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APPLETONS'

CYCLOPEDIA OF TECHNICAL

DRAWING.

EMBRACING

Jjrinnplts of

AS APPLIED TO

PRACTICAL DESIGN.

WITH NUMEROUS ILLUSTRATIONS OF

TOPOGRAPHICAL, MECHANICAL, ENGINEERING,

ARCHITECTURAL, PERSPECTIVE, AND

FREE-HAND DRAWING.

EDITED BY

W. E. WORTHEN, C. E.

NEW YORK:

D. APPLETON AND COMPANY,

1, 3, AND 5 BOND STREET.

1892.

COPYRIGHT, 1885,

BY D. APPLETON AND COMPANY.

PREFACE.

" AT the suggestion of the publishers, this work was undertaken to form

one of their series of dictionaries and cyclopedias. In this view, it has been

the intention to make it a complete course of instruction and book of refer-

ence to the mechanic, architect, and engineer. It has not, therefore, 'been

confined to the explanation and illustration of the methods of projection, and

the delineation of objects which might serve as copies to the draughtsman,

matters of essential importance for the correct and intelligible representation

of every form ; but it contains the means of determining the amount and

direction of strains to which different parts of a machine or structure may be

subjected, and the rules for disposing and proportioning of the material em-

ployed, to the safe and permanent resistance of those strains, with practical

applications of the same. Thus, while it supplies numerous illustrations in

every department for the mere copyist, it also affords suggestions and aids

to the mechanic in the execution of new designs. And, although the arrang-

ing and properly proportioning alone of material in a suitable direction, and

adequately to the resistance of the strains to which it might be exposed,

would produce a structure sufficient in point of strength for the purposes for

which it is intended, yet, as in many cases the disposition of the material

may be applied not only practically, but also artistically, and adapted to the

reception of ornament, under the head of Architectural Drawing, the general

characteristics of various styles have been treated of and illustrated, with

brief remarks on proportion and the application of color." . . . 1857.

Since its first publication, this work has been subjected from time to time

to revision. It has now been deemed necessary to almost entirely rearrange

and rewrite it ; to add largely to the subject-matter and to the illustrations,

introducing examples of later practice and experience ; to extend the scope

of the work, and make it more nearly a cyclopaedia of drawing and design.

There are no changes in the principles of projection as applied to drawing,

and no marked improvement in drawing-instruments ; but in the present

practice finished drawings in shade and color are exceptional. It is suffi-

cient, for almost every purpose, for the draughtsman to make accurate projec-

tions with pencil on paper, and trace them afterward on cloth. The pencil-

drawings can be readily altered or amended, and, where there are many repe-

iv PREFACE.

titions of the same parts, but a single one may be drawn. On the tracing

they are made complete, and these are preserved as originals in the office,

while sun-prints of them are used for details of construction in the shop, or

distributed as circulars among customers.

In the sale of former editions of this work, it has been found that its

success has been largely due to its value as a book of design. Great attention

has therefore been given to secure practical illustration of constructions and

machines of recent date ; the nature of materials in common use has been

more extensively treated, and the character and effect of stresses and strains,

their kind and direction, more fully explained, with as simple rules as possible

to determine them for practical application.

Of late years the science of " graphics " has become of great importance,

and is here fully illustrated in its varied applications, showing not only this

method of recording the facts of the statistician, and affording comparisons

of circumstances and times, the growth of population, the quantities and cost

of agricultural and mechanical production, and of their transport, movements

of trade, fluctuations of value, the atmospheric conditions, death-rates, etc.,

but also in its application to the plotting of formulae for their ready solution,

by the draughtsman and designer. For many of the rules in this work the

results of the formulae of various authors have been plotted graphically, and

the rule given one deemed of the greatest weight, not always by average,

but most consistent with our own experience.

In astronomical calculations every decimal may have its importance. It

is not so in those of the mechanical or architectural designer ; solutions by

graphics are sufficient for their purpose, and, simpler than mathematical cal-

culations, they are thus less liable to error ; it is very good practice to use one

as a check on the other. It is to be remarked that inaccuracy in facts, and

carelessness in observation, are not eliminated from an equation by closeness

of calculation, and when factors are not established within the limits of units

it is useless to extend the results to many places of decimals. It is of the

utmost importance to know at first well the object and purposes of the

design, the stresses to which its parts are to be subjected, and the strength

and endurance of the materials of which it is to be composed. In establish-

ing rules for ourselves, be sure of the facts, and that there are enough of

them for a general application. Rules are necessary, but their application

and usefulness depend largely on the experience of the user, and life must

be a record of applications and effects. It is comparatively easy to make

a work strong enough ; but to unite economy with proportion is difficult.

To make the work complete in itself, so as to form a sort of single book

for most of the purposes of the draughtsman and designer embracing the

profession of surveyor, engineer, and architect tables of logarithms, latitudes

and departures, squares and cubes, and square and cube roots, weights and

measures, and weights of material, have been added.

w.

CONTENTS.

PAGES

CONSTRUCTION OF GEOMETRICAL PROBLEMS 1-39

Drawing of lines straight, curved, and parallels, angles, perpendicular ; bisecting

angles; arcs and circles, 15. On polygons and circles; triangles, parallelograms,

squares ; circles, angles ; polygons ; inscribed and described circles ; pentagons, hexa-

gons, octagons ; table of polygonal angles, 23. On the ellipse, parabola, hyperbola,

cycloid, epicycloid, involute and spiral, 33. Use of triangle and square, 33. Areas

of figures, 37. To draw squares of given proportionate sizes, 39.

