ON THE FIGURE OF THE EARTH, 13 



difference In obfervations made in nearly the fame latitudes, Obfervations 

 does the author think it fufficient to account for the great dif- p^i^y^l^t^"* 

 agreement in the refults from the comparifon of diftant obfer- memoir on the 

 vations? Is it not much more probable, without giving up the ^|^"^^ °^ "** 

 elliptic figure, that fome of the obfervers may have ufed dif- 

 ferent ftandard meafures from the reft, or not made proper al- 

 lowances for the alteration of their lengths in different temper- 

 atures? In (hort, this circumftance appears to me fufficient to 

 account for fome fmall local irregularities, but wholly inade- 

 quate to explain the great differences in the general refults. 



The author then proceeds to point out feveral methods of 

 calculating the dimenfions of the earth from terreftrial meafure- 

 ments. The firfl applies to the cafe where two arches of the 

 meridian are given in different latitudes, which, under the mofl 

 favourable circumflances, is incomparably the mofl accurate 

 that can be employed. The rules he gives are certainly verjr 

 fimple, and in fome refpe6ls new; but he feems to be mif- 

 taken when he afferts, that the calculation muft be made bf 

 rules quite different from thofe that have been hitherto given. 

 Euler's * is effentially the fame with his own; and Du Sejour, 

 Legendre, Delambre, &c. have given many accurate theo- 

 rems, which may be applied to this purpofe. The fecond me- 

 thod is, from comparing a degree of the meridian in any lati- 

 tude with a degree of the curve perpendicular to the meri- 

 dian in the fame latitude ; and the third from the meafures of 

 degrees of the curve perpendicular to the meridian in differ- 

 ent latitudes. His theorems for both are very accurate and 

 fimple. But the principal novelty of Mr. Play fair's paper is, 

 the method hepropofes of finding the figure of the earth from 

 the length of a flraight line or chord joining two places whofe 

 geographical fituations are given. As he has left the folution 

 of this problem to fome future occafion, the following perhaps 

 may not be unacceptable : 



Let PAO (Plate III. Fig. 1 .) reprefent one quarter of the Solution of the 

 ellipfis, by the revolution of which round the femi-conjugate fi^'^]^'^'" {""^ 

 axis PC, half the terreflrial fpheroid is generated. Let C figure of the 

 be the center of the earth, P the pole, C O the radius of the ^^^^^> ^''O'" '^= 

 equator=a, C P half the polar axis=/>, and c=the com pref- joining two °^ 

 fion at the poles, or the excefs of a above b. Let A in the known places, 



&c. 

 • Memoircs de L'Academie Royale des Sciences Belles Lettres 

 a Berlin, 1753. 



meridian 



