Chapter I: Part 1

Transcriber’s Notes

Text printed in italics in the source document has been transcribed
_between underscores_, bold face text =between equal signs=. Small
capitals have been replaced with ALL CAPITALS.

More Transcriber’s Notes may be found at the end of this text.

SELF-HELP

MECHANICAL DRAWING

AN EDUCATIONAL TREATISE

“_LEARN TO DO A THING BY DOING IT._”--_OLD PROVERB_

SELF-HELP
MECHANICAL DRAWING

_AN EDUCATIONAL TREATISE_

BY
N. HAWKINS, M. E.

_Author of Handbook of Calculations, etc._

_New York_: THEO. AUDEL & CO., Publishers
1902

_Copyrighted
by
Theo. Audel & Co.
New York
1902_

_This work
is
most kindly and
respectfully dedicated to
THE COMING MAN
who at the present time
is undoubtedly devoting
a goodly share of
his spare time to
the study of
drawing._

Preface.

_It is because of a personal and practical experience of the advantage to be gained by the possession of a knowledge of drawing, that the author is prompted to undertake the rather pleasant task of producing a self-help book relating to the subject._

_Since the days of youthful endeavor, the author has passed through an extended experience of mechanical life, and scarcely ever without chalk, pencil or instrument in hand, to illustrate by sketch or drawing, the tools to be employed, or to picture the finished product; accordingly, throughout this work, words of explanation and the drawings will go together to aid the diligent student._

_It has been said by an eminent writer, that “one workman is superior to another--other circumstances being the same--directly in proportion to his knowledge in drawing, and those who are ignorant of it must in many respects be subservient to others who have obtained that knowledge.”_

_It has been also said that no man is fitted to be foreman of a shop who cannot draw, and it is generally true that no one will be appointed to that position, except temporarily, who does not possess some knowledge of the art, either “freehand” or instrumental._

_It is a question how far a good working knowledge of drawing can be attained without a teacher; it is true that but few have become proficient without such aid, but it is equally true that “self-help” has been the key note to all advancement._

_The author received personal instruction in several ways and times, at home, in school, in an architect’s office, and under an experienced mechanical engineer, but it was in the early morning hours of a bright summer time--lang syne--that he made his first serious attempt to master the art of mechanical drawing. It was a struggle and a battle to hold himself down to “the board” to the finish, but it was a victory--one, won over slothfulness and impatience, and of such a nature as to warrant the use of the term “self-help” to the encouragement of others._

_In conclusion two sentiments may be added; if a good working knowledge of drawing is “worth the while” then, 1, the student should be thoroughly in earnest in acquiring it; 2, he should be willing to take sufficient time and give much hard study to gain the skill necessary for success._

_This persistence is not irksome. It carries its own reward, and the results are definite and sure._

“_One step and then another, and the longest walk is ended;
One stitch and then another, and the largest rent is mended.
One brick upon another, and the highest wall is made;
One flake upon another, and the deepest snow is laid._”

Introduction.

Drawing is one of the arts; art relates to something to be done, and art in the industrial and mechanical sense aims chiefly at utility, and is governed by exact rules; hence mechanical drawing--so-called--tends first to be useful and helpful, and second to accuracy in execution, including most minute details; it aspires to the perfection of nature in adaptability of the means to the end.

Drawing constitutes a universal language, to acquire which is a matter of importance, for by its use one is able to illustrate the form and dimensions of an object, device, or utility, in very much less time, and far more clearly, than by a verbal description.

To a person who may not be able perfectly to understand the language of a country, to be able to draw is an aid and a safeguard; to use the words of Sir Joshua Reynolds, “the pencil speaks the language of every land.”

In extensive iron works and metal-working establishments the designer and draughtsman is always in demand. His services are indispensable and his position is a highly responsible one. It becomes his special province to design improvements, to furnish sketches and to make finished drawings; to calculate strains, strength, power, motion, weight, friction and durability. All this and much more is the professional draughtsman’s work.

In “directory” classification, he who accomplishes such comprehensive results as above described is termed a “Draughtsman,” but the word has as wide a meaning as “Engineer,” which takes in civil, mechanical, naval, sanitary, steam and other engineering specialists. So, in drafting, it includes the office boy employed in making blue prints, it embraces the copyists, tracers and assistants, as well as the head draughtsman and chief engineer.

Consequently the range is wide, and the line hard to draw between draughtsmen who work with their hands, and those who work with their brains. It may be added that the best men are too frequently undervalued, owing to the unavoidable difficulty in distinguishing the difference in true worth, between the two widely separated classes.

It may be remarked that they only draw well who draw intelligently; aptness in this, as in many other virtues, is a matter of slow growth, “here a line and there a line”--it’s the proper direction, not the rate of progress, that counts in the end.

There are several methods of drawing--1, Free-hand; 2, Instrumental; 3, Geometrical; 4. Perspective. In the first the work, also termed sketching, is executed by pencil, pen, crayon, or even paint-brush; in the second the result is attained by the use of rule, tee-square, drawing pen, etc.; this method is also denominated mechanical drawing, and suggests the title of this volume.

The great usefulness, not to say necessity, of readiness in executing accurately, drawings “to scale,” is emphasized by the fact that now, more than ever, is all machinery designed, and it may almost be said, is “built,” in the draughting room--this is a valuable hint relating to “reading” drawings.

It is wise, as well as easy, to begin at the beginning of things; thus, it is altogether the good part to mount a ladder by the first and second rounds rather than to attempt it by taking the third, sixth, ninth, etc.--especially are first and second rounds the very best to start upon; “Chalk-work,” is the first subject introduced, next, that of “Free-hand.” These are the first steps leading upward in this most agreeable attainment--skill in illustrating and designing of objects, tools, and utilities.

