188 Mr. A. Schuster on the Disruptive Discharge 

 centres of the spheres, we obtain 

 ca = 2a + e, 



e/a = c-2 = k 2 . 



Also from (2), 



c=(l + q *)/ q =P + 2, (10) 



and hence 



l?=(l-q)*/q,ork=(l- q )l x /q. 



From (10) it follows that 



F+4=(l + ?) 2 /?, 



and therefore that 



(l±5li & =(F + 4)/^ ki/F+*=±= S ^ ■ (11) 



(1— q) •Jq 2 



Equation (6) now becomes 



*' + * o 



y 2k log q ' 



and the series (7), after substitution of -^- in terms of log q, 

 becomes 



n / lo ^=2lo^ + 48 logg+ 230i log q + 1935360 lo g?+'-- 



We have still to express log q in powers of h 

 Differentiating (10) we find 



<i-i)= 



2kdk, 



1 <fy 2^ _ __2 



2 d£ 2 2 -l V& 2 + 4 

 dlog?__ _2 __ 1 



from(ll); 



A + -' 



~~dk~ ~~ 2 \2 ) ^2 , 2*2!V2/ 2*2*2 , 3!V2 / / ^ , " 



^ 3 i ^ 75 3.5 77 

 -log j =*- 0T2 5 + 5 . 2 6 . 2 r " 772^3 ! * + " ' " 



Sk 5 __ 5 

 "* 24 640 7168 " f "*" 



