﻿608 The late W. Gordon Brown on the 



the tubes of force we have so far assumed that two oppositely 

 directed tubes at the same point exactly cancel each other in 

 their effects, if they are moving with the same velocity. 

 Now, just as the electrical theory of matter explains all the 

 phenomena of neutral bodies as due to the existence of the 

 equal mixture of positive and negative electricity, which on 

 the two-fluid theory was supposed to have no recognizable 

 physical properties, so on the lines of force theory we may 

 perhaps speculate with advantage on the possibility of ex- 

 plaining by means of properties of equal mixtures of 

 oppositely directed tubes the phenomenon of gravitation, 

 which seems for many reasons to be on a different level from 

 the ordinary electrical phenomena. Let us consider the 

 potential energy of such a mixture of tubes. So long as we 

 choose an element of area large enough to include many 

 tubes, the density of energy ^ED must always vanish ; but 

 as we take smaller and smaller elements of area, there will 

 be an increasing probability of the number of tubes passing 

 through it in one direction being not quite equal to the number 

 passing through it in the opposite direction : in other words, 

 what to ordinary microscopic electrical measurements is a uni- 

 form absence of electric displacement may consist of alternate 

 regions of opposite displacement so small that only the mean 

 field of a considerable number of regions is measured. Such 

 a field would have positive potential energy ; but since the 

 more closely the tubes are packed, the smaller is the element 

 of area we can take without considering this effect, it seems 

 reasonable to suppose that the effect will become smaller the 

 more numerous are the tubes of either sign. Not improbably 

 a mathematical form might be given to this hypothesis which 

 would explain and locate the energy of gravitation. Let 

 dei, — de x ; de 2 , —de* 2 , be pairs of opposite charges ; r 1? r 2 

 the (small) distances apart of the components of each pair ; 

 and R the distance between the pairs. Then if the hypothesis 

 could be so formulated that the potential energy of the 

 system would include a term of the form 



—yde 1 2 de 2 2 

 r l r 2 R ' 



where 7 is a positive constant, the law of gravitation would 

 be completely satisfied, and gravitational mass would be 

 identified exactly with electromagnetic mass ; for 



del 



n 



is proportional to the element of electromagnetic mass due 

 to two elements of de Y , —de v . 



