292 ATTRACTION. 



11 HM the attraction >t' the spheroid similar to the Lrivcn 

 One and passin.r through the attracted particle, is tin- sann! 

 as that of any other similar and similarly situated concentric 

 spheroid comprising /// '/ jxirticl /// tofftOM. Hence 



a split-mida! shell the surfaces of which arc similar, similarly 

 situated, and concentric, attracts a particle within it equally 

 in all directions. This has been already established . 

 Art. 15. 



It we put the ellipticity of the spheroid = e, and sup 

 every small so that we may neglect its square, we ha\ 

 the oblate spheroid, since c a (1 - e), 



c 

 e* 1 -- i = 1 (1 e) 2 = 2e approximately. 





After expansion and reduction we shall obtain approximately 



For the prolate spheroid, since a = c (1 e), 



e'=l- = l-(l-e)=2e. 

 After expansion and reduction we shall obtain approximately 



228. If instead of the spheroid we take an ellipsoid whose 

 -axes arc a, b, c, it may "be shewn that 



cos* 6 sin OtlO 



f t V(* cos 1 0+ c* sin' 0J </(F cos* + c* sin' 6) ' 



and the values of A and J5 may be found by symmetrical 

 changes in the letters a, i, c and/, //. //. 



we change a, , c into a (1 -f w), i (1 -f n), c (1 -f ?i) 

 respt-' '-ssion for < n > tins unchanyvd; and BO 



also the expressions for yl and B remain unchanged. This 



