CURVATURE OF THE EARTH

275

Thus, in fig. 1, the circumference of the small circle ismore curved than that of the large circle, in the inverseratio of the lesser to the greater radius. The curvatureof circles is, therefore, in an inverse ratio to the length oftheir radii. When a radius, consequently, is very large,the curvature of the circle appears to be almost nothing.

Application to the curvature of the Earth .—The radiusof the earth, for example, being more than six millionmetres, its great circle is a million times less curved thana circle with a radius of six metres , and eight milliontimes less curved than such a circle as the wheel of a car-riage.* Its curvature, therefore, is not apparent to us inshort spaces, and only becomes perceptib.e when at sea,or on vast plains.

A knowledge of the curvature of the earth enables us tomeasure, by approximation, the height of mountains and ofthe sea-coast, when we know also the distance of thesefrom the point where we are at the moment.

Let AB, fig. 2, be the radius of the earth, and CD the mountain,the summit of which, D, begins to disappear from the eye of avoyager who has proceeded from D and arrived at B. If we knowthe distance BC, drawing the radius ACD, we can immediately,measure CD. When the angle BAC is very small, the arc BC isvery nearly equal to a perpendicular let fall from B on AD. Weshall then have, very nearly,

AB : BC : : BC : CD;

that is to say, that the radius of the earth is to the distance BC ofthe mountain from the spot where the voyager is, as this distance is

BC 2

to CD, the height of the mountain; consequently, CD = —

Ad>

Seamen, when they know the height CD of the masts,the hull, or any other part of a vessel, judge of the dis-tance she is from them by an inverse method, which, du-ring war, is of very great importance.

We have just seen that the radius of different circles

* The measures of the original have been preserved in the trans-lation, on account of the proportion involved in them. The actuallength of the radius of the earth is 7,290,901 yards. See page 51.

Tr.