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MECHANICAL DRAWING SELF-TAUGHT:

COMPRISING

INSTRUCTIONS IN THE SELECTION AND
PREPARATION OF DRAWING
INSTRUMENTS,

_ELEMENTARY INSTRUCTION IN PRACTICAL
MECHANICAL DRAWING_;

TOGETHER WITH

EXAMPLES IN SIMPLE GEOMETRY AND ELEMENTARY MECHANISM,
INCLUDING SCREW THREADS, GEAR WHEELS,
MECHANICAL MOTIONS, ENGINES AND BOILERS.

BY JOSHUA ROSE, M.E.,

AUTHOR OF "THE COMPLETE PRACTICAL MACHINIST,"
"THE PATTERN MAKER'S ASSISTANT,"
"THE SLIDE VALVE"

ILLUSTRATED BY THREE HUNDRED AND THIRTY ENGRAVINGS.

PHILADELPHIA:
HENRY CAREY BAIRD & CO.,
INDUSTRIAL PUBLISHERS, BOOKSELLERS AND IMPORTERS,
810 WALNUT STREET.

LONDON:
SAMPSON LOW, MARSTON, SEARLE & RIVINGTON,
CROWN BUILDINGS, 188 FLEET STREET.
1887.




Copyright by
JOSHUA ROSE.
1883.

PHILADELPHIA.

COLLINS, PRINTER




PREFACE.


The object of this book is to enable the beginner to learn to make
simple mechanical drawings without the aid of an instructor, and to
create an interest in the subject by giving examples such as the
machinist meets with in his every-day workshop practice. The plan of
representing in many examples the pencil lines, and numbering the order
in which they are marked, the author believes to possess great
advantages for the learner, since it is the producing of the pencil
lines that really proves the study, the inking in being merely a
curtailed repetition of the pencilling. Similarly when the drawing of a
piece, such, for example, as a fully developed screw thread, is shown
fully developed from end to end, even though the pencil lines were all
shown, yet the process of construction will be less clear than if the
process of development be shown gradually along the drawing. Thus
beginning at an end of the example the first pencil lines only may be
shown, and as the pencilling progresses to the right-hand, the
development may progress so that at the other or left-hand end, the
finished inked in and shaded thread may be shown, and between these two
ends will be found a part showing each stage of development of the
thread, all the lines being numbered in the order in which they were
marked. This prevents a confusion of lines, and makes it more easy to
follow or to copy the drawing.

It is the numerous inquiries from working machinists for a book of this
kind that have led the author to its production, which he hopes and
believes will meet the want thus indicated, giving to the learner a
sufficiently practical knowledge of mechanical drawing to enable him to
proceed further by copying such drawings as he may be able to obtain, or
by the aid of some of the more expensive and elaborate books already
published on the subject.

He believes that in learning mechanical drawing without the aid of an
instructor the chief difficulty is overcome when the learner has become
sufficiently familiar with the instruments to be enabled to use them
without hesitation or difficulty, and it is to attain this end that the
chapter on plotting mechanical motions and the succeeding examples have
been introduced; these forming studies that are easily followed by the
beginner; while sufficiently interesting to afford to the student
pleasure as well as profit.

NEW YORK, _February, 1883_.




CONTENTS.


CHAPTER I.

THE DRAWING BOARD.

The T square                                                          18

The triangles                                                         19

Curves                                                                21

Selecting and testing drawing instruments                             22

Lead pencils                                                          23

Mixing India ink                                                      25

The drawing paper                                                     26

Tracing paper                                                         29

The ink                                                               30

Testing and selecting India ink                                       30

Draftsmen's measuring rules                                           33


CHAPTER II.

THE PREPARATION AND USE OF THE INSTRUMENTS.

Preparing the lining pen for use                                      34

The shapes of the lining pen points                                   35

Oil stoning pen points                                                36

Preparing the circle pen for use                                      38

The shape for circle pen points                                       38

Shaping circle pens for very small circles                            39

A form of pen point recently introduced; forming the pen point        39

The method of oil-stoning circle pen points                           40

The needle point and pen point                                        42

How to use the circle pen                                             43

German instrument to avoid slipping of a needle point                 44

How to use the lining pen                                             45

Applying the ink to the bow-pen                                       46

Using a straight line or lining pen with a T square                   47


CHAPTER III.

LINES AND CURVES.

Explanation of simple geometrical terms; radius; explanation of
    conventional dotted lines                                         48

A line at a right angle to another; a point; parallel lines           49

A line produced; a line bisected; a line bounding a circle; an arc of a
    circle; segments of a circle; the chord of an arc; a quadrant of a
    circle                                                            50

A sector of a circle; a line tangent to a circle; a semicircle; centre of
    a circle; axis of a cylinder; to draw a circle that shall pass through
    three given points                                                51

To find the centre from which an arc of a circle has been struck; the
    degrees of a circle                                               52

The protractor                                                        53

To find the angle of one line to another                              54

To find the angles of three lines one to the other                    55

Acute angles and obtuse angles                                        57

Triangles; right angle triangle; obtuse angle triangle; equilateral
    triangle; isosceles triangle                                      58

Scalene triangle; a quadrangle; quadrilateral or tetragon             59

Rhomboid; trapezoid; trapezium                                        60

The construction of polygons                                          61

The names of regular polygons                                         62

The angles of regular polygons; the ellipse                           63

Form of a true ellipse                                                69

The use of a trammel for drawing an ellipse                           72

To draw a parabola mechanically                                       73

To draw a parabola by lines                                           74

To draw a heart cam                                                   75


CHAPTER IV.

SHADOW LINES AND LINE-SHADING.

Section lining or cross-hatching                                      77

To represent cylindrical pieces one within the other; to represent a
    number of pieces one within the other                             78

To represent pieces put together and having slots or keyways through
    them.                                                             79

Effects of shading or cross-hatching                                  80

Lines in sectional shading or cross-hatching made to denote the material
    of which the piece is composed--lead, wood, steel, brass, wrought
    iron, cast iron                                                   81

Line-shading                                                          82

The shade line to indicate the shape of piece; representation of a
    washer                                                            83

A key drawn with a shade line; shade line applied to a nut; a German
    pen regulated to draw lines of various breadths                   84

Example of line-shading in perspective drawing, shown in a pipe threading
    stock and die                                                     85

A cylindrical pin line-shaded; two cylindrical pieces that join each
    other; a lathe centre; a piece having a curved outline            86

Line-shading applied to a ball or sphere; applied to a pin in a socket
    shown in section                                                  87

A piece of tube, where the thickness of the tube is shown; where the
    hollow or hole is seen, the piece shown in section; where the body is
    bell-mouthed and the hollow curve shown by shading                88

Example of line-shading to denote the relative distances of various
    surfaces from the eye                                             89

Line-shading to denote that the piece represented is of wood; shade-lines
    being regular or irregular                                        90


CHAPTER V.

MARKING DIMENSIONS.

Examples in marking dimensions                                        91


CHAPTER VI.

THE ARRANGEMENT OF DIFFERENT VIEWS.

The different views of a mechanical drawing; elevation; plan; general
    view; a figure to represent a solid cylinder                      94

To represent the different sides of a cube; the use of a cross to denote a
    square                                                            95

A triangular piece requires two or three views                        96

To represent a ring having hexagon cross section; examples; a rectangular
    piece in two views                                                98

The position of the piece when in its place determines the name of the
    view in the drawing                                              103

View of a lever                                                      105

Best method of projecting one view from another; the two systems of
    different views of a piece                                       106


CHAPTER VII.

EXAMPLES IN BOLTS, NUTS AND POLYGONS.

To represent the thread of a small screw                             112

A bolt with a hexagon head                                           113

United States standard sizes for forged or unfinished bolts and nuts 116

The basis of the Franklin Institute or United States standard for bolts
    and nuts; hexagonal or hexagon heads of bolts                    118

Comparison of hexagon and square heads of bolts; chamfers            120

Without chamfer; best plan for view of both square and hexagon heads 123

Drawing different views of hexagon heads                             125

To draw a square-headed bolt; to draw the end view of a hexagon head 125

Use of the triangle to divide circles                                129

Scales giving the length of the sides of polygons                    135

To find what a square body which measures one inch on each side measures
    across the corners; to find what diameter a cylindrical piece of
    wood must be turned to which is to be squared, and each side of which
    square must measure an inch                                      136

To find a radius across corners of a hexagon or a six sided figure, the
    length of a side being an inch                                   138

To draw a stud                                                       142

To pencil in a cap nut; pencilling for a link having the hubs on one side
    only                                                             145

Link with hubs on both sides; pencil lines for a double eye or a knuckle
    joint                                                            146

Double eye or knuckle joint with an offset; a connecting rod end     147

A rod end with a round stem                                          148

A bolt with a square under the head                                  149

Example in which the corner where the round stem meets the square
    under the head is sharp; a centre punch giving an example in
    which the flat sides gradually run out upon a circle, the edges
    forming curves                                                   150


CHAPTER VIII.

SCREW THREADS AND SPIRALS.

Screw threads for small bolts with the angles of the thread drawn in, and
    the method of doing this                                         152

A double thread; a round top and bottom thread such as the Whitworth
    thread; a left hand thread; to draw screw threads of a large
    diameter                                                         156

Drawing the curves for screw threads                                 157

To draw the United States standard thread                            160

To draw a square thread                                              162

Form of template for drawing the curves of threads                   165

To show the thread depth in a top or end view of a nut; to draw a spiral
    spring                                                           166

To obtain an accurate division of the lines that divide the pitch    167


CHAPTER IX.

EXAMPLES FOR PRACTICE.

A locomotive spring; a stuffing box and gland; working drawings of a
    coupling rod; dimensions and directions marked; a connecting rod
    drawn and put together as it would be for the lathe, vise, or erecting
    shop                                                             169

Drawings for the blacksmith                                          172

A locomotive frame                                                   174

Reducing scales                                                      175

Making a drawing to scale                                            177


CHAPTER X.

PROJECTIONS.

A spiral wound around a cylinder whose end is cut off at an angle    178

A cylindrical body joining another at a right-angle; a Tee for
    example                                                          180

Other examples of Tees                                               181

Example of a cylinder intersecting a cone                            186

A cylindrical body whose top face if viewed from one point would appear as
    a straight line, or from another a circle                        188


CHAPTER XI.

DRAWING GEAR WHEELS.

Names of the curves and lines of gear teeth                          193

How to draw spur wheel teeth                                         194

Professor Willis' scale of tooth proportions                         195

The application of the scale                                         197

How to find the curve for the tooth face                             198

To trace hypocycloides for the flanks of teeth                       200

Sectional view of a section of a wheel for showing the dimensions through
    the arms and hub                                                 202

To draw an edge view of a wheel; rules for drawing the teeth of wheels;
    bevel gear wheels                                                203

The construction to find the curves                                  204

To draw the arcs for the teeth                                       205

To draw the pitch circle of the inner and small end of the pinion
    teeth                                                            206

One-half of a bevel gear and an edge view projected from the same    207

A pair of bevel wheels shown in section; drawing of a part of an Ames
    lathe feed motion; small bevel gears                             208

Example in which part of the gear is shown with teeth in, and the
    remainder illustrated by circles; drawings of part of the feed
    motion of a Niles horizontal tool work boring mill               209

Three bevel gears, one of which is line-shaded; the construction of oval
    gearing; Professor Rankine's process for rectifying and subdividing
    circular arcs                                                    210

Various examples of laying out gear wheels                           214


CHAPTER XII.

PLOTTING MECHANICAL MOTIONS.

To find how much motion an eccentric will give to its rod            223

To find how much a given amount of motion of a long arm will move the
    short arm of a lever                                             224

Example of the end of a lever acting directly on a shoe; a short arm
    having a roller acting upon a larger roller                      225

A link introduced in the place of the roller to find the amount of motion
    of the rod; a lever actuating a plunger in a vertical line, to find
    how much a given amount of motion of the long arm will actuate the
    plunger                                                          226

Two levers upon their axles or shafts, the arms connected by a link and
    one arm connected to a rod                                       227

A lever arm and cam in one piece on a shaft, a shoe sliding on the line,
    and held against the cam face by the rod, to find the position of the
    face of the shoe against the cam                                 228

To find the amount of motion imparted in a straight line to a rod,
    attached to an eccentric strap                                   229

Examples in drawing the cut off cams employed instead of eccentrics on
    river steamboats in the Western and Southern States. Different views
    of a pair of cams                                                232

The object of using a cam instead of an eccentric                    234

Method of drawing or marking out a full stroke cam                   237

Illustration of the lines embracing cut off cams of varying limits of
    cut-off                                                          240

Part played by the stroke of the engine in determining the conformation
    of cut-off cams; manner of finding essential points of drawings of
    cutoff cams                                                      241

A cam designed to cut off the steam at five-eighths of the piston
    stroke                                                           244

Three-fourths and seven-eighths cams                                 246

Necessary imperfections in the operations of cut-off cams            247

Drawing representing the motion which a crank imparts to a connecting
    rod                                                              249

Plotting out the motion of a shaper link quick return                250

Plotting out the Whitworth quick return motion employed in machines  253

Finding the curves for moulding cutters                              257


CHAPTER XIII.

EXAMPLES IN LINE-SHADING AND DRAWING FOR LINE-SHADED
ENGRAVINGS.

Arrangement of idle pulleys to guide bolts from one pulley to another;
    representation of a cutting tool for a planing machine           264

Drawings for photo-engraving                                         267

Drawing for an engraver in wood; drawings for engravings by the wax
    process                                                          268

Engraving made by the wax process from a print from a wood engraving;
    engravings of a boiler drilling machine                          269


CHAPTER XIV.

SHADING AND COLORING DRAWINGS.

Coloring the journals of shafts; simple shading; drawing cast-iron,
    wrought iron, steel and copper                                   277

Points to be observed in coloring and shading;  drawings to be
    glued around their edges to the drawing board; to maintain an even
    shade of color; mixing colors                                    278

To graduate the depth of tint for a cylindrical surface              279

The size and use of brushes; light in shading; example for shading a
    Medart pulley                                                    280

Brush shading                                                        281

To show by the shading that the surfaces are highly polished;
    representation of an oil cup; representation of an iron planing
    machine                                                          282

Example in shading of Blake's patent direct acting steam pump        284

Example of shading an independent condenser                          288


CHAPTER XV.

EXAMPLES OF ENGINE WORK.

Drawings of an automatic high speed engine; side and end views of the
    engine; vertical section of the cylinder through the valve face  289

Valve motion; governor                                               292

Pillow box, block crank-pin, wheel and main journal                  294

Side and edge view of the connecting rod                             295

A two hundred horse power horizontal steam boiler for a stationary engine;
    cross sectional view of the boiler shell                         296

Side elevation, end view of the boiler, and setting                  297

Working drawings of a one hundred horse power engine; plan and side
    view of the bed plate, with the main bearing and guide bars; cross
    sections of the bed plate; side elevation of the cylinder, with end
    view of the same                                                 299

Steam chest side and horizontal cross section of the cylinder; steam chest
    and the valves; cam wrist plate and cut-off mechanism; shaft for the
    cam plate; cross head; side view and section through the centre of
    the eccentric and strap                                          301

Construction of the connecting rod                                   303

INDEX                                                                305




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|Transcriber's note: In this text $T$ indicates a larger capital letter.|
+-----------------------------------------------------------------------+




MECHANICAL DRAWING

SELF-TAUGHT.

CHAPTER I.

_THE DRAWING BOARD._


A Drawing Board should be of soft pine and free from knots, so that it
will easily receive the pins or tacks used to fasten down the paper. Its
surface should be flat and level, or a little rounding, so that the
paper shall lie close to its surface, which is one of the first
requisites in making a good drawing. Its edges should be straight and at
a right angle one to the other, and the ends of the battens B B in
Figure 1 should fall a little short of the edge A of the board, so that
if the latter shrinks they will not protrude. The size of the board of
course depends upon the size of the paper, hence it is best to obtain a
board as small as will answer for the size of paper it is intended to
use. The student will find it most convenient as well as cheapest to
learn on small drawings rather than large ones, since they take less
time to make, and cost less for paper; and although they require more
skill to make, yet are preferable for the beginner, because he does not
require to reach so far over the board, and furthermore, they teach him
more quickly and effectively. He who can make a fair drawing having
short lines and small curves can make a better one if it has large
curves, etc., because it is easier to draw a large than a very small
circle or curve. It is unnecessary to enter into a description of the
various kinds of drawing boards in use, because if the student purchases
one he will be duly informed of the kinds and their special features,
while if he intends to make one the sketch in Figure 1 will give him all
the information he requires, save that, as before noted, the wood must
be soft pine, well seasoned and free from knots, while the battens B
should be dovetailed in and the face of the board trued after they are
glued and driven in. To true the edges square, it is best to make the
two longest edges parallel and straight, and then the ends may be
squared from those long edges.

[Illustration: Fig. 1.]

THE $T$ SQUARE.

Drawing squares or T squares, as they are termed, are made of wood, of
hard rubber and of steel.

There are several kinds of T squares; in one the blade is solid, as it
is shown in Figure 5 on page 20; in another the back of the square is
pivoted, so that the blade can be set to draw lines at an angle as well
as across the board, which is often very convenient, although this
double back prevents the triangles, when used in some positions, from
coming close enough to the left hand side of the board. In an improved
form of steel square, with pivoted blade, shown in Figure 2, the back is
provided with a half circle divided into the degrees of a circle, so
that the blade can be set to any required degree of angle at once.

[Illustration: Fig. 2.]

[Illustration: Fig. 3.]

[Illustration: Fig. 4.]


THE TRIANGLES.

[Illustration: Fig. 5.]

Two triangles are all that are absolutely necessary for a beginner. The
first is that shown in Figure 3, which is called a triangle of 45
degrees, because its edge A is at that angle to edges B and C. That in
Figure 4 is called a triangle of 60 degrees, its edge A being at 60
degrees to B, and at 30 degrees to C. The edges P and C are at a right
angle or an angle of 90 degrees in both figures; hence they are in this
respect alike. By means of these triangles alone, a great many straight
line drawings may be made with ease without the use of a drawing square;
but it is better for the beginner to use the square at first. The manner
of using these triangles with the square is shown in Figure 5, in which
the triangle, Figure 3, is shown in three positions marked D E F, and
that shown in Figure 4 is shown in three positions, marked respectively
G H and I. It is obvious, however, that by turning I over, end for end,
another position is attained. The usefulness in these particular
triangles is because in the various positions shown they are capable of
use for drawing a very large proportion of the lines that occur in
mechanical drawing. The principal requirement in their use is to hold
them firmly to the square-blade without moving it, and without
permitting them to move upon it. The learner will find that this is best
attained by so regulating the height of the square-blade that the line
to be drawn does not come down too near the bottom of the triangle or
edge of the square-blade, nor too high on the triangle; that is to say,
too near its uppermost point. It is the left-hand edge of the triangle
that is used, whenever it can be done, to produce the required line.

[Illustration: Fig. 6.]


CURVES.

To draw curves that are not formed of arcs or parts of circles,
templates called curves are provided, examples of these forms being
given in Figure 6. They are made in wood and in hard rubber, the latter
being most durable; their uses are so obvious as to require no
explanation. It may be remarked, however, that the use of curves gives
excellent practice, because they must be adjusted very accurately to
produce good results, and the drawing pen must be held in the same
vertical plane, or the curve drawn will not be true in its outline.


DRAWING INSTRUMENTS.

It is not intended or necessary to enter into an elaborate discussion of
the various kinds of drawing instruments, since the purchaser can obtain
a good set of drawing instruments from a reputable dealer by paying a
proportionate price, and must _per force_ learn to use such as his means
enable him to purchase. It is recommended that the beginner purchase as
good a set of instruments as his means will permit, and that if his
means are limited he purchase less than a full set of instruments,
having the same of good quality.

All the instruments that need be used in the examples of this book are
as follows:

A small spring bow-pen for circles, a lining pen or pen for straight
lines, a small spring bow-pencil for circles, a large bow-pen with a
removable leg to replace by a divider leg or a pencil leg, and having an
extension piece to increase its capacity.

The spring bow-pen should have a stiff spring, and should be opened out
to its full capacity to see that the spring acts well when so opened
out, keeping the legs stiff when opened for the larger diameters. The
purchaser should see that the joint for opening and closing the legs is
an easy but not a loose fit on the screw, and that the legs will not
move sideways. To test this latter, which is of great importance in the
spring bow-pencil as well as in the pen, it is well to close the legs
nearly together and taking one leg in one hand and the other leg in the
other hand (between the forefinger and thumb), pushing and pulling them
sideways, any motion in that direction being sufficient to condemn the
instrument. It is safest and best to have the two legs of the bow-pen
and pencil made from one piece of metal, and not of two separate pieces
screwed together at the top, as the screw will rarely hold them firmly
together. The points should be long and fine, and as round as possible.
In very small instruments separate points that are fastened with a screw
are objectionable, because, in very small circles, they hide the point
and make it difficult to apply the instrument to the exact proper point
or spot on the drawing.

The joints of the large bow or circle-pen should also be somewhat stiff,
and quite free from side motion, and the extension piece should be
rigidly secured when held by the screw. It is a good plan in purchasing
to put in the extension piece, open the joint and the pen to their
fullest, and draw a circle, moving the pen in one direction, and then
redraw it, moving it in the other direction, and if one line only
appears and that not thickened by the second drawing, the pen is a good
one.

The lead pencil should be of hard lead, and it is recommended that they
be of the H, H, H, H, H, H, in the English grades, which corresponds to
the V, V, H, of the Dixon grade. The pencil lines should be made as
lightly as possible; first, because the presence of the lead on the
paper tends to prevent the ink from passing to the paper; and, secondly,
because in rubbing out the pencil lines the ink lines are reduced in
blackness and the surface of the paper becomes roughened, so that it
will soil easier and be harder to clean. In order to produce fine pencil
lines without requiring a very frequent sharpening of the pencil it is
best to sharpen the pencil as in Figures 7 and 8, so that the edge shall
be long in the direction in which it is moved, which is denoted by the
arrow in Figure 7. But when very fine work is to be done, as in the case
of Patent Office drawings, a long, round point is preferable, because
the eye can see plainer just where the pencil will begin to mark and
leave off; hence the pencil lines will not be so liable to overrun.

[Illustration: Fig. 7.]

[Illustration: Fig. 8.]

In place of the ordinary wood-covered lead pencils there may be obtained
at the drawing material stores pencil holders for holding the fine,
round sticks of lead, and these are by far the best for a learner. They
are easier to sharpen, and will slip in the holder, giving warning when
the draftsman is pressing them too hard on the paper, as he is apt to
do. The best method of trimming these leads, as also lead pencils after
they have been roughly shaped, is with a small fine file, holding the
file still and moving the pencil; or a good piece of emery paper or sand
paper is good, moving the pencil as before.

All lines in pencilling as in inking in should begin at the left hand
and be drawn towards the right, or when triangles are used the lines are
begun at the bottom and drawn towards the top or away from the
operator. The rubber used should not be of a harsh grade, since that
will roughen the face of the paper and probably cause the ink to run.
The less rubbing out the better the learner will progress, and the more
satisfaction he will receive from the results. If it becomes necessary
to scratch out it is best done with a penknife well sharpened, and not
applied too forcibly to the paper but somewhat lightly, and moved in
different and not all in one direction. After the penknife the rubber
may sometimes be used to advantage, since it will, if of a smooth grade,
leave the paper smoother than the knife. Finally, before inking in, the
surface that has been scraped should be condensed again by rubbing some
clean, hard substance over it which will prevent the ink from spreading.
The end of a paper-cutter or the end of a rounded ivory handled drawing
instrument is excellent for this purpose.

[Illustration: Fig. 9.]

[Illustration: Fig. 10.]

It is well to use the rubber for general purposes in such a way as to
fit it for special purposes; thus, in cleaning the sheet of paper, the
rubber may be applied first, as in Figure 9, as at A, and then as at B,
and if it be moved sideways at the same time it will wear to the form
shown in Figure 10, which will enable it to be applied along a line that
may require to be rubbed out without removing other and neighboring
lines. If the rubber is in the form of a square stick one end may be
bevelled, as in Figure 11, which is an excellent form, or it may be made
to have a point, as in Figure 12. The object is in each case to enable
the rubber action to be confined to the desired location on the paper,
so as to destroy its smooth surface as little as possible.

[Illustration: Fig. 11.]

[Illustration: Fig 12.]

For simple cleaning purposes, or to efface the pencil lines when they
are drawn very lightly, squares of sponge-rubber answer admirably, these
being furnished by the dealers in drawing materials.

A piece of bread will answer a similar purpose, but it is less
convenient.

For glazed surface paper, as Bristol-board, the smoothest rubber must be
used, the grade termed velvet rubber answering well.


THE DRAWING PAPER.

Whatever kind of drawing paper be used it should be kept dry, or the
ink, however good it may be, will be apt to run and make a thick line
that will not have the sharp, clean edges necessary to make lines look
well.

Drawing paper is made in various qualities, kinds, and forms, as
follows: The sizes and names of paper made in sheets are:

Cap,                13 x 16 inches.
Demy,               20 x 15    "
Medium,             22 x 17    "
Royal,              24 x 19    "
Super Royal,        27 x 19    "
Imperial,           30 x 21    "
Elephant,           28 x 22    "
Columbier,          34 x 23    "
Atlas,              33 x 26    "
Theorem,            34 x 28    "
Double Elephant,    40 x 26    "
Antiquarian,        52 x 31    "
Emperor,            40 x 60    "
Uncle Sam,          48 x 120   "

the thickness of the sheets increasing with their size. Some sheets of
paper are hot pressed, to give a smoother surface, and thus enable
cleaner-edged lines to be drawn.

[Illustration: Fig. 13.]

For large drawings paper is made in rolls of various widths, but as
rolled paper is troublesome to lay flat upon the drawing board, it is
recommended to the learner to obtain the sheets, which may be laid
sufficiently flat by means of broad headed pins, such as shown in Figure
13, which are called thumb tacks. These are forced through the paper
into the board at each corner, as in Figure 14 at _f_. On account of the
large diameter of the stems of these thumb tacks, which unduly pierce
and damage the board, and on account also of their heads, by reason of
their thickness, coming in the way of the square blade, it will be
found preferable to use the smallest sizes of ordinary iron tacks, with
flat heads, whose stems are much finer and heads much thinner than thumb
tacks. The objection to ordinary tacks is that they are more difficult
to remove, but they are, as stated, more desirable for use.

[Illustration: Fig. 14.]

[Illustration: Fig. 15.]

If the paper is nearly the full size of the board, it does not much
matter as to its precise location on the board, but otherwise it is best
to place it as near the left-hand edge of the board as convenient, as is
shown in Figure 14.

The lower edge, D, Figure 15, of the paper, however, should not be
placed too near the edge, A, of the board, because if the end P of the
square back comes down below the edge of the board, it is more difficult
to keep the square back true against the end of the board.

The paper must lie flat upon and close to the surface of the board, and
a sufficient number of tacks must be used to effect this purpose.

Drawings that are to be intricate, or to contain a great many lines, as
a drawing of an engine or of a machine, are best pasted or glued all
around the edges of the paper, which should first be dampened; but as
the learner will scarcely require to make such drawings until he is
somewhat familiar with and well practised in the use of the instruments,
this part of the subject need not be treated here.


TRACING PAPER.

For taking tracings from drawings tracing paper or tracing cloth is
used. They require to be stretched tightly and without wrinkles upon the
drawing. To effect this object the mucilage should be thick, and the
tracing paper should be dampened with a sponge after it is pasted. It
must be thoroughly dry before use, or the ink will run.

Tracing cloth must be fastened by pins or thumb tacks, and not dampened.
The drawing should be made on the polished side of the cloth, and any
coloring to be done should be on the other side, and done after the
tracing is removed from the drawing.


THE INK.

India ink should always be used for mechanical drawing: First, because
it lies upon and does not sink into the paper, and is, therefore, easily
erased; and, secondly, because it does not corrode or injure the drawing
instruments.

India ink is prepared in two forms--in the stick and in a liquid form.
The stick ink is mixed in what are termed saucers, or cabinet saucers,
one being placed above the other, so as to exclude the dust from
settling in it, and also to prevent the rapid evaporation to which it is
subject.

The surface of the saucer should be smooth, as any roughness grinds the
ink too coarsely, whereas the finer it is ground or mixed the easier it
will flow, the less liability to clog the instruments, and the smoother
and more flat it will lie upon the paper. In mixing the ink only a small
quantity of water should be used, the stick of ink being pressed
_lightly_ upon the saucer and moved quickly, the grinding being
continued until the ink is mixed quite thickly. This will grind the ink
fine as it is mixed, and more water may be added to thin it. It is best,
however, to let the ink be somewhat thick for use, and to keep it
covered when not in use; and though water may be added if it gets too
thick, yet ink that has once dried should not be mixed up again, as it
will not work so well after having once dried.

Of liquid inks the Higgins ink is by far the best, being quite equal to
and much more convenient for use than the best stick ink.

The difference between a good and an inferior India ink lies chiefly in
the extent to which the lamp-black, which is the coloring matter, forms
with the water a chemical solution rather than a mechanical mixture. In
inferior ink the lamp-black is more or less held in suspension, and by
prolonged exposure to the air will separate, so that on being spread the
solid particles will aggregate by themselves and the water by itself.

This explains why draughtsmen will, after the ink has been exposed to
the air for an hour or two, add a drop of mucilage to it; the mucilage
thickening the solution, adding weight to the water, and deferring the
separation of the lamp-black.

A good India ink is jet black, flows easily, lies close to, does not
stand upon or sink into the paper, and has an even lustre, the latter
being an indication of fineness. The more perfect the incorporation of
the lamp-black with the water the easier the ink will flow, the less
liable it is to clog the instruments, the more even and sharp the edges
of the lines, and the finer the lines that may be drawn.

Usually India ink can only be tested by actual trial; but since it is
desirable to test before purchasing it, it may be mentioned that one
method is to mix a little on the finger nail, and if it has a "bronzy"
gloss it is a good indication. It should also spread out and dry without
any tendency to separate.

The best method of testing is to mix a very little, and drop a single
drop in a tumbler of clear water. The best ink will diffuse itself over
the surface, and if the water is disturbed will diffuse itself through
the water, leaving it translucent and black, with a slight tinge of
bronze color. A coarser ink will act in a similar manner, but make the
water somewhat opaque, with a blue-black, or dull, ashy color. A still
coarser ink will, when diffused over the surface of the water, show fine
specks, like black dust, on the surface. This is readily apparent,
showing that the mixture of the ink is not homogeneous.

When it is an object to have the lines of a drawing show as black as
possible, as for drawings that are to be photo-engraved, the ink should
be mixed so thickly as to have a tendency to lift when a body, such as a
lead pencil, is lifted out of it. For Patent Office drawings some will
mix it so thickly that under the above test it appears a little stringy.

The thicker the ink can be used the better, because the tendency of the
carbon to separate is less; and it is for this reason that the test
mentioned with a tumbler of water is so accurate. When ink is to be used
on parchment, or glossy tracing-paper, it will flow perfectly if a few
drops of ox-gall be mixed with it; but on soft paper, or on bristol
board, this will cause the ink to spread.

For purposes of measurement, there are special rules or scales of steel
and of paper manufactured. The steel rules are finely and accurately
divided, and some are of triangular form, so that when laid upon the
paper the lines divided will lie close to the paper, and the light will
fall directly on the ruled surface. Triangular rules or scales are
therefore much superior to flat ones. The object of having a paper rule
or scale is, that the paper will expand and contract under varying
degrees of atmospheric moisture, the same as the drawing paper does.

Figure 16 represents a triangular scale, having upon it six different
divisions of the inch. These are made in different patterns, having
either decimal divisions or the vulgar fractions. Being made of steel,
and nickel-plated, they are proof against the moisture of the fingers,
and are not subject to the variation of the wooden scale.

[Illustration: Fig. 16.]




CHAPTER II.

_THE PREPARATION AND USE OF THE INSTRUMENTS._


The points of drawing instruments require to be very accurately prepared
and shaped, to enable them to make clean, clear lines. The object is to
have the points as sharp as they can be made without cutting the paper,
and the curves as even and regular as possible.

[Illustration: Fig. 17.]

[Illustration: Fig. 18.]

The lining pen should be formed as in Figure 17, which presents an edge
and a front view of the points. The inside faces should be flat across,
and slightly curved in their lengths, as shown. If this curve is too
great, as shown exaggerated in Figure 18, the body of the ink lies too
near the point and is apt to flow too freely, running over the pen-point
and making a thick, ragged line. On the other hand, if the inside faces,
between which the ink lies, are too parallel and narrow near the points,
the ink dries in the pen, and renders a too frequent cleaning necessary.
Looking at the face of the pen as at A in Figure 17, its point should
have an even curve, as shown, the edge being as sharp as it can be made
without cutting the drawing paper. Upon this quality depends the
fineness and cleanness of the lines it will make. This thin edge should
extend around the curve as far as the dotted line, so that it will be
practicable to slant the pen in either of the directions shown in Figure
19; and it is obvious that its thickness must be equal around the arc,
so that the same thickness of line will be drawn whether the pen be held
vertical or slanted in either direction.

[Illustration: Fig. 19.]

[Illustration: Fig. 20.]

The outside faces of the pen should be slightly curved, so that when
held vertically, as in Figure 20 (the dotted line representing the
centre of the length of the instrument), and against the square blade S,
the point will meet the paper a short distance from the lower edge of S
as shown. By this means it is not necessary to adjust the square edge
exactly coincident with the line, but a little way from it. This is an
advantage for two reasons: first, the trouble of setting the square-edge
exactly coincident is avoided, and, secondly, the liability of the ink
to adhere to the edge of the square-blade and flow on to the paper and
make a thick, ragged line, is prevented.

The square being set as near to the line as desired, the handle may be
held at such an angle that the pen-point will just meet the line when
sloped either as in Figure 21 or 22. If, however, the <DW72> be too much
in the direction shown in Figure 21, practice is necessary to enable the
drawing of straight lines if they be long ones, because any variation in
the angle of the instrument to the paper obviously vitiates the
straightness of the line. If, on the other hand, the square be too close
to the line, and the pen therefore requires to be sloped as in Figure
22, the ink flowing from the pen-point is apt to adhere to the
square-edge, and the result will be a ragged, thick line, as shown in
Figure 23.

[Illustration: Fig. 21.]

[Illustration: Fig. 22.]

[Illustration: Fig. 23.]

[Illustration: Fig. 24.]

[Illustration: Fig. 25.]

[Illustration: Fig. 26.]

Each of the legs should be of equal thickness at the pen-point edge, so
that when closed together the point will be in the middle of the edge.
The width and curve of each individual point should be quite equal, and
the easiest method of attaining this end is as follows:

Take a small slip of Arkansas oil-stone, and with the pen-points closed
firmly by the screw trim the pen-edges to the required curve as shown at
A, Figure 17, making the curve as even as possible. Then stone the faces
until this curve is brought up to a sharp edge at the point between the
two pen-legs forming the point.

Next take a piece of 000 French emery paper, lay it upon some flat body
like the blade of a square, and smooth the curve of the edge enough to
take off the fine, sharp edge left by the oil-stone; then apply the
outside flat faces of the pen to the emery paper again, bringing the
pen-edge up sharp.

The emery paper will simply have smoothed and polished the surfaces,
still leaving them too sharp, so sharp as to cut the paper, and to take
off this sharp edge (which must first be done on the inside faces) open
the pen-points as wide as the screw will permit. Then wrap one thickness
of the emery paper upon a thin blade, as upon a drawing-triangle, and
pass the open pen-points over it, and move the instrument endwise,
taking care to keep the inside face level with the surface of the emery
paper, so that the pen-points shall not cut through. Next close the
pen-points with the screw until they nearly, but not quite, touch, and
sweep the edge of the pen-point along the emery paper under a slight
pressure, so moving the handle that at each stroke the whole length
around the curved end of the pen will meet the emery surface. During
this motion the inside faces of the pen-point must be held as nearly
vertical as possible, so as to keep the two halves of the pen-point
equal.

The pen is now ready for use, and will draw a fine and clean line.

It is not usual to employ emery paper for the purpose indicated, but it
will be found very desirable, since it leaves a smoother surface and
edge than the oil-stone alone.

Circle-pens are more difficult to put in order than the straight-line
pen, especially those for drawing the smallest circles, which cannot be
well drawn unless the pen is of the precise right shape and in the best
condition.

A circle-pen is shown in Figure 24, in which A represents the point-leg
and B the pen-leg. The point-leg must be the longest because it requires
to enter the drawing paper before the pen meets the surface. The point
should be sharp and round, for any edges or angles on it will cause it
to widen the hole in the paper when it is rotated. To shape the points
to prevent the enlargement of the centre in the paper is one of the most
important considerations in the use of this instrument, especially when
several circles require to be drawn from the same centre. To accomplish
this end the inside of the point-leg should be, as near as possible,
parallel to the length of the instrument (which is denoted in Figure 24
by the dotted line) when the legs are closed, as in the figure. If the
point is at an angle, as shown in Figure 25, it is obvious that rotating
it will enlarge the top of the centre in the drawing paper. The point
should be sharp and smooth on its circumferential surface, and so much
longer than the pen-point that it will have sufficient hold in the paper
when the instrument stands vertical and the pen-point meets the surface
of it, which amount is about 1/64th of an inch.

We may now consider the shape of the pen-point. Its inside surfaces
should be flat across and to the curve shown in Figure 24, not as shown
exaggerated in Figure 25, because in the latter the body of the ink will
be too near the pen-point, and but little can be placed in it without
causing it sometimes to flow over the edges and down the outside of the
pen.

A form of pen-point recently introduced is shaped as in Figure 26, the
object being to have a thin stream of ink near the marking pen-point and
the main body of the ink near at hand, instead of extending up the pen,
as would be the case with Figure 24. The advantage thus gained is that
the ink lies in a more solid body, and having less area of surface
exposed to the air will not dry so quickly in the pen; but this is more
than offset by the liability of the ink to flow over the crook at A, and
cause the pen to draw a thick ragged line. The pen-point must be
slightly inclined toward the needle-point, to the end that they may
approach each other close enough for drawing very small circles, but it
should also stand as nearly vertical as will permit that end to be
attained. As this pen is for drawing small circles only, it does not
require much ink, and hence may be somewhat close together, as in Figure
24; this has the advantage that the point is not hidden from
observation.

In forming the pen-point the greatest refinement is necessary to enable
the drawing of very small true circles, say 1/16th of an inch, or less,
in diameter. The requirements are that the pen-point shall meet the
surface of the paper when the needle-point has entered it sufficiently
to give the necessary support, and that the instrument shall stand
vertical, as shown by the dotted line in Figure 24. Also, that the pen
shall then touch the paper at a point only, this point being the apex of
a fine curve; that this curve be equal on each side of the point of
contact with the paper; that both halves forming the pen be of equal
thickness and width at the pointed curve; and that the point be as sharp
as possible without cutting the paper.

The best method of attaining these ends is as follows: On each side of
the pen make, with an oil-stone, a flat place, as C D, Figure 27 (where
the pen-point is shown magnified), thus bringing both halves to an edge
of exactly equal length, and leaving the point flat at D. These flat
places must be parallel to one another and to the joint between the two
halves of the pen. As the oil-stone may leave a slightly ragged edge, it
is a good plan to take a piece of 00 French emery paper, lay it on a
flat surface, and holding the instrument vertically remove the fine edge
D until it will not cut. Then with the oil-stone shape the curved edge
as in Figure 28, taking care that the curve no more than brings the flat
place D up to a true curve and leaves the edge sharp, with only the very
point touching the paper, which is represented in the cut by the
horizontal line.

[Illustration: Figures 27. 28. 29. 30. 31. 32.]

The point must have a sharp edge all around the curve, and the two
halves must be exactly equal in width, for if one half is wider than the
other, as in Figure 29 at a, or as in Figure 30 at b, it will be
impossible to draw a very small circle true. So, likewise, the two
halves of the pen must be of exactly equal length, and not one half
longer than the other, as in Figures 31 or 32, which would tend to cut
the paper, and also render the drawing of true small circles
impracticable.

When the pen is closed to draw a very small circle the two halves of the
pen-leg should have an equal degree of contact with the surface of the
paper, and then as the legs are opened out to draw larger circles the
contact of the outside half of the pen will have less contact with the
paper. The smaller the circle, the more difficult it is to keep the
point-leg from slipping out of the centre, and the more difficult it is
to draw a clear line and true circle; hence the points should be shaped
to the best advantage for drawing these small circles, by oil-stoning
the pen, as already described, and then finishing it as follows:

After the oil-stoning, open the two valves of the pen-leg wide enough to
admit a piece of 000 French emery paper wrapped once around a very thin
blade, and move the pen endwise as described for the straight-line pen.
This will smooth the inner surfaces and remove any fine wire-edge that
the oil-stone may leave. Close the two halves of the pen again, and
lightly emery-paper the outside faces, which will leave the edge sharp
enough to cut the paper. The removal of the sharp edge still left, to
the exact degree, requires great care. It may best be done by closing
the pen until its two halves very nearly, but not quite, touch, then
adjust it to mark a circle of about 3/16 inch diameter, and strike a
number of circles in different locations upon the surface of a piece of
0000 French emery paper.

In marking these circles, however, let the instrument stand out of the
perpendicular, and do very little while standing vertically. Indeed, it
is well to strike a number of half-circles, first from right to left and
then from left to right, and finally draw a full circle, sloping the pen
on one side, gradually raising it vertically, and finally sloping it to
the other side. This will insure that the pen has contact at its extreme
point, and leave that point fine and keen, but not enough so to cut the
paper. To test the pen, draw small circles with the pen rotated first in
one direction and then in the other, closing its points so as to mark a
fine line, which, if the pen is properly shaped, will be clear and fine,
while if improperly formed the circle drawn with the pen rotated in one
direction will not coincide with that drawn while rotating it in the
other. The same circle may be drawn over several times to make a
thorough test. If a drawing instrument will draw a fine line correctly,
it will be found to answer for thick lines which are more easily made.

In thus preparing the instruments, the operator will find that if he
occasionally holds the points in the right position with regard to the
light, he will be able to see plainly if the work is proceeding evenly
and equally, for if one-half of the pen is thicker at the point or edge
than the other, it will show a brighter line. This is especially the
case with instruments that have become dull by use, for in that case the
edges will be found quite bright, and any inequality of thickness shows
plainly.

[Illustration: Fig 33.]

[Illustration: Fig. 34.]

