OBLATENESS

, of the earth, the flatness about the poles, or the diminution of the polar axis in respect of the equatorial. The ratio of these two axes has been determined in various ways; sometimes by the measures of different degrees of latitude, and sometimes by the length of pendulums vibrating seconds in different latitudes, &c; the results of all which, as well as accounts of the means of determining them, see under the articles Earth and Degree. To what is there said, may be added the following, from An Account of the Experiments made in Russia concerning the Length of a Pendulum which swings Seconds, by Mr. Krafst, contained in the 6th and 7th volumes of the New Petersburgh Transactions, for the years 1790 and 1793. These experiments were made at different times, and in various parts of the Russian empire: Mr. Krafft has collected and compared them, with a view to investigate the consequences that may be deduced from them. From the whole he concludes, that the length p of a pendulum, which swings seconds in any given latitude l<*> and in a temperature of 10 degrees of Reaumur's thermometer, may be determined by the following equation, in lines of a French foot: viz, .

This expression agrees, very nearly, not only with all the experiments made on the pendulum in Russia, but also with those of Mr. Graham, and those of Mr. Lyons in 79° 50′ north latitude, where he found its length to be 441.38 lines.

It also shews the augmentation of gravity from the equator to the parallel of a given latitude l: for, putting g for the gravity under the equator, G for that under the pole, and z for that under the latitude l; Mr. Krafft finds ; and consequently :

From this proportion of Gravity under different latitudes, Mr. Krafft deduces, that on the hypothesis of the earth's being a homogeneous ellipsoid, its oblateness must be 1/190; instead of 1/230, which ought to be the result of this hypothesis: but on adopting the supposition that the earth is a heterogeneous ellipsoid, he finds its Oblateness, as deduced from these experiments, to be 1/297; which agrees with that resulting from the measurement of degrees of the meridian.

This confirms an observation of M. De la Place, that, if the hypothesis of the earth's homogeneity be given up, then do theory, the measurement of degrees of latitude, and experiments with the pendulum, all agree in their result with respect to the Oblateness of the earth.