298 Maxwell. 



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 



-a, (1) 



where < denotes the electrostatic potential defined by the 

 equation 



4>-{\\(p'lr) dx'dy'dz', 



p being the density of electric charge at the point (x, y, z'), and 

 where a denotes the vector-potential, defined by the equation 



a={\[(i'lr)dx'dy'dz, 



J J J 



i' being the conduction-current at (x', y\ z'). We suppose the 

 specific inductive capacity and the magnetic permeability to 

 be everywhere unity. 



Lorenz proposed to replace these by the equations 



= \\\{p(t-r/c)/r\dx'dy'dz', 

 {i'(t-r/c)/r}dx'dy'd3f' 9 



the change consists in replacing the values which p and i' 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', y, z) 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', y', z') at the previous instant (t - r/c) : as if the potentials 

 were propagated outwards from the charges and currents with 

 velocity c. The functions <f> and a formed in this way are 

 generally known as the retarded potentials. 



