118 Of the Figure of the Earth. 



it must be determined from the resolu tion of the va lue 

 of py and q, in the equation R X 1 — 32+— ^j^= 



rxl — 5*-f*l^J5, which I leave to the analyst. My 



object has been principally to show, by a mathematical 

 process, similar to what mathematicians have instituted 

 for the solution of this problem, the necessary connec- 

 tion, and dependence, between the measures of degrees, 

 in diiferent latitudes of the earth, and the proportion of 

 its axis, and equatorial diameter. Many other inferences 

 might be deduced from the foregoing algebraic equa- 

 tion, involving these relations ; but I have already done 

 •enough, to prove, that mathematicians have been correct 

 in their ideas respecting the species of figure which must 

 result from the inequality of the degrees of the meridian, 

 near the equator and pole ; and that those philosophers, 

 who have embraced contrary notions, have been led into 

 them, from specious resemblances, in the properties of 

 mathematical figures, and a want of that comprehension 

 of the more profound principles, which is essential in the 

 investigation of truth, in difficult and abstruse inquiries 

 of geometry. 



