Wave Propagation over Parallel Wires. 623" 



If this is substituted for w n in S 2 and S 2 o£ equation (44), 

 some easy simplifications give 



C-^CJl-A/b), ...... (52) 



where 



1 + k 2 s 2 



G - = l^F 5 2 C 53 ) 



The limiting value of the correction factor is therefore C m , 

 and this is a function only of the parameter Jc = a/c. The 

 asymptotic formula (54) can be used under the following, 

 conditions and in accordance with the following rule : — If 

 the series X k 2n s 2n converges to a required order of approxi- 

 mation in a finite number of terms w, then the correction 

 factor C may be calculated from (53) provided the argu- 

 ment b is such that 



b > n 2 > 5. 



The correction-factor formulae need not be further con- 

 sidered here, as they are fully discussed in section III. We 

 shall therefore now proceed to complete the solution of the 

 problem by formulating the propagation factor y. In this 

 discussion it will be assumed that h x . . . h n and q 1 . . . q n have 

 been evaluated in accordance with the methods fully dis- 

 cussed above. For non-magnetic wires they may be calcu- 

 lated from (41) and (42), while in other cases any of the 

 methods of successive approximations discussed above may 

 be applied to equations (34). 



The propagation factor y is determined by applying the 

 law curl E=— fjbipYL to any appropriate surface, the contour 

 of which includes a lino segment dz in the surface of each 

 wire and two lines in the dielectric joining their corre- 

 sponding ends. The most convenient surface to take is a 

 plane surface in the plane of the axes bounded by the 



Wife # 2. 



V-yVd: 



elements dz in the inner or adjacent surfaces of the wires 

 and the straight lines in the dielectric joining the corre- 

 sponding ends of the elements dz, as shown in the cross- 

 section sketch herewith. 



