokes, leading 
the pool of color down over the surface, taking up the surplus 
at the bottom by wiping the brush out quickly and picking up 
with it the excess color. Stir the color each time the brush is 
dipped into the saucer. Tints should be made in light washes, 
depth of color being obtained if necessary by repeating the wash. 
To get an even color it is well to go over the surface first with a 
wash of clear water. 

Diluted colored inks may be used for washes instead of water 
color. 

Mounting Tracing Paper. 

Tracings are mounted for display, on white mounts, either by 
"tipping" or "floating." To tip a drawing brush a narrow 
strip of glue or paste around the under edge, dampen the right 
side of the drawing by stroking with a sponge very slightly 
moistened, and stretch the paper gently with the thumbs on 
opposite edges, working from the middle of the sides toward the 
corners. 

To float a drawing make a very thin paste and brush a light 
coat over the entire surface of the mount, lay the tracing paper 
in position and stretch into contact with the board as in 
tipping. If 'air bubbles occur force them out by rubbing from 
the center of the drawing out, laying a piece of clean paper over 
the drawing to protect it. 



268 ENGINEERING DRAWING 

Mounting on Cloth. 

It is sometimes necessary to mount drawings or maps on cloth. 
The following methods are used: 

Hot mounting is best for both heavy and thin paper. For 
heavy paper, tack down mounting cloth with another cloth 
under, put 1/2 pint library paste with 1/2 oz. water in pan 
and bring to boil. With broad brush paste back of drawing or 
print quickly, working from center out, turn over and place on 
cloth. Have hot iron ready and iron print from center out, in 
circular motion, ironing fast until edges are stuck, then removing 
tacks to release the steam and ironing till dry. Never iron on 
the back, as the steam formed will cause blisters. 

Cold paste 'may be used for hurry work, applying it to the 
cloth instead of the paper, and ironing as before. 

For mounting thin paper. The print to be mounted is rolled, 
face in, on a large roller (a roll of detail paper may be used), 
hot paste applied starting at end, the print rolled off on the 
cloth, and followed up as fast as unrolled by hot irons. If cold 
paste is used apply it to the cloth. Never attempt to apply 
cold paste on thin paper. 

Cold Mounting. When hot irons are not available, prints 
may be mounted by stretching cloth tightly on table, applying 
paste, and rolling with photographic print roller, leaving the 
cloth stretched until perfectly dry. 

Methods of Copying Drawings. 

Drawings are often copied on opaque paper by laying the 
drawing over the paper and pricking through with a needle 
point, turning the upper sheet back frequently and connecting 
the points. Prickers may be purchased, or may be m,ade easily 
by forcing a fine needle into a soft wood handle. They may be 
used to advantage also in accurate drawing, in transferring 
measurements from scale to paper. 

Transfer by Rubbing. 

This method is used extensively by architects, and may be 
used to good advantage in transferring any kind of sketch or de- 
sign to the paper on which it is to be rendered. 

The original is made on any paper, and may be worked over, 
changed, and marked up until the design is satisfactory. Lay 



NOTES ON COMMERCIAL PRACTICE 269 

a piece of tracing paper over the original and trace the outline 
carefully. Turn the tracing over and retrace the outline just 
as carefully on the other side, using a medium soft pencil (perhaps 
H or 2H) with a sharp point. Turn back to first position and tack 
down smoothly over the paper on which the drawing is to be 
made, registering the tracing to proper position by center or 
reference lines on both tracing and drawing. Now transfer the 
drawing by rubbing the tracing with the rounded edge of a 
knife handle or other instrument (a smooth-edged coin held 
between thumb and forefinger and scraped back and forth is 
commonly used), holding a small piece of tracing cloth with 
smooth side up between the rubbing instrument and the paper, 
to protect the paper. Do not rub too hard, and be sure that 
neither the cloth nor paper move while rubbing. 

Very delicate drawings can be copied with great accuracy in 
this manner. 

If the drawing is symmetrical about any axis the reversed 
tracing need not be made, but the rubbing can be made from 
the first tracing by reversing it about the axis of symmetry. 



P&fffeGtoss 




FIG. 448. A transparent drawing board. 

Several rubbings can be made from one tracing, and when the 
same figure or detail must be repeated several times on a drawing 
much time can be saved by drawing it on tracing paper and 
rubbing it in the several positions. 

A Transparent Drawing Board. 

A successful device for copying drawings on opaque paper is 
illustrated in Fig. 448. A wide frame of white pine carrying a 
piece of plate glass set flush with the top, is hinged to a base 
lined with bright tin. A sliding bar carries two show-case lamps, 
whose light may thus be concentrated under any part of the 



2fO 



ENGINEERING DRAWING 



drawing. Ventilation and protection from overheating is provided 
by the ground glass and air space between it and the plate glass. 

