462 



NA TURE 



[March 19, 1885 



Rayleigh independently invented unequally loaded mole- 

 cules which overcome the difficulty, but give a wave 

 surface different from Huyghens', and Stokes has proved 

 experimentally that Huyghens' construction is very accu- 

 rate. Hence this way of escape is denied to us. 



In treating of the propagation of waves in an isotropic 

 (and later in an aeolotropic) medium, methods of Thom- 

 son and Tait's Natural Philosophy, and his own article, 

 " Elasticity," in the " Encyclopaedia Britannica," are used ; 

 abc are distortions about Ox, Oy, and Oz, e/gare dilata- 

 tions along Ox, Oy, Oz. The equation of the energy E is 

 a quadratic in a bcefg, containing twenty-one coefficients, 

 some of which are annulled by isotropy. 



If 



P = 



dE 



de 



dE 



da 



,Q 



dE 



df 



dE 



,R 



dg . 

 dE' 



dE 



db dc 



and if p be the density, and £ a displacement along Ox, 

 we obtain the equation 



, a 2A = 

 dt" 



dP ,d_U dT 

 dx dy dz' 



Moreover, if n be the rigidity modulus, k the bulk 

 modulus, 8 the cubic dilatation, and m = k -\- ^ n, we 

 have 



P = (//, - n) 8, 



ids 1 «f\ 

 = n(-r- +-r), 



\dz dxP 



with similar expressions for Q, R, S, U. 



Thence he shows that the equation 



d-^ 



d 8 , , , 



111 — + n v 3 £, 



in an mconi- 



d x 



1 -m. .1 j»- du . dv . dw ,-, 



(with the condition — — + — -f- — = O 

 dx dy dz 



pressible substance), contains every possible solution, and 

 he proceeds to discuss special cases of the general solution 

 which may be true of waves propagated by molecules 

 through the ether. Here his desire for physical concep- 

 tions appears, and his hatred of mathematical asphasia. 

 He considers the case of a ball moving to and fro, of a 

 ball twisting about an axis, of a globe becoming alternately 

 prolate and oblate, of a rod twisted in opposite directions 

 at the two ends, and of the Thomson-Helmholtz molecule 

 which is a heavy mass connected by massless springs 

 with a massless inclosing shell, or there may be several 

 shells inclosing each other, connected by springs with a 

 dense mass in the centre (far more dense than the ether). 



Here he discusses the manner in which a molecule may 

 be supposed to give off its vibrations to the ether. Does 

 it gradually increase in intensity and gradually die out, 

 or how does it act ? Here is what he says on this much- 

 neglected point at p. 94 : — 



" The kind of thing that the luminous vibrator consists 

 in seems to me to be a sudden initiation of a set of 

 vibrations and a sequence of vibrations from that initia- 

 tion which will naturally become of smaller and smaller 

 amplitude. . . . Why a sudden start ? Because I believe 

 that the light of the natural flame or of the arc light or 

 of any other known source of light must be the result of 

 sudden shocks from a number of vibrators. Take the 

 light obtained by striking two quartz pebbles together. 

 You have all seen that. There is one of the very simplest 

 sources of light. . . . What sort of a thing can the light 

 be that proceeds from striking two quartz pebbles to- 

 gether ? Under what circumstances can we conceive a 

 group of waves of light to begin gradually and to end 

 gradually ? You know what takes place in the excitation 

 of a fiddle-string or a tuning-fork by a bow. The vibra- 

 tions gradually get up from zero to a maximum, and then, 

 when you take the bow off, gradually subside. I cannot 



see anything like that in the source of light. On the 

 contrary, it seems to me to be all shocks — a sudden 

 beginning and gradual subsidence." 



The light coming from a single shock is, of course, 

 polarised always in the same direction. Sellmeier's de- 

 ductions from Fizeau's experiment shows that there is no 

 serious fading in 50,000 vibrations. Helmholtz introduces 

 viscous terms which absorb the energy and might pre- 

 vent the possibility of 50,000 vibrations from one shock. 

 That is a retrograde step. Absorption can be explained 

 without viscous terms. 



Such speculations, when coming from one of less grasp 

 of physical facts, would attract but little attention. But 

 here all kinds of useful suggestions are continually thrown 

 out for experiment and for hypotheses. He is striving to 

 get at the physical meaning of radiation, absorption, 

 anomalous dispersion, fluorescence, and phosphorescence, 

 and here is what he says on some of these points at 

 p. 90 :— 



" But there are cases in which we have that tremendous 

 jangling, and that is in the fluorescence of such a thing 

 as uranium glass, which lasts for several seconds after the 

 exciting light is taken away, and then again in phosphor- 

 escence that lasts for hours and days. There have been 

 exceedingly interesting beginnings in the way of experi- 

 ments already made, but I think no one has found whether 

 initial refraction is exactly the same as permanent refrac- 

 tion. For this purpose we might use Becquerel's phos- 

 phoroscope, or we might take such an appliance as Prof. 

 Michaelson has been using for light, and get something 

 enormously more searching than Becquerel's phosphoro- 

 scope, and try whether, in the first hundredth of a second, 

 there is any indication of a different wave-velocity from 

 that which you would have when white light passes con- 

 tinuously in the usual manner of refraction. If in the 

 methods employed for ascertaining the velocity of light 

 in a transparent body . . . we apply a lest for an instan- 

 taneous refraction, I have no doubt we shall get negative 

 results, but yet properties of ultimate importance. We 

 might take bodies in which, like uranium glass, the phos- 

 phorescence lasts only a few seconds ; and then, again, 

 bodies in which phosphorescence lasts for minutes and 

 hours. With some of these we should have anomalous 

 dispersion, gradually fading away after a time. I should 

 think that by experimenting, and so on, we should find 

 some very interesting results of this kind." 



In his mathematics he suppresses the condensational 

 wave, and, in doing so, makes reference to the electro- 

 magnetic theory of light, which, he thinks, has added 

 nothing to our physical conceptions of the ether. In 

 treating, further on, of reflection and refraction, he speaks 

 a great deal of the pressural wave, which many authors 

 have called a condensational wave. I find that in some 

 points my notes are fuller than the reporter's. I cannot 

 lind there the following characteristic passage about the 

 pressural wave : — " People have tried to muddle this. 

 The pressural wave has been the difficulty. Cauchy 

 starved the animal, M'Cullagh and Neumann didn't know 

 of its existence, H aught on put it in an Irish car and it 

 wouldn't go, Green and Rayleigh treated it according to 

 its merits.'' 



With regard to the possibility of a condensational wave, 

 and to the electro-magnetic theory of light, we find, on 

 pp. 40-41 :— 



" We ignore this condensational wave in the theory of 

 light. We are sure that its energy, at all events, if it is 

 not null, is very small in comparison with the luminiferous 

 vibrations we are dealing with. But to say that it is 

 absolutely null would be an assumption we have no right 

 to make. When we look through the little universe that 

 we know, and think of the transmission of electrical 

 force and of the transmission of magnetic force, and of 

 the transmission of light, we have no right to assume 

 that there is not something else that our philosophy does 