A single word of advice before introducing the elementary work connected with mechanical drawing: if the student should experience difficulty in mastering the diagrams and curves abounding in this book, let him consult an experienced draughtsman or teacher, who, by a few strokes of a lead pencil, can easily make them plain; that knowledge--which cannot be printed or self-taught--termed _the Craftsman’s Art_, is communicated largely by personal telling and showing, from man to man; in drawing, this help should be thankfully availed of, when necessity arises.

NOTE.--Sketching is often in demand because there is no time for
finished or careful drawings, and the one who can draw a few lines in
a moment to let a sudden necessity be known, is the man of the hour.
All candidates for First Class Engineer’s Certificates in marine
service in the navy have to undergo an examination in rough drawing;
this is intended not so much as a proof of the applicant possessing
the capability of a draughtsman, but in the event of any injury to the
engines in his charge, so that he may be able to send to his
Superintendent a rough drawing of the particular part, properly
dimensioned, so that it could be worked from, and time saved on the
arrival of the ship at the port where the repairs are to be done.

“_No matter how thorough our education may have been at the first,
rules and formulas will slip from the memory, and every day’s
experience gives additional evidence of the truth of the old adage
that_ ‘THE KEY THAT RESTS, RUSTS.’”--SIMPSON BALLARD.

The Plan of the Work.

The purpose or scope of this work may be briefly stated: It is to aid the aspiring student in making the first advance towards a thorough and useful knowledge of drawing in its several divisions, as elsewhere defined.

The method to be followed in presenting the subject will be the natural order clearly and simply defined, as “from the less to the greater.”

The first subject to be discussed comes under the heading of chalk-work, _i. e._, such drawings as can be executed on a blackboard, a floor, or even on more primitive surfaces, such as a smooth stone or board.

This is indeed a lowly beginning, but the author is quite confident it will awaken as much interest as any part of the book--even in the most experienced in the art of drawing, as to them it will revive the ambitions and first crude attempts made in the golden days of their youth.

Let it be clearly understood by all, and especially by those who wish to learn drawing, that the study of this delightful art does not require any special qualification. We need only ask one question: Have you learned to write? If so, be assured you may learn to draw, but to all the same rule applies, first the elements of the art, and afterwards the more advanced study.

It is not expected that all should exhibit a decided taste for drawing, for the possession of this is rather a gift of nature than the result of education; but a knowledge of principles and a certain amount of executive ability may be obtained by every one of average capacity, and whatever the natural power may be, it will be increased and developed by exercise; if the progress is steady and continuous and in the right direction, success is sure to crown the work.

The second division of the book will be free-hand drawing, _i. e._, that which is executed without instruments. Nothing to instruct has been spared in this important step in the path of advancement.

The illustrations accompanying the two opening sections have been made designedly elementary, for there are many who have a taste for drawing and who have a desire to learn, who from place of residence or other circumstances have not the opportunity of receiving the assistance of a master. To such this book presents itself as a friend directing to the right road, talking, reasoning, and explaining by the way.

The “chalk-work” and “free-hand” sections of the book relate to the foundations upon which all must rest who seek the aid to be derived from the art; hence, the following pages are written with a view to encourage all, and those who are prepared to follow the directions given in them may look forward to the possession of sufficient drawing power to add to their usefulness in after life.

At this point of attainment there arises a need to know the meaning of many words and phrases used by draughtsmen; these are grouped alphabetically from A to Z under the heading of,----

Useful Terms and Definitions: Memorizing these few pages will be of benefit, as an intimate knowledge of the language of the drawing office stamps a man as worthy of a hearing, and assures attention to anything which he may write or say pertaining to the art.

After the Definitions the subject explained will be the Instruments and Materials used in mechanical drawings; following in due course appear Geometrical and Mechanical Drawing, Gearing, Linear Perspective, Projection, Shading, Tracing, Lettering, Drawing Office Rules, Reading Drawings, Useful Tables and a General Index, to which the student is referred. A careful reading is requested to the following helpful note.

Grateful acknowledgment is made to George Perrott, Esq., M. E., for practical and technical assistance throughout the work, and to Theo. Lucas, Engineer, for text and illustrations in the portions of the book relating to Linear Perspective and Projection.

NOTE.--In MACHINERY Prof. Chas. H. Benjamin says, referring to
drawing, under heading “How and what to study,” “... I have so far
said nothing about drawing, for I do not think it of much use to learn
that, until you know what you want of it. All this time that you have
been studying mechanism you should have had a sketch book or pad of
note paper, and made free hand sketches of mechanical movements which
interested you and of various machine details. You should accustom
yourself to use drawing as a means of expressing ideas, just as you
use written words, so that it becomes a second nature to you to sketch
anything you wish to remember or describe. If you work from
blue-prints in the shop, or if you can borrow some to study, this will
help you to understand how a drawing is made. You can get some drawing
instruments at any time and begin to practice on drawing straight
lines and circles, so as to become familiar with the instruments. And
here it will be of great benefit to you if you can attend an evening
drawing school for one night in the week at least.

“When you have become sufficiently familiar with the principles of
drawing, a book on mechanism will tell you how to draw gear teeth and
cams, and how to design various link motions. Make up your own
problems from what you see in the shop and make your drawing a means
to an end and not the principal thing; it is of little use to be able
to make a nice drawing unless you know what to draw and why.