The frame has a piece of felt glued on the bottom and may be 
used on the top of any table where connection with an electric 
light outlet is convenient. 

Drawings even in pencil may be copied readily on the heaviest 
paper or Bristol-board by the use of this device. 




FIG. 449. Pantograph. 

The Pantograph. 

The principle of the pantograph, used for reducing or enlarging 
drawings in any proportion, is well known. Its use is often of 
great advantage. It consists essentially of four bars, which for 
any setting must form a parallelogram, and have the pivot, 




FIG. 450. Suspended pantograph. 

tracing point, and marking point in a straight line; and any 
arrangement of four arms conforming to this requirement will 
work in true proportion. Referring to Fig. 449 the scale of 
enlargement is PM/PT or AM/AB. For corresponding reduc- 
tion the tracing point and marking point are exchanged. 



NOTES ON COMMERCIAL PRACTICE 



2ft 



The inexpensive wooden form of Fig. 449 is sufficiently accurate 
for ordinary outlining. A suspended pantograph with metal 
arms, for accurate engineering work, is shown in Fig. 450. 

Drawings may be copied to reduced or enlarged scale by using 
the proportional dividers. 

The well-known method of proportional squares is often used 
for reduction and enlargement. The drawing to be copied is 
ruled in squares of convenient size, or, if it is undesirable to mark 
on the drawing, a sheet of ruled tracing cloth or celluloid is laid 
over it, and the copy made freehand on the paper, which has 
been ruled in corresponding squares, larger or smaller, Fig. 451. 




FIG. 451. Enlargement by squares. 

About Tracings. 

Sometimes it is desired to add an extra view, or a title, to a 
print without putting it on the tracing. This may be done by 
drawing the desired additions on another piece of cloth of the 
same size as the original, and printing the two tracings together. 

A figure may be taken out of a tracing, and another inserted 
by making an " inlay, " laying the new piece under the tracing and 
cutting through both together with a sharp knife, then fastening 
the new piece in the hole with collodion. 

Do not take up a blot with a blotter, but scoop it up with the 
finger, leaving a smear. Erase the smear when dry, with a 
pencil eraser. 



272 ENGINEERING DRAWING 

To prevent smearing in cleaning, titles if printed from type on 
tracing cloth should be printed in an ink not affected by benzine. 
Local printers are often unable to meet this requirement, but 
there are firms which make a specialty of this kind of printing. 

Preserving Drawings. 

A drawing, tracing, or blue print which is to be handled much 
may be varnished with a thin coat of white shellac. 

Prints made on sensitized cloth will withstand hard usage. 

A method of imbedding drawings in sheet celluloid, making 
them water- and grease-proof, is carried on by the Dodge Motor 
Map Co., N. Y. The cost is about fifty cents a square foot. 

Blue prints for shop use are often mounted for preservation 
and convenience, by pasting on' tar board or heavy press board 
and coating with white shellac or Damar varnish. A coat of 
white glue under the varnish will aid still further in making the 
drawings washable. 

Tracings to which more or less frequent reference will be made 
should be filed flat in shallow drawers. Sets of drawings pre- 
served only for record are often kept in tin tubes numbered and 
filed systematically. A pasteboard tube with screw cover is also 
made for this purpose. It is lighter than tin and withstands 
fire and water even better. 

Fireproof storage vaults should always be provided in connec- 
tion with drafting rooms. 




FIG. 452. 

Miscellaneous hints. 

A temporary adjustment of a T-square may be made by put- 
ting a thumb tack in the head, Fig. 452. 

A homemade ellipsograph has been made on the principle of 
the pin-and-string method of Fig. 90 by adding a clip to the 
compass pen to hold the string, which will pull the leg in as the 
compass, with its center at 0, moves from B to D. 



NOTES ON COMMERCIAL PRACTICE 273 

If much ruling in red ink is done, a pen for the purpose with 
nickel plated or german silver blades is advisable. 

A steel edge to a drawing board is made of an angle iron planed 
straight and set flush with the edge. With this edge and a 
steel T-square very accurate plotting may be done. These are 
often used in bridge offices. 



CHAPTER XV. * 
BIBLIOGRAPHY OF ALLIED SUBJECTS. 

The present book has been written as a general treatise on the 
language of Engineering Drawing. The following short classi- 
fied list of books is given both to supplement this book, whose 
scope permitted only the mention or brief explanation of some 
subjects, and as an aid to those who might desire the recommen- 
dation of a book on some branch of drawing or engineering. 

Architectural Drawing. 

Ware, Wm. R. The American Vignola. 2 v. 9 1/2x12 1/2. 
Scranton, 1906. 

Part I, The Five Orders. 76 pp., 18 pi. $2.50. 
Part II, Arches and Vaults, Roofs and Domes, Doors 
and Windows, Walls and Ceilings, Steps and 
Staircases. 50 pp., 19 pi. $2.50. 

