1921-22.] The Faraday-Tube Theory of Electro-Magnetism. 237 
of force we have so far assumed that two oppositely directed tubes at 
the same point exactly cancel each otlier 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 exist- 
ence of the equal mixture of positive and negative electricity, which on 
the two-fluid theory was supposed to have no recognisable physical pro- 
perties, so on the lines of force theory we may perhaps speculate with 
advantage on the possibility of explaining 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 JED 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 uniform 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 consider- 
ing 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 de^,—de^\ de.^,—de.^^ 
be pairs of opposite charges ; ^he (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^^ded 
rp'oR 
where y is a positive constant, the law of gravitation would be completely 
satisfied, and gravitational mass would be identified exactly with electro- 
magnetic mass ; for 
de^ 
is proportional to the element of electro-magnetic mass due to two elements 
of charge de -^ , — de ^ . 