“Drawing is a convenient tool as an aid in expressing to others the
ideas which you wish to convey; in all cases take the problems and the
ideas from your every-day work and that which is around you; your
success will depend upon the close connection which you keep at all
times between your acquired knowledge and your practical work.”

General List of Contents.

INTRODUCTION, 1-24

CHALK WORK, 25-38

PRELIMINARY TERMS AND DEFINITIONS, 39-52

FREEHAND DRAWING, 53-78

GEOMETRICAL DRAWING, 79-100

DRAWING MATERIALS AND INSTRUMENTS, 101-134

MECHANICAL DRAWING, 135-188

PENCILING, 139-147

PROJECTION, 148-164

INKING IN DRAWINGS, 167-170

LETTERING DRAWINGS, 171-175

DIMENSIONING DRAWINGS, 176-179

SHADING DRAWINGS, 180-181

SECTION LINING AND COLORS, 182-185

REPRODUCING DRAWINGS, 186-188

DRAWING OFFICE RULES, 189-195

GEARING, 197-208

DESIGNING GEARS, 209-216

WORKING DRAWINGS, 219-227

READING WORKING DRAWINGS, 228-230

PATENT OFFICE RULES FOR DRAWINGS, 231-236

USEFUL HINTS AND “POINTS,” 237-244

LINEAR PERSPECTIVE, 245-265

PERSONAL, BY THE EDITOR, 281

USEFUL TABLES, 269-280

REFERENCE INDEX, 283

The peculiarity of all art is that it cannot
be communicated in writing alone, craft is a
term which is synonymous with art; a craft
requires manual dexterity which cannot be
taught in books.

Chalk Work.

The blackboard has been well called the great weapon of the modern educator; this is especially true in reference to instruction in an art dealing with lines, curves and figures.

Many a man can chalk out on a blackboard, or on a piece of sheet-iron, or on the floor, just what he wants to show, and make his meaning very plain; hence, in every workshop, and many other places, a blackboard is more than useful, and it has been said that no draughting office is complete without one.

Fig. 6 represents a chalk-crayon.

Figs. 7 and 8 need no explanation, as they represent two forms of the well-known blackboard.

Chalk lines have this advantage--they are easily altered or rubbed out when not needed any longer. The work executed upon a blackboard is mostly done by hand, without aid from instruments; a few tools, however, are useful--such as, 1, large wooden blackboard compasses holding a crayon, which are made and sold by the trade in size twelve inches to thirty inches in length; 2, a straight-edge; and 3, some crayons. With the compasses circles and part of the circle can be made, and with the straight-edge the larger lines can be drawn.

These instruments are shown on page 29, and are, 1, compasses, for holding chalk for making circles; 2, a tee-square; 3, a straight-edge; 4, a protractor for measuring angles; 5, a triangle 60° and 30°; 6, a brass holder for crayons.

Blackboard Drawing.--The use of a blackboard comes principally and properly under the head of free-hand drawing, but its importance is such that a separate division of the volume is assigned to it.

Thus, chalk-work may be considered the first lesson in “free-hand,” as all the examples can also be most profitably practiced with pencil and paper.

Very rapid drawing upon the board should not be encouraged, as it is likely not to be accurate enough; again, the board should be entirely free from grease. Cloths, sponges or chamois skin rubbers may be used to erase or change the chalk marks. Vertical lines should be drawn from above downward; short lines should be drawn with the fingers alone, those somewhat longer with the hand, using the wrist-joint; the still longer lines with the forearm, using the elbow-joint; those longer yet with the whole arm, using the shoulder-joint; lines should always be drawn with a uniform motion, slow enough for the eye to follow.

Practice in chalk-work should alternate with sketching in a sketchbook and with geometrical drawing--to be hereafter described. The student should practice a short time on the board, at least once a week; large sizes are the most profitable for the representations to be made; when drawing in different directions the hand should be turned, not the paper or board; the hand should never be allowed to obstruct the sight, hence the hand and fingers should be held in a position of freedom--with fingers not nearer than 1¹⁄₂ or 2 inches from the board.

NOTE.--The first lesson of any kind the author received in drawing was
to make a straight line; this was effected by holding the pencil
nearly erect and guiding it along by the aid of the little finger held
pressed against the edge of a board; this was a useful item of
knowledge, as proved by passing years.

A well-known artist, in telling his early experience, said: “The first
thing I was taught was to draw a line, divide it, erect a
perpendicular from its center, and afterwards to divide the angle made
by the perpendicular.” In answer to a question asking how long he was
kept at the lines, he replied, “about two months--or a month or two,”
indicating that even the longer time would have been well spent in
learning to draw a straight line.

PREPARATORY PRACTICE IN DRAWING.

Every visible object is bounded by lines which enable the observer to determine its shape. If these lines are straight or curved, the shape of the object is regular; if broken, the shape of the object is irregular.

The elements, then, of form are lines, straight, curved, or broken, and these, therefore, furnish the beginning of all instruction in free-hand or mechanical drawing.

PERPENDICULAR LINES.

Fig. 15 shows six lines--upright and perpendicular, with points or “dots” indicated at the top and bottom of each line; to draw these, proceed thus:

The learner should stand with his right shoulder opposite the board, and the weight of the hand and the arm should be allowed to fall naturally; now, make on the board two points, one being six inches above the other, these being merely “dots,” shown at the ends of the lines, figs. 15, etc., and made with two motions; the line between the points should now be drawn not too quickly from the upper to the lower point; three movements of the hand and arm complete the line; to draw the other five lines the movements have simply to be repeated.

