187. The variation of the time of oscillation of a pendulum in different parts of the earth, discovered by Richer in 1672 (chapter VIII., § 161), indicated that the earth was probably not a sphere. Newton pointed out that this departure from the spherical form was a consequence of the mutual gravitation of the particles making up the earth and of the earth’s rotation. He supposed a canal of water to pass from the pole to the centre of the earth, and then from the centre to a point on the equator (B O _a_ A in fig. 72), and then found the condition that these two columns of water O B, O A, each being attracted towards the centre of the earth, should balance. This method involved certain assumptions as to the inside of the earth, of which little can be said to be known even now, and consequently, though Newton’s general result, that the earth is flattened at the poles and bulges out at the equator, was right, the actual numerical expression which he found was not very accurate. If, in the figure, the dotted line is a circle the radius of which is equal to the distance of the pole B from the centre of the earth O, then the actual surface of the earth extends at the equator beyond this circle as far as A, where, according to Newton, _a_ A is about 1∕230 of O B or O A, and according to modern estimates, based on actual measurement of the earth as well as upon theory (chapter X., § 221), it is about 1∕293 of O A. Both Newton’s fraction and the modern one are so small that the resulting flattening cannot be made sensible in a figure; in fig. 72 the length _a_ A is made, for the sake of distinctness, nearly 30 times as great as it should be. [Illustration: FIG. 72.—The spheroidal form of the earth.] Newton discovered also in a similar way the flattening of Jupiter, which, owing to its more rapid rotation, is considerably more flattened than the earth; this was also detected telescopically by Domenico Cassini four years after the publication of the _Principia_. 188. The discovery of the form of the earth led to an explanation of the precession of the equinoxes, a phenomenon which had been discovered 1,800 years before (chapter II., § 42), but had remained a complete mystery ever since.