Simple proportions for drawing the classic orders; and their 

application in composition. 

A book every architectural draftsman should have. 

Martin, Clarence A. Details of Building Construction. 
33 pi. 9 1/2x12 1/2. $2.00. Bates & Guild,. 1905. 

Suggestive details of domestic architecture representing good 
practice, principally in wood, as windows, cornices, etc. 

Snyder, Frank M. Building Details. Issued in parts of 
10 pi. each, 16x22. $2.25 net. N. Y., 1906 

Selections of fully dimensioned details, principally of large 
buildings, from the drawings of various representative 
architects. 

Descriptive Geometry. 

Church, Albert E. Elements of Descriptive Geometry. 
286 pp., 6x8 1/2 rev. ed. $2.25 net. American Book Co., 1911. 

This book has been a standard ever since its original publica- 
tion in 1864. The present revision is by Geo. M. Bartlett. 

Anthony and Ashley. Descriptive Geometry. 134 pp. ,34 
pi., obi. 6x7 1/2. $2.00. D. C. Heath & Co., 1909. 
A comprehensive elementary treatise. 
274 



BIBLIOGRAPHY OF ALLIED SUBJECTS 275 

MacCord, C. W. Elements of Descriptive Geometry. 248 
pp., 6x9. $3.00. Wiley, 1902. 

Particularly good on auxiliary planes and warped surfaces. 

Gears and Gearing. 

Logue, Charles H. American Machinist Gear Book, 348 pp., 
6x9. $2.50. McGraw-Hill, 1910. 

"Simplified tables and formulas for designing, and practical 
points in cutting all commercial types of gears." 

Grant, George B. A Treatise on Gear Wheels, 103 pp., 
6x9. Phila. Gear Works, 1906. 

A practical book on the designing and cutting of gears. 

Anthony, G. C. The Essentials of Gearing. 84 pp., 15 fold- 
ing pi., obi. 6x7 1/2. $1.50. D. C. Heath & Co., 1897. 

An elementary text-book on the drawing of tooth outlines. 

Stutz, Charles C. Formulas in Gearing. 6x9, 5th ed., 183 
pp., $2.00. Brown and Sharpe Mfg. Co., 1907. 
Useful formulas for gear design. 

Handbooks. 

A great many "pocket size" handbooks, with tables, formulas, 
and information are published for the different branches of 
the engineering profession, and draftsmen keep the ones 
pertaining to their particular line at hand for ready reference. 
Attention is called, however, to the danger of using handbook 
formulas and figures without understanding the principles 
upon which they are based. " Handbook designer" is a term 
of reproach applied not without reason to one who depends 
wholly upon these aids without knowing their theory or 
limitations. 

Among the best known of these reference books are the 
following: 

American Civil Engineers' Pocketbook, Mansfield Merriman, 
ed. in chief. 1380 pp. $5.00 net. Wiley, 1911. 

A new book by a corps of well-known engineers. 

American Machinists' Handbook, and Dictionary of Shop 
Terms, by F. H. Colvin and Frank A Stanley. 513 pp. $3.00 net. 
McGraw-Hill, 1908. 

" A reference book on machine-shop and drawing-room data, 
methods and definitions." 

Architects' and Builders' Pocketbook, F. E. Kidder. 
15th ed., 1661 pp. $5.00. Wiley, 1908. 

The standard architects' reference book. 



276 ENGINEERING DRAWING 

Cambria Steel. A Handbook of Information Relating to 
Structural Steel Manufactured by the Cambria Steel Co. 468 pp. 
$1.00. Phila., 1907. 

A standard book for structural steel designers. 

Carnegie. Pocket Companion containing Useful Informa- 
tion and Tables appertaining to the Use of Steel as manufactured 
by the Carnegie Steel Co. 345 pp. $2.00. Pittsburg, 1903. 

Catalogue of Bethlehem Structural Shapes, Manufactured 
by Bethlehem Steel Co. ,72 pp. Bethlehem, Pa., 1909. 
Contains tables for shapes rolled by this company. 

Civil Engineers' Pocketbook, J. C. Trautwine. 19th ed., 
1257 pp. $5.00 net. Trautwine Co., Phila., 1909. 

The best known reference book for civil engineers. 

Electrical Engineers' Pocketbook. H. A. Foster, ed., 
1599 pp. $5.00. D. Van Nostrand, N. Y., 1908. 

"A handbook of useful data for electricians and electrical 
engineers." 

Handbook of Cost Data. H. P. Gillette. 1841 pp. $5.00. 
Myron C. Clark, Chicago, 1910. 

For civil engineers and contractors. 

Mechanical Engineers' Pocketbook. Wm. Kent. 8th ed., 
1461 pp. $5.00 net. Wiley, 1910. 

" A reference book of rules, tables, data, and formulae, for the 
use of engineers, mechanics, and students." Universally 
known by mechanical engineers. 