If the student pronounces to himself “one,” “two,” “three,” at each motion, it will be helpful; in this exercise, fig. 15, the aim is to make six lines, each line being parallel to the first. Again, in the example, it is intended that the lower point should be made first, next the upper, and lastly the line drawn from the upper to the lower point, but the order may be reversed; at _one_ the upper point, at _two_ the lower, at _three_ the stroke upwards to complete the line.

HORIZONTAL LINES.

To make these as shown in fig. 16, proceed as follows: With the word _one_ make a point, with _two_ another point six inches at the left, with _three_ draw a straight line from the left point to the right. All added lines should be parallel: for practice, reverse the process thus, _one_, make a “point,” at _two_ another point at the right, at _three_ draw line to the left.

The student will note that the two motions--at the words _one_ and _two_--are to fix the positions of the ends of the lines; this practice will be found useful in the most advanced examples and an item of elementary practice never to be forgotten--like the help to be derived by the first round of a ladder.

OBLIQUE LINES.

In drawing oblique straight lines as shown in fig. 17, at the word _one_ let the student make the lower point; at the word _two_ the upper, a little to the right of the lower; at the word _three_ draw a line quickly from the upper to the lower point. In pronouncing the words _one_, _two_, _three_, let the student make the additional parallel lines.

As shown in fig. 18, at the word _one_ make the lower point; at the word _two_ the upper point, a little _to the left_; at the word _three_ draw a line rapidly from the upper to the lower point, and “timing” the process by repeating _one_, _two_, _three_, make the additional parallel lines.

BROKEN LINES.

A broken line is composed of two or more straight lines at angles to each other (see fig. 19). To draw them begin (saying) _one_, make a point; _two_ a point below at the left; _three_, a point above at the left; _four_, draw a line from the left hand point to the lower point; at the word _five_, from the lower point to the upper right hand point. For practice draw numerous lines in the same way, keeping them parallel to each other, as shown in fig. 20.

In example, fig. 21, the arrangement of the points is changed--let the student draw at the words, as follows: _One_, a point; _two_, a point above at the left; _three_, a point below at the left; _four_, draw from the point at the left to the upper point; _five_, from the upper point to the lower right hand point; continue to add parallel lines to complete the figure as shown.

Figs. 22 and 23 are given as examples to practice, making first the points and then the connecting lines and afterward the parallel lines to complete the figures.

CURVED LINES.

To draw curved lines, as shown in fig. 24. At the word _one_, point; at the word _two_, point three inches directly above; _three_, at the same distance above again make a point; now draw a curve as shown, joining the middle point and the upper point; now draw the curve as shown below it; finally complete figure as shown.

Figs. 25 to 30 are to be practiced, making first the points and then connecting them by the curves to complete the figures.

When two or more students are working together, with each having a blackboard, the counting may be in concert--or a teacher could count for a class. In these line examples care should be used in making them of uniform length. There is a difference to be noted between a crooked line and a broken line, the latter being a straight line and the former deviating from it.

Square chalk crayons are the best for hand work, as lines of an even or uniform width can be drawn with them.

A very fine effect is produced by using two thicknesses of chalk, one being double the thickness of the other; the heavy lines being used on the shade side of objects will produce a good effect, giving thickness and body to the object.

Round chalk crayons are used in the compasses to draw circles, but hand lines drawn with them are not so neat as those produced with the square-shaped chalk.

To obliterate or remove the construction, or false lines made on the blackboard, a wooden handle two inches in diameter with a cone end 3 or 4 inches long, covered with chamois skin or soft cloth tightly wrapped round the cone and fastened with a tack or drawing pin, makes the best implement to erase lines not required, the point of the cone will remove these without destroying the lines or curves which meet them.

Sponges, chamois skin or cloth rubbers are used to rub out the chalk drawings and clean the blackboard.

The best height for a diagram on the blackboard is not higher than the head, nor lower than the elbow.

Horizontal lines should be made from the left to the right; the body and arm being moved with the hand, and kept in the same relative position with it, will steady the hand.

Curved lines to the left should be drawn first, enabling the eye to take in not only the curve in process of formation but that already made.

Passing the crayon in the hand, over the intended curve previous to marking it, will guide the eye and give confidence to the hand in chalking the curve.

A proper distance from the blackboard is essential, the face being about two feet away from it.

Draw with the whole arm extended from the shoulder-joint, not from the elbow or wrist.

Preliminary Terms and Definitions.

Like all the arts, drawing has a nomenclature of its own, and nothing can be more helpful to the beginner than to know the name of things relating to the art of drawing. This is a language almost peculiar to itself, and used daily and hourly by many thousands of superintendents, foremen and master mechanics, as well as by owners, designers and draughtsmen, hence its introduction at this early stage.

=ALTITUDE.=--This is the elevation of an object above its base, or the
perpendicular distance between the top and bottom of a figure.

=ANGLE= is the difference in the direction of two lines which meet or
tend to meet. The lines are called _the sides_ and the point of
meeting, the _vertex_ of the lines.

To make an angle apparent, the two lines must meet in a point, as _A
B_ and _A C_, which meet in the point _A_, as shown in fig. 33.

Angles are measured by degrees.

A _Degree_ is one of the three hundred and sixty equal parts of the
space about a point in a plane.

Angles are distinguished in respect to magnitude by the terms Right,
Acute and Obtuse Angles.

A _Right Angle_ is that formed by one line meeting another, so as to
make equal angles with that other.

The lines forming a right angle are _perpendicular to each other_.

An _Acute Angle_ is less than a right angle. See Fig. 35.

An _Obtuse Angle_ is greater than a right angle. See Fig. 36.

