NEWTON S PRINCIPIA. 325 



f- 1 



-j e V I e 2 siri&quot; 1 e \ z. 

 e I J 



For brevity s sake call the coefficients of or, y, z, A, A, B. 

 Then, according to the notation of last chapter, we have 



X=-(A-co 2 ):r 

 Y=-(A-^)y 

 Z = -Bz 



The equation to the surface is 



or (A w 2 )2-^ + (A o?}ydy + Ezdz 

 integrating we have 



A w 2 



^ (x* -f y 2 ) 4 z 2 = constant, 



the equation to a spheroid; hence the equilibrium is 

 possible. The eccentricity will be given by 



A -co 2 



or by substitution 



,2 



-f 



TT p 



3 co 2 



The quantity 7 - is the same as 



4 7T p 



- a _ centrifugal force at equator 

 4 equatorial gravity 



and this we usually denote by the letter m. Hence the 

 equation to find e becomes 



T 3 



