These difficulties led Maxwell to abandon the hypothesis of collisions between hard spherical molecules, and to attack the problem on the assumption of action of a more general character between the particles. This is done in his paper ‘On the Dynamical Theory of Gases