It follows, from what has been said, that the needle-point and pen-point
should stand vertical when in use, and to effect this the instruments,
except in the smallest sizes, are provided with joints, such as shown at
A and B in the bow-pencil or circle-pencil, in Figure 33. These joints
should be sufficiently stiff that they will not move too easily, and yet
will move rather than that the legs should sensibly spring without
moving at the joint. The needle-point leg should be adjusted by means of
the joint, to stand vertical, and the same remarks apply equally to the
pen-leg; but in the case of the pencil-leg it is the pencil itself and
not the leg that requires attention, the joint B being so adjusted that
the pencil either stands vertical, or, what is perhaps preferable, so
that it stands inclined slightly towards the needle-point. In
sharpening the pencil the inner face C may be made concave or at least
vertical and flat, and the outer convex or else bevelled and flat,
producing a fine and long edge rounded in its length of edge. In using
the circle-pencil and circle-pen it will be found more convenient to
rotate it in the direction of the arrow in Figure 34. It should be held
lightly to the paper, and the learner will find that he has a natural
tendency to hold it too firmly and press it too heavily, which is
_especially to be avoided_.

If in drawing a small circle the needle-point slips out of the paper, it
is because the pencil-point is too long; or, what is the same thing, the
needle-point does not protrude far enough out from the leg. Or if the
instrument requires to be leaned over too much to make the pencil or pen
mark, it is because the pen or pencil is not far enough out, and this
again may cause the needle-point to slip out of the paper.

[Illustration: Fig. 35.]

[Illustration: Fig. 36.]

In Figure 35 is shown a German instrument especially designed to avoid
this slipping. The peculiarity of this instrument consists in the
arrangement of the centre point, which remains stationary whilst the pen
or pencil, resting by its own weight on the paper, is guided round by
gently turning, without pressure, the small knob at the upper end of the
tube. By this means the misplacing or sliding of the centre-point and
the cutting of the paper by the pen are avoided. By means of this fixed
centre-point any number of concentric circles may be drawn, without
making a hole of very distinguishable size on the paper.

[Illustration: Fig 37.]

In applying the ink to the bow-pen as to all other instruments, care
must be taken that the ink lies between the points only and not on the
outside, for in the latter case the ink will flow down too freely and
make a broad, ragged line, perhaps getting on the edge of the square
blade or triangle, and causing a blot of ink on the drawing.

In using a straight line or lining pen with a T square it may be used as
in Figure 36, being nearly vertical, as shown, and moved from left to
right as denoted by the arrow, S representing the square blade. But in
using it, or a pencil, with a straight edge or a triangle unsupported by
the square blade, the latter should be steadied by letting the fingers
rest upon it while using the instrument, the operation being shown in
Figure 37. The position, Figure 36, is suitable for long lines, and that
in Figure 37 for small drawings, where the pen requires close adjustment
to the lines.




CHAPTER III.

_LINES AND CURVES._


Although the beginner will find that a study of geometry is not
essential to the production of such elementary examples of mechanical
drawing as are given in this book, yet as more difficult examples are
essayed he will find such a study to be of great advantage and
assistance. Meantime the following explanation of simple geometrical
terms is all that is necessary to an understanding of the examples
given.

The shortest distance between two points is termed the radius; and, in
the case of a circle, means the distance from the centre to the
perimeter measured in a straight line.

[Illustration: Fig. 38.]

[Illustration: Fig. 39.]

[Illustration: Fig. 40.]

Dotted lines, thus, <----->, mean the direction and the points at which a
dimension is taken or marked. Dotted lines, thus,-----, simply connect
the same parts or lines in different views of the object. Thus in
Figure 38 are a side and an end view of a rivet, and the dotted lines
show that the circles on the end view correspond to the circle of the
diameters of the head and of the stem, and therefore represent their
diameters while showing that both are round. A straight line is in
geometry termed a right line.

A line at a right angle to another is said to be perpendicular to it;
thus, in Figures 39, 40, and 41, lines A are in each case perpendicular
to line B, or line B is in each case perpendicular to line A.

A point is a position or location supposed to have no size, and in cases
where necessary is indicated by a dot.

[Illustration: Fig. 41.]

[Illustration: Fig. 42.]

[Illustration: Fig. 43.]

Parallel lines are those equidistant one from the other throughout their
length, as in Figure 42. Lines maybe parallel though not straight; thus,
in Figure 43, the lines are parallel.

[Illustration: Fig. 44.]

[Illustration: Fig. 45.]

[Illustration: Fig. 46.]

A line is said to be _produced_ when it is extended beyond its natural
limits: thus, in Figure 44, lines A and B are _produced_ in the point C.

A line is bisected when the centre of its length is marked: thus, line A
in Figure 45 is bisected, at or in, as it is termed, _e_.

The line bounding a circle is termed its circumference or periphery and
sometimes the perimeter.

A part of this circumference is termed an arc of a circle or an arc;
thus Figure 46 represents an arc. When this arc has breadth it is termed
a segment; thus Figures 47 and 48 are segments of a circle. A straight
line cutting off an arc is termed the chord of the arc; thus, in Figure
48, line A is the chord of the arc.

[Illustration: Fig. 47.]

[Illustration: Fig. 48.]

[Illustration: Fig. 49.]

[Illustration: Fig. 50.]

[Illustration: Fig. 51.]

A quadrant of a circle is one quarter of the same, being bounded on two
of its sides by two radial lines, as in Figure 49.

When the area of a circle that is enclosed within two radial lines is
either less or more than one quarter of the whole area of the circle the
figure is termed a sector; thus, in Figure 50, A and B are both sectors
of a circle.

A straight line touching the perimeter of a circle is said to be tangent
to that circle, and the point at which it touches is that to which it is
tangent; thus, in Figure 51, line A is tangent to the circle at point B.
The half of a circle is termed a semicircle; thus, in Figure 52, A B and
C are each a semicircle.

[Illustration: Fig. 52.]

[Illustration: Fig. 53.]

The point from which a circle or arc of a circle is drawn is termed its
centre. The line representing the centre of a cylinder is termed its
axis; thus, in Figure 53, dot _d_ represents the centre of the circle,
and line _b b_ the axial line of the cylinder.

To draw a circle that shall pass through any three given points: Let A B
and C in Figure 54 be the points through which the circumference of a
circle is to pass. Draw line D connecting A to C, and line E connecting
B to C. Bisect D in F and E in G. From F as a centre draw the semicircle
O, and from G as a centre draw the semicircle P; these two semicircles
meeting the two ends of the respective lines D E. From B as a centre
draw arc H, and from C the arc I, bisecting P in J. From A as a centre
draw arc K, and from C the arc L, bisecting the semicircle O in M. Draw
a line passing through M and F, and a line passing through J and Q, and
where these two lines intersect, as at Q, is the centre of a circle R
that will pass through all three of the points A B and C.

[Illustration: Fig. 54.]

[Illustration: Fig. 55.]

To find the centre from which an arc of a circle has been struck: Let A
A in Figure 55 be the arc whose centre is to be found. From the extreme
ends of the arc bisect it in B. From end A draw the arc C, and from B
the arc D. Then from the end A draw arc G, and from B the arc F. Draw
line H passing through the two points of intersections of arcs C D, and
line I passing through the two points of intersection of F G, and where
H and I meet, as at J, is the centre from which the arc was drawn.

A degree of a circle is the 1/360 part of its circumference. The whole
circumference is supposed to be divided into 360 equal divisions, which
are called the degrees of a circle; but, as one-half of the circle is
simply a repetition of the other half, it is not necessary for
mechanical purposes to deal with more than one-half, as is done in
Figure 56. As the whole circle contains 360 degrees, half of it will
contain one-half of that number, or 180; a quarter will contain 90, and
an eighth will contain 45 degrees. In the protractors (as the
instruments having the degrees of a circle marked on them are termed)
made for sale the edges of the half-circle are marked off into degrees
and half-degrees; but it is sufficient for the purpose of this
explanation to divide off one quarter by lines 10 degrees apart, and the
other by lines 5 degrees apart. The diameter of the circle obviously
makes no difference in the number of decrees contained in any portion of
it. Thus, in the quarter from 0 to 90, there are 90 degrees, as marked;
but suppose the diameter of the circle were that of inner circle _d_,
and one-quarter of it would still contain 90 degrees.

[Illustration: Fig. 56.]

So, likewise, the degrees of one line to another are not always taken
from one point, as from the point O, but from any one line to another.
Thus the line marked 120 is 60 degrees from line 180, or line 90 is 60
degrees from line 150. Similarly in the other quarter of the circle 60
degrees are marked. This may be explained further by stating that the
point O or zero may be situated at the point from which the degrees of
angle are to be taken. Here it may be remarked that, to save writing the
word "degrees," it is usual to place on the right and above the figures
a small  deg., as is done in Figure 56, the 60 deg. meaning sixty degrees, the
 deg., of course, standing for degrees.

[Illustration: Fig. 57.]

Suppose, then, we are given two lines, as _a_ and _b_ in Figure 57, and
are required to find their angle one to the other. Then, if we have a
protractor, we may apply it to the lines and see how many degrees of
angle they contain. This word "contain" means how many degrees of angle
there are between the lines, which, in the absence of a protractor, we
may find by prolonging the lines until they meet in a point as at _c_.
From this point as a centre we draw a circle D, passing through both
lines _a_, _b_. All we now have to do is to find what part, or how much
of the circumference, of the circle is enclosed within the two lines. In
the example we find it is the one-twelfth part; hence the lines are 30
degrees apart, for, as the whole circle contains 360, then one-twelfth
must contain 30, because 360/12 = 30.

[Illustration: Fig. 58.]

If we have three lines, as lines A B and C in Figure 58, we may find
their angles one to the other by projecting or prolonging the lines
until they meet as at points D, E, and F, and use these points as the
centres wherefrom to mark circles as G, H, and I. Then, from circle H,
we may, by dividing it, obtain the angle of A to B or of B to A. By
dividing circle I we may obtain the angle of A to C or of C to A, and by
dividing circle G we may obtain the angle of B to C or of C to B.

[Illustration: Fig. 59.]

It may happen, and, indeed, generally will do so, that the first attempt
will not succeed, because the distance between the lines measured, or
the arc of the circle, will not divide the circle without having the
last division either too long or too short, in which case the circle may
be divided as follows: The compasses set to its radius, or half its
diameter, will divide the circle into 6 equal divisions, and each of
these divisions will contain 60 degrees of angle, because 360 (the
number of degrees in the whole circle) /6 (the number of divisions) =
60, the number of degrees in each division. We may, therefore, subdivide
as many of the divisions as are necessary for the two lines whose
degrees of angle are to be found. Thus, in Figure 59, are two lines, C,
D, and it is required to find their angle one to the other. The circle
is divided into six divisions, marked respectively from 1 to 6, the
division being made from the intersection of line C with the circle. As
both lines fall within less than a division, we subdivide that division
as by arcs _a_, _b_, which divide it into three equal divisions, of
which the lines occupy one division. Hence, it is clear that they are at
an angle of 20 degrees, because twenty is one-third of sixty. When the
number of degrees of angle between two lines is less than 90, the lines
are said to form an acute angle one to the other, but when they are at
more than 90 degrees of angle they are said to form an obtuse angle.
Thus, in Figure 60, A and C are at an acute angle, while B and C are at
an obtuse angle. F and G form an acute angle one to the other, as also
do G and B, while H and A are at an obtuse angle. Between I and J there
are 90 degrees of angle; hence they form neither an acute nor an obtuse
angle, but what is termed a right-angle, or an angle of 90 degrees. E
and B are at an obtuse angle. Thus it will be perceived that it is the
amount of inclination of one line to another that determines its angle,
irrespective of the positions of the lines, with respect to the circle.

[Illustration: Fig. 60.]


TRIANGLES.

A right-angled triangle is one in which two of the sides are at a right
angle one to the other. Figure 61 represents a right-angled triangle, A
and B forming a right angle. The side opposite, as C, is called the
hypothenuse. The other sides, A and B, are called respectively the base
and the perpendicular.

[Illustration: Fig. 61.]

[Illustration: Fig. 62.]

[Illustration: Fig. 63.]

[Illustration: Fig. 64.]

An acute-angled triangle has all its angles acute, as in Figure 63.

An obtuse-angled triangle has one obtuse angle, as A, Figure 62.

When all the sides of a triangle are equal in length and the angles are
all equal, as in Figure 63, it is termed an equilateral triangle, and
either of its sides may be called the base. When two only of the sides
and two only of the angles are equal, as in Figure 64, it is termed an
isosceles triangle, and the side that is unequal, as A in the figure, is
termed the base.

[Illustration: Fig. 65.]

[Illustration: Fig. 66.]

When all the sides and angles are unequal, as in Figure 65, it is termed
a scalene triangle, and either of its sides may be called the base.

The angle opposite the base of a triangle is called the vertex.

[Illustration: Fig. 67.]

[Illustration: Fig. 68.]

A figure that is bounded by four straight lines is termed a quadrangle,
quadrilateral or tetragon. When opposite sides of the figure are
parallel to each other it is termed a parallelogram, no matter what the
angle of the adjoining lines in the figure may be. When all the angles
are right angles, as in Figure 66, the figure is called a rectangle. If
the sides of a rectangle are of equal length, as in Figure 67, the
figure is called a square. If two of the parallel sides of a rectangle
are longer than the other two sides, as in Figure 66, it is called an
oblong. If the length of the sides of a parallelogram are all equal and
the angles are not right angles, as in Figure 68, it is called a rhomb,
rhombus or diamond. If two of the parallel sides of a parallelogram are
longer than the other two, and the angles are not right angles, as in
Figure 69, it is called a rhomboid. If two of the parallel sides of a
quadrilateral are of unequal lengths and the angles of the other two
sides are not equal, as in Figure 70, it is termed a trapezoid.

[Illustration: Fig. 69.]

[Illustration: Fig. 70.]

[Illustration: Fig. 71.]

If none of the sides of a quadrangle are parallel, as in Figure 71, it
is termed a trapezium.

THE CONSTRUCTION OF POLYGONS.

[Illustration: Fig. 71_a_.]

[Illustration: Fig. 72.]

The term polygon is applied to figures having flat sides equidistant
from a common centre. From this centre a circle may be struck that will
touch all the corners of the sides of the polygon, or the point of each
side that is central in the length of the side. In drawing a polygon,
one of these circles is used upon which to divide the figure into the
requisite number of divisions for the sides. When the dimension of the
polygon across its corners is given, the circle drawn to that dimension
circumscribes the polygon, because the circle is without or outside of
the polygon and touches it at its corners only. When the dimension
across the flats of the polygon is given, or when the dimension given is
that of a circle that can be inscribed or marked within the polygon,
touching its sides but not passing through them, then the polygon
circumscribes or envelops the circle, and the circle is inscribed or
marked within the polygon. Thus, in Figure 71 _a_, the circle is
inscribed within the polygon, while in Figure 72 the polygon is
circumscribed by the circle; the first is therefore a circumscribed and
the second an inscribed polygon. A regular polygon is one the sides of
which are all of an equal length.


NAMES OF REGULAR POLYGONS.

A figure of 3 sides is called a Trigon.
     "      4   "        "      Tetragon.
  polygon   5   "        "      Pentagon.
     "      6   "        "      Hexagon.
     "      7   "        "      Heptagon.
     "      8   "        "      Octagon.
     "      9   "        "      Enneagon or Nonagon.

[Illustration: Fig. 73.]

[Illustration: Fig. 74.]

The angles of regular polygons are designated by their degrees of angle,
"at the centre" and "at the circumference." By the angle at the centre
is meant the angle of a side to a radial line; thus in Figure 73 is a
hexagon, and at C is a radial line; thus the angle of the side D to C is
60 degrees. Or if at the two ends of a side, as A, two radial lines be
drawn, as B, C, then the angles of these two lines, one to the other,
will be the "angle at the centre." The angle at the circumference is the
angle of one side to its next neighbor; thus the angle at the
circumference in a hexagon is 120 degrees, as shown in the figure for
the sides E, F. It is obvious that as all the sides are of equal length,
they are all at the same angle both to the centre and to one another. In
Figure 74 is a trigon, the angles at its centre being 120, and the angle
at the circumference being 60, as marked.

The angles of regular polygons:

Trigon, at the centre, 120 deg., at the circumference, 60 deg..
Tetragon,     "         90 deg.,    "         "        90 deg..
Pentagon,     "         72 deg.,    "         "       108 deg..
Hexagon,      "         60 deg.,    "         "       120 deg..
Octagon,      "         45 deg.,    "         "       135 deg..
Enneagon,     "         40 deg.,    "         "       140 deg..
Decagon,      "         36 deg.,    "         "       144 deg..
Dodecagon,    "         30 deg.,    "         "       150 deg..


THE ELLIPSE.

An ellipse is a figure bounded by a continuous curve, whose nature will
be shown presently.

The dimensions of an ellipse are taken at its extreme length and
narrowest width, and they are designated in three ways, as by the length
and breadth, by the major and minor axis (the major axis meaning the
length, and the minor the breadth of the figure), and the conjugate and
transverse diameters, the transverse meaning the shortest, and the
conjugate the longest diameter of the figure.

In this book the terms major and minor axis will be used to designate
the dimensions.

The minor and major axes are at a right angle one to the other, and
their point of intersection is termed the axis of the ellipse.

In an ellipse there are two points situated upon the line representing
the major axis, and which are termed the foci when both are spoken of,
and a focus when one only is referred to, foci simply being the plural
of focus. These foci are equidistant from the centre of the ellipse,
which is formed as follows: Two pins are driven in on the major axis to
represent the foci A and B, Figure 75, and around these pins a loop of
fine twine is passed; a pencil point, C, is then placed in the loop and
pulled outwards, to take up the slack of the twine. The pencil is held
vertical and moved around, tracing an ellipse as shown.

[Illustration: Fig. 75.]

Now it is obvious, from this method of construction, that there will be
at every point in the pencil's path a length of twine from the final
point to each of the foci, and a length from one foci to the other, and
the length of twine in the loop remaining constant, it is demonstrated
that if in a true ellipse we take any number of points in its curve, and
for each point add together its distance to each focus, and to this add
the distance apart of the foci, the total sum obtained will be the same
for each point taken.

[Illustration: Fig. 76.]

[Illustration: Fig. 77.]

In Figures 76 and 77 are a series of ellipses marked with pins and a
piece of twine, as already described. The corresponding ellipses, as A
in both figures, were marked with the same loop, the difference in the
two forms being due to the difference in distance apart of the foci.
Again, the same loop was used for ellipses B in both figures, as also
for C and D. From these figures we perceive that--

1st. With a given width or distance apart of foci, the larger the
dimensions are the nearer the form of the figure will approach to that
of a circle.

2d. The nearer the foci are together in an ellipse, having any given
dimensions, the nearer the form of the figure will approach that of a
circle.

3d. That the proportion of length to width in an ellipse is determined
by the distance apart of the foci.

4th. That the area enclosed within an ellipse of a given circumference
is greater in proportion as the distance apart of the foci is
diminished; and,

5th. That an ellipse may be given any required proportion of width to
length by locating the foci at the requisite distance apart.

The form of a true ellipse may be very nearly approached by means of the
arcs of circles, if the centres from which those arcs are struck are
located in the most desirable positions for the form of ellipse to be
drawn.

[Illustration: Fig. 78.]

Thus in Figure 78 are three ellipses whose forms were pencilled in by
means of pins and a loop of twine, as already described, but which were
inked in by finding four arcs of circles of a radius that would most
closely approach the pencilled line; _a b_ are the foci of all three
ellipses A, B, and C; the centre for the end curves of _a_ are at _c_
and _d_, and those for its side arcs are at _e_ and _f_. For B the end
centres are at _g_ and _h_, and the side centres at _i_ and _j_. For C
the end centres are at _k_, _l_, and the side centres at _m_ and _n_.
It will be noted that, first, all the centres for the end curves fall on
the line of the length or major axis, while all those for the sides fall
on the line of width or the minor axis; and, second, that as the
dimensions of the ellipses increase, the centres for the arcs fall
nearer to the axis of the ellipse. Now in proportion as a greater number
of arcs of circles are employed to form the figure, the nearer it will
approach the form of a true ellipse; but in practice it is not usual to
employ more than eight, while it is obvious that not less than four can
be used. When four are used they will always fall somewhere on the lines
on the major and minor axis; but if eight are used, two will fall on the
line of the major axis, two on the line of the minor axis, and the
remaining four elsewhere.

[Illustration: Fig. 79.]

In Figure 79 is a construction wherein four arcs are used. Draw the line
_a b_, the major axis, and at a right angle to it the line _c d_, the
minor axis of the figure. Now find the difference between the length of
half the two axes as shown below the figure, the length of line _f_
(from _g_ to _i_) representing half the length of the figure (as from
_a_ to _e_), and the length or radius from _g_ to _h_ equalling that
from _e_ to _d_; hence from _h_ to _i_ is the difference between half
the major and half the minor axis. With the radius (_h i_), mark from
_e_ as a centre the arcs _j k_, and join _j k_ by line _l_. Take half
the length of line _l_ and from _j_ as a centre mark a line on _a_ to
the arc _m_. Now the radius of _m_ from _e_ will be the radius of all
the centres from which to draw the figure; hence we may draw in the
circle _m_ and draw line _s_, cutting the circle. Then draw line _o_,
passing through _m_, and giving the centre _p_. From _p_ we draw the
line _q_, cutting the intersection of the circle with line _a_ and
giving the centre _r_. From _r_ we draw line _s_, meeting the circle and
the line _c, d_, giving us the centre _t_. From _t_ we draw line _u_,
passing through the centre _m_. These four lines _o_, _q_, _s_, _u_ are
prolonged past the centres, because they define what part of the curve
is to be drawn from each centre: thus from centre _m_ the curve from _v_
to _w_ is drawn, from centre _t_ the curve from _w_ to _x_ is drawn.
From centre _r_ the curve from _x_ to _y_ is drawn, and from centre _p_
the curve from _y_ to _v_ is drawn. It is to be noted, however, that
after the point _m_ is found, the remaining lines may be drawn very
quickly, because the line _o_ from _m_ to _p_ may be drawn with the
triangle of 45 degrees resting on the square blade. The triangle may be
turned over, set to point _p_ and line _q_ drawn, and by turning the
triangle again the line _s_ may be drawn from point _r_; finally the
triangle may be again turned over and line _u_ drawn, which renders the
drawing of the circle _m_ unnecessary.

To draw an elliptical figure whose proportion of width to breadth shall
remain the same, whatever the length of the major axis may be: Take any
square figure and bisect it by the line A in Figure 80. Draw, in each
half of the square, the diagonals E F, G H. From P as a centre with the
radius P R draw the arc S E R. With the same radius draw from O as a
centre the arc T D V. With radius L C draw arc R C V, and from K as a
centre draw arc S B T.

[Illustration: Fig. 80.]

[Illustration: Fig. 81.]

A very near approach to the true form of a true ellipse may be drawn by
the construction given in Figure 81, in which A A and B B are centre
lines passing through the major and minor axis of the ellipse, of which
_a_ is the axis or centre, _b c_ is the major axis, and _a e_ half the
minor axis. Draw the rectangle _b f g c_, and then the diagonal line _b
e_; at a right angle to _b e_ draw line _f h_, cutting B B at _i_. With
radius _a e_ and from _a_ as a centre draw the dotted arc _e j_, giving
the point _j_ on line B B. From centre _k_, which is on the line B B and
central between _b_ and _j_, draw the semicircle _b m j_, cutting A A at
_l_. Draw the radius of the semicircle _b m j_, cutting it at _m_, and
cutting _f g_ at _n_. With the radius _m n_ mark on A A at and from _a_
as a centre the point _o_. With radius _h o_ and from centre _h_ draw
the arc _p o q_. With radius _a l_ and from _b_ and _c_ as centres, draw
arcs cutting _p o q_ at the points _p q_. Draw the lines _h p r_ and _h
q s_ and also the lines _p i t_ and _q v w_. From _h_ as a centre draw
that part of the ellipse lying between _r_ and _s_, with radius _p r_;
from _p_ as a centre draw that part of the ellipse lying between _r_ and
_t_, with radius _q s_, and from _q_ as a centre draw the ellipse from
_s_ to _w_, with radius _i t_; and from _i_ as a centre draw the ellipse
from _t_ to _b_ and with radius _v w_, and from _v_ as a centre draw the
ellipse from _w_ to _c_, and one-half of the ellipse will be drawn. It
will be seen that the whole construction has been performed to find the
centres _h_, _p_, _q_, _i_ and _v_, and that while _v_ and _i_ may be
used to carry the curve around on the other side of the ellipse, new
centres must be provided for _h_ _p_ and _q_, these new centres
corresponding in position to _h_ _p_ _q_. Divesting the drawing of all
the lines except those determining its dimensions and the centres from
which the ellipse is struck, we have in Figure 82 the same ellipse drawn
half as large. The centres _v_, _p_, _q_, _h_ correspond to the same
centres in Figure 81, while _v'_, _p'_, _q'_, _h'_ are in corresponding
positions to draw in the other half of the ellipse. The length of curve
drawn from each centre is denoted by the dotted lines radiating from
that centre; thus, from _h_ the part from _r_ to _s_ is drawn; from _h'_
that part from _r'_ to _s'_. At the ends the respective centres _v_ are
used for the parts from _w_ to _w'_ and from _t_ to _t'_ respectively.

[Illustration: Fig. 82.]

[Illustration: Fig. 83.]

The most correct method of drawing an ellipse is by means of an
instrument termed a trammel, which is shown in Figure 83. It consists of
a cross frame in which are two grooves, represented by the broad black
lines, one of which is at a right angle to the other. In these grooves
are closely fitted two sliding blocks, carrying pivots E F, which may be
fastened to the sliding blocks, while leaving them free to slide in the
grooves at any adjusted distance apart. These blocks carry an arm or rod
having a tracing point (as pen or pencil) at G. When this arm is swept
around by the operator, the blocks slide in the grooves and the
pen-point describes an ellipse whose proportion of width to length is
determined by the distance apart of the sliding blocks, and whose
dimensions are determined by the distance of the pen-point from the
sliding block. To set the instrument, draw lines representing the major
and minor axes of the required ellipse, and set off on these lines
(equidistant from their intersection), to mark the required length and
width of ellipse. Place the trammel so that the centre of its slots is
directly over the point or centre from which the axes are marked (which
may be done by setting the centres of the slots true to the lines
passing through the axis) and set the pivots as follows: Place the
pencil-point G so that it coincides with one of the points as C, and
place the pivot E so that it comes directly at the point of intersection
of the two slots, and fasten it there. Then turn the arm so that the
pencil-point G coincides with one of the points of the minor axis as D,
the arm lying parallel to B D, and place the pivot F over the centre of
the trammel and fasten it there, and the setting is complete.

[Illustration: Fig. 84.]

To draw a parabola mechanically: In Figure 84 C D is the width and H J
the height of the curve. Bisect H D in K. Draw the diagonal line J K
and draw K E, cutting K at a right angle to J K, and produce it in E.
With the radius H E, and from J as a centre, mark point F, which will be
the focus of the curve. At any convenient distance above J fasten a
straight-edge A B, setting it parallel to the base C D of the parabola.
Place a square S with its back against the straight-edge, setting the
edge O N coincident with the line J H. Place a pin in the focus F, and
tie to it one end of a piece of twine. Place a tracing-point at J, pass
the twine around the tracing-point, bringing down along the square-blade
and fasten it at N, with the tracing-point kept against the edge of the
square and the twine kept taut; slide the square along the
straight-edge, and the tracing-point will mark the half J C of the
parabola. Turn the square over and repeat the operation to trace the
other half J D. This method corresponds to the method of drawing an
ellipse by the twine and pins, as already described.

[Illustration: Fig. 85.]

To draw a parabola by lines: Bisect the width A B in Figure 85, and
divide each half into any convenient number of equal divisions; and
through these points of division draw vertical lines, as 1, 2, 3, etc.
(in each half). Divide the height A D at one end and B E at the other
into as many equal divisions as the half of A B is divided into. From
the points of divisions 1, 2, 3, etc., on lines A D and B E, draw lines
pointing to C, and where these lines intersect the corresponding
vertical lines are points through which the curve may be drawn. Thus on
the side A D of the curve, the intersection of the two lines marked 1 is
a point in the curve; the intersection of the two lines marked 2 is
another point in the curve, and so on.


TO DRAW A HEART CAM.

[Illustration: Fig. 86.]

Draw the line A B, Figure 86, equal to the length of stroke required.
Divide it into any number of equal parts, and from C as a centre draw
circles through the points of division. Draw the outer circle and divide
its circumference into twice as many equal divisions as the line A B was
divided into. Draw radial lines from each point of division on the
circle, and the points of intersection of the radial lines with the
circles are points for the outline of the cam, and through these points
a curved line may be drawn giving the shape of the cam. It is obvious
that the greater the number of divisions on A B, the more points and the
more perfect the curve may be drawn.




CHAPTER IV.

_SHADOW LINES AND LINE SHADING._

SECTION LINING OR CROSS-HATCHING.


When the interior of a piece is to be shown as a piece cut in half, or
when a piece is broken away, as is done to make more of the parts show,
or show more clearly, the surface so broken away or cut off is
section-lined or cross-hatched; that is to say, diagonal lines are drawn
across it, and to distinguish one piece from another these lines are
drawn at varying angles and of varying widths apart. In Figure 87 is
given a view of three cylindrical pieces. It may be known to be a
sectional view by the cross-hatching or section lines. It would be a
difficult matter to represent the three pieces put together without
showing them in section, because, in an outline view, the collars and
recesses would not appear. Each piece could of course be drawn
separately, but this would not show how they were placed when put
together. They could be shown in one view if they were shaded by lines
and a piece shown broken out where the collars and, recesses are, but
line shading is too tedious for detail drawings, beside involving too
much labor in their production.

[Illustration: Fig. 87.]

Figure 88 represents a case in which there are three cylindrical pieces
one within the other, the two inner ones being fastened together by a
screw which is shown dotted in in the end view, and whose position along
the pieces is shown in the side view. The edges of the fracture in the
outer piece are in this case cross-hatched, to show the line of
fracture.

[Illustration: Fig. 88.]

[Illustration: Fig. 89.]

In cross-hatching it is better that the diagonal lines do not quite meet
the edges of the piece, than that they should in the least overrun, as
is shown in Figure 89, where in the top half the diagonals slightly
overrun, while in the lower half they do not quite meet the outlines of
the piece.

In Figure 90 are shown in section a number of pieces one within the
other, the central bore being filled with short plugs. All the
cross-hatching was done with the triangle of 60 degrees and that of 90
degrees. It is here shown that with these two triangles only, and a
judicious arrangement of the diagonals, an almost infinite number of
pieces may be shown in cross section without any liability of mistaking
one for the other, or any doubt as to the form and arrangement of the
pieces; for, beside the difference in spacing in the cross-hatching,
there are no two adjoining pieces with the diagonals running in the same
direction. It will be seen that the narrow pieces are most clearly
defined by a close spacing of the cross-hatching.

[Illustration: Fig. 90.]

In Figure 91 are shown three pieces put together and having slots or
keyways through them. The outer shell is shown to be in one piece from
end to end, because the cross-hatching is not only equally spaced, but
the diagonals are in the same direction; hence it would be known that D,
F, H, and E were slots or recesses through the piece. The same remarks
apply to piece B, wherein G, J, K are recesses or slots. Piece C is
shown to have in its bore a recess at L. In the case of B, as of A,
there would be no question as to the piece being all one from end to
end, notwithstanding that the two ends are completely severed where the
slots G, I, come, because the spacing and direction of the
cross-hatching are equal on each side of the slots, which they would not
be if they were separate pieces.

[Illustration: Fig. 91.]

[Illustration: Fig. 92.]

Section shading or cross-hatching may sometimes cause the lines of the
drawing to appear crooked to the eye. Thus, in Figure 92, the key edge
on the right appears curved inwards, while on the left the key edge
appears curved outwards, although such is not actually the case. The
same effect is produced in Figure 93 on the right-hand edge of the key,
but not on the left-hand edge.

[Illustration: Fig. 93]

[Illustration: Fig. 94.]

A remarkable instance of this kind is shown in Figure 94, when the
vertical lines appear to the eye to be at a considerable angle one to
the other, although they are parallel.

The lines in sectional shading or cross-hatching may be made to denote
the material of which the piece is to be composed. Thus Professor Unwin
has proposed the system shown in the Figures 95 and 96. This may be of
service in some cases, but it would involve very much more labor than it
is worth in ordinary machine shop drawings, except in the case of cast
iron and wood, these two being shown in the simplest and the usual
manner. It is much better to write the name of the material beneath the
piece in a detail drawing.

[Illustration: Fig. 95.]

[Illustration: Fig. 96.]


LINE SHADING.

Mechanical drawings are made to look better and to show more distinctly
by being line shaded or shaded by lines. The simplest form of line
shading is by the use of the shade or shadow line.

In a mechanical drawing the light is supposed, for the purposes of line
shading or of coloring, to come in from the upper left-hand corner of
the drawing paper; hence it falls directly upon the upper and left-hand
lines of each piece, which are therefore represented by fine lines,
while the right hand and lower edges of the piece being on the shadow
side may therefore, with propriety, be represented by broader lines,
which are called shadow or shade lines. These lines will often serve to
indicate the shape of some part of the piece represented, as will be
seen from the following examples. In Figure 97 is a piece that contains
a hole, the fact being shown by the circle being thickened at A. If the
circle were thickened on the other side as at B, in Figure 98, it would
show that it represented a cylindrical stem instead of a hole.

[Illustration: Fig. 97.]

[Illustration: Fig. 98.]

[Illustration: Fig. 99.]

In Figure 99 is represented a washer, the surfaces that are in the
shadow side being shown in a shade line or shadow line, as it is often
called.

In Figure 100 is a key drawn with a shade line, while in Figure 101 the
shade line is shown applied to a nut. The shade line may be produced in
straight lines by drawing the line twice over, and slightly inclining
the pen, or by opening the pen points a little. For circles, however, it
may be produced either by slightly moving the centre from which the
circle is drawn, or by going over the shade part twice, and slightly
pressing the instrument as it moves, so as to gradually spring the legs
farther apart, the latter plan being generally preferable.

[Illustration: Fig. 100.]

[Illustration: Fig. 101.]

[Illustration: Fig. 102.]

Figure 102 shows a German pen, that can be regulated to draw lines of
various breadths. The head of the adjusting screw is made rather larger
than usual, and is divided at the under side into twenty divisional
notches, each alternate notch being marked by a figure on the face. By
this arrangement a uniform thickness of line may be maintained after
filling or clearing the pen, and any desired thickness may be repeated,
without any loss of time in trial of thickness on the paper. A small
spring automatically holds the divided screw-head in any place. With
very little practice the click of the spring in the notches becomes a
sufficient guide for adjustment, without reference to the figures on the
screw-head. Another meritorious feature of this pen is that it is armed
with sapphire points, which retain their sharpness very long, and thus
save the time and labor required to keep ordinary instruments in order
for the performance of fine work.

An example of line shading in perspective drawing is shown in the
drawing of a pipe threading stock and die in Figure 103.

[Illustration: Fig. 103.]

Shading by means of lines may be used with excellent effect in
mechanical drawing, not only to distinguish round from flat surfaces,
but also to denote to the eye the relative distances of surfaces. Figure
104 represents a cylindrical pin line shaded. As the light is supposed
to come in from the upper left-hand corner, it will evidently fall more
upon the left-hand half of the stem, and of the collar or bead, hence
those parts are shaded with lighter or finer lines than the right-hand
sides are.

[Illustration: Fig. 104.]

[Illustration: Fig. 105.]

Two cylindrical pieces that join each other may be line shaded at
whatever angle they may join. Figure 105 represents two such pieces, one
at a right angle to the other, both being of equal diameter.

[Illustration: Fig. 106.]

Figure 106 represents a drawing of a lathe centre shaded by lines, the
lines on the taper parts meeting those on the parallel part A, and
becoming more nearly parallel to the axis of the piece as the centre of
the piece is approached. The same is the case where a piece having a
curved outline is drawn, which is shown in Figure 107, where the set of
the bow-pen is gradually increased for drawing the shade lines of the
curves. The centres of the shade curves fall in each case upon a line at
a right angle to the axis of the piece, as upon the lines A, B, C, the
dotted lines showing the radius for each curve.

[Illustration: Fig. 107.]

The lines are made finer by closing the pen points by means of the screw
provided for that purpose. The pen requires for this purpose to be
cleaned of the ink that is apt to dry in it.

In Figure 108 line shading is shown applied to a ball or sphere, while
in Figure 109 it is shown applied to a pin in a socket which is shown in
section. By showing the hollow in connection with the round piece, the
difference between the two is quite clearly seen, the light falling
most upon the upper half of the pin and the lower half of the hole. This
perhaps is more clearly shown in the piece of tube in Figure 110, where
the thickness of the tube showing is a great aid to the eye. So,
likewise, the hollow or hole is more clearly seen where the piece is
shown in section, as in Figure 111, which is the case even though the
piece be taper as in the figure. If the body be bell-mouthed, as in
Figure 112, the hollow curve is readily shown by the shading; but to
line shade a hollow curve without any of these aids to the eye, as say,
to show a half of a tin tube, is a very difficult matter if the piece
is to look natural; and all that can be done is to shade the top darkly
and let the light fall mostly at and near the bottom. An example of line
shading to denote the relative distances from the eye of various
surfaces is given in Figure 113, where the surfaces most distant are the
most shaded. The flat surfaces are lined with lines of equal breadth,
the degrees of shading being governed by the width apart of the lines.

[Illustration: Fig. 108.]

[Illustration: Fig. 109.]

[Illustration: Fig. 110.]

[Illustration: Fig. 111.]

[Illustration: Fig. 112.]

[Illustration: Fig. 113.]

Line shading is often used to denote that the piece represented is to be
of wood, the shade lines being in some cases regular in combination with
regular ones, or entirely irregular, as in Figure 114.

[Illustration: Fig. 114.]




CHAPTER V.

_MARKING DIMENSIONS._


The dimensions of mechanical drawings are best marked in red ink so that
they will show plainly, and that the lines denoting the points at which
the dimension is given shall not be confounded with the lines of the
drawing.

The dimension figures should be as large as the drawing will
conveniently admit; and should be marked at every point at which a
shoulder or change of form or dimension occurs, except in the case of
straight tapers which have their dimensions marked at each end of the
taper.

In the case of a single piece standing by itself the dimension figures
may be marked all standing one way, so as to be read without changing
the position of the operator or requiring to turn the drawing around.
This is done in Figure 115, which represents the drawing of a key. The
figures are here placed outside the drawing in all cases where it can be
done, which, in the case of a small drawing, leaves the same clearer.

[Illustration: Fig. 115.]

In Figure 116 the dimensions are marked, running parallel to the
dimension for which they are given, so that all measures of length stand
lengthwise, and those of breadth across the drawing.

[Illustration: Fig. 116.]

Figure 117 represents a key with a sharp-cornered step in it. Here the
two dimensions forming the steps cannot both be coincident with it;
hence they are marked as near to it as convenient, it being understood
that they apply to the step, and not to one side of it. When the step
has a round instead of a sharp corner, the radius of the arc of the
corner may be marked, as shown in Figure 118.

[Illustration: Fig. 117.]

Figure 119 represents a key drawn in perspective, so that all the
dimensions may be marked on one view. Perspective sketches may be used
for single pieces, as they denote the shape of the piece more clearly to
the eye. On account of the skill required in their production, they are
not, however, used in mechanical drawing, except as in the case of
Patent-Office or similar drawings, where the form and construction
rather than the dimension is the information sought to be conveyed.

[Illustration: Fig. 118.]

[Illustration: Fig. 119.]




CHAPTER VI.

_THE ARRANGEMENT OF DIFFERENT VIEWS._

THE DIFFERENT VIEWS OF A MECHANICAL DRAWING.


The word _elevation_, as applied to mechanical drawing, means simply a
view; hence a side elevation is a side view, or an end elevation is an
end view.

The word _plan_ is employed in place of the word top; hence a plan view
is a top view, or a view looking down upon the top of the piece.

A _general_ view means a view showing the machine put together or
assembled, while a detail drawing is one containing a detail, as a part
of the machine or a single piece disconnected from the other parts of
the whole machine.

It is obviously desirable in a mechanical drawing to present the piece
of work in as few views as possible, but in all cases there must be a
sufficient number to permit of the dimensions in every necessary
direction to be marked on the drawing. Suppose, then, that in Figure 120
we have to represent a solid cylinder, whose length equals its diameter,
and it is obvious that both the diameter and length may be marked in the
one view given; hence, a second view, such as shown by the circle in
Figure 121, is unnecessary, except it be to distinguish the body from a
cube, in which the one view would also be sufficient whereon to mark
all the dimensions necessary to enable the piece to be made. It happens,
however, that a cube and a cylinder are the only two figures upon which
all the dimensions can be marked on one view of the piece, and as
cylindrical pieces are much more common in machine work than cubes are,
it is taken for granted that, where the pieces are cylindrical, but one
view shall be used, and that where they are cubes either two views shall
be given, or where they are square a cross shall be marked upon the
parts that are square; thus, in Figure 122, is shown a cross formed by
the lines A B across the face of the drawing, which saves making a
second view.

[Illustration: Fig. 120.]

[Illustration: Fig. 121.]

[Illustration: Fig. 122.]

[Illustration: Fig. 123.]

It would appear that under some conditions this might lead to error; as,
for example, take the piece in Figure 123, and there is nothing to
denote which is the length and which is the diameter of the piece, but
there is a certain amount of custom in such cases than will usually
determine this point; thus, the piece will be given a name, as pin or
disk, the one denoting that its diameter is less than its length, and
the other that its diameter is greater than its length. In the absence
of any such name, it would be in practice assumed that it was a pin and
not a disk; because, if it were a disk, it would either be named or
shaded, or a second view given to show its unusual form, the disk being
a more unusual form than the pin-form in mechanical structures. As an
example of the use of the cross to denote a square, we have Figure 124,
which represents a piece having a hexagon head, section _a_, _a'_, that
is rectangular, a collar _b_, a square part _c_, and a round stem _d_.
Here it will be noted that it is the rectangular part _a_, _a'_, that
renders necessary two views, and that in the absence of the cross, yet
another view would be necessary to show that part _c_ is square.

[Illustration: Fig. 124.]

[Illustration: Fig. 125.]

