(A) 



Vibrations of Light with Electrical Currents. 291 



r 

 a few feet ; hence - is an infinitely small magnitude. Hence 



the following members of the above series are everywhere quite 

 inappreciable, provided only that the differential quotients of 

 the components of the current of the second and third order be 

 not very great as compared with the time, which comes into 

 play here also. 



Hence the equations for the propagation of electricity, as re- 

 gards the experiments on which they rest, are just as valid as 

 equations (1), if, by the aid of the equation (4) and its two ana- 

 logous equations, the following form be assigned to them, 



--«<£+$» 



— <§+?$)■ j 



where, for brevity's sake, we put 



•=j]F^'-'('-3' 



These equations are distinguished from equations (1) by con- 

 taining, instead of U, V, W, the somewhat less complicated 

 members «, /3, y ; and they express further that the entire action 

 between the free electricity and the electrical currents requires 

 time to propagate itself — an assumption not strange in science, 

 and which may in itself be assumed to have a certain degree of 

 probability. For in accordance with the formulae found, the 

 action in the point x y z at the moment t does not depend on 

 the simultaneous condition in the point x' y' z\ but on the con- 



T 



dition in which it was at the moment t ; that is, so much 



a 



time in advance as is required to traverse the distance r with the 



constant velocity a. 



The constant a which enters into equations (A) should, from 



c 

 the foregoing, be made equal - ; closer investigations, however, 



