Heroes of Science: Physicists

by William Garnett

A more important discovery was that of double refraction temporarily produced in viscous liquids. Maxwell found that a quantity of Canada balsam, if stirred, acquired double-refracting powers, which it retained for a short period, until the stress temporarily induced had disappeared.

But Maxwell's investigations in optics must be regarded as his play; his real work lay in the domains of electricity and of molecular physics.

In 1738 Daniel Bernouilli published an explanation of atmospheric pressure on the hypothesis that air consists of a number of minute particles moving in all directions, and impinging on any surface exposed to their action. In 1847 Herapath explained the diffusion of gases on the hypothesis that they consisted of perfectly hard molecules impinging on one another and on surfaces exposed to them, and pointed out the relation between their motion and the temperature and pressure of a gas. The present condition of the molecular theory of gases, and of molecular science generally, is due almost entirely to the work of Joule, Clausius, Boltzmann, and Maxwell. To Maxwell is due the general method of solving all problems connected with vast numbers of individuals—a method which he called the statistical method, and which consists, in the first place, in separating the individuals into groups, each fulfilling a particular condition, but paying no attention to the history of any individual, which may pass from one group to another in any way and as often as it pleases without attracting attention. Maxwell was the first to estimate the average distance through which a particle of gas passes without coming into collision with another particle. He found that, in the case of hydrogen, at standard pressure and temperature, it is about 1/250000 of an inch; for air, about 1/389000 of an inch. These results he deduced from his experiments on viscosity, and he gave a complete explanation of the viscosity of gases, showing it to be due to the "diffusion of momentum" accompanying the diffusion of material particles between the passing streams of gas.

One portion of the theory of electricity had been considerably developed by Cavendish; the application of mathematics to the theory of attractions, and hence to that of electricity, had been carried to a great degree of perfection by Laplace, Lagrange, Poisson, Green, and others. Faraday, however, could not satisfy himself with a mathematical theory based upon direct action at a distance, and he filled space, as we have seen, with tubes of force passing from one body to another whenever there existed any electrical action between them. These conceptions of Faraday were regarded with suspicion by mathematicians. Sir William Thomson was the first to look upon them with favour; and in 1846 he showed that electro-static force might be treated mathematically in the same way as the flow of heat; so that there are, at any rate, two methods by which the fundamental formulæ of electro-statics can be deduced. But it is to Maxwell that mathematicians are indebted for a complete exposition of Faraday's views in their own language, and this was given in a paper wherein the phenomena of electro-statics were deduced as results of a stress in a medium which, as suggested by Newton and believed by Faraday, might well be that same medium which serves for the propagation of light; and "the lines of force" were shown to correspond to an actual condition of the medium when under electrical stress. Maxwell, in fact, showed, not only that Faraday's lines formed a consistent system which would bear the most stringent mathematical analysis, but were more than a conventional system, and might correspond to a state of stress actually existing in the medium through which they passed, and that a tension along these lines, accompanied by an equal pressure in every direction at right angles to them, would be consistent with the equilibrium of the medium, and explain, on mechanical principles, the observed phenomena. The greater part of this work he accomplished while an undergraduate at Cambridge. He showed, too, that Faraday's conceptions were equally applicable to the case of electro-magnetism, and that all the laws of the induction of currents might be concisely expressed in Faraday's language. Defining the positive direction through a circuit in which a current flows as the direction in which a right-handed screw would advance if rotating with the current, and the positive direction around a wire conveying a current as the direction in which a right-handed screw would rotate if advancing with the current, Maxwell pointed out that the lines of magnetic force due to an electric current always pass round it, or through its circuit, in the positive direction, and that, whenever the number of lines of magnetic force passing through a closed circuit is changed, there is an electro-motive force round the circuit represented by the rate of diminution of the number of lines of force which pass through the circuit in the positive direction.

The words in italics form a complete statement of the laws regulating the production of currents by the motion of magnets or of other currents, or by the variation of other currents in the neighbourhood. Maxwell showed, too, that Faraday's electro-tonic state, on the variation of which induced currents depend, corresponds completely with the number of lines of magnetic force passing through the circuit.

