worked out myself about the year 1854, and in which I found a velocity comparable with the velocity of light. . . . That is a very different case from this, and I have waited in vain to see how we can get any justification of the way of putting it in the so-called electro-magnetic theory of light." In those parts of the lectures which deal with wave propagation in an isotropic medium, by far the most interesting parts are those which treat of the conditions at bounding surfaces, whether these surfaces be reflecting and refracting surfaces or surfaces of radiating molecules, or surfaces of absorbing molecules. Lord Rayleigh's investigations and his own on the likelihood of the density or the rigidity of the substance composing a molecule differing from that of the ether are also full of interest. Much of this part of the subject has been thoroughly worked out before, but here the treatment is so original, the language is so suggestive, and I need hardly say that the whole course of lectures is so pregnant with useful ideas, that every one who reads this part will be well repaid. Having now roughly indicated the novel points and the general mode of treatment of the problem in molar dynamics, I propose in the next notice to give some account of the problem in molecular dynamics, which occupied half of the time. II. In the present article Sir William Thomson's spring and shell molecule will be described and its theory sketched, in so far as this has been investigated with the view of getting over some of the difficulties which surround the wave theory of light. In Helmholtz's memoir on anomalous dispersion, a sketch of such a theory was published. But this new molecule differs from that of Helmholtz in several points, chiefly in the fact that absorption is not accounted for by any viscous action in the molecule dissipating the energy of vibration into low grade heat. Most readers who have ever visited the natural philosophy lecture-room in Glasgow University will recognize a very old friend in this new molecule, where they have seen it vibrating, I suppose, any time since the University occupied its present site. In appearance the molecule has been changed, but its theory as taught to the students there is identical. For a description of this molecule let us refer to page 10 of the lectures:-- "Imagine for a moment that we make a rude mechanical model. Let this be an infinitely rigid spherical shell; let there be another absolutely rigid shell inside of that, and so on, as many as you please. Naturally we might think of something more continuous than that, but I only wish to call attention to a crude mechanical explanation possibly of the effects of dispersion. Suppose we had luminiferous ether outside, and that this hollow space is of very small diameter in comparison with the wave length. Let zig-zag springs connect the outer rigid boundary with boundary number two. I use a zig-zag, not a spiral, spring which has the helical properties which we are not ready for yet, such properties as sugar and quartz have in disturbing the luminiferous vibrations. Suppose we have shells two and three also connected by a sufficient number of zig-zag springs, and so on; and let there be a solid nucleus in the centre with spring connections between it and the shell outside of it. If there is only one of these interior shells, you will have one definite period of vibration. Suppose you take away everything except that one interior shell; displace that shell and let it vibrate. The period of its vibration is perfectly definite. If you have an immense number of such shells with movable molecules inside of them, distributed through some portion of the luminiferous ether, you will put it into a condition in which the velocity of propagation of the wave will be different from what it is in the homogeneous luminiferous ether. You have what is called for, viz. a definite period; and the relation between the period of vibration in the light considered and the period of the free vibration of the shell will be fundamental in respect to the attempt of a mechanism of that kind to represent the phenomena of dispersion. "If you take away everything except the one shell, you will have almost exactly, I think, the view of Helmholtz's paper-a crude model as it were of what Helmholtz makes his paper on anomalous dispersion. Helmholtz, besides that, supposes a certain degree or coefficient of viscous resistance against the vibration of the inner shell, relatively to the outer one. holtz does not reduce it to a gross mechanical form like this, but merely assumes particles connected with the luminiferous ether and assumes a viscous motion to operate against the motion of the particles." Helm In the lectures the action of such a molecule when subjected to forced vibrations was illustrated by a model of ingenious construction, which among the irreverent passed by the name of the "wiggler." A steel wire was hung vertically, and five or six lathes 2 feet long and 2 inches wide were attached in a horizontal position to the wire, each one having three pins fixed in it for this purpose. These lathes were loaded at their ends, the weight on each lathe being less than that on the one above it. The lowest lathe was attached to a pendulum arrangement which impressed