Mutual Induction between two Circular Currents. 605 

 From (1) we get 



have 



we have 



where A is the constant of integration. 



Rejecting k' 2 and higher terms in the expression for Y, 



A+— ° = 2tt--- l 2 W T , -8?rl ( logyy),, — ^dk' 

 c x c 1 c l + c 2 &k' J \ 8 /:V(l — &') 



Ci0i+c 2 ) fe &' J °^ v ; 



= 8 ^W og4 F + H^ lo 4 + *' 



+ |^logi, + |^]. 



To determine the constant, we observe that the quantity 

 independent of c 1 on the right-hand side is 877-. Hence, 

 in view of the actual value of M , we get A = 87r. 



Accordingly 



It will be seen that if we put c 2 — c 1 =a?, and reject powers 



about x 2 , the first two terms reduce to 4zir\ c 2 logy 2 L 



which agrees with Maxwell's result. *- 1 -" 



3. In the case of two parallel wires at a small distance 

 apart, /a = 0, and we have 



~ ^ Cx \cj n(n+ 1) \ dfi ) [\ dfi ) 



+ uaw d ^+'y 



Since (^f Ptt )o =0 ' 



fd? n d?Y n \ =() &c 



\ dfx dfx 2 ) 7 