A rectangular piece always requires two views and sometimes three. In
Figure 125, for example, is a piece that would require a side view to
show the length and breadth, and an edge view to show the thickness.
Suppose the piece to be wedge-shaped in any direction; then another view
will be necessary, as is shown in Figs. 126 and 127. In the former the
wedge or taper is in the direction of its length, while in the latter it
is in the direction of its thickness. Outline views, however, will not
in some cases show the form of the figure, however many views be
presented. An example of this is given in Figure 128, which represents a
ring having a hexagon cross section. A sectional edge view is here
necessary in order to show the hexagonal form. Another example of this
kind, which occurs more frequently in practice, is a cupped ring such as
shown in Figure 129.

[Illustration: Fig. 126.]

[Illustration: Fig. 127.]

[Illustration: Fig. 128.]

[Illustration: Fig. 129.]


EXAMPLES.

Let it be required to draw a rectangular piece such as is shown in two
views in Figure 130, and the process for the pencil lines is as follows:

[Illustration: Fig. 130.]

With the bow-pencil set to half the required length and breadth of the
square the arcs 1, 2, 3 and 4, in Figure 131, are marked, and then the
lines 5 and 6, letting them run past the width of the arcs 3 and 4.
There is no need to pencil in lines 7 and 8, since they can be inked in
without pencilling, because it is known that they must meet the arcs 3
and 4 and terminate at the lines 5 and 6. The top and bottom lines of
the edge view are merely prolongations of lines 5 and 6; hence the lines
9 and 10 are drawn the requisite distance apart for the thickness and to
meet the top and bottom lines. The lines are then inked in, the pencil
lines rubbed out, and the drawing will appear as in Figure 130.

[Illustration: Fig. 131.]

[Illustration: Fig. 132.]

Suppose, however, that the piece has a step in it, as in Figure 132, and
the pencilling will be as in Figure 133. From the centre, the arcs 1, 2,
3 and 4 for the outer, and arcs 5, 6, 7 and 8 for the inner square are
marked; lines 9 and 10, and their prolongations, 11 and 12, for the
edge view, are then pencilled; lines 13 and 14, and their prolongations,
15 and 16, are then pencilled, and dots to show the locations for lines
21 and 22 maybe marked and the pencilling is complete. Lines 17, 18, 19,
20, 21, 22, and 23 may then be inked in, in the order named, and then
lines 9, 10, 11, 12, 13, 14, 15 and 16, when the inking in will be
complete.

[Illustration: Fig. 133.]

In inking in horizontal lines begin at the top and mark in each line as
the square comes to it; and in inking the vertical ones begin always at
the left hand line and mark the lines as they are come to, moving the
square or the triangle to the right, and great care should be taken not
to let the lines cross where they meet, as at the corners, since this
would greatly impair the appearance of the drawing.

These figures have been drawn without the aid of a centre line, because
from their shapes it was easy to dispense with it, but in most cases a
centre line is necessary; thus in Figure 134 we have a body having a
number of steps. The diameters of these steps are marked by arcs, as in
the previous examples, and their lengths may be marked by applying the
measuring rule direct to the drawing paper and making the necessary
pencil mark.

But it would be tedious to mark the successive steps true one with the
other by measuring each step, because one step would require to be
pencilled in before the next could be marked. To avoid this the centre
line 1, Figure 134, is first marked, and the arcs for the steps are then
marked as shown. Centre lines are also necessary to show the alignment
of one part to another; thus in Figure 135 is a cube with a hole passing
through it. The dotted lines in the side view show that the hole passes
clear through the piece and is a parallel one, while the centre line,
being central to the outline throughout the piece, shows that the hole
is equidistant, all through, from the walls of the piece.

[Illustration: Fig. 134.]

[Illustration: Fig. 135.]

The pencil lines for this piece would be marked as in Figure 136, line 1
representing the centre line from which all the arcs are marked. It will
be noted that the length of the piece is marked by arcs which occur,
because being a cube the set of the compasses for arcs 2, 3, 4 and 5
will answer without altering to mark arcs 6 and 7.

[Illustration: Fig. 136.]

If the hole in the piece were a taper or conical one, it would be
denoted by the dotted lines, as in Figure 137, and that the taper is
central to the body is shown by these dotted lines being equidistant
from the centre line.

[Illustration: Fig. 137.]

Suppose one of the sides to be tapered, as is the side A, in Figure 138,
and that the hole is not central, and both facts will be shown by the
centre lines 1 and 2 in the figure. The measurement of face A would be
marked from A to line B at each end, but the distance the hole was out
of the centre would be marked by the distance between the centre line 2
and the edge C of the piece.

[Illustration: Fig. 138.]

If the hole did not pass entirely through the piece, the dotted lines
would show it, as in Figure 139.

[Illustration: Fig. 139.]

[Illustration: Fig. 140.]

The designations of the views of a piece of work depend upon the
position in which the piece stands, when in place upon the machine of
which it forms a part. Thus in Figure 140 is a lever, and if its shaft
stood horizontal when the piece is in place in the machine, the view
given is an end one, but suppose that the shaft stood vertical, and the
same view becomes a plan or top view.

[Illustration: Fig. 141.]

[Illustration: Fig. 142.]

In Figure 142 is a view of a lever which is a side view if the lever
stands horizontal, and lever B hangs down, or a plan view if the shaft
stands horizontal, but lever B stands also horizontal. We may take the
same drawing and turn it around on the paper as in Figure 143, and it
becomes a side view if the shaft stands vertical, and a plan view if the
shaft stands horizontal and arm D vertical above it.

In a side or an end view, the piece that projects highest in the drawing
is highest when upon the machine; also in a side elevation the piece
that is at the highest point in the drawing extends farthest upward when
the piece is on the machine. But in a plan or top view the height of
vertical pieces is not shown, as appears in the case of arm D in Figure
143.

[Illustration: Fig. 143.]

In either of the levers, Figures 142 or 143, all the dimensions could be
marked if an additional view were given, but this will not be the case
if an eye have a slot in it, as at E, in Figure 144, or a jaw have a
tongue in it, as at F: hence, end views of the eye and the jaw must be
given, which may be most conveniently done by showing them projected
from the ends of those parts as in the figure.

This naturally brings us to a consideration as to the best method of
projecting one view from another. As a general rule, the side elevation
or side view is the most important, because it shows more of the parts
and details of the work; hence it should be drawn first, because it
affords more assistance in drawing the other views.

[Illustration: Fig. 144.]

There are two systems of placing the different views of a piece. In the
first the views are presented as the piece would present itself if it
were laid upon the paper for the side view, and then turned or rolled
upon the paper for the other views, as shown in Figure 145, in which the
piece consists of five sections or members, marked respectively A, B, C,
D, and E. Now if the piece were turned or rolled so that the end face of
B were uppermost, and the member E was beneath, it will, by the
operation of turning it, have assumed the position in the lower view
marked position 2; while if it were turned over upon the paper in the
opposite direction it would assume the position marked 3. This gives to
the mind a clear idea of the various views and positions; but it
possesses some disadvantages: thus, if position 1 is a side elevation or
view of the piece, as it stands when in place of the machine, then E is
naturally the bottom member; but it is shown in the top view of the
drawing, hence what is actually the bottom view of the piece (position
3) becomes the top view in the drawing. A second disadvantage is that if
we desire to put in dotted lines, to show how one view is derived from
the other, and denote corresponding parts, then these dotted lines must
be drawn across the face of the drawing, making it less distinct; thus
the dotted lines connecting stem E in position 1 to E in position 3,
pass across the faces of both A and B of position 1.

[Illustration: Fig. 145.]

[Illustration: Fig. 146.]

In a large drawing, or one composed of many members or parts, it would,
therefore, be out of the question to mark in the dotted lines. A
further disadvantage in a large drawing is that it is necessary to go
from one side of the drawing to the other to see the construction of the
same part.

[Illustration: Fig. 147.]

To obviate these difficulties, a modern method is to suppose the piece,
instead of rolling upon the paper, to be lifted from it, turned around
to present the required view, and then moved upwards on the paper for a
top view, sideways for a side view, and below for a bottom view. Thus
the three views of the piece in Figure 145 would be as in Figure 146,
where position 2 is obtained by supposing the piece to be lifted from
position 1, the bottom face turned uppermost, and the piece moved down
the paper to position 2, which is a bottom view of the piece, and the
bottom view in the drawing. Similarly, if the piece be lifted from
position 1, and the top face in that figure is turned uppermost, and the
piece is then slid upwards on the paper, view 3 is obtained, being a top
view of the piece as it lies in position 1, and the top view in the
drawing. Now suppose we require to find the shape of member B, then in
Figure 145 we require to look at the top of position 1, and then down
below to position 2.

[Illustration: Fig. 148.]

But in Figure 146 we have the side view and end view both together,
while the dotted lines do not require to cross the face of the side
view. Now suppose we take a similar piece, and suppose its end faces,
as F, G, to have holes in them, which require to be shown in both views,
and under the one system the drawing would, if the dotted lines were
drawn across, appear as in Figure 147, whereas under the other system
the drawing would appear as in Figure 148. And it follows that in cases
where it is necessary to draw dotted lines from one view to the other,
it is best to adopt the new system.




CHAPTER VII.

_EXAMPLES IN BOLTS, NUTS, AND POLYGONS._


[Illustration: Fig. 149.]

[Illustration: Fig. 150.]

[Illustration: Fig. 151.]

Let it be required to draw a machine screw, and it is not necessary, and
therefore not usual in small screws to draw the full outline of the
thread, but to represent it by thick and thin lines running diagonally
across the bolt, as in Figure 149, the thick ones representing the
bottom, and the thin ones the top of the thread. The pencil lines would
be drawn in the order shown in Figure 150. Line 1 is the centre line,
and line 2 a line to represent the lower side of the head; from the
intersection of these two lines as a centre (as at A) short arcs 3 and
6, showing the diameter of the thread, are marked, and the arcs 5 and 6,
representing the depth of the thread, are marked. The arc 7,
representing the head, is then marked. The vertical lines 8, 9, 10, and
11 are then marked, and the outline of the screw is complete. The thick
lines representing the bottom of the thread are next marked in, as in
Figure 151, extending from line 9 to line 10. Midway between these lines
fine ones are made for the tops of the thread. All the lines being
pencilled in, they may be inked in with the drawing instruments, taking
care that they do not overrun one another. When the pencil lines are
rubbed out, the sketch will appear as in Figure 149.

[Illustration: Fig. 152.]

For a bolt with a hexagon head the lines would be drawn in the order
shown in Figure 152. At a right-angle to centre line 1, line two is
drawn. The pencil-compasses are then set to half the diameter of the
bolt, and from point A arcs 3 and 6 are pencilled, thus showing the
width of the front flat of the head, as well as the diameter of the
stem. From the point where these arcs meet line 2, and with the same
radius, arcs 5 and 6 are marked, showing the widths of the other two
flats of the head. The thickness of the head and the length of the bolt
head may then be marked either by placing a rule on line 1 and marking
the short lines (such as line 7) a cross line 1, or the pencil-compasses
may be set to the rule and the lengths marked from point A. In the
United States standard for bolt heads and nuts the thickness of the head
is made equal to the diameter of the bolt. With the compasses set for
the arcs 3 and 4, we may in two steps, from A along the centre line,
mark off the thickness of the head without using the rule. But as the
rule has to be applied along line 1 to mark line 7 for the length of the
bolt, it is just as easy to mark the head thickness at the same time.
The line 8 showing the length of the thread may be marked at the same
time as the other lengths are marked, and the outlines 9, 10, 11, 12, 13
may be drawn in the order named. We have now to mark the arcs at the top
of the flats of the head to show the chamfer, and to explain how these
arcs are obtained we have in Figure 153 an enlarged view of the head. It
is evident that the smallest diameter of the chamfer is represented by
the circle A, and therefore the length of the line B must equal A. It is
also evident that the outer edge of the chamfer will meet the corners at
an equal depth (from the face of the nut), as represented by the line C
C, and it is obvious that the curves that represent the outline of the
chamfer on each side of the head or nut will approach the face of the
head or nut at an equal distance, as denoted by the line D D. It follows
that the curve must in each case be such as will, at each of its ends,
meet the line C, and at its centre meet the line D D, the centres of the
respective curves being marked in the figure by X.

[Illustration: Fig. 153.]

It is sufficiently accurate, therefore, for all practical purposes to
set the pencil on the centre-line at the point A in Figure 152 and mark
the curve 14, and to then set the compasses by trial to mark the other
two curves of the chamfer, so that they shall be an equal distance with
arc 14 from line 9, and join lines 10 and 13 at the same distance from
line 9 that 14 joins lines 3 and 4, so that as in Figure 153 all three
of the arcs would touch a line as C, and another line as D.

[Illustration: Fig. 154.]

The United States standard sizes for forged or unfinished bolts and nuts
are given in the following table, Figure 154 showing the dimensions
referred to in the table.

UNITED STATES STANDARD DIMENSIONS OF BOLTS AND NUTS.

KEY:
A: Nominal. D.
B: Effective.[*]
C: Standard Number of threads per inch.

------------------------+----------------------------+---------------------
         BOLT.          |      BOLT HEAD AND NUT.    |
------------------------+-----------------+----------+----------+----------
  Diameter.   |         | Long diameter,  | Short    |          |
-------+------|         | I, or diameter  | diameter |          |
       |      |         | across corners. | of       |          |
       |      |         |--------+--------| hexagon  |          |
   A   | B    |   C     | Hexa-  | Square.| and      |          |
       |      |         | gon.   |        | square,  | Depth of | Depth of
       |      |         |        |        | or width | nut,     | bolt
       |      |         |        |        | across J.| H.       | head, K.
-------+------+---------+--------+--------+----------+----------+----------
   1/4 | .185 |  20     |    9/16|   23/32|    1/2   |    1/4   |   1/4
  5/16 | .240 |  18     |   11/16|   27/32|    19/32 |    5/16  |   19/64
   3/8 | .294 |  16     |   25/32|   31/32|    11/16 |    3/8   |   11/32
  7/16 | .345 |  14     |   29/32| 1-3/32 |    25/32 |    7/16  |   25/64
   1/2 | .400 |  13     | 1      | 1-1/4  |    7/8   |    1/2   |   7/16
  9/16 | .454 |  12     | 1-1/8  | 1-3/8  |    31/32 |    9/16  |   31/64
   5/8 | .507 |  11     | 1-7/32 | 1-1/2  |  1-1/16  |    5/8   |   17/32
   3/4 | .620 |  10     | 1-7/16 | 1-3/4  |  1-1/4   |    3/4   |   5/8
   7/8 | .731 |   9     | 1-21/32| 2-1/32 |  1-7/16  |    7/8   |   23/32
 1     | .837 |   8     | 1-7/8  | 2-5/16 |  1-5/8   |  1       |   13/16
 1-1/8 | .940 |   7     | 2-3/32 | 2-9/16 |  1-13/16 |  1-1/8   |   29/32
 1-1/4 |1.065 |   7     | 2-5/16 | 2-27/32|  2       |  1-1/4   | 1
 1-3/8 |1.160 |   6     | 2-17/32| 3-3/32 |  2-3/16  |  1-3/8   | 1-3/32
 1-1/2 |1.284 |   6     | 2-3/4  | 3-11/32|  2-3/8   |  1-1/2   | 1-3/16
 1-5/8 |1.389 |   5-1/2 | 2-31/32| 3-5/8  |  2-9/16  |  1-5/8   | 1-9/32
 1-3/4 |1.491 |   5     | 3-3/16 | 3-7/8  |  2-3/4   |  1-3/4   | 1-3/8
 1-7/8 |1.616 |   5     | 3-13/32| 4-5/32 |  2-15/16 |  1-7/8   | 1-15/32
 2     |1.712 |   4-1/2 | 3-19/32| 4-13/32|  3-1/8   |  2       | 1-9/16
 2-1/4 |1.962 |   4-1/2 | 4-1/32 | 4-15/16|  3-1/2   |  2-1/4   | 1-3/4
 2-1/2 |2.176 |   4     | 4-15/32| 5-15/32|  3-7/8   |  2-1/2   | 1-15/16
 2-3/4 |2.426 |   4     | 4-29/32| 6      |  4-1/4   |  2-3/4   | 2-1/8
 3     |2.629 |   3-1/2 | 5-11/32| 6-17/32|  4-5/8   |  3       | 2-5/16
 3-1/4 |2.879 |   3-1/2 | 5-25/32| 7-1/16 |  5       |  3-1/4   | 2-1/2
 3-1/2 |3.100 |   3-1/4 | 6-7/32 | 7-19/32|  5-3/8   |  3-1/2   | 2-11/16
 3-3/4 |3.317 |   3     | 6-5/8  | 8-1/8  |  5-3/4   |  3-3/4   | 2-7/8
  ...  |3.567 |   3     | 7-1/16 | 8-21/32|  6-1/8   |  4       | 3-1/16
 4-1/4 |3.798 |   2-7/8 | 7-1/2  | 9-3/16 |  6-1/2   |  4-1/4   | 3-1/4
 4-1/2 |4.028 |   2-3/4 | 7-15/16| 9-23/32|  6-7/8   |  4-1/2   | 3-7/16
 4-3/4 |4.256 |   2-5/8 | 8-3/8  |10-1/4  |  7-1/4   |  4-3/4   | 3-5/8
 5     |4.480 |   2-1/2 | 8-13/16|10-25/32|  7-5/8   |  5       | 3-13/16
 5-1/4 |4.730 |   2-1/2 | 9-1/4  |11-5/16 |  8       |  5-1/4   | 4
 5-1/2 |4.953 |   2-3/8 | 9-11/16|11-27/32|  8-3/8   |  5-1/2   | 4-3/16
 5-3/4 |5.203 |   2-3/8 |10-3/32 |12-3/8  |  8-3/4   |  5-3/4   | 4-3/8
 6     |5.423 |   2-1/4 |10-17/32|12-29/32|  9-1/8   |  6       | 4-9/16
-------+------+---------+--------+--------+----------+----------+----------
* Diameter at the root of the thread.

The basis of the Franklin Institute or United States standard for the
heads of bolts and for nuts is as follows:

The short diameter or width across the flats is equal to one and
one-half times the diameter plus 1/8 inch for rough or unfinished bolts
and nuts, and one and one-half times the bolt diameter plus, 1/16 inch
for finished heads and nuts. The thickness is, for rough heads and nuts,
equal to the diameter of the bolt, and for finished heads and nuts 1/16
inch less.

[Illustration: Fig. 155.]

[Illustration: Fig. 156.]

The hexagonal or hexagon (as they are termed in the shop) heads of bolts
may be presented in two ways, as is shown in Figures 155 and 156.

The latter is preferable, inasmuch as it shows the width across the
flats, which is the dimension that is worked to, because it is where the
wrench fits, and therefore of most importance; whereas the latter gives
the length of a flat, which is not worked to, except incidentally, as it
were. There is the objection to the view of the head, given in Figure
156, however, that unless it is accompanied by an end view it somewhat
resembles a similar view of a square head for a bolt. It may be
distinguished therefrom, however, in the following points:

If the amount of chamfer is such as to leave the chamfer circle (as
circle A, in Figure 153) of smaller diameter than the width across the
flats of the bolt-head, the outline of the sides of the head will pass
above the arcs at the top of the flats, and there will be two small flat
places, as A and B, in Figure 156 (representing the angle of the
chamfer), which will not meet the arcs at the top of the flats, but will
join the sides above those arcs, as in the figure; which is also the
case in a similar view of a square-headed bolt. It may be distinguished
therefrom, however, in the following points:

If the amount of chamfer is such as to leave the chamfer circle (A,
Figure 153) of smaller diameter than the width across the flats of the
bolt-head, the outline of the sides will pass above the arc on the
flats, as is shown in Figure 157, in which the chamfer A meets the side
of the head at B, and does not, therefore, meet the arc C. The length of
side lying between B and D in the side view corresponds with the part
lying between E and F in the end view.

[Illustration: Fig. 157.]

If we compare this head with similar views of a square head G, both
being of equal widths, and having their chamfer circles at an equal
distance from the sides of the flats, and at the same angle, we perceive
at once that the amount of chamfer necessary to give the same distance
between the chamfer circle and the side of the bolt (that is, the
distance from J to K, being equal to that from L to M), the length of
the chamfer N for the square head so greatly exceeds the length A for
the hexagon head that the eye detects the difference at once, and is
instinctively informed that G must be square, independently of the fact
that in the case of the square head, N meets the arc O, while in the
hexagon head, A, which corresponds to N, does not meet the arc C, which
corresponds to O.

When, however, the chamfer is drawn, but just sufficient to meet the
flats, as in the case of the hexagon H, and the square I, in Figure 157,
the chamfer line passes from the chamfer circle to the side of the head,
and the distinction is greater, as will be seen by comparing head H with
head I, both being of equal width, having the same angle of chamfer, and
an amount just sufficient to meet the sides of the flats. Here it will
be seen that in the hexagon H, each side of the head, as P, meets the
chamfer circle A. Whereas, in the square head these two lines are joined
by the chamfer line Q, the figures being quite dissimilar.

[Illustration: Fig. 158.]

It is obvious that whatever the degree or angle of the chamfer may be,
the diameter of the chamfer circle will be the same in any view in
which the head may be presented. Thus, in Figure 158, the line G in the
side view is in length equal to the diameter of circle G, in the end
view, and so long as the angle of the chamfer is forty-five degrees, as
in all the views hitherto given, the width of the chamfer will be equal
at corresponding points in the different views; thus in the figure the
widths A and B in the two views are equal.

[Illustration: Fig. 159.]

If the other view showing a corner of the head in front of the head be
given, the same fact holds good, as is shown in Figure 159. That the two
outside flats should appear in the drawing to be half the width of the
middle flat is also shown in Figure 158, where D and E are each half the
width of C. Let us now suppose, that the chamfer be given some other
angle than that of 45 degrees, and we shall find that the effect is to
alter the curves of the chamfer arcs on the flats, as is shown in Figure
160, where these arcs E, C, D are shown less curved, because the chamfer
B has more angle to the flats. As a result, the width or distance
between the arcs and line G is different in the two views. On this
account it is better to draw the chamfer at 45 degrees, as correct
results may be obtained with the least trouble.

If no chamfer at all is to be given, a hexagon head may still be
distinguished from a square one, providing that the view giving three
sides of the head, as in Figure 158, is shown, because the two sides D
and E being half the width of the middle one C, imparts the information
that it is a hexagon head. If, however, the view showing but two of the
sides and a corner in front is given, and no chamfer is used, it could
not be known whether the head was to be hexagon or square, unless an end
view be given, as in Figure 161.

[Illustration: Fig. 160.]

If the view showing a full side of the head of a square-headed bolt is
given, then either an end view must be given, as in Figure 162, or else
a single view with a cross on its head, as in Figure 163, may be given.

It is the better plan, both in square and hexagon heads, to give the
view in which the full face of a flat is presented, that is, as in
Figures 155 and 163; because, in the case of the square, the length of a
side and the width across the head are both given in that view; whereas
if two sides are shown, as in Figure 161, the width across flats is not
given, and this is the dimension that is wanted to work to, and not the
width across corners. In the case of a hexagon the middle of the three
flats is equal in width to the diameter of the bolt, and the other two
are one-half its width; all three, therefore, being marked with the same
set of compasses as gives the diameter of the body of the bolt, were as
shown in Figure 152. For the width across flats there is an accepted
standard; hence there is no need to mark it upon the drawing, unless in
cases where the standard is to be departed from, in which event an end
view may be added, or the view showing two sides may be given.

[Illustration: Fig 161.]

[Illustration: Fig. 162.]

[Illustration: Fig. 163.]

[Illustration: Fig. 164.]

To draw a square-headed bolt, the pencil lines are marked in the order
shown by figures in Figure 164. The inking in is done in the order of
the letters _a_, _b_, _c_, etc. It will be observed that pencil lines 2,
9, and 10 are not drawn to cross, but only to meet the lines at their
ends, a point that, as before stated, should always be carefully
attended to.

[Illustration: Fig. 165]

To draw the end view of a hexagon head, first draw a circle of the
diameter across the flats, and then rest the triangle of 60 degrees on
the blade _s_ of the square, as at T 1, in Figure 165, and mark the
lines _a_ and _b_. Reverse the triangle, as at T 2, and draw lines _c_
and _d_. Then place the triangle as in Figure 166, and draw the lines
_e_ and _f_.

[Illustration: Fig. 166.]

If the other view of the head is to be drawn, then first draw the lines
_a_ and _b_ in Figure 167 with the square, then with the 60 degree
triangle, placed on the square S, as at T 1, draw the lines _c_, _d_,
and turning the square over, as at T 2, mark lines _e_ and _f_.

[Illustration: Fig. 167.]

If the diameter across corners of a square head is given, and it be
required to draw the head, the process is as follows: For a view showing
one corner in front, as in Figure 168, a circle of the given diameter
across corners is pencilled, and the horizontal centre-line _a_ is
marked, and the triangle of 45 degrees is rested against the square
blade S, as in position T 1, and lines _b_ and _c_ marked, _b_ being
marked first; and the triangle is then slid along the square blade to
position T 1, when line _c_ is marked, these two lines just meeting the
horizontal line _a_, where it meets the circle. The triangle is then
moved to the left, and line _d_, joining the ends of _b_ and _c_, is
marked, and by moving it still farther to the left to position T 2, line
_e_ is marked. Lines _b_, _c_, _d_, and _e_ are, of course, the only
ones inked in.

[Illustration: Fig. 168.]

[Illustration: Fig. 169.]

If the flats are to lie in the other direction, the pencilling will be
done as in Figure 169. The circle is marked as before, and with the
triangle placed as shown at T 1, line _a_, passing through the centre of
the circle, is drawn. By moving the triangle to the right its edge B
will be brought into position to mark line _b_, also passing through
the centre of the circle. All that remains is to join the ends of these
two lines, using the square blade for lines _c_, _d_, and the triangle
for _e_ and _f_, its position on the square blade being denoted at T 3;
lines _c_, _d_, _e_, _f_, are the ones inked in.

[Illustration: Fig. 170.]

For a hexagon head we have the processes, Figures 170 and 171. The
circle is struck, and across it line _a_, Figure 170, passing through
its centre, the triangle of sixty degrees will mark the sides _b_, _c_,
and _d_, _e_, as shown, and the square blade is used for _f_, _g_.

[Illustration: Fig. 171.]

The chamfer circles are left out of these figures to reduce the number
of lines and so keep the engraving clear. Figure 171 shows the method of
drawing a hexagon head when the diameter across corners is given, the
lines being drawn in the alphabetical order marked, and the triangle
used as will now be understood.

[Illustration: Fig. 172.]

[Illustration: Fig. 173.]

It may now be pointed out that the triangle may be used to divide
circles much more quickly than they could be divided by stepping around
them with compasses. Suppose, for example, that we require to divide a
circle into eight equal parts, and we may do so as in Figure 172, line
_a_ being marked from the square, and lines _b_, _c_ and _d_ from the
triangle of forty-five degrees; the lines to be inked in to form an
octagon need not be pencilled, as their location is clearly defined,
being lines joining the ends of the lines crossing the circle, as for
example, lines _e_, _f_.

Let it be required to draw a polygon having twelve equal sides, and the
triangle of sixty is used, marking all the lines within the circle in
Figure 173, except _a_, for which the square blade is used; the only
lines to be inked in are such as _b_, _c_. In this example there is a
corner at the top and bottom, but suppose it were required that a flat
should fall there instead of a corner; then all we have to do is to set
the square blade S at the required angle, as in Figure 174, and then
proceed as before, bearing in mind that the point of the circle nearest
to the square blade, straight-edge, or whatever the triangle is rested
on, is always a corner of a polygon having twelve sides.

[Illustration: Fig. 174.]

[Illustration: Fig. 175.]

In both of these examples we have assumed that the diameter across
corners of the polygon was given, but suppose the diameter across the
flats were given, and the construction is a little more complicated.
Circle _a_, _a_, in Figure 175, is drawn of the required diameter across
the flats, and the lines of division are drawn across with the triangle
of 60 as before; the triangle of 45 is then used to draw the four lines,
_b_, _c_, _d_, _e_, joining the ends of lines _i_, _j_, _k_, _l_, and
touching the inner circle, _a_, _a_. The outer circle is then pencilled
in, touching the lines of division where they meet the lines _b_, _c_,
_d_, _e_, and the rest of the lines for the sides of the polygon may
then be drawn within the outer circle, as at _g_, _h_.

[Illustration: Fig. 176.]

It is obvious, also, that the triangle may be used to draw slots
radiating from a centre, as in Figure 176, where it is desired to draw a
chuck-plate having 6 slots. The triangle of 60 is used to draw the
centre lines, _a_, _b_, _c_, etc., for the slots. From the centre, the
arcs _e_, _f_, _g_, _h_, etc., are marked, showing where the centres
will fall for describing the half circles forming the ends of the slots.
Then half circles, _i_, _j_, _k_, _l_, etc., being drawn, the sides of
the slots may be drawn in with the triangle, and the outer circle and
the slots inked in.

If the slots are not to radiate from the centre of the circle the
process is as follows:

The outer circle _a_, Figure 177, being drawn, an inner one _b_ is
drawn, its radius equalling the amount; the centres of the slots are to
point to one side of the centre of circle _a_. The triangle is then used
to divide the circle into the requisite number of divisions _c_ for the
slots, and arcs _i, j_, are then drawn for the lengths of the slots. The
centre lines _e_ are then drawn, passing through the lines _c_, and the
arcs _i, j_, etc., and touching the perimeter of the inner circle _b_;
arcs _f, g_, are then marked in, and their sides joined with the
triangle adjusted by hand. All that would be inked in black are the
outer circle and the slots, but the inner circle _b_ and a centre line
of one of the slots should be marked in red ink to show how the
inclination of the slot was obtained, and therefore its amount.

[Illustration: Fig. 177.]

For a five-sided figure it is best to step around the circumference of
the circle with the compasses, but for a three-sided one, or trigon, the
construction is as follows: It will be found that the compasses set to
the radius of a circle will accurately divide it into six equal
divisions, as is shown in Figure 178; hence every other one of these
divisions will be the location for a corner of a trigon.

The circle being drawn, a line A, 179, is drawn through its centre, and
from its intersection with the circle as at _b_, here a step on each
side is marked as _c_, _d_, then lines _c_ to _d_, and _c_ and _d_ to
_e_, where A meets, the circle will describe a trigon. If the figure is
to stand vertical, all that is necessary is to draw the line _a_
vertical, as in Figure 180. A ready method of getting the dimension
across corners, across the flats, or the length of a side of a given
polygon, is by means of diagrams, such as shown in the following
figures, which form excellent examples for practice.

[Illustration: Fig. 178.]

[Illustration: Fig. 179.]

[Illustration: Fig. 180.]

Draw the line O P, Figure 181, and at a right angle to it the line O B;
divide these two lines into parts of one inch, as shown in the cut,
which is divided into inches and quarter inches, and from these points
of division draw lines crossing each other as shown.

[Illustration: Fig. 181.]

From the point O, draw diagonal lines, at suitable angles to the line O
P. As shown in the cut, these diagonal lines are marked:

40   degrees for 5 sided figures.
45     "      "  6   "      "
49     "      "  7   "      "
52-1/2 "      "  8   "      "
55-1/2 "      "  9   "      "

But still others could be added for figures having a greater number of
sides.

1. Now it will be found as follows: Half the diameter, or the radius of
a piece of cylindrical work being given, and the number of sides it is
to have being stated, the length of one side will be the distance
measured horizontally from the line O B to the diagonal line for that
particular number of sides.

EXAMPLE.--A piece of work is 2-1/2 inches in diameter, and is required
to have 9 sides: what will be the length of the sides or flats?

Now the half diameter or radius of 2-1/2 inches is 1-1/4 inches. Then
look along the line O B for 1-1/4, which is denoted in the cut by
figures and the arrow A; set one point of the compasses at A, and the
other at the point of crossing of the diagonal line with the 1-1/4
horizontal line, as shown in the figure at _a_, and from A to _a_ is the
length of one side.

Again: A piece of work, 4 inches in diameter, is to have 9 sides: how
long will each side be?

Now half of 4 is 2, hence from B to _b_ is the length of each side.

But suppose that from the length of each side, and the number of sides,
it is required to find the diameter to which to turn the piece; that is,
its diameter across corners, and we simply reverse the process thus: A
body has 9 sides, each side measures 27/32: what is its diameter across
corners?

Take a rule, apply it horizontally on the figure, and pass it along till
the distance from the line O B to the diagonal line marked 9 sides
measures 27/32, which is from 1-1/4 on O B to _a_, and the 1-1/4 is the
radius, which, multiplied by 2, gives 2-1/2 inches, which is the
required diameter across corners.

For any other number of sides the process is just the same. Thus: A
body is 3-1/2 inches in diameter, and is to have 5 sides: what will be
the length of each side? Now half of 3-1/2 is 1-3/4; hence from 1-3/4 on
the line O B to the point C, where the diagonal line crosses the 1-3/4
line, is the length of each of the sides.

2. It will be found that the length of a side of a square being given,
the size of the square, measured across corners, will be the length of
the diagonal line marked 45 degrees, from the point O to the figures
indicating, on the line O B or on the line O P, the length of one side.

EXAMPLE.--A square body measures 1 inch on each side: what does it
measure across the corners? Answer: From the point O, along diagonal
line marked 45 degrees, to the point where it crosses the lines 1 (as
denoted in the figure by a dot).

Again: A cylindrical piece of wood requires to be squared, and each side
of the square must measure an inch: what diameter must the piece be
turned to?

Now the diagonal line marked 45 degrees passes through the 1-inch line
on O B, and the inch line on O P, at the point where these lines meet;
hence all we have to do is to run the eye along either of the lines
marked inch, and from its point of meeting the 45 degrees line, to the
point O, is the diameter to turn the piece to.

There is another way, however, of getting this same measurement, which
is to set a pair of compasses from the line 1 on O B, to line 1 on O P,
as shown by the line D, which is the full diameter across corners. This
is apparent, because from point O, along line O B, to 1, thence to the
dot, thence down to line 1 on O P, and along that to O, encloses a
square, of which either from O to the dot, or the length of the line D,
is the measurement across corners, while the length of each side, or
diameter across the flats, is from point O to either of the points 1, or
from either of the points 1 to the dot.

[Illustration: Fig. 182.]

After graphically demonstrating the correctness of the scale we may
simplify it considerably. In Figure 182, therefore, we have applications
shown. A is a hexagon, and if one of its sides be measured, it will be
found that it measures the same as along line 1 from O B to the diagonal
line 45 degrees, which distance is shown by a thickened line.

At 1-1/2 is shown a seven-sided figure, whose diameter is 3 inches, and
radius 1-1/2 inches, and if from the point at 1-1/2 (along the thickened
horizontal line), to the diagonal marked 49 degrees, be measured, it
will be found exactly equal to the length of a side on the polygon.

At C is shown part of a nine-sided polygon, of 2-inch radius, and the
length of one of its sides will be found to equal the distance from the
diagonal line marked 52-1/2 degrees, and the line O B at 2.

Let it now be noted that if from the point O, as a centre, we describe
arcs of circles from the points of division on O B to O P, one end of
each arc will meet the same figure on O P as it started from at O B, as
is shown in Figure 181, and it becomes apparent that in the length of
diagonal line between O and the required arc we have the radius of the
polygon.

EXAMPLE.--What is the radius across corners of a hexagon or six-sided
figure, the length of a side being an inch?

Turning to our scale we find that the place where there is a horizontal
distance of an inch between the diagonal 45 degrees, answering to
six-sided figures, is along line 1 (Figure 182), and the radius of the
circle enclosing the six-sided body is, therefore, an inch, as will be
seen on referring to circle A. But it will be noted that the length of
diagonal line 45 degrees, enclosed between the point O and the arc of
circle from 1 on O B to one on O P, measures also an inch. Hence we may
measure the radius along the diagonal lines if we choose. This, however,
simply serves to demonstrate the correctness of the scale, which, being
understood, we may dispense with most of the lines, arriving at a scale
such as shown in Figure 183, in which the length of the side of the
polygon is the distance from the line O B, measured horizontally to the
diagonal, corresponding to the number of sides of the polygon. The
radius across corners of the polygon is that of the distance from O
along O B to the horizontal line, giving the length of the side of the
polygon, and the width across corners for a given length of one side of
the square, is measured by the length of the lines A, B, C, etc. Thus,
dotted line 2 shows the length of the side of a nine-sided figure, of
2-inch radius, the radius across corners of the figure being 2 inches.

[Illustration: Fig. 183.]

The dotted line 2-1/2 shows the length of the side of a nine-sided
polygon, having a radius across corners of 2-1/2 inches. The dotted line
1 shows the diameter, across corners, of a square whose sides measure an
inch, and so on.

[Illustration: Fig. 184.]

This scale lacks, however, one element, in that the diameter across the
flats of a regular polygon being given, it will not give the diameter
across the corners. This, however, we may obtain by a somewhat similar
construction. Thus, in Figure 184, draw the line O B, and divide it into
inches and parts of an inch. From these points of division draw
horizontal lines; from the point O draw the following lines and at the
following angles from the horizontal line O P.

[Illustration: Fig. 185.]

A line at 75 deg. for polygons having 12 sides.
    "     72 deg.         "      "    10   "
    "     67-1/2 deg.     "      "     8   "
    "     60 deg.         "      "     6   "

From the point O to the numerals denoting the radius of the polygon is
the radius across the flats, while from point O to the horizontal line
drawn from those numerals is the radius across corners of the polygon.

[Illustration: Fig. 186.]

A hexagon measures two inches across the flats: what is its diameter
measured across the corners? Now from point O to the horizontal line
marked 1 inch, measured along the line of 60 degrees, is 1 5-32nds
inches: hence the hexagon measures twice that, or 2 5-16ths inches
across corners. The proof of the construction is shown in the figure,
the hexagon and other polygons being marked simply for clearness of
illustration.

[Illustration: Fig. 187.]

[Illustration: Fig. 188.]

Let it be required to draw the stud shown in Figure 185, and the
construction would be, for the pencil lines, as shown in Figure 186; line
1 is the centre line, arcs, 2 and 3 give the large, and arcs 4 and 5
the small diameter, to touch which lines 6, 7, 8, and 9 may be drawn.
Lines 10, 11, and 12 are then drawn for the lengths, and it remains to
draw the curves in. In drawing these curves great exactitude is required
to properly find their centres; nothing looks worse in a drawing than an
unfair or uneven junction between curves and straight lines. To find the
location for these centres, set the compasses to the required radius for
the curve, and from the point or corner A draw the arcs _b_ and _c_,
from _c_ mark the arc _e_, and from _b_ the arc _d_, and where _d_ and
_e_ cross is the centre for the curve _f_.

[Illustration: Fig. 189.]

Similarly for the curve _h_, set the compasses on _i_ and mark the arc
_g_, and from the point where it crosses line 6, draw the curve _h_. In
inking in it is best to draw in all curves or arcs of circles first, and
the straight lines that join them afterward, because, if the straight
lines are drawn first, it is a difficult matter to alter the centres of
the curves to make them fall true, whereas, after the curves are drawn
it is an easy matter, if it should be necessary, to vary the line a
trifle, so as to make it join the curves correctly and fair. In inking
in these curves also, care must be taken not to draw them too short or
too long, as this would impair the appearance very much, as is shown in
Figure 187.

[Illustration: Fig. 190.]

[Illustration: Fig. 191.]

To draw the piece shown in Figure 188, the lines are drawn in the order
indicated by the letters in Figure 189, the example being given for
practice. It is well for the beginner to draw examples of common
objects, such as the hand hammer in Figure 190, or the chuck plate in
Figure 191, which afford good examples in the drawing of arcs and
circles.

In Figure 191 _a_ is a cap nut, and the order in which the same would be
pencilled in is indicated by the respective numerals. The circles 3 and
4 represent the thread.

[Illustration: Fig. 191 _a_.]

In Figure 192 is shown the pencilling for a link having the hubs on one
side only, so that a centre line is unnecessary on the edge view, as
all the lengths are derived from the top view, while the thickness of
the stem and height of the hubs may be measured from the line A. In
Figure 193 there are hubs (on both sides of the link) of unequal height,
hence a centre line is necessary in both views, and from this line all
measurements should be marked.

[Illustration: Fig. 192.]

[Illustration: Fig. 193.]

In Figure 194 are represented the pencil lines for a double eye or
knuckle joint, as it is sometimes termed, an example that it is
desirable for the student to draw in various sizes, as it is
representative of a large class of work.

These eyes often have an offset, and an example of this is given in
Figure 195, in which A is the centre line for the stem distant from the
centre line B of the eyes to the amount of offset required.

[Illustration: Fig. 194.]

[Illustration: Fig. 195.]

[Illustration: Fig. 196.]

[Illustration: Fig. 197.]

In Figure 196 is an example of a connecting rod end. From a point, as A,
we draw arcs, as B C for the width, and E D for the length of the block,
and through A we draw the centre line. It is obvious, however, that we
may draw the centre line first, and apply the measuring rule direct to
the paper, and mark lines in place of the arcs B, C, D, E, and F, G,
which are for the stem. As the block joins the stem in a straight line,
the latter is evidently rectangular, as will be seen by referring to
Figure 197, which represents a rod end with a round stem, the fact that
the stem is round being clearly shown by the curves A B. The radius of
these curves is obtained as follows: It is obvious that they will join
the rod stem at the same point as the shoulder curves do, as denoted by
the dotted vertical line. So likewise they join the curves E F at the
same point in the rod length as the shoulder curves, both curves in fact
being formed by the same round corner or shoulder. The centre of the
radius of A or B must therefore be the same distance from the centre of
the rod as is the centre from which the shoulder curve is struck, and at
the same time at such a distance from the corner (as E or F) that the
curve will meet the centre line of the rod at the same point in its
length as the shoulder curves do.

[Illustration: Fig. 198.]

Figure 198 gives an example, in which the similar curved lines show that
a part is square. The figure represents a bolt with a square under the
head. As but one view is given, that fact alone tells us that it must be
round or square. Now we might mark a cross on the square part, to denote
that it is square; but this is unnecessary, because the curves F G show
such to be the case. These curves are marked as follows: With the
compasses set to the radius E, one point is rested at A, and arc B is
drawn; then one point of the compass is rested at C, and arc D is drawn;
giving the centre for the curve F by a similar process on the other
side of the figure, curve G is drawn. Point C is obtained by drawing the
dotted line across where the outline curve meets the stem. Suppose that
the corner where the round stem meets the square under the head was a
sharp one instead of a curve, then the traditional cross would require
to be put on the square, as in Figure 199; or the cross will be
necessary if the corner be a round one, if the stem is reduced in
diameter, as in Figure 200.

[Illustration: Fig. 199.]

[Illustration: Fig. 200.]

[Illustration: Fig. 201.]

