ATTRACTIONS OF ELLIPSOIDS OF VARIABLE DENSITIES. 421 



F («', y', %') = - x'fix, y', a') = - ar' (when / = 1), 



and hence by Noll, F{x',y',%') — — a'l'. In this way the series (29) 

 again reduces itself to a single term, in which 



and the particular value H^ corresponding thereto, by omitting the super- 

 fluous constant /(fj2,i,'i — tk will be (No 10), 



Ho — a. 

 These substituted in the general formula (30) as before, immediately give 



A" . ^""^^UJ ,3,, ,„ c ^'-'^dh 

 A = -^ ; — 7- « o C Pa / — rr — , 



and consequently by reduction since a^ = x, 



A=xA' + A''=-^-l-^r^l a'b'c'x f^^ (36). 



r ( "^ ] " 



The value of A just given belongs to the density 



' _ fi _ ^" y! _ ?!\^ 



Hence we immediately obtain without calculation the corresponding 

 values 



1 dV_ ^^^^U) ,,, , f h^-'^dh 



1 dV *'"'' (2) ,-, , rU-'^'dh 



2^5 r 

 r 



C = :; , -y— = ;f — r" abc% / — , ^ . 



l~2~j 



31 2 



