Lord Kelvin: An account of his scientific life and work

by Andrew Gray

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."