THE 



PHILOSOPHICAL MAGAZINE 

 AND JOURNAL. 



30 th NOVEMBER 1826. 



XL VI I. On the Grounds for adopting the Ellipticity of the 

 Earth deduced by Captain Sabine from his Experiments 

 with the Pendulum in his Work lately published. By James 

 Ivory, Esq. M.A. F.R.S.* 



THHE experiments with the pendulum are now very nu- 

 -■- merous ; and as different ellipticities may be deduced from 

 different combinations of them, it becomes a question, How 

 we are to distinguish the true ellipticity, from others that may 

 be occasioned merely by accidental irregularities. We do 

 not here allude to small changes in the ellipticity, of the same 

 order as the unavoidable errors of observation, which must 

 occur in different combinations of the most accurate experi- 

 ments ; but to such considerable variations as may lead to dif- 

 ferent opinions about the figure of the earth. 



Suppose we have 25 independent experiments, that being 

 the number we owe to the labours of M. Biot, Captain Kater, 

 and Captain Sabine. By applying the method of the least 

 squares, an ellipticity is obtained which, we will allow, repre- 

 sents all the 25 experiments better than any other. But the 

 experiments employed in the calculation are much more nu- 

 merous than is necessary for determining the figure of the 

 earth. If the earth be an elliptical spheroid two experiments 

 alone, one near the equator and the other at a distance from 

 it, are sufficient for finding the ellipticity. There is no doubt 

 an advantage in combining a great number, provided they 

 are consistent among themselves ; because by this means the 

 unavoidable discrepancies of observation are in some degree 

 compensated, and a mean result is obtained that must ap- 

 proach very nearly to the true figure. But when many ex- 

 perimental quantities are combined in one calculation, it is dif- 

 ficult to distinguish those which are consistent with one an- 

 other, and really belong to the true figure of the earth, from 

 others which, on account of accidental anomalies, cannot pos- 

 sibly be reconciled with the same figure, at least without ad- 

 mitting very considerable errors. It may be said indeed, that 

 * Communicated by the Author. 



Vol. 68. No. 343. Nov. 1826. ? 2 S upon 



