TRANSACTIONS OF SECTION A. 679 



matter and ether is, in a crystal, a function of the direction of ■vibration, the appa- 

 rent or effective density of the ether in such a body will depend on the direction of 

 displacement. 



Now these hypotheses will conduct us by strict mathematical reasoning to laws 

 for the propagation, reflexion and refraction, double refraction and polarisation, 

 dispersion, absorption, and anomalous dispersion and aberration of light which are 

 in complete accordance with the most accurate experiments. 



The rotatory polarisation of quartz, sugar, and other substances points to a more 

 complicated action between the ether and matter than is contemplated above ; and, 

 accordingly, other terms have to be introduced iuto the equations to account for 

 these eflects. It will be noted as a defect, and perhaps a fatal one, that the 

 connection between electricity and light is not hinted at, but I hope to return to 

 that point shortly. 



Such a medium as I have described is afforded us by the labile ether of Lord 

 Kelvin. It is an elastic solid or quasi-solid incapable of transmitting normal waves. 

 The quantity A is zero, but Lord Kelvin has shown that the medium would 

 still be stable provided its boundaries are fixed, or, which comes to the same thing, 

 provided it extends to infinity. Such a medium would collapse if it were not 

 held fixed at its boundaries ; but if it be held fixed, and if then all points on any 

 closed spherical surface in the medium receive a small normal displacement, so that 

 the matter within the surface is compressed into a smaller volume, there will be 

 no tendency either to aid or to prevent this compression, the medium in its new 

 state will still be in equilibrium, the stresses in any portion of it which remains 

 unaltered in shape are independent of its volume, and are functions only of the 

 rigidity and, implicitly, of the forces which hold the boundary of the whole medium 

 fixed. 



A soap film affords in two dimensions an illustration of such a medium ; the 

 tension at any point of the film does not depend on the dimensions ; we may 

 suppose the film altered in area in any way we please — so long as it remains 

 continuous — without changing the tension. AVaves of displacement parallel to the 

 surface of the film would not be transmitted. But such a film in consequence of 

 its tension has an apparent rigidity for displacements normal to its surface : it can 

 transmit transverse waves with a velocity which depends on the tension. Now 

 the labile ether is a medium which has, in three dimensions, characteristics re- 

 sembling those of the two-dimensional film. Its fundamental property is that 

 the potential energy per unit volume, in an isotropic body, so far as it arises from 

 a given strain, is proportional to the square of the resultant twist. In an incom- 

 pressible elastic ether this potential energy depends upon the shearing strain. 

 Given such a medium — and there is nothing impossible in its conception — the main 

 phenomena of light follow as a necessary consequence. We have a mechanical 

 theory by the aid of which we can explain the phenomena ; we can go a few steps 

 behind the symbols we use in our mathematical processes. Lord Kelvin, again, 

 has shown us how such a medium might be made up of molecules having rotation 

 in such a way that it could not be distinguished from an ordinary fluid in respect 

 to any irrotational motion ; it would, however, resist rotational movements with a 

 force proportional to the twist, just the force required ; the medium has no real 

 rigidity, but only a quasi-rigidity conferred on it by its rotational motion. The 

 actual periodic displacements of such a medium may constitute light. We may 

 claim, then, with some confidence to have a mechanical theory of light. 



But nowadays the ether has other functions to perform, and there is another 

 theory to consider, which at present holds the field. Maxwell's equations of the 

 electromagnetic field are practically identical with those of the quasi-labile ether. 

 The symbols which occur can have an electromagnetic meaning; we speak of 

 permeability and inductive capacity instead of rigidity and density, and take as 

 our variables the electric or magnetic displacements instead of the actual displace- 

 ment or the rotation. 



Still such a theory is not mechanical. Electric force acts on matter charged 

 with electricity, and the ratio of the force to the charge can be measured in mecha- 

 nical units. A fundamental conception in Maxwell's theory is electric displacement, 