DRAWING INSTRUMENTS 40-77

Description and use ; rulers ; triangles; T-square; parallel ruler ; sweeps and vari-

able curves ; drawing pens ; dotting point ; pricking point ; compasses ; dividers ;

beam compasses ; porportional dividers ; scales ; scale guard ; diagonal scales ; ver-

nier scales ; sector ; protractors ; pantagraphs ; camera lucida ; drawing table and

board, 56. Drawing paper ; tracing paper ; tracing cloth ; mouth glue ; damp stretch-

ing paper ; mounting paper and drawings, 59. Management of the instruments ;

ink ; exercises with drawing pen ; various letters and numerals ; cross-section paper ;

diagrams showing use of cross-section paper, 77.

ORTHOGRAPHIC PROJECTION 78-109

Definitions; points; straight line; solid, 81. Simple bodies; pyramid; prism,

87. Construction of the conic sections, 90. Penetration or intersection of solids ;

cylinders, cone, and sphere ; cylinder and ring ; sphere and prism ; cone and prism ;

cone and cylinder, 102. Of the helix, 104. Development of surfaces ; cylinder ;

cone; sphere, 107. Shade-lines, 109.

SHADES AND SHADOWS 110-136

Of a point : straight line ; solid ; circle ; pyramid ; cylinder ; cone ; shadows cast

upon a cylinder by various-shaped caps ; shadows cast upon a prism ; shadows upon

the interior of a cylinder, hollow hemisphere, a niche, a sphere ; line of shade on the

surface of a ring, grooved pulley, square-threaded nut and screw, triangular-threaded

nut and screw, 126. Manipulation of shading and shadows methods of tinting;

surfaces in the light ; surfaces in shade ; shading by flat tints ; by softened tints,

129. Elaboration of shading and shadows; examples of finished shading; on con-

cave surfaces, spheres, ring, cone, flat surfaces ; colors for tints ; expeditious way of

shading a cylinder ; body color ; margin of light ; washing ; conventional tints for

materials, 136.

PLOTTING ; 137-148

Scales ; scales prescribed by different commissions, 138. Variation of compass,

1 39. Plotting compass surveys ; balancing error ; plotting by latitudes and depart-

ures ; area by latitudes and departures ; area by triangles ; plotting by offsets, 147.

System of division of United States land, 148.

VI

CONTENTS.

PAGES

TOPOGRAPHICAL DRAWING 149-180

Conventional signs ; representation of hills ; contour lines, 156. Railway surveys ;

profiles; sections, land plans, 159. Hydrometrical or marine surveys, conventionali-

ties, 160. Geological and statistical features, 162. Transferring ; pricking through;

by tracing; blue-print process; copying-glass; transfer-paper; pantagraph, 165.

Map projections ; perspective projection on planes ; developed perspective projec-

tions ; projections by developing elements ; projections conforming to some arbi-

trary condition ; polyconic adopted by United States Coast Survey ; De Lorgne's

projection; M creator's chart, 171. Colored topography ; conventional colors ; direc-

tions; finishing; lettering; titles, 180.

MATERIALS 181-199

Earth and rocks, 182. Building materials ; wood, 185. Stones; technical terms

masonry; granitic stones, argillaceous stones ; sandstones ; limestone, 188. Artificial

building material ; bricks ; tile ; terra-cotta ; mortars ; limes ; cement ; concrete ;

plastering, 191. Metals; conventional hatchings ; iron; steel; other metals; specific

gravity ; weight ; melting-point ; resistance to crushing and tension ; results of Prof.

Thurston's tests of metals, 196. Sulphur; glass; rubber; paints; coals, 199.

MECHANICS 200-219

Force ; center of gravity ; levers ; wheel and axle ; pulley ; inclined plane ; wedge ;

screw ; inclined forces ; parallelogram of forces ; hydraulic press ; velocity of falling

bodies; friction, 212. Mechanical work or effect; horse-power, etc.; water-power;

wind ; steam ; steam worked expansively ; cut-offs ; compound engines ; indicator

cards, 219.

MACHINE DESIGN AND MECHANICAL CONSTRUCTIONS 220-361

Stress ; dead load ; strength of posts and columns ; Phoenix columns, etc. ; shear-

ing stresses ; torsional stress ; transverse stress ; strength of beams ; tables of dimen-

sions of channel beams and angle-iron ; composite beams ; bolts and nuts ; strength

of bolts ; washers ; shafts and axles ; journals ; keys ; car-axles ; shafting ; bear-

ings ; couplings; clutch; pulleys; belts; ropes, 275. Gearing; epicycloidal teeth;

projections of a spur-wheel and bevel-wheel, 294. Drawing of screws, 297. Fric-

tional gearing, 299. Ropes and chains ; hooks ; levers ; cranks ; connecting-rods ;

steam-engine ; working-beam ; parallel-motion links ; steam-cylinders and pistons,

331. Valves ; hydrants, 342. Riveted joints for boilers ; boilers, 351. Wrought-

iron pipe connections, 355. Frames ; governors ; fly-wheels ; air-chambers, 361.

ENGINEERING DRAWING 362-460

Foundations ; sheet-piling ; retaining-walls ; foundations for piei^s, etc., 375.

Dams ; locks of canals ; conduits ; reservoirs, 395. Water-pipes, 398. Sewers, 401.