Mechanical Engineers' Reference Book. H. H. Suplee. 
3rd ed., 922 pp. $5.00 net. J. B. Lippincott, Phila., 1907. 

" A handbook of tables, formulas, and methods for engineers, 
students, and draftsmen." 

Standard Handbook for Electrical Engineers. 3rd ed., 
1500 pp. $4.00 net. McGraw-Hill, 1910. 

Contains a more complete theoretical treatment than Foster. 
Of particular value to students. 

Machinery Data Sheets, 6x9 "Machinery" N. Y. 

A series of data sheets for designers, published as supplements 
to the periodical. Back numbers cut and bound may be 
purchased. 

Lettering. 

French (Thos. E.) and Meiklejohn, (R). The Essentials 
of Lettering. 3d ed., 76 pp., 6x9. $1.00. McGraw-Hill, 1911. 
" A manual for students and designers." 



BIBLIOGRAPHY OF ALLIED SUBJECTS 277 

Reinhardt, Chas. W. Lettering for Draftsmen, Engineers, 
and Students. 23 pp., 8 pi., 8x11. $1.00 net. D. Van Nostrand, 
1895. 

A complete analysis of the single-stroke "Reinhardt" letter. 

Machine Drawing and Design. 

A great many text-books and reference books have been 
written on machine drawing and designing. A few only are 
noted here. 

Unwin, William C. Elements of Machine Design. 

Part I, General principles, fastenings and transmission 
machinery, new ed., 531 pp., 5 1/2x8 1/2. 
$2.50. Longmans, Green & Co., 1909. 
Part II, Engine details 431 pp., 5x7. $2.00. Longmans, 

Green & Co., 1902. 

A standard English text-book widely used in this country. 
Spooner, Henry J. Machine Design, Construction, and 
Drawing. 691 pp., 5 1/2x8 1/2. $3.50 net. Longmans, Green 
& Co., 1910. 

Another English text-book conforming to .modern English 
engineering practice. 

Cathcart, W. E. L. Machine Design. 

Part I, Fastenings, 6x9 1/2, 291 pp. $3.00 net. Van 
Nostrand, 1903. 

A good reference book giving modern American data from 
best practice. 

Kimball and Barr. Elements of Machine Design. 446 pp., 
6x9. $3.00.- Wiley, 1909. 

A text-book with discussion of the fundamental principles of 
design. 

Reid (John S.) and Reid (David). A Text-book of Mechani- 
cal drawing and Elementary Machine Design. 439 pp., 6x9. 
$3.00. Wiley, 1910. 

Contains an interesting summary of an investigation into 
present practice in drafting-room conventions and methods. 

Jepson, George. Cams and the Principles of their Construc- 
tion. 59 pp., 6x9. $1.50 net. Van Nostrand, 1905. 

A short discussion of various forms of cams and the methods 
of drawing them. 

Mechanism. 

Robinson, S. W. Principles of Mechanism. A Treatise on 
the Modification of Motion by means of the Elementary Combina- 
18 



278 ENGINEERING DRAWING 

tions of Mechanism, or of the Parts of Machines. 309 pp., 6x9. 

$3.00. Wiley, 1900. 

The authority on non-circular gearing. Treatment mainly 
by graphics instead of analysis. 

Barr, John H. Kinematics of Machinery. 2nd ed., 264 pp., 

6x9. $2.50. Wiley, 1911. 

" A brief treatise on constrained motion of machine elements." 
(Revised by Edgar H. Wood.) 

Dunkerley, S. Mechanism. 2nd ed., 448 pp., 6x9. $3.00. 

Longmans, Green & Co., 1907. 

A modern text-book on the kinematics of machines, used in 
English colleges. 

Perspective. 

Ware, Wm. R. Modern Perspective, a Treatise upon the 
Principles and Practice of Plane and Cylindrical Perspective, 
6th ed., 336 pp., 5x7 1/2 and atlas of plates. $4.00. MacMillan, 
1900. 

An exhaustive work. 

Longfellow, Wm. P. P. Applied Perspective for Architects 
and Painters. 8x11, 95 pp., 33 pi. $2.50 net. Houghton, 
Mifflin & Co., 1901. 

A practical book on architectural perspective. 

Fuchs, Otto. Handbook on Linear Perspective, Shadows 
and Reflections. 8x10, 34 pp., 13 folding pi. $1.00 Ginn & Co., 
1902. 

An elementary presentation in problem form, for artists and 
architects. 

Wilson, Victor T. Freehand Perspective. 5 1/2x9, 257 pp. 
$2.50. Wiley, 1900. 

A thorough discussion of the principles and their application 
in freehand sketching. 

Mathewson, Frank E. Perspective Sketching from Work- 
ing Drawings. 5x8, 77 pp. $1.00. The Taylor-Holden Co., 
1908. 

