360 On the Attraction of Ellipsoids. 



Let pyramids thus related be indefinitely multiplied, and 

 the ellipsoid will be simultaneously exhausted from the three 

 points A, B, C. 



Hence the sum of the whole attractions at A, B, C, divided 

 respectively by the lengths of the corresponding axes, will be 

 2irfifp, or, 



ABC 



PROPOSITION IV. 



To find an expression for the potential V of a system of par- 

 tides at a point M, ivhose distance from the centre of gravity of the 

 system is very great compared with the mutual distances of the 

 particles. 



It is proved by Poisson,* that if the origin of co-ordinates 

 be at the centre of gravity of the system 



x ', /', z being the co-ordinates of the distant point, and / its 

 distance from the origin. Let now the principal axes at that 

 centre be taken as axes of co-ordinates ; then, since 



m = 0, 2#s dm = 0, ^yz dm = ; 



Hence, if A, B, C be the three principal moments of inertia, 

 and / the moment of inertia of the system round OM, 



(6) 



* Mecamque, torn .i. p. 178. 