Gas-supply, 402. Roads, 407. Roofs and bridges; piers, 432. Arch-bridges; sus-

pension-bridges, 438. Boiler-setting ; chimneys, 444. Location of machines ; ma-

chine foundations, 449. Tunnels, 453. Railway stock, 458. Wave-line principle of

ship construction, 460.

ARCHITECTURAL DRAWING

Details of construction ; concrete walls, 468. Frames and floors ; fire-resisting

floors, 474. Groined ceilings, 476. Doors ; windows ; moldings, 485. Stairs, 492.

Fireplaces ; flues ; roofs ; gutters ; plastering, 495. Proportions and distribution of

rooms and passages, 500. Plans and elevations of buildings ; stores and warehouses,

521. School-houses, 531. Churches, theatres, lecture-rooms, music and legislative

halls ; hospitals, 542. Stables ; cow-houses ; greenhouses, 547. Ventilation and

warming, 555. Plumbing, 564. Greek and Roman orders of architecture, 596. Or-

naments of the Renaissance ; principles of design, 601.

461-601

CONTENTS.

vn

PAGES

PERSPECTIVE DRAWING 602-624

Angular perspective, 610. Parallel perspective, 624.

ISOMETRICAL DRAWING 625-638

FREE-HAND DRAWING

Geometrical figures and design, 643. Proportions of the human frame, 647.

Figure drawing, 650. Forms of animals, 653. Illustrations from different artists,

664.

APPENDIX

Extracts from New York building laws, 670. Patent-Office drawings, 670. Men-

suration ; properties of triangles, 672. Lineal measure, 672. Table of inches in

decimals of a foot, 673. Table of measures of surface, 673. Table of measures of

capacity ; dry measure ; weights ; cubic measure, 674. Table of weight of rolled

iron, 675. Table of weight of wrought-iron and brass plates and wire, 676. Table

of weight of wrought-iron welded tubes ; boiler tubes ; driven-well tubes ; heavy

wrought galvanized iron spiral riveted pipes, 678. Table of copper and brass rods,

678. Table of number of Burden's rivets in 100 pounds, 679. Table of number of

wrought spikes to a keg, 679. Table of length of cut nails and spikes, and number

in a pound, 680. Table of weights of lead pipe per foot, 680. Table of the weight

of a cubic foot of water at different temperature?, 680. Table of properties of satu-

rated steam, 682. Table of mean pressures in steam cylinders at different rates of

expansion, 683. The flow of water, with table of discharge over weir, 685. Flow

of water through pipes and sewers, 689. Flow of air through pipes, 690. Table of

circumferences and areas of circles, 695. Table of squares, cubes, square and cube

roots of numbers, 703. Table of latitudes and departures, 709. Table of natural

sines and cosines, 718. Logarithms of numbers, 735.

INDEX.

DESCRIPTION OF PLATES.

PLATES I TO XIV.

SCRAPS.

639-664

665-735

DESCRIPTION OF PLATES.

PLATE

I. Shading of prism and cylinder by flat tints. Referred to on pages

126-7.

II. Shading of cylinder and segment of hexagonal pyramid. Referred to

on pages 128-9.

Ill, IV. Finished shading and shadows of different solids. Referred to on

page 131.

V. Shades and shadows on screws. Referred to on page 126.

VI. Example of topographical drawing, done entirely with the pen.

VII. The same, with the brush, in black.

VIII. The same, with the brush, in color. Referred to on page 174.

IX. Contoured map of Staten Island, shaded by superimposed washes,

the washes increasing in intensity or strength as required to pro-

duce the effect.

X. Geological map of part of New Jersey, colored to show the different

formations.

XI. Finished, shaded sectional view, colored to show the different metals,

of a balanced leather cup-valve. The body is of cast-iron ; the

piston, brass ; packing, leather ; piston-rod, wrought-iron this

last not distinctively colored.

XII. Finished perspective drawing, with shades and shadows, of a large

bevel-wheel and two pinions, with shifting clutches.

XIII. Front elevation of a building, in color.

XIV. Perspective view of Gothic church, finished in color.

XV. Plan, elevation, and section of bevel-wheel, pinion, and clutches,

shown in perspective Plate XII.

XVI to XX. Details of progressive perspective projections of Plate XV, as

shown completed in Plate Xll.

APPLETONS'

CYCLOPAEDIA OF DRAWING,

CONSTRUCTION OF GEOMETRICAL PROBLEMS.

MOST persons, at some time, have made use of the simple drawing instru-

ments, pencils, straight-edges or rulers, and compasses or dividers with change-

able points, and many suppose that there can be no skill in their use ; but to

one critical in these matters there are great differences to be observed even in

common drawings, in the straightness and uniformity of the lines, and in the

care of the surface of the paper.

Select for the geometrical problems and

for usual drawings a No. 3 or H H H pen-

cil. It should be sharpened to a cone-point

(Fig. 1). Where a pencil is used for drawing

lines only, some draughtsmen sharpen the

pencil to a wide edge, like a chisel.

In drawing a straight line, hold the ruler

firmly with the left hand ; with the right

hand hold the pencil lightly but without

FlG - 1 - slackness, and a little inclined in the direc-

tion of the line to be drawn, keeping the pencil against the edge of the

ruler, and in the same relative position to the edge during the whole operation,

of drawing the line.

2 CONSTRUCTION OF GEOMETRICAL PROBLEMS.

To draw a clean line and preserve the point of the pencil, the part of the

cone a little above the point of the pencil should bear against the edge of the

ruler, and the pencil should be carried steadily while drawing. Any oscilla-

tion will throw the point farther from or nearer the ruler, and the line will

not be straight (Fig. 2).

