362 On the Attraction of Ellipsoids. 



Now, 



dV M , 3 3 rf7 



: = - -r-^ = -7- COS a + 7^-77 (^1 + J? + (7- 37) COSo + 7:-^ 3-,, 

 /7-T* /** x* * x**" /Y/>* 



bnv / A// ,-w/ (.(it'- 



F=-^= 0' 3 R -37} 0' 3 dl 



dy' r' 2 2/ 4 2r' 3 dy n 



z= _<*r^M , _s_ (A+s + c _ 3r ,, 3 di 



but, 



-7) cos a' di 2 (B -7) cos 0' rf/ 



Hence we have 



Jf 3 . . , 3^i cos a' 



= -^ cos a + -^r, (A + B + C - 57) cos a + - 

 r 2 2r 4 





3 35 cos 8' 



TI (^ + +-57)008/3' + p^, (7) 



' M 5 (7-57 1 ) ' 3Cr os 



. '2 / O,.'4 \ / 



Now, 



Q = X cos a 4 F cos j3 + Z cos 70 ; 

 but, 



sin (f> cos a = cos /3 cos 7' - cos 7 cos 3 > 



sin ^ cos j3 = cos 7 cos a' - cos a cos 7', 

 sin cos 70 = cos a cos jS 7 - cos j3 cos a' ; 

 The following relations, moreover, exist : 



a 2 cos a' = rp cos a, i 2 cos 3' = ?'/> cos 3, c 2 0087' = r/j 0087 : (8) 



hence, by substitution, we have 



J 2 c 2 c 2 - a 2 



cos a = -. cos 3' cos y' cos 3o = ; cos 7' cos a', 



j9>- sin </> pr sin 



COS 7o = - 



COS a COS 



pr sm 



