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XXY. On the Coefficient of Potential of Two Conducting 



Spheres. 



To the Editors of the Philosophical Magazine. 

 Gentlemen, 



IN my paper " On the Coefficient of Potential of Two Con- 

 ducting Spheres" (Phil. Mag. March 1918), there is 

 an error in the determination of the values of one of the two 

 series in terms of a, b, and c. 



Denoting ab by p 2 and c 2 - a 2 — b 2 by P, the series Gr is 



1 + p + p_ p * ^ k*--2ky k»-'dpw+p*^- - - ' 



where each denominator is obtained from the two preceding 

 ones by multiplying the immediately preceding one by k 2 and 

 subtracting the other multiplied by p 4 '. 

 Similarly, 



c T p V p ~| 



F * = d^b 2 L 1+ h* + h 2 k 2 -p ± + k*(IM*-p*)- P W + J' 



t. MJ ^- 2 + ac)(c 2 -b 2 -ac) 

 where A 2 denotes 2 _, 2 , and the same rule 



holds for determining the denominators inside the brackets. 

 Any number of terms of qu and g 12 can be written down 

 without difficulty. 

 Thus, 



a 2 b a 3 b 2 



■9n~ a + c 2-tf + (c 2 -b 2 + ac)(c 2 -b 2 -ac) 



aW 



+ ~(c 2 -b 2 + ac){c 2 -b 2 -ac)(c 2 -a 2 -b 2 )- a?b 2 {c 2 - b 2 ) 

 a*U 



-a 2 b 2 (c 2 -b 2 + ac)(c 2 -b 2 -ac) 

 + ...., and 



ab [\ ab ___ 



^ 12 ~~7L + c 2 -a 2 -b 2+ [c 2 -a 2 -b 2 ) 2 -a 2 b 2 



+ 



(c 2 -a 2 -b 2 y-2a 2 b\c 2 -a 2 -b 2 ) 



•••] 



Yours faithfully, 



Alex. Anderson. 



