18 BELL SYSTEM TECHNICAL JOURNAL 



nent radially symmetrical waves oriented on the axes of the conductors; 

 to this the actual wave approximates in important transmission systems. 

 We shall now introduce the consequences of the foregoing assump- 

 tions into the differential equations of the problem. 



IV 



Referring to equations (10), these may be replaced in the conductors 

 only where 7^ is very small compared with v^ and 7 is a very small 

 quantity, by the approximation: 



dy 



(13) 



V- [ dx 7 dy 



v^ ydy 7 dx 



Therefore in the conductors the vector components M^, My are de- 

 rivable by spatial differentiation from Ez. E^, Ey are not in general 

 so derivable on account of the factor I/7, a very large quantity, 

 which appears with Mz. (It appears that yE^ and Ms may be of 

 comparable orders of magnitude.) We assume, however, for reasons 

 discussed above, that both Ejc and Ey are very small compared with 

 Ez in the conductors. 



In the dielectric, where v"- and 7- are of comparable orders of magni- 

 tude, the foregoing approximations are not valid and the rigorous 

 equations must be employed. Returning to equations (10) and 

 writing for convenience y'^jir = /3, we have 



I — ^ [ dy 7 dx 



y 1 — p [ dx y dy 



E =^-J-|A£ _lAi/ 



y 1 — (3 [ dy 7 3x 



In equations (13) and (14), x and y may be any orthogonal co- 

 ordinate system. Let us suppose that they are so chosen that x is 



(14) 



