392 Mr. George J. Allman's Account of 



(11); now 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 -nail, therefore, be 



P = -ii£(OS,xS,T,), 



the letters with suffixes referring to the small ellipsoid. 



The attracting ellipsoids being confocal, their ellipsoids of gyration are con- 

 focal also ; hence it follows, that 



^ (^, + A + G - 3/.) = ^ + 5 + C - 3/, 



and ' OSi X S,T, = OSx ST. 



It appears from this, that the central and transverse components of the at- 

 traction of a sold ellipsoid of uniform density, and whose ellipticities are small, 



solved part of the attraction in that direction ; and the differential coefficient with relation to any 



angle (the sign being changed as before) gives the component in the plane of that angle of the 



moment of the attractive force. 



Hence, 



dV M 1 



since 



dl „ 



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



but 



f x' — - y ' y7 j F {x'^ + y'-) = 0, where F is any function. 



2r"\ dy' " cla/j It'^ \ dy' " dx' ) \ r" )' 



., 3{A-B) , ^, 

 .•. JV = ^— — 5 cos a' cos p'. 



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. 



