Wave Propagation over Parallel Wires. 611 



It will be found convenient to write the field equations in 

 the form : 



i*-*&--£&*'& B - ■ • • (1 > 



(»> 2 -^ H -Sf, B -^! H -> • • • (2) 



(m'- 7 %= T lE.. + w|H.,, . . . (3). 



(^-^E^^E. + m^I^H,. . . . (4) 

 From equations (3) and (4), 



_^H,=| a .E y -|E, (5). 



We now introduce the assumption, essential to the sub- 

 sequent analysis, that 7 and p\v are very small quantities of 

 comparable orders of magnitude. That is to say, they ate 

 very small compared with unity and also compared with 

 the value of m in the conductors. The justification for these 

 assumptions and their immediate corollaries, introduced 

 oh initio, resides in the fact that the solution obtained by 

 their aid actually satisfies the necessary conditions in trans- 

 mission systems of ordinary dimensions, even if the frequency 

 exceeds a million cycles per second. 



From equations (3), (4), and (5) it follows that the electric 

 force in the plane normal to the axis of propagation is of the 

 order of magnitude of <y/(m 2 — <y 2 ) compared with the axial 

 component E z . In the conductors this is a very small 

 quantity of the order of magnitude of y/iirX/jip, while in the 

 dielectric it is a large quantity of the order of magnitude 

 of I/7. Consequently in the conductors the electric force in 

 the plane normal to the axis of propagation will he ignored 

 in comparison with E. ; in the dielectric, however, the 

 former is large compared with the latter. By corresponding 

 considerations the axial magnetic force H z is very small 

 compared with the magnetic force in the plane XY, both in 

 the conductors and in the dielectric. 



As a consequence of the foregoing, the magnetic force in 

 the conductors is derivable from 



f*ipK x =-^-E 2i (6> 



flippy = g - E; (7> 



which replace (1) and (2). 



