366 On the Attraction of Ellipsoids. 



regarded as very great, compared with the axes of this ellipsoid. 

 The components of the attraction of this small ellipsoid on the 

 distant point are given by the expressions (10) and (11) : now as 

 the attractions of two confocal ellipsoids on an external point are 

 in the same direction, and proportional to their masses : the 

 components of the attraction of the proposed ellipsoid will, 

 therefore, be 



the letters with suffixes referring to the small ellipsoid. 



The attracting ellipsoids being confocal, their ellipsoids of 

 gyration are confocal also ; hence it follows that 



(A l + B, + d - 37,) = A + B + C - 31, 



and 



OS, x S,T, = OS x ST. 



before) gives the component in the plane of that angle of the moment of the 

 attractive force. 

 Hence, 



dr' r' 2 2r' 4 

 since 



g-o. 



dr 

 Again, if N be the component of the moment of the attractive force round OZ, 



but 



=->.. y > V, 



dy ' dx' 



d d \ 



x! -3-7 - y' I F (x'~ + y'~) = where F is any function ; 

 dy ax I 



( 

 \ 



3 / , d , d \_ 3 f , d , d \ (Ax'* 4- By" 2 + Cz' 2 \ 

 2/5 ( X dy~'~ y M)~27* T dy'~ ~ ~~ ~ 



.-. N= -- - - - - (cos a' cos'). 

 r 3 



The two other components of the moment may be similarly obtained. The 

 remainder of the proof is the same as in the former part of this note. 