A good elementary book on freehand perspective. 
Frederick, Frank Forrest. Simplified Mechanical Perspec- 
tive, 54 pp., 7x10, 75 cents. The Manual Arts Press, 1909. 

An elementary explanation of linear perspective. 
Rendering. 

Maginnis, Charles D. Pen Drawing. An Illustrated Treat- 
ise. 130 pp., 5x7 1/2. $1.00 net. Bates & Guild, 1904. 

By a well-known architect. Should be in the library of every 
architectural draftsman. 



BIBLIOGRAPHY OF ALLIED SUBJECTS 279 

Frederick, Frank F. The Wash Method of Handling Water 
Color. 16 pp., 7x10. 50 cents. Manual Arts Press, 1908. 
A helpful little guide in the use of water color. 

Shades and Shadows. 

McGoodwin, Henry. Architectural Shades and Shadows. 
118 pp., 9 1/2x12. $3.00. Bates & Guild, 1904. 

The principles of casting shadows, and their application on 
architectural forms. 

Sheet Metal. 

Kittredge, Geo. W. The New Metal Worker Pattern Book. 
429 pp., 9x11 1/2. $5.00. David Williams, N. Y., 1911. 

An exhaustive treatise on the principles and practice of pattern 
cutting as applied to sheet metal work. 

Stereotomy. 

French (A. W.) and Ives (H. C.). Stereotomy. 119 pp., 
21 folding pi., 6x9. $2.50. Wiley, 1902. 

Contains practical examples of the application of stone cut- 
ting in architectural and engineering structures. 

Warren, S. E. Stereotomy, Problems in Stone Cutting. 

126 pp., 10 folding pi., 6x9. $2.50.' Wiley, 1893. 
For civil engineering students. 

Structural Drawing. 

Morris, Clyde T. Designing and Detailing of Simple Steel 
Structures. 201 pp., 6x9. $2.75. Eng. News, N. Y., 1909. 

A clear and concise text for both students and practical men. 

Surveying. 

Johnston, J. B. The theory and Practice of Surveying. 
17th ed. Rewritten by L. S. Smith, 921 pp., 5 1/2x8. $3.50 net. 

Wiley, 1911. 

A standard work on surveying. 

Breed and Hosmer. The Principles and Practice of Sur- 
veying. 2 v., 6x9. Wiley, 1908. 

V. I, 546 pp., Plane and Topographic Surveying. $3.00. 
V. II, 432 pp., Higher Surveying. $2.50. 

Another standard work with very full discussion of drafting- 
room practice. 

Tracy, John C. Plane Surveying. 792 pp., 4x7. $3.00. 

Wiley, 1907. 

A text-book and manual in convenient handbook form. A 
thorough and practical book on plane surveying. 



280 ENGINEERING DRAWING 

Technic and Standards. 

Follows, Geo. H. Universal Dictionary of Mechanical 
Drawing, 60 pp., 8x11. $1.00. Eng. News, N. Y., 1906. 

A book of proposed standards and conventions to introduce 

better uniformity. 

Reinhardt, Charles W. The Technic of Mechanical Draft- 
ing. 3rd ed., 42 pp., 11 pi. $1.00. Eng. News, N. Y., 1909. 

A guide to good technic, particularly for drawing for 
reproduction, with excellent examples of work. 

Topographical Drawing. 

Reed, Lieut. H. A. Topographical Drawing and Sketching, 
Including Applications of Photography. 2 v. in one, 140 + 88 
pp., 26 folding pi., 9x12. $5.00. Wiley, 1890. 

An exhaustive text and reference book on the subject. 

Daniels, Frank T. A Text-book of Topographical Drawing. 
144 pp., 6x7 1/2. $1.50. D. C. Heath & Co., 1908. 

A well arranged book on ink and color topography, with 
practical problems. 

Wilson, H. M. Topographic Surveying. 3rd ed., 910 pp., 
6x9. $3.50. Wiley, 1908. 

A complete work on topographic surveying, containing a 
chapter on topographical drawing. 



INDEX 



INDEX 



A. 

Acme threads, 159 
Adjustable head T-square, 10 
Air-brush, 255 

A. L. A. M. standard bolts, 165 
Alignment, profile, 246 

test for, 7 

Allen set screw, 167 
Alphabet of lines, 39 
Alteneder, Theo., 5 

bottle holder, 22 
Arc, to rectify, 49 

through three points, 48 

tangent to two lines, 48 
Architectural drawing, 214 
books on, 274 

symbols, 220 
Architect's scale, 11 
Arkansas oil stone, 257 
Artist, 1, 66 
Assembly drawing, 147 
Auxiliary views, 74, 75, 76 

problems, 91 
Axes, of revolution, 82, 83 

isometric, 124 

reversed, 127 
Axonometric projection, 133 

sketching, 207 

B. 

