362 On the Attraction of Ellipsoids. 



Now, 



dV M , 3 3 dl 



but, 



dl ^(A-I)cosa t dl 

 dx'~ / ' 4/ 



Hence we have 



M , 3 .. , 



X = 2 GOSa + -^ (A + B + C- 51) COS a + -- 



(7) 



M , 3 , 3(7 cos 7 r 



' 



r 



Now, 



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

 but, 



sin cos a = cos (3 cos 7' - cos 7 cos $ , 



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

 sin cos 70 = cos a cos j3' - cos /3 cos a' ; 

 The following relations, moreover, exist : 



a z cos a = rp cos a, b z cos /3' = r/? cos |3, c z cos 7' = rp cos 7 : (8) 



hence, by substitution, we have 



b z c z c z - a z 



COS = : COS /3' COS 7', COS j3 = : COS 7' COS a', 



pr sin jw- sin < 



COS 70 = : COS a' COS/3'. 



pr sin 4 



