Capacity of Electrolytes. 353 



dV" ~ /Tr iN fsina . „ sin 2a . ft/1 , ..sin 3a . 0/1 I 



_ » -2(K+ 1) {-gpsm 9+p - w - sin 26 + p 2 -^-«n 30 + . . . j 



1 dV" , n/1 ^ n Tsina . Qx sin 2a . „ sin 3a . oa , ") 



-.-^^=+2(K-l)|-^sin6> + p- [ ^sin2^ + ^- 1 ^-sin36> + ...j 



To find the value of B (equation B), we integrate with 

 respect to 6 between and 27T the three terms under the 

 integral sign. 



I 



f 2 " a/rfV"\' , ,„, 1l2 fsina sin 2« , 2 sin2asin3a , J 

 J cos^)<W=4^(K + l) '{— jp + , 2 gs +...} 



n/dY" l\ 2 ia . /T7 1N2 ( sinasin 2a , 9 sin 2a sin 3a , ■) 

 «(- 5r --)rf<'=^(K-l) 8 {— ^ +P— ga + •••} 



Substituting in equation B we have, since 



„ LK" . ,K'-K"(sinasin2a , 9 sin 2a sin 3a, ) ,_, 

 B=^ r . / ,.4^.4 £F - gr/ (— ^— +P W +..j(E) 



But Tjirp 2 = v, the volume of the cylinder. 



A 

 sin a = -. 



• o o AB 

 sin 2a = 2-j-r. 



sm3« = 3-g^. s . 



For the case of a conducting cylinder, as carbon, K f is un- 

 known ; but owing to its conductivity, the distribution of 

 potential is the same as though K' were infinite. Hence 



K7--K" 

 K' + K" ' 



Substituting these values in equation E, we have, 



±v Wl A 2 Bf . p 2 „B 2 -A : 



B = 



7T *^ ' R 6 t R 2 R 2 + "-| 



In the experiment A 2 = 5B 2 , B = l*22 cm., and in the case 

 of carbon cylinders, v = 2*85 c.c, the volume of one cylinder. 

 Substituting these values in the formula, and neglecting the 