forced vibrations upon the system, the period being adjustable. The theory of such a system is the same as that of the molecule described above. But in working out the theory a third type of vibrator was used, the identical one which vibrates in the lecture room at Glasgow. This is a series of weights attached to each other by vertical springs which can be stretched. The highest is the heaviest, and the others are arranged in the order of weight. Calling P the lathe with forced vibrations (corresponding to the external massless shell acted on by the ether) and its displacement, my, my, &c., are the successive masses, 41, 42, &c., are their displacements dui dr 2 1 — (mix2 + mi + 1 x 0 i + 1 + . . . + m,x,®), +3 Xi and since the right hand member is essentially negative, it follows that all the u's diminish with increase of period. The critical cases occur when the period of forced vibration agrees with the natural period of any of the shells or lathes. When the forced vibration is very rapid, all successive masses move in opposite directions. When the forced period is slower, u becomes zero, and is infinite-i. e., the vibration of the lowest mass is infinite in comparison with the forced vibrator, and so with the other vibrators. When the forced period is slower, u, becomes negative, i.e., the lowest mass begins to vibrate in the same direction as the forced vibrator. Successive critical cases occur as the forced period reaches the natural periods of successive vibrators. At the critical period for any one vibrator, all those below it are vibrating in one direction, while the critical one and those above it are executing very large vibrations in opposite directions successively. These critical periods are admirably adapted for explaining absorption and also anomalous dispersion. In highly absorbing media which cut off a band of light from the spectrum, the refractive index for colors neighboring to the band is remarkable; thus light of greater wave-length than the band is refracted more, and light of less wave-length than the band is refracted less than in normal substances. Lord Rayleigh considered this to be due to the mutual influence of the vibrating molecule and ether. If the point of support of a pendulum is vibrated in a different period, the period of the pendulum is changed. Lommel seems to have been the first to make dispersion depend upon associated matter. The influence of a large number of the spring and shell molecules distributed through the ether upon the velocity of light in that medium is examined and shown to depend upon the wave-length or period. Finally at p. 108 we obtain the following formula: 0 or u1 The critical periods denoted by K, are the roots of 0. Vibrations of the molecule in these periods can evidently communicate no motion to the surrounding ether, for 0 for finite values of zi. On the contrary, if & has an actual value in one of these periods z must be infinite. In other words, the energy of motions of the ether in these periods is infinitely rapidly absorbed into the molecule. An example men. tioned by bir Wm. Thomson is to vibrate a watch in the period of its hair spring; the balance wheel will soon vibrate enormously and break, bir Wm. Thomson said on this point before he introduced the mathematical analysis of the subject (p. 37); “If you want to hurry up a particle (or a swing, for example) you shove it at the end of one d 0 in an incompressible substance), dn ds (with the condition + + dx dy dz contain 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 conceptions appears, and his hatred of mathematical aphasia. 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 initiation 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 are 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 together? 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 vibrations 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 deductions 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 prevent 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 phosphorescence that lasts for hours and days. There have been exceedingly interesting beginnings in the way of experiments already made, but I think no one has found whether initial refraction is exactly the same as permanent refraction. For this purpose we might use Becquerel's phosphoroscope, or we might take such an appliance as Prof. Michaelson has been using for light, and get something enormously more searching than Becquerel's phosphoroscope, 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 continuously in the usual manner of refraction. If in the methods employed for ascertaining the velocity of light in a transparent body . . . we apply a test for an instantaneous refraction, I have no doubt we shall get negative results, but yet properties of ultimate importance. We might take bodies in which, like uranium ... and of the not someth right to as luminiferou which are es very small e proceed. 