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CONTENTS.
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6. To find the centre of a given circle,
ARITHMETICAL SIGNS,
ALGEBRAIC SYMBOLS,
PRACTICAL GEOMETRY,.
1. From any given point, in a straight line, to erect a perpendicular,
2, 8. When a perpendicular is to be made at or near the end of a given
line,
4. To bisect any given angle,
5. To find the centre of a circle, or radius, that shall cut any three
given points, not in a direct line,
7. To find the length of any given arc of a circle,
8. Through any given point, to draw a tangent to a circle,
9. To draw from or to the circumference of a circle lines tending
towards the centre, when the centre is inaccessible,
10, 11. To describe an arc, or segment of a circle, of large radii,
12. To describe an ellipse, having the two diameters given,
13, 14. To describe an elliptic arch, the width and rise of span being
.given,
15. To describe a parabola, the dimensions being given,
13
15
16
17
18
16. To obtain by measurement the length of any direct line, though
intercepted by some material object, .
19
17. A round piece of timber being given, out of which to cut a beam of
strongest section,.
20
18. To measure the distance between two objects, both being inacces-
sible,
19, 20. To ascertain the distance, geometrically, of any inaccessible
object on an equal plane,
20, 21
21. To and the proper position for an eccentric, in relation to the crank
in a steam-engine, the angle of eccentric rod, and travel of the
valve, being given,
22. The throw of an eccentric, and the travel of the valve in a steam-
engine, also the length of one lever for communicating motion to
the valve, being given, to determine the proper length for the
other,
23. To inscribe any regular polygon in a given circle,
24. To construct a square upon a given right line,
25. To form a square equal in area to a given triangle,
26. To form a square equal in area to a given rectangle,
27. To find the length for a rectangle whose area shall be equal to that
of a given square, the breadth of the rectangle being also given,
28. To bisect any given triangle, .
29. To describe a circle of greatest diameter in a given triangle,
30. To form a rectangle of greatest surface, in a given triangle,
DECIMAL ARITHMETIC, •
Reduction,
8. To find the area of a triangle,.
4. Any two sides of a right-angled triangle being given, to find
the third side,
5. To find the area of any regular polygon,
Table of multipliers for polygons from three to twelve sides,
1. The breadth of a polygon given, to find the radius of a circle
to contain that polygon,
2. The radius of a circle given, to find the length of side,.
3. The length of side given, to find the radius,
6. Having the diameter of a circle given, to find the circumference;
or the circumference given, to find the diameter,
7. To find the length of any arc of a circle,
8. To find the diameter of a circle, by having the chord and versed
sine given,
9. To find the area of an ellipsis, or oval,
10. To find the area of a parabola, or its segment,
Some of the properties of a circle,
11. To find the area of a sector of a circle,
12. To find the area of a segment of a circle,
13. To find the area of a circular ring or space included between two
concentric circles,
14. To find the area of an ellipsis,.:
MENSURATION OF SOLIDS,
1. To find the convex surface and solid content of a cylinder,.
2. To determine the dimensions of any cylindrical vessel, whereby
to contain the greatest cubical contents, bounded by the least
superficial surface,
8. To find the surface and solid content of a cone or
or pyramid,
4. To find the surface of the frustum of a cone or pyramid,
5. To find the solid content of the frustum of a cone,
6. To find the solid content of the frustum of a pyramid,.
7. To find the solidity of a wedge,
PAGK
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8. To find the convex surface and solid content of a sphere or globe,
9. To find the convex surface and solid content of the segment of a
sphere,
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40
10. To find the solidity of a spheroid,.
11. To find the solidity of the segment of a spheroid when the base
is circular or parallel to the revolving axis,
12. To find the convex surface and sclid content of a cylindric ring, DECIMAL APPROXIMATIONS, for facilitating Calculations in Men- suration,
INSTRUMENTAL ARITHMETIC, or Utility of the Slide Rule,
Numeration,
To multiply numbers by the rule,
To divide numbers upon the rule,
Proportion, or rule of three direct,
Rule of three inverse, .
