102 



INVESTI8ATI0H OF CIRTAIN THEOREMS 



No complete re 

 fults have yet 

 been had as to 

 the figure and 



Snumer&tion. 



III. 



Jnvejligation of certain Theorems relating to the Figure of the 

 Earth . By ]ofin ?LAYFAiK, F. R. S. Edin. and Profejfbr 

 of Mathematics in the Univerfity of Edinburgh. ♦ 



1. 1 HE obfervations which have been made to determine 

 the magnitude and figure of the earth, have not hitherto led 

 to refults completely fatisfadlory. They have indeed demon- 

 magnitude of the ftrated the compreflion or oblatenefs of the terreftrial fperoid, 

 but they have left an uncertainty as to the quantity of that 

 comprelfion, extending from about the one hundred and feven- 

 tieth, to the three hundred and thirtieth part of the radius of 

 the equator. Between thefe two quantities, the former of 

 which is nearly double of the latter, mod of the refults are 

 placed, but in fuch a manner that thofe beft entitled to credit 

 are much nearer to the leaft extreme than to the greateft. Sir 

 Ifaac Newton, as is well known, fuppofing the earth to be of 

 uniform denlity, atfigned for the compreflion at the poles ^j-^, 

 nearly a mean between the two limits juft mentioned ; and it 

 is probable, that, if the compreflion is lefs than this, it is owing 

 to the increafe of the denfity towards the centre. Bofcovich, 

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

 the pofitive and negative errors equal, found the difference of 

 the axes of the meridian = yj^. By comparing the degrees 

 xneafured by Father Leifganig in Germany, with eight others 

 that have been meafured in different latitudes. La Lande finds 

 YTT, and, fupprefling the degree in Lapland, which appears to 

 err in excefs, jjy ^^^ the compreflion. La Place makes it 

 Sejour y^y, and, laftly, Carouge and La Lande y^-^. 

 Thefe refults, which reduce the eccentricity of the meridians 

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

 obfervations of the length of the pendulum made in different 

 latitudes. Were the earth a homogeneous body. Sir Ifaac 

 Newton demonftrated, that the diminution of gravity undet 

 the equator would be = ^TZt expreffed by the fame fraftion 

 with the comprefCon at the poles. M. Clairault made after- 

 wards a very important addition to this theorem : for ^le 

 ihewed, that, if the earth be not homogeneous, but have a 





The refults of 

 obfervcd eccen- 

 tricity agree 

 with the com- 

 puiarions de- 

 duced from the 

 length of the 

 fecond^ pendu- 

 lum. 



♦ Edinburgh Tranf. Vol. V. 



denfity 