11. that, unless th tion and refrac tion. Waves waves of distort mediums withou we come to the s with these conde by supposing the mind to be exami of condensational after all, the elect Suppose that we hav that, through some a is alternately positiv will be the cause of spherical conductors a machine, and the quot. "It is perfectly cer neighborhood of the e negatively electrified ele per second of time, with positive, and the same t. what is the potential at ea revolution was made fast Every one believes that, if million times, or millions from fulfilling the electrost: neighborhood. It is absolute would give rise to electrical electrical waves are condens probably it would be that the mously faster than the propaga conscious, when speaking of thi electro-magnetic theory of ligh impulse along an insulated wir *The passage may be found on p. 233. enly for reasons indicated by Sir Wm. T subsequently by letters, which have been TLY lieve it is the first time hat I have not touched a chance 'Surely there may be such a thing found to exemplify this kind The purely physical bent of the author's reasoning is well shown in The model of an electro-magnetic ether described by Prof. Fitzgerald on March 28, to the Physical Society, founded on Clerk Maxwell's celebrated papers in the Philosophical Magazine in 1860 and 1861, goes a long way to clear away the objection raised by Sir William Thomson. In reading these lectures, it must be remembered that they are uncor rected verbatim reports, and one is surprised at seeing that the matter is so continuous and readable. A considerable freshness is given by the conversational interludes and remarks, which would not perhaps have appeared in a written work. As mentioned before, Sir William spoke of the pressural wave as an animal; this was very happy, as he had just before called it the bête noir of the mathematicians. He says at p. 34:-"I do not like the words 'paradoxical phenomenon.' 'Curious phenomenon' or 'interesting phenomenon' would be better. There is no paradox in science, We may call it a dynamor, but not a parador?" At p. 115 he says:--"The struggle of 1815 (that is not the same idea as la grande guerre de 1815) was, who was to rule the waves, Cauchy or Poisson?" To many it will seem, after reading these lectures containing a review of what has been done and suggestions of what might be done, that certain facts are hopelessly irreconcilable with the wave-theory of light. Sir William Thomson has certainly not shirked a single difficulty, and perhaps has even made them look more glaring than is necessary. But, if this be an error, it is on the right side, The reporter has introduced into the volume some doggerel rhymes read by a certain student of the lectures at a farewell dinner at Baltimore given by President Gilman : *These reports are generally quite verbatim, but I am sure Sir William Thomson is not responsible for this characteristic Americanism.-G. F.—(lee on this note, letters in Science, of " A. G.", June 5, p. 454, and "E. W. C.", June 19, p. 494.-A. S. H.). 114 Moreover, if n be ilatation, and m = with similar expre Thence he shows (with the condition contain every possi "The kind of thing "But there are cases in that is in the fluorescence o several seconds after the e phosphorescence that lasts fo ingly interesting beginnings think no one has found whe permanent refraction. For 1 phoroscope, or we might take been using for light, and get Becquerel's phosphoroscope, a second, there is any indication you would have when white li of refraction. If in the metho light in a transparent body. refraction, I have no doubt we s of ultimate importance. We r ti.e In [No. 41. inv.re of the wave-length. I therefore lay it aside for the present, but with, perfect faith that the principle of explanation of the thing is there," 1st on returning to this country, a more complete theory of the gyrostatan le vie was worked out, sent to America, and incorporated in the lectures, in tuy next and concluding notice I shall touch on the further devel qments if space permits. III. Ire proveeding with new parts of this subject, I wish to say a few w abot "fdeling while Rome is burning." Sir William Thomson writes to me that the expression was used while discussing some mathemta al trivitlity, and he wishes to be relieved of the imputation of speaking dispompestfully of averenious dispersion, which he says is quite as in partant as dochie reactim. I grant this, but my interpretation of his it when I heard the lecture was that so many possible ways had best, steun of explaining anomalous dispersion that it was mere child's plavr tolde-playing to discuss it while the burning question of double reir, ti n awaited explanation, upon which question seems to depend the We safety of the wave-theory of light, that theory being in imminent danger of destruction therefrom. Islow give a brief account of the gyrostatic molecules, crude and in prved. The crude one is a fly-wheel inside a massless shell. Here there is no gyrostatic action opposing a motion of translation, but only opposing a motion of rotation. This is the molecule which was stated to give the wrong kind of variation of magneto-optic rotation with variation of wave lerth The improved gyrostatic molecule (p. 320 consists of tw fly-wheels on one axis. But the aris is cut in two in the middle between them, are the parts titted together by a ball and cylinder joint. The other en is of the £a.f axes are supported in ball-and-socket joints in the male shell. So far as rotation of the shell is concerned, this acts like ne gyrtat, the axis always remaining in one