ELECTRICAL TRANSMISSION ALONG WIRES 17 



First we have to define what we mean by conductor and by dielectric; 

 the significance of these definitions will appear in the course of the 

 analysis. A conducting medium is one in which coV^^ is very small 

 compared with 4xX/xw; while a dielectric medium is one in which 

 47rX/xco is very small compared with oi^lv^. The intermediate cases 

 will not be discussed in the present paper; in the following it will be 

 assumed that the conductors and dielectrics satisfy these definitions.^ 



The assumptions which we make at the outset in the approximate 

 solution may now be listed and qualitatively justified as follows: 



1. The propagation constant 7 is an extremely small quantity and 

 its real part is not large compared with its imaginary part. Since | 7 1 is 

 of the order of magnitude of w 10"^", it is evident that 7 is very small 

 even for frequencies of millions of cycles per second. As regards the 

 second restriction, if the real part of 7 is large compared with 

 the imaginary, the wave will be damped out in a few wave-lengths, and 

 the system cannot efficiently transmit energy. 



2. In the conductors the axial electric intensity E^ is large compared 

 with the component normal to Z. This restriction means that the 

 dissipation in the conductors due to the axial currents is large com- 

 pared with the dissipation due to the charging currents. Evidently 

 this restriction is necessary for the efficient transmission of energy. 



3. In the dielectric the axial electric intensity is small compared with 

 the normal electric intensity. The justification of this assumption is 

 as follows: The propagation of energy occurs in the dielectric, and is 

 normal to the direction of the electric intensity. Since the usefully 

 transmitted energy is propagated along the axis of transmission and 

 the propagation normal to the axis simply means dissipation, the axial 

 electric intensity must be small compared with the normal component 

 for efficient transmission. 



4. The axial magnetic intensity H^ is everywhere small compared 

 with the normal intensity. The justification of this assumption de- 

 pends on the same arguments as (3). 



As regards (3) and (4) it will be remarked that in the ideal plane 

 wave propagation both E^ and M^ are zero. In the case of imperfect 

 conductors E^, in the dielectric is not zero but may be regarded as a 

 first order small quantity, ilfz on the other hand is to be regarded 

 as a second order small quantity because it not only vanishes for the 

 case of perfect conductors but also vanishes for the case of imperfect 

 conductors for the case where the wave is made up of a set of compo- 



* In accordance with these definitions, conductors and dielectrics depend for 

 their classifications on the frequency, as well as their electrical constants. The 

 definition of conductor means that the displacement current is negligible compared 

 with the conduction current. 