FIG. 2.

In the use of the compasses do not make a hole through the paper with the

needle or sharp point, but only into the paper sufficient to maintain the

position.

Keep the paper clean, and use rubber as little as possible.

As drawing is based on geometrical principles, we commence with geo-

metrical definitions and problems to give the learner some knowledge of

the science of geometry, with a valuable exercise in the use of drawing

instruments.

Geometrically a point is defined as position merely : in drawing, the posi-

tions of points are marked on the paper by prick-marks of a needle or sharp

point, and by the dot of a pencil ; sometimes inclosed O, sometimes designated

by the intersection of two short lines X >.

Geometrically lines have but one dimension, .length, and the direction

of a line is the direction from point to point of the points of which the

line is composed : in drawing, lines are visible marks of pencil or pen upon

paper.

FIG. 3.

A straight line is such as can be drawn along the edge of the ruler, and is

one in which the direction is the same throughout. In drawing a straight line

through two given points, place the edge of the ruler very near to and at equal

distances from the points, as the point of the pencil or pen should not be in

contact with the edge of the ruler (Fig. 3).

Lines in geometry and drawing are generally of limited extent. A given

CONSTRUCTION OF GEOMETRICAL PROBLEMS.

3

FIG. 4.

or known line is one established on paper or fixed by dimensions. Lines of

the same length are equal.

To draw Curved Lines. Insert the pencil-point in the compasses, and open

them to a suitable extent. With the needle or sharp point resting on the

paper describe a line with the pencil around this point ; the line thus

described is usually called a circle more strictly it is the circumference of a

circle the circle being the space inclosed. A portion

of a circumference is an arc. The point around

which the circumference is described is the center

of the circle (Fig. 4).

If a line be drawn from the center to the circum-

ference it is called a radius. As it is the length

embraced between the points of the compasses, it is

often called by mechanics the sweep.

If a line be drawn through the center, and limited

by the circumference, it is called the diameter, and is

equal to two radii.

A radius is a semi-diameter ; a diameter is the longest line that can be con-

tained within a circumference. Lines limited by the circumference, and which

are not diameters, are chords.

It will be observed that arcs are lines which are continually changing the

directions, and are called curved lines, but there are other curved lines than

those described by compasses, of which the construction will be explained

hereafter.

Besides straight and curved lines there are often lines, in drawing, which

can neither be drawn by rulers or compasses, as lines representing the direc-

tions of brooks and rivers, the margins of lakes and seas, points in which are

established by surveys, defined on paper, and connected by hand-drawing.

These may be called irregular or crooked lines.

Where it is necessary to distinguish lines by names, we place at their

extremities letters or figures, as A B, 1 2 ; the line A B, or 1 2.

But in lines other than straight, or of considerable extent, it is often necessary

to introduce intermediate letters and figures, as a a a.

In the following problems, unless otherwise implied or designated, where

lines are mentioned, straight lines are intended.

If we conceive a straight line to move sideways in a single direction, it will

sweep over a surface which is called a plane. All drawings are projections on

planes of paper or board.

Two lines drawn on paper, and having the same direction, can never come

any nearer each other, and must always be at the same distance apart, however

far extended. Such lines are called parallel lines.

4: CONSTRUCTION OF GEOMETRICAL PROBLEMS.

PEOB. L To draw a line parallel to a given line, and at a given distance

from it (Fig. 5).

Draw the line A B for the given line, and take in the compasses the dis-

tance A C the distance at which the other line is to be drawn. On A, as a

Jj

FIG. 5.

FIG. 6.

center, describe an arc, and on B, as a center, another arc ; draw the line C D

just touching these two arcs, which will be the parallel line required.

PKOB. II. To draw a line parallel to a given line through a given point

outside this line (Fig. 6).

Draw the given line A B, and mark the given point C. With C as a centei,

find an arc that shall only just touch A B ; and with B as a center, and the

same radius, describe an arc D. Draw through the point C a line just touching

this last arc, and the line C D will be the parallel line required.

Two lines in the same plane, not parallel to each other, will come together

if extended sufficiently far. The coming together, cutting, or intersection of

two lines, is called an angle (Fig. 7).

If but two lines come together, the angle may be designated by a single

letter at the vertex, as the angle E.

But, if three or more lines have a common vertex, the angles are designated

by the lines of which they are composed, as the angle D B C of the lines D B

D

FIG, 8

and B C ; the angle A B C of A B and B C ; the angle A B D of A B and B D.

The letter at the vertex is not repeated, and must always be the central letter.

Describe a circle (Fig. 8). Draw the diameter A B. From A and B

as centers, with any opening of the compasses greater than the radius,

describe two arcs cutting each other as at D. Through the intersection

of these arcs and the center C, draw the line D E. D E makes, with the

diameter A B, four angles, viz., A C D, D B, B C E, and E C A. Angles

A*

CONSTRUCTION OF GEOMETRICAL PROBLEMS.

are equal whose lines have equal inclination tfc^ach other, and whose lines, if

placed one on the other, would coincide. By construction, the points C and D

have, respectively, equal distances from A and B ; the line D C can not, there-

fore, be inclined more to one side than to the other, and the angle A C D must

be equal to the angle BCD. Such angles are called right angles. It can be

readily proved that all the four angles, formed by the intersection of D E with

A B, are equal, and are right angles.

The angles A C D and D C B, on the same side of A B, are called adjacent

angles ; as also DOB and B C E, on the same side of D E.