Babbitt metal, 174 
Beam compass, 18 
Bill of material, 152, 181 

examples of, 154 
Black prints, 251 
Blue line prints, 251 
Blue print paper, 250 

frame, 250 

from typewritten sheet, 251 

machines, 251 

mounting, 272 

to change, 251 



Blue printing, 249 
Bolts, 162 

A. L. A. M. standard, 165 

table of U. S. standard, 163 
Books, 274 
Border pen, 17 
Bottle holders, 22 
Bow instruments, 8 

use of, 33 

Breaks, conventional, 176 
Briggs pipe thread, 168 
Bristol board, 15, 270 

patent office, 263 
Broken section, 79 
Brown prints, 251 
Buttress thread, 159 

C. 

Cabinet projection, 133 
Cap screws, 165 
Castellated nut, 165 
Cautions, 46 
Cavalier projection, 129 
Checking, 178 
Chinese white, 248, 255 
Circle, involute of, 56 

isometric, 125, 126 

oblique, 132 

to draw, 32 

to shade, 86 
Circular arc through three points, 

48 

City plat, 254 

Clinographic projection, 134 
Colored inks, 248, 267 
Commercial sizes, 177 
Compass, 7 

beam, 18 

use of, 31 
Cones, development of, 105 

development of oblique, 108 

intersection of, 114 



283 



284 



INDEX 



Cones, intersection with cylinder, 
112 

shading, 260 
Conic sections, 50 
Conical helix, 157 
Conjugate axes, 52 
Contour map, 230, 237 
Contour pen, 17 
Contours, 235 
Conventional symbols, see Symbols 

threads, 159, 160 
Copying drawings, 

by pantograph, 270 

by pricking, 268 

by proportional squares, 271 

by rubbing, 268 

by tracing, 248 

by transparent drawing board, 

269 
Cross-hatching, 80 

conventional, 175 

instruments for, 19 

on patent drawings, 264 
Cross-section paper, 206 
Crystallography, 134, 135 
Culture, symbols for, 240 
Curve, ogee, 48 

to ink with circle arcs, 54 
Curve pen, 17 
Curves, 14 

use of, 41 
Cycloid, 55 
Cylinders, development of, 102 

intersection of, 111 

intersection with cones, 112 

shading, 260 

D. 

Design drawing, 147 
Details, architectural, 226 
Detail drawing, 147 

papers, 16 

pen, 8 
Descriptive geometry, 66 

books on, 274 
Development, 101 

cone, 101 

cylinder, 102 



Development, elbow, 103 

hexagonal prism, 102 

oblique cone, 108 

octagonal dome, 105 

pyramid, 105 

sphere, 107 

truncated cone, 105 
Dimensions, 150 

architectural, 226 

of threads, 162 

on sketches, 204 

on structural drawings, 180 

problems for, 185 
Dimetric projection, 133 
Display drawings, 215 

maps, 232 
Dividers, 7 

hairspring, 7 

plain, 7 

proportional, 17 

use of, 27 
Dotted section, 80 
Dotting pen, 21 
Double curved surfaces, 100 

development of, 107 

shading, 262 
Drafting machine, 20 
Drawing boards, 9 

patent office, 265 

steel edge for, 273 

transparent, 269 
Drawing from description, problems, 

98 
Drawing paper, 15 

pencils, 13 
Drop pen, 19, 180 
Duplication, 248 

E. 

Elbow, development of, 103 
Electrical symbols, 176 

for wiring, 221 
Elevations, 223 
Ellipse, 50 

approximate, four centers, 53, 

54 

eight centers, 53 
conjugate axes, 52 



INDEX 



285 



Ellipse, parallelogram method, 52 
pin and string method, 52 
trammel method, 51 

Ellipsograph, 51 

Engineers' scale, 11, 35 

English T-square, 10 

Epicycloid, 55 

Erasing shields, 22 

Exercises, in orthographic projec- 
tion, 73 
in reading, 144 
in sketching, 213 
in use of instruments, 42 

F. 

Farm survey, 230 

Fastenings, 156 

Faulty lines, 38 

Finish mark, 152 

First angle projection, 70 

Five-centered arch, 53 

Flat scales, 12 

Flexible curves, 15 

Floating, 267 

Floor plans, 222, 223 

Form in drawing, 23 

Forms of threads, 158 

Freehand drawing, 2, 201, 214 

French curve, 14, 41 

G. 

Gardener's ellipse, 52 
Gears, 173 

books on, 275 
Geometry, applied, 47 

descriptive, 66 
Good form, 23 

Gore method of development, 107 
Grouping, 148 

H. 

Hachuring, 237 
Half section, 79 

isometric, 129 

problems, 95 
Half-tones, 255 
Handbooks, 275 
Headless set screw, 167 



Heart cam, 57 
Helical spring, 158 
Helix, 157 
Hill shading, 236 
Hook-spring bows, 8 
Hot mounting, 268 
Hyperbola, 50, 55 
Hypocycloid, 55 

I. 

