SPHALROWICO-ELLIPTICORVM. 1 t t 



\"*-,m V2WIK [mm—nn) imm--Tin)*x 



n ' n mn inmi/i* 



^ ( ( 2mm-nn)xVx-{-2mnnVx) 



(mm —nn)' 1 / 

 161 



\: i ^{(3m*—2mmnn—n*)x t +$mn 1 (m t -$-n' l )x-4m' t n*} 



— ■^^T^{{W-^mmnn-n')x 2 Vx-^a t mn 2 {2m , -{-n z )xVx- 

 , ^m 2 n"Vx) etc. 



Qiiae expreflio multiplicata per dx dabit attractionem- 

 corpufculi in A fiti ad difcum ellipticum craflitiei d x. 

 Huius ergo integrale fi pomtur xzzz^m dabit attradtionem 

 punfti A ad totam fphaeroidem j quae attra&io iequen- 

 tem habebit valorem 



~C+rrrn 2 {mm-nn) 

 I n " 7i 



91" -i^m (mm— nn)^ 



~7iT n 5 



qiii reductus in fequentem fbrmam abit 



Q. E. I. 



Corollarium 



Si difterentia inter m et « fit minima ita vt fit »* 

 zzzn-\-dz erit grauitas fiib aequatore in noftra fphaeroide 

 r~47r(7 H — - z — ^-) , cum contra grauitas fub polo in~ 

 tienta fit — ^{- z -\- t zf'~ l z^c) j ^ vt g^uitas fub polo 

 maior fit parte 4^(77—7^). Si fit n-.m—ioo-. 101 

 fiet grauitas fab polo ad grauitatem fub aequatorevt 509 

 ad 50 8, 



Probic» 



