Lord Kelvin: An account of his scientific life and work

by Andrew Gray

CHAPTER XIV

THE BALTIMORE LECTURES

The Baltimore Lectures were delivered in 1884 at Johns Hopkins University, soon after the Montreal meeting of the British Association. The subject chosen was the Wave Theory of Light; and the idea underlying the course was to discuss the difficulties of this theory to "Professorial fellow-students in physical science." A stenographic report of the course was taken by Mr. A. S. Hathaway, and was published soon after. The lectures were revised by Lord Kelvin, and the book now known as The Baltimore Lectures was published just twenty years later (in 1904) at the Cambridge University Press. It is absolutely impossible in such a memoir as the present to give any account of the discussions contained in the lectures as now published. The difficulties dealt with can for the most part only be understood by those who are acquainted with the wave theory of light in its details, and such readers will naturally go direct to the book itself.

Some of the difficulties, however, were frequently alluded to in Lord Kelvin's ordinary lectures, and all his old students will remember the animation with which he discussed the apparent anomaly of a medium like the luminiferous ether, which is of such enormous rigidity that (on the elastic solid theory) a wave of transverse oscillation is propagated through it with a speed of 3 × 10¹⁰ centimetres (186,000 miles) per second, and yet appears to offer no impediment to the slow motion of the heavenly bodies. For Lord Kelvin adopted the elastic solid theory of propagation of light as "the only tenable foundation for the wave theory of light in the present state of our knowledge," and dismissed the electromagnetic theory (his words were spoken in 1884, it is to be remembered) with the statement of his strong view that an electric displacement perpendicular to the line of propagation, accompanied by a magnetic disturbance at right angles to both, is inadmissible.

And he goes on to say that "when we have an electromagnetic theory of light," electric displacement will be seen as in the direction of propagation, with Fresnelian vibrations perpendicular to that direction. In the preface, of date January 1904, the insufficiency of the elastic solid theory is admitted, and the question of the electromagnetic theory again referred to. He says there that the object of the Baltimore Lectures was to ascertain how far the phenomena of light could be explained within the limits of the elastic solid theory. And the answer is "everything non-magnetic; nothing magnetic." But he adds, "The so-called electromagnetic theory of light has not helped us hitherto," and that the problem is now fully before physicists of constructing a "comprehensive dynamics of ether, electricity, and ponderable matter which shall include electrostatic force, magnetostatic force, electromagnetism, electrochemistry, and the wave theory of light."

All this is exceedingly interesting, for it seems to make clear Lord Kelvin's attitude with respect to the electromagnetic theory of Maxwell, which is now regarded by most physicists as affording on the whole a satisfactory account, if not a dynamical theory in the sense understood by Lord Kelvin, of light-propagation. That there is an electric displacement perpendicular to the direction of propagation and a magnetic displacement (or motion) perpendicular to both seems proved by the experiments of Hertz, and the velocity of propagation of these disturbances has been found to be that of light. Of course it remains to be found out in what the electric and magnetic changes consist, and whether the ether has or has not an atomic structure. Towards the answer to this question on electromagnetic presuppositions some progress has already been made, principally by Larmor. And, after all, while we may imagine that we know something more definite of dynamical actions on ponderable matter, it is not quite certain that we do: we are more familiar with them, that is almost all. We know, for example, that at every point in the gravitational field of the earth we may set up a gravitation vector, or field-intensity; for a particle of matter there is subjected to acceleration along that direction. But of the rationale of the action we know nothing, or next to nothing. So we set up electric and magnetic vectors in an insulating medium, corresponding to electric and magnetic effects which we can observe; and it is not too much to say that we know hardly less in this case than we do in the other, of the inner mechanism of the action of which we see the effects.

Returning to the difficulty of the elastic solid theory, that while its rigidity is enormous, it offers no obstacle to the planets and other heavenly bodies which move through it, it may be interesting to recall how Lord Kelvin used to deal with it in his elementary lectures. The same discussion was given in the Introductory Lecture at Baltimore. The difficulty is not got over by an explanation of what takes place: it is turned by showing that a similar difficulty exists in reconciling phenomena which can be observed every day with such ordinary materials as pitch or shoemakers' wax. A piece of such wax can be moulded into a tuning-fork or a bell, and will then, if struck, sound a musical note of definite pitch. This indicates, for rapidly alternating deformations started by a force of short duration, the existence of internal forces of the kind called elastic, that is, depending on the amount of deformation caused, not on the rate at which the deformation is increasing or diminishing, as is the case for the so-called "viscous forces" which are usually displayed by such material. But the tuning-fork or bell, if left lying on the table, will gradually flatten down into a thin sheet under only its own weight. Here the deformation is opposed only by viscous forces, which, as the change is very slow, are exceedingly small.

But let a large slab of it, three or four inches thick, be placed in a glass jar ten or twelve inches in diameter, already partly filled with water, and let some ordinary corks be imprisoned beneath, while some lead bullets are laid on the upper surface. After a month or two it will be found that the corks have disappeared from the water into the wax, and that the orifices which they made in entering it have healed up completely; similarly the bullets have sunk down into the slab, leaving no trace behind. After two or three months more, the corks will be seen to be bursting their way out through the upper surface of the slab, and the bullets will be found in the water below. The very thing has taken place that would have happened if water had been used instead of pitch, only it has taken a very much longer time to bring it about. The corks have floated up through the wax in consequence of hydrostatic upward force exerted by the wax acting as a fluid; and the bullets have sunk down in consequence of the excess of their weights above the upward hydrostatic force exerted on them as on the corks. The motion in both cases has been opposed by the viscous forces called into play.