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APPLETONS'

CYCLOPEDIA OF TECHNICAL

DRAWING.

EMBRACING

Jjrinnplts of

AS APPLIED TO

PRACTICAL DESIGN.

WITH NUMEROUS ILLUSTRATIONS OF

TOPOGRAPHICAL, MECHANICAL, ENGINEERING,

ARCHITECTURAL, PERSPECTIVE, AND

FREE-HAND DRAWING.

EDITED BY

W. E. WORTHEN, C. E.

NEW YORK:

D. APPLETON AND COMPANY,

1, 3, AND 5 BOND STREET.

1892.

COPYRIGHT, 1885,

BY D. APPLETON AND COMPANY.

PREFACE.

" AT the suggestion of the publishers, this work was undertaken to form

one of their series of dictionaries and cyclopedias. In this view, it has been

the intention to make it a complete course of instruction and book of refer-

ence to the mechanic, architect, and engineer. It has not, therefore, 'been

confined to the explanation and illustration of the methods of projection, and

the delineation of objects which might serve as copies to the draughtsman,

matters of essential importance for the correct and intelligible representation

of every form ; but it contains the means of determining the amount and

direction of strains to which different parts of a machine or structure may be

subjected, and the rules for disposing and proportioning of the material em-

ployed, to the safe and permanent resistance of those strains, with practical

applications of the same. Thus, while it supplies numerous illustrations in

every department for the mere copyist, it also affords suggestions and aids

to the mechanic in the execution of new designs. And, although the arrang-

ing and properly proportioning alone of material in a suitable direction, and

adequately to the resistance of the strains to which it might be exposed,

would produce a structure sufficient in point of strength for the purposes for

which it is intended, yet, as in many cases the disposition of the material

may be applied not only practically, but also artistically, and adapted to the

reception of ornament, under the head of Architectural Drawing, the general

characteristics of various styles have been treated of and illustrated, with

brief remarks on proportion and the application of color." . . . 1857.

Since its first publication, this work has been subjected from time to time

to revision. It has now been deemed necessary to almost entirely rearrange

and rewrite it ; to add largely to the subject-matter and to the illustrations,

introducing examples of later practice and experience ; to extend the scope

of the work, and make it more nearly a cyclopaedia of drawing and design.

There are no changes in the principles of projection as applied to drawing,

and no marked improvement in drawing-instruments ; but in the present

practice finished drawings in shade and color are exceptional. It is suffi-

cient, for almost every purpose, for the draughtsman to make accurate projec-

tions with pencil on paper, and trace them afterward on cloth. The pencil-

drawings can be readily altered or amended, and, where there are many repe-

iv PREFACE.

titions of the same parts, but a single one may be drawn. On the tracing

they are made complete, and these are preserved as originals in the office,

while sun-prints of them are used for details of construction in the shop, or

distributed as circulars among customers.

In the sale of former editions of this work, it has been found that its

success has been largely due to its value as a book of design. Great attention

has therefore been given to secure practical illustration of constructions and

machines of recent date ; the nature of materials in common use has been

more extensively treated, and the character and effect of stresses and strains,

their kind and direction, more fully explained, with as simple rules as possible

to determine them for practical application.

Of late years the science of " graphics " has become of great importance,

and is here fully illustrated in its varied applications, showing not only this

method of recording the facts of the statistician, and affording comparisons

of circumstances and times, the growth of population, the quantities and cost

of agricultural and mechanical production, and of their transport, movements

of trade, fluctuations of value, the atmospheric conditions, death-rates, etc.,

but also in its application to the plotting of formulae for their ready solution,

by the draughtsman and designer. For many of the rules in this work the

results of the formulae of various authors have been plotted graphically, and

the rule given one deemed of the greatest weight, not always by average,

but most consistent with our own experience.

In astronomical calculations every decimal may have its importance. It

is not so in those of the mechanical or architectural designer ; solutions by

graphics are sufficient for their purpose, and, simpler than mathematical cal-

culations, they are thus less liable to error ; it is very good practice to use one

as a check on the other. It is to be remarked that inaccuracy in facts, and

carelessness in observation, are not eliminated from an equation by closeness

of calculation, and when factors are not established within the limits of units

it is useless to extend the results to many places of decimals. It is of the

utmost importance to know at first well the object and purposes of the

design, the stresses to which its parts are to be subjected, and the strength

and endurance of the materials of which it is to be composed. In establish-

ing rules for ourselves, be sure of the facts, and that there are enough of

them for a general application. Rules are necessary, but their application

and usefulness depend largely on the experience of the user, and life must

be a record of applications and effects. It is comparatively easy to make

a work strong enough ; but to unite economy with proportion is difficult.

To make the work complete in itself, so as to form a sort of single book

for most of the purposes of the draughtsman and designer embracing the

profession of surveyor, engineer, and architect tables of logarithms, latitudes

and departures, squares and cubes, and square and cube roots, weights and

measures, and weights of material, have been added.

w.

CONTENTS.

PAGES

CONSTRUCTION OF GEOMETRICAL PROBLEMS 1-39

Drawing of lines straight, curved, and parallels, angles, perpendicular ; bisecting

angles; arcs and circles, 15. On polygons and circles; triangles, parallelograms,

squares ; circles, angles ; polygons ; inscribed and described circles ; pentagons, hexa-

gons, octagons ; table of polygonal angles, 23. On the ellipse, parabola, hyperbola,

cycloid, epicycloid, involute and spiral, 33. Use of triangle and square, 33. Areas

of figures, 37. To draw squares of given proportionate sizes, 39.