Figure 201 represents a centre punch, giving an example, in which the
flat sides gradually run out upon a circle, the edges forming curves, as
at A, B, etc. The length of these curves is determined as follows: They
must begin where the taper of the punch joins the parallel, or at C, C,
and they must end on that part of the taper stem where the diameter is
equal to the diameter across the flats of the octagon. All that is to be
done then is to find the diameter across the flats on the end view, and
mark it on the taper stem, as at D, D, which will show where the flats
terminate on the taper stem. And the curved lines, as A, B, may be drawn
in by a curve that must meet at the line C, and also in a rounded point
at line D.




CHAPTER VIII.

_SCREW THREADS AND SPIRALS._


[Illustration: Fig. 202.]

[Illustration: Fig. 203.]

The screw thread for small bolts is represented by thick and thin lines,
such as was shown in Figure 152, but in larger sizes; the angles of the
thread also are drawn in, as in Figure 202, and the method of doing this
is shown in Figure 203. The centre line 1 and lines 2 and 3 for the full
diameter of the thread being drawn, set the compasses to the required
pitch of the thread, and stepping along line 2, mark the arcs 4, 5, 6,
etc., for the full length the thread is to be marked. With the triangle
resting against the $T$-square, the lines 7, 8, 9, etc. (for the full
length of the thread), are drawn from the points 4, 5, 6, on line 2.
These give one side of the thread. Reversing the drawing triangle,
angles 10, 11, etc., are then drawn, which will complete the outline of
the thread at the top of the bolt. We may now mark the depth of the
thread by drawing line 12, and with the compasses set on the centre line
transfer this depth to the other side of the bolt, as denoted by the
arcs 13 and 14. Touching arc 14 we mark line 15 for the thread depth on
that side. We have now to get the slant of the thread across the bolt.
It is obvious that in passing once around the bolt the thread advances
to the amount of the pitch as from _a_ to _b_; hence, in passing half
way around, it will advance from _a_ to _c_; we therefore draw line 16
at a right-angle to the centre line, and a line that touches the top of
the threads at _a_, where it meets line 2, and also meets line 16, where
it touches line 3, is the angle or <DW72> for the tops of the threads,
which may be drawn across by lines, as 18, 19, 20, etc. From these lines
the sides of the thread may be drawn at the bottom of the bolt, marking
first the angle on one side, as by lines 21, 22, 23, etc., and then the
angles on the other, as by lines 24, 25, etc.

[Illustration: Fig. 204.]

There now remain the bottoms of the thread to draw, and this is done by
drawing lines from the bottom of the thread on one side of the bolt to
the bottom on the other, as shown in the cut by a dotted line; hence, we
may set a square blade to that angle, and mark in these lines, as 26,
27, 28, etc., and the thread is pencilled in complete.

If the student will follow out this example upon paper, it will appear
to him that after the thread had been marked out on one side of the
bolt, the angle of the thread might be obtained, as shown by lines 16
and 17, and that the bottoms of the thread as well as the tops might be
carried across the bolt to the other side. Figure 204 represents a case
in which this has been done, and it will be observed that the lines
denoting the bottom of the thread do not meet the bottoms of the thread,
which occurs for the reason that the angle for the bottom is not the
same as that for the top of the thread.

[Illustration: Fig. 205.]

[Illustration: Fig. 206.]

In inking in the thread, it enhances the appearance to give the bottom
of the thread and the right-hand side of the same, heavy shade lines,
as in Figure 202, a plan that is usually adopted for threads of large
diameter and coarse pitch.

A double thread, such as in Figure 205, is drawn in the same way, except
that the slant of the thread is doubled, and the square is to be set for
the thread-pitch A, A, both for the tops and bottoms of the thread.

[Illustration: Fig 207.]

A round top and bottom thread, as the Whitworth thread, is drawn by
single lines, as in Figure 206. A left-hand thread, Figure 207, is
obviously drawn by the same process as a right-hand one, except that the
slant of the thread is given in the opposite direction.

For screw threads of a large diameter it is not uncommon to draw in the
thread curves as they appear to the eye, and the method of doing this is
shown in Figure 208. The thread is first marked on both sides of the
bolt, as explained, and instead of drawing, straight across the bolt,
lines to represent the tops and bottoms of the thread, a template to
draw the curves by is required. To get these curves, two half-circles,
one equal in diameter to the top, and one equal to the bottom of the
thread, are drawn, as in Figure 208.

[Illustration: Fig. 208.]

These half-circles are divided into any convenient number of equal
divisions: thus in Figure 208, each has eight divisions, as _a_, _b_,
_c_, etc., for the outer, and _i_, _j_, _k_, etc., for the inner one.
The pitch of the thread is then divided off by vertical lines into as
many equal divisions as the half-circles are divided into, as by the
lines _a_, _b_, _c_, etc., to _o_. Of these, the seven from _a_, to _h_,
correspond to the seven from _a'_ to _g'_, and are for the top of the
thread, and the seven from _i_ to _o_ correspond to the seven on the
inner half-circle, as _i_, _j_, _k_, etc. Horizontal lines are then
drawn from the points of the division to meet the vertical lines of
division; thus the horizontal dotted line from _a'_ meets the vertical
line _a_, and where they meet, as at A, a dot is made. Where the dotted
line from _b'_ meets vertical line _b_, another dot is made, as at B,
and so on until the point G is found. A curve drawn to pass from the top
of the thread on one side of the bolt to the top of the other side, and
passing through these points, as from A to G, will be the curve for the
top of the thread, and from this curve a template may be made to mark
all the other thread-tops from, because manifestly all the tops of the
thread on the bolt will be alike.

For the bottoms of the thread, lines are similarly drawn, as from _i'_
to meet _i_, where dot I is marked. J is got from _j'_ and _j_, while K
is got from the intersection of _k'_ with _k_, and so on, the dots from
I to O being those through which a curve is drawn for the bottom of the
thread, and from this curve a template also may be made to mark all the
thread bottoms. We have in our example used eight points of division in
each half-circle, but either more or less points maybe used, the only
requisite being that the pitch of the thread must be divided into as
many divisions as the two half-circles are. But it is not absolutely
necessary that both half-circles be divided into the same number of
equal divisions. Thus, suppose the large half-circle were divided into
ten divisions, then instead of the first half of the pitch being divided
into eight (as from _a_ to _h_) it would require to have ten lines. But
the inner half-circle may have eight only, as in our example. It is more
convenient, however, to use the same number of divisions for both
circles, so that they may both be divided together by lines radiating
from the centre. The more the points of division, the greater number of
points to draw the curves through; hence it is desirable to have as many
as possible, which is governed by the pitch of the thread, it being
obvious that the finer the pitch the less the number of distinct and
clear divisions it is practicable to divide it into. In our example the
angles of the thread are spread out to cause these lines to be thrown
further apart than they would be in a bolt of that diameter; hence it
will be seen that in threads of but two or three inches in diameter the
lines would fall very close together, and would require to be drawn
finely and with care to keep them distinct.

[Illustration: Fig. 208 _a_.]

[Illustration: Fig. 209.]

The curves for a United States standard form of thread are obtained in
the same manner as from the $V$ thread in Figure 208, but the thread
itself is more difficult to draw. The construction of this thread is
shown in Figure 208, it having a flat place at the top and at the bottom
of the thread. A common $V$ thread has its sides at an angle of 60
degrees, one to the other, the top and bottom meeting in a point. The
United States standard is obtained from drawing a common $V$ thread and
dividing its depth into eight equal divisions, as at _x_, in Figure 208
_a_, and cutting off one of these divisions at the top and filling in
one at the bottom to form flat places, as shown in the figure. But the
thread cannot be sketched on a bolt by this means unless temporary lines
are used to get the thread from, these temporary lines being drawn to
represent a bolt one-fourth the depth of the thread too large in
diameter. Thus, in Figure 208 _a_, it is seen that cutting off
one-eighth the depth of the thread reduces the diameter of the thread.
It is necessary, then, to draw the flat place on top of the thread
first, the order of procedure being shown in Figure 209. The lines for
the full diameter of the thread being drawn, the pitch is stepped off by
arcs, as 1, 2, 3, etc.; and from these, arcs, as 4, 5, 6, etc., are
marked for the width of the flat places at the tops of the threads.
Then one side of the thread is marked off by lines, as 7, which meet the
arcs 1, 2, 3, etc., as at _a_, _c_, etc. Similar lines, as 8 and 9, are
marked for the other side of the thread, these lines, 7, 8 and 9,
projecting until they cross each other. Line 10 is then drawn, making a
flat place at the bottom of the thread equal in width to that at the
top. Line 12 is then drawn square across the bolt, starting from the
bottom of the thread, and line 13 is drawn starting from the corner _f_
on one side of the thread and meeting line 12 on the other side of the
thread, which gives the angle for the tops of the thread. The depth of
the thread may then be marked on the other side of the bolt by the arcs
_d_ and _e_, and the line 14. The tops of all the threads may then be
drawn in, as by lines 15, 16, 17 and 18, and by lines, as 19, etc., the
thread sides may be drawn on the other side of the bolt. All that
remains is to join the bottoms of the threads by lines across the bolt,
and the pencil lines will be complete, ready to ink in. If the thread is
to be shown curved instead of drawn straight across, the curve may be
obtained by the construction in Figure 208, which is similar to that in
Figure 207, except that while the pitch is divided off into 16
divisions, the whole of these 16 divisions are not used to get the
curves, some of them being used twice over; thus for the bottom the
eight divisions from _b_ to _i_ are used, while for the tops the eight
from _g_ to _o_ are used. Hence _g_, _h_ and _i_ are used for getting
both curves, the divisions from _a_ to _b_ and from _o_ to _p_ being
taken up by the flat top and bottom of the thread. It will be noted that
in Figure 207, the top of the thread is drawn first, while in Figure
208 the bottom is drawn first, and that in the latter (for the U.S.
standard) the pitch is marked from centre to centre of the flats of the
thread.

[Illustration: Fig. 210.]

To draw a square thread the pencil lines are marked in the order shown
in Figure 210, in which 1 represents the centre line and 2, 3, 4 and 5,
the diameter and depth of the thread. The pitch of the thread is marked
off by arcs, as 6, 7, etc., or by laying a rule directly on the centre
line and marking with a lead pencil. To obtain the slant of the thread,
lines 8 and 9 are drawn, and from these line 10, touching 8 and 9 where
they meet lines 2 and 5; the threads may then be drawn in from the arcs
as 6, 7, etc. The side of the thread will show at the top and the bottom
as at A B, because of the coarse pitch and the thread on the other or
unseen side of the bolt slants, as denoted by the lines 12, 13; and
hence to draw the sides A B, the triangle must be set from one thread to
the next on the opposite side of the bolt, as denoted by the dotted
lines 12 and 13.

[Illustration: Fig. 211.]

If the curves of the thread are to be drawn in, they may be obtained as
in Figure 211, which is substantially the same as described for a V
thread. The curves _f_, representing the sides of the thread, terminate
at the centre line _g_, and the curves _e_ are equidistant with the
curves _c_ from the vertical lines _d_. As the curves _f_ above the
line are the same as _f_ below the line, the template for _f_ need not
be made to extend the whole distance across, but one-half only; as is
shown by the dotted curve _g_, in the construction for finding the curve
for square-threaded nuts in Figure 212.

[Illustration: Fig. 212.]

[Illustration: Fig. 213.]

A specimen of the form of template for drawing these curves is shown in
Figure 213; _g_ _g_, is the centre line parallel to the edges R, S;
lines _m_, _n_, represent the diameter of the thread at the top, and
_o_, _p_, that at the bottom or root; edge _a_ is formed to the points
(found by the constructions in the figures as already explained) for the
tops of the thread, and edge _f_ is so formed for the curve at the
thread bottoms. The edge, as S or R, is laid against the square-blade to
steady it while drawing in the curves. It may be noted, however, that
since the curve is the same below the centre line as it is above, the
template may be made to serve for one-half the thread diameter, as at
_f_, where it is made from _o_ to _g_, only being turned upside down to
draw the other half of the curve; the notches cut out at _x_, _x_, are
merely to let the pencil-lines in the drawing show plainly when setting
the template.

When the thread of a nut is shown in section, it slants in the opposite
direction to that which appears on the bolt-thread, because it shows the
thread that fits to the opposite side of the bolt, which, therefore,
slants in the opposite direction, as shown by the lines 12 and 13 in
Figure 210.

In a top or end view of a nut the thread depth is usually shown by a
simple circle, as in Figure 214.

[Illustration: Fig. 214.]

To draw a spiral spring, draw the centre line A, and lines B, C, Figure
215, distant apart the diameter the spring is to be less the diameter of
the wire of which it is to be made. On the centre line A mark two lines
_a b_, _c d_, representing the pitch of the spring. Divide the distance
between _a_ and _b_ into four equal divisions, as by lines 1, 2, 3,
letting line 3 meet line B. Line _e_ meeting the centre line at line
_a_, and the line B at its intersection with line 3, is the angle of the
coil on one side of the spring; hence it may be marked in at all the
locations, as at _e f_, etc. These lines give at their intersections
with the lines C and B the centres for the half circles _g_, which being
drawn, the sides _h_, _i_, _j_, _k_, etc., of the spring, may all be
marked in. By the lines _m_, _n_, _o_, _p_, the other sides of the
spring may be marked in.

[Illustration: Fig. 215.]

The end of the spring is usually marked straight across, as at L. If it
is required to draw the coils curved instead of straight across, a
template must be made, the curve being obtained as already described for
threads. It may be pointed out, however, that to obtain as accurate a
division as possible of the lines that divide the pitch, the pitch may
be divided upon a diagonal line, as F, Figure 216, which will greatly
facilitate the operation.

[Illustration: Fig. 216.]

Before going into projections it may be as well to give some examples
for practice.

[Illustration: Fig. 219. (Page 169.)]




CHAPTER IX.

_EXAMPLES FOR PRACTICE._


Figure 217 represents a simple example for practice, which the student
may draw the size of the engraving, or he may draw it twice the size. It
is a locomotive spring, composed of leaves or plates, held together by a
central band.

[Illustration: Fig. 217.]

Figure 218 is an example of a stuffing box and gland, supposed to stand
vertical, hence the gland has an oil cup or receptacle.

In Figure 219 are working drawings of a coupling rod, with the
dimensions and directions marked in.

It may be remarked, however, that the drawings of a workshop are, where
large quantities of the same kind of work is done, varied in character
to suit some special departments--that is to say, special extra drawings
are made for these departments. In Figures 220 and 221 is a drawing of a
connecting rod drawn, put together as it would be for the lathe, vise or
erecting shop.

[Illustration: Fig. 218.]

[Illustration: Fig. 219.]

[Illustration: Fig. 220.]

[Illustration: Fig. 221.]

To the two views shown there would be necessary detail sketches of the
set screws, gibbs, and keys, all the rest being shown; the necessary
dimensions being, of course, marked on the general drawing and on the
details.

In so simple a thing as a connecting rod, however, there would be no
question as to how the parts go together; hence detail drawings of each
separate piece would answer for the lathe or vise bands.

But in many cases this would not be the case, and the drawing would
require to show the parts put together, and be accompanied with such
detail sketches as might be necessary to show parts that could not be
clearly defined in the general views.

The blacksmith, for example, is only concerned with the making of the
separate pieces, and has no concern as to how the parts go together.
Furthermore, there are parts and dimensions in the general drawing with
which the blacksmith has nothing to do.

Thus the location and dimensions of the keyways, the dimensions of the
brasses, and the location of the bolt holes, are matters that have no
reference to the blacksmith's work, because the keyways, bolt holes, and
set-screw holes would be cut out of the solid in the machine shop. It is
customary, therefore, to send to the blacksmith shop drawings containing
separate views of each piece drawn to the shape it is to be forged; and
drawn full size, or else on a scale sufficiently large to make each part
show clearly without close inspection, marking thereon the full sizes,
and stating beneath the number of pieces of each detail. (As in Figure
222, which represents the iron work of the connecting rod in Figure
220). In some cases the finished sizes are marked, and it is left to the
blacksmith's judgment how much to leave for the finishing. This is
undesirable, because either the blacksmith is left to judge what parts
are to be finished, or else there must be on the drawing instructions on
this point, or else signs or symbols that are understood to convey the
information. It is better, therefore, to make for the blacksmith a
special sketch, and mark thereon the full-forged sizes, stating on the
drawing that such is the case.

[Illustration: Fig. 222]

As to the material of which the pieces are to be made, the greater part
of blacksmith work is made of wrought iron, and it is, therefore,
unnecessary to write "wrought iron" beneath each piece. When the pieces
are to be of steel, however, it should be marked on the drawing and
beneath the piece. In special cases, as where the greater part of the
work of the shop is of steel, the rule may, of course, be reversed, and
the parts made of iron may be the ones marked, whereas when parts are
sometimes of iron, and at others of steel, each piece should be marked.

As a general rule the blacksmith knows, from the custom of the shop or
the nature of the work, what the quality or kind of iron is to be, and
it is, therefore, only in exceptional cases that they need to be
mentioned on the drawing. Thus in a carriage manufactory, Norway or
Swede iron will be found, as well as the better grades of refined iron,
but the blacksmith will know what iron to use, for certain parts, or the
shop may be so regulated that the selection of the iron is not left to
him. In marking the number of pieces required, it is better to use the
word "thus" than the words "of this," or "off this," because it is
shorter and more correct, for the forging is not taken off the drawing,
nor is it of the same; the drawing gives the shape and the size, and the
word "thus" conveys that idea better than "of," "off," or "like this."

In shops where there are many of the same pieces forged, the blacksmith
is furnished with sheet-iron templates that he can lay directly upon the
forging and test its dimensions at once, which is an excellent plan in
large work. Such templates are, of course, made from the drawings, and
it becomes a question as to whether their dimensions should be the
forged or the finished ones. If they are the forged, they may cause
trouble, because a forging may have a scant place that it is difficult
for the blacksmith to bring up to the size of the template, and he is in
doubt whether there is enough metal in the scant place to allow the job
to clean up. It is better, therefore, to make them to finished sizes, so
that he can see at once if the work will clean up, notwithstanding the
scant place. This will lead to no errors in large work, because such
work is marked out by lines, and the scant part will therefore be
discovered by the machinist, who will line out the piece accordingly.

Figure 223 is a drawing of a locomotive frame, which the student may as
well draw three or four times as large as the engraving, which brings us
to the subject of enlarging or reducing scales.


REDUCING SCALES.

[Illustration: Fig. 223.]

[Illustration: Fig. 224.]

[Illustration: Fig. 225.]

It is sometimes necessary to reduce a drawing to a smaller scale, or to
find a minute fraction of a given dimension, such fraction not being
marked on the lineal measuring rules at hand. Figure 224 represents a
scale for finding minute fractions. Draw seven lines parallel to each
other, and equidistant draw vertical lines dividing the scale into
half-inches, as at _a_, _b_, _c_, etc. Divide the first space _e d_ into
equal halves, draw diagonal lines, and number them as in the figure. The
distance of point 1, which is at the intersection of diagonal with the
second horizontal line, will be 1/24 inch from vertical line _e_. Point
2 will be 2/24 inch from line _e_, and so on. For tenths of inches there
would require to be but six horizontal lines, the diagonals being drawn
as before. A similar scale is shown in Figure 225. Draw the lines A B, B
D, D C, C A, enclosing a square inch. Divide each of these lines into
ten equal divisions, and number and letter them as shown. Draw also the
diagonal lines A 1, _a_ 2, B 3, and so on; then the distances from the
line A C to the points of intersection of the diagonals with the
horizontal lines represent hundredths of an inch.

Suppose, for example, we trace one diagonal line in its path across the
figure, taking that which starts from A and ends at 1 on the top
horizontal line; then where the diagonal intersects _horizontal_ line 1,
is 99/100 from the line B D, and 1/100 from the line A C, while where it
intersects _horizontal_ line 2, is 98/100 from line B D, and 2/100 from
line A C, and so on. If we require to set the compasses to 67/100 inch,
we set them to the radius of _n_, and the figure 3 on line B D, because
from that 3 to the vertical line _d_ 4 is 6/10 or 60/100 inch, and from
that vertical line to the diagonal at _n_ is seven divisions from the
line C D of the figure.

In making a drawing to scale, however, it is an excellent plan to draw a
line and divide it off to suit the required scale. Suppose, for example,
that the given scale is one-quarter size, or three inches per foot; then
a line three inches long may be divided into twelve equal divisions,
representing twelve inches, and these may be subdivided into half or
quarter inches and so on. It is recommended to the beginner, however, to
spend all his time making simple drawings, without making them to scale,
in order to become so familiar with the use of the instruments as to
feel at home with them, avoiding the complication of early studies that
would accompany drawing to scale.




CHAPTER X.

_PROJECTIONS._


In projecting, the lines in one view are used to mark those in other
views, and to find their shapes or curvature as they will appear in
other views. Thus, in Figure 225_a_ we have a spiral, wound around a
cylinder whose end is cut off at an angle. The pitch of the spiral is
the distance A B, and we may delineate the curve of the spiral looking
at the cylinder from two positions (one at a right-angle to the other,
as is shown in the figure), by means of a circle having a circumference
equal to that of the cylinder.

The circumference of this circle we divide into any number of
equidistant divisions, as from 1 to 24. The pitch A B of the spiral or
thread is then divided off also into 24 equidistant divisions, as marked
on the left hand of the figure; vertical lines are then drawn from the
points of division on the circle to the points correspondingly numbered
on the lines dividing the pitch; and where line 1 on the circle
intersects line 1 on the pitch is one point in the curve. Similarly,
where point 2 on the circle intersects line 2 on the pitch is another
point in the curve, and so on for the whole 24 divisions on the circle
and on the pitch. In this view, however, the path of the spiral from
line 7 to line 19 lies on the other side of the cylinder, and is marked
in dotted lines, because it is hidden by the cylinder. In the
right-hand view, however, a different portion of the spiral or thread is
hidden, namely from lines 1 to 13 inclusive, being an equal proportion
to that hidden in the left-hand view.

[Illustration: Fig. 225 _a_.]

The top of the cylinder is shown in the left-hand view to be cut off at
an angle to the axis, and will therefore appear elliptical; in the
right-hand view, to delineate this oval, the same vertical lines from
the circle may be carried up as shown on the right hand, and horizontal
lines may be drawn from the inclined face in one view across the end of
the other view, as at P; the divisions on the circle may be carried up
on the right-hand view by means of straight lines, as Q, and arcs of
circle, as at R, and vertical lines drawn from these arcs, as line S,
and where these vertical lines S intersect the horizontal lines as P,
are points in the ellipse.

Let it be required to draw a cylindrical body joining another at a
right-angle; as for example, a Tee, such as in Figure 226, and the
outline can all be shown in one view, but it is required to find the
line of junction of one piece, A, with the other, B; that is, find or
mark the lines of junction C. Now when the diameters of A and B are
equal, the line of junction C is a straight line, but it becomes a
curved one when the diameter of A is less than that of B, or _vice
versa_; hence it may be as well to project it in both cases. For this
purpose the three views are necessary. One-quarter of the circle of B,
in the end view, is divided off into any number of equal divisions; thus
we have chosen the divisions marked _a_, _b_, _c_, _d_, _e_, etc.; a
quarter of the top view is similarly divided off, as at _f_, _g_, _h_,
_i_, _j_; from these points of division lines are projected on to the
side view, as shown by the dotted lines _k_, _l_, _m_, _n_, _o_, _p_,
etc., and where these lines meet, as denoted by the dots, is in each
case a point in the line of junction of the two cylinders A, B.

[Illustration: Fig. 226.]

[Illustration: Fig. 227.]

Figure 227 represents a Tee, in which B is less in diameter than A;
hence the two join in a curve, which is found in a similar manner, as is
shown in Figure 227. Suppose that the end and top views are drawn, and
that the side view is drawn in outline, but that the curve of junction
or intersection is to be found. Now it is evident that since the centre
line 1 passes through the side and end views, that the face _a_, in the
end view, will be even with the face _a'_ in the side view, both being
the same face, and as the full length of the side of B in the end view
is marked by line _b_, therefore line _c_ projected down from _b_ will
at its junction with line _b'_, which corresponds to line _b_, give the
extreme depth to which _b'_ extends into the body A, and therefore, the
apex of the curve of intersection of B with A. To obtain other points,
we divide one-quarter of the circumference of the circle B in the top
view into four equal divisions, as by lines _d_, _e_, _f_, and from the
points of division we draw lines _j_, _i_, _g_, to the centre line
marked 2, these lines being thickened in the cut for clearness of
illustration. The compasses are then set to the length of thickened line
_g_, and from point _h_, in the end view, as a centre, the arc _g'_ is
marked. With the compasses set to the length of thickened line _i_, and
from _h_ as a centre, arc _i'_ is marked, and with the length of
thickened line _j_ as a radius and from _h_ as a centre arc _j'_ is
marked; from these arcs lines _k_, _l_, _m_ are drawn, and from the
intersection of _k_, _l_, _m_, with the circle of A, lines _n_, _o_, _p_
are let fall. From the lines of division, _d_, _e_, _f_, the lines _q_,
_r_, _s_ are drawn, and where lines _n_, _o_, _p_ join lines _q_, _r_,
_s_, are points in the curve, as shown by the dots, and by drawing a
line to intersect these dots the curve is obtained on one-half of B.
Since the axis of B is in the same plane as that of A, the lower half of
the curve is of the same curvature as the upper, as is shown by the
dotted curve.

[Illustration: Fig. 228.]

In Figure 228 the axis of piece B is not in the same plane as that of D,
but to one side of it to the distance between the centre lines C, D,
which is most clearly seen in the top view. In this case the process is
the same except in the following points: In the side view the line _w_,
corresponding to the line _w_ in the end view, passes within the line
_x_ before the curve of intersection begins, and in transferring the
lengths of the full lines _b_, _c_, _d_, _e_, _f_ to the end view, and
marking the arcs _b'_, _c'_, _d'_, _e'_, _f'_, they are marked from the
point _w_ (the point where the centre line of B intersects the outline
of A), instead of from the point _x_. In all other respects the
construction is the same as that in Figure 227.

[Illustration: Fig. 229.]

In these examples the axis of B stands at a right-angle to that of A.
But in Figure 229 is shown the construction where the axis of B is not
at a right-angle to A. In this case there is projected from B, in the
side view, an end view of B as at B', and across this end at a
right-angle to the centre line of B is marked a centre line C C of B',
which is divided as before by lines _d_, _e_, _f_, _g_, _h_, their
respective lengths being transferred from W as a centre, and marked by
the arcs _d'_, _e'_, _f'_, which are marked on a vertical line and
carried by horizontal lines, to the arc of A as at _i_, _j_, _k_. From
these points, _i_, _j_, _k_, the perpendicular lines _l_, _m_, _n_, _o_,
are dropped, and where these lines meet lines _p_, _q_, _r_, _s_, _t_,
are points in the curve of intersection of B with A. It will be observed
that each of the lines _m_, _n_, _o_, serves for two of the points in
the curve; thus, _m_ meets _q_ and _s_, while _n_ meets _p_ and _t_, and
_o_ meets the outline on each side of B, in the side view, and as _i_,
_j_, _k_ are obtained from _d_ and _e_, the lines _g_ and _h_ might have
been omitted, being inserted merely for the sake of illustration.

In Figure 230 is an example in which a cylinder intersects a cone, the
axes being parallel. To obtain the curve of intersection in this case,
the side view is divided by any convenient number of lines, as _a_, _b_,
_c_, etc., drawn at a right-angle to its axis A A, and from one end of
these lines are let fall the perpendiculars _f_, _g_, _h_, _i_, _j_;
from the ends of these (where they meet the centre line of A in the top
view), half-circles _k_, _l_, _m_, _n_, _o_, are drawn to meet the
circle of B in the top view, and from their points of intersection with
B, lines _p_, _q_, _r_, _s_, _t_, are drawn, and where these meet lines
_a_, _b_, _c_, _d_ and _e_, which is at _u_, _v_, _w_, _x_, _y_, are
points in the curve.

[Illustration: Fig. 230.]

[Illustration: Fig. 231.]

It will be observed, on referring again to Figure 229, that the branch
or cylinder B appears to be of elliptical section on its end face,
which occurs because it is seen at an angle to its end surface; now the
method of finding the ellipse for any given degree of angle is as in
Figure 231, in which B represents a cylindrical body whose top face
would, if viewed from point I, appear as a straight line, while if
viewed from point J it would appear in outline a circle. Now if viewed
from point E its apparent dimension in one direction will obviously be
defined by the lines S, Z. So that if on a line G G at a right angle to
the line of vision E, we mark points touching lines S, Z, we get points
1 and 2, representing the apparent dimension in that direction which is
the width of the ellipse. The length of the ellipse will obviously be
the full diameter of the cylinder B; hence from E as a centre we mark
points 3 and 4, and of the remaining points we will speak presently.
Suppose now the angle the top face of B is viewed from is denoted by the
line L, and lines S', Z, parallel to L, will be the width for the
ellipse whose length is marked by dots, equidistant on each side of
centre line G' G', which equal in their widths one from the other the
full diameter of B. In this construction the ellipse will be drawn away
from the cylinder B, and the ellipse, after being found, would have to
be transferred to the end of B. But since centre line G G is obviously
at the same angle to A A that A A is to G G, we may start from the
centre line of the body whose elliptical appearance is to be drawn, and
draw a centre line A A at the same angle to G G as the end of B is
supposed to be viewed from. This is done in Figure 231 _a_, in which the
end face of B is to be drawn viewed from a point on the line G G, but at
an angle of 45 degrees; hence line A A is drawn at an angle of 45
degrees to centre line G G, and centre line E is drawn from the centre
of the end of B at a right angle to G G, and from where it cuts A A, as
at F, a side view of B is drawn, or a single line of a length equal to
the diameter of B may be drawn at a right angle to A A and equidistant
on each side of F. A line, D D, at a right angle to A A, and at any
convenient distance above F, is then drawn, and from its intersection
with A A as a centre, a circle C equal to the diameter of B is drawn;
one-half of the circumference of C is divided off into any number of
equal divisions as by arcs _a_, _b_, _c_, _d_, _e_, _f_. From these
points of division, lines _g_, _h_, _i_, _j_, _k_, _l_ are drawn, and
also lines _m_, _n_, _o_, _p_, _q_, _r_. From the intersection of these
last lines with the face in the side view, lines _s_, _t_, _u_, _t_,
_w_, _x_, _y_, _z_ are drawn, and from point F line E is drawn. Now it
is clear that the width of the end face of the cylinder will appear the
same from any point of view it may be looked at, hence the sides H H are
made to equal the diameter of the cylinder B and marked up to centre
line E.

[Illustration: Fig. 231 _a_.]

[Illustration: Fig. 232.]

It is obvious also that the lines _s_, _z_, drawn from the extremes of
the face to be projected will define the width of the ellipse, hence we
have four of the points (marked respectively 1, 2, 3, 4) in the ellipse.
To obtain the remaining points, lines _t_, _u_, _v_, _w_, _x_, _y_
(which start from the point on the face F where the lines _m_, _n_, _o_,
_p_, _q_, _r_, respectively meet it) are drawn across the face of B as
shown. The compasses are then set to the radius _g_; that is, from
centre line D to division _a_ on the circle, and this radius is
transferred to the face to be projected the compass-point being rested
at the intersection of centre line G and line _t_, and two arcs as 5 and
6 drawn, giving two more points in the curve of the ellipse. The
compasses are then set to the length of line _h_ (that is, from centre
line D to point of division _b_), and this distance is transferred,
setting the compasses on centre line G where it is intersected by line
_u_, and arcs 7, 8 are marked, giving two more points in the ellipse. In
like manner points 9 and 10 are obtained from the length of line _i_, 11
and 12 from that of _j_; points 13 and 14 from the length of _k_, and 15
and 16 from _l_, and the ellipse may be drawn in from these points.

It may be pointed out, however, that since points 5 and 6 are the same
distance from G that points 15 and 16 are, and since points 7 and 8 are
the same distance from G that points 13 and 14 are, while points 9 and
10 are the same distance from G that 11 and 12 are, the lines, _j_, _k_,
_l_ are unnecessary, since _l_ and _g_ are of equal length, as are also
_h_ and _k_ and _i_ and _j_. In Figure 232 the cylinders are line shaded
to make them show plainer to the eye, and but three lines (_a_, _b_,
_c_) are used to get the radius wherefrom to mark the arcs where the
points in the ellipse shall fall; thus, radius _a_ gives points 1, 2, 3
and 4; radius _b_ gives points 5, 6, 7 and 8, and radius _c_ gives 9,
10, 11 and 12, the extreme diameter being obtained from lines S, Z, and
H, H.




CHAPTER XI.

_DRAWING GEAR WHEELS._


The names given to the various lines of a tooth on a gear-wheel are as
follows:

In Figure 233, A is the face and B the flank of a tooth, while C is the
point, and D the root of the tooth; E is the height or depth, and F the
breadth. P P is the pitch circle, and the space between the two teeth,
as H, is termed a space.

[Illustration: Fig. 233.]

[Illustration: Fig. 234.]

It is obvious that the points of the teeth and the bottoms of the
spaces, as well as the pitch circle, are concentric to the axis of the
wheel bore. And to pencil in the teeth these circles must be fully
drawn, as in Figure 234, in which P P is the pitch circle. This circle
is divided into as many equal divisions as the wheel is to have teeth,
these divisions being denoted by the radial lines, A, B, C, etc. Where
these divisions intersect the pitch circle are the centres from which
all the teeth curves may be drawn. The compasses are set to a radius
equal to the pitch, less one-half the thickness of the tooth, and from a
centre, as R, two face curves, as F G, may be marked; from the next
centre, as at S, the curves D E may be marked, and so on for all the
faces; that is, the tooth curves lying between the outer circle X and
the pitch circle P. For the flank curves, that is, the curve from P to
Y, the compasses are set to a radius equal to the pitch; and from the
sides of the teeth the flank curves are drawn. Thus from J, as a centre
flank, K is drawn; from V, as a centre flank, H is drawn, and so on.

The proportions of the teeth for cast gears generally accepted in this
country are those given by Professor Willis, as average practice, and
are as follows:

Depth to pitch line, 3/10 of the pitch.
Working depth,       6/10     "    "
Whole depth,         7/10     "    "
Thickness of tooth,  5/11     "    "
Breadth of space,    6/11     "    "

Instead, however, of calculating the dimensions these proportions give
for any particular pitch, a diagram or scale may be made from which they
may be taken for any pitch by a direct application of the compasses. A
scale of this kind is given in Figure 235, in which the line A B is
divided into inches and parts to represent the pitches; its total length
representing the coarsest pitch within the capacity of the scale; and,
the line B C (at a right-angle to A B) the whole depth of the tooth for
the coarsest pitch, being 7/10 of the length of A B.

[Illustration: Fig. 235.]

The other diagonal lines are for the proportion of the dimensions marked
on the figure. Thus the depth of face, or distance from the pitch line
to the extremity or tooth point for a 4 inch pitch, would be measured
along the line B C, from the vertical line B to the first diagonal. The
thickness of the tooth would be for a 4 inch pitch along line B C from B
to the second diagonal, and so on. For a 3 inch pitch the measurement
would be taken along the horizontal line, starting from the 3 on the
line A B, and so on. On the left of the diagram or scale is marked the
lbs. strain each pitch will safely transmit per inch width of wheel
face, according to Professor Marks.

[Illustration: Fig. 236.]

The application of the scale as follows: The pitch circles P P and P'
P', Figure 236, for the respective wheels, are drawn, and the height of
the teeth is obtained from the scale and marked beyond the pitch
circles, when circles Q and Q' may be drawn. Similarly, the depths of
the teeth within the pitch circles are obtained from the scale or
diagram and marked within the respective pitch circles, and circles R
and R' are marked in. The pitch circles are divided off into as many
points of equal division, as at _a_, _b_, _c_, _d_, _e_, etc., as the
respective wheels are to have teeth, and the thickness of tooth having
been obtained from the scale, this thickness is marked from the points
of division on the pitch circles, as at _f_ in the figure, and the tooth
curves may then be drawn in. It may be observed, however, that the tooth
thicknesses will not be strictly correct, because the scale gives the
same chord pitch for the teeth on both wheels which will give different
arc pitches to the teeth on the two wheels; whereas, it is the arc
pitches, and not the chord pitches, that should be correct. This error
obviously increases as there is a greater amount of difference between
the two wheels.

The curves given to the teeth in Figure 234 are not the proper ones to
transmit uniform motion, but are curves merely used by draughtsmen to
save the trouble of finding the true curves, which if it be required,
may be drawn with a very near approach to accuracy, as follows, which is
a construction given by Rankine:

Draw the rolling circle D, Figure 237, and draw A D, the line of
centres. From the point of contact at C, mark on D, a point distant from
C one-half the amount of the pitch, as at P, and draw the line P C of
indefinite length beyond C. Draw the line P E passing through the line
of centres at E, which is equidistant between C and A. Then increase the
length of line P F to the right of C by an amount equal to the radius A
C, and then diminish it to an amount equal to the radius E D, thus
obtaining the point F and the latter will be the location of centre for
compasses to strike the face curve.

[Illustration: Fig. 237.]

[Illustration: Fig. 238.]

Another method of finding the face curve, with compasses, is as follows:
In Figure 238 let P P represent the pitch circle of the wheel to be
marked, and B C the path of the centre of the generating or describing
circle as it rolls outside of P P. Let the point B represent the centre
of the generating circle when it is in contact with the pitch circle at
A. Then from B mark off, on B C, any number of equidistant points, as
D, E, F, G, H, and from A mark on the pitch circle, with the same
radius, an equal number of points of division, as 1, 2, 3, 4, 5. With
the compasses set to the radius of the generating circle, that is, A B,
from B, as a centre, mark the arc I, from D, the arc J, from E, the arc
K, from F, and so on, marking as many arcs as there are points of
division on B C. With the compasses set to the radius of divisions 1, 2,
etc., step off on arc M the five divisions, N, O, S, T, V, and at V will
be a point on the epicycloidal curve. From point of division 4, step off
on L four points of division, as _a_, _b_, _c_, _d_; and _d_ will be
another point on the epicycloidal curve. From point 3, set off three
divisions, and so on, and through the points so obtained draw by hand,
or with a scroll, the curve.

[Illustration: Fig. 239.]

Hypocycloids for the flanks of the teeth maybe traced in a similar
manner. Thus in Figure 239, P P is the pitch circle, and B C the line of
motion of the centre of the generating circle to be rolled within P P.
From 1 to 6 are points of equal division on the pitch circle, and D to I
are arc locations for the centre of the generating circle. Starting
from A, which represents the location for the centre of the generating
circle, the point of contact between the generating and base circles
will be at B. Then from 1 to 6 are points of equal division on the pitch
circle, and from D to I are the corresponding locations for the centres
of the generating circle. From these centres the arcs J, K, L, M, N, O,
are struck. The six divisions on O, from _a_ to _f_, give at _f_ a point
in the curve. Five divisions on N, four on M, and so on, give,
respectively, points in the curve.

There is this, however, to be noted concerning the construction of the
last two figures. Since the circle described by the centre of the
generating circle is of a different arc or curve to that of the pitch
circle, the length of an arc having an equal radius on each will be
different. The amount is so small as to be practically correct. The
direction of the error is to give to the curves a less curvature, as
though they had been produced by a generating circle of larger diameter.
Suppose, for example, that the difference between the arc _a_, _b_, and
its chord is .1, and that the difference between the arc 4, 5, and its
chord is .01, then the error in one step is .09, and, as the point _f_
is formed in five steps, it will contain this error multiplied five
times. Point _d_ would contain it multiplied three times, because it has
three steps, and so on.

The error will increase in proportion as the diameter of the generating
is less than that of the pitch circle, and though in large wheels,
working with large wheels, so that the difference between the radius of
the generating circle and that of the smallest wheel is not excessive,
it is so small as to be practically inappreciable, yet in small wheels,
working with large ones, it may form a sensible error.

[Illustration: Fig. 240.]

For showing the dimensions through the arms and hub, a sectional view of
a section of the wheel may be given, as in Figure 240, which represents
a section of a wheel, and a pinion, and on these two views all the
necessary dimensions may be marked.

[Illustration: Fig. 240 _a_. (Page 203.)]

If it is desired to draw an edge view of a wheel (which the student will
find excellent practice), the lines for the teeth may be projected from
the teeth in the side view, as in Figure 240 _a_. Thus tooth E is
projected by drawing lines from the corners A, B, C, in the side view
across the face in the edge view, as at A, B, C in the latter view, and
similar lines may be obtained in the same way for all the teeth.

When the teeth of wheels are to be cut to form in a gear-cutting
machine, the thickness of the teeth is nearly equal to the thickness of
the spaces, there being just sufficient difference to prevent the teeth
of one wheel from becoming locked in the spaces of the other; but when
the teeth are to be cast upon the wheel, the tooth thickness is made
less than the width of the space to an amount that is usually a certain
proportion of the pitch, and is termed the side clearance. In all
wheels, whether with cut or cast teeth, there is given a certain amount
of top and bottom clearance; that is to say, the points of the teeth of
one wheel do not reach to the bottom of the spaces in the other. Thus in
the Pratt and Whitney system the top and bottom clearance is one-eighth
of the pitch, while in the Brown and Sharpe system for involute teeth
the clearance is equal to one-tenth the thickness of the tooth.

In drawing bevil gear wheels, the pitch line of each tooth on each
wheel, and the surfaces of the points, as well as those at the bottom of
the spaces, must all point to a centre, as E in Figure 241, which centre
is where the axes of the shafts would meet. It is unnecessary to mark in
the correct curves for the teeth, for reasons already stated, with
reference to the curves for a spur wheel. But if it is required to do
so, the construction to find the curves is as shown in Figure 242, in
which let A A represent the axis of one shaft, and B that of the other
of the pair of bevil wheels that are to work together, their axes
meeting at W; draw the line E at a right angle to A A, and representing
the pitch circle diameter of one wheel, and draw F at a right angle to
B, and representing the pitch circle of the other wheel; draw the line G
G, passing through the point W and the point T, where the pitch circles
or lines E F meet, and G G will be the line of contact of the tooth of
one wheel upon the tooth of the other wheel; or in other words, the
pitch line of the tooth.

[Illustration: Fig. 241.]

[Illustration: Fig. 242.]

