CHAMBERS'S EDUCATIONAL COURSE-EDITED
BY W. AND R. CHAMBERS.

A TREATISE

OF

PRACTICAL MATHEMATICS.

PART SECOND.

CONTAINING

LAND-SURVEYING-GAUGING-PROJECTILES-SPHERICAL TRIGONOMETRY

-ASTRONOMICAL PROBLEMS-NAVIGATION-

AND OTHER SUBJECTS.

Br A. BELL,

FORMERLY MATHEMATICAL MASTER IN DOLLAR

INSTITUTION.

EDINBURGH:

WILLIAM AND ROBERT CHAMBERS;

W. S. ORR AND CO., LONDON; W. CURRY JUN. AND CO., DUBLIN ;

AND SOLD BY ALL BOOKSELLERS.

1842.

HARVARD UNIVERSITY LIBRARY

EDINBURGH:
W. AND R. CHAMBERS.

CONTENTS OF PART SECOND.

LAND-SURVEYING.

Surveying with the Chain and Cross,

Surveying with the Chain, Cross, and Theodolite,

Surveying with the Plane Table,

Division of Land,

Inclined Lands,

STRENGTH OF MATERIALS.

Measure of Absolute Strength-Relative Strength,

Neutral Axis-Axis of Rotation,

Various kinds of Force,

Table of Constants for Strength and Flexibility,

Problems,

Problems referring to the Strength of Cast-Iron,

Table of Data for Crushing Forces,

Principles and Definitions of Terms,

Tables of Multipliers, Divisors, and Gauge Points,

The Sliding Rule for Gauging,

Cask Gauging,

Table of Mean Diameters,

Table of Contents of Standard Casks,

Malt Gauging,

The Diagonal Rod,

Problems,

Problems,

GAUGING.

-

WEIGHTS AND DIMENSIONS OF BALLS AND SHELLS.

PILING OF BALLS AND SHELLS.

Maxims,

Field Fortifications,

PROJECTILES.

The Parabolic Theory of Projectiles,

Projectiles on Horizontal Planes,

Geometrical Construction of Problems,

Projectiles on Inclined Planes,

Practical Gunnery,

Table of Actual and Potential Ranges in Terms of F,

Problems.

FORTIFICATION.

Permanent Fortification,

Definitions of Terms,

Profile of the Principal Works,

Horizontal Section,

Construction of a Front,

Outworks-Ravelin-Tenailles, &c.,

Cormontaigne's and the Modern System,

Intrenchments of Armies,

Attack and Defence of a Fortress,

PROJECTIONS.

Definitions,

Stereographic Projection of the Sphere,

Projection of Cases in Right-Angled Trigonometry,

Projection of Cases in Oblique-Angled Trigonometry,

STEREOGRAPHIC PROJECTION OF THE CASES OF SPHERICAL

TRIGONOMETRY.

SPHERICAL TRIGONOMETRY.

Definitions,

Right-Angled Spherical Trigonometry,

Quadrantal Triangles,

Oblique-Angled Spherical Trigonometry,

Other Solutions of the Cases of Oblique-Angled Spherical Trigo-

nometry,

ASTRONOMICAL PROBLEMS.

Circles and other parts of the Celestial Sphere,

Definitions,

Preliminary Problems,

Proportional Logarithms,

Augmentation of Moon's Semi-diameter,

Contraction of the same,

The Sun's Semi-diameter,

To find the Parallax in Altitude of a Celestial Body,

Reduction of Equatorial Parallax,

To find the Refraction of a Celestial Body,

To find the Depression of the Visible Horizon,

Problems regarding Altitude,

Problems regarding Sideral and Mean Time,

Problems regarding Culminations,

Problems regarding Altitudes, Declinations, Latitudes, &c., of

Celestial Bodies,

Methods of Determining Time,

The Equation of Equal Altitudes,

Methods of finding Latitude,

Lunar Distances,

The Longitude found by Lunar Distances,

Mercator's Sailing,

Nautical Astronomy,

To find the Variation of the Compass,

Plane Construction,

Conical Projection,

Stereographic Projection,

Globular Projection,

Mercator's Construction,

Reduction of one of two Altitudes to the place at which the other

was taken,

CONSTRUCTION OF MAPS AND CHARTS.

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