DRAWING INSTRUMENTS 40-77

Description and use ; rulers ; triangles; T-square; parallel ruler ; sweeps and vari-

able curves ; drawing pens ; dotting point ; pricking point ; compasses ; dividers ;

beam compasses ; porportional dividers ; scales ; scale guard ; diagonal scales ; ver-

nier scales ; sector ; protractors ; pantagraphs ; camera lucida ; drawing table and

board, 56. Drawing paper ; tracing paper ; tracing cloth ; mouth glue ; damp stretch-

ing paper ; mounting paper and drawings, 59. Management of the instruments ;

ink ; exercises with drawing pen ; various letters and numerals ; cross-section paper ;

diagrams showing use of cross-section paper, 77.

ORTHOGRAPHIC PROJECTION 78-109

Definitions; points; straight line; solid, 81. Simple bodies; pyramid; prism,

87. Construction of the conic sections, 90. Penetration or intersection of solids ;

cylinders, cone, and sphere ; cylinder and ring ; sphere and prism ; cone and prism ;

cone and cylinder, 102. Of the helix, 104. Development of surfaces ; cylinder ;

cone; sphere, 107. Shade-lines, 109.

SHADES AND SHADOWS 110-136

Of a point : straight line ; solid ; circle ; pyramid ; cylinder ; cone ; shadows cast

upon a cylinder by various-shaped caps ; shadows cast upon a prism ; shadows upon

the interior of a cylinder, hollow hemisphere, a niche, a sphere ; line of shade on the

surface of a ring, grooved pulley, square-threaded nut and screw, triangular-threaded

nut and screw, 126. Manipulation of shading and shadows methods of tinting;

surfaces in the light ; surfaces in shade ; shading by flat tints ; by softened tints,

129. Elaboration of shading and shadows; examples of finished shading; on con-

cave surfaces, spheres, ring, cone, flat surfaces ; colors for tints ; expeditious way of

shading a cylinder ; body color ; margin of light ; washing ; conventional tints for

materials, 136.

PLOTTING ; 137-148

Scales ; scales prescribed by different commissions, 138. Variation of compass,

1 39. Plotting compass surveys ; balancing error ; plotting by latitudes and depart-

ures ; area by latitudes and departures ; area by triangles ; plotting by offsets, 147.

System of division of United States land, 148.

VI

CONTENTS.

PAGES

TOPOGRAPHICAL DRAWING 149-180

Conventional signs ; representation of hills ; contour lines, 156. Railway surveys ;

profiles; sections, land plans, 159. Hydrometrical or marine surveys, conventionali-

ties, 160. Geological and statistical features, 162. Transferring ; pricking through;

by tracing; blue-print process; copying-glass; transfer-paper; pantagraph, 165.

Map projections ; perspective projection on planes ; developed perspective projec-

tions ; projections by developing elements ; projections conforming to some arbi-

trary condition ; polyconic adopted by United States Coast Survey ; De Lorgne's

projection; M creator's chart, 171. Colored topography ; conventional colors ; direc-

tions; finishing; lettering; titles, 180.

MATERIALS 181-199

Earth and rocks, 182. Building materials ; wood, 185. Stones; technical terms

masonry; granitic stones, argillaceous stones ; sandstones ; limestone, 188. Artificial

building material ; bricks ; tile ; terra-cotta ; mortars ; limes ; cement ; concrete ;

plastering, 191. Metals; conventional hatchings ; iron; steel; other metals; specific

gravity ; weight ; melting-point ; resistance to crushing and tension ; results of Prof.

Thurston's tests of metals, 196. Sulphur; glass; rubber; paints; coals, 199.

MECHANICS 200-219

Force ; center of gravity ; levers ; wheel and axle ; pulley ; inclined plane ; wedge ;

screw ; inclined forces ; parallelogram of forces ; hydraulic press ; velocity of falling

bodies; friction, 212. Mechanical work or effect; horse-power, etc.; water-power;

wind ; steam ; steam worked expansively ; cut-offs ; compound engines ; indicator

cards, 219.

MACHINE DESIGN AND MECHANICAL CONSTRUCTIONS 220-361

Stress ; dead load ; strength of posts and columns ; Phoenix columns, etc. ; shear-

ing stresses ; torsional stress ; transverse stress ; strength of beams ; tables of dimen-

sions of channel beams and angle-iron ; composite beams ; bolts and nuts ; strength

of bolts ; washers ; shafts and axles ; journals ; keys ; car-axles ; shafting ; bear-

ings ; couplings; clutch; pulleys; belts; ropes, 275. Gearing; epicycloidal teeth;

projections of a spur-wheel and bevel-wheel, 294. Drawing of screws, 297. Fric-

tional gearing, 299. Ropes and chains ; hooks ; levers ; cranks ; connecting-rods ;

steam-engine ; working-beam ; parallel-motion links ; steam-cylinders and pistons,

331. Valves ; hydrants, 342. Riveted joints for boilers ; boilers, 351. Wrought-

iron pipe connections, 355. Frames ; governors ; fly-wheels ; air-chambers, 361.

ENGINEERING DRAWING 362-460

Foundations ; sheet-piling ; retaining-walls ; foundations for piei^s, etc., 375.

Dams ; locks of canals ; conduits ; reservoirs, 395. Water-pipes, 398. Sewers, 401.

