4 II^FESTIGATION of certain THEOREMS 



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

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

 increafe of the denfity towai'd 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 — ^. By comparing the degrees mea- 



fured by Father Leisganig in Germany, with eight others 

 that have been meafured in different latitudes. La Lande finds 



-^, and, fupprefTmg the degree in Lapland, which appears to 

 err in excefs, -^ for the comprefHon. La Place makes it 

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



321 3*^7 ^ 



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 = ^, exprelTed by the fame fradion with 

 the comprefllon 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 fundliori of the diflance from the centre, the two frac- 

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

 ti6n of gravity at the equator, when added together, mufl be of 

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



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

 cluded, from the bell and mofl recent obfervations, to be longer 

 at the pole than at the equator by -^^t and this, taken from — , 



leaves -^ for the comprefTion at the poles. 



a. But 



