678 DEPORT— 1893. 



results on other points. And so the first attempt to construct a mechanical theory 

 of light failed. We have learnt much from it. At the death of Green the sub- 

 ject had advanced far beyond the point at which Fresnel left it. The causes of the 

 failure are known, and the directions in which to look for modifications have been 

 pointed out. 



Now I believe that the effort to throw any theory into mechanical form, to 

 conceive a model which is a concrete representation of the truth, to arrive at that 

 which underlies our mathematical equations wherever possible, is of immense 

 value to every student. Such a course, I am well aware, has its dangers. It may 

 he thought that we ascribe to the reality all the properties of the model, that, in 

 the case of the ether, we look upon it as a collection of gyrostatic molecules and 

 springs, or of pulleys and indiarubber bands, instead of viewing it from the standpoint 

 of Maxwell, who hoped, writing of his own model, ' that by such mechanical 

 fictions, anyone who vmderstands the provisional and temporary character of his 

 hypothesis will find himself helped rather than hindered in his search after the true 

 interpretation of the phenomena.' Professor Boltzmann, in his most interesting- 

 paper on ' The Methods of Theoretical Physics,' ^ has quoted these words, and has 

 expressed far more ably than I can hope to do the idea I wish to convey. 



The elastic solid theory, then, has failed ; but are we therefore without any 

 mechanical theory of light ? Are we again reduced to merely writing down our 

 equations, and calling some quantity which appears in them the amplitude of the 

 light vibration, and the square of that quantity the intensity of the light ? Or can 

 we take a further step ? Let us inquire what the properties of the ether must be 

 ■which will lead us by strict reasoning to those equations which we know represent 

 the laws of the propagation of light. 



These equations resemble in many respects those of an elastic solid ; let us,, 

 then, for a moment identify the displacement in a light-wave with an actual dis- 

 placement of a molecule of some medium having properties resembling that of a 

 solid. Then this medium must have rigidity or quasi-rigidity in order that it may 

 transmit transverse waves ; at the same time it must be incapable of transmitting 

 normal waves, and this involves the supposition that the quantity A which appears 

 in Green's equations must vanish or be infinite. To suppose it infinite is to recur to 

 the incompressible solid theory ; we will assume, therefore, that it is zero. Re- 

 flexion and refraction show us that the ether in a transparent medium such as 

 glass diflers in properties from that in air. It may differ either (1) in density or 

 effective density,- or (2) in rigidity or efl'ective rigidity. The laws of double re- 

 fraction and the phenomena of the scattering of light by small particles show us that 

 the difierence is, in the main, in density or effective density ; the rigidity of the 

 ether does not greatly vary in different media. Dispersion, absorption, and ano- 

 malous dispersion all tell us that in some cases energy is absorbed from the light- 

 vibrations by the matter through which they pass, or, to be more general, by some- 

 thing very intimately connected with the matter. 



We do not know sufficient to say what that action must be ; we can, however, 

 try the consequences of various hypotheses. Guided by the analogy of the motion 

 of a solid in a fluid, let us assume that the action is proportional to the acceleration 

 of the ether particles relative to the matter, and, further, that imder certain circum- 

 stances some of the energy of the ether particles is transferred to the matter, thus 

 setting them in vibration. If such action be assumed, the actual density of the ether 

 may be the same in all media, the mathematical expression for the forces wiU lead 

 to the same equations as those we obtain by supposing that there is a variation of 

 density, and since it is clearly reasonable to suppose that this action between 



> Pltil. Mag., July 189.3. 



* The equations of motion for a medium such as is supposed above can be 

 written — 



p X acceleration of ether + p' x acceleration of matter = 2 b x function of ether 

 displacements, and their differential coefficients witli respect to the coordinates 

 + 2 b' X similar function for matter displacements. 



The quantity p may be spoken of as the effective ether density, the quantities b. 

 as the effective elasticity or rigidity. 