Gas-supply, 402. Roads, 407. Roofs and bridges; piers, 432. Arch-bridges; sus-

pension-bridges, 438. Boiler-setting ; chimneys, 444. Location of machines ; ma-

chine foundations, 449. Tunnels, 453. Railway stock, 458. Wave-line principle of

ship construction, 460.

ARCHITECTURAL DRAWING

Details of construction ; concrete walls, 468. Frames and floors ; fire-resisting

floors, 474. Groined ceilings, 476. Doors ; windows ; moldings, 485. Stairs, 492.

Fireplaces ; flues ; roofs ; gutters ; plastering, 495. Proportions and distribution of

rooms and passages, 500. Plans and elevations of buildings ; stores and warehouses,

521. School-houses, 531. Churches, theatres, lecture-rooms, music and legislative

halls ; hospitals, 542. Stables ; cow-houses ; greenhouses, 547. Ventilation and

warming, 555. Plumbing, 564. Greek and Roman orders of architecture, 596. Or-

naments of the Renaissance ; principles of design, 601.

461-601

CONTENTS.

vn

PAGES

PERSPECTIVE DRAWING 602-624

Angular perspective, 610. Parallel perspective, 624.

ISOMETRICAL DRAWING 625-638

FREE-HAND DRAWING

Geometrical figures and design, 643. Proportions of the human frame, 647.

Figure drawing, 650. Forms of animals, 653. Illustrations from different artists,

664.

APPENDIX

Extracts from New York building laws, 670. Patent-Office drawings, 670. Men-

suration ; properties of triangles, 672. Lineal measure, 672. Table of inches in

decimals of a foot, 673. Table of measures of surface, 673. Table of measures of

capacity ; dry measure ; weights ; cubic measure, 674. Table of weight of rolled

iron, 675. Table of weight of wrought-iron and brass plates and wire, 676. Table

of weight of wrought-iron welded tubes ; boiler tubes ; driven-well tubes ; heavy

wrought galvanized iron spiral riveted pipes, 678. Table of copper and brass rods,

678. Table of number of Burden's rivets in 100 pounds, 679. Table of number of

wrought spikes to a keg, 679. Table of length of cut nails and spikes, and number

in a pound, 680. Table of weights of lead pipe per foot, 680. Table of the weight

of a cubic foot of water at different temperature?, 680. Table of properties of satu-

rated steam, 682. Table of mean pressures in steam cylinders at different rates of

expansion, 683. The flow of water, with table of discharge over weir, 685. Flow

of water through pipes and sewers, 689. Flow of air through pipes, 690. Table of

circumferences and areas of circles, 695. Table of squares, cubes, square and cube

roots of numbers, 703. Table of latitudes and departures, 709. Table of natural

sines and cosines, 718. Logarithms of numbers, 735.

INDEX.

DESCRIPTION OF PLATES.

PLATES I TO XIV.

SCRAPS.

639-664

665-735

DESCRIPTION OF PLATES.

PLATE

I. Shading of prism and cylinder by flat tints. Referred to on pages

126-7.

II. Shading of cylinder and segment of hexagonal pyramid. Referred to

on pages 128-9.

Ill, IV. Finished shading and shadows of different solids. Referred to on

page 131.

V. Shades and shadows on screws. Referred to on page 126.

VI. Example of topographical drawing, done entirely with the pen.

VII. The same, with the brush, in black.

VIII. The same, with the brush, in color. Referred to on page 174.

IX. Contoured map of Staten Island, shaded by superimposed washes,

the washes increasing in intensity or strength as required to pro-

duce the effect.

X. Geological map of part of New Jersey, colored to show the different

formations.

XI. Finished, shaded sectional view, colored to show the different metals,

of a balanced leather cup-valve. The body is of cast-iron ; the

piston, brass ; packing, leather ; piston-rod, wrought-iron this

last not distinctively colored.

XII. Finished perspective drawing, with shades and shadows, of a large

bevel-wheel and two pinions, with shifting clutches.

XIII. Front elevation of a building, in color.

XIV. Perspective view of Gothic church, finished in color.

XV. Plan, elevation, and section of bevel-wheel, pinion, and clutches,

shown in perspective Plate XII.

XVI to XX. Details of progressive perspective projections of Plate XV, as

shown completed in Plate Xll.

APPLETONS'

CYCLOPAEDIA OF DRAWING,

CONSTRUCTION OF GEOMETRICAL PROBLEMS.

MOST persons, at some time, have made use of the simple drawing instru-

ments, pencils, straight-edges or rulers, and compasses or dividers with change-

able points, and many suppose that there can be no skill in their use ; but to

one critical in these matters there are great differences to be observed even in

common drawings, in the straightness and uniformity of the lines, and in the

care of the surface of the paper.

Select for the geometrical problems and

for usual drawings a No. 3 or H H H pen-

cil. It should be sharpened to a cone-point

(Fig. 1). Where a pencil is used for drawing

lines only, some draughtsmen sharpen the

pencil to a wide edge, like a chisel.

In drawing a straight line, hold the ruler

firmly with the left hand ; with the right

hand hold the pencil lightly but without

FlG - 1 - slackness, and a little inclined in the direc-

tion of the line to be drawn, keeping the pencil against the edge of the

ruler, and in the same relative position to the edge during the whole operation,

of drawing the line.

2 CONSTRUCTION OF GEOMETRICAL PROBLEMS.

To draw a clean line and preserve the point of the pencil, the part of the

cone a little above the point of the pencil should bear against the edge of the

ruler, and the pencil should be carried steadily while drawing. Any oscilla-

tion will throw the point farther from or nearer the ruler, and the line will

not be straight (Fig. 2).

