452 Mr. S. Butterworth on the Coefficients of 



8. When # = the circles are coplanar. 

 If r>c, /jl = 0, v 2 — -g — 1 and the mutual induction is 



2c 2 



M 1 = 4WAa[x 1 -2-^^(x 1 --)(l ^ J 



45 j^_ f / _ 8 c 2 8c*\ 

 8192A 2 a 2 \ l \ 3r 2 + 3rV 



_/97 214 c 2 214 c 4 \"\ "I 



( ^60~ 45 r 2_i ~ 45 WJ '■'■J' 



. . (24) 

 in which X^log, 16 *^ . 



T 



This formula holds good when the two circles intersect. 

 If r<c, v = 0, /jl 2 = 1 g? an( i the mutual induction is 



M ] ' = WAa[x 1 '-2 + A^J (v-|)(l + /»')-- -Ja-M) 2 } 



-^(l- M ) 2 (7 + 2 / x + 7 /t 2 )j+ ...], 

 . . . (25) 



in which \i = log e _-^ — - • 



This formula holds when one circle is entirely inside the 

 other. 



If r = c, the two circles touch internally and the mutual 

 induction is 



+ •••}, • (26) 



-hich V'=log. 16V ^ . 



Ill WJ 



It is interesting to notice the similarity between formulae 

 (26) and (10). 