Obtuse and acute angles are also called _oblique angles_; and lines
which are neither parallel nor perpendicular to each other are called
_oblique lines_.

The _Vertex_ or _Apex_ of an angle is the point in which the including
lines meet.

An angle is commonly designated by a letter at its vertex; but when
two or more angles have their vertices at the same point, they cannot
be thus distinguished.

For example, when the three lines _A B_, _A C_, and _A D_ in fig. 37
meet in the common point _A_, we designate either of the angles
formed, by three letters, placing that at the vertex between those at
the opposite extremities of the including lines. Thus, we say, the
angle _B A C_, etc.

=APEX.=--The summit or highest point of an object.

=ARC.=--See circle.

=AXIS OF A SOLID.=--An imaginary straight line passing through its
center.

=AXIS OF A FIGURE.=--A straight line passing through the center of a
figure, and dividing it into two equal parts.

=BASE.=--The base of a solid figure is that on which it stands--the
lowest part.

=BISECT.=--To divide into two equal parts.

=BISECTOR.=--A line which bisects.

=CIRCLE.=--A _Circle_ is a plane figure bounded by one uniformly
curved line, all of the points in which are at the same distance from
a certain point within, called the _Center_.

The _Circumference_ of a circle is the curved line that bounds it.

The _Diameter_ of a circle is a line passing through its center, and
terminating at both ends in the circumference, as _A C B_.

The _Radius_ of a circle is a line extending from its center to any
point in the circumference. It is one-half of the diameter. All the
diameters of a circle are equal, as are also all the radii _C D_, _C
B_ and _C A_.

An _Arc_ of a circle is any portion of the circumference, as _B D_ and
_A D_.

_Semi-Circle._--Half a circle formed by bisecting it with a diameter,
as _A C B_. Fig. 38.

An angle having its vertex at the center of a circle is measured by
the arc intercepted by its sides. Thus, the arc _A D_ measures the
angle _A C D_, and in general, to compare different angles, we have
but to compare the arcs, included by their sides, of the equal circles
having their centers at the vertices of the angles.

=CIRCUMSCRIBE.=--To draw a line of figures about or outside, such as a
circle drawn around a square touching its corners or angles.

_Inscribe._--To draw a line or figure inside or on the interior, such
as a circle drawn within a square touching its sides.

=CONCAVE.=--Curving inwardly.

=CONE.=--A solid body or figure having a circle for its base, and its
top terminated in a point or vertex.

=CONSTRUCTION.=--The making of any object.

=CONTOUR.=--The outline of the general appearance of an object.

=CONVERGENCE.=--Lines extending towards a common point.

=CONVEX.=--Rising or swelling into a round form--the opposite to
concave.

=CORNER.=--The point of meeting of the edges of a solid, or the two
sides of a plane figure.

=CROSS-HATCHES.=--In free-hand drawing the use of lines crossing each
other to produce light and shade effects.

=CURVE.=--A line of which no part is straight.

_Reversed Curve._--One whose curvature is first in one direction and
then in the opposite direction.

_Spiral Curve._--A plain curve which winds about and recedes,
according to some law, from its point of beginning, which is called
its center.

=CYLINDER.=--A solid bounded by a curved surface and by two opposite
faces called bases; the bases may be any curved figures and give the
name to the cylinder; thus a circular cylinder is one whose bases are
circles.

=CYLINDRICAL.=--Having the general form of a cylinder.

=DEGREE.=--The 360th part of a circle.

=DESCRIBE.=--To make or draw a curved line; to draw a plan.

=DESIGN.=--Any arrangement or combination to produce desired results
in industry or art. To delineate a form or figure by drawing the
outline--a sketch.

=DEVELOP.=--To unroll or lay out.

=DIAGONAL.=--A right line drawn from angle to angle of a quadrilateral
or many angled figure and dividing it into two parts.

=DIAMETER.=--A right line passing through the center of a circle or
other round figure terminated by the curve and dividing the figure
symmetrically into two equal parts.

=EDGE.=--The intersection of any two surfaces.

=ELEVATION.=--The term elevation, vertical projection and _front
view_--applied to drawings--all have the same meaning.

=FACE.=--One of the plane surfaces of a solid; it may be bounded by
straight or curved edges.

=FINISHING.=--Completing a drawing whose lines have been determined by
erasing unnecessary lines and strengthening and accentuating where
this is needed.

=FORESHORTENING.=--Apparent decrease in length, owing to objects being
viewed obliquely; thus a wheel, when seen obliquely, instead of
appearing round, presents the appearance of an ellipse.

=FREE-HAND.=--Executed by the hand unaided by instruments.

=GENERATED.=--Produced by.

=GEOMETRIC.=--According to geometry.

=HALF-TINT.=--The shading produced by means of parallel equidistant
lines.

=HEMISPHERE.=--Half a sphere obtained by bisecting a sphere by a
plane.

=HORIZONTAL.=--Parallel to the surface of smooth water. In drawing, a
line drawn parallel to the top and bottom of the sheet is called
horizontal.

=INSCRIBE.=--See circumscribe--its opposite.

=INSTRUMENTAL.=--By the use of instruments.

=LINE.=--A line has length, only, as A C; a right line is a straight
line, the shortest line that can be drawn between two points, A----C.

_Straight._ One which has the same direction throughout its entire
length.

_Curved._ One no part of which is straight.

_Broken._ One composed of different successive straight lines.

_Mixed._ One of straight and curved lines.

_Center._ A line used to indicate the center of an object.

_Construction._ A working line used to obtain required lines.