FIG. 2.

In the use of the compasses do not make a hole through the paper with the

needle or sharp point, but only into the paper sufficient to maintain the

position.

Keep the paper clean, and use rubber as little as possible.

As drawing is based on geometrical principles, we commence with geo-

metrical definitions and problems to give the learner some knowledge of

the science of geometry, with a valuable exercise in the use of drawing

instruments.

Geometrically a point is defined as position merely : in drawing, the posi-

tions of points are marked on the paper by prick-marks of a needle or sharp

point, and by the dot of a pencil ; sometimes inclosed O, sometimes designated

by the intersection of two short lines X >.

Geometrically lines have but one dimension, .length, and the direction

of a line is the direction from point to point of the points of which the

line is composed : in drawing, lines are visible marks of pencil or pen upon

paper.

FIG. 3.

A straight line is such as can be drawn along the edge of the ruler, and is

one in which the direction is the same throughout. In drawing a straight line

through two given points, place the edge of the ruler very near to and at equal

distances from the points, as the point of the pencil or pen should not be in

contact with the edge of the ruler (Fig. 3).

Lines in geometry and drawing are generally of limited extent. A given

CONSTRUCTION OF GEOMETRICAL PROBLEMS.

3

FIG. 4.

or known line is one established on paper or fixed by dimensions. Lines of

the same length are equal.

To draw Curved Lines. Insert the pencil-point in the compasses, and open

them to a suitable extent. With the needle or sharp point resting on the

paper describe a line with the pencil around this point ; the line thus

described is usually called a circle more strictly it is the circumference of a

circle the circle being the space inclosed. A portion

of a circumference is an arc. The point around

which the circumference is described is the center

of the circle (Fig. 4).

If a line be drawn from the center to the circum-

ference it is called a radius. As it is the length

embraced between the points of the compasses, it is

often called by mechanics the sweep.

If a line be drawn through the center, and limited

by the circumference, it is called the diameter, and is

equal to two radii.

A radius is a semi-diameter ; a diameter is the longest line that can be con-

tained within a circumference. Lines limited by the circumference, and which

are not diameters, are chords.

It will be observed that arcs are lines which are continually changing the

directions, and are called curved lines, but there are other curved lines than

those described by compasses, of which the construction will be explained

hereafter.

Besides straight and curved lines there are often lines, in drawing, which

can neither be drawn by rulers or compasses, as lines representing the direc-

tions of brooks and rivers, the margins of lakes and seas, points in which are

established by surveys, defined on paper, and connected by hand-drawing.

These may be called irregular or crooked lines.

Where it is necessary to distinguish lines by names, we place at their

extremities letters or figures, as A B, 1 2 ; the line A B, or 1 2.

But in lines other than straight, or of considerable extent, it is often necessary

to introduce intermediate letters and figures, as a a a.

In the following problems, unless otherwise implied or designated, where

lines are mentioned, straight lines are intended.

If we conceive a straight line to move sideways in a single direction, it will

sweep over a surface which is called a plane. All drawings are projections on

planes of paper or board.

Two lines drawn on paper, and having the same direction, can never come

any nearer each other, and must always be at the same distance apart, however

far extended. Such lines are called parallel lines.

4: CONSTRUCTION OF GEOMETRICAL PROBLEMS.

PEOB. L To draw a line parallel to a given line, and at a given distance

from it (Fig. 5).

Draw the line A B for the given line, and take in the compasses the dis-

tance A C the distance at which the other line is to be drawn. On A, as a

Jj

FIG. 5.

FIG. 6.

center, describe an arc, and on B, as a center, another arc ; draw the line C D

just touching these two arcs, which will be the parallel line required.

PKOB. II. To draw a line parallel to a given line through a given point

outside this line (Fig. 6).

Draw the given line A B, and mark the given point C. With C as a centei,

find an arc that shall only just touch A B ; and with B as a center, and the

same radius, describe an arc D. Draw through the point C a line just touching

this last arc, and the line C D will be the parallel line required.

Two lines in the same plane, not parallel to each other, will come together

if extended sufficiently far. The coming together, cutting, or intersection of

two lines, is called an angle (Fig. 7).

If but two lines come together, the angle may be designated by a single

letter at the vertex, as the angle E.

But, if three or more lines have a common vertex, the angles are designated

by the lines of which they are composed, as the angle D B C of the lines D B

D

FIG, 8

and B C ; the angle A B C of A B and B C ; the angle A B D of A B and B D.

The letter at the vertex is not repeated, and must always be the central letter.

Describe a circle (Fig. 8). Draw the diameter A B. From A and B

as centers, with any opening of the compasses greater than the radius,

describe two arcs cutting each other as at D. Through the intersection

of these arcs and the center C, draw the line D E. D E makes, with the

diameter A B, four angles, viz., A C D, D B, B C E, and E C A. Angles

A*

CONSTRUCTION OF GEOMETRICAL PROBLEMS.

are equal whose lines have equal inclination tfc^ach other, and whose lines, if

placed one on the other, would coincide. By construction, the points C and D

have, respectively, equal distances from A and B ; the line D C can not, there-

fore, be inclined more to one side than to the other, and the angle A C D must

be equal to the angle BCD. Such angles are called right angles. It can be

readily proved that all the four angles, formed by the intersection of D E with

A B, are equal, and are right angles.

The angles A C D and D C B, on the same side of A B, are called adjacent

angles ; as also DOB and B C E, on the same side of D E.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65