Ink, drawing, 13 

for printing on cloth, 272 

frozen, 46 

stick, 13 

to remove, 249, 271 
Inking, 35, 36, 37, 248 

order of, 149 
Instruments, list of, 4, 5 

patterns of, 7 

selection of, 4 

spring bow, 8 

use of, 23 

Intersection of surfaces, 111 
Involute, 56 
Irregular curves, 14, 41 
Isometric details, 226 

drawing, 122 

K. 

Kelsey triangle, 22 
Knuckle thread, 159 

L. 

Lengthening bar, 33 
Left-handed person, 25 
Lettering, 58 

architectural, 227 

books on, 276 

on maps, 242 

on working drawings, 153 

pen, to make, 258 

pens, 13, 17, 59 

single stroke, 58 

triangle, 10 
Line shading, 88, 259 
Lines, alphabet of, 39 

faulty, 38 

tangent, 38 



286 



INDEX 



Lines, to divide by trial, 28 

to divide geometrically, 47 

to draw parallel, 30 

to draw perpendicular, 30 

Lithography, 256 

Logarithmic spiral curves, 14 

Lock nuts, 164 

M. 

Machine drawing, 145 
books on, 277 

screws, 167 
Maltese cross, 44 
Mapping pens, 14 
Maps, classification of, 229 

reproduction of, 256 
Mechanical drawing, 2 
Mechanigraph, 252 
Mechanism, books on, 277 
Millwork details, 226 
Mosaic, 215 
Mounting on cloth, 268 

tracing paper, 267 

N. 

National Electrical Contractors 
Association Symbols, 221 
Negative prints, 251 
Notes and specifications, 152, 227 
Non-isometric lines, 124 

O. 

Oblique projection, 129 

sketching in, 207 
Octagon, to inscribe in square, 48 
Octagonal dome, development of, 

105 

"Official Gazette," 265 
Offset construction, 125, 131 

measuring, 205 
Ogee curve, 48 
Old Roman letters, 228 
Order of penciling, 148 
Order of inking, 149 
Orthographic projection, 66, 122, 
145 



P. 



Pantograph, 270 



Paper, bond, 248 

Bristol board, 15 

detail, 16 

drawing, 15 

profile, 245 

to mount, 268 

to stretch, 265 

tracing, 220, 248 

Whatman's, 15 
Parabola, 50, 54 
Patent office drawing, 263 

example of, 265 
Patterns, 100 
Payzant pen, 18 
Pencil, 24 

for sketching, 202 

to sharpen, 24 

compass, 32 

eraser, 15 

pointer, 13 

Penciling, order of, 148 
Pencils, 13 
Pens, border, 17 

curve, 17 

dotting, 21 

drop or rivet, 19 

double, 16 

for lettering, 13, 59 

Payzant, 18 

railroad, 17 

ruling, 7 

to sharpen, 257 
use of, 36 

Shepard, 18 

Swede, 8 
Perspective, 65, 122 

angular, 212 p 

books on, 278 

parallel, 210 

rendering, 215 

sketching in, 207 
Photo-mechanical processes, 252 
Pipe, dimensions of, 169 

fittings, 170 

threads, 168 
Pivot joint, 5, 6 
Plans, architectural, 220 
Plate girder, 182 



INDEX 



287 



Plats, 230 

city, 234 

subdivisions, 231 
Poch6 rendering, 215 
Polygon, to transfer, 48 
Potassium bichromate, 251 
Preparation for drawing, 24 
Prism, development of, 102 
Problems, 

Assembly and detail drawings, 
195 

Auxiliary projections, 91 

Bolts, screws and pipes, 181 

Cabinet projection, 142 

Checking, 197 

Development of cones, 117 
cylinders, 116 
prisms, 115 
pyramids, 116 

Dimensioning, 185 

Drawing from description, 98 

Drawing from sketches, 186 

Half sections, 95 

Intersection of cylinders, 118 
cylinder and cone, 119 
prisms, 118 

surfaces and planes, 121 
surfaces and planes, 121 
two cones, 121 

Isometric drawing, 137 

Isometric sections, 138 

Machine parts, 187 

Miscellaneous, 197 

Oblique drawing, 139 

Orthographic projection, 88 

Sectional views, 93 

Triangulation, 117 

True length of lines, 97 

Use of instruments, 42 
Profiles, 245, 246 
Projection, axonometric, 133 

cabinet, 133 

clinographic, 134 

dimetric, 133 

first angle, 70 

isometric, 123 

oblique, 129 

orthographic, 66 



Projection, sectional, 77 

Protractor, 19 

Pyramid, development of, 105 

R. 

