12 Prof. J. Larmor on Electromagnetic Induction 



pose the ends of the line in its former position (1) and in a 

 near position (2) at a very short distance 

 from it, to be connected so as to form a 

 closed circuit, the number of tubes of 

 force on the positive side of the line will 

 be diminished by the number which pass 

 through this closed circuit supposed cir- 

 culating in the direction of the isolated 

 arrows. The diminution is therefore 

 equal to the flux of the vector potential 

 along (2) minus its flux along (1), 

 together with its fluxes along the two 

 lines of motion of the ends of the open 

 line. Thus, when the line has moved from (1) to (2), we must 

 suppose the potential at each end diminished by the flux of the 

 vector potential along the line of motion of that end. There- 

 fore in the equations for electromotive force we must include 

 terms for the change of the rate of variation of this flux as we 

 pass from point to point of the conductor ; that is, instead of 

 the true electrostatic potential <E>, we shall get from our equa- 

 tions <& + <J>' ; where <&' is the scalar product of vector potential 

 and velocity of the point supposed connected with the moving 

 system of axes, and is therefore 



-(4: +«!+=£)• 



We have thus deduced from first principles the result obtained 

 by Maxwell analytically by transformation from his equations 

 of the electromagnetic field. 



The method that we have adopted also brings before us very 

 clearly what it is on which the term <£>' really depends. It 

 will have different values according as we take one or another 

 body in the system to be absolutely at rest; and as there is no 

 criterion of absolute rest at all, so far as matter is concerned, 

 we must conclude that the true value of <£>' is that derived from 

 axes fixed with reference to some system or medium which 

 is the seat of the electromagnetic action. 



We conclude, then, that when a constant electromagnetic 

 system is moving through this medium in any manner, the 

 effect produced by the relative motion is an electrostatic 

 charge of the system of such character that its potential is <£>'. 

 This static charge, however, itself exerts a magnetic effect by 

 virtue of its motion ; but it is easy to see that this depends on 

 v 2 , and is therefore very minute. We know nothing of the 

 relation of this medium to ponderable matter : the motion of 



