Wave Propagation over Parallel Wires. 621 



where s is the series ratio 



1+ ri* + Tr* + Hrr*". + "- 



2 ,„ ;-■,, 5.6.7 

 3 ! 



i + f:^+ T V^ + 



= 2l =w^ ^ 



Having thus solved equations (35) for the variables 

 j)i -.'P n , it is easy to show from (34) and (35) that if we 

 write 



■the variables d Y . . . d n satisfy the system of equations : 



dn=(Pn^)Pn-~^- l P^\{d). . . (39) 



The system of equations (39) in d Y . . . d n admit of solution 

 by successive approximations, as discussed in connexion 

 with the solution of the corresponding system of equa- 

 tions (34) in q 1 . . . q . For the important case of non- 

 magnetic conductors, however, a very close approximation 

 to the exact solution is obtained by replacing (39) by the 

 approximations : 



d. = fo-l)PnH-l>*pJr+ 1 ii- ■ • ( 40 ) 



This gives to the same order of approximation 



% = p n p,M-i) n np«a-piW ,+i pi- ■ ■ m 



Since by (32) h u = qjcr n , this gives for non-magnetic 

 conductors 



We are now in a position to formulate the proximity 

 effect correction factor C of equation (20), which involves 

 the harmonic coefficient ~h x . . . h n . From (42) to the same 

 order of approximation as (40) 



>i-l "*" ' n-l 



where g denotes the function 



_ a/2 u , ( Uq + v ) - -0] {u — »o) t A on 



