Equations in a Homogeneous Isotropic Medium. 45 



In passing, I may remark that, in my interpretation of 

 Maxwell's views, it is not his vector-potential A, the so-called 

 electrokinetic momentum, that should have the physical idea 

 of momentum associated with it, but the magnetic induction B. 

 To illustrate, consider Maxwell's theory of a linear circuit of 

 no resistance, the simplest case of persistence of momentum. 

 We may express the fact by saying that the induction through 

 the circuit remains constant, or that the line-integral of A 

 along or in the circuit remains constant. These are perfectly 

 equivalent. Now if we pass to an infinitely small closed 

 circuit, the line-integral of A becomes B itself (per unit area). 

 But if we consider an element of length only, we get lost at 

 once. 



Again, the magnetic energy being associated with B, 

 (and H), so should be the momentum. 



Suppose also we take the property that the line-integral of 



— A is the E.M.F. in a circuit, and then consider —A as the 

 electric force of induction at a point. Its time-integral is A. 

 But this is an electromotive impulse, not momentum. 



Lastly, whilst B (or H) defines a physical property at a 

 point, A does not, but depends upon the state of the whole 

 field, to an infinite distance. In fact it sums up, in a certain 

 way, the effect which would arise at a point from disturbances 

 coming to it from all parts of the field. It is therefore, like 

 the scalar electric potential, a mathematical concept merely, 

 not indicative in any way of the actual state of the medium 

 anywhere. 



The time-integral of H, whose curl is proportional to the 

 displacement, has equal claims to notice as a mathematical 

 function which is of occasional use for facilitating calculations, 

 but which should not, in my opinion, be elevated to the rank 

 of a fundamental quantity, as was done by Maxwell with 

 respect to A. 



Independently of these considerations, the fact that A has 

 often a scalar potential parasite, and also the other function, 

 causes sometimes great mathematical complexity and indi- 

 stinctness ; and it is, for practical reasons, best to murder the 

 whole lot, or at any rate merely employ them as subsidiary 

 functions. 



17. Returning to the telegraph-circuit, let the initial state 

 be one of uniform V on the whole of the left side of the origin, 

 V = on the right side, and C = everywhere. The diagram 

 will serve to show roughly what happens in the three principal 

 cases. 



First of all we have ABCD to represent the curve of Vq, 

 the origin being at C. When the disturbance has reached Z, 