_Dotted._ A line composed of short dashes. - - - - - -

_Dash._ A line composed of long dashes. -- -- --

_Dot_ and _Dash_. A line composed of dots and dashes alternating. -- ·
-- · --

_Dimension._ A line upon which a dimension is placed.

_Full._ An unbroken line, usually representing a visible edge. ------

_Shadow._ A line about twice as wide as the ordinary full line.

A straight line is often called simply a line, and a curved line a
curve.

=LONGITUDINAL.=--In the direction of the length of an object.

=MODEL.=--A form used for study.

=OBLIQUE.=--Neither horizontal nor vertical.

=OBLONG.=--A rectangle with unequal sides.

=OVAL.=--A plane figure resembling the longitudinal section of an egg;
or elliptical in shape.

=OVERALL.=--The entire length.

=PARALLEL.=--Having the same direction and everywhere equally distant.

=PATTERN.=--That which is used as a guide or copy in making things.

_Flat._ One made of paper or other thin material.

_Solid._ One which reproduces the form and size of the object to be
made.

=PERIMETER.=--The boundary of a closed plane figure.

=PERPENDICULAR.=--At an angle of 90°.

=PERSPECTIVE.=--View; drawing objects as they appear to the eye from
any given distance and situation, real or imaginary.

=PLAN.=--Plan, horizontal projection and _top view_ have the same
meaning.

=PLANE FIGURE.=--A part of a plane surface bounded by straight or
curved lines, or by both combined.

=POLYGON.=--A plane figure bounded by straight lines called the sides
of the polygon. The least number of sides that can bound a polygon is
three. Polygons bounded by a greater number of sides than four are
denominated only by the number of sides.

A polygon of five sides is called a _Pentagon_; of six, a _Hexagon_;
of seven, a _Heptagon_; of eight, an _Octagon_; of nine, a _Nonagon_,
etc.

_Diagonals_ of a polygon are lines joining the vertices of angles not
adjacent.

The _Perimeter_ of a polygon is its boundary considered as a whole.

The _Base_ of a polygon is the side upon which the polygon is supposed
to stand.

The _Altitude_ of a polygon is the perpendicular distance between the
base and a side or angle opposite the base.

A _Quadrilateral_ is a polygon having four sides and four angles.

A _Parallelogram_ is a quadrilateral which has its opposite sides
parallel.

The side upon which a parallelogram stands and the opposite side are
called respectively its lower and upper bases.

A _Rectangle_ is a parallelogram having its angles right angles.

A _Square_ is an equilateral rectangle, fig. 41.

A _Rhomboid_ is an oblique-angled parallelogram.

A _Rhombus_ is an equilateral rhomboid, fig. 42.

A _Trapezium_ is a quadrilateral having no two sides parallel, fig.
43.

A _Trapezoid_ is a quadrilateral in which two opposite sides are
parallel, and the other two oblique, fig. 44.

=A POLYHEDRON= is a solid bounded by planes. There are five regular
solids which are shown in figs. 45, 46, 47, 48 and 49. A regular solid
is bounded by similar and regular plane figures.

Fig. 45.--The _tetrahedron_, bounded by four equilateral triangles.

Fig. 46.--The _hexahedron_, or cube, bounded by six squares.

Fig. 47.--The _octahedron_, bounded by eight equilateral triangles.

Fig. 48.--The _dodecahedron_, bounded by twelve pentagons.

Fig. 49.--The _icosahedron_, bounded by twenty equilateral triangles.

=PRISM.=--A solid whose bases or ends are very similar plane figures,
and whose sides are parallelograms; prisms are called triangular,
square, etc., according as the bases are triangles, squares, etc.

=PRODUCE.=--To continue or extend.

=PROFILE.=--An outline or contour.

=PROJECTION.=--The view of an object obtained upon a plane by
projecting lines perpendicular to the plane.

=QUADRANT.=--The fourth part; a quarter; the quarter of a circle.

=QUADRISECT.=--To divide into four equal parts.

=SECTION.=--A projection upon a plane parallel to a cutting plane
which intersects any object. The section generally represents the part
behind the cutting plane, and represents the cut surfaces by diagonal
lines.

=SECTIONAL.=--Showing the section made by a plane.

=SHADOW.=--Shade and shadow have about the same meaning.

=SOLID.=--A solid has three dimensions--length, breadth and thickness.

=SPHERE.=--A solid bounded by a curved surface every point of which is
equally distant from a point within called the center.

=SURFACE.=--The boundary of a solid. It has but two dimensions--length
and breadth. Surfaces are plane or curved.

A _Plane Surface_ is one upon which a straight line can be drawn in
any direction.

A _Curved Surface_ is one no part of which is plane.

The surface of the sphere is curved in every direction, while the
curved surfaces of the cylinder and cone are straight in one
direction.

The surface of a solid is no part of the solid, but is simply the
boundary of the solid. It has two dimensions only, and any number of
surfaces put together will give no thickness.

=SYMMETRY.=--_Design._ A proper adjustment or adaptation of parts to
one another and to the whole.

=TRISECT.=--To divide into three equal parts.

=TRIANGLE.=--A triangle is a polygon having three sides and three
angles. _Tri_ is a Latin prefix signifying three; hence a Triangle is
literally a figure containing three angles.

A _Scalene Triangle_ is one in which no two sides are equal. See fig.
50.

An _Isosceles Triangle_ is one in which two of the sides are equal.
See fig. 51.

An _Equilateral Triangle_ is one in which the three sides are equal.
An _Equiangular Triangle_ is one having its three angles equal. An
_Acute-Angled Triangle_ is one in which each angle is acute.

