On the Attraction of Ellipsoids. 363 



Substituting these values for cos o , cos /3 , cos 70, in the expres- 

 sion for Q, and observing that 



cos a' cosao + cos/3' cosj3 + 0087' 00370 = 0, 

 we get 



3Jf 2 (& 2 -c 2 ) + & 2 (c 2 -a 2 ) + c 2 (a 2 -& 2 ) , 



cos a cos p cos 7=0. (9) 



TT . 



r * pr sm 



PROPOSITION VI. 



The same things being supposed, to find the other Components 

 of the Attraction, namely H, in the direction of the centre of gravity 

 MO, and P in the transverse direction TS. 



To find R ; 



R = X cos a + Y cos /3' + Z cos 7' ; 



2/ 4 





r' 2 2r' 4 v 

 To find P ; 



P = X cos ai + Y cos /3i + Z cos 7! ; 

 but, 



sin ^ cos ai = cos a' cos ^ - cos a, 



sin0 cos/3i= cos/3'cos0 - cos/3, 



sin cos 7! = cos 7' cos - cos 7. 



Substituting for cos a, cos/3, 0087 their values from (8), we get 



COSai = COS a', COS)3i = ; COS ]3', 



pr sm ^ pr sin 



<?-p* 



COS 71 = : COS 7 . 



Substituting these values of cos !, cos/Si, 0087!, and observing 



that 



cos a cos 01 + cos j3' cos /3i + cos 7' cos y L = 0, 