He also showed that, when a conductor conveying a current is free to move in a magnetic field, or magnets are free to move in the neighbourhood of such a conductor, the system will assume that condition in which the greatest possible number of lines of magnetic force pass through the circuit in the positive direction.

But Maxwell was not content with showing that Faraday's conceptions were consistent, and had their mathematical equivalents,—he proceeded to point out how a medium could be imagined so constituted as to be able to perform all the various duties which were thus thrown upon it. Assuming a medium to be made up of spherical, or nearly spherical, cells, and that, when magnetic force is transmitted, these cells are made to rotate about diameters coinciding in direction with the lines of force, the tension along those lines, and the pressure at right angles to them, are accounted for by the tendency of a rotating elastic sphere to contract along its polar axis and expand equatorially so as to form an oblate spheroid. By supposing minute spherical particles to exist between the rotating cells, the motion of one may be transmitted in the same direction to the next, and these particles may be supposed to constitute electricity, and roll as perfectly rough bodies on the cells in contact with them. Maxwell further imagined the rotating cells, and therefore, à fortiori, the electrical particles, to be extremely small compared with molecules of matter; and that, in conductors, the electrical particles could pass from molecule to molecule, though opposed by friction, but that in insulators no such transference was possible. The machinery was then complete. If the electric particles were made to flow in a conductor in one direction, passing between the cells, or molecular vortices, they compelled them to rotate, and the rotation was communicated from cell to cell in expanding circles by the electric particles, acting as idle wheels, between them. Thus rings of magnetic force were made to surround the current, and to continue as long as the current lasted. If an attempt were made to displace the electric particles in a dielectric, they would move only within the substance of each molecule, and not from molecule to molecule, and thus the cells would be deformed, though no continuous motion would result. The deformation of the cells would involve elastic stress in the medium. Again, if a stream of electric particles were started into motion, and if there were another stream of particles in the neighbourhood free to flow, though resisted by friction, these particles, instead of at once transmitting the rotary motion of the cells on one side of them to the cells on the other side, would at first, on account of the inertia of the cells, begin to move themselves with a motion of translation opposite to that of the primary current, and the motion would only gradually be destroyed by the frictional resistance and the molecular vortices on the other side made to revolve with their full velocity. A similar effect, but in the opposite direction, would take place if the primary current ceased, the vortices not stopping all at once if there were any possibility of their continuing in motion. The imaginary medium thus serves for the production of induced currents.

The mechanical forces between currents and magnets and between currents and currents, as well as between magnets and currents, were accounted for by the tension and pressure produced by the molecular vortices. When currents are flowing in the same direction in neighbouring conductors, the vortices in the space between them are urged in opposite directions by the two currents, and remain almost at rest; the lateral pressure exerted by those on the outside of the conductors is thus unbalanced, and the conductors are pushed together as though they attracted each other. When the currents flow in opposite directions in parallel conductors, they conspire to give a greater velocity to the vortices in the space between them, than to those outside them, and are thus pushed apart by the pressure due to the rotation of the vortices, as though they repelled each other. In a similar way, the actions of magnets on conductors conveying currents may be explained. The motion of a conductor across a series of lines of magnetic force may squeeze together and lengthen the threads of vortices in front, and thus increase their speed of rotation, while the vortices behind will move more slowly because allowed to contract axially and expand transversely. The velocity of the vortices thus being greater on one side of the wire than the other, a current must be induced in the wire. Thus the current induced by the motion of a conductor in a magnetic field may be accounted for.

This conception of a medium was given by Maxwell, not as a theory, but to show that it was possible to devise a mechanism capable, in imagination at least, of producing all the phenomena of electricity and magnetism. "According to our theory, the particles which form the partitions between the cells constitute the matter of electricity. The motion of these particles constitutes an electric current; the tangential force with which the particles are pressed by the matter of the cells is electro-motive force; and the pressure of the particles on each other corresponds to the tension or potential of the electricity."

When a current is maintained in a wire, the molecular vortices in the surrounding space are kept in uniform motion; but if an attempt be made to stop the current, since this would necessitate the stoppage of the vortices, it is clear that it cannot take place suddenly, but the energy of the vortices must be in some way used up. For the same reason it is impossible for a current to be suddenly started by a finite force. Thus the phenomena of self-induction are accounted for by the supposed medium.