The application of this to the luminiferous ether is immediate. Let the ether be regarded as a substance which can perform vibrations only "when times and forces are suitable," that is, when the forces producing distortion act for only an infinitesimal time (as in the starting of the tuning-fork by a small blow), and are not too great. Vibrations may be set up locally, and the medium may have a true rigidity by which they are propagated to more remote parts; that is to say, waves travel out from the centre of disturbance. On the other hand, if the forces are long continued, even if they be small, they produce continuously increasing change of shape. Thus the planets move seemingly without resistance.

The conclusion is that the apparently contradictory properties of the ether are no more mysterious than the properties of pitch or shoemakers' wax. And, after all, matter is still a profound mystery.

Dynamical illustrations, which old Glasgow students will recognise, appear continually in the lectures. They will remember, almost with affection, the system of three particles (7 lb. or 14 lb. weights!) joined together in a vertical row by stout spiral springs of steel, which were always to be taken as massless, and will recall Lord Kelvin's experiments with them, demonstrating the three modes of vibration of a system of three masses, each of which influenced those next it on the two sides. Here they will find the problem solved for any number of particles and intervening springs, and the solution applied to an extension of the massive molecule which von Helmholtz imbedded in the elastic ether, and used to explain anomalous dispersion. A highly complex molecule is suggested, consisting of an outer shell embedded in the ether as in the simpler case, a second shell within that connected to the outer by a sufficient number of equal radial springs, a third within and similarly connected to the second by radial springs, and so on. This molecule will have as many modes of vibration as there are sets of springs, and can therefore impart, if it is set into motion, a complex disturbance to the ether in which it is imbedded.

The modification of this arrangement by which Lord Kelvin explained the phosphorescence of such substances as luminous paint is also described, and will be recognised by some as an old friend. A number, two dozen or so, of straight rods of wood eighteen inches long are attached to a steel wire four or five inches apart, like steps on a ladder made with a single rope along the centres of the steps. The wire is so attached to each rod that the rod must turn with the wire if the latter is twisted round. Each rod is loaded with a piece of lead at each end to give it more moment of inertia about the wire. The wire, with this "ladder" attached to it, is rigidly attached to the centre of a cross-bar at the top, which can be made to swing about the wire as an axis and so impart twisting vibrations to the wire in a period depending on this driver. Sliding weights attached to the bar enable its moment of inertia to be changed at pleasure. The lower end of the wire carries a cross-bar with two vanes, immersed in treacle in a vessel below. When the period of the exciter was very long the waves of torsion did not travel down the "ladder," but when the period was made sufficiently short the waves travelled down and were absorbed in the treacle below. In the former case the vibrations persisted; the case was analogous to that of phosphorescence.

Fig. 18.

Incidentally a full and very attractive account of the elastic solid theory is given in these lectures, accompanied as it is by characteristic digressions on points of interest which suggest themselves, and on topics on which the lecturer held strong opinions, such, for example, as the absurd British system of weights and measures. The book reads in many places like a report of some of the higher mathematical lectures which were given every session at Glasgow; and on that account, if on no other, it will be read by the old students of the higher class with affectionate interest. But the discussions of the great fundamental difficulty presented at once by dispersion—the fact, that is, that light of different wave lengths has different velocities in ordinary transparent matter—the discussions of the various theories of dispersion that have been put forward, the construction of the molecules, gyrostatic and non-gyrostatic, with all their remarkable properties, which Lord Kelvin invents in order to frame a dynamical mechanism which will imitate the action of matter as displayed in the complex manifestations of the optical phenomena, not only of isotropic matter, but of crystals, will ever afford instruction to every mathematician who has the courage to attack this subject, and remain as a monument to the extraordinary genius of their author.

A subject is touched on in these lectures which has not been dealt with in the present review of Lord Kelvin's work. By four lines of argument—by the heat of combination of copper and zinc, together with the difference of electric potential developed when these metals are put in contact, from the thickness of a capillary film of soap and water (measured by Rücker and Reinold) just before it gives way, and the work spent in stretching it, from the kinetic theory of gases and the estimated length of free path of a particle (given also by Loschmidt and by Johnstone Stoney), and from the undulatory theory of light—Lord Kelvin estimated superior and inferior limits to the "size of the atoms" of bodies, or, more properly speaking, of the molecular structure of the matter. We cannot discuss these arguments—and they can be read at leisure by any one who will consult Volume I (Constitution of Matter) of Lord Kelvin's Popular Lectures and Addresses, for his Royal Institution Lecture on the subject, there given in full—but we may state his conclusion. Let a drop of water, a rain drop, for example, be magnified to the size of the earth, that is, from a sphere a quarter of an inch, or less, in diameter to a sphere 8000 miles in diameter, and let the dimensions of the molecular structure be magnified in the same proportion. "The magnified structure would be more coarse-grained than a heap of small shot, but probably less coarse-grained than a heap of cricket-balls."

Of course, it is not intended here to convey the idea that the molecules are spheres like shot or cricket-balls; they undoubtedly have a structure of their own. And no pronouncement is made as to the divisibility or non-divisibility of the molecules. All that is alleged is that if the division be carried to a minuteness near to or beyond that of the dimensions of the structure, portions of the substance will be obtained which have not the physical properties of the substance in bulk.

The recent interesting researches of chemists and physicists into phenomena which seem to demonstrate the disintegration, not merely of molecules, but even of the atomic structure of matter, attracted Lord Kelvin's attention in his last years, and suo more he endeavoured to frame dynamical explanations of electronic (or, as he preferred to call it, "electrionic") action. But though keenly interested in all kinds of research, he turned again and again to the older theories of light, and his dynamical representations of the ether and of crystals, with renewed vigour and enthusiasm.

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