Inductance of Two Parallel Wires. 271 



When he is small, on reduction 



A = C K -B2:^-) 2 \ 

 . 2C 2B„» (by 



4Co 4B^ ^°°, _ /jy. 

 A 2 c 2 + A 2 c 2 



A2 — T^9 4 



and so on, very convergent series being obtained if - is small. 



c 



The reflected wave o£ (82) becomes, near the second wire, 



H = BoJo(V) + S 1 "BJ,(7i / o) cos *</>, . . (86) 

 where 



B, = &K, . ^ -£>, (K, +I +K.A 



The ratios a/c, b/c, will be retained to the second power 

 only. To this order, 



Bo= fS^o| CoKo _ B/li ^ +XiCo J _ _ (g7) 



Bj will only subsequently be required to the first order, 

 and becomes 



B 1 = ^Ki.CoKo (88) 



a 



We note that the change in B due to taking account of 

 a x c 3 . . . . is of order a 2 /c 2 as stated in the previous section. 



So far as the current is concerned, the internal potential 

 produced in the second wire is 



= —&'•<*>• < 89 > 



and a potential 



H = C Jo {hr) + 2" C s J s (hr) cos s0 . . . (90) 



is incident again on the first wire, where 



Co = ^d - • B Ko + *2 4 B s ~ K s 



= §.B K +^B, to order J 



(b 2 \ a 2 b 2 



CoKo-B^^j + X^Co-^-^ipiCo^ (91) 

 6 / C C 