Railroad pen, 17 
Record strip, 153 
Red ink, 248, 273 
Reducing glass, 254 
Reinhardt letters, 63, 228, 242 
Relief, 236 

symbols for, 240 
Rendering, 215 
Reproduction, 252 
Reversed axes, 127 
Revolution, 81 

problems, 96 

to isometric position, 122 
Revolved section, 79, 226 
Reynolds Bristol board, 15, 263 
Rib, section through, 146 
Rivet pen, 19 
Rivets, 180 

Rondinella triangle, 22 
Roof truss, 183 
Rubbing a copy, 268 
Ruling pens, 7 

to sharpen, 257 

use of, 35, 36, 37 
Ruled surfaces, 100 
Rules for dimensioning, 150, 151 

for oblique drawing, 130 

S. 

Scales, architects', 11 

engineers', 11 

flat, 12 

triangular, 12 

use of, 34 
Screws, machine, 167 

various, 168 
Screw threads, 157 
Section, architectural, 225 

isometric, 129 

through rib, 146 

wall, 224 
Sectional views, 77, 78, 79, 80 

problems, 93 



288 



INDEX 



Section liners, 19 

lining, 80 

conventional, 175 
on patent drawings, 264 
Set screws, 167 
Sewer map, 234 

Shades and shadows, book on, 279 
Shade lines, 86 

isometric, 129 

on maps, 232 

on patent drawings, 264 
Sheet metal, 101 

book on, 279 
Shepard pen, 18 
Single curved surfaces, 100 

to shade, 260 
Single stroke inclined letters, 61 

vertical letters, 59 
Sketching, 201 

architectural, 215 

by pictorial methods, 206 

from memory, 203 

in orthographic, 203 

on cross-section paper, 206 
Specifications, 152, 214, 227 
Spiral of Archimedes, 57 
Sphere, development of, 107 

in isometric drawing, 127 

shading, 262 
Spring bow instruments, 8 

use of, 33 
Stages, in drawing bolt head, 164 

in drawing threads, 160 

in inking, 149 

in penciling, 148 
Stair details, 226 
Stereotomy, books on, 279 
Stick ink, 13 
Structural drawing, 179, 180 

book on, 279 

examples of, 182, 183 
Street paving intersection, 43 
Studs, 166 

Style in drawing, 148 
Subdivision maps, 231 
Surfaces, classification of, 100 
Surveying, books on, 279 
Swastika, 43 



Swede pen, 8 

Swivel pen, 17 

Symbols, for materials, 175 

architectural, 220 

culture, 240 

electrical, 176, 221 

oil and gas, 242 

relief, 240 

riveting, 180 

topographic, 239 

vegetation, 242 

water features, 241 

wiring, 221 

T. 

T-square, 9, 10, 11 

use of, 25 
Table, A. L. A. M., bolts, 165 

cap screws, 166 

cast iron pipe fittings, 170 

malleable pipe fittings, 171 

standard pipe dimensions, 169 

U. S. standard bolts, 163 
Tapped holes, 160 
Technic and standards, books on, 

280 

Technical sketching, 2, 201 
Test for alignment, 7 
Test for triangles, 11 
Threads, forms of, 158 
Thumb tacks, 12 
Tinting, 267 
Tipping, 267 
Titles, 64 

architectural, 228 

on maps, 242 

on working drawings, 153, 155 

printed, 155, 156 
Tit quill pen, 14 
Tongue joint, 5 
Topographic symbols, 239 
Topographical drawing, 235 

books on, 280 
Tracing cloth, 248 
Tracing paper, 220, 269 

to mount, 267 
Tracings, 249, 271 

filing, 272 



INDEX 



289 



Transfer by rubbing, 268 
Transition pieces, 209 
Transparentizing, 251 
Trial method of dividing a line, 28 
Triangles, 10 

special forms, 21 

test for, 11 

use of, 29 

Triangular scales, 12 
Triangulation, 107 
True length of lines, 84, 85 

problems, 97 

True size of inclined surfaces, 74 
Turned section, 79, 226 

U. 

Universal drafting machine, 20 
U. S. Geological survey maps, 245 
U. S. N. Conventional symbols, 175 

V. 

Van Dyke paper, 251 
Vanishing points, 209 

of oblique lines, 213 
Vegetation symbols, 242 



Vertical drawing board, 21 
Violation of rules, 145 

W. 

Warped surfaces, 100 
Wash drawings, 215 

reproduction of, 255 
Water color tinting, 267 
Water features, symbols for, 241 
Water lining, 238 
Wax process, 255 
Wedge point pencil, 24 
Whatman paper, 15 
Whitworth thread, 159 
Wiring symbols, 221 
Working drawings, 145 

architectural, 220 

classes of, 147 
Worm thread, 159 

Z. 

Zange triangle, 22 
Zinc etching, 252 

cost of, 255 
Zone method of 'development, 107 



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