OF ELLIPSOIDS OP VARIABLE DENSITIES. 2J3 



Again, the same general theory being applied to the value 

 of A" given above, we get 



F(x' 9 y\ z) = - x'f(x' 9 y\ z'} = -x' (when/= 1), 



and hence by No. 11, F(x f , y y z} = a'f> In this way the 

 series (29) again reduces itself to a single terra, in which 



&'=', and * = -', 

 and the particular value H Q corresponding thereto, by omitting 



the superfluous constant , 2 ,, 2 - ^ will be (No. 10), 



y (Q> ~r -T G ) 



These substituted in the general formula (30) as before, imme- 

 diately give 



, 7 



A,> r/ /- dh 



A" 



2 



and consequently by reduction since f = x, 





The value of ^4 just given belongs to the density 



Hence we immediately obtain without calculation the cor- 

 responding values 



1 dV 



J ~ 



\-ri dz 



