248 Prof. H. Hennessy on the 



and from the ordinary treatises on Mechanics it readily 

 appears that for a spheroid, 



C =^<*% A=B = ^7ra 2 6(a 2 + Z> 2 ), 



where b is the semipolar and a the semiequatorial axis. 

 Hence we have 



C-A %a%-a%-a 2 b z a*b-a 2 b* {a 2 -b 2 ) 2 , 

 a 2 ~2\ i a*)> 



C ~ " 2a 4 6 ~ 2a 4 6 2a 4 6 



a 2 -6 2 1A ft* 



2 

 and 



2(0- A) /, b 2 









In a spheroidal shell for whose inner surface the semiaxes 

 are b x and a l3 we have the moments of inertia with respect to 

 the axes by taking the moments for the inner spheroid 

 bounded by b x and a x from those of the outer spheroid. 



Calling the former Ci and A 1? we have, as before, 



8 4 



Ci = jgirai*&i, A 1 = — Tra^i^ + ^i 2 ). 



Calling C x and A x the moments of inertia of the shell, we 

 have, therefore, 



Ci = ~ir(« 4 *-VM, A 1 = ^7r[a 2 5(a 2 + ft 2 )-a 1 2 6 1 (a 1 2 + 5 1 2 )] J 



and hence 



1 -A 1 _ g a % a -ff)-a 1 8 & 1 (a 1 a --6 1 8 ) 

 Cx ~ 2(a 4 6-a 1 4 6 1 ) 



^(l-g)-aA(l-g) 



2(a 4 6-a 1 4 6 l ) 

 If e and ^ be the outer and inner ellipticities of the shell, 

 1 b b x 



and if e — e\ y 



b_bi 

 a cii 

 In this case 



U 1 ~ 2(a 1 b-a 1 %) ~z{ ai 1 )' 



