504 BELL SYSTEM TECHNICAL JOURNAL 



ticial modilications, would apply to sound waves, for instance. There are 

 two fundamental equations of transmission of an electromagnetic state, 

 expressing Faraday's law of induction of an electromotive force by a mag- 

 netic displacement current and Ampere-Maxwell's law of induction of a 

 magnetomotive force by an electric current. In their most general mathe- 

 matical form the equations are 



/ 



J^.d^=-lj\^ti^is, 



I 



H. ds = I j p:v. dS + II gE„ dS + ^^ II tE,. dS, 



(10) 



where the subscript s indicates components tangential to a closed path of 

 integration and the subscript n designates components normal to any 

 surface bounded by this closed path. Thus on the left we have ''sums" of 

 infinitesimal emf's and mmf's as we travel round some closed curve either 

 on the surface of a wire or just in free space, and on the right we have total 

 magnetic and electric currents linked with this curve. According to our 

 present physical conceptions the magnetic current is always a displacement 

 current defined as the time rate of change of magnetic flux or ''displacement". 

 Not. that there is anything inconceivable about an actual flow of magnetic 

 charge; it is simply that so far there has been no satisfactory evidence of 

 its existence. In the mathematical analysis it has long been a custom to 

 consider magnetic charges of opposite signs as if they existed; but this is 

 merely for convenience. 



The electric current, on the other hand, consists of three components: 

 the convection current whose density is the product of the electric charge 

 density p and the velocity v\ the conduction current whose density is pro- 

 portional to the electric intensity (the gE term in the above equation) and 

 the displacement current defined as the time rate of change of the electric 

 displacement. Strictly speaking, the conduction current is a convection 

 current but of such a kind that it would be extremely awkward to think of 

 it in terms of charged particles and their velocities. 



At the same time the statistical result of the irregular movements of 

 these particles can be expressed, for purposes of transmission of an electro- 

 magnetic state, as a continuous movement of charge encountering some 

 resistance. There are, of course, such phenomena as resistance noise which 

 are thus automatically excluded from consideration. 



In general to these electromagnetic transmission equations we should 

 add the dynamical equations of motion of electric charge; this is essential 

 when dealing with vacuum tubes. But, in considering passive transmission 

 systems, we either omit the convection current altogether, or else assume 