A _Right-Angled Triangle_ is one which has one of the angles a right
angle. See fig. 53.

An _Obtuse-Angled Triangle_ is one having an obtuse angle. Fig. 54.

Equiangular triangles are also equal sided, and vice versa.

=VERTICAL.=--Upright or perpendicular. Vertical and perpendicular are
not synonymous terms.

=VERTEX.=--See Angle, Quadrilateral, Triangle. The vertex of a solid
is the point in which its axis intersects the lateral surface.

=VIEW.=--See Elevation. Views are called front, top, right or left
side, back, or bottom, according as they are made on the different
planes of projection. They are also sometimes named according to the
part of the object shown, as edge view, end view, or face view.

=WORKING DRAWING.=--One which gives all the information necessary to
enable the workman to construct the object.

Free-Hand Drawing.

A free-hand drawing is executed with the unaided hand and eye, without guiding instruments or other artificial help. It is necessary to be known that all drawing required cannot possibly be done by rule and compass, but that some portions must be drawn “free-hand,” trusting to the eye alone.

Hence, it is important that the student should be able to sketch at sight from objects he may see, or to draw roughly, with a piece of chalk or a pencil, pieces of mechanism required to be represented.

Practice in free-hand should go along with mechanical drawing as progress is made, and thus cultivating both branches equally.

“A simple sketch will often,” as has been rather roughly said, “express more than yards of talk.”

Even a slight sketch refreshes the memory, and in the case of the preparation of a complete set of drawings, with a view to the making of a thoroughly finished mechanical drawing, the proper course to pursue is, to make a general sketch, letter the various parts for reference, and then prepare a series of detailed sketches, similarly lettered, and diffuse with dimensions.

Everyone, whatever his specialty, feels to-day that the ability to sketch rapidly and clearly is among the absolute necessities for correct and prompt transactions of business, in giving and executing orders and doing business with persons outside his profession.

Mistakes and misunderstandings may be averted by means of rough sketches taken at the time and shown for confirmation; this also saves assistants from getting into trouble, especially if they pin the sketch to the order, for reference, in case of the arising of any dispute. These are a few of the advantages of knowing how to sketch quickly and correctly.

In “free-hand” any sort of pencil is better than none, but there is a considerable advantage in having a good serviceable article--a pencil not too soft nor too hard, and one which will retain its point for some little time.

Fig. 55 shows the approved position in which the pencil should be held while sketching. The pencil should be held firmly between the thumb and first finger of the right hand; press the second finger against the pencil at the opposite side to the thumb pressure, so that the pencil is firmly held by the contact of the thumb and two fingers--the third and fourth fingers just coming into easy reach of the paper surface--the wrist or ball of the hand resting lightly on the surface of the work--the arm resting on the desk or drawing-board for steadiness.

The motion of the pencil is produced from the movement of the fingers and thumb, principally in the vertical strokes, and the horizontal strokes are produced by fingers and thumb, combined with a wrist or elbow motion; the oblique lines and curves are produced with a free movement, with nothing cramped or confined about the finger joints.

POSITION.

It should be observed that nothing is more prejudicial to good execution than the habit of leaning over the paper, which ought to be placed on a surface sufficiently inclined to bring every portion equally under the eye, thus obviating the necessity of leaning forward. All support to the figure should be obtained by resting on the left arm, the right being left free for work. By attention to these rules that awkwardness of position, so detrimental to a good figure, will be avoided. It is better to have the light on the left hand, as in this direction the shadow of the pencil does not interfere with the view of the drawing.

HOW TO CUT A PENCIL.

Hold the pencil firmly in the left hand, as in the drawing, allowing about an inch to project beyond the fingers, and turn it gradually as the knife removes the wood. The knife should be held so that the blade alone projects beyond the fingers, and the part of it nearest the handle used for cutting. The pencil should be placed against the inside of the thumb of the right hand, as in the drawing (fig. 56), and the wood removed by slight shaving. The lead should not be cut at the same time as the wood, but rested on the thumb and pared gently afterwards; by attention to these directions the pencil will be economized.

HOW TO DRAW STRAIGHT LINES.

Before a line is drawn, the point at which it is to commence and the point where it is to end, should be known; and let it be distinctly understood that _this judgment of the eye_, and placing of points, should invariably precede the drawing of every line.

The first effort should, therefore, be to produce a line of points exactly parallel with the upper edge of the paper, and at equal distances from each other. Commence with point _A_ and place the point _B_ carefully level with it, now place a slip of paper against these points in the original, mark their distance apart, and see if the same proportion has been given in your copy; if not, make the necessary correction. Proceed with the next point, examine it, and so on to the end of the line. When this is complete, examine each point in succession, to try if it is at the same distance from the top of the paper; when this is correct, proceed to draw the first level line. Hold the pencil as in the drawing, fig. 57, keeping the elbow near the side; join _A_ to _B_ by one light, steady stroke, produced by a movement of the wrist, and add stroke upon stroke until the line is of the required depth. Continue this process to the end of the line of points. Now place the point _D_ at the right distance below the _A_, proceed with the points for another line as before, and continue the lines until the paper is covered. In producing the stroke the pencil should not be jerked, or any stop be made between the points, but the movement should be even throughout, and it is much better to produce each line by several soft strokes, as _the repetition of delicate lines induces lightness of touch and freedom of hand_; and it is also no small advantage that lines thus produced are more easily removed by the India rubber, should they require correction.

TO DRAW THE FIRST OBLIQUE LINE.

