21)0 :\< TMN. OBLAT1 si-m:i:uih. 



Equation (2) will irive two values for r, one positive and the 



other negative; these values we may deimtc l.y r, and fJ 

 where 



find the whole attraction of the spheroid parallel to 

 the axis of x, we first integrate the expression 



with respeet to r between the limits r = and r=r,, and also 

 between the limits r = and r = r t , and take the diH'enm.-; 

 we thus obtain 



psin'flcos^fa-r,) 



tliis must be integrated between and TT for </>, and and TT 

 for ^. If A denote the whole attraction parallel to the axis 

 of x, acting towards the origin, we have then 



n*F 

 T-. sin* 



W O ^ 



We may simplify this expression by omitting those terms 

 which vanish oy the principles of the Integral Calculus ; thus 



A *s * Pfsfottcwtyi 

 A = 2//>c* , . , r t 



J J c sin 6/ + a 



(l-C08*0)8in 



f c*+(a 2 -^< 



Tr/pc 8 f- | _a ^sin ^ 

 a c "J o j c . f ( a *_ c ') 



2-Tr/pc 8 f a 1 



18 



Let c* = a* (1 *); then the result may be writ 



A = 



