476 



NA TURE 



[September 14, 1893 



potheses. Cauchy's and the earlier theories do not represent 

 the facts either in an elastic solid or in the ether. At present 

 we are not concerned with the cause of this ; we must recognise 

 it as the first attempt to explain on a mechanical basis the phe- 

 nomena observed. According to his theory in its final form, there 

 are, in an i sotropic med ium, two waves which travel with veloci- 

 ties Va/p and Vfi/p, A and B being constants and p the 

 density. Adopting Cauchy's molecular hypothesis, there must 

 be a definite relation between A and B. 



A truer view of the theory of elasticity is given by Green in 

 his paper read before the Cambridge Philosophical Society in 

 1837. This theory involves the two constants, but they are 

 independent, and to account for certain optical effects A must 

 either vanish or be infinite. The first supposition was, until a 

 few years since, thought to be inconsistent » ith stability ; the 

 second leads to consequences which in part agree with the 

 results of optical experiment, but which diff'er fatally from those 

 reiults on other points. And so the first attempt to construct a 

 mechanical iheory of light failed. We have learnt much from 

 it. At the death of Green the subject 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 ihe 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 be 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 gyroslatic 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 fiction.^, anyone who understands 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." Prof. Boltzmann, in his 

 most interesting paper on "The Methods of Theoretical Physics " 

 {Phil. Mag., July, 1893) 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 Ihe propagation 

 ol 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 displacement of a molecule of some 

 medium having properties resembling that of a solid. Then this 

 medium mu^t have rigidity or quasi-rigidity in order that it may 

 transmit transverse waves ; at the same time it must be in- 

 capable of transmitting normal waves, and this involves the 

 supposition that the quantity A which appears in Green's equa- 

 tions must vanish or be infinite. To suppose it infinite is to 

 recur to the incompressible solid theory ; we will assume, there- 

 fore, that it is zero. Reflexion and refraction show us that the 

 ether in a transparent medium such as glass differs in proper- 

 ties from that in air. It may differ either (i) in density or 

 effective density,' or (2) in rigidity or effective rigidity. The 

 laws of double refraction, and the phenomena of the scattering 

 of light by small particles, show us that the difference is, in the 

 main, in density or effective density ; the rigidity of the ether 

 does not greatly vary in different media. Dispersion, absorp- 

 tion, and anomalous dlsper>ion all tell us that in some cases 

 energy is absorbed from the light vibrations by the matter 

 ..Ihrough 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 mu?t be ; 

 we cm, however, try the consequences of various hypotheses. 



1 Tlie equations of motion for a medium such as is supposed above can be 

 written — 



p X acceleration of ether -(- p' x accelerp.tion of matter =S B X function 

 of ether displacements, and their differential coefficients » ith respect to the 

 co-ordinates _-f 2 B' X similar function fur matter displacements. 



The quantity p may be spoken of as the effective ether density, the quanti- 

 ties B as the eff^^clive elasticity or rigidity. 



Guided by the analogy of the motion of a solid in a fluid, let m 

 assume that the action is proportional to the acceleration of th( 

 ether particles relative to the matter, and, further, that undei 

 certain circumstances some of the energy of the ether particle! 

 is transferred to the matter, thus setting them In vibration, I 

 such action be assumed, the actual density of the ether maj 

 be the same in all media, the mathematical expri ssion for th< 

 forces will lead to the same equations as those ve ob'ain bj 

 supposing that there is a variation of density, and sin e it 

 is clearly reasonable to suppose that this action letweer 

 matter and ether is, In a crystal a function of the direction o! 

 vibration, the apparent or effective density of the ether in sucli 

 a body will depend on the direction of displacement. 



Now these hypotheses will conduct us by strict mathematics 

 reasoning to laws for the propagation, reflexion and refraction, 

 double refraction and polarisation, dispersion, absorption, an<l 

 anomalous dispersion and aberration of light which are ir 

 complete accordance with the most accurate experiments. 



The rotatory polarisation of quartz, sugar, and other sub- 

 stances points to a more complicated action between the ethei 

 and matter than is contemplated above ; and, accordingly 

 other terms have to be introduced into the equations to accoun 

 for these effects. It will be noted as a defect, and perhap»8 

 fatal one, that the connection between electricity and light r 

 not hinted at, but I hope to return to that point shortly. 



Such a medium as I have described is afforded u:i by tbi 

 labile ether of Lord Kelvin. It is an elastic solid or quasi 

 solid incapable of transmitting normal waves. The qcantity t 

 is zero, but Lord Kelvin has shown that the medium wouli 

 still be stable provided its boundaries are fixed, or, v\hich come 

 to the same thing, provided it extends to infinity. Such : 

 medium would collapse if it were not held fixed at it 

 boundaries ; but if it be held fixed, and if then all points Oi 

 any closed .spherical surface in the medium receive a sma' 

 normal displacement, so that the matter within the surface i 

 compressed into a smaller volume, there will be no tendenc 

 either to aid or to prevent this compression, the medium in it 

 new state will still be in equilibrium, the stresses in any porlio 

 of it which re.-nains unaltered in shape are independi.'nt of it 

 volume, and are functions only of the rigidity and, implicitly, i 

 the forces which hold the boundary of the whole medium fixec 



A soap film affords in two dimensions an illustration of sue 

 a medium; the tension at any point of the film does not depen 

 on the dimensions ; we may suppose the film altered In area I 

 any way we please — so long us it remains continuous — withoi 

 changing the tension. Waves of displacement parallel to th 

 surface of the film would not be transmitted. But such a filn- 

 in consequence of its tension, has an apparent rigidity for di; 

 placements normal to its surface ; it can transmit Iransvers 

 waves with a velocity which depends on the tension. Now tti 

 labile ether is a medium which has, in three dimension! 

 characteristics resembling those of the two-dimensional film. Ii 

 fundamental property is that the potential energy per iin ' 

 volume. In an isotropic body, so far as it arises from a give 

 strain, is proportional to the square of the resultant twist. Ina 

 incompressible elastic ether this potential energy depends upc 

 the shearing strain. Given such a medium — and there is nothin 

 impossible in its conception — the main phenomena of ligf 

 folio* as a necessary consequence. We have a mechanic 

 theory by the aid of which we can explain the phenoinena ; w 

 can go a few steps behind the symbols we use in our malht 

 matical processes. Lord Kelvin, again, has shown us how sue 

 a medium might be made up of molecules having rotation I 

 such away that it could not be distinguished from an oidinat 

 fluid in respect to any irrotational motion ; it would, howere 

 resist rotational movements with a force proportionate to ll 

 twist, just the force required ; the medium has no real rigiditj 

 but only a quasi-rigidity conferred on It by its rotational motioi! 

 The actual periodic displacements of such a medium ns 

 constitute light. We may claim, then, with some confidence!, 

 have a mechanical theory of light. 



But nowadays the ether has other functions to perform, anj 

 there is another iheory to consider, which at present holds In: 

 field. Maxwell's equations of the electromagnetic field «ri 

 practically identical with those of the quasi-labile ether. Th 

 symbols which occur can have an eleclrotnagnetic meaning; f| 

 speak of permeability and inducti-ve capacity instead of rigidil, 

 and density, and take as our variables the electric or magneii 

 displacements instead of the actual displacement or it; 

 rotation. 



NO. 1246, VOL. 48] 



