Page:A history of the theories of aether and electricity. Whittacker E.T. (1910).pdf/318

 appreciable in ordinary laboratory experiments, would be capable of accounting for the propagation of electrical effects through space with a finite velocity. We have seen that in Neumann's theory the electric force E was determined by the equation

where φ denotes the electrostatic potential defined by the equation

ρ&prime; being the density of electric charge at the point (x&prime;, y&prime;, z&prime;), and where a denotes the vector-potential, defined by the equation

ι&prime; being the conduction-current at (x&prime;, y&prime;, z&prime;). We suppose the specific inductive capacity and the magnetic permeability to be everywhere unity.

Lorenz proposed to replace these by the equations

the change consists in replacing the values which ρ&prime; and ι&prime; have at the instant t by those which they have at the instant (t - r/c), which is the instant at which a disturbance travelling with velocity c must leave the place (x&prime;, y&prime;, z&prime;) in order to arrive at the place (x, y, z) at the instant t. Thus the values of the potentials at (x, y, z) at any instant t would, according to Lorenz's theory, depend on the electric state at the point (x&prime;, y&prime;, z&prime;) at the previous instant (t - r/c): as if the potentials were propagated outwards from the charges and currents with velocity c. The functions φ and a formed in this way are generally known as the retarded potentials.