VENUS.

EQUATION OF THE SUN'S LONGITUDE.

THE ELONGATION.

Arg. Sun's mean long.-Venus's Aphelion. Arg. Venus's long.-Sun's equated long.

JUPITER.

Arg. Jupiter's mean long-the Aphelion. Arg. Sun's longitude-Jupiter's longitude.

MATHEMATICAL GEOGRAPHY.

CHAPTER I.

Universal Geography-MathematicalSpherical figure of the Earth. UNIVERSAL GEOGRAPHY is the science that conveys to us a knowledge of the earth, both as a distinct and independent body in the universe, and as connected with a system of heavenly bodies. The figure, structure and dimensions of the earth, the properties and mutual relations of its parts-the features of its surface-its productions and inhabitants-and the laws which govern, or partially affect it as a heavenly bodyare all included within the comprehensive term of universal geography. This definition, or rather description of the objects of geography, serves as the basis of M. Malte-Brun's elaborate work;* but it manifestly embraces a great variety of subjects, commonly classed and treated of under distinct heads of natural philosophy. To avoid, therefore, the confusion of ideas which the extensiveness of this definition may give rise to, it will be convenient to reduce its terms within the limits usually assigned to geography. And we are the rather induced to do this, because the interests of science have been promoted in no slight degree, by a judicious and welldefined arrangement of its parts, which at once excludes a great number of fanciful resemblances, and like a division of labour in mechanical employments, renders every branch more easy to be acquired, and more likely to be extended and improved.

In its proper and more confined sense, geography comprises a knowledge of the figure and dimensions of the earth, and the situation of places upon it-of the natural and political features and divisions of its surface-and of its various productions and inhabitants. These particulars may be arranged under three heads, namely, mathematical, physical, and general geography.

• See Malte-Brun's Universal Geography.

MATHEMATICAL GEOGRAPHY is that branch of the general science which is derived from the application of mathematical truths to the figure of the earth. Of this we shall treat first, because the other branches of geography owe to it much of their accuracy and perfection.

The figure of the earth is manifestly the first subject for inquiry;-for the principles by which we may ascertain the various truths that lie within the altogether different, on the different scope of mathematical geography, are circular plain, a cylinder, or a sphere. suppositions of the earth being a flat

A great variety of appearances, both on the surface of the earth and in the heavens, (which will be described presently) prove conclusively, that the earth is a spherical or round body. The possession of this important truth enables known mathematical properties of the the geographer, by the application of the sphere, to solve many interesting problems, the most useful of which is to determine the relative situation of places upon the earth's surface. For this and some other practical purposes, the earth is taken to be a perfect sphere; and although this supposition be not strictly true, it is sufficiently near the truth to be adopted without sensible error in the investigations into which it is commonly introduced. The nature and quantity of its deviation from a perfectly spherical shape will be for future inquiry.

At what particular period of the world the spherical figure of the earth was first discovered, cannot now be ascertained. It is natural to suppose, that the curiosity of mankind would early be directed to the shape of the earth they lived upon. But when first it engaged their attention, it fared with this as with all other parts of what is called natural philosophy. Men were led to entertain the most erroneous notions of it, by trusting too much to single appearances. Deceived by the plain-like appearance of the earth, and disregarding all other

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