

the Foundations of Dynamics. 31 



have penetrated the walls, is expressed quite clearly by 

 Mr. Heaviside's equation 



conv eu = e, 



where e is the energy per unit volume, u is its velocity of loco- 

 motion, and where conv. stands for SV> or d/dx + d/dy + d/dz. 

 But Mr. Heaviside is not satisfied with this simple equation 

 of continuity, and proceeds to complicate it by introducing: — 



(1) Intrinsic sources ; i. e. creation or fourth-dimensional 

 apparition of energy ; of which the chief example is the 

 gravitation bogey, whose path and nature no man jet knows. 



(2) Flux of energy travelling not with matter at a 

 definite speed, but in some other way so that its speed is 

 uncertain. For example of this he instances radiation, but 

 surely that has a definite enough velocity. He might have 

 instanced conduction of heat ; but there again, treated merely 

 as a flux of energy, the amount crossing unit area per second 

 is definite enough. Mr. Heaviside would probably agree, 

 but would prefer not to analyse it into two factors e and u ; 

 and to this I cannot object. 



(3) But to his third category Q, the rate of waste of energy, 

 I am bound to object. The insertion of dissipation of energy 

 as if it were a mysterious disappearance term, is open to the 

 objection suggested above against (1), and also to the objection 

 that it unduly elevates the available portion of energy into 

 being the whole of it. 



So long as these various terms are only introduced for prac- 

 tical purposes, i. e. to direct attention to what might otherwise 

 get overlooked, they are well enough ; but they must not be 

 supposed to represent the reality of things. It is true that the 

 case of gravitation, if it be transmitted instantaneously, as 

 seems not unlikely, is a curious simulacrum of action at a 

 distance ; whereby of course energy could be generated de novo 

 inside closed boundaries readily enough ; but infinite speed 

 of transmission only requires infinite incompressibility in a 

 medium, it does not dispense with a medium ; and if a medium 

 of transmission exists, as all analogy and coherence urges if 

 not insists, then gravitation is no exception, and its energy 

 must pass through the walls in order to get inside a boundary, 

 although it may pass through at an infinite pace. It may 

 be better, however, not to assume the pace infinite till proved, 

 but to have a term in the most general energy-equations 

 expressive of the possible propagation of gravitation in time, 

 notwithstanding that its speed is unknown and certainly 

 excessively great. 



I may refer to another reply I have made to Mr. Heaviside 

 in 'Nature,' vol xlvii. p. 293 (January 26, 1893). 