Draw lines, as H and I, representing the tooth breadth. From W, as a
centre, draw on each side of G G dotted lines, as P, representing the
height of the tooth above and below the pitch line G G. At a right angle
to G G draw the line J K; and from where this line meets B, as at Q,
mark the arc _a_, which will represent the pitch circle for the large
diameter of the pinion D. [The smallest wheel of a pair of gears is
termed the pinion.] Draw the arc _b_ for the height, and circle _c_ for
the depth of the teeth, thus defining the height of the tooth at that
end. Similarly from P, as a centre mark (for the large diameter of wheel
C,) arcs _g_, _h_, and _i_, arc _g_ representing the pitch circle, _i_
the height, and _h_ the depth of the tooth. On these arcs draw the
proper tooth curves in the same manner as for spur wheels; that is,
obtain the curves by the construction shown in Figures 237, or by those
in Figures 238 and 239.

To obtain the arcs for the other end of the tooth, draw line M M
parallel to line J K; set the compasses to the radius R L, and from P,
as a centre, draw the pitch circle _k_. For the depth of the tooth draw
the dotted line _p_, meeting the circle _h_ and the point W. A similar
line, from _i_ to W, will give the height of the tooth at its inner end.
Then the tooth curves may be drawn on these three arcs, _k_, _l_, _m_,
in the same as if they were for a spur wheel.

Similarly for the pitch circle of the inner and small end of the pinion
teeth, set the compasses to radius S L, and from Q as a centre mark the
pitch circle _d_. Outside of _d_ mark _e_ for the height above pitch
lines of the tooth, and inside of _d_ mark the arc _f_ for the depth
below pitch line of the tooth at that end. The distance between the
dotted lines as _p_, represents the full height of the tooth; hence _h_
meets _p_, which is the root of the tooth on the large wheel. To give
clearance and prevent the tops of the teeth on one wheel from bearing
against the bottoms of the spaces in the other wheel, the point of the
pinion teeth is marked below; thus arc _b_ does not meet _h_ or _p_, but
is short to the amount of clearance. Having obtained the arcs _d_, _e_,
_f_, the curves may be marked thereon as for a spur wheel. A tooth thus
marked is shown at _x_, and from its curves between _b_ and _c_, a
template may be made for the large diameter or outer end of the pinion
teeth. Similarly for the wheel C the outer end curves are marked on the
arcs _g_, _h_, _i_, and those for the other end of the tooth are marked
between the arcs _l_, _m_.

[Illustration: Fig. 243. (Page 207.)]

[Illustration: Fig. 244.]

Figure 243 represents a drawing of one-half of a bevil gear, and an edge
view projected from the same. The point E corresponds to point E in
Figure 241, or W in 242. The line F shows that the top surface of the
teeth points to E. Line G shows that the pitch line of each tooth points
to E, and lines H show that the bottom of the surface of a space also
points to E. Line 1 shows that the sides of each tooth point to E. And
it follows that the outer end of a tooth is both higher or deeper and
also thicker than its inner end; thus J is thicker and deeper than end K
of the tooth. Lines F G, representing the top and bottom of a tooth in
Figure 243, obviously correspond to dotted lines _p_ in Figure 242. The
outer and inner ends of the teeth in the edge view are projected from
the outer and inner ends in the face view, as is shown by the dotted
lines carried from tooth L in the face view, to tooth L in the edge
view, and it is obvious from what has been said that in drawing the
lines for the tooth in the edge view they will point to the centre E.

[Illustration: Fig. 245.]

To save work in drawing bevil gear wheels, they are sometimes drawn in
section or in outline only; thus in Figure 244 is shown a pair of bevil
wheels shown in section, and in Figure 245 is a drawing of a part of an
Ames lathe feed motion. B C D and E are spur gears, while G H and I are
bevil gears, the cone surface on which the teeth lie being left blank,
save at the edges where a tooth is in each case drawn in. Wheel D is
shown in section so as to show the means by which it may be moved out of
gear with C and E. Small bevil gears may also be represented by simple
line shading; thus in Figure 247 the two bodies A and C would readily be
understood to be a bevil gear and pinion. Similarly small spur wheels
may be represented by simple circles in a side view and by line shading
in an edge view; thus it would answer every practical purpose if such
small wheels as in Figures 246 and 247 at D, F, G, K, P, H, I and J,
were drawn as shown. The pitch circles, however, are usually drawn in
red ink to distinguish them.

[Illustration: Fig. 251. (Page 209.)]

[Illustration: Fig. 246.]

[Illustration: Fig. 247.]

In Figure 248 is an example in which part of the gear is shown with
teeth in, and the remainder is illustrated by circles.

In Figure 250 is a drawing of part of the feed motions of a Niles Tool
Works horizontal boring mill, Figure 251 being an end view of the same,
_f_ is a friction disk, and _g_ a friction pinion, _g'_ is a rack, F is
a feed-screw, _p_ is a bevil pinion, and _q_ a bevil wheel; _i_, _m_,
_o_, are gear wheels, and _J_ a worm operating a worm-pinion and the
gears shown.

Figure 249 represents three bevil gears, the upper of which is line
shaded, forming an excellent example for the student to copy.

[Illustration: Fig. 248.]

The construction of oval gearing is shown in Figures 252, 253, 254, 255,
and 256. The pitch-circle is drawn by the construction for drawing an
ellipse that was given with reference to Figure 81, but as that
construction is by means of arcs of circles, and therefore not strictly
correct, Professor McCord, in an article on elliptical gearing, says,
concerning it and the construction of oval gearing generally, as
follows:

[Illustration: Fig. 249. (Page 210.)]

[Illustration: Fig. 250.]

[Illustration: Fig. 252.]

"But these circular arcs may be rectified and subdivided with great
facility and accuracy by a very simple process, which we take from Prof.
Rankine's "Machinery and Mill Work," and is illustrated in Figure 252.
Let O B be tangent at O to the arc O D, of which C is the centre. Draw
the chord D O, bisect it in E, and produce it to A, making O A=O E; with
centre A and radius A D describe an arc cutting the tangent in B; then O
B will be very nearly equal in length to the arc O D, which, however,
should not exceed about 60 degrees; if it be 60 degrees, the error is
theoretically about 1/900 of the length of the arc, O B being so much
too short; but this error varies with the fourth power of the angle
subtended by the arc, so that for 30 degrees it is reduced to 1/16 of
that amount, that is, to 1/14400. Conversely, let O B be a tangent of
given length; make O F=1/4 O B; then with centre F and radius F B
describe an arc cutting the circle O D G (tangent to O B at O) in the
point D; then O D will be approximately equal to O B, the error being
the same as in the other construction and following the same law.

[Illustration: Fig. 253.]

The extreme simplicity of these two constructions and the facility with
which they may be made with ordinary drawing instruments make them
exceedingly convenient, and they should be more widely known than they
are. Their application to the present problem is shown in Figure 253,
which represents a quadrant of an ellipse, the approximate arcs C D, E,
E F, F A having been determined by trial and error. In order to space
this off, for the positions of the teeth, a tangent is drawn at D, upon
which is constructed the rectification of D C, which is D G, and also
that of D E in the opposite direction, that is, D H, by the process just
explained. Then, drawing the tangent at F, we set off in the same manner
F I = F E, and F K = F A, and then measuring H L = I K, we have finally
G L, equal to the whole quadrant of the ellipse.

[Illustration: Fig. 254.]

Let it now be required to lay out twenty-four teeth upon this ellipse;
that is, six in each quadrant; and for symmetry's sake we will suppose
that the centre of one tooth is to be at A, and that of another at C,
Figure 253. We, therefore, divide L G into six equal parts at the points
1, 2, 3, etc., which will be the centres of the teeth upon the rectified
ellipse. It is practically necessary to make the spaces a little greater
than the teeth; but if the greatest attainable exactness in the
operation of the wheels is aimed at, it is important to observe that
backlash, in elliptical gearing, has an effect quite different from that
resulting in the case of circular wheels. When the pitch-curves are
circles, they are always in contact; and we may, if we choose, make the
tooth only half the breadth of the space, so long as its outline is
correct. When the motion of the driver is reversed, the follower will
stand still until the backlash is taken up, when the motion will go on
with a perfectly constant velocity ratio as before. But in the case of
two elliptical wheels, if the follower stand still while the driver
moves, which must happen when the motion is reversed if backlash exists,
the pitch-curves are thrown out of contact, and, although the continuity
of the motion will not be interrupted, the velocity ratio will be
affected. If the motion is never to be reversed, the perfect law of the
velocity ratio due to the elliptical pitch-curve may be preserved by
reducing the thickness of the tooth, not equally on each side, as is
done in circular wheels, but wholly on the side not in action. But if
the machine must be capable of acting indifferently in both directions,
the reduction must be made on both sides of the tooth: evidently the
action will be slightly impaired, for which reason the backlash should
be reduced to a minimum. Precisely what _is_ the minimum is not so easy
to say, as it evidently depends much upon the excellence of the tools
and the skill of the workman. In many treatises on constructive
mechanism it is variously stated that the backlash should be from
one-fifteenth to one-eleventh of the pitch, which would seem to be an
ample allowance in reasonably good castings not intended to be finished,
and quite excessive if the teeth are to be cut; nor is it very obvious
that its amount should depend upon the pitch any more than upon the
precession of the equinoxes. On paper, at any rate, we may reduce it to
zero, and make the teeth and spaces equal in breadth, as shown in the
figure, the teeth being indicated by the double lines. Those upon the
portion L H are then laid off upon K I, after which these divisions are
transferred to the ellipse by the second of Prof. Rankine's
constructions, and we are then ready to draw the teeth.

The outlines of these, as of any other teeth upon pitch-curves which
roll together in the same plane, depend upon the general law that they
must be such as can be marked out upon the planes of the curves, as they
roll by a tracing-point, which is rigidly connected with and carried by
a third line, moving in rolling contact with both the pitch-curves. And
since under that condition the motion of this third line, relatively to
each of the others, is the same as though it rolled along each of them
separately while they remained fixed, the process of constructing the
generated curves becomes comparatively simple. For the describing line
we naturally select a circle, which, in order to fulfil the condition,
must be small enough to roll within the pitch ellipse; its diameter is
determined by the consideration that if it be equal to A P, the radius
of the arc A F, the flanks of the teeth in that region will be radial.
We have, therefore, chosen a circle whose diameter, A B, is
three-fourths of A P, as shown, so that the teeth, even at the ends of
the wheels, will be broader at the base than on the pitch line. This
circle ought strictly to roll upon the true elliptical curve; and
assuming, as usual, the tracing-point upon the circumference, the
generated curves would vary slightly from true epicycloids, and no two
of those used in the same quadrant of the ellipse would be exactly
alike. Were it possible to divide the ellipse accurately, there would be
no difficulty in laying out these curves; but having substituted the
circular arcs, we must now roll the generating circle upon these as
bases, thus forming true epicycloidal teeth, of which those lying upon
the same approximating arc will be exactly alike. Should the junction of
two of these arcs fall within the breadth of a tooth, as at D, evidently
both the face and the flank on one side of that tooth will be different
from those on the other side; should the junction coincide with the edge
of a tooth, which is very nearly the case at F, then the face on that
side will be the epicycloid belonging to one of the arcs, its flank a
hypocycloid belonging to the other; and it is possible that either the
face or the flank on one side should be generated by the rolling of the
describing circle partly on one arc, partly on the one adjacent, which,
upon a large scale, and where the best results are aimed at, may make a
sensible change in the form of the curve.

The convenience of the constructions given in Figure 252 is nowhere
more apparent than in the drawing of the epicycloids, when, as in the
case in hand the base and generating circles may be of incommensurable
diameters; for which reason we have, in Figure 254, shown its
application in connection with the most rapid and accurate mode yet
known of describing those curves. Let C be the centre of the base
circle; B, that of the rolling one; A, the point of contact. Divide the
semi-circumference of B into six equal parts at 1, 2, 3, etc.; draw the
common tangent at A, upon which rectify the arc A 2 by process No. 1;
then by process No. 2 set out an equal arc A 2 on the base circle, and
stepping it off three times to the right and left, bisect these spaces,
thus making subdivisions on the base circle equal in length to those on
the rolling one. Take in succession as radii the chords A 1, A 2, A 3,
etc., of the describing circle, and with centres 1, 2, 3, etc., on the
base circle, strike arcs either externally or internally, as shown
respectively on the right and left; the curve tangent to the external
arcs is the epicycloid, that tangent to the internal ones the
hypocycloid, forming the face and flank of a tooth for the base circle.

[Illustration: Fig. 255.]

In the diagram, Figure 253, we have shown a part of an ellipse whose
length is ten inches, and breadth six, the figure being half size. In
order to give an idea of the actual appearance of the combination when
complete, we show in Figure 255 the pair in gear, on a scale of three
inches to the foot. The excessive eccentricity was selected merely for
the purpose of illustration. Figure 255 will serve also to call
attention to another serious circumstance, which is, that although the
ellipses are alike, the wheels are not; nor can they be made so if there
be an even number of teeth, for the obvious reason that a tooth upon one
wheel must fit into a space on the other; and since in the first wheel,
Figure 255, we chose to place a tooth at the extremity of each axis, we
must in the second one place there a space instead; because at one time
the major axes must coincide; at another, the minor axes, as in Figure
255. If, then, we use even numbers, the distribution, and even the forms
of the teeth, are not the same in the two wheels of the pair. But this
complication may be avoided by using an odd number of teeth, since,
placing a tooth at one extremity of the major axes, a space will come at
the other.

It is not, however, always necessary to cut teeth all round these
wheels, as will be seen by an examination of Figure 256, C and D being
the fixed centres of the two ellipses in contact at P. Now P must be on
the line C D, whence, considering the free foci, we see that P B is
equal to P C, and P A to P D; and the common tangent at P makes equal
angles with C P and P A, as is also with P B and P D; therefore, C D
being a straight line, A B is also a straight line and equal to C D. If
then the wheels be overhung, that is, fixed on the ends of the shafts
outside the bearings, leaving the outer faces free, the moving foci may
be connected by a rigid link A B, as shown.

[Illustration: Fig. 256.]

This link will then communicate the same motion that would result from
the use of the complete elliptical wheels, and we may therefore
dispense with the most of the teeth, retaining only those near the
extremities of the major axes, which are necessary in order to assist
and control the motion of the link at and near the dead-points. The arc
of the pitch-curves through which the teeth must extend will vary with
their eccentricity; but in many cases it would not be greater than that
which in the approximation may be struck about one centre; so that, in
fact, it would not be necessary to go through the process of rectifying
and subdividing the quarter of the ellipse at all, as in this case it
can make no possible difference whether the spacing adopted for the
teeth to be cut would "come out even" or not, if carried around the
curve. By this expedient, then, we may save not only the trouble of
drawing, but a great deal of labor in making, the teeth round the whole
ellipse. We might even omit the intermediate portions of the pitch
ellipses themselves; but as they move in rolling contact their retention
can do no harm, and in one part of the movement will be beneficial, as
they will do part of the work; for if, when turning, as shown by the
arrows, we consider the wheel whose axis is D as the driver, it will be
noted that its radius of contact, C P, is on the increase; and so long
as this is the case the other wheel will be compelled to move by contact
of the pitch lines, although the link be omitted. And even if teeth be
cut all round the wheels, this link is a comparatively inexpensive and a
useful addition to the combination, especially if the eccentricity be
considerable. Of course the wheels shown in Figure 255 might also have
been made alike, by placing a tooth at one end of the major axis and a
space at the other, as above suggested. In regard to the variation in
the velocity ratio, it will be seen, by reference to Figure 256, that if
D be the axis of the driver, the follower will in the position there
shown move faster, the ratio of the angular velocities being P x D/P x
B; if the driver turn uniformly, the velocity of the follower will
diminish, until at the end of half a revolution, the velocity ratio will
be P x B/P x D; in the other half of the revolution these changes will
occur in a reverse order. But P D = L B; if then the centres B D are
given in position, we know L P, the major axis; and in order to produce
any assumed maximum or minimum velocity ratio, we have only to divide L
P into segments whose ratio is equal to that assumed value, which will
give the foci of the ellipse, whence the minor axis may be found and the
curve described. For instance, in Figure 255 the velocity ratio being
nine to one at the maximum, the major axis is divided into two parts, of
which one is nine times as long as the other; in Figure 256 the ratio is
as one to three, so that the major axis being divided into four parts,
the distance A C between the foci is equal to two of them, and the
distance of either focus from the nearest extremity of the major axis is
equal to one, and from the more remote extremity is equal to three of
these parts.




CHAPTER XII.

_PLOTTING MECHANICAL MOTIONS._


[Illustration: Fig. 257.]

Let it be required to find how much motion an eccentric will give to its
rod, the distance from the centre of its bore to the centre of the
circumference, which is called the throw, being the distance from A to B
in Figure 257. Now as the eccentric is moved around by the shaft, it is
evident that the axis of its motion will be the axis A of the shaft.
Then from A as a centre, and with radius from A to C, we draw the dotted
circle D, and from E to F will be the amount of motion of the rod in the
direction of the arrow.

This becomes obvious if we suppose a lead pencil to be placed against
the eccentric at E, and suppose the eccentric to make half a revolution,
whereupon the pencil will be pushed out to F. If now we measure the
distance from E to F, we shall find it is just twice that from A to B.
We may find the amount of motion, however, in another way, as by
striking the dotted half circle G, showing the path of motion of B, the
diameter of this path of motion being the amount of lateral motion given
to the rod.

[Illustration: Fig. 258.]

In Figure 258 is a two arm lever fast upon the same axis or shaft, and
it is required to find how much a given amount of motion of the long arm
will move the short one. Suppose the distance the long arm moves is to
A. Then draw the line B from A to the axis of the shaft, and the line C
the centre line of the long arm. From the axis of the shaft as a centre,
draw the circle D, passing through the eye or centre E of the short arm.
Take the radius from F to G, and from E as a centre mark it on D as at
H, and H is where E will be when the long arm moves to A. We have here
simply decreased the motion in the same proportion as one arm is shorter
than the other. The principle involved is to take the motion of both
arms at an equal distance from their axis of motion, which is the axis
of the shaft S.

[Illustration: Fig. 259.]

In Figure 259 we have a case in which the end of a lever acts directly
upon a shoe. Now let it be required to find how much a given motion of
the lever will cause the shoe to slide along the line _x_; the point H
is here found precisely as before, and from it as a centre, the dotted
circle equal in diameter to the small circle at E is drawn from the
perimeter of the dotted circle, a dotted line is carried up and another
is carried up from the face of the shoe. The distance K between these
dotted lines is the amount of motion of the shoe.

In Figure 260 we have the same conditions as in Figure 259, but the
short arm has a roller acting against a larger roller R. The point H is
found as before. The amount of motion of R is the distance of K from J;
hence we may transfer this distance from the centre of R, producing the
point P, from which the new position may be marked by a dotted circle as
shown.

[Illustration: Fig. 260.]

In Figure 261 a link is introduced in place of the roller, and it is
required to find the amount of motion of rod R. The point H is found as
before, and then the length from centre to centre of link L is found,
and with this radius and from H as a centre the arc P is drawn, and
where P intersects the centre line J of R is the new position for the
eye or centre Q of R.

[Illustration: Fig. 261.]

In Figure 262 we have a case of a similar lever actuating a plunger in a
vertical line, it being required to find how much a given amount of
motion of the long arm will actuate the plunger. Suppose the long arm to
move to A, then draw the lines B C and the circle D. Take the radius or
distance F, G, and from E mark on D the arc H. Mark the centre line J of
the rod. Now take the length from E to I of the link, and from H as a
centre mark arc K, and at the intersection of K with J is where the eye
I will be when the long arm has moved to A.

[Illustration: Fig. 262.]

In Figure 263 are two levers upon their axles or shafts S and S'; arm A
is connected by a link to arm B, and arm C is connected direct to a rod
R. It is required to find the position of centre G of the rod eye when D
is in position E, and when it is also in position F. Now the points E
and F are, of course, on an arc struck from the axis S, and it is
obvious that in whatever position the centre H may be it will be
somewhere on the arc I, I, which is struck from the centre S'. Now
suppose that D moves to E, and if we take the radius D, H, and from E
mark it upon the arc I as at V, then H will obviously be the new
position of H. To find the new position of G we first strike the arc J,
J, because in every position of G it will be somewhere on the arc J, J.
To find where that will be when H is at V, take the radius H, G, and
from V as a centre mark it on J, J, as at K, which is the position of G
when D is at E and H is at V. For the positions when D is at F we repeat
the process, taking the radius D, H, and from F marking P, and with the
radius H, G, and from P as a centre marking Q; then P is the new
position for H, and Q is that for G.

[Illustration: Fig. 263.]

In Figure 264 a lever arm A and cam C are in one piece on a shaft. S is
a shoe sliding on the line _x_, and held against the cam face by the rod
R; it is required to find the position of the face of the shoe against
the cam when the end of the arm is at D.

Draw line E from D to the axis of the shaft and line F. From the shaft
axis as a centre draw circle W; draw line J parallel to _x_. Take the
radius G H, and from K as a centre mark point P on W; draw line Q from
the shaft axis through P, and mark point T. From the shaft axis as a
centre draw from T an arc, cutting J at V, and V is the point where the
face of the shoe and the face of the cam will touch when the arm stands
at D.

[Illustration: Fig. 264.]

Let it be required to find the amount of motion imparted in a straight
line to a rod attached to an eccentric strap, and the following
construction may be used. In Figure 265 let A represent the centre of
the shaft, and, therefore, the axis about which the eccentric revolves.
Let B represent the centre of the eccentric, and let it be required to
find in what position on the line of motion _x_, the centre C of the rod
eye will be when the centre B of the eccentric has moved to E. Now since
A is the axis, the centre B of the eccentric must rotate about it as
denoted by the circle D, and all that is necessary to find the position
of C for any position of eccentric is to mark the position of B on
circle D, as at E, and from that position, as from E, as a centre, and
with the length of the rod as a radius, mark the new position of C on
the line _x_ of its motion. With the centre of the eccentric at B, the
line Q, representing the faces of the straps, will stand at a right
angle to the line of motion, and the length of the rod is from B to C;
when the eccentric centre moves to E, the centre line of the rod will be
moved to position P, the line Q will have assumed position R, and point
C will have moved from its position in the drawing to G on line _x_. If
the eccentric centre be supposed to move on to F, the point C will move
to H, the radii B C, E G, and F H all being equal in length. Now when
the eccentric centre is at E it will have moved one-quarter of a
revolution, and yet the point C will only have moved to G, which is not
central between C and H, as is denoted by the dotted half circle I.

[Illustration: Fig. 265.]

On the other hand, while the eccentric centre is moving from E to F,
which is but one-quarter of a revolution, the rod end will move from G
to H. This occurs because the rod not only moves _endwise_, but the end
connected to the eccentric strap moves towards and away from the line
_x_. This is shown in the figure, the rod centre line being marked in
full line from B to _x_. And when B has moved to E, the rod centre line
is marked by dotted line E, so that it has moved away from the line of
motion B _x_. In Figure 266 the eccentric centre is shown to stand at an
angle of 45 degrees from line _q_, which is at a right angle to the line
of motion _x x_, and the position of the rod end is shown at C, J and H
representing the extremes of motion, and G the centre of the motion.

[Illustration: Fig. 266.]

If now we suppose the eccentric centre to stand at T, which is also an
angle of 45 degrees to _q_, then the rod end will stand at K, which is
further away from G than C is; hence we find that on account of the
movement of the rod out of the straight end motion, the motion of the
rod end becomes irregular in proportion to that of the eccentric, whose
action in moving the eye C of the rod in a straight line is increased
(by the rod) while it is moving through the half rotation denoted by V
in figure, and diminished during the other half rotation.

In many cases, as, for example, on the river steamboats in the Western
and Southern States, cams are employed instead of eccentrics, and the
principles involved in drawing or marking out such cams are given in the
following remarks, which contain the substance of a paper read by Lewis
Johnson before the American Society of Mechanical Engineers. In Figure
267 is a side view of a pair of cams; one, C, being a full stroke cam
for operating the valve that admits steam to the engine cylinder; and
the other, D, being a cam to cut off the steam supply at the required
point in the engine stroke. The positions of these cams with relation to
the position of the crank-pin need not be commented upon here, more than
to remark that obviously the cam C must operate to open the steam inlet
valve in advance of cam D, which operates to close it and cause the
steam to act expansively in the cylinder, and that the angle of the
throw line of the cut-off valve D to the other cam or to the crank-pin
varies according as it is required to cut off the steam either earlier
or later in the stroke.

[Illustration: Fig. 267.]

The cam yoke is composed of two halves, Y and Y', bolted together by
bolts B, which have a collar at one end and two nuts at the other end,
the inner nuts N N enabling the letting together of the two halves
of the yoke to take up the wear. It is obvious that as the shaft
revolves and carries the cam with it, it will, by reason of its shape,
move the yoke back and forth; thus, in the position of the parts shown
in Figure 267, the direction of rotation being denoted by the arrow, cam
C will, as it rotates, move the yoke to the left, and this motion will
occur from the time corner _a_ of the cam meets the face of Y' until
corner _b_ has passed the centre line _d_. Now since that part of the
circumference lying between points _a_ and _b_ of the cam is an arc of a
circle, of which the axis of the shaft is the centre, the yoke will
remain at rest until such time as _b_ has passed line _d_ and corner _a_
meets the jaw Y of the yoke; hence the period of rest is determined by
the amount of circumference that is made concentric to the shaft; or, in
other words, is determined by the distance between _a_ and _b_.

The object of using a cam instead of an eccentric is to enable the
opening of the valves abruptly at the beginning of the piston stroke,
maintaining a uniform steam-port opening during nearly the entire length
of stroke, and as abruptly closing the valves at the termination of the
stroke.

Figure 268 is a top view of the mechanism in Figure 267; and Figure 269
shows an end view of the yoke. At B, in Figure 268, is shown a guide
through which the yoke-stem passes so as to be guided to move in a
straight line, there being a guide of this kind on each side of the
yoke.

[Illustration: Fig. 268.]

The two cams are bolted to a collar that is secured to the crank-shaft,
and are made in halves, as shown in the figures and also in Figures 270
and 271, which represent cams removed from the other mechanism. To
enable a certain amount of adjustment of the cams upon the collar, the
bolts which hold them to the collar fit closely in the holes in the
collar, but the cams are provided with oblong bolt holes as shown, so
that the position of either cam, either with relation to the other cam
or with relation to the crank-pin, can be adjusted to the extent
permitted by the length of the oblong holes.

[Illustration: Fig. 269.]

The crank is assumed in the figures to be on its dead centre nearest to
the engine cylinder, and to revolve in the direction of the arrows. The
cams are so arranged that their plain unflanged surfaces bolt against
the collar.

The method of drawing or marking out a full stroke cam, such as C in
Figure 267, is illustrated in Figure 272, in which the dimensions are
assumed to be as follows:

Diameter of crank shaft, 7-1/2 inches; travel of cam, 3 inches; width of
yoke, 18 inches.

[Illustration: Fig. 270.]

The circumference of the cam is composed of four curved lines, P, P', K
1, and K 2. The position of the centre of the crank shaft in this
irregularly curved body is at X. The arcs K 1 and K 2 differ in radius,
but are drawn from the same point, X, and hence are concentric with the
crank shaft.

The arcs P, P', are of like radius, but are drawn from the opposite
points S, S', shown at the intersection of the arcs P, P', with the
arc K 1. Thus arcs P, P', are eccentric to the crank shaft.

[Illustration: Fig. 271.]

[Illustration: Fig. 272.]

[Illustration: Fig. 273.]

To draw the cam place one point of the dividers at X, which is the
centre of the crank shaft, and draw the circle E equal to width of yoke,
18 inches. Through this centre X, draw the two right lines A and B. On
the line B, at the intersection of the curved line E, draw the two
vertical lines A 1, A 1. With a radius of 10-1/2 inches, and with one
point of the dividers at X, draw the arc K 1. With a radius of 7-1/2
inches, and one point of the dividers at X, draw the arc K 2. With a
radius of 18 inches, and one point of the dividers at the intersection
of the arc E, with the vertical line A 1 at S, draw the arc P opposite
to S, and let it merge or lose itself in the curved line K 2. Draw the
other curved line P' from the other point S, and we have a full stroke
cam of the dimensions required, and which is represented in Figure 273,
removed from the lines used in constructing it.

[Illustration: Fig. 274.]

The engravings from and including Figure 274 illustrate the lines
embracing cut-off cams of varying limits of cut-off, but all of like
travel and dimensions, which are the same as those given for the full
stroke cam in Figure 272.

In drawing cut-off cams, the stroke of the engine plays a part in
determining their conformation, and in the examples shown this is
assumed to be 4 feet. Figure 274 illustrates the manner of finding
essential points in drawing or marking out cut-off cams. With X as a
centre, and a radius of 2 feet, draw the circle E 1, showing the path of
the crank-pin in making a revolution. This circle has a diameter of 4
feet, equal to the stroke of the engine. Draw the horizontal line B,
passing through the centre of circle E 1. Within the limits of circle E
1, subdivide line B into eight equal parts, as at 1, 2, 3, 4, etc. Draw
the vertical lines, 1, 2, 3, 4, etc., until they each intersect the
circle E 1.

[Illustration: Fig. 275.]

With X as a centre, draw the circle E, having a diameter of 18 inches,
equal to the space in the yoke embracing the cam.

From the centre X draw the series of radial lines through the points of
intersection of the vertical lines 1, 2, 3, 4, etc., from the circle E
1, and terminating at X. We will now proceed to utilize the scale
afforded by Figure 274, in laying off the cut-off cam shown in Figure
276, of half stroke limit.

[Illustration: Fig. 276.]

With X as a centre, draw the circle E, Figure 275, having a diameter of
18 inches. Bisect this circle with the straight lines A and B, which
bear the same relation to their enclosing circle that the lines A, B,
do to the circle E in Figure 274.

[Illustration: Fig. 277.]

It will be observed, in Figure 274, that the vertical line A is (at the
top half) also No. 4, representing 4/8, or half of the stroke. With a
radius of 18 inches, and one point of the dividers placed at V, which is
at the intersection of the circle E with the horizontal line B in Figure
275, draw the arc P. With the same radius and with one compass point
rested at V', draw the arc P'; then two arcs, P and P', intersecting at
the point S.

With the same radius and one point of the compasses at S, draw the arc H
H. The arcs K 1 and K 2 are drawn from the centre X, with a radius of
10-1/2 for K 1 and 7-1/2 inches for K 2, and only serve in a half
stroke cam to intersect the curved lines already drawn, as shown in
Figure 275. In practice, the sharp corner at S would be objectionable,
owing to rapid wear at this point; and hence a modification of the
dimensions for this half stroke cam would be required to obtain a larger
wearing surface at the point S, but the cam of this limit (1/2 stroke)
is correctly drawn by the process described with reference to Figure
275, the outline of the cam so constructed being shown in Figure 276.

[Illustration: Fig. 278.]

In Figure 278 is shown a cam designed to cut off the steam at
five-eighths of the piston stroke, the construction lines being given
in Figure 277, for which draw circle E and straight lines A and B, as in
the preceding example. By reference to Figure 274 it will be observed
that the diagonal line drawn through circle E at 5 is drawn from the
straight line marked 5, which intersects circle E 1, and as this
straight line 5 represents five-eighths of the stroke laid off on line
B, it determines the limit of cut-off on the five-eighths cam in Figure
277.

[Illustration: Fig. 279.]

Turning then to Figure 274, take on circle E the radius from radial line
4 to radial line 5, and mark it in Figure 277 from the vertical line
producing V'.

Now, with a radius of 18 inches, and one point of the dividers fixed at
point V, forming the intersection of the circle E with the horizontal
line B, draw the arc P. With the same radius, and one point of the
dividers fixed at point V', draw the opposite arc P'. With a radius of
10-1/2 inches from the centre X, draw the arc K 1, intersecting lines P
P', at S S. With a radius of 7-1/2 inches, draw the curved line K 2,
opposite to curved line K 1. Now, with a radius of 18 inches, and one
point of the dividers fixed alternately at S S, draw the arcs H, H, from
their intersection with the circle E, until they merge into the curved
line K 2. These curved lines embrace a cut-off cam of five-eighths
limit, shown complete in Figure 278.

[Illustration: Fig. 280.]

From the instructions already given it should be easy to understand that
the three-fourths and seven-eighths cams, shown in Figures 279, 280, 281
and 282, are drawn by taking the points of their cut-off from the same
scale shown in Figure 274, at the diagonal points 6 and 7, intersecting
circle E in that figure; and cut-off cams of intermediate limit of
cut-off can be drawn by further subdividing the stroke line B, in Figure
274, into the required limits.

[Illustration: Fig. 281.]

Cut-off cams of any limit are necessarily imperfect in their operations
as to uniformity of cut-off from opposite ends of the slides, not from
any defect in the rule for laying them off, but from the well-known fact
of the crank pin travelling a greater distance, while driven by the
piston from the centre of the cylinder, through its curved path from the
cylinder, over its centre, and back to the centre of the cylinder, than
in accomplishing the remaining distance of its path in making a complete
revolution; and, although the subdivisions of eighths of the stroke
line B, in Figure 274, does not truly represent a like division of the
piston stroke, owing to deviation, caused by inclination of the
connecting rod in traversing from the centres to half stroke, still it
will be found that laying off a cut-off cam by this rule is more nearly
correct than if the divisions on stroke line B were made to correspond
exactly with a subdivision of piston stroke into eighths.

[Illustration: Fig. 282.]

The cut-off in cams laid off by the rules herein described is greater in
travelling from one side of the slides than in travelling from the
opposite end, one cut-off being more than the actual cut-off of piston
stroke, and the other less; and in practical use, owing to play or lost
motion in the connections from cam to valve, the actual cut-off is less
than the theoretical; hence cut-off cams are usually laid off to
compensate for lost motion; that is, laid off with more limit; for
instance, a five-eighths cam would be laid off to cut-off at
eleven-sixteenths instead of five-eighths.

[Illustration: Fig. 283.]

Figure 283 represents the motion a crank, C, imparts to a connecting
rod, represented by the thick line R, whose end, B, is supposed to be
guided to move in a straight line. The circle H represents the path of
the crank-pin, and dots 1, 2, 3, etc., are 24 different crank-pin
positions equidistant on the circle of crank-pin revolution. Suppose the
crank-pin to have moved to position 1, and with the compasses set to the
length of the rod R, we set one point on the centre of position 1, and
mark on the line of motion _m_ the line _a_, which will be the position
rod end B will have moved to. Suppose next that the crank-pin has moved
into position 2, and with the compass point on the centre of 2 we mark
line 2, showing that while the crank-pin moved from 1 to 2, the rod end
moved from _a_ to _b_; by continuing this process we are enabled to
discern the motion for the whole of the stroke. The backward stroke will
be the same, for corresponding crank-pin positions, for both strokes;
thus, when the rod end is at 7 the crank-pin may be at 7 or at 17. This
fact enables us to find the positions for the positions later than 6, on
the other side of the circle, as at 17, 16, 15, etc., which keeps the
engraving clear.

[Illustration: Fig. 284.]

In Figure 284 a pinion, P, drives a gear-wheel, D, on which there is a
pin driving the sliding die A in the link L, which is pivoted at C, and
connected at its upper end to a rod, R, which is connected to a bolt, B,
fast to a slide, S. It is required to find the motion of S, it moving in
a straight line, dotted circle H' representing the path of the pin in
the sliding die A, arc H representing the line of motion of the upper
end of link L, and lines N, O, its centre line at the extreme ends of
its vibrating motion. In Figure 285 the letters of reference refer to
the same parts as those in Figure 284. We divide the circle H' of pin
motion into 24 equidistant parts marked by dots, and through these we
draw lines radiating from centre, C, and cutting arc H, obtaining on the
arc H the various positions for end Z of rod R, these positions being
marked respectively 1, 2, 3, 4, etc., up to 24. With a pair of
compasses set to the length of rod R from 1 on H, as a centre, we mark
on the line of motion of the slide, line _a_, which shows where the
other end of rod R will be (or in other words, it shows the position of
bolt B in Figure 284), when the centre of A, Figure 284, is in position
1, Figure 285.

[Illustration: Fig. 285.]

From 2 on arc H, we mark with the compasses line _b_ on line M, showing
that while the pin moved from 1 to 2, the rod R would move slide S,
Figure 284, from _a_ to _b_, in Figure 285. From 3 we mark _c_, and so
on, all these marks being above the horizontal line M, representing the
line of motion, and being for the forward stroke. For the backward
stroke we draw the dotted line from position 17 up to arc H, and with
the compasses at 17 mark a line beneath the line M of motion, pursuing
the same course for all the other pin motions, as 18, 19, etc., until
the pin arrives again at position 24, and the link at O, and has made a
full revolution, and we shall have the motion of the forward stroke
above and that of the backward one below the line of motion of the
slide, and may compare the two.

[Illustration: Fig. 286.]

[Illustration: Fig. 287.]

[Illustration: Fig. 288.]

[Illustration: Fig. 289.]

Figures 286 and 287 represent the Whitworth quick return motion that is
employed in many machines. F represents a frame supporting a fixed
journal, B, on which revolves a gear-wheel, G, operated by a pinion, P.
At A is an arm having journal bearing in B at C. This arm is driven by a
pin, D, fast in the gear, G; hence as the gear revolves, pin D moves A
around on C as a centre of motion. A is provided with a slot carrying a
pin, X, on which is pivoted the rod, R. The motion of end N of the rod R
being in a straight line, M, it is required to find the positions of N
during twenty-four periods in one revolution of G. In Figure 288 let H'
represent the path of motion of the driving pin D, about the centre of
B, and H the path of motion of X about the centre C; these two centres
corresponding to the centres of B and C respectively, in Figure 287. Let
the line M correspond to the line of motion M in Figure 286. Now since
it is the pin D, Figure 287, that drives, and since its speed of
revolution is uniform, we divide its circle of motion H' into
twenty-four equal divisions, and by drawing lines radiating from centre
C, and passing through the lines of division on H' we get on circle H
twenty-four positions for the pin X in Figure 286. Then setting the
compasses to the length of the rod (R, Figure 286), we mark from
position 1 on circle H as a centre line, _a_; from position 2 on H we
mark line _b_, and so on for the whole twenty-four positions on circle
H, obtaining from _a_ to _n_ for the forward, and from _n_ to _y_ for
the motion during the backward stroke. Suppose now that the mechanism
remaining precisely the same as before, the line M of motion be in a
line with the centres C, B, instead of at a right angle to it, as it is
in Figure 286, and the motion under this new condition will be as in
Figure 289; the process for finding the amount of motion along M from
the motion around H being precisely as before.

[Illustration: Fig. 290.]

In Figure 290 is shown a cutter-head for a wood moulding machine, and it
is required to find what shape the cutting edge of the cutter must be
to form a moulding such as is shown in the end view of the moulding in
the figure. Now the line A A being at a right angle to the line of
motion of the moulding as it is passed beneath the revolving cutter, or,
what is the same thing, at a right angle to the face of the table on
which the moulding is moved, it is obvious that the highest point C of
the moulding will be cut to shape by the point C of the cutter; and that
since the line of motion of the end of the cutter is the arc D, the
lowest part of the cutter action upon the moulding will be at point E.
It will also be obvious that as the cutter edge passes, at each point,
its length across the line A A, it forms the moulding to shape, while
all the cutting action that occurs on either side of that line is
serving simply to remove material. All that we have to consider,
therefore, is the action on line A A.

It may be observed also that the highest point C of the cutter edge must
not be less than 1/4 inch from the corner of the cutter head, which
gives room for the nut N (that holds the cutter to the head) to pass
over the top of the moulding in a 2-1/2 inch head. In proportion as the
heads are made larger, however, less clearance is necessary for the nut,
as is shown in Figure 291, the cutter edge extending to C, and therefore
nearly up to the corner of the head. Its path of motion at C is shown by
dotted arc B, which it will be observed amply clears the nut N. In
practice, however, point C is not in any size of cutter-head placed
nearer than 1/4 inch from corner X of the cutter-head.

To find the length of the cutter edge necessary to produce a given depth
of moulding, we may draw a circle _i_, Figure 292, equal in diameter to
the size of the cutter head to be used, and line A A. The highest point
of cutting edge being at _e_, and the lowest at g, then circles _d_ and
_f_ represent the line of motion of these two points; and if we mark the
cutter in, the necessary length of cutting edge on the cutter is
obviously from _a_ to _b_.

[Illustration: Fig. 291.]

[Illustration: Fig. 292.]

Now the necessary depth of cutter edge being found for any given
moulding, or part of a moulding, the curves for the edge may be found as
follows: Suppose the moulding is to be half round, as in the end view in
Figure 290. The width of the cutter must of course equal the width of
the moulding, and the length or depth of cutting edge required may be
found from the construction shown in Figure 292; hence all that remains
is to find the curve for the cutting edge. In Figure 293, let A A
represent the centre of the cutter width, its sides being F F', and its
end B B. From centre C draw circle D, the upper half of which will serve
to represent the moulding. Mark on A the length or depth the cutting
edge requires to be, ascertaining the same from the construction shown
in Figure 292, and mark it as from C to K'. Then draw line E E, passing
through point K. Draw line G, standing at the same angle to A A as the
face _h b_, Figure 292, of the cutter does to the line A A, and draw
line H H, parallel to G. From any point on G, as at I, with radius J,
draw a quarter of a circle, as K. Mark off this quarter circle into
equal points of division, as by 1, 2, 3, etc., and from these points of
division draw lines, as _a_, _b_, _c_, etc.; and from these lines draw
horizontal lines _d_, _e_, _f_, etc. Now divide the lower half of circle
D into twice as many equal divisions as quarter circle K is divided
into, and from these points of division draw perpendiculars _g_, _h_,
_i_, etc. And where these perpendiculars cross the horizontal lines, as
_d_, will be points through which the curve may be drawn, three of such
points being marked by dots at _p_, _q_, _r_. If the student will, after
having drawn the curve by this construction, draw it by the construction
that was explained in connection with Figure 79, he will find the two
methods give so nearly identical curves, that the latter and more simple
method may be used without sensible error.

[Illustration: Fig. 293.]

[Illustration: Fig. 294.]

When the curves of the moulding are not arcs of circles they may be
marked as follows:

Take the drawing of the moulding and divide each member or step of it by
equidistant lines, as _a_, _b_, _c_, _d_, _e_, _f_, _g_, in Figure 294;
above the moulding draw lines representing the cutter, and having found
the depth of cutting edge for each member by the construction shown in
Figure 292, finding a separate line, _a b_, for each member of the
moulding, transfer the depths so found to the face of the cutter; divide
the depth of each member of the cutter into as many equal divisions as
the corresponding member of the moulding is divided into, as by lines
_h_, _i_, _j_, _k_, _l_, _m_, _n_. Then draw vertical lines, as _o_,
_p_, _q_, _r_, etc.; and where these lines meet the respective lines
_h_, _i_, _j_, etc., are points in the curve, such points being marked
on the cutter by dots.




