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Still there would be much labor of computation which may be saved by the use of tables of external secants and versed sines, which have been employed with great success recently by the Eugineers on the Ohio and Mississippi Railroad, and which, with the formulas and rules necessary for their application to the laying down of curves, drawn up by Mr. HASLETT, one of the Engineers of that Road, are now for the first time given to the public. This portion of the volume alone, by the great abridgment of labor for which it pro. vides the means, and the simplicity and convenience of the mattewhich it furnishes, will give it an extensive circulation among Practical Engineers

But besides this, the Architect, the Shipbuilder, the Mason, the Carpenter, the Joiner, the Manufacturer and Artisan in iron and every species of material, will find rules and recipes for all kinds of estimates, computations, constructions, compositions, mixtures, et cetera, which will excite surprise at their number, novelty, and value to every one.

The contents of this volume are of so varied a nature that it was not deemed necessary to make any strenuous efforts to arrange them systematically. Being solely intended for a book of reference, the relative order of the subjects is immaterial; and the copious Table of Contents and Index afford all the assistance that can be desired by those who wish to consult its pages.

THE EDITOR,
COLUMBIA COLLEGE,

Sept. 1855

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16

28. To biseot any given triangle, .

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CONTENTS.

PAGE

ARITAMETICAL SIGNS,

13

ALGEBRAIC SYMBOLS,

15

PRACTICAL GEOMETRY, :

16

1. From any given point, in a straight line, to erect a perpendicular, 16

2,8. When a perpendicular is to be made at or near the end of a given

line,

4. To bisect any given angle,

16

0. To find the centre of a circle, or radius, that shall cut

any

three

given points, not in a direct line,

17

6. To find the centre of a given circle,

17

7. To find the length of any given arc' of a circle,

17

8. Through any given point, to draw a tangent to a circle,

17

9. To draw from or to the circumference of a circle lines tending

towards the centre, when the centre is inaccessible,

17

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,

18, 19

15. To describe a parabola, the diinensions being given,

19

16. To obtain by measurement the length of any direct line, though

intercepted by some inaterial 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,

20

19, 20. To' ascertain the distance, geometrically, of any inaccessible

object on an equal plane,

21. To find the proper posiiion for an eccentric, in relation to the crank

in a steam-engine, the angle of eccentric rod, and travel of the

valve, being given,

21

2. 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,

2. To inscribe any, regular polygon in a given circle,

24. To construct a square upon a given right line,

* To form a square equal in area to a given triangle,

no 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 rantangle "eing also given,

To describe a circle of greatest dian 1:

en triangle,

20. To form a rectangle of greatest surf-

i triangle,

lormal ARITHMETIC,
Reduction,

CONT

84

85

MENSURATION, .

27

MEKSURATION OF SUPERFICIES,

27

1. To find the area of any parallelogram,

28

2. To find the ares of' a trapezoid,

28

8. To find tbe area of a triangle,

98

4. Any two sides of a right-angled triangle being given, to ind

the third side,

29

5. To find the area of any regular polygon,

80

Table of multipliers for polygons from three to twelve sides,

81

1. The breadth of a polygon given, to find the radius of a circle

to contain that polygon,

81

2. The radius of a circle given, to find the length of side, 81

3. The length of side given, to find the radius,

31

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,

82

8. To find the diameter of a circle; by baving 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,

34

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,..

35

14. To find the area of an ellipsis, .

MENSURATION OF SOLIDS,

36

1. To find the convex surface and solid content of a cylinder, +86

2. To determine the dimensions of any cylindrical vessel, whereby

to contain the greatest cubical contents, bounded by the least

superficial surface,

86

8. To And the surface and solid content of a cone or pyrumid, 87

4. To find the sarface of the frustum of a cone or pyramid,

87

5. To find the solid content of the frustum of a cone,

87

6. To find the solid content of the frustum of a pyramid,

88

7. To find the solidity of a wedge,

89

8. To find the convex surface and solid content of a sphere or globe, 88

9. To find the convex surface and solid content of the segment of a

sphere,

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,

CCIMAL APPROXIMATIONS, for "facilitating Calculations in Men-

suration,

41

I STRUMENTAL ARITHMETIC, or Utility of the Slide Rule,

Numeration,

To multiply numbers by the rule,

To divile 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,

Monsuration of surface,

Tables of gauge points for the engineer's rule and the common slide

rule,

Mensuration of solidity and nacity,

Land surveying, .

Power of steam-engines,

of engine boilers,

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ON THE VELOCITY. OF WHEELS, DRUMS, PULLEYS, &o.

Meno Steam POWER AND THE STEAM.ENGINE,

To estimate the amount of advantage gained by using stearn expan

sively in a team-engine,"

To calculate the effect of a lever and weight upon the safety-valve of

steam boiler, &c., ..

To find the proper diameter for a safety-valve,

General proportions of locomotive engines,

Steam-engine, boilers, and their proportions,

of the pressure of steam, in inches of mercury, it different tempera
Temperature of steam at different pressures in atmospheres,
The elastic force of steam, and corresponding temperature of the wote

with which it is in contact, .
The force and temperature of steam in atmospheres,
Table of the heating power of various substances, exhibiting the aimosi

quantity of water evaporated by given weights, &c.,

Nominal borse-power of low pressure engines,

Nominal horse-power of high pressure engines,"

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