

Maxwell. 287 



and displacement-currents), so that there is no magnetization, 

 we have 



V 2 A = - curl curl A = - curl H 



= - 47TS, 



so that the vector-potential is connected with the total current 

 by an equation of the same form as that which connects the 

 scalar potential with the density of electric charge. To these 

 potentials Maxwell inclined to attribute a physical significance ; 

 he supposed i// to be analogous to a pressure subsisting in the 

 mass of particles in his model, and A to be the measure of 

 the electrotonic state. The two functions are, however, of 

 merely analytical interest, and do not correspond to physical 

 entities. For let two oppositely-charged conductors, placed 

 close to each other, give rise to an electrostatic field throughout 

 all space. In such a field the vector-potential A is everywhere 

 zero, while the scalar potential $ has a definite value at every 

 point. Now let these conductors discharge each other ; the 

 electrostatic force at any point of space remains unchanged 

 until the point in question is reached by a wave of disturbance, 

 which is propagated outwards from the conductors with the 

 velocity of light, and which annihilates the field as it passes 

 over it. But this order of events is not reflected in the 

 behaviour of Maxwell's functions ;// and A ; for at the instant 

 of discharge, ^ is everywhere annihilated, and A suddenly 

 acquires a finite value throughout all space. 



As the potentials do not possess any physical significance, 

 it is desirable to remove them from the equations. This was 

 afterwards done by Maxwell himself, who* in 1868- proposed 

 to base the electromagnetic theory of light solely on the 

 equations 



curl H = 47rS, 



- curl E = B, 



together with the equations which define S in terms of E, and B 

 in terms of H. 



* Phil. Trans, clviii (1868), p. 643 : Maxwell's Scient. Papers, ii, p. 125. 



