I. Investigation of certain Theorems relating to the Fi- 

 gure of the Earth. By John Playfair, F. R. S. Edin. 

 and Profejfor of Mathematics in the Univerfity of Edinburgh^ 



[Read Feb. 5. 1798.] 



1. np'HE obfervatlons which have been made to determine the 

 J. magnitude and figure of the earth, have not hitherto 

 led to refults completely fatisfaftory. They have indeed de- 

 monftrated the compreflion or oblatenefs of the terreftrial fphe- 

 roid, but they have left an uncertainty as to the quantity of 

 that compreflion, extending from about the one hundred and 

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

 of the equator. Between theft two quantities, the former of 

 which is nearly double of the latter, moft of the refults are pla- 

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

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

 NtwTON, as is well known, fuppofing the earth to be of uni- 

 form denfity, afligned for the compreflion at the poles -^, near- 

 Part L a 2 Iv 



