Assuming the above reasoning to be correct, it follows, that the rate of descent of falling bodies will be accelerated in the transition from the equator to the poles. Now, it has been before stated that the pendulum is a falling body; therefore, with the same length of pendulum, the oscillations at the pole should be faster than at the equator. Theory, in this case, is verified; for it has been proved by experiments, repeated again and again, that a pendulum oscillating 86,400 times in a mean day at the equator, will give the same number of oscillations at any other point, provided its length is made longer in the exact ratio as the square of the sine of the latitude. The sequence to be derived from all the foregoing considerations is, that the whole decrease of gravitation from the equator to the poles is 0.005.1449, which subtracted from the 1/155.2 gives the amount of compression of the earth to be nearly 1/285.26. But this form of the earth would give the excess of the equatorial axis over the polar about 26¹⁄₂ miles. The measurement is confirmed by Mr. Ivory in his investigations on the five principal measurements of arcs of the meridian in Peru, India, France, England, and Lapland. He found that the law required an ellipsoid of revolution whose equatorial radius should be 3,962.824 miles, and the polar 3,949.585 miles; the difference is 13.239 miles; this quantity multiplied by two gives 26.478 as the excess of one diameter over the other. Thus, by two different processes the figure of the earth has been determined; but another remains that is the result of pure analysis, derived from the nutation and precession of the equinoxes--for, as explained before, these effects are caused by the excess of matter at the earth’s equator. The calculation does not lead us to certainty, but it does show the compression to be comprised between the two fractions ¹⁄₂₇₀ and ¹⁄₅₇₃. There is this advantage in the lunar theory, that it takes the earth as a whole, disregarding any irregularities of surface, or the local attractions that influence the pendulum--the difficulties of measuring an arc of the meridian being an obstacle to perfect accuracy.