NOTES ON THE THEORY OF ELECTRONS 7 



In the case of a magneto-motive force produced by a conduction 

 current of electricity, this cutting of lines of electric force across the 

 closed curve is due primarily to the motion of the electrons (at least 

 according to the modern views). Let us consider a constant current 

 of electrons flowing in the positive direction around a circuit 

 through the line 1 in Fig. 1. As each electron with its charge flows 

 around the circuit once, the entire number of its lines of force 4 tt e 

 cut across the line 1. At some instant during its motion, the eled- 

 tron passes through the surface S^ and, the number of its lines run- 

 ning through this surface in the positive direction, decreases by the 

 amount 4 tt e. Hence, on the whole, the change in the number of lines 

 of force through this surface, due to the motion of this electron, is zero. 

 The current has been assumed constant. Hence, as a whole, the number 

 of lines passing through S^ remains the same; which means that as a 

 whole just as many lines of force are withdrawn from the positive 

 direction through the surface, owing to the passage of electrons 

 through S^ as are thrust through by cutting the edge of the surface. 

 But the magneto-motive force equals the number of lines of force 

 cutting through 1 per second, and therefore equals 4 tt times the sum 

 of the electron charges passing through S^ per second. This latter 

 we consider to be the current through S^. The same is true of any 

 other surface, Sg bounded by 1, and hence the sum of the electrons 

 passing through S^ per second, is the same as through Sg, or the 

 total sum of the charges passing outward through the closed surface 

 Sj S, per second is zero. This means that the flow of electrons is 

 similar to that of an incompressible fluid. 



Let us consider now the case of a variable current. We have 

 very strong reasons for believing that in this case, too, the magneto- 

 motive force around any closed line in space equals 4 tt times the 

 total current through any closed surface bounded by the line, but 

 in making up the total current we must add to the conduction cur- 

 rent that which Maxwell called the displacement current. This means 

 that the total current into any closed space equals the total current out 

 of it, or that even in the variable state a current of electricity fills 

 space exactly as if it were the flow of an incompressible fluid. 