line. But if the shell be ir, titless, the ether can only give translational movement to it, and the dis le gyretat produces a gyrostatic effect when the molerne is avverated in vay directán except along the axis. Ine special fun toon of this molecule is to explain magneto- rota a iti puneti ts of ration the same, the velocity of propagation of s 1 cant depending on the form of the gyrostats, & is the **ty of the processioral rotation of the gyrosents, and is the ftat, n of the gyrostats. This is a totally diferent law to the thede prostatic molecule, and is in acordance with :t * ■ we have ne prend gyrostati molecules inbelled in the other, 01, ate potatiors will affect the velocity of propagation in the mate That Loveries, but their transiti ns will affect the velocity in the ***** chieflated. But observe that by dzirishing the size of the •es the idence of the rotational tia dirisbe, but the infu**** transational notion remains the same on the awam poim that jar gyrostati's velocity is kept the same and the mir of mass of ~> mass of molecule remains the same. Hence, if we have small • Dolecules, the law which agrees with experiment alone 077 form p. 244, which was written by Sit Van Thomson from " This is a very satisfactory state of affairs, and I believe it is the first time that Sir William Thomson's hint about this phenomenon, so long ago thrown out, has been developed. There is still so much matter in the lectures that I have not touched upon that I am in some difficulty as to what to omit. But I certainly should like to transcribe nearly the whole of the last lecture. This is of course impossible, but I will claim a little space for some remarks on Rankine's beautiful but futile attempt to get over the fatal difficulty of double refraction (p. 271): "Suppose here a massless rigid lining of our ideal cavity in the luminiferous ether. Let there be a massive, heavy molecule inside, with fluid around it. The main thing is that this molecule, which only affects the effective inertia of the ether by adding its own mass to the moving mass of the ether, has æolotropy of inertia. Imagine this spherule (drawing on the board an oblate spheroid with axis vertical) moving first in a horizontal direction. The effective inertia of this sheath will be altered if it moves to and fro in a vertical direction, there being, by hypothesis, liquid between it and the ether. The density of this mass must be greater than the density of the liquid, that is all. If there is danger of its coming to the sides of the cavity, let there be springs to keep it in place, if you like, but let its connection with the lining of the cavity be in the main through fluid pressure. Then its effective inertia is different in different directions, This fluid lining seems to hit off the very thing we wanted. Now comes Rankine's want of strength. He cut around the edges of it, and, I think, rather jumped at it, and put down a wave-surface the same as Fresnel's, and said that it came to that. But, alas! Stokes (long before Lord Rayleigh suggested it) showed that it would give a different surface from Fresnel's. Lord Rayleigh, in repeating Rankine's suggestion, showed his strength where Rankine was not so strong in mathematical powers of grappling with a difficult mathematical problem. Lord Rayleigh is a man vho grapples with a difficulty and sees how much he can do with it. He uts it aside if he cannot solve it, but he never shirks it. Rankine was ot a mathematician in that sense at all. Lord Rayleigh finds, not Fresel's wave-surface, but a wave-surface differing from Fresnel's by certain erms appearing in reciprocals instead of directly." Now Stokes has shown that Huyghen's construction satisfies experiment ith great accuracy, and hence Rankine's effort fails. The desperate contion of the wave-theory is shown by the words penned by Lord Rayleigh fore he knew of Stokes's experiments (p. 272): "Should the verdict go ainst the view of the present paper, it is hard to see how any consistent eory is possible which shall embrace at once the laws of scattering, gular reflection and double refraction." It appears, then, that after all the labor which has been expended upon the ve theory of light, it fails absolutely, and, as it seems, hopelessly, in two nts of primary importance. One is the extinction of the ray polarised by retion; the other is double refraction. In other matters we have difficulties, we can see a possible means of escape. Here there seems to be none. Before concluding this series of articles I wish to say a little more about manner of their delivery. It is a rare experience for students to have opportunity of studying the workings of a great mind while grappling 1 a problem. This is what occurred during the three weeks of the Balore lectures. During the whole of this period one or two ardent ents were hunting up references in the Peabody Library, &c., and literfilled Sir William Thomson's rooms with the results of their searches, Sir William generally read these books. He says (p. 76): "An interble number of books have been brought to me, and in every one of I have found something very important." But at p. 98 he says: "I nother quarter-hundredweight of books on the subject. I have not yet them all through." In this way he often came for the