CHAPTER XIII.

_EXAMPLES IN LINE-SHADING AND DRAWINGS FOR LINE-SHADED ENGRAVINGS._


Although in workshop drawings, line-shading is rarely employed, yet
where a design rather than the particular details of construction is to
be shown, line-shading is a valuable accessory. Figure 295, for example,
is intended to show an arrangement of idle pulleys to guide belts from
one pulley to another; the principle being that so long as the belt
passes to a pulley moving in line with the line of rotation of the
pulley, the belt will run correctly, although it may leave the pulley at
considerable angle. When a belt envelops two pulleys that are at a right
angle to each other, two guide pulleys are needed in order that the belt
may, in passing to each pulley, move in the same plane as the pulley
rotates in, and the belt is in this case given what is termed a quarter
twist.

It will be observed that by the line-shading even the twist of the belt
is much more clearly shown than it would be if left unshaded.

An excellent example of shading is given in Figure 296, which is
extracted from the _American Machinist_, and represents a cutting tool
for a planing machine. The figure is from a wood engraving, but the
effect may be produced by lines, the black parts being considered as
simply broad black lines.

[Illustration: Fig. 295.]

The drawings from which engravings are made are drawn to conform to the
process by which the engraving is to be produced. Drawings that are
shaded by plain lines may be engraved by three methods. First, the
drawing may be photo-engraved, in which process the drawing is
photographed on the metal, and every line appears in the engraving
precisely as it appears in the drawing.

[Illustration: Fig. 296.]

For this kind of engraving the drawing may be made of any convenient
size that is larger than the size of engraving to be produced, the
reduction of size being produced in the photographing process. Drawings
for photo-engraving require to have the lines jet black, and it is to
be remembered that if red centrelines are marked on the drawing, they
will be produced as ordinary black lines in the engraving.

The shading on a drawing to be photo-engraved must be produced by lines,
and not by tints, for tints, whether of black or of colors, will not
photo-engrave properly.

It is generally preferred to make the drawing for a photo-engraving
larger than the engraving that is to be made from it, a good proportion
being to make the drawing twice the length the engraving is to be. This
serves to reduce the magnitude of any roughness in the lines of the
drawing, and, therefore, to make the engraving better than the drawing.

The thickness of the lines in the drawing should be made to suit the
amount of reduction to be made, because the lines are reduced in
thickness in the same proportion as the engraving is reduced from the
drawing. Thus the lines on an engraving reduced to one-half the
dimensions of the drawing would be one-half as thick as the lines on the
drawing.

Drawings for photo-engraving should be made on smooth-faced paper; as,
for example, on Bristol board; and to make the lines clean and clear,
the drawing instruments should be in the best of condition, and the
paper or Bristol board quite dry. The India rubber should be used as
little as possible on drawings to be photo-engraved, because, if used
before the lines are inked in, it roughens the surface of the paper, and
the inking lines will be less smooth and even at their edges; and for
this reason it is better not to rub out any lines until all the lines
have been inked in. If used to excess after the lines have been inked in
it serves to reduce the blackness of the lines, and may so pale them
that they will not properly photo-engrave.

To make a drawing for an engraver in wood it would be drawn directly on
the face of the box-wood block, on which it is to be engraved. The
surface of the block is first whitened by a white water color, as
Chinese white. If the drawing that is to be used as a copy is on
sufficiently thin paper, its outline may be traced over by pencil lines,
and the copy may then be laid face down on the wood block and its edges
held to the block by wax, the pencilled lines being face to the block.
The outline may then be again traced over with a pencil or pointed
instrument, causing the imprint of the lead pencil lines to be left on
the whitened surface of the block. If the copy is on paper too thick to
be thus employed, a tracing may be made and used as above; it being
borne in mind that the tracing must be laid with the pencilled lines on
the block, because what is the right hand of the drawing on the block is
the left hand in the print it gives. The shading on wood blocks is given
by tints of India ink aided by pencilled lines, or of course pencilled
lines only may for less artistic work be used. Another method is to
photograph the drawing direct upon the surface of the wood block; it is
unnecessary, however, to enter into this part of the subject.

The third method of producing an engraving from a drawing is by means of
what is known as the wax process. Drawings for this process should be
made on thin paper, for the following reasons: The process consists,
briefly stated, in coating a copper plate with a layer of wax about 1/32
inch deep, and in drawing upon the wax the lines to compose the
engraving, which lines are produced by means of tools that remove the
wax down to the surface of the copper.

The plate and wax are then placed in a battery and a deposit of copper
fills in the lines and surface of the wax, thus forming the engraving.
Now if the drawing is made on thin paper, the engraver coats the surface
of the drawing with a dry red pigment, and with a pointed instrument
traces over the lines of the drawing, which causes them to leave a red
imprint on the surface of the wax, and after the drawing is removed the
engraver cuts these imprinted lines in the wax. If the drawing is on
thick paper, this method of transferring the drawing to the wax cannot
be used, and the engraver may take a tracing from the drawing and
transfer from the tracing to the wax. It is obvious, also, that for wax
engravings the drawing should be made of the same size that the
engraving is required to be, or otherwise the tracing process described
cannot be used. Figure 297 represents an engraving made by the wax
process from a print from a wood engraving, and it is obvious that since
all the lines drawn on the wax sink down to the surface of the copper
plate, the shading is virtually composed of lines, the black surfaces
being where the lines have been sufficiently close together and broad to
remove all the wax enclosed within those surfaces.

[Illustration: Fig. 297.]

[Illustration: Fig. 298.]

The wax process is, however, more suitable for engravings in plain
outline only, and is especially excellent when the parts are small and
the lines fall close together; as, for example, in Figures 298 and 299,
which are engravings of a boiler drilling machine, and were produced
for the _American Machinist_ by tracing over a wood engraving from
London, "Engineering" in the manner already described. The fineness and
cleanness of the lines in the wax process is here well illustrated, the
disposition of the parts being easily seen from the engraving, and
easily followed in connection with the following description:

The machine consists of two horizontal bed-plates A 1 and A 2, made with
$V$ slides on top, and placed at right angles to each other. Upon each
of the bed-plates is fitted a vertical arm B 1 and B 2, each of which
carries two saddles, C 1 and C 2, these being each adjustable vertically
on its respective arm by means of rack and pinion and hand wheels D 1
and D 2. The saddles are balanced so that the least possible exertion is
sufficient to adjust them. The vertical arms, B 1 and B 2, are cast each
with a round foot by which the arms are attached to the square boxes E 1
and E 2, which are fitted to the $V$ slides on the horizontal beds A 1
and A 2, and are adjustable thereon by means of screw and ratchet motion
F 1 and F 2. Each of the square boxes has cast on it a small arm G 1 and
G 2, carrying studs upon which run pinions gearing into the circular
racks at the foot of the vertical arms. The square boxes have each a
circular groove turned in the top to receive the bolts by which the
vertical arms are connected to them, and thus the vertical arms, and
with them the drill spindles N 1 and N 2, are adjustable radially with
the boiler--the adjustment being effected by means of the pinions and
circular racks. The pinions are arranged so that they can be worked with
the same screw key that is used for the bolts in the circular grooves.

The shell to be drilled is placed upon the circular table H, which is
carried by suitable framework adjustable by means of screw on a $V$
slide I, placed at an angle of 45 deg. with the horizontal bed-plates. By
this arrangement, when the table is moved along I, it will approach to
or recede from all the drills equally. J 1 and J 2 are girders forming
additional bearings for the framework of the table. The bed-plates and
slides for the table are bolted and braced together, making the whole
machine very firm and rigid. Power is applied to the machine through the
cones K 1 and K 2, working the horizontal and vertical shafts L 1 and L
2, etc. On the vertical shafts are fitted coarse pitch worms sliding on
feather keys, and carried with the saddles C 1 and C 2, etc. The worms
gearing with the worm wheels M 1 and M 2 are fitted on the sleeves of
the steel spindles N 1 and N 2. The spindles are fitted with self-acting
motions O 1 and O 2, which are easily thrown in and out of gear.

The machine is also used for turning the edge of the flanges which some
makers prefer to have on the end plates of marine boilers. The plates
are very readily fixed to the circular table H, and the edge of the
flange trued up much quicker than by the ordinary means of chipping.
When the machine is used for this purpose, the cross beam P, which is
removable, is fastened to the two upright brackets R 1 and R 2. The
cross beam is cast with $V$ slides at one side for a little more than
half its length from one end, and on the opposite side for the same
length, but from the opposite end. The $V$ slides are each fitted with a
tool box S 1 and S 2, having a screw adjustment for setting the tool to
the depth of cut, and adjustable on the $V$ slides of the cross beam to
the diameter of the plate to be turned. This arrangement of the machine
is also used for cutting out the furnace mouths in the boiler ends. The
plate is fastened to the circular table, the centre of the hole to be
cut out being placed over the centre of table; one or both of the tool
boxes may be used. There is sufficient space between the upright
brackets R 1 and R 2, to allow that section of a boiler end which
contains the furnace mouths to revolve while the holes are being cut
out; the plate belonging to the end of a boiler of the largest diameter
that the machine will take in for drilling. The holes cut out will be
from 2 feet 3 inches in diameter and upwards. Power for using the
turntable is applied through the cone T. The bevel wheels, worms, worm
wheels, and pinions for driving the tables are of cast steel, which is
necessary for the rough work of turning the flanges.

[Illustration: Fig. 299. (Page 275.)]

As to the practical results of using the machine, the drills are driven
at a speed of 340 feet per minute at the cutting edges. A jet of
soapsuds plays on each drill from an orifice 1/32 in. in diameter, and
at a pressure of 60 lbs. per square inch. A joint composed of two 1-inch
plates, and having holes 1 and one-eighth in. in diameter, can be
drilled in about 2-1/2 minutes, and allowing about half a minute for
adjusting the drill, each drill will do about 20 holes per hour. The
machine is designed to stand any amount of work that the drills will
bear. The time required for putting on the end of a boiler and turning
the flange thereon (say 14 feet diameter) is about 2-1/2 hours;
much, however, depends on the state of the flanges, as sometimes
they are very rough, while at others very little is necessary to true
them up. The time required for putting on the plate containing the
furnace mouths and cutting out three holes 2 feet 6 in. in diameter, the
plate being 1 and one-eighth in. thick, is three hours. Of course, if
several boilers of one size are being made at the same time, the holes
in two or more of these plates can be cut out at once. The machine is of
such design that it can be placed with one of the horizontal bed-plates
(say A 1), parallel and close up to a wall of the boiler shop; and when
the turning apparatus is being used, the vertical arm B 2 can be
swiveled half way round on its square box E 2, and used for drilling and
tapping the stay holes in marine boiler ends after they are put
together; of course sufficient room must be left between bed-plate A 2,
and the wall of boiler shop parallel with it, to allow for reception of
the boiler to be operated upon.

It would obviously be quite difficult to draw such drawings as in
Figures 298 and 299 on thin paper, so as to enable the drawing to be
traced on the wax direct by the process before described, unless indeed
the draftsman had considerable experience in fine work; hence, it is not
uncommon to make the drawing large, and on ordinary drawing paper. The
engraver then has the drawing photographed on the surface of the wax,
and works to the photograph. The letters of reference in wax engravings
are put in by impressing type in the wax, and in this connection it may
be remarked that the letters I and O should not be used on drawings to
be engraved by the wax process, unless they are situated outside the
outlines of the drawing, because the I looks so much like part of a
dotted line that it is often indistinguishable therefrom, while the O
looks like a circle or an ellipse.




CHAPTER XIV.

_SHADING AND COLORING DRAWINGS._


The shading or coloring of drawings by tints is more employed in large
drawings than in small ones, and in Europe than in the United States;
while on the other hand tinting by means of line-shading is more
employed in the United States than in Europe, and more on small drawings
than on large ones.

Many draftsmen adopt the plan of coloring the journals of shafts, etc.,
with a light tint, giving them the deepest tint at the circumference to
give them a cylindrical appearance. This makes the drawing much clearer
and takes but little time to do, and is especially advantageous where
the parts are small or on a small scale, so that the lines are
comparatively close together.

For simple shading purposes black tints of various degrees of darkness
may be employed, but it is usual to tint brass work with yellow. Cast
iron with India ink, wrought iron with Prussian blue, steel with as
light purple tint produced by mixing India ink, Prussian blue and a
tinge of crimson lake. Copper is tinted red. On plane surfaces an even
tint of color is laid, but if the surfaces are cylindrical they are
usually  deeper at and near the circumference, and are tinted
over the colors with light tints of India ink to show their cylindrical
form.

If a drawing is to be  or shaded with India ink the paper should
be glued all around its edges to the drawing board, and then dampened
evenly all over with a sponge, which will cause the paper to shrink and
lay close to the surface of the drawing board. If, in applying a color
or a tint, the color dries before the whole surface is , the
color will not be of an equal shade; hence it is necessary before
applying the color to dampen the surface, if it is a large one, so that
the color at one part shall not get dry before there has been time to go
over the whole surface; a more even depth of color is attained by the
application of several coats of a light tint, than with one coat, giving
the full depth of color. But if the paper is not allowed to dry
sufficiently between the coats, or if it has been made too wet previous
to the application of the colors, it will run in places, leaving other
hollows into which the color will flow, making darker- spots. To
avoid this the paper may be dried somewhat by the application of clean
blotting paper.

To maintain an even shade of color, it is necessary to slightly stir up
the color each time the brush is dipped into the color saucer or
palette, especially when the coloring is composed of mixed colors,
because the coloring matter is apt to separate from the water and sink
to the bottom.

So, also, in mixing colors it is best to apply the end of the color to
the surface of the palette and not to apply the brush direct to the cake
of color, because the color is more completely mixed by contact with
the palette than it can be by the brush, which may retain a speck of
color that will, unless washed out, make a streak upon the drawing.

To graduate the depth of tint for a cylindrical surface, it is best to
mix several, as, say three depths or degrees of tint, and to first use
the darkest, applying it in the direction in which the piece is to be
shaded darkest. The width this dark application should be is obviously
determined by the diameter of the piece. The next operation is to
lighten or draw the part, line or streak thus dark , causing it
to get paler and paler as it approaches the axial line of the piece or
cylinder. This lightening is accomplished as follows: The dark streak is
applied along such a length of the piece that it will not dry before
there has been time to draw it out or lighten it on the side towards the
axis. A separate brush may then be wetted and drawn along the edge of
the dark streak in short strokes, causing the color to run outwards and
become lighter as it approaches the axis. It will be found that during
this process the brush will occasionally require washing in water,
because from continuous contact with the dark streak the tint it
contains will darken. When the first coat has been laid and spread or
drawn out from end to end of the piece, the process may be repeated two
or three times, the most even results being obtained by making the first
dark streak not too dark, and going over the drawing several times, but
allowing the paper to get very nearly dry between each coat. In small
cylindrical bodies, as, say 1/4 inch in diameter, the darkest line of
shadow may be located at the lines representing the diameter of the
piece, but in pieces of larger diameter the darkest line may be located
at a short distance from the line that denotes the diameter or perimeter
on the shadow or right-hand side of the piece, as is shown in many of
the engravings that follow. It is obvious that if a drawing is to have
dimensions marked on it, the coloring or tinting should not be deep
enough to make it difficult to see the dimension figures.

The size of the brush to be used depends, of course, upon the size of
the piece to be shaded or , and it is best to keep one brush for
the dark tint and to never let the brush dry with the tint in it, as
this makes it harsh. In a good brush the hairs are fine, lie close
together when moistened, are smooth and yet sufficiently stiff or
elastic to bend back slightly when the pressure is removed. If, when
under pressure and nearly dry, the hairs will separate or the brush has
no elasticity in it, good results cannot be obtained. All brushes should
be well dried after use.

The light in shading is supposed to come in at the left-hand corner of
the drawing, as was explained with reference to the shade line.

Excellent examples to copy and shade with the brush are given as
follows:

Figure 300 represents a Medart pulley, constructed by the Hartford Steam
Engineering Company; the arms and hub are cast in one piece, and the rim
is a wrought iron band riveted to the arms, whose ends are turned or
ground true with the hub bore. The figure is obviously a wood engraving,
but it presents the varying degrees of shade or shadow with sufficient
accuracy to form a good example to copy and brush shade with India ink.
Figure 301 represents a similar pulley with a double set of arms,
forming an excellent example in perspective drawing, as well as for
brush-shading.

[Illustration: Fig. 300.]

In brush-shading as with line-shading, the difficulties increase with an
increase in the size of the piece, and the learner will find that after
he has succeeded tolerably well in shading these small pulleys, it will
be quite difficult, but excellent practice to shade the large pulley in
Figure 302.

One of the principal considerations is to not let the color dry at the
edges in one part while continuing the shading in another part of the
same surface, hence it is best to begin at the edge or outline of the
drawing and carry the work forward as quickly as possible, occasionally
slightly wetting with water edges that require to be left while the
shading is proceeding in another direction.

[Illustration: Fig. 301.]

When it is required to show by the shading that the surfaces are highly
polished, the lighter parts of the shading are made to contain what may
be termed splashes of lighter and darker shadow, as in Figure 303, which
represents an oil cup, having a brass casing enclosing a glass cylinder,
which appears through the openings in the brass shell.

Figure 304 represents an iron planing machine whose line-shading is so
evenly effected that it affords an excellent example of shading. Its
parts are similar to those shown in the iron planer in Figure 297, save
that it carries two sliding heads, so as to enable the use,
simultaneously, of two cutting tools.

[Illustration: Fig. 304. (Page 282.)]

[Illustration: Fig. 302.]

A superior example in shading is shown in Figures 305 and 306, which
represent a plan and a sectional view of the steam-cylinder of a Blake's
patent direct-acting steam-pump. The construction of the parts is as
follows: A is the steam-piston, H 1 and H are the cylinder
steam-passages; M is the cylinder exhaust port.

[Illustration: Fig. 303.]

[Illustration: Fig. 305.]

The main valve, whose movement alternately opens the ports for the
admission of steam to, and the escape of steam from, the main cylinder,
is divided into two parts, one of which, C, slides upon a seat on the
main cylinder, and at the same time affords a seat for the other part,
D, which slides upon the upper face of C. As shown in the engravings, D
is at the left-hand end of its stroke, and C at the opposite or
right-hand end of its stroke. Steam from the steam-chest, J, is
therefore entering the right-hand end of the main cylinder through the
ports E and H, and the exhaust is escaping through the ports H 1, E 1, K
and M, which causes the main piston A to move from right to left. When
this _piston_ has nearly reached the left-hand end of its cylinder, the
tappet arm, T, attached to the piston-rod, comes in contact with, and
moves the valve rod collar O 1 and valve rod P, and thus causes C,
together with the supplemental valves R and S S 1, which form, with C,
_one casting_, to be moved from right to left. This movement causes
steam to be admitted to the left-hand end of the supplemental cylinder,
whereby its piston B will be forced towards the right, carrying D to the
opposite or right-hand end of its stroke; for the movement of S closes N
(the steam-port leading to the right-hand end), and the movement of S 1
opens N 1 (the steam-port leading to the opposite or left-hand end), at
the same time the movement of V opens the right-hand end of this
cylinder to the exhaust, through the exhaust ports X and Z. The parts C
and D now have positions opposite to those shown in the engravings, and
steam is therefore entering the main cylinder through the ports E 1 and
H 1, and escaping through the ports H, E, K and M, which causes the main
piston A to move in the opposite direction, or from left to right, and
operations similar to those already described will follow, when the
piston approaches the right-hand end of its cylinder. By this simple
arrangement the pump is rendered positive in its action; that is, it
will instantly start and continue working the moment steam is admitted
to the steam-chest, while at the same time the piston is enabled to move
as slowly as the nature of the duty may require. It will be noted that
in Figure 305, the ports of C are shown through D, whose location is
marked by dark shading. This obviously is not correct, because D being
above C should be shaded lighter than C, and again the ports E 1 and K
could not show dark through the port D. They might, of course, be shown
by dotted outlines, but they would not appear to such advantage, and on
this account it is permissible where artistic effect is sought, the
object being to subserve the shading to making the mechanism and its
operation clearly and readily understood.

[Illustration: Fig. 306.]

Figure 307 affords another excellent example for shading. It consists of
an independent condenser, whose steam-cylinder and valve mechanism is
the same as that described with reference to Figures 305 and 306.

[Illustration: Fig. 307. (Page 288.)]

[Illustration: Fig. 308. (Page 289.)]

[Illustration: Fig. 309. (Page 289.)]

[Illustration: Fig. 310--SECTION OF CYLINDER AND STEAM CHEST. (Page
289.)]




CHAPTER XV.

_EXAMPLES IN ENGINE WORK._


In the figures from 308 to 328 inclusive are given three examples in
engine work, all these drawings being from _The American Machinist_.
Figures 308 to 314 represent drawings of an automatic high speed engine
designed and made by Professor John E. and William A. Sweet, of
Syracuse, New York. Figure 308 is a side and 309 an end view of the
engine. Upon a bed-plate is bolted two straight frames, between which,
at their upper ends, the cylinder is secured by bolts. The guides for
the cross-head are bolted to the frame, which enables them to be readily
removed to be replaned when necessary. The hand wheel and rod to the
right are to operate the stop-cock for turning on and off the steam to
the steam-chest.

The objects of the design are as follows: Figure 310 is a vertical
section of the cylinder through the valve face, also showing the valve
in section, and it will be seen that the lower steam passage enters the
cylinder its full depth below the inside bottom, and that the whole
inside bottom surface of the cylinder <DW72>s or inclines towards the
entrance of this passage. The object of this is to overcome the
difficulty experienced from the accumulation of water in the cylinder,
which, in the vertical engine, is usually a source of considerable
annoyance and frequently the cause of accident.

Any water that may be present in the bottom finds its way by gravity to
the port steam entrance, and is forced out by and with the exhaust steam
at or before the commencement of the return stroke.

To assist in the escape of water from the top of the cylinder, the
piston is made quite crowning at that end, the effect of which is to
collect the water in a narrow band, instead of spreading it over a large
surface. This materially assists in its escape, and at the same time
presents a large surface for the distribution of any water that may not
find its way out in advance of the piston.

The piston is a single casting unusually long and light, and is packed
with four spring rings of 3/8 inch square brass wire.

The valve is a simple rectangular plate, working between the valve face
and a cover plate, the cover plate being held in its proper position,
relative to the back of the valve, by steam pressure against its outer
surface, and by resting against loose distance pieces between its inner
surface and the valve seat. This construction admits of the valve
leaving the seat, if necessary, to relieve the cylinder from water, as
in the instance of priming, and also, by the reduction of these pieces,
admits of ready adjustment to contact, should it become necessary.

[Illustration: Fig. 311--VALVE MOTION.]

The cover plate is provided with recesses on its inner surface which
exactly correspond with the ports in the valve face, and the
corresponding ports and recesses are kept in communication with each
other by means of relief passages in the valve. From this it will be
seen that the valve is subjected to equal and balanced pressure on each
of its sides, and hence, is in equilibrium.

The valve is operated through the valve motion, shown in Figure 311, the
eccentric rod of which hooks on a slightly tapered block that turns on
the pin of the rock arm, like an ordinary journal box.

The expansion, or cut-off, is automatically regulated by the operation
of the governor in swinging the slotted eccentric in a manner
substantially equivalent to moving it across the shaft, but is however
favorably modified by the arrangement of the rock arm, which, in
combination with the other motions, neutralizes the unfavorable
operation of the usual shifting eccentric, and which, in connection with
the large double port opening, provides for a good use of steam from 0
to 3/4 stroke.

The governor shown in Figure 312 is of the disc and single ball type,
the centrifugal force of the ball being counteracted by a powerful
spring. Friction is reduced to a minimum in the governor connection, by
introducing steel rollers and hardened steel plates in such a manner as
to provide rolling instead of sliding motion.

In order that a governor shall correctly perform its functions, it is
unquestionably necessary that it have power largely in excess of the
work required of it, and also that the friction shall represent a very
low percentage of that power. In respect to this, especial means have
been employed to reduce the friction; the valve being balanced,
requires but little power to move it, while the governor ball being made
heavy for the purpose of counterbalancing the weight of the eccentric
and strap, its centrifugal force when the engine is at full speed is
enormous, the spring to counteract it having to sustain from _two to
three thousand pounds_. Under these circumstances, as might be expected,
the regulation is remarkably good. This is a very important
consideration in an engine working under the conditions of a roll-train
engine.

[Illustration: Fig. 312--GOVERNOR.]

[Illustration: Fig. 313--SECTION OF PILLOW BLOCK.]

Figure 313 represents a section of the pillow block box, crank-pin and
wheel, together with the main journal. It will be seen that the end of
the box next the crank wheel has a circular groove around its outside,
and that a corresponding groove in the crank wheel projects over this
groove. From this latter groove an oil hole of liberal size extends, as
shown, to the surface of the crank-pin. Any oil placed at the upper part
of the groove on the box finds its way by gravity into the groove in
the crank wheel, and is carried by centrifugal force to the outside
surface of the crank-pin; so that whatever other means of lubrication
may be employed, this one will always be positive in its action. This
cut also shows the manner in which the box overlaps the main journal and
forms the oil reservoir.

[Illustration: Fig. 314--CONNECTING ROD. (Page 295.)]

Another feature in the construction of this box is the means by which it
is made to adjust itself in line with the shaft. It will be observed
that it rests on the bottom of the jaws of the frame on two inclined
surfaces, which form equal angles with the axis of the shaft when in its
normal position, and that by moving longitudinally in either direction,
as may be necessary, the box will accommodate itself to a change in the
alignment of the shaft. In order that it may be free to move for this
purpose it is not fitted with the usual fore and aft flanges. By this
means any slight derangement, as in either the outboard or inboard
bearing wearing down the fastest, is taken care of, the movement of the
box on the inclined surfaces being for this purpose equivalent to the
operation of a ball and socket bearing.

Figure 314 gives a side and an edge view of the connecting rod, the rod
being in section in the edge view, and the brasses in section lined in
both views.

The cross-head pin, it will be observed, is tapered, and is drawn home
in the cross-head by a bolt; the sides of the pin are flattened somewhat
where the journal is, so that the pin may not wear oval, as it is apt to
do, because of the pull and thrust strain of the rod brasses falling
mainly upon the top and bottom of the journal, where the most wear
therefore takes place. The brasses at the crossed end are set up by a
wedge adjustable by means of the screw bolts shown. The cross-head wrist
pin being removable from the cross-head enables the upper end of the rod
to have a solid end, since it can be passed into place in the crossed
and the wrist pin inserted through the two. The lower ends of the
connecting-rod and the crank-pin possess a peculiar feature, inasmuch as
by enlarging the diameter of the crank-pin, the ends of the brasses
overlap, to a certain extent, the ends of the journal, thus holding the
oil and affording increased lubrication. The segments that partly
envelop the cross-head pin and crank-pin, and are section lined in two
directions, producing crossing section lines, or small squares, show
that the brasses are lined with babbitt metal, which is represented by
this kind of cross-hatching. These drawings are sufficiently open and
clear to form very good examples to copy and to trace on tracing paper.

[Illustration: Fig. 315.]

[Illustration: Fig. 316. (Page 296.)]

[Illustration: Fig. 317.]

Figures 315, 316 and 317 represent, in place upon its setting, a 200
horse-power horizontal steam-boiler for a stationary engine, and are the
design of William H. Hoffman. The cross-sectional view of the boiler
shell in Figure 315 shows the arrangement of the tubes, which, having
clear or unobstructed passages between the vertical rows of tubes,
permits the steam to rise freely and assists the circulation of the
water. The dry pipe (which is also shown in Figure 316) is a perforated
pipe through which the steam passes to the engine cylinder, its object
being to carry off the steam as dry as possible; that is to say, without
its carrying away with the steam any entrained water that may be
held in suspension. Figure 316 is a side elevation with the setting
shown in section, and Figure 317 is an end view of the boiler and
setting at the furnace end. The boiler is supported on each side by
channel iron columns, these being riveted to the boiler shell angle
pieces which rest upon the columns. The heat and products of combustion
pass from the furnace along the bottom of the boiler, and at the end
pass into and through the tubes and thence over the top of the boiler
to the chimney flue. There is shown in the bridge wall an opening, and
its service is to admit air to the gases after they have passed the
bridge wall, and thus complete the combustion of such gases as
may have remained unconsumed in the furnace. The cleansing
door at one end and that lined with asbestos at the other, are to admit
the passage of the tube cleaners. The asbestos at the top of the boiler
shell is to protect it from any undue rise in temperature, steam being a
poorer conductor of heat than water, and it being obvious that if one
side of the boiler is hotter than the other it expands more from the
heat and becomes longer, causing the boiler to bend, which strains and
weakens it. The sides of the setting are composed of a double row of
brick walls with an air space of three inches between them, the object
being to prevent as far as possible the radiation of heat from the
walls. The brick-staves are simply stays to hold the brick work together
and prevent its cracking, as it is apt, in the absence of staying, to
do.

[Illustration: Fig. 318. (Page 299.)]

Figures from 318 to 330 are working drawings of a 100-horse engine,
designed also by William H. Hoffman.

Figure 318 represents a plan and a side view of the bed-plate with the
main bearing and the guide bars in place. The cylinder is bolted at the
stuffing box end to the bed-plate, and is supported at the outer end by
an expansion link pivoted to the bed-plate. The main bearing is provided
with a screw for adjusting the height of the bottom piece of the
bearing, and thus taking up the wear. The guide bars are held to the bed
in the middle as well as at each end.

Figures 319 and 320 represent cross sections of the bed-plate.

[Illustration: Fig. 319--CROSS SECTION OF BED PLATE NEAR JUNCTION WITH
CYLINDER. (Page 299.)]

[Illustration: Fig. 320.]

[Illustration: Fig. 321--100 H.P. HORIZONTAL STEAM-ENGINE--ELEVATION OF
CYLINDER--SCALE 1-1/2" = 1 FOOT. (Page 299.)]

[Illustration: Fig. 322--100 H.P. HORIZONTAL STEAM-ENGINE--END VIEW OF
CYLINDER--SCALE 1-1/2" = 1 FOOT. (Page 299.)]

Figure 321 represents a side elevation of the cylinder, and Figure 322
an end view of the same, the expansion support being for the purpose of
permitting the cylinder to expand and contract under variations of
temperature without acting to bend the bed-plate, while at the same time
the cylinder is supported at both ends. The cylinder and cylinder covers
are jacketted with live steam in the steam-spaces shown.

[Illustration: Fig. 323--100 H.P. ENGINE--OUTSIDE VIEW OF CYLINDER AND
STEAM-CHEST. (Page 301.)]

[Illustration: Fig. 324--SECTIONAL VIEW OF CYLINDER AND VALVES--SCALE
1-1/2 INCHES = 1 FOOT. (Page 301.)]

[Illustration: Fig. 325--PLAN OF CUT-OFF DEVICE. (Page 301.)]

[Illustration: Fig. 326--WORKING DRAWING OF 100 H.P. ENGINE--DETAILS OF
MAIN VALVE MOTION--SCALE 3" = 1 FOOT. (Page 301.)]

[Illustration: Fig. 328--100 H.P. HORIZONTAL STEAM-ENGINE--CROSS HEAD.
(Page 301.)]

[Illustration: Fig. 329.
Fig. 329 _a_. Working Drawings of 100 H.P. Steam Engine--Eccentric and
Eccentric Strap--Scale: 3" = 1 Foot. (Page 301.)]

[Illustration: Fig. 330--100 H.P. HORIZONTAL STEAM-ENGINE--CONNECTING
ROD. (Page 303.)]

A view of the steam-chest side of the cylinder is given in Figure 323,
and a horizontal cross section of the cylinder, the steam-chest and the
valves, is shown in Figure 324. The main valves are connected by a right
and left hand screw, to enable their adjustment, as are also the cut-off
valves.

Figures 325 and 326 show the cam wrist plate and the cut-off mechanism.
The cam wrist plate, which is of course vibrated by the eccentric rod,
has an inclined groove, whose walls are protected from wear by steel
shoes. In this groove is a steel roller upon a pin attached to the bell
crank operating the main valve stem. The operation of the groove is to
accelerate the motion imparted from the eccentric to the valve at one
part of the latter's travel, and <DW44> it at another, the accelerated
portion being during the opening of the port for steam admission, and
during its closure for cutting off, which enables the employment of a
smaller steam-port than would otherwise be the case.

The shaft for the cam plate is carried in a bearing at one end, and fits
in a socket at the other, the socket and bearing being upon a base plate
that is bolted to the bed-plate of the engine; a side view of the
construction being shown in Figure 327.

Figure 328 represents the cross-head, whose wrist pin is let into the
cross-head cheeks, so that it may be removed to be turned up true. The
clip is to prevent the piston rod nut from loosening back of itself.

Figure 329 represents a side view; and Figure 329 _a_ a section through
the centre of the eccentric and strap.

[Illustration: Fig. 327--WORKING DRAWING OF 100 H.P.
STEAM-ENGINE.--WRIST PLATE.--3" = 1 FOOT.]

The eccentric is let into the strap and is provided with an eye to
receive a circular nut by means of which the length of the eccentric rod
may be adjusted, a hexagon nut being upon the other or outer end of the
eye.

Figure 330 shows the construction of the connecting rod, the brasses of
which are adjustable to take up the wear and to maintain them to correct
length, notwithstanding the wear, by means of a key on each side of each
pair of brasses, the keys being set up by nuts and secured by check
nuts.




INDEX.

Ames' lathe feed motion, drawing a part of, 208.

Angle of three lines, one to the other, to find, 55, 56.
  of two lines, one to the other, to find, 54, 55, 56.

Angles, acute and obtuse, 57.

Arc of a circle, an, 50.

Arcs, construction with four, 67, 68.

Arcs for the teeth of wheels, to draw, 205.

Arrangement of different views, 94-111.

Automatic high speed engine, drawings of, 289.

Axis of a cylinder, 51.
  of an ellipse, 63.


Ball or sphere, representation of by line-shading, 87, 88.

Bed-plate, cross section of, 299.
  plan and side view of, with main bearing and guide bars, 299.

Bell-mouthed body, representation of by line-shading, 88, 89.

Bevelled gear, one-half of, and an edge view projected from the same, 207.
  one of which is line-shaded, 210.
  wheels, 203.

Bevelled gears, small, 208.

Bevelled wheels, a pair of, in section, 208.

Bisected line, 50.

Black lines of a drawing, how to produce, 32.

Blacksmith, drawings for the, 172.

Blake's patent direct acting steam pump, 284, 285.

Boiler drilling machine, a, 269, 270.

Boiler, end view of, 297.
  shell, sectional view of, 296.

Bolt heads and nuts, United States standard, 114, 118.
  to draw a square-headed, 125.
  with a hexagon head, to draw. 113, 114.
  with a square under the head, 149.

Bolts and nuts, dimensions of United States standard, 117.
  United States standard, forged or unfinished, 116.

Bolts, nuts and polygons, examples in, 112-151.

Bow pen, applying the ink to, 46.
  large, with a removable leg, 22.

Brass, representation of, by cross-hatching, 82.

Bread for rubbing out, 26.

Bristol board, use of rubber on, 26.

Brush-shading, 281.

Brushes, size and use of, 280.


Cam, a, and a lever arm in one piece on a shaft, a shoe sliding on the
    line, and held against the cam face by the rod, to find the position
    of the face of the shoe against the cam, 228.
  a full stroke, method of drawing or marking out, 237-241.
  designed to cut off steam at five-eighths of the piston stroke, 244-246.
  heart, to draw, 75, 76.
  object of using, instead of eccentric, 234.

Cam wrist plate, and cut-off mechanism, 301.

Cams, cut-off, employed instead of eccentrics on steamboats, examples in
    drawing, 232.
  finding the essential points of drawings of, 241-244.
  necessary imperfections in the operations of, 247-249.
  part played by the stroke of the engine in determining the conformation
    of, 241.
  three-fourths and seven-eighths, 246, 247.

Cap nut, to pencil in a, 143.

Cast iron, representation of, 277.
  representation of by cross-hatching, 82.

Centre from which an arc of a circle has been struck, to find, 52.

Centre of a circle, 51.

Centre punch in which the flat sides run out upon a circle, the edges
    forming curves, 150.

Chamfer circles of bolt heads, 120-123.
  of Franklin Institute bolt head, 119.

Chord of an arc, 50.

Chuck plate with six slots, to draw, 131.

Circle, degrees of a, 52-55.
  pencil and circle pen, use of, 43, 44.
  pens, 37, 38.
  that shall pass through any three given points, to draw, 51.
  to divide into six divisions, 56, 57.

Circles, to divide with the triangle, 129.
  for bolt heads, to draw, 128.
  German instrument for drawing, 44, 45.
  use of the instrument in forming, 42-45.

Circular arcs, Rankine's process for rectifying and subdividing, 210.

Circumference, 50.

Collar, a representation of, 96.

Coloring and shading, points to be observed in, 278.

Color, to maintain an even shade of, 278.

Colors, mixing, 278.

Condenser, independent, 288.

Cone, cylinder intersecting a, 186.

Connecting rod, 169, 295, 303.
  drawing representing the motion
  which a crank imparts to a, 249, 250.
  end, 147.

Copper, representation of, 277.

Corner where the round stem meets the square under the head, 150.

Coupling rod, working drawings of a, 169.

Crank, drawing representing the motion which it imparts to a connecting
    rod, 249.
  pin and wheel, 294.

Cross-hatching or section lining, 77-82.
  made to denote material of which the piece is composed, 81, 82.
  may sometimes cause the lines of the drawing to appear crooked to the
    eye, 80, 81.
  representation by, of a section of a number of pieces one within the
    other, the central bore being filled with short plugs, 78, 79.
  representation by, of three pieces put together, having slots or keyways
    through them, 79, 80.
  the diagonal lines in, should not meet the edges of the piece, 78.

Cross-head, 301.

Cross, use of, to designate a square, 95, 96.

Cube, with a hole passing through it, to draw, 101, 102.

Cupped ring, representation of, 98.

Curved outline, representation of, 86, 87.

Curve for tooth face, how to find, 198.
  representation of the radius for, 87.

Curves and lines, 48-76.
  of gear teeth, names of, 193.

Curves for moulding cutter, to find the, 257-263.
  of thread, template for drawing, 165.
  of wheels, construction, to find, 204.
  screw threads, drawing, 159.
  templates called, 21.
  use of, in practice, 21.

Cut-off cams, employed instead of eccentrics on steamboats, examples in
    drawing, 232.
  manner of finding essential points of drawings of, 241-244.
  necessary imperfections in the operations of, 247-249.
  part played by the stroke of the engine in determining the conformation
    of, 241.

Cut-off mechanism, 301.

Cutting tool for a planing machine, representation of, 264-266.

Cylinder, 299.
  a solid, representation of, 94, 95.
  intersecting a cone, 186
  of an engine, 299-301.
  of an engine, drawing of, 289.

Cylindrical body joining another at a right angle, a, 180.
  body whose top face, if viewed from one point, would appear as a straight
    line, or if from another as a circle, 188.
  piece of wood, which is to be squared, and each side of which square must
    be an inch, to find the diameter, 136.
  pieces and cubes, representation of, 95.
  pieces, representation of, by cross-hatching, 77, 78.

Cylindrical pieces, representation of three, one within the other, by
  cross-hatching, 78.
  pieces that join each other, representation of, 86.
  pin line-shaded, representation of, 86.


Decagon, a, 63.

Degrees of a circle, 52-55.

Diameter of a cylindrical piece of wood, which is to be squared, and each
    side of which square must measure an inch, to find, 136.

Diamond, a, 59, 60.

Different views, arrangement of, 94-111.

Dimension figures in mechanical drawing, 91.

Dimensions, marking, 91-93.

Distances, relative from the eye, representation of, by line-shading, 89.

Dodecagon, a, 63.

Dotted lines, use of, 48.

Double eye, or knuckle-joint, pencil lines for, 146.
  or knuckle-joint, with an offset, 147.

Double thread, 156.

Drawing board, 17, 18.
  fastening the drawing to, 278.
  size of, 18.
  small, advantage of, to student, 18.

Drawing for engraver on wood, 268.
  gear wheels, 193-222.

Drawing instruments, 22-26.
  parts of, 34.
  selecting and testing, 22.

Drawing paper, 26-29.
  different qualities, kinds and forms, 26, 27.
  location of on the drawing board, 28, 29.

Drawing the curves for screw threads, 159.
  to scale, making a, 177.

Drawings for engraving, necessity of conforming to the particular process
    of, 266.
  for engravings by the wax process, 268, 269.

Drawings for photo-engraving, 266.
  for the blacksmith, 172.
  shading and coloring, 277-288.

Drilling machine, a boiler, 269, 270.


Eccentric and strap, 301.
  to find how much motion it will give to its rod, 223.

Edge view of a wheel, to draw, 203.

Elevation, 94.

Ellipse, dimensions of, how taken and designated, 63.
  form of a true, 66.
  most correct method of drawing, 72.
  the, 63-75.

Elliptical figure, whose proportion of width to breadth shall remain the
    same, whatever the length of the major axis, 69.

Emery paper, use of on the lining pen, 37.

Ennagon, a, 62, 63.

Engine work, examples of, 289-303.

Engine, working drawings of a 100 horse-power, 299.

Engravings by the wax process, drawings for, 268, 269.

Examples for practice, 169-177
  in bolts, nuts and polygons, 112-151.
  of engine work, 289-303.
  of work with nine sides, 135.


Feed motion of a Niles horizontal tool work boring mill, 209.

Five-sided figure, to draw, 132, 133.

Flanks of teeth to trace hypocycloides, for, 200.

Foci of an ellipse, 64.

Franklin Institute or United States Standard for heads of bolts and of
    nuts, basis of, 118.

Full stroke cam, method of drawing or marking out a, 237-241.


Gear, part of, showing the teeth in, the remainder illustrated by
    circles, 209.

Gear teeth, names of the curves and lines of, 193.

Gear wheels, drawing, 193-222.
  various examples for laying out, 214-222.

Gearing oval, construction of, 210.

General view, 94.

Geometrical terms, simple explanation of, 48.

Geometry, advantage of to the draughtsman, 48.

Governor of an engine, 292, 293.

Guide bolts from one pulley to another, arrangement of idle pulleys
    to, 264.


Heart cam, to draw, 75, 76.

Hexagon, a, 62, 63.
  head, representation of a piece with, 96.
  head, to draw the end view of, 125, 126, 127.
  headed screw, to draw, 113, 114.
  radius across corners, 138.

Hexagonal form, representation of, 98.
 or hexagon heads of bolts, 118, 119.

