4 INVESTIGATION of certain THEOREMS 



ly a mean between the two limits jufl mentioned; and it is pro- 

 bable, that, if the comprefTion is lefs than this, it is owing to the 

 increafe of the denfity toward the centre. Boscovich, taking 

 a mean from all the meafures of degrees, fo as to make the po- 

 fitive and negative errors equal, found the difference of the 



axes of the meridian rr — ^. By comparing the degrees mea- 



fured by Father Leisganig in Germany, with eight others 

 that have been meafured in different latitudes, LaLande finds 



— , and» fupprefhng the degree in Lapland, which appears to 



err in excefs, ~ for the comprefTion. La Place makes it 



— ; Sejour — , and, laflly, Carouge and La Lande — . 

 321' J 307' ' y ' 300 



These refults, which reduce the excentricity of the meridians 

 fo much lower than was once fuppofed, agree well with the ob- 

 fervations of the length of the pendulum made in different lati- 

 tudes. Were the earth a homogeneous body, Sir Isaac New- 

 ton demonftrated, that the diminution of gravity under the 



equator would be ~ |fe expreffed by the fame fraction with 



the comprefTion at the poles. M. Clairault made afterwards 

 a very important addition to this theorem : for he fhewed, that, 

 if the earth be not homogeneous, but have a denfity that varies 

 with any function of the diftance from the centre, the two frac- 

 tions, expreffing the comprefTion at the poles, and the diminu- 

 tion of gravity at the equator, when added together, mufl be of 

 the fame amount as in the homogeneous fpheroid, that is, 



mufl be n — - or - — . Now, the fecond pendulum is con- 

 cluded, from the befl and moft recent obfervations, to be longer 

 at the pole than at the equator by jj-, and this, taken from **£ 



leaves rr - for the compreflion at the poles. 



a, But 