Square and cube roots of numbers,
The mean proportion between two numbers,
Mensuration of surface,
Tables of gauge-points for the engineer's rule and the common slide
rule,
Mensuration of solidity and capacity,
Land surveying,.
Power of steam-engines,
Of engine boilers,
THE LAWS OF MOTION,.
To find the velocity of a falling body at the end of any number of
seconds,
To find the space passed over by a falling body in any number of
seconds,.
To find the space passed over by a falling body when the velocity is
given,
Rules and formula when a body is acted on by any force,
Rule for finding the accelerating force of a body,
Time of a body falling down an inclined plane,
The time of oscillation of a simple pendulum,.
Centrifugal force,
The centre of gyration,
The centre of percussion,
ON WORK,
Horse-power,
To find the units of work in raising a given weight a given height,
Man-power,
Work of animals,.
Traction of horses at various rates of travelling,
Accumulated work,
Work done by machines,
The horse-power of an engine,
On the strength of animals,
To Calculate the Different Parts of a Crane as respects Me-
chanical Advantage,
Equilibrium and Pressure of Beams-the Parallelogram of
Forces,
SPECIFIC GRAVITY, .
Table of specific gravities,
Weight of given bulks of water and air,
THE MECHANICAL POWERS, AND THEIR APPLICATION,
The Lever,
The Wheel and Axle, .
The Pulley,
The Inclined Plane,
The Wedge,
The Screw,
TOOTHED WHEELS,
ON THE VELOCITY OF WHEELS, DRUMS, PULLEYS, &c.
STEAM POWER and the STEAM ENGINE,
To estimate the amount of advantage gained by using steam expan-
sively in a steam-engine,
To calculate the effect of a lever and weight upon the safety-valve of
steam boiler, &c.,.
Of the pressure of steam, in inches of mercury, &t different tempera-
Temperature of steam at different pressures in atmospheres,
The elastic force of steam, and corresponding temperature of the water
with which it is in contact,.
The force and temperature of steam in atmospheres,
Table of the heating power of various substances, exhibiting the atmost
quantity of water evaporated by given weights, &c.,
Nominal horse-power of low pressure engines,
Nominal horse-power of high pressure engines,
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62
63
Proportions of condensing engines,
Revolutions per mile of driving wheels, and consumption of steam and
water for each sized wheel,.
Pressure of steam exclusive of that of the atmosphere,
Pressure exerted by the elastic force of steam at various degrees of
temperature,.
AMALGAMS,
85
.
88
89
TABLE OF GRADIENTS, and Resistance per Ton for each,
Ultimate Breaking Weight in Tons of Cast-Iron Pillars,
Table of Strengths of Cast-Iron Shafts,
Strength of the Teeth of Cast-Iron Wheels,
Method of Ascertaining the Weight of Pipes of Various Me-
Weight of Cast-Iron Balls,
Table of the Weight of Flat and Rolled Iron,
Bore and Weight of Cocks; Weight of Lead, Lead Pipe, and
Copper Tubing,
134
STRENGTH OF MATERIALS,
135
Table of tenacities, resistances to compression, &c., of the common
materials of construction,
Table showing the weight a beam of cast-iron one inch in breadth will
sustain,
187
Resistance of bodies to flexure by vertical pressure,
141
Dimensions of cylindrical columns of cast-iron to sustain given loads,
Elasticity of torsion,
142
143
Table of the weight of a superficial foot of plate or sheet iron, copper,
and brass,
144
Comparative weights of different bodies, .
145
The mensuration of timber-flat or broad measure, cubic or solid
MENSURATION OF CIRCLES: Table of the Diameters, Circumfe-
rences and Areas of Circles,
160
Table of the circumferences and areas of circles, from 1 to 50 feet,
advancing by an inch,
IVORY,
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174