14 BELL SYSTEM TECHNICAL JOURNAL 



My = — ^x -^A,, 



oz ox 



M^ = —Ay -^A„ 



'" "' (6) 



and 



dx 



^ A,+i-Ay-\-^A^+ p'-^ = 0. (7) 



In technical transmission problems we are largely concerned with 

 propagation along a uniform transmission system, composed of straight 

 parallel conductors. That is to say, the transmission system does not 

 vary geometrically or in its electrical constants along the axis of 

 transmission, taken as the axis of Z. It is known that in such trans- 

 mission systems exponentially ^ propagated waves exist. We therefore 

 modify the general equations by assuming that the wave (and all 

 vector components) vary with t and z as exp (icot — yz), y being 

 entitled the propagation constant. As a consequence of this assumption 

 it is easily shown that the vectors E and M are derivable from the 

 wave functions F, $, as follows: 



M. = -^F-y-^@, 

 dy dx 



My= -^F-y^e, 

 dx dy 



M,= - (j^2 _ y)0, 



^'= -¥x^-d-y®^ 



Ey= -±^+'@, 

 dy dx 



Ez = — —-^— F=y^ — F. 

 dz 



The wave functions F and •I' are not independent but are connected by 

 the relation 



^2$ = yf, (9) 



' This means that the wave involves the axial coordinate z only exponentially. 



