270 Dr. J. W. Nicholson on the 



The first term alone contributes to the current crossing any 

 section of the first wire. It causes an internal potential 



H =-ir*w • • • • • (»> 



in accordance with previous calculation, and a reflected wave 

 H = - Mi K (ihr) + i^ =1 ^^K s (ihr) cos s0. (82) 



We now introduce the fact that the squares of ha, hb, he may 

 be ignored. Thus 



K = - log {he), 

 — % 



'to 

 Kn = - ^- {YJhc) + lirSnQic) } 



K/(Jia) = -2»- 1 7i!/(*7ia) M + 1 . 

 If 



^(i.^A/jHf^V . (83) 

 * V ka J/(£a)// \ ka J s \ka)r J 



and fi s be the corresponding quantity for the second wire, it 

 appears on reduction that 



B0 a n 8 (Kb)*i' 



~ 2 2s -i5!5-l! 



_ Bfj, s h s b 2s i> s 



s I 2 S ~V 



(84) 



The coefficients of type c s therefore rapidly become small, 

 especially if c/h is large. If he is large and lib small the 

 convergence is still more rapid, but the first form of c s is to 

 be used. 6 S itself decreases rapidly as he increases. 



Accordingly, when c is so large that the approximate 

 values above cannot be used for the functions K n (t/*c), the 

 result will be correct to the extent of an error of order h 2 a 2 , 

 and this case needs no further consideration. 