Prepare three rows of points down the side of the paper, on the left hand; examine them to see that they are at equal distances from the side and from each other; hold the pencil as in the drawing, fig. 58, move the elbow a little from the side, and join the points _A_ and _B_ with one light line, produced by a movement of the fingers and thumb, repeating the strokes until the line is of the requisite depth; proceed to join _B_ to _C_, taking care previously to bring the hand a little down the paper, as the line from _A_ to _C_ is too long to be produced from one position. When the three rows of points are filled, make another set, examine them and proceed as before. By these means the paper will be covered with oblique lines, and if the points have been placed exactly, the sheet will have a neat and regular appearance.

NOTE.--The drawings of hands are introduced to show the positions for
holding the pencil, and are not intended for copying.

It is a common, and at the same time highly injurious habit, to draw this line by a movement of the wrist, the fingers remaining rigid. This may be detected by watching the action of the thumb; if it bends as the line is produced, all is right; but if it does not the wrist is at work.

TO DRAW THE UPRIGHT OR PERPENDICULAR LINE.

This line demands the greatest attention, and any care bestowed upon it will be amply repaid in the after studies.

Commence by placing a line of points down the side of the paper, examine them very carefully to see that they are all the same distance from its edge, hold the pencil as in the drawing, fig. 59, move the elbow well out from the side, and join the points by a movement of the fingers and thumb. When one line is complete, place the points for the next, and examine them from the edge of the paper, not from the line just drawn. Proceed in this manner until the paper is covered.

There is in most cases a tendency to place the points for this line in a slightly inclined direction, as in writing, though in some instances the tendency is the opposite, a thoroughly correct eye in this respect being a rare gift: and it may be useful to suggest that the paper be so placed that the line of points to be produced may be exactly in front of the eye.

TO DRAW THE SECOND OBLIQUE LINE.

Prepare three rows of points down the side of the paper, examine them for correctness of position, hold the pencil as in the drawing, fig. 60, remove the elbow as far as possible from the side, and join the points by a movement of the fingers and thumb, and continue the exercise until the paper is covered.

It will be noticed that each change in direction of the line to be drawn, has been accompanied with a corresponding change in the position of the elbow and wrist. The following simple rule will assist the memory when placing the hand for any given line; the pencil should be held so that it may form a T with the line to be drawn:

For the horizontal line, elbow near the side.

For the first oblique, elbow a little removed.

For the perpendicular, elbow more removed.

For the second oblique, elbow most removed.

Wrist lines.

Finger and thumb lines.

Wrist lines.]

It may also be interesting to notice, with regard to the movements by which lines are produced, that they are divided into two systems; the first is that of the wrist, which includes the horizontal, and lines in nearly the same direction; the second is that of the fingers and thumb, by which all other lines are formed. The following diagram exhibits the two systems and their various lines grouped, and it will be observed that there is a space marked (a) between the two sets, which may be considered neutral ground. Lines in this direction may be produced by either movement, as may be most convenient, but it will always be found that these lines are the most trying to the hand.

ON FIGURES FORMED OF STRAIGHT LINES.

Before commencing this subject, let it be clearly understood that future success will, in a great measure, depend upon the amount of care bestowed upon it. The aim should be to obtain absolute accuracy, and for this end the copies should be tested by the most careful measurements, and corrected until they are true with the originals, but it should be distinctly understood that these measurements are only to be made after the eye and hand have done their best.

NOTE.--To some it may appear that too much time and care has been
bestowed on mere lines, but let it be understood that a good system of
line drawing is the basis of all education--the slightest outline by a
hand thus trained has a bold, free and masterly character; and with
regard to shading, which is simply an aggregation of good lines, it is
only by such a practiced hand its most charming effects can be
produced.

Fig. 66: Place the points _A_, _B_. Examine them to see that they are the same distance apart as in the original, and that they are level; place the point _C_ exactly under _A_, and make _A C_ equal in distance to _A B_; now place the point _D_ opposite _C_ and under _B_; try the distances between each point to see that they are the same; divide each side by a point half way, and then draw the lines.

Fig. 67: Repeat the last figure and add the lines _A_ and _B_, taking great care that the points for them are correctly placed.

Fig. 68: Commence with the square as before; then join the half-way points.

Fig. 69: After the square is drawn, place the points _A_ and _B_ at the right height above the half-way points, and _C_, _D_ at the proper distance from the corners, then draw the figure.

Fig. 70: The greatest care should be taken with the squares for this and the following figure, as the slightest error in them will destroy the symmetry of the drawing within; when the square is completed, join the opposite corners, and place on the crossed lines the points _B_, _C_, _D_, _E_; examine these to see that they are each at the same distance from the centre _A_, and that this distance is equal to the space from _A_ to the sides of the square; when all are proved to be correct, complete the figure.

Fig. 71: Repeat the last drawing with, if possible, greater exactness, and outside the octagon place the points _A_, _B_, _C_, _D_, etc.; examine each of these points to see that they are all at the same distance from the centre, and then complete the figure.

ON CURVED LINES.

The right position of the hand for drawing any curved line is that required for a straight line which would touch the extremities of the curve. The straight lines given in the exercises are valuable, not only as a guide to the position of the hand, but as an assistance to the eye when forming the curves or examining them after they are produced.

The direction given for drawing a straight line was to form it by one steady movement from point to point, without any jerk or stop by the way. This instruction requires to be changed for the curve, _which is better produced by several short strokes_, thus:

or by overlapping lines, any outside bits being cleared away with India rubber.

These exercises will test the drawing power and try the patience of the pupil, but they are worthy of all the care which can be bestowed, which in future efforts will meet with its full reward.