PHYSICAL AND MATHEMATICAL SCIENCES. 3 29

is supposed to be homogeneous ; and though Newtonwas necessitated to supply some data of the calculationupon assumptions which have been since found not al-together exact, yet, upon the whole, the modern inves-tigations give a result differing very little from his,which makes the proportion that of 230 to 229-

As yet, however, there were no measurements fromwhich the least hint of any such actual deviation from asupposed perfect sphericity in the earth’s figure hadbeen suggested. But there were certain facts latelydisclosed, which, though not appearing to the generalityof astronomers to have any relation to such a subject,yet, in the mind of Newton, were instantly associatedwith it in the closest connection.

From the spheroidal figure it followed, that the in-tensity of gravity at different parts of the surfacewould be different ; and would decrease, in going fromthe pole to the equator, in proportion to the square of thesine of the latitude. The vibrations of a pendulum de-pend entirely on the force of gravity : hence, the samependulum, near the equator, ought to vibrate moreslowly than in higher latitudes. We have beforeseen that this was precisely the fact which had been ob-served by Richer, Varin, and Des Hayes, and had excitedso much astonishment.

Another investigation, closely connected with this fact,perhaps exhibits in a still stronger light the surprisingpowers of the genius with which Newton was gifted forseizing remote analogies, and bringing to bear upon thesame point, facts and arguments apparently of themost widely dissimilar character.

We have already seen that the successive observationsof astronomers had disclosed the fact, that the equinoc-tial point, or intersection of the plane of the earth’sequator with that of its orbit, is constantly but slowlychanging its position, and retrograding in the order ofthe zodiac. This was termed the precession of equi-noxes, and the amount of it had been assigned as aboutfifty seconds annually.