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ELEMENTS OF PLANE AND SPHERICAL TRIGO-
NOMETRY, with the FIRST PRINCIPLES of ANA-
LYTIC GEOMETRY; being the Substance of the first
part of the Senior Course of Mathematics, taught in the
Belfast Institution.

A New Edition of this Work will be published in a short time, with the remain-
ing part of the Course, consisting principally of the Elements of the Differential and
Integral Calculus.

A TREATISE ON ARITHMETIC, in Theory and Prac-
tice; with an APPENDIX, containing an Introduction to
Mensuration. Fourth Edition. Stereotyped. Price 3/6 bd.
"This work ought to be ranked with the very best of the class to which it belongs."
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"The several rules are arranged in the most natural succession, and their illustrations
reduced to their most simple and instructive form."-London Monthly Review.

A KEY to the last-mentioned Work, containing the Method
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GEOGRAPHY.*

INTRODUCTION.

THE figure of the earth is nearly that of a globe or sphere.†

In Geography and Astronomy, certain circles are supposed to be described on the sphere. Of these, any one whose plane passes through the centre, and which therefore divides the sphere into equal parts, or hemispheres, is called a great circle. All others are called small or less circles.

If the circumference of a circle be divided into 360 equal parts, each of them is called a degree. Each degree is subdivided into 60 equal parts, called minutes; and each minute into 60 equal parts, called

Geography is a description of the earth; and is distinguished by different names, according to the nature of the subjects considered. Mathematical Geography treats of the figure and magnitude of the earth, of the latitudes and longitudes of places; and of globes, maps, and other artificial contrivances and instruments for illustration. This part of Geography is connected, in a considerable degree, with astronomy, especially when it is made to comprehend the consideration of the earth as a planet. Physical Geography treats of the materials of which the earth is composed; of the forms of the various parts of its surface; of the atmosphere; of climate; of the various productions, animal and vegetable, found on its surface; and of other particulars respecting its natural condition. Political Geography treats of laws, modes of government, religion, learning, customs, and other subjects arising from the agency of man considered as a moral and political being. Other names which are sometimes given to particular parts of Geography, such as Ancient, Modern, Descriptive, Maritime, &c. are easily understood from the terms.

† A globe or sphere is a body of such a figure, that all points of the surface are equally distant from a point within it called the centre. A

seconds.* Degrees, minutes, and seconds, are denoted by the characters, °, 0 ,',". Thus, 23° 27′ 54′′ means 23 degrees, 27 minutes, 54 seconds.

The earth performs a revolution round the sun in a year, moving in a path which is called its orbit.

While moving round the sun, the earth, each day, revolves on a line passing through its centre, and called its axis.

The points in which the axis cuts the surface, are called the poles of the earth: one of them the north pole; the other, the south pole.

A great circle which has all points of its circumference equally distant from the poles, is called the equator. This circle divides the earth into the northern and southern hemispheres.

A semicircle which extends from one pole to the other, and through any particular place, is called the meridian of that place.+

The latitude of a place on the earth's surface, is its distance from the equator, measured in degrees on its meridian. Latitude is of two kinds, north and south, according to the situation of the place in respect to the equator.‡

* A fourth part of the circumference is called a quadrant: a quadrant, therefore, contains 90°. It is evident that the magnitudes of degrees, minutes, and seconds, will depend on the magnitude of the circle of whose circumference they are parts. Thus, if the circumference be 360 yards, each degree will evidently be a yard: while, if the former be 180 miles, the latter will be half a mile. The average length of a degree on the earth's surface, is about 69 miles.

The remaining part of the entire circle is sometimes called the anti-meridian. Some writers call the entire circle the meridian.

The less the latitude of any place is, the greater, in general, is the heat of its climate. This, however, is much modified by the elevation of the place above the level of the sea, the heat being less as the place is more elevated. The temperature is also influenced by contiguity to heated plains of sand, or to frozen regions; and places that are near the sea, enjoy a more equable temperature, than places more reIt has been generally thought also, that the heat is considerably greater in the northern hemisphere, than in the corresponding latitudes in the southern. The difference, however, if there be any, is probably much less than is generally supposed.

mote.