314 ELECTROSTATICS. [FT. II. CH. VII. 



d = d 2 d 1} the distance apart of the lines of centers, together 

 with the radii R l} R 2 . We must therefore solve the equations 



(I6) 4 = agl, (17) d, = a'?, 



(18) ^ = 20-, (19) a, = 2a, 



(20) d. 2 d l = d, 



so as to obtain r 1? r 2 , a, d l} d 2) in terms of R 1} ^ 2 , d We need for 

 use only the ratio 7*1/7*2 . Eliminating c? 1} c? 2 from (20) by (16) and 

 (1 8), (17) and (19), 



and a by (18), (19), 



(22) jR%- Ri Tl ^ 



'Zr 2 LT^ 



Taking the sum and difference of these two equations we obtain 



(23) R z r 2 - R^ = d, 



/ \ -*-*'9 -*-* / l 7 



( 2 4) - = d - 

 Multiplying these equations together 



or 



a quadratic for rjr^ or ra/r^ Solving we obtain 







It is easily seen that taking the square root with one sign makes 

 the whole expression the reciprocal of its value with the other 

 sign. Consequently we use the upper or lower sign according as 

 r 2 is greater or less than ?v The capacity is accordingly 



( 27 ) K = 



, 

 log "~ 2R& 



} ' 

 I 



which for d = becomes 1/2 log(^ 2 /-R,) as in 144. 



