diminution of gravity in going from the Poles to the equator is about 1180 part. And if we subtract the fraction 1180 from the fraction 1115, the remainder scarcely differs from 1300, showing that according to this theory the ellipticity of the earth ought to be 1300, or the proportion of the earth's diameters ought to be as 300 : 299. And this is exactly the same proportion which has been found from triangulation surveys and Zenith Sector, as described to you in a former lecture. This, therefore is a very remarkable proof of the correctness of the theory of gravitation, when applied with proper attention to all the circumstances.
There is another very curious method of determining the ellipticity of the earth, which also depends upon the theory of gravitation. I have said that the attraction of a spheroid upon any external body is not the same as the attraction of a sphere; and therefore the attraction of the earth upon the moon is not the same as if the earth were a sphere. There is therefore a small irregularity in the motions of the moon depending on the earth's ellipticity; and it is very remarkable that, whatever be the succession of densities of the strata of the earth, this irregularity is found upon the theory of gravitation to depend upon nothing but the ellipticity of the earth's surface. And therefore, if we observe the moon's motions so carefully as to discover the amount of this irregularity, and if we make the proper calculation from it, we can find the ellipticity of the earth. The ellipticity thus determined agrees well with that found from the surveys: and thus another proof is given of the correctness of the theory of gravitation. It may not be amiss to state here that the motions of Jupiter's Satellites are much disturbed by the ellipticity of Jupiter's body.
