Equations in a Hoinogeneous Isotropic Medium. 47 



through unit distance to the left, and then take the difference 

 between the new and the old curves, we shall obtain the curves 

 showing how an initial distribution of V or C through unit- 

 distance at the origin divides and spreads. In the case of 

 curve 2, we have clean splitting without a trace of diffusion. 

 In the other cases there is a diffused disturbance left behind 

 between the terminal waves, positive in case 1, negative in 

 case 3. But I have sufficiently described this matter in a 

 former paper^. 



October 18, 1888. 



POSTSCEIPT. 



On the Metaphysical Nature of the Propagation of the 

 Potentials. 



At the recent Bath Meeting of the British Association there 

 was considerable discussionf in Section A on the question of 

 the propagation of electric potential. I venture therefore to 

 think that the following remarks upon this subject may be of 

 interest. 



According to the way of regarding the electromagnetic 

 quantities I have consistently carried out since January 1885, 

 the question of the propagation of, not merely the electric 

 potential ■^, but the vector potential A, does not present 

 itself as one for discussion ; and, when brought forward, 

 proves to be one of a metaphysical nature. 



We make acquaintance, experimentally, not with potentials, 

 but with forces, and we formulate observed facts with the 

 least amount of hypothesis, in terms of the electric force E 

 and magnetic force H. In MaxwelFs development of Fara- 

 day's views, E and H actually represent the state of the 

 medium anj^where. (It comes to the same thing if we con- 

 sider the fluxes, but less conveniently in general.) Granting 

 this, it is perfectly obvious that in any case of propagation, 

 since it is a physical state that is propagated, it is E and H 

 that are propagated. 



Now, in a limited class of cases, E is expressible as — V^* 

 Considerations of mathematical simphcity alone then direct 

 the mathematician's atteation to ^ and its investigation, 

 rather than to that of E directly. But when this is possible the 

 field is steady, and no question of propagation presents itself 



* "Electromagnetic Waves," § 7 (Phil. Mag. Feb. 1888). 

 t See Prof. Lodge's " Sketch of the Electrical Papers read in Section A," 

 the ' Electrician,' September 21 and 28, 1888. 