first time upon ches bearing on the question in hand. Thus (p. 77): "I only found norning that Lommel also goes on to double refraction of light in Is [with imbedded molecules]. The very problem I am breaking ad against." Evidence is always cropping up that the author is in abit of going farther into a subject by original mathematical is than by reading up Pople's work. I will give some les. Speaking of a Rankine to cubic asymmetry, a chance-'Surely there may be such a thing found to exemplify this kind of asymmetry; would it not be likely to be found in crystals of the cubic class?' Stokes he knew almost everything-instantly said: 'Oh, Sir David Brewster thought he had found it in cubic crystals, but there was an explanation that it seemed to be owing to the effect of the cleavage planes or the separation of the crystal into several crystalline lamina" " (p. 158). Then again he says:-"I am ashamed to say that I never heard of anomalous dispersion until after I found it lurking in the formulas. I said to myself, 'These formulas would imply that, and I never heard of it;' and when I looked into the matter I found, to my shame, that a thing which had been known by others for eight or ten years I had not known until I found it in the dynamics" (p. 120). Once more we find :-"I was thinking about this, three days ago, and said to myself, 'There must be bright lines of reflection from bodies in which we have those molecules that can produce intense absorption. Speaking about it to Lord Rayleigh at breakfast, he informed me of this paper of Stokes's, and I looked and saw that what I had thought of was there. It was known perfectly well, but the molecule first discovered it to me. I am exceedingly interested about these things, since I am only beginning to find out what everybody else knew, such as anomalous dispersion, and those quasi colors, and so on" (p. 282). The purely physical bent of the author's reasoning is well shown in speaking of Rankine's work at p. 270: "I do not think I would like to suggest that Rankine's molecular hypothesis is of very great importance. The title is of more importance than anything else in the work. Rankine was that kind of genius that his names were of enormous suggestiveness, but we cannot say that always of the substance. We cannot find a foundation for a great deal of his mathematical writings, and there is no explanation of his kind of matter. I never satisfy myself until I can make a mechanical model of a thing. If I can make a mechanical model, I can understand it. As long as I cannot make a mechanical model all the way through, I cannot understand; and that is why I cannot get the electro-magnetic theory. I firmly believe in an electro-magnetic theory of light, and that, when we understand electricity and magnetism and light, we shall see them all together as parts of a whole. But I want to understand light as well as I can without introducing things that we understand even less of. That is why I take plain dynamics. I can get a model in plain dynamics, I cannot in electro-magnetics. But so soon as we have rotators to take the parts of magnets and something imponderable to take the part of magnetism, and realize by experiment Maxwell's beautiful ideas of electric displacements, and so on, then we shall see electricity, magnetism, and light closely united and grounded in the same system." The model of an electro-magnetic ether described by Prof. Fitzgerald on March 28, to the Physical Society, founded on Clerk Maxwell's celebrated papers in the Philosophical Magazine in 1860 and 1861, goes a long way to clear away the objection raised by Sir William Thomson. In reading these lectures, it must be remembered that they are uncorrected verbatim reports, and one is surprised at seeing that the matter is so continuous and readable. A considerable freshness is given by the conversational interludes and remarks, which would not perhaps have appeared in a written work. As mentioned before, Sir William spoke of the pressural wave as an animal; this was very happy, as he had just before called it the bête noir of the mathematicians. He says at p. 34:-"I do not like the words 'paradoxical phenomenon.' 'Curious phenomenon' or 'interesting phenomenon' would be better. There is no paradox in science. We may call it a dynamox, but not a paradox." At p. 115 he says:-"The struggle of 1815 (that is not the same idea as la grande guerre de 1815) was, who was to rule the waves, Cauchy or Poisson?" To many it will seem, after reading these lectures containing a review of what has been done and suggestions of what might be done, that certain facts are hopelessly irreconcilable with the wave-theory of light. Sir William Thomson has certainly not shirked a single difficulty, and perhaps has even made them look more glaring than is necessary. But, if this be an error, it is on the right side. The reporter has introduced into the volume some doggerel rhymes read by a certain student of the lectures at a farewell dinner at Baltimore given by President Gilman: *These reports are generally quite verbatim, but I am sure Sir William Thomson is not responsible for this characteristic Americanism.-G. F.-(See on this note, letters in Science, of "A. G.", June 5, p. 454, and "E. W. C.", June 19, p. 494.-A. S. H.). |