Hole, representation of by shade or shadow line, 83.

Hollows in connection with round pieces, representations of, 87-89.

Hypocycloides for the flanks of teeth, to trace, 200.


Independent condenser, 288.

India ink, advantages of in drawing, 30.
  difference between good and inferior, 31.
  good, characteristics of, 31.

India ink, Higgins', 30.
  mixing, 25.
  testing, 31, 32.
  the two forms of, 30.
  to be used thick, 32.
  use of, 30.
  use of on parchment, 32.

Ink, applying, to the bow pen, 46.
  for drawing, 30-33.

Instruments, preparation and use of, 34-47.

Iron planing machine, representation of, 282.

Iron, wrought and cast, representation of by cross-hatching, 82.


Journal, 294.

Journals of shafts, 277.


Key, a, drawn in perspective, 92, 93.
  drawing of a, 91.
  marking the dimensions of on a drawing, 92.
  representation of with a shade line, 84.

Knuckle-joint, pencil eye for, 146.
  with an offset, 147.


Large bow or circle pen, joints of, 23.

Lathe centre, representation of, 86.

Lathe feed motion, drawing of a part of a, 208.

Lead pencils for drawing, 23.

Lead, representation of by cross-hatching, 82.

Left-hand thread, 156.

Lever, a, actuating a plunger in a vertical line, to find how much a given
    amount of motion of the long arm will actuate the plunger, 226.
  and shaft, drawing, 103, 104, 105.
  arm and cam, in one piece on a shaft, a shoe sliding on the line, and
    held against the cam face by the rod, to find the position of the face
    of the shoe against the cam, 228.
  example of the end of a, acting directly on a shoe, 225.
  to find how much a given amount of motion of a long arm will move the
  short arm of a lever, 224.

Levers, two, upon their axles or shafts, the arms connected by a link, and
    one arm connected to a rod, 227.

Light in shading, 280.
  management of, in mechanical drawing, 82, 83.

Line-shaded engravings, drawing for, 264-276.

Line-shading, 77-90.
  and drawing for line-shaded engravings, 264-276.
  in perspective drawing of a pipe-threading stock and die, 85.
  mechanical drawing made to look better and show more distinctly by, 82.
  simplest form of, 82.

Lines and curves, 48-76.

Lines in pencilling, where to begin, 24, 25.

Lining pen, 22.

Lining pen, form of, 34-37.

Lining pen, use of with a T square, 45, 47.

Link introduced in the place of a roller, to find the amount of motion of
    the rod, 226.
  quick return, plotting out the motion of a shaper, 250-253.

Links, pencilling for, 145, 146.

Locomotive frame, 174.
  spring, 169.


Machine screw, to draw, 112, 113.

Main journal, 294.

Marking dimensions, 91-93.

Measuring rules, draughtsman's, 33.

Mechanical motions, plotting, 223-263.

Motion an eccentric will give to its rod, to find, 223.
  a shaper link, quick return, plotting out, 250-253.
  imparted in a straight line to a rod, attached to an eccentric strap, to
    find the amount of, 229-231.
  which a crank imparts to a connecting rod, 249, 250.

Motions, plotting mechanical, 223-263.

Moulding cutter, finding the curves for, 257-263.


Niles' horizontal tool work boring mill, feed motion of a, 209.

Nonagon, a, 62.

Nut, a representation of the shade line on, 84.
  cap, to pencil in a, 145.
  to show the thread depth in the top or end view of a, 166.

Nuts' and bolts, dimensions of United States Standard, 117.

Nuts and polygons, examples in, 112-151.


Octagon, a, 62, 63.

Oil cup, representation of, 282, 284.

Outline views, 97, 98.

Oval gearing, construction of, 210.


Paper cutter, the form of the end of, 25.
  rules or scales, 32.

Parabola, to draw by lines, 74, 75.
  to draw mechanically, 73, 74.

Parallel lines, 49.

Parallelogram, 59, 60.

Parchment, use of India ink on, 32.

Pen, German, regulated to draw lines of various breadths, 84, 85.
  lining, form of, 34-37.

Pen point, forming the, 39, 40.
  form of recently introduced, 39.

Pen points, oil-stoning, 36.

Pen, with sapphire points, 85.

Pens, circle, 37, 38.
  used in drawing, 22.

Pencil holders for sticks of lead, 24.
  lines in drawing, 23.
  sharpening for fine work, 24.

Pencilling for a link, having the hubs on one side only, 145.
  in a cap nut, 145.

Penknife and rubber scratching out, 25.

Pentagon, a, 62, 63.

Perimeter, the, 50.

Periphery, 50.

Perpendicular line, 49.

Perspective sketches to denote the shape of the piece, 93.

Photo-engraving, drawings for, 266, 267.

Piece of work should, in mechanical drawing, be presented in as few views
    as possible, 94.

Pillow block box, 294.

Pin, in a socket, in section, representation of, 87, 88.

Pinion teeth, to draw to the pitch of the inner and small end of, 206.

Pins and discs, discrimination of, in mechanical drawing, 96.

Pipe threading stock and die, drawing of, 85.

Pitch circle of the inner and small end of, to draw, 206.
  to obtain a division of the lines that divide, 167.

Plan, 94.

Planing machine, a cutting tool for, 264-266.

Plotting mechanical motions, 223-263.
  out the motion of a shaper link quick return, 250-253.

Point, a, 49.

Points of drawing instruments, 34.

Polished surfaces, to show by shading, 282.

Polygon of twelve equal sides, to draw, 129, 130.

Polygons, bolts and nuts, examples of, 112-151.
  construction of, 61.
  designation of the angles of, 62.
  names of regular, 62, 63.
  scales giving the lengths of the sides of, 135.

Preparation and use of the instruments, 34-47.

Produced line, 50.

Projecting one view from another, 106.

Projections, 178-192.

Protractors, 53.

Pulley, Medart, shading a, 280.

Pulleys, arrangement of idle, to guide bolts from one pulley to
    another, 264.


Quadrangle, quadrilateral or tetragon, 59.

Quadrant of a circle, 50.

Quick return motion, Whitworth, plotting out, 253-256.


Radius across corners of a hexagon, 138.

Rankine's process for rectifying and subdividing circular arcs, 210.

Reducing scales, 175.

Rectangle, a, 59, 60.

Rectangular piece, a, to draw in two views, 98, 99.
  requires two or three views, 96, 97.
  representation of, 96.

Red ink, marking dimensions of mechanical drawings in, 91.

Rhomboid, a, 60.

Rhomb, rhombus or diamond, 54, 60.

Right line, a, 49.

Ring with a hexagon cross section, 98.

Rivet, side and end views of, 49.

Roller, example of a short arm having a, acting upon a larger roller, 225.

Rod, attached to an eccentric strap, to find the amount of motion imparted
    in a straight line to a, 229-231.
  end with a round stem, 148.

Round stem, a representation of, 96.
  top and bottom thread, 156.

Rubber, 25.
  form of, 26.
  proper uses of, 25.
  sponge, 26.
  the use of, 25.
  to be used on Bristol board, 26.
  velvet, 26.

Rule, steel, 32.


Sapphire points, pen with, 85.

Scale for diameter of a regular polygon, 140.
  of tooth proportions, 195.
  triangular, 33.

Scales, for measurement and drawing, 32.
  reducing, 175.

Scratching out, 25.

Screw machine, to draw, 112, 113.
  thread, United States standard, to draw, 159-160.
  threads and spirals, 152-168.
  threads, drawing the curves for, 159.
  threads for small bolts, with the angles of the threads drawn in,
    152-155.

  threads of a large diameter, 156.

Section lining or cross-hatching, 77-82.

Sectional view of a section of a wheel, for showing dimensions through arms
    and hub, 202.

Sector of a circle, 51.

Segment of a circle, 50.

Semicircle, 51.

Shade curve, representation of, 87.
  line produced for circles, 84.

Shade line, produced in straight lines, 84.
  or shadow line, 82.

Shading a Medart pulley, 280.
  and coloring, points to be observed in, 278.
  brush, 281.
  by means of lines to distinguish round from flat surfaces, and denote
    relative distances of surfaces, 85.
  example in, of a Blake's patent direct acting steam pump, 284, 285.
  example of, in an independent condenser, 288.
  light in, 280.
  simple, 277.
  to show by, that the surfaces are highly polished, 282.

Shadow line, 82.
  lines and line shading, 77-90.

Shaft for cam plate, 301.

Shaper link, quick return, plotting out the motion of a, 250-253.

Shoe against a cam, to find the position of the face of, 228.

Side elevation, drawing a, 106.

Sides or flats of work, to find the lengths of, 135, 136.

Slots not radiating from a centre, to draw, 131, 132.
  radiating from a centre, 131.

Spiral spring, to draw, 166.

Spiral wound round a cylinder, whose end is cut off at an angle, 178.

Spirals and screw threads, 152-168.

Sponge, rubber, 26.

Spring bow pencil, for circles, 22.
  pen, for circles, 22, 23.

Spring, spiral, to draw, 166.

Spur wheel teeth, how to draw, 194.

Square, a, 59, 60.
  body, which measures one inch on each side, to find what it measures
    across the corners, 136.

Square part, a representation of, 96.
  parts, use of a cross to designate, 95, 96.
  thread, to draw a, 162-164.

Steam boiler, horizontal, for stationary engine, 296.
  chest and valves, 301.
  chest side, and horizontal cross section of cylinder, 301.
  pump, Blake's patent direct acting, 284, 285.

Steel, representation of, 277.
  representation of by cross-hatching, 82.
  square, improved, with pivoted blade, 19.

Steps, to draw a piece containing, 99-101.

Stock and die, pipe-threading, drawing of, 85.

Straight line in geometry termed a right line, 49.
  or lining pen, use of with a T square, 45, 47.

Stud, to draw a, 142.

Stuffing-box and gland, 169.

Surface of the paper, condensing after rubbing out, 25.

Surfaces, highly polished, to show by shading, 282.


Tacks for drawing paper, 27, 28.

Tangent, 51.

Taper or conical hole, to denote in drawing, 102.
  sides in a drawing, 102, 103.

Tees, 180.

Teeth of wheels, rules for drawing, 203.
  pinion, to draw the pitch of the inner and small end of, 206.
  spur wheel, how to draw, 194.
  to trace hypocycloides for the flanks of, 200.

Template for drawing the curves of thread, 165.

Templates called curves, 21.

T square, 18, 19.

T squares, different kinds of, 19.

Tetragon, a, 59, 62, 63.

Thread, a double, 156.
  a round top and bottom, 156.
  depth in the top or end view of a nut, to show, 166.
  left hand, 156.
  square, to draw a, 162-164.
  Whitworth, 156.

Threads of a large diameter, 156.

Thumb tacks for drawing paper, 27.

Tint, to graduate the depth of, for a cylindrical surface, 279.

Tooth face, how to find the curve for, 198.
  proportions, Willis' scale of, 195.

Tracing cloth, 29.
  paper, 29.

Trammel, use of in drawing an ellipse, 72.

Trapezium, 60.

Trapezoid, a, 60.

Triangle, equilateral, 58, 59.
  isosceles, 58, 59.
  obtuse, 58.
  right angle, 58.
  scalene, 59.
  use of in dividing circles, 129.
  use of in drawing polygons, 129, 130.
  use of to draw slots radiating from a centre, 131.

Triangles, 19-21, 58-60.
  requirements in use of, 20, 21.
  to draw, 133.
  using with the square, 20.

Triangular scale, 33.

Trigon, a, 62, 63.

True ellipse, a near approach to the form of, 69-72.


United States standard bolts and nuts, 114-118.
  standard thread, to draw, 159, 160.


Valve of an engine, 290-292.

Valves, 301.

Vertex, the, 59.

Views, different arrangement of, 94-111.
  of a piece of work, designations of, 103, 104.
  of a piece, two systems of placing, 106-111.


Washer, a, representation of the shadow side of, 83.

Wax process, drawings for engravings by, 268, 269.
  engraving from a print from a wood engraving, 269.

Wedge-shaped piece, representation of a, 97.

Wheel, edge view of a, to draw, 203.
  sectional view of a section of a, 202.

Wheels, construction, to find the curves of, 204.
  to draw the arcs for the teeth of, 205.

Whitworth thread, 156.
  quick return motion, plotting out, 253-256.

Willis' scale of tooth proportions, 195.
  application of, 197.

Wood engraving, drawing for, 268.

Wood, representation of by cross-hatching, 82.
  representation of, regular and irregular shade lines in, 90.

Wrought iron, representation of, 277.
  representation of by cross-hatching, 82.




CATALOGUE

OF

Practical and Scientific Books

PUBLISHED BY

HENRY CAREY BAIRD & CO.

INDUSTRIAL PUBLISHERS, BOOKSELLERS AND IMPORTERS,

810 Walnut Street, Philadelphia.

[Illustration: Pointing Finger] Any of the Books comprised in this
Catalogue will be sent by mail, free of postage, to any address in the
world, at the publication prices.

[Illustration: Pointing Finger] A Descriptive Catalogue, 96 pages, 8vo.,
will be sent free and free of postage, to any one in any part of the
world, who will furnish his address.

[Illustration: Pointing Finger] Where not otherwise stated, all of the
Books in this Catalogue are bound in muslin.


$AMATEUR MECHANICS' WORKSHOP:$

A treatise containing plain and concise directions for the manipulation
of Wood and Metals, including Casting, Forging, Brazing, Soldering and
Carpentry. By the author of the "Lathe and Its Uses." Third edition.
Illustrated. 8vo. $3.00

$ANDRES.--A Practical Treatise on the Fabrication of Volatile and Fat
Varnishes, Lacquers, Siccatives and Sealing Waxes.$

From the German of ERWIN ANDRES, Manufacturer of Varnishes and Lacquers.
With additions on the Manufacture and Application of Varnishes, Stains
for Wood, Horn, Ivory, Bone and Leather. From the German of DR. EMIL
WINCKLER and LOUIS E. ANDES. The whole translated and edited by WILLIAM
T. BRANNT. With 11 illustrations. 12mo. $2.50

$ARLOT.--A Complete Guide for Coach Painters:$

Translated from the French of M. ARLOT, Coach Painter; for eleven years
Foreman of Painting to M. Eherler, Coach Maker, Paris. By A.A. FESQUET,
Chemist and Engineer. To which is added an Appendix, containing
Information respecting the Materials and the Practice of Coach and Car
Painting and Varnishing in the United States and Great Britain. 12mo.
$1.25

$ARMENGAUD, AMOROUX, AND JOHNSON.--The Practical Draughtsman's Book of
Industrial Design, and Machinist's and Engineer's Drawing Companion$:

Forming a Complete Course of Mechanical Engineering and Architectural
Drawing. From the French of M. Armengaud the elder, Prof. of
Design in the Conservatoire of Arts and Industry, Paris, and
MM. Armengaud the younger, and Amoroux, Civil Engineers. Rewritten
and arranged with additional matter and plates, selections from
and examples of the most useful and generally employed mechanism
of the day. By WILLIAM JOHNSON, Assoc. Inst. C.E. Illustrated
by fifty folio steel plates, and fifty wood-cuts. A new edition, 4to.,
half morocco      $10.00

$ARMSTRONG.--The Construction and Management of Steam Boilers$:

By R. ARMSTRONG, With an Appendix by ROBERT MALLET,
C.F., F.R.S. Seventh Edition. Illustrated. 1 vol. 12mo. $75.00

$ARROWSMITH.--Paper-Hanger's Companion$:

A Treatise in which the Practical Operations of the Trade are
Systematically laid down: with Copious Directions Preparatory to
Papering; Preventives against the Effect of Damp on Walls; the
various Cements and Pastes Adapted to the Several Purposes of
the Trade; Observations and Directions for the Panelling and
Ornamenting of Rooms, etc. By JAMES ARROWSMITH. 12mo., cloth $1.25

$ASHTON.--The Theory and Practice of the Art of Designing Fancy Cotton
and Woollen Cloths from Sample$:

Giving full instructions for reducing drafts, as well as the methods of
spooling and making out harness for cross drafts and finding any required
reed; with calculations and tables of yarn. By FREDERIC T.
ASHTON, Designer, West Pittsfield, Mass. With fifty-two illustrations.
One vol. folio       $10.00

$AUERBACH--CROOKES.--Anthracen$:

Its Constitution, Properties, Manufacture and Derivatives, including
Artificial Alizarin, Anthrapurpurin, etc., with their applications in
Dyeing and Printing. By G. AUERBACH. Translated and edited
from the revised manuscript of the Author, by WM. CROOKES, F.R.
S., Vice-President of the Chemical Society. 8vo.     $5.00

$BAIRD.--Miscellaneous Papers on Economic Questions. By Henry Carey
Baird.$ (_In preparation._)

$BAIRD.--The American Cotton Spinner, and Manager's and Carder's Guide$:

A Practical Treatise on Cotton Spinning; giving the Dimensions and
Speed of Machinery, Draught and Twist Calculations, etc.; with
notices of recent Improvements: together with Rules and Examples
for making changes in the sizes and numbers of Roving and Yarn.
Compiled from the papers of the late ROBERT H. BAIRD. 12mo.
      $1.50

$BAIRD.--Standard Wages Computing Tables:$

An Improvement in all former Methods of Computation, so arranged that
wages for days, hours, or fractions of hours, at a specified rate per
day or hour, may be ascertained at a glance. By T. SPANGLER BAIRD.
Oblong folio $5.00

$BAKER.--Long-Span Railway Bridges:$

Composing Investigations of the Comparative Theoretical and Practical
Advantages of the various Adopted or Proposed Type Systems of
Construction; with numerous Formulae and Tables. By B. BAKER. 12mo. $1.50

$BAKER.--The Mathematical Theory of the Steam-Engine:$

With Rules at length, and Examples worked out for the use of Practical
Men. By T. BAKER, C.E., with numerous Diagrams. Sixth Edition, Revised
by Prof. J.R. YOUNG. 12mo. $75.00

$BARLOW.--The History and Principles of Weaving, by Hand and by Power:$

Reprinted, with Considerable Additions, from "Engineering," with a
chapter on Lace-making Machinery, reprinted from the Journal of the
"Society of Arts." By ALFRED BARLOW. With several hundred illustrations.
8vo., 443 pages $10.00

$BARR.--A Practical Treatise on the Combustion of Coal:$

Including descriptions of various mechanical devices for the Economic
Generation of Heat by the Combustion of Fuel, whether solid, liquid or
gaseous. 8vo. $2.50

$BARR.--A Practical Treatise on High Pressure Steam Boilers:$

Including Results of Recent Experimental Tests of Boiler Materials,
together with a Description of Approved Safety Apparatus, Steam Pumps,
Injectors and Economizers in actual use. By WM. M. BARR. 204
Illustrations. 8vo. $3.00

$BAUERMAN.--A Treatise on the Metallurgy of Iron:$

Containing Outlines of the History of Iron Manufacture, Methods of
Assay, and Analysis of Iron Ores, Processes of Manufacture of Iron and
Steel, etc., etc. By H. BAUERMAN, F.G.S., Associate of the Royal School
of Mines. Fifth Edition, Revised and Enlarged. Illustrated with numerous
Wood Engravings from Drawings by J.B. JORDAN. 12mo. 2.00

$BAYLES.--House Drainage and Water Service:$

In Cities, Villages and Rural Neighborhoods. With Incidental
Consideration of Certain Causes Affecting the Healthfulness of
Dwellings. By JAMES C. BAYLES, Editor of "The Iron Age" and "The Metal
Worker." With numerous illustrations. 8vo. cloth, $3.00

$BEANS.--A Treatise on Railway Curves and Location of Railroads:$

By E.W. BEANS, C.E. Illustrated. 12mo. Tucks $1.50

$BECKETT.--A Rudimentary Treatise on Clocks, and Watches and Bells:$

By Sir EDMUND BECKETT, Bart., LL. D., Q.C.F.R.A.S. With numerous
illustrations. Seventh Edition, Revised and Enlarged. 12mo. $2.25

$BELL.--Carpentry Made Easy$:

Or, The Science and Art of Framing on a New and Improved System
With Specific Instructions for Building Balloon Frames, Barn
Frames, Mill; Frames, Warehouses, Church Spires, etc. Comprising
also a System of Bridge Building, with Bills, Estimates of Cost,
and valuable Tables. Illustrated by forty four plates, comprising
nearly 200 figures. By WILLIAM E. BELL, Architect and Practical
Builder. 8vo. $5.00

$BEMROSE.--Fret-Cutting and Perforated Carving.$

With fifty three practical illustrations By W. BEMROSE, JR. 1 vol.
quarto. $3.00

$BEMROSE.--Manual of Buhl-work and Marquetry.$ With Practical
Instructions for Learners, and ninety  designs By W.
BEMROSE, JR. 1 vol. quarto. $3.00

$BEMROSE.--Manual of Wood Carving.$

With Practical Illustrations for Learners of the Art, and Original
and Selected Designs. By WILLIAM BEMROSE, JR. With an Introduction
by LLEWELLYN JEWITT, F.S.A., etc. With 128 illustrations, 4to.
$3.00

$BILLINGS.--Tobacco$

Its History, Variety, Culture, Manufacture, Commerce, and Various
Modes of Use. By E.R. BILLINGS. Illustrated by nearly 200
engravings. 8vo. $3.00

$BIRD.--The American Practical Dyers' Companion.$

Comprising a Description of the Principal Dye Stuffs and Chemicals
used in Dyeing, their Natures and Uses, Mordants, and How Made,
with the best American, English, French and German processes for
Bleaching and Dyeing Silk, Wool, Cotton, Linen, Flannel, Felt,
Dress Goods, Mixed and Hosiery Yarns, Feathers, Grass, Felt, Fur,
Wool, and Straw Hats, Jute Yarn, Vegetable Ivory, Mats, Skins,
Furs, Leather, etc., etc. By Wood, Aniline, and other Processes,
together with Remarks on Finishing Agents, and Instructions in the
Finishing of Fabrics, Substitutes for Indigo, Water Proofing of
Materials, Tests and Purification of Water, Manufacture of Aniline
and other New Dye Wares, Harmonizing Colors, etc., etc., embracing
in all over 800 Receipts for Colors and Shades, _accompanied by 170
Dyed Samples of Raw Materials and Fabrics_ By F.J. BIRD, Practical
Dyer, Author of "The Dyers' Hand Book." 8vo. $10.00

$BLINN.--A Practical Workshop Companion for Tin, Sheet-Iron, and
Copper-plate Workers.$

Containing Rules for describing various kinds of Patterns used by
Tin, Sheet Iron, and Copper plate Workers, Practical Geometry;
Mensuration of Surfaces and Solids, Tables of the Weights of
Metals, Lead pipe, etc., Tables of Areas and Circumferences of
Circles, Japan, Varnishes, Lackers, Cements, Compositions, etc.,
etc. By LEROY J. BLINN, Master Mechanic. With over One Hundred
Illustrations. 12mo. $2.50

$BOOTH.--Marble Worker's Manual.$

Containing Practical Information respecting Marbles in general,
their Cutting, Working and Polishing, Veneering of Marble, Mosaics,
Composition and Use of Artificial Marble, Stuccos, Cements,
Receipts. Secrets, etc., etc. Translated from the French by M.L.
BOOTH. With an Appendix concerning American Marbles. 12mo, cloth
$1.50

$BOOTH and MORFIT.--The Encyclopaedia of Chemistry, Practical and
Theoretical.$

Embracing its application to the Arts, Metallurgy, Mineralogy,
Geology, Medicine and Pharmacy. By JAMES C. BOOTH, Melter and
Refiner in the United States Mint, Professor of Applied Chemistry
in the Franklin Institute, etc., assisted by CAMPBELL MORFIT,
author of "Chemical Manipulations," etc. Seventh Edition. Complete
in one volume. royal 8vo., 978 pages, with numerous wood cuts and
other illustrations. $5.00

$BRAMWELL.--The Wool Carder's Vade-Mecum$.

A Complete Manual of the Art of Carding Textile Fabrics. By W.C.
BRAMWELL. Third Edition, revised and enlarged. Illustrated pp. 400.
12mo. $2.50

$BRANNT.--A Practical Treatise on the Raw Materials and the
Distillation and Rectification of Alcohol, and the Preparation of
Alcoholic Liquors, Liqueurs, Cordials, Bitters, etc.$:

Edited chiefly from the German of Dr. K. Stammer, Dr. F. Elsner,
and E. Schubert. By WM T. BRANNT. Illustrated by thirty one
engravings. 12mo. $2. 50

$BRANNT--WAHL.--The Techno-Chemical Receipt Book.$

Containing several thousand Receipts covering the latest, most
important, and most useful discoveries in Chemical Technology, and
their Practical Application in the Arts, and the Industries. Edited
chiefly from the German of Drs. Winckler, Elsner, Heintze,
Mierzinski, Jacobsen, Koller and Heinzerling with additions by
WM.T. BRANNT and WM.H. WAHL, PH. D. Illustrated by 78 engravings.
12mo. 495 pages. $2.00

$BROWN.--Five Hundred and Seven Mechanical Movements.$

Embracing all those which are most important in Dynamics,
Hydraulics, Hydrostatics, Pneumatics, Steam Engines, Mill and other
Gearing, Presses, Horology and Miscellaneous Machinery, and
including many movements never before published, and several of
which have only recently come into use. By HENRY T. BROWN. 12mo.
$1.00

$BUCKMASTER.--The Elements of Mechanical Physics.$

By J.C. BUCKMASTER. Illustrated with numerous engravings. 12mo.
$1.50

$BULLOCK.--The American Cottage Builder.$

A Series of Designs, Plans and Specifications, from $200 to
$20,000, for Homes for the People, together with Warming,
Ventilation, Drainage, Painting and Landscape Gardening. By JOHN
BULLOCK, Architect and Editor of "The Rudiments of Architecture and
Building," etc., etc. Illustrated by 75 engravings. 8vo. $3.50

$BULLOCK.--The Rudiments of Architecture and Building.$

For the use of Architects, Builders, Draughtsmen, Machinists,
Engineers and Mechanics. Edited by JOHN BULLOCK author of "The
American Cottage Builder." Illustrated by 250 Engravings. 8vo.
$3.50

$BURGH.--Practical Rules for the Proportions of Modern Engines and
Boilers for Land and Marine Purposes.$

By N.P. BURGH, Engineer. 12mo. $1.50

$BURNS.--The American Woolen Manufacturer$:

A Practical Treatise on the Manufacture of Woolens, in two parts.
Part First gives full and explicit instructions upon Drafting,
Cross-Drawing, Combining Weaves, and the correct arrangement of
Weights, Colors and Sizes of Yarns to produce any desired fabric.
Illustrated with diagrams of various weavings, and twelve samples
of cloth for explanation and practice. Part Second is fully
supplied with extended Tables, Rules, Examples, Explanations, etc.;
gives full and practical information, in detailed order, from the
stock department to the market, of the proper selection and use of
the various grades and staples of wool, with the admixture of
waste, cotton and shoddy; and the proper application and economical
use of the various oils, drugs, dye stuffs, soaps, belting, etc.
Also, the most approved method for Calculating and Estimating the
Cost of Goods, for all Wool, Wool Waste and Cotton and Cotton
Warps. With Examples and Calculations on the Circular motions of
Wheels, Pinions, Drums, Pulleys and Gears, how to speed them, etc.
The two parts combined form a whole work on the American way of
manufacturing more complete than any yet issued. By GEORGE C.
BURNS. 8vo.

$BYLES.--Sophisms of Free Trade and Popular Political Economy
Examined.$

By a BARRISTER (SIR JOHN BARNARD BYLES, Judge of Common Pleas).
From the Ninth English Edition, as published by the Manchester
Reciprocity Association. 12mo. $1.25

$BOWMAN.--The Structure of the Wool Fibre in its Relation to the
Use of Wool for Technical Purposes$:

Being the substance, with additions, of Five Lectures, delivered at
the request of the Council, to the members of the Bradford
Technical College, and the Society of Dyers and Colorists. By F.H.
BOWMAN, D. Sc., F.R.S.E., F.L.S. Illustrated by 32 engravings. 8vo.
$6.50

$BYRN.--The Complete Practical Distiller:$

Comprising the most perfect and exact Theoretical and Practical
Description of the Art of Distillation and Rectification; including
all of the most recent improvements in distilling apparatus;
instructions for preparing spirits from the numerous vegetables,
fruits, etc; directions for the distillation and preparation of all
kinds of brandies and other spirits, spirituous and other
compounds, etc. By M. LA FAYETTE BYRN, M.D. Eighth Edition. To
which are added Practical Directions for Distilling, from the
French of Th. Fling, Brewer and Distiller. 12mo.

$BYRNE.--Hand-Book for the Artisan, Mechanic, and Engineer$:

Comprising the Grinding and Sharpening of Cutting Tools, Abrasive
Processes, Lapidary Work, Gem and Glass Engraving, Varnishing and
Lackering, Apparatus, Materials and Processes for Grinding and

Polishing, etc. By OLIVER BYRNE. Illustrated by 185 wood
engravings. 8vo. $5.00

$BYRNE.--Pocket-Book for Railroad and Civil Engineers$:

Containing New, Exact and Concise Methods for Laying out Railroad
Curves, Switches, Frog Angles and Crossings; the Staking out of
work; Levelling; the Calculation of Cuttings; Embankments;
Earthwork, etc. By OLIVER BYRNE. 18mo., full bound, pocket-book
form. $1.75

$BYRNE.--The Practical Metal-Worker's Assistant$:

Comprising Metallurgic Chemistry; the Arts of Working all Metals
and Alloys; Forging of Iron and Steel; Hardening and Tempering;
Melting and Mixing; Casting and Founding; Works in Sheet Metal; the
Processes Dependent on the Ductility of the Metals; Soldering; and
the most Improved Processes and Tools employed by Metal-Workers.
With the Application of the Art of Electro-Metallurgy to
Manufacturing Processes; collected from Original Sources, and from
the works of Holtzapffel, Bergeron, Leupold, Plumier, Napier,
Scoffern, Clay, Fairbairn and others. By OLIVER BYRNE. A new,
revised and improved edition, to which is added an Appendix,
containing The Manufacture of Russian Sheet-Iron. By JOHN PERCY,
M.D., F.R.S. The Manufacture of Malleable Iron Castings, and
Improvements in Bessemer Steel. By A.A. FESQUET, Chemist and
Engineer. With over Six Hundred Engravings, Illustrating every
Branch of the Subject. 8vo. $7.00

$BYRNE.--The Practical Model Calculator$:

For the Engineer, Mechanic, Manufacturer of Engine Work, Naval
Architect, Miner and Millwright. By OLIVER BYRNE. 8vo., nearly 600
pages. $4.50

$CABINET MAKER'S ALBUM OF FURNITURE$:

Comprising a Collection of Designs for various Styles of Furniture.
Illustrated by Forty-eight Large and Beautifully Engraved Plates.
Oblong, 8vo. $3.50

$CALLINGHAM.--Sign Writing and Glass Embossing$:

A Complete Practical Illustrated Manual of the Art. By JAMES
CALLINGHAM. 12mo. $1.50

$CAMPIN.--A Practical Treatise on Mechanical Engineering$:
Comprising Metallurgy, Moulding, Casting, Forging, Tools, Workshop
Machinery, Mechanical Manipulation, Manufacture of Steam-Engines,
etc. With an Appendix on the Analysis of Iron and Iron Ores. By
FRANCIS CAMPIN, C.E. To which are added, Observations on the
Construction of Steam Boilers, and Remarks upon Furnaces used for
Smoke Prevention; with a Chapter on Explosions. By R. ARMSTRONG,
C.E., and JOHN BOURNE. Rules for Calculating the Change Wheels for
Screws on a Turning Lathe, and for a Wheel-cutting Machine.
By J. LA NICCA. Management of Steel, Including Forging, Hardening,
Tempering, Annealing, Shrinking and Expansion; and the
Case-hardening of Iron. By G. EDE. 8vo. Illustrated with
twenty-nine plates and 100 wood engravings. $5.00

$CAREY.--A Memoir of Henry C. Carey.$

By DR. WM. ELDER. With a portrait. 8vo., cloth $.75

$CAREY.--The Works of Henry C. Carey:$

$Harmony of Interests:$ Agricultural, Manufacturing and Commercial.
8vo. $1.50

$Manual of Social Science.$ Condensed from Carey's "Principles of
Social Science." By KATE MCKEAN. 1 vol. 12mo. $2.25

$Miscellaneous Works.$ With a Portrait. 2 vols. 8vo. $6.00

$Past, Present and Future.$ 8vo. $2.50

$Principles of Social Science.$ 3 volumes, 8vo. $10.00

$The Slave-Trade, Domestic and Foreign;$ Why it Exists, and How it
may be Extinguished (1853). 8vo. $2.00

$The Unity of Law:$ As Exhibited in the Relations of Physical,
Social, Mental and Moral Science (1872). 8vo. $3.50

$CLARK.--Tramways, their Construction and Working$:

Embracing a Comprehensive History of the System. With an exhaustive
analysis of the various modes of traction, including horse-power,
steam, heated water and compressed air; a description of the
varieties of Rolling stock, and ample details of cost and working
expenses. By D. KINNEAR CLARK. Illustrated by over 200 wood
engravings, and thirteen folding plates. 2 vols. 8vo. $12.50

$COLBURN.--The Locomotive Engine$:

Including a Description of its Structure, Rules for Estimating its
Capabilities, and Practical Observations on its Construction and
Management. By ZERAH COLBURN. Illustrated. 12mo. $1.00

$COLLENS.--The Eden of Labor; or, the Christian Utopia.$

By T. WHARTON COLLENS, author of "Humanics," "The History of
Charity," etc. 12mo. Paper cover, $1.00; Cloth $1.25

$COOLEY.--A Complete Practical Treatise on Perfumery$:

Being a Hand-book of Perfumes, Cosmetics and other Toilet Articles.
With a Comprehensive Collection of Formulae. By ARNOLD J. COOLEY.
12mo. $1.50

$COOPER.--A Treatise on the use of Belting for the Transmission of
Power.$

With numerous illustrations of approved and actual methods of
arranging Main Driving and Quarter Twist Belts, and of Belt
Fastenings. Examples and Rules in great number for exhibiting and
calculating the size and driving power of Belts. Plain, Particular
and Practical Directions for the Treatment, Care and Management of
Belts. Descriptions of many varieties of Beltings, together with
chapters on the Transmission of Power by Ropes; by Iron and Wood
Frictional Gearing; on the Strength of Belting Leather; and on the
Experimental Investigations of Morin, Briggs, and others. By JOHN
H. COOPER, M.E. 8vo. $3.50

$CRAIK.--The Practical American Millwright and Miller.$

By DAVID CRAIK, Millwright. Illustrated by numerous wood engravings
and two folding plates. 8vo. $5.00

$CRISTIANI.--A Technical Treatise on Soap and Candles$:

With a Glance at the Industry of Fats and Oils. By R.S. CRISTIANI,
Chemist. Author of "Perfumery and Kindred Arts." Illustrated by 176
engravings. 581 pages, 8vo. $7.50

$CRISTIANI.--Perfumery and Kindred Arts$:

A Comprehensive Treatise on Perfumery, containing a History of
Perfumes from the remotest ages to the present time. A complete
detailed description of the various Materials and Apparatus used in
the Perfumer's Art, with thorough Practical Instruction and careful
Formulae, and advice for the fabrication of all known preparations
of the day, including Essences, Tinctures, Extracts, Spirits,
Waters, Vinegars, Pomades, Powders, Paints, Oils, Emulsions,
Cosmetics, Infusions, Pastilles, Tooth Powders and Washes, Cachous,
Hair Dyes, Sachets, Essential Oils, Flavoring Extracts, etc.; and
full details for making and manipulating Fancy Toilet Soaps,
Shaving Creams, etc., by new and improved methods. With an Appendix
giving hints and advice for making and fermenting Domestic Wines,
Cordials, Liquors, Candies, Jellies, Syrups, Colors, etc.,
and for Perfuming and Flavoring Segars, Snuff and Tobacco, and
Miscellaneous Receipts for various useful Analogous Articles. By
R.S. CRISTIANI, Consulting Chemist and Perfumer, Philadelphia. 8vo.
$5.00

$CUPPER.--The Universal Stair-Builder$:

Being a new Treatise on the Construction of Stair-Cases and
Hand-Rails; showing Plans of the various forms of Stairs, method of
Placing the Risers in the Cylinders, general method of describing
the Face Moulds for a Hand-Rail, and an expeditious method of
Squaring the Rail. Useful also to Stonemasons constructing Stone
Stairs and Hand-Rails; with a new method of Sawing the Twist Part
of any Hand-Rail square from the face of the plank, and to a
parallel width. Also, a new method of forming the Easings of the
Rail by a gauge; preceded by some necessary Problems in Practical
Geometry, with the Sections of Prismatic Solids. Illustrated by 29
plates. By R.A. CUPPER, Architect, author of "The Practical
Stair-Builder's Guide." Third Edition. Large 4to.

$DAVIDSON.--A Practical Manual of House Painting, Graining,
Marbling, and Sign-Writing$:

Containing full information on the processes of House Painting in
Oil and Distemper, the Formation of Letters and Practice of
Sign-Writing, the Principles of Decorative Art, a Course of
Elementary Drawing for House Painters, Writers, etc., and a
Collection of Useful Receipts. With nine  illustrations of
Woods and Marbles, and numerous wood engravings. By ELLIS A.
DAVIDSON. 12mo. $3.00

$DAVIES.--A Treatise on Earthy and Other Minerals and Mining$:

By D.C. DAVIES, F.G.S., Mining Engineer, etc. Illustrated by 76
Engravings. 12mo. $5.00

$DAVIES.--A Treatise on Metalliferous Minerals and Mining$: By D.C.
DAVIES, F.G.S., Mining Engineer, Examiner of Mines, Quarries and
Collieries. Illustrated by 148 engravings of Geological Formations,
Mining Operations and Machinery, drawn from the practice of all
parts of the world. 2d Edition, 12mo., 450 pages. $5.00

$DAVIES.--A Treatise on Slate and Slate Quarrying$:

Scientific, Practical and Commercial. By D.C. DAVIES, F.G.S.,
Mining Engineer, etc. With numerous illustrations and folding
plates. 12mo. $2.50

$DAVIS.--A Practical Treatise on the Manufacture of Bricks, Tiles,
Terra-Cotta, etc.$:

Including Common, Pressed, Ornamentally Shaped, and Enamelled Bricks,
Drain-Tiles, Straight and Curved Sewer-Pipes, Fire-Clays, Fire-Bricks,
Terra-Cotta, Roofing-Tiles, Flooring-Tiles, Art-Tiles, Mosaic Plates,
and Imitation of Intarsia or Inlaid Surfaces; comprising every important
Product of Clay employed in Architecture, Engineering, the
Blast-Furnace, for Retorts, etc., with a History and the Actual
Processes in Handling, Disintegrating, Tempering, and Moulding the Clay
into Shape, Drying Naturally and Artificially, Setting and Burning,
Enamelling in Polychrome Colors, Composition and Application of Glazes,
etc.; including Full Detailed Descriptions of the most modern Machines,
Tools, Kilns, and Kiln-Roofs used. By CHARLES THOMAS DAVIS. Illustrated
by 228 Engravings and 6 Plates. 8vo., 472 pages $5.00

$DAVIS.--The Manufacture of Leather$:

Being a description of all of the Processes for the Tanning,
Tawing, Currying, Finishing and Dyeing of every kind of Leather;
including the various Raw Materials and the Methods for Determining
their Values; the Tools, Machines, and all Details of Importance
connected with an Intelligent and Profitable Prosecution of the
Art, with Special Reference to the Best American Practice. To which
are added Complete Lists of all American Patents for Materials,
Processes, Tools, and Machines for Tanning, Currying, etc. By
CHARLES THOMAS DAVIS. Illustrated by 302 engravings and 12 Samples
of Dyed Leathers. One vol., 8vo., 824 pages $10.00

$DAWIDOWSKY--BRANNT.--A Practical Treatise on the Raw Materials and
Fabrication of Glue, Gelatine, Gelatine Veneers and Foils,
Isinglass, Cements, Pastes, Mucilages, etc.$:

Based upon Actual Experience. By F. DAWIDOWSKY, Technical Chemist.
Translated from the German, with extensive additions, including a
description of the most Recent American Processes, by WILLIAM T.
BRANNT, Graduate of the Royal Agricultural College of Eldena,
Prussia. 35 Engravings. 12mo. $2.50

$DE GRAFF.--The Geometrical Stair-Builders' Guide$:

Being a Plain Practical System of Hand-Railing, embracing all its
necessary Details, and Geometrically Illustrated by twenty-two
Steel Engravings; together with the use of the most approved
principles of Practical Geometry. By SIMON DE GRAFF, Architect.
4to. $2.50

$DE KONINCK--DIETZ.--A Practical Manual of Chemical Analysis and
Assaying:$

As applied to the Manufacture of Iron from its Ores, and to Cast
Iron, Wrought Iron, and Steel, as found in Commerce. By L.L. DE
KONINCK, Dr. Sc, and E. DIETZ, Engineer. Edited with Notes, by
ROBERT MALLET, F.R.S., F.S.G., M.I.C.E., etc. American Edition,
Edited with Notes and an Appendix on Iron Ores, by A.A. FESQUET,
Chemist and Engineer. 12mo. $2.50

$DUNCAN.--Practical Surveyor's Guide:$

Containing the necessary information to make any person of common
capacity, a finished land surveyor without the aid of a teacher. By
ANDREW DUNCAN. Illustrated. 12mo. $1.25

$DUPLAIS--A Treatise on the Manufacture and Distillation of
Alcoholic Liquors:$

Comprising Accurate and Complete Details in Regard to Alcohol from
Wine, Molasses, Beets, Grain, Rice, Potatoes, Sorghum, Asphodel,
Fruits, etc.; with the Distillation and Rectification of Brandy,
Whiskey, Rum, Gin, Swiss Absinthe, etc., the Preparation of
Aromatic Waters. Volatile Oils or Essences, Sugars, Syrups,
Aromatic Tinctures, Liqueurs, Cordial Wines, Effervescing Wines,
etc., the Ageing of Brandy and the improvement of Spirits, with
Copious Directions and Tables for Testing and Reducing Spirituous
Liquors, etc., etc. Translated and Edited from the French of MM.
DUPLAIS, Aine et Jeune. By M. MCKENNIE, M.D. To which are added the
United States Internal Revenue Regulations for the Assessment and
Collection of Taxes on Distilled Spirits. Illustrated by fourteen
folding plates and several wood engravings. 743 pp. 8vo. $10.00

$DUSSAUCE.--A General Treatise on the Manufacture of Vinegar:$

Theoretical and Practical. Comprising the various Methods, by the
Slow and the Quick Processes, with Alcohol, Wine, Grain, Malt,
Cider, Molasses, and Beets; as well as the Fabrication of Wood
Vinegar, etc., etc. By Prof. H. DUSSAUCE. 8vo. $5.00

$DUSSAUCE.--Practical Treatise on the Fabrication of Matches, Gun
Cotton, and Fulminating Powder.$

By Professor H. DUSSAUCE. 12mo. $3.00

$DYER AND COLOR-MAKER'S COMPANION:$

Containing upwards of two hundred Receipts for making Colors, on
the most approved principles, for all the various styles and
fabrics now in existence; with the Scouring Process, and plain
Directions for Preparing, Washing-off, and Finishing the Goods.
12mo. $1.25

$EDWARDS.--A Catechism of the Marine Steam-Engine,$

For the use of Engineers, Firemen, and Mechanics. A Practical Work
for Practical Men. By EMORY EDWARDS, Mechanical Engineer.
Illustrated by sixty-three Engravings, including examples of the
most modern Engines. Third edition, thoroughly revised, with much
additional matter. 12mo. 414 pages $2.00

$EDWARDS.--Modern American Locomotive Engines,$

Their Design, Construction and Management. By EMORY EDWARDS.
Illustrated 12mo. $2.00

$EDWARDS.--Modern American Marine Engines, Boilers, and Screw
Propellers$,

Their Design and Construction. Showing the Present Practice of the
most Eminent Engineers and Marine Engine Builders in the United
States. Illustrated by 30 large and elaborate plates. 4to. $5.00

$EDWARDS.--The Practical Steam Engineer's Guide$

In the Design, Construction, and Management of American Stationary,
Portable, and Steam Fire Engines, Steam Pumps, Boilers, Injectors,
Governors, Indicators, Pistons and Rings, Safety Valves and Steam
Gauges. For the use of Engineers, Firemen, and Steam Users. By
EMORY EDWARDS. Illustrated by 119 engravings. 420 pages. 12mo.
$2.50

$ELDER.--Conversations on the Principal Subjects of Political
Economy.$

By Dr. WILLIAM ELDER. 8vo. $2.50

$ELDER.--Questions of the Day$,

Economic and Social. By Dr. WILLIAM ELDER. 8vo. $3.00

$ELDER.--Memoir of Henry C. Carey.$

By Dr. WILLIAM ELDER. 8vo. cloth. $.75

$ERNI.--Mineralogy Simplified.$

Easy Methods of Determining and Classifying Minerals, including
Ores, by means of the Blowpipe, and by Humid Chemical Analysis,
based on Professor von Kobell's Tables for the Determination of
Minerals, with an Introduction to Modern Chemistry. By HENRY ERNI,
A.M., M.D., Professor of Chemistry. Second Edition, rewritten,
enlarged and improved. 12mo. $3.00

$FAIRBAIRN.--The Principles of Mechanism and Machinery of
Transmission$

Comprising the Principles of Mechanism, Wheels, and Pulleys,
Strength and Proportions of Shafts, Coupling of Shafts, and
Engaging and Disengaging Gear. By SIR WILLIAM FAIRBAIRN, Bait. C.E.
Beautifully illustrated by over 150 wood-cuts. In one volume, 12mo.
$2.50

$FITCH.--Bessemer Steel$,

Ores and Methods, New Facts and Statistics Relating to the Types of
Machinery in Use, the Methods in Vogue, Cost and Class of Labor
employed, and the Character and Availability of the Ores utilized
in the Manufacture of Bessemer Steel in Europe and in the United
States; together with opinions and excerpts from various accepted
authorities. Compiled and arranged by THOMAS W. FITCH. 8vo. $3.00

$FLEMING.--Narrow Gauge Railways in America.$

A Sketch of their Rise, Progress, and Success. Valuable Statistics
as to Grades, Curves, Weight of Rail, Locomotives, Cars, etc. By
HOWARD FLEMING. Illustrated, 8vo. $1.50

$FORSYTH.--Book of Designs for Headstones, Mural, and other
Monuments$:

Containing 78 Designs. By JAMES FORSYTH. With an Introduction by
CHARLES BOUTELL, M.A. 4 to., cloth $5.00

$FRANKEL--HUTTER.--A Practical Treatise on the Manufacture of
Starch, Glucose, Starch-Sugar, and Dextrine:$

Based on the German of LADISLAUS VON WAGNER, Professor in the Royal
Technical High School, Buda-Pest, Hungary, and other authorities.
By JULIUS FRANKEL, Graduate of the Polytechnic School of Hanover.
Edited by ROBERT HUTTER, Chemist, Practical Manufacturer of
Starch-Sugar. Illustrated by 58 engravings, covering every branch
of the subject, including examples of the most Recent and Best
American Machinery. 8vo., 344 pp. $3.50


$GEE.--The Goldsmith's Handbook:$

Containing full instructions for the Alloying and Working of Gold,
including the Art of Alloying, Melting, Reducing, Coloring,
Collecting, and Refining; the Processes of Manipulation, Recovery
of Waste; Chemical and Physical Properties of Gold; with a New
System of Mixing its Alloys; Solders, Enamels, and other Useful
Rules and Recipes. By GEORGE E. GEE. 12mo. $1.75


$GEE.--The Silversmith's Handbook:$

Containing full instructions for the Alloying and Working of
Silver, including the different modes of Refining and Melting the
Metal; its Solders; the Preparation of Imitation Alloys; Methods of
Manipulation; Prevention of Waste; Instructions for Improving and
Finishing the Surface of the Work; together with other Useful
Information and Memoranda. By GEORGE E. GEE, Jeweller. Illustrated.
12mo. $1.75


$GOTHIC ALBUM FOR CABINET-MAKERS:$

Designs for Gothic Furniture. Twenty-three plates. Oblong $2.00


$GREENWOOD.--Steel and Iron:$

Comprising the Practice and Theory of the Several Methods Pursued
in their Manufacture, and of their Treatment in the Rolling-Mills,
the Forge, and the Foundry. By WILLIAM HENRY GREENWOOD, F.C.S.
Asso. M.I.C.E., M.I.M.E., Associate of the Royal School of Mines.
With 97 Diagrams, 536 pages. 12mo. $2.00


$GREGORY.--Mathematics for Practical Men:$

Adapted to the Pursuits of Surveyors, Architects, Mechanics, and
Civil Engineers. By OLINTHUS GREGORY. 8vo., plates. $3.00


$GRIER.--Rural Hydraulics:$

A Practical Treatise on Rural Household Water Supply. Giving a full
description of Springs and Wells, of Pumps and Hydraulic Ram, with
Instructions in Cistern Building, Laying of Pipes, etc. By W.W.
GRIER. Illustrated 8vo. $.75


$GRIMSHAW.--Modern Milling:$

Being the substance of two addresses delivered by request, at the
Franklin Institute, Philadelphia, January 19th; and January 27th,
1881. By ROBERT GRIMSHAW, Ph. D. Edited from the Phonographic
Reports. With 28 Illustrations. 8vo. $1.00


$GRIMSHAW.--Saws:$

The History, Development, Action, Classification, and Comparison of
Saws of all kinds. _With Copious Appendices._ Giving the details
of Manufacture, Filing. Setting, Gumming, etc. Care and Use of
Saws; Tables of Gauges; Capacities of Saw-Mills; List of
Saw-Patents, and other valuable information. By ROBERT GRIMSHAW.
Second and greatly enlarged edition, _with Supplement_, and 354
Illustrations. Quarto $4.00

$GRIMSHAW.--A Supplement to Grimshaw on Saws$:

Containing additional practical matter, more especially relating to the
Forms of Saw-Teeth, for special material and conditions, and to the
Behavior of Saws under particular conditions. 120 Illustrations. By
ROBERT GRIMSHAW. Quarto. $2.00

$GRISWOLD.--Railroad Engineer's Pocket Companion for the Field$:

Comprising Rules for Calculating Deflection Distances and Angles,
Tangential Distances and Angles, and all Necessary Tables for
Engineers; also the Art of Levelling from Preliminary Survey to the
Construction of Railroads, intended Expressly for the Young
Engineer, together with Numerous Valuable Rules and Examples. By W.
GRISWOLD. 12 mo., tucks $1.75

$GRUNER.--Studies of Blast Furnace Phenomena$:

By M.L. GRUNER, President of the General Council of Mines of
France, and lately Professor of Metallurgy at the Ecole des Mines.
Translated, with the author's sanction, with an Appendix, by L.D.
B. GORDON, F.R.S.E., F.G.S. 8vo. $2.50

$GUETTIER.--Metallic Alloys$:

Being a Practical Guide to their Chemical and Physical Properties,
their Preparation, Composition, and Uses. Translated from the
French of A. GUETTIER, Engineer and Director of Founderies, author
of "La Fouderie en France," etc., etc. By A.A. FESQUET, Chemist and
Engineer. 12mo. $3.00

$HASERICK.--The Secrets of the Art of Dyeing Wool, Cotton, and
Linen$,

Including Bleaching and Coloring Wool and Cotton Hosiery and Random
Yarns. A Treatise based on Economy and Practice. By E.C. HASERICK.
_Illustrated by 323 Dyed Patterns of the Yarns or Fabrics._ 8vo.
$25.00

$HATS AND FELTING$:

A Practical Treatise on their Manufacture. By a Practical Hatter.
Illustrated by Drawings of Machinery, etc. 8vo. $1.25

$HENRY.--The Early and Later History of Petroleum$:

With Authentic Facts in regard to its Development in Western
Pennsylvania. With Sketches of the Pioneer and Prominent Operators,
together with the Refining Capacity of the United States. By J.T.
HENRY. Illustrated 8vo.

$HOFFER.--A Practical Treatise on Caoutchouc and Gutta Percha$,

Comprising the Properties of the Raw Materials, and the manner of
Mixing and Working them; with the Fabrication of Vulcanized and
Hard Rubbers, Caoutchouc and Gutta Percha Compositions,
Water-proof

Substances, Elastic Tissues, the Utilization of Waste, etc., etc.
From the German of RAIMUND HOFFER. By W.T. BRANNT. Illustrated
12mo. $2.50

$HOFMANN.--A Practical Treatise on the Manufacture of Paper in all
its Branches$:

By CARL HOFMANN, Late Superintendent of Paper-Mills in Germany and
the United States; recently Manager of the "Public Ledger" Paper
Mills, near Elkton, Maryland. Illustrated by 110 wood engravings,
and five large Folding Plates. 4to., cloth; about 400 pages. $50.00

$HUGHES.--American Miller and Millwright's Assistant$:

By WILLIAM CARTER HUGHES. 12mo. $1.50

$HULME.--Worked Examination Questions in Plane Geometrical
Drawing$:

For the Use of Candidates for the Royal Military Academy, Woolwich;
the Royal Military College, Sandhurst; the Indian Civil Engineering
College, Cooper's Hill; Indian Public Works and Telegraph
Departments; Royal Marine Light Infantry; the Oxford and Cambridge
Local Examinations, etc. By F. EDWARD HULME, F.L.S., F.S.A.,
Art-Master Marlborough College. Illustrated by 300 examples. Small
quarto. $3.75

$JERVIS.--Railroad Property$:

A Treatise on the Construction and Management of Railways; designed
to afford useful knowledge, in the popular style, to the holders of
this class of property; as well as Railway Managers, Officers, and
Agents. By JOHN B. JERVIS, late Civil Engineer of the Hudson River
Railroad, Croton Aqueduct, etc. 12mo., cloth $2.00

$KEENE.--A Hand-Book of Practical Gauging$:

For the Use of Beginners, to which is added a Chapter on
Distillation, describing the process in operation at the
Custom-House for ascertaining the Strength of Wines. By JAMES B.
KEENE, of H.M. Customs. 8vo. $1.25

$KELLEY.--Speeches, Addresses, and Letters on Industrial and
Financial Questions$:

By HON. WILLIAM D. KELLEY, M.C. 544 pages, 8vo. $3.00

$KELLOGG.--A New Monetary System$:

The only means of Securing the respective Rights of Labor and
Property, and of Protecting the Public from Financial Revulsions.
By EDWARD KELLOGG. Revised from his work on "Labor and other
Capital." With numerous additions from his manuscript. Edited by
MARY KELLOGG PUTNAM. $Fifth edition.$ To which is added a
Biographical Sketch of the Author. One volume, 12mo.

Paper cover. $1.00

Bound in cloth. $1.50

$KEMLO.--Watch-Repairer's Hand-Book$:

Being a Complete Guide to the Young Beginner, in Taking Apart,
Putting Together, and Thoroughly Cleaning the English Lever and
other Foreign Watches, and all American Watches. By F. KEMLO,
Practical Watchmaker. With Illustrations. 12mo. $1.25

$KENTISH.--A Treatise on a Box of Instruments$,

And the Slide Rule; with the Theory of Trigonometry and Logarithms,
including Practical Geometry, Surveying, Measuring of Timber, Cask
and Malt Gauging, Heights, and Distances. By THOMAS KENTISH. In one
volume, 12mo. $1.25

$KERL.--The Assayer's Manual$:

An Abridged Treatise on the Docimastic Examination of Ores, and
Furnace and other Artificial Products. By BRUNO KERL, Professor in
the Royal School of Mines; Member of the Royal Technical Commission
for the Industries, and of the Imperial Patent-Office, Berlin.
Translated from the German by WILLIAM T. BRANNT, Graduate of the
Royal Agricultural College of Eldena, Prussia. Edited by WILLIAM H.
WAHL, Ph. D., Secretary of the Franklin Institute, Philadelphia.
Illustrated by sixty-five engravings. 8vo. $3.00

$KINGZETT.--The History, Products, and Processes of the Alkali
Trade$:

Including the most Recent Improvements. By CHARLES THOMAS KINGZETT,
Consulting Chemist. With 23 illustrations. 8vo. $2.50

$KINSLEY.--Self-Instructor on Lumber Surveying$:

For the Use of Lumber Manufacturers, Surveyors, and Teachers. By
CHARLES KINSLEY, Practical Surveyor and Teacher of Surveying. 12mo.
$2.50

$KIRK.--The Founding of Metals$:

A Practical Treatise on the Melting of Iron, with a Description of
the Founding of Alloys; also, of all the Metals and Mineral
Substances used in the Art of Founding. Collected from original
sources. By EDWARD KIRK, Practical Foundryman and Chemist.
Illustrated. Third edition. 8vo. $2.50

$KITTREDGE.--The Compendium of Architectural Sheet-Metal Work$:

Profusely Illustrated. Embracing Rules and Directions for
Estimates, Items of Cost, Nomenclature, Tables of Brackets,
Modillions, Dentals, Trusses, Stop-Blocks, Frieze Pieces, etc.
Architect's Specification, Tables of Tin-Roofing, Galvanized Iron,
etc., etc. To which is added the Exemplar of Architectural
Sheet-Metal Work, containing details of the Centennial Buildings,
and other important Sheet-Metal Work, Designs and Prices of
Architectural Ornaments, as manufactured for the Trade by the
Kittredge Cornice and Ornament Company, and a Catalogue of
Cornices, Window-Caps, Mouldings, etc., as manufactured by the
Kittredge Cornice and Ornament Company. The whole supplemented by a
full Index and Table of Contents. By A.O. KITTREDGE. 8vo., 565
pages.

$LANDRIN.--A Treatise on Steel$:

Comprising its Theory, Metallurgy, Properties, Practical Working,
and Use. By M.H.C. LANDRIN, Jr., Civil Engineer. Translated from
the French, with Notes, by A.A. FESQUET, Chemist and Engineer. With
an Appendix on the Bessemer and the Martin Processes for
Manufacturing Steel, from the Report of Abram S. Hewitt,
United States Commissioner to the Universal Exposition, Paris,
1867. 12mo. $3.00

$LARDEN.--A School Course on Heat$:

By W. LARDEN, M.A. 321 pp. 12mo. $2.00

$LARDNER.--The Steam-Engine$:

For the Use of Beginners. By DR. LARDNER. Illustrated. 12mo. $.75

$LARKIN.--The Practical Brass and Iron Founder's Guide$:

A Concise Treatise on Brass Founding, Moulding, the Metals and
their Alloys, etc.; to which are added Recent Improvements in the
Manufacture of Iron, Steel by the Bessemer Process, etc., etc. By
JAMES LARKIN, late Conductor of the Brass Foundry Department in
Reany, Neafie & Co.'s Penn Works, Philadelphia. Fifth edition,
revised, with extensive additions. 12mo. $2.25

$LEROUX.--A Practical Treatise on the Manufacture of Worsteds and
Carded Yarns$:

Comprising Practical Mechanics, with Rules and Calculations applied
to Spinning; Sorting, Cleaning, and Scouring Wools; the English and
French Methods of Combing, Drawing, and Spinning Worsteds, and
Manufacturing Carded Yarns. Translated from the French of CHARLES
LEROUX, Mechanical Engineer and Superintendent of a Spinning Mill,
by HORATIO PAINE, M.D., and A.A. FESQUET, Chemist and Engineer.
Illustrated by twelve large Plates. To which is added an Appendix,
containing Extracts from the Reports of the International Jury, and
of the Artisans selected by the Committee appointed by the Council
of the Society of Arts, London, on Woolen and Worsted Machinery and
Fabrics, as exhibited in the Paris Universal Exposition, 1867. 8vo.
$5.00

$LEFFEL.--The Construction of Mill-Dams$:

Comprising also the Building of Race and Reservoir Embankments and
Head-Gates, the Measurement of Streams, Gauging of Water Supply,
etc. By JAMES LEFFEL & CO. Illustrated by 58 engravings. 8vo. $2.50

$LESLIE.--Complete Cookery$:

Directions for Cookery in its Various Branches. By MISS LESLIE.
Sixtieth thousand. Thoroughly revised, with the addition of New
Receipts. In 12mo., cloth $1.50

$LIEBER.--Assayer's Guide$:

Or, Practical Directions to Assayers, Miners, and Smelters, for the
Tests and Assays, by Heat and by Wet Processes, for the Ores of all
the principal Metals, of Gold and Silver Coins and Alloys, and of
Coal, etc. By OSCAR M. LIEBER. 12mo. $1.25

$LOVE.--The Art of Dyeing, Cleaning, Scouring, and Finishing, on
the Most Approved English and French Methods$:

Being Practical Instructions in Dyeing Silks, Woolens, and Cottons,
Feathers, Chips, Straw, etc. Scouring and Cleaning Bed and Window
Curtains, Carpets, Rugs, etc. French and English Cleaning, any
Color or Fabric of Silk, Satin, or Damask. By THOMAS LOVE, a
Working Dyer and Scourer. Second American Edition, to which
are added General Instructions for the use of Aniline Colors. 8vo.
343 pages $5.00

$LUKIN.--Amongst Machines$:

Embracing Descriptions of the various Mechanical Appliances used in
the Manufacture of Wood, Metal, and other Substances. 12mo. $1.75

$LUKIN.--The Boy Engineers$:

What They Did, and How They Did It. With 30 plates. 18mo. $1.75

$LUKIN.--The Young Mechanic$:

Practical Carpentry. Containing Directions for the Use of all kinds
of Tools, and for Construction of Steam-Engines and Mechanical
Models, including the Art of Turning in Wood and Metal. By JOHN
LUKIN, Author of "The Lathe and Its Uses," etc. Illustrated. 12mo
$1.75

$MAIN and BROWN.--Questions on Subjects Connected with the Marine
Steam-Engine$:

And Examination Papers; with Hints for their Solution. By THOMAS J.
MAIN, Professor of Mathematics, Royal Naval College, and THOMAS
BROWN, Chief Engineer, R.N. 12mo., cloth. $1.50

$MAIN and BROWN.--The Indicator and Dynamometer$:

With their Practical Applications to the Steam-Engine. By THOMAS J.
MAIN, M.A.F.R., Ass't S. Professor Royal Naval College, Portsmouth,
and THOMAS BROWN, Assoc. Inst. C.E., Chief Engineer R.N., attached
to the R.N. College. Illustrated. 8vo. $1.50

$MAIN and BROWN.--The Marine Steam-Engine.$

By THOMAS J. MAIN, F.R. Ass't S. Mathematical Professor at the
Royal Naval College, Portsmouth, and THOMAS BROWN, Assoc. Inst.
C.E., Chief Engineer R.N. Attached to the Royal Naval College. With
numerous illustrations. 8vo. $5.00

$MARTIN.--Screw-Cutting Tables, for the Use of Mechanical
Engineers$:

Showing the Proper Arrangement of Wheels for Cutting the Threads of
Screws of any Required Pitch; with a Table for Making the Universal
Gas-Pipe Thread and Taps. By W.A. MARTIN, Engineer. 8vo. .50

$MICHELL.--Mine Drainage$:

Being a Complete and Practical Treatise on Direct-Acting
Underground Steam Pumping Machinery. With a Description of a large
number of the best known Engines, their General Utility and the
Special Sphere of their Action, the Mode of their Application, and
their Merits compared with other Pumping Machinery. By STEPHEN
MICHELL. Illustrated by 137 engravings. 8vo., 277 pages. $6.00

$MOLESWORTH.--Pocket-Book of Useful Formulae and Memoranda for Civil
and Mechanical Engineers.$

By GUILFORD L. MOLESWORTH, Member of the Institution of Civil
Engineers, Chief Resident Engineer of the Ceylon Railway.
Full-bound in Pocket-book form $1.00

$MOORE.--The Universal Assistant and the Complete Mechanic$:

Containing over one million Industrial Facts, Calculations,
Receipts, Processes, Trades Secrets, Rules, Business Forms, Legal
Items, Etc., in every occupation, from the Household to the
Manufactory. By R. MOORE. Illustrated by 500 Engravings. 12mo.
$2.50

$MORRIS.--Easy Rules for the Measurement of Earthworks$:

By means of the Prismoidal Formula. Illustrated with Numerous
Wood-Cuts, Problems, and Examples, and concluded by an Extensive
Table for finding the Solidity in cubic yards from Mean Areas. The
whole being adapted for convenient use by Engineers, Surveyors,
Contractors, and others needing Correct Measurements of Earthwork.
By ELWOOD MORRIS, C.E. 8vo. $1.50

$MORTON.--The System of Calculating Diameter, Circumference, Area,
and Squaring the Circle$:

Together with Interest and Miscellaneous Tables, and other
information. By JAMES MORTON. Second Edition, enlarged, with the
Metric System. 12mo. $1.00

$NAPIER.--Manual of Electro-Metallurgy$:

Including the Application of the Art to Manufacturing Processes. By
JAMES NAPIER. Fourth American, from the Fourth London edition,
revised and enlarged. Illustrated by engravings. 8vo. $1.50

$NAPIER.--A System of Chemistry Applied to Dyeing.$

By JAMES NAPIER, F.C.S. A New and Thoroughly Revised Edition.
Completely brought up to the present state of the Science,
including the Chemistry of Coal Tar Colors, by A.A. FESQUET,
Chemist and Engineer. With an Appendix on Dyeing and Calico
Printing, as shown at the Universal Exposition, Paris, 1867.
Illustrated. 8vo. 422 pages $5.00

$NEVILLE.--Hydraulic Tables, Coefficients, and Formulae, for finding
the Discharge of Water from Orifices, Notches, Weirs, Pipes, and
Rivers$:

Third Edition, with Additions, consisting of New Formulae for the
Discharge from Tidal and Flood Sluices and Siphons; general
information on Rainfall, Catchment-Basins, Drainage, Sewerage,
Water Supply for Towns and Mill Power. By JOHN NEVILLE, C.E.M.R.
I.A.; Fellow of the Royal Geological Society of Ireland. Thick
12mo. $3.50

$NEWBERY.--Gleanings from Ornamental Art of every style$:

Drawn from Examples in the British, South Kensington, Indian,
Crystal Palace, and other Museums, the Exhibitions of 1851 and
1862, and the best English and Foreign works. In a series of 100
exquisitely drawn Plates, containing many hundred examples. By
ROBERT NEWBERY. 4to. $12.50

$NICHOLLS.--The Theoretical and Practical Boiler-Maker and
Engineer's Reference Book$:

Containing a variety of Useful Information for Employers of Labor,
Foremen and Working Boiler-Makers, Iron, Copper, and Tinsmiths,

Draughtsmen, Engineers, the General Steam-using Public, and for the
Use of Science Schools and Classes. By SAMUEL NICHOLLS. Illustrated
by sixteen plates, 12mo. $2.50

$NICHOLSON.--A Manual of the Art of Bookbinding$:

Containing full instructions in the different Branches of
Forwarding, Gilding, and Finishing. Also, the Art of Marbling
Book-edges and Paper. By JAMES B. NICHOLSON. Illustrated. 12mo.,
cloth $2.25

$NICOLLS.--The Railway Builder$:

A Hand-Book for Estimating the Probable Cost of American Railway
Construction and Equipment. By WILLIAM J. NICOLLS, Civil Engineer.
Illustrated, full bound, pocket-book form. $2.00

$NORMANDY.--The Commercial Handbook of Chemical Analysis$:

Or Practical Instructions for the Determination of the Intrinsic or
Commercial Value of Substances used in Manufactures, in Trades, and
in the Arts. By A. NORMANDY. New Edition, Enlarged, and to a great
extent rewritten. By HENRY M. NOAD, Ph.D., F.R.S., thick 12mo.
$5.00

$NORRIS.--A Handbook for Locomotive Engineers and Machinists$:

Comprising the Proportions and Calculations for Constructing
Locomotives; Manner of Setting Valves; Tables of Squares, Cubes,
Areas, etc., etc. By SEPTIMUS NORRIS, M.E. New edition.
Illustrated, 12mo. $1.50

$NORTH.--The Practical Assayer$:

Containing Easy Methods for the Assay of the Principal Metals and
Alloys. Principally designed for explorers and those interested in
Mines. By OLIVER NORTH. Illustrated. 12mo.

$NYSTROM.--A New Treatise on Elements of Mechanics$:

Establishing Strict Precision in the Meaning of Dynamical Terms:
accompanied with an Appendix on Duodenal Arithmetic and Metrology.
By JOHN W. NYSTROM, C.E. Illustrated. 8vo. $2.00

$NYSTROM.--On Technological Education and the Construction of Ships
and Screw Propellers$:

For Naval and Marine Engineers. By JOHN W. NYSTROM, late Acting
Chief Engineer, U.S.N. Second edition, revised, with additional
matter. Illustrated by seven engravings. 12mo. $1.50

$O'NEILL.--A Dictionary of Dyeing and Calico Printing$:

Containing a brief account of all the Substances and Processes in
use in the Art of Dyeing and Printing Textile Fabrics; with
Practical Receipts and Scientific Information. By CHARLES O'NEILL,
Analytical Chemist. To which is added an Essay on Coal Tar Colors
and their application to Dyeing and Calico Printing. By A.A.
FESQUET, Chemist and Engineer. With an appendix on Dyeing and
Calico Printing, as shown at the Universal Exposition, Paris, 1867.
8vo., 491 pages. $5.00

$ORTON.--Underground Treasures$:

How and Where to Find Them. A Key for the Ready Determination of
all the Useful Minerals within the United States. By JAMES ORTON,
A.M., Late Professor of Natural History in Vassar College, N.Y.;
Cor. Mem. of the Academy of Natural Sciences, Philadelphia, and of
the Lyceum of Natural History, New York; author of the "Andes and
the Amazon," etc. A New Edition, with Additions. Illustrated. $1.50

$OSBORN.--The Metallurgy of Iron and Steel$:

Theoretical and Practical in all its Branches; with special
reference to American Materials and Processes. By H.S. OSBORN, LL.
D., Professor of Mining and Metallurgy in Lafayette College,
Easton, Pennsylvania. Illustrated by numerous large folding plates
and wood-engravings. 8vo. $25.00

$OVERMAN.--The Manufacture of Steel$:

Containing the Practice and Principles of Working and Making Steel.
A Handbook for Blacksmiths and Workers in Steel and Iron, Wagon
Makers, Die Sinkers, Cutlers, and Manufacturers of Files and
Hardware, of Steel and Iron, and for Men of Science and Art. By
FREDERICK OVERMAN, Mining Engineer, Author of the "Manufacture of
Iron," etc. A new, enlarged, and revised Edition. By A.A. FESQUET,
Chemist and Engineer. 12mo. $1.50

$OVERMAN.--The Moulder's and Founder's Pocket Guide$:

A Treatise on Moulding and Founding in Green-sand, Dry-sand, Loam,
and Cement; the Moulding of Machine Frames, Mill-gear, Hollow-ware,
Ornaments, Trinkets, Bells, and Statues; Description of Moulds for
Iron, Bronze, Brass, and other Metals; Plaster of Paris, Sulphur,
Wax, etc.; the Construction of Melting Furnaces, the Melting and
Founding of Metals; the Composition of Alloys and their Nature,
etc., etc. By FREDERICK OVERMAN, M.E. A new Edition, to which is
added a Supplement on Statuary and Ornamental Moulding, Ordnance,
Malleable Iron Castings, etc. By A.A. FESQUET, Chemist and
Engineer. Illustrated by 44 engravings. 12mo. $2.00

$PAINTER, GILDER, AND VARNISHER'S COMPANION$:

Containing Rules and Regulations in everything relating to the Arts
of Painting, Gilding, Varnishing, Glass-Staining, Graining,
Marbling, Sign-Writing, Gilding on Glass, and Coach Painting and
Varnishing; Tests for the Detection of Adulterations in Oils,
Colors, etc.; and a Statement of the Diseases to which Painters are
peculiarly liable, with the Simplest and Best Remedies. Sixteenth
Edition. Revised, with an Appendix. Containing Colors and
Coloring--Theoretical and Practical. Comprising descriptions of a
great variety of Additional Pigments, their Qualities and Uses, to
which are added, Dryers, and Modes and Operations of Painting, etc.
Together with Chevreul's Principles of Harmony and Contrast of
Colors. 12mo. Cloth $1.50

$PALLETT.--The Miller's, Millwright's, and Engineer's Guide.$

By HENRY PALLETT. Illustrated. 12mo. $3.00

$PEARSE.--A Concise History of the Iron Manufacture of the American
Colonies up to the Revolution, and of Pennsylvania until the
present time.$

By JOHN B. PEARSE. Illustrated 12mo. $2.00

$PERCY.--The Manufacture of Russian Sheet-Iron.$

By JOHN PERCY, M.D., F.R.S., Lecturer on Metallurgy at the Royal
School of Mines, and to The Advance Class of Artillery Officers at
the Royal Artillery Institution, Woolwich; Author of "Metallurgy."
With Illustrations. 8vo., paper 50 cts.

$PERKINS.--Gas and Ventilation$:

Practical Treatise on Gas and Ventilation. With Special Relation to
Illuminating, Heating, and Cooking by Gas. Including Scientific
Helps to Engineer-students and others. With Illustrated Diagrams.
By E.E. PERKINS. 12mo., cloth $1.25

$PERKINS AND STOWE.--A New Guide to the Sheet-iron and Boiler
Plate Roller$:

Containing a Series of Tables showing the Weight of Slabs and Piles
to Produce Boiler Plates, and of the Weight of Piles and the Sizes
of Bars to produce Sheet-iron; the Thickness of the Bar Gauge in
decimals; the Weight per foot, and the Thickness on the Bar or Wire
Gauge of the fractional parts of an inch; the Weight per sheet, and
the Thickness on the Wire Gauge of Sheet-iron of various dimensions
to weigh 112 lbs. per bundle; and the conversion of Short Weight
into Long Weight, and Long Weight into Short. Estimated and
collected by G.H. PERKINS and J.G. STOWE. $2.50

$POWELL--CHANCE--HARRIS.--The Principles of Glass Making.$

By HARRY J. POWELL, B.A. Together with Treatises on Crown and Sheet
Glass; by HENRY CHANCE, M.A. And Plate Glass, by H.G. HARRIS,
Asso. M. Inst. C.E. Illustrated 18mo. $1.50

$PROTEAUX.--Practical Guide for the Manufacture of Paper and
Boards.$

By A. PROTEAUX. From the French, by HORATIO PAINE, A.B., M.D. To
which is added the Manufacture of Paper from Wood, by HENRY T.
BROWN. Illustrated by six plates. 8vo.

$PROCTOR.--A Pocket-Book of Useful Tables and Formulae for Marine
Engineers.$

By FRANK PROCTOR. Second Edition, Revised and Enlarged. Full bound
pocket-book form. $1.50

$REGNAULT.--Elements of Chemistry.$

By M.V. REGNAULT. Translated from the French by T. FORREST BETTON,
M.D., and edited, with Notes, by JAMES C. BOOTH, Melter and Refiner
U.S. Mint, and WILLIAM L. FABER, Metallurgist and Mining Engineer.
Illustrated by nearly 700 wood engravings. Comprising nearly 1,500
pages. In two volumes, 8vo., cloth $7.50

$RIFFAULT, VERGNAUD, and TOUSSAINT.--A Practical Treatise on the
Manufacture of Colors for Painting$:

Comprising the Origin, Definition, and Classification of Colors;
the Treatment of the Raw Materials; the best Formulae and the Newest
Processes for the Preparation of every description of Pigment, and
the Necessary Apparatus and Directions for its Use; Dryers; the
Testing, Application, and Qualities of Paints, etc., etc. By MM.
RIFFAULT, VERGNAUD, and TOUSSAINT. Revised and Edited by M.F.
MALEPEYRE. Translated from the French, by A.A. FESQUET, Chemist and
Engineer. Illustrated by Eighty engravings. In one vol., 8vo., 659
pages. $7.50

$ROPER.--A Catechism of High-Pressure, or Non-Condensing
Steam-Engines$:

Including the Modelling, Constructing, and Management of
Steam-Engines and Steam Boilers. With valuable illustrations. By
STEPHEN ROPER, Engineer. Sixteenth edition, revised and enlarged.
18mo., tucks, gilt edge. $2.00

$ROPER.--Engineer's Handy-Book$:

Containing a full Explanation of the Steam-Engine Indicator, and
its Use and Advantages to Engineers and Steam Users. With Formulae
for Estimating the Power of all Classes of Steam-Engines; also,
Facts, Figures, Questions, and Tables for Engineers who wish to
qualify themselves for the United States Navy, the Revenue Service,
the Mercantile Marine, or to take charge of the Better Class of
Stationary Steam-Engines. Sixth edition. 16mo., 690 pages, tucks,
gilt edge. $3.50

$ROPER.--Hand-Book of Land and Marine Engines$:

Including the Modelling, Construction, Running, and Management of
Land and Marine Engines and Boilers. With illustrations. By STEPHEN
ROPER, Engineer. Sixth edition. 12mo., tucks, gilt edge. $3.50

$ROPER.--Hand-Book of the Locomotive$:

Including the Construction of Engines and Boilers, and the
Construction, Management, and Running of Locomotives. By STEPHEN
ROPER. Eleventh edition. 18mo., tucks, gilt edge. $2.50

$ROPER.--Hand-Book of Modern Steam Fire-Engines.$

With illustrations. By STEPHEN ROPER, Engineer. Fourth edition,
12mo., tucks, gilt edge. $3.50

$ROPER.--Questions and Answers for Engineers.$

This little book contains all the Questions that Engineers will be
asked when undergoing an Examination for the purpose of procuring
Licenses, and they are so plain that any Engineer or Fireman of
ordinary intelligence may commit them to memory in a short time. By
STEPHEN ROPER, Engineer. Third edition. $3.00

$ROPER.--Use and Abuse of the Steam Boiler.$

By STEPHEN ROPER, Engineer. Eighth edition, with illustrations.
18mo., tucks, gilt edge. $2.00

$ROSE.--The Complete Practical Machinist$:

Embracing Lathe Work, Vise Work, Drills and Drilling, Taps and
Dies, Hardening and Tempering, the Making and Use of Tools, Tool
Grinding, Marking out Work, etc. By JOSHUA ROSE. Illustrated by 356
engravings. Thirteenth edition, thoroughly revised and in great
part rewritten. In one vol., 12mo., 439 pages. $2.50

$ROSE.--Mechanical Drawing Self-Taught$:

Comprising Instructions in the Selection and Preparation of Drawing
Instruments, Elementary Instruction in Practical Mechanical
Drawing, together with Examples in Simple Geometry and Elementary
Mechanism, including Screw Threads, Gear Wheels, Mechanical Motions,
Engines and Boilers. By JOSHUA ROSE, M.E., Author of "The Complete
Practical Machinist," "The Pattern-maker's Assistant," "The
Slide-valve." Illustrated by 330 engravings. 8vo., 313 pages. $4.00

$ROSE.--The Slide-Valve Practically Explained$:

Embracing simple and complete Practical Demonstrations of the
operation of each element in a Slide-valve Movement, and
illustrating the effects of Variations in their Proportions by
examples carefully selected from the most recent and successful
practice. By JOSHUA ROSE, M.E., Author of "The Complete Practical
Machinist," "The Pattern-maker's Assistant," etc. Illustrated by 35
engravings. $1.00

$ROSS.--The Blowpipe in Chemistry, Mineralogy and Geology$:

Containing all Known Methods of Anhydrous Analysis, many Working
Examples, and Instructions for Making Apparatus. By LIEUT.-COLONEL
W.A. ROSS, R.A.F., G.S. With 120 Illustrations. 12mo. $1.50

$SHAW.--Civil Architecture$:

Being a Complete Theoretical and Practical System of Building,
containing the Fundamental Principles of the Art. By EDWARD SHAW,
Architect. To which is added a Treatise on Gothic Architecture,
etc. By THOMAS W. SILLOWAY and GEORGE M. HARDING, Architects. The
whole illustrated by 102 quarto plates finely engraved on copper.
Eleventh edition. 4to. $10.00

$SHUNK.--A Practical Treatise on Railway Curves and Location, for
Young Engineers.$

By WILLIAM F. SHUNK, Civil Engineer. 12mo. Full bound pocket-book
form. $2.00

$SLATER.--The Manual of Colors and Dye Wares.$

By J.W. SLATER. 12mo. $3.75

$SLOAN.--American Houses$:

A variety of Original Designs for Rural Buildings. Illustrated by
twenty-six  Engravings, with Descriptive References. By
SAMUEL SLOAN, Architect, author of the "Model Architect," etc. etc.
8vo. $1.50

$SLOAN.--Homestead Architecture$:

Containing Forty Designs for Villas, Cottages, and Farm-houses,
with Essays on Style, Construction, Landscape Gardening, Furniture,
etc., etc. Illustrated by upwards of 200 engravings. By SAMUEL
SLOAN, Architect. 8vo. $3.50

$SMEATON.--Builder's Pocket-Companion$:

Containing the Elements of Building, Surveying, and Architecture;
with Practical Rules and Instructions connected with the subject.
By A.C. SMEATON, Civil Engineer, etc. 12mo. $1.50

$SMITH.--A Manual of Political Economy.$

By E. PESHINE SMITH. A new Edition, to which is added a full Index.
12mo. $1.25

$SMITH.--Parks and Pleasure-Grounds:$

Or Practical Notes on Country Residences, Villas, Public Parks, and
Gardens. By CHARLES H.J. SMITH, Landscape Gardener and Garden
Architect, etc., etc. 12mo. $2.00

$SMITH.--The Dyer's Instructor:$

Comprising Practical Instructions in the Art of Dyeing Silk,
Cotton, Wool, and Worsted, and Woolen Goods; containing nearly 800
Receipts. To which is added a Treatise on the Art of Padding; and
the Printing of Silk Warps, Skeins, and Handkerchiefs, and the
various Mordants and Colors for the different styles of such work.
By DAVID SMITH, Pattern Dyer. 12mo. $3.00

$SMYTH.--A Rudimentary Treatise on Coal and Coal-Mining.$

By WARRINGTON W. SMYTH, M.A., F.R.G., President R.G.S. of Cornwall.
Fifth edition, revised and corrected. With numerous illustrations.
12mo. $1.75

$SNIVELY.--A Treatise on the Manufacture of Perfumes and Kindred
Toilet Articles.$

By JOHN H. SNIVELY, Phr. D., Professor of Analytical Chemistry in
the Tennessee College of Pharmacy. 8vo. $3.00

$SNIVELY.--Tables for Systematic Qualitative Chemical Analysis.$

By JOHN H. SNIVELY, Phr. D. 8vo. $1.00

$SNIVELY.--The Elements of Systematic Qualitative Chemical
Analysis:$

A Hand-book for Beginners. By JOHN H. SNIVELY, Phr. D. 16mo. $2.00

$STEWART.--The American System:$

Speeches on the Tariff Question, and on Internal Improvements,
principally delivered in the House of Representatives of the United
States. By ANDREW STEWART, late M.C. from Pennsylvania. With a
Portrait, and a Biographical Sketch. 8vo. $3.00

$STOKES.--The Cabinet-Maker and Upholsterer's Companion:$

Comprising the Art of Drawing, as applicable to Cabinet Work;
Veneering, Inlaying, and Buhl-Work; the Art of Dyeing and Staining
Wood, Ivory, Bone, Tortoise-Shell, etc. Directions for Lackering,
Japanning, and Varnishing; to make French Polish, Glues, Cements,
and Compositions; with numerous Receipts, useful to workmen
generally. By J. STOKES. Illustrated. A New Edition, with an
Appendix upon French Polishing, Staining, Imitating, Varnishing,
etc., etc. 12mo. $1.25

$STRENGTH AND OTHER PROPERTIES OF METALS:$

Reports of Experiments on the Strength and other Properties of
Metals for Cannon. With a Description of the Machines for Testing
Metals, and of the Classification of Cannon in service. By Officers
of the Ordnance Department, U.S. Army. By authority of the
Secretary of War. Illustrated by 25 large steel plates. Quarto.
$10.00

$SULLIVAN.--Protection to Native Industry.$

By Sir EDWARD SULLIVAN, Baronet, author of "Ten Chapters on Social
Reforms." 8vo. $1.50

$SYME.--Outlines of an Industrial Science.$

By DAVID SYME. 12mo. $2.00

$TABLES SHOWING THE WEIGHT OF ROUND, SQUARE, AND FLAT BAR IRON,
STEEL, ETC.,$

By Measurement. Cloth. 63

$TAYLOR.--Statistics of Coal:$

Including Mineral Bituminous Substances employed in Arts and
Manufactures; with their Geographical, Geological, and Commercial
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      *       *       *       *       *

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WITH ADDITIONS BY
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Transcriber's Notes:
Opening quote on folio page 210 was eliminated due to ambiguity of the
extent of the quote: Quote: "But these circular arcs....
Conventional text emphasis coding $...$ used for bolded text.






End of Project Gutenberg's Mechanical Drawing Self-Taught, by Joshua Rose

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