Page:A history of the theories of aether and electricity. Whittacker E.T. (1910).pdf/307

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

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 ψ 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 ψ 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 ψ and A; for at the instant of discharge, ψ 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

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