Page:Popular Astronomy - Airy - 1881.djvu/268

254 of internal structure may be, you can say that there is a certain relation between the ellipticity of the earth and the degree of alteration of gravity from the poles to the equator. Suppose you take a vulgar fraction to express the proportion of the whole diameter by which the earth is flattened at the Poles, and suppose you take another vulgar fraction to express the proportion of the whole gravity by which the gravity is diminished as you go from the Poles to the equator; if you add the two fractions together, whatever be the succession of densities of the different fluid strata of the earth, the sum of those two fractions will be $1⁄115$. This particular value $1⁄115$ depends upon the velocity of the earth's rotation; if the earth revolved in a longer or shorter time than 24 hours of sidereal time, the sum must be a different quantity.

We are enabled thus by the pendulum experiments, which give us the law of change of gravity, to infer what is the ellipticity of the earth, provided the law of gravitation be true, (for that has been the basis of the whole investigation.) When, by means of the pendulum, we have got the variation of the law of gravity, we have only to express it by a fraction, and to subtract that fraction from $1⁄115$, and we get another fraction which expresses the compression of the earth, or the difference between the two axes divided by one of them. And if the compression or ellipticity of the earth which we find by this process (depending entirely on the law of gravitation) agrees with that which we find from trigonometrical surveys and the use of the Zenith Sector, (in which the law of gravitation is not concerned at all,) this will be a strong proof of the correctness of the law of gravitation. Now, the proportion of gravity at the Poles and the equator is found to be about 180 : 179, so that the