( 121 ) 



The common part of the spheres is now given 1\> 

 "2 2 



3 ' T 3 



JT 



- , 4 - (] , <V (■«' -f «V - <? 3 ) o' (*' + o 3 - cT a ') 



2# 2a- 



(*' + <7, 3 - Q»)» (0* -f- g» — g> »)» -1 



24 a; 8 " + " 24 .r 3 



and the total part subtracted too much from V by 



»,(«.— l)Vr 2 1 



*»* ^ J I g («HO*' --(<>■ + <V)*'- 



+ 



(16) 



1 1 



4 v " ' ^12 



, n iK~ 1)/ 1 

 * = *■- — --V+Vfl'] 



The value of £„! + «, is found by adding (12), (14) and (17) 

 to (7) and substituting the obtained value in (8). By successive 

 reductions we get 



" 2 r 4 A 



X(»p»i) = X(»i)[ V— "i- no*— (v t — 1)- jra,* -f 



jr 5 



■ö° — 



+ 



8 I 1 

 a* a * _j_ -a* a* o, 8 )4 



9 2 36 



V \9 

 17 (r a -l)(i>,- 2) 



36" — "*"■ + " -Tr-^(-i8V4^ »JJ(i8) 



It is easily seen that to the degree of approximation now required, 

 X (n^ is represented by 



X(»l)=ll(* r -('\-l)g-*'<V + 



17 (*, - 1) (», - 2) 



36 



* f «V . (19) 



Substituting these values in (5), taking the logarithm of the result, 

 and developing this logarithm in ascending powers of — , we find 



¥ _ r I »i w i'-r- 2cw i w i + »» w «' , 

 ~ 28 V 



+Z 



%^ F~3 ^ 0] 



(»,-!) (y -2) 15 



36 



+ 



+ 



> loqV no' - no. 3 — — i-UL : -.J^r a 



L,\_ y F 3 F 3 ■ K» 36 ' 



16 Wl (>.-!) 5 (»,- 1) 1 „, („, - 1) 



(20) 



