236 Proceedings of the Poyal Society of Edinburgh. [Sess 
Differentiating with respect to x we have the force per unit length 
K ' ^"dxdt\ • • • • 
Equating therefore expressions (45) and (47) and dividing by we have 
1 dhj , d^y dhj , dhf 
or 
(47) 
di- ai-2 
(48) 
exhibiting the uniform propagation with velocity c independent of the 
general motion of the tube. 
The relation between the electro-magnetic disturbance and the displace- 
ment y of the tube is easily seen to be given by 
K 
• (^ 9 ) 
H, 
^// 1 
dt ^ 
(50) 
But while in plane-polarised radiation the displacement of the tube 
from its normal position is thus perpendicular to the plane of polarisation, 
in circularly polarised rays it is easy to see that the reverse is the case. 
10. The intention in presenting the theory of Faraday tubes in the 
present form was to suggest possibilities of modification which might 
explain various phenomena of which no entirely satisfactory electrical 
explanation has been given so far. 
In making attempts of this kind we may, for instance, take advantage 
in various ways of the fact that the electric displacement has been con- 
sidered as a mean value taken over a small, but not infinitesimal, area. 
From this point of view the Maxwellian theory is microscopical, and a 
more microscopical theory may be what is required in various regions of 
modern physics. 
Again, the present theory rests on the localisation of electric and 
magnetic energy as functions of D and H, and on the derivation from 
these of equations of motion. Hence it would be comparatively simple 
to estimate the effects either of a modified distribution of energy, or of 
substituting any different hypothesis for the principle of action. 
Lastly, quite a variety of hypotheses are possible as to the exact nature 
of the electric particles. 
11. It will be observed that in describing the properties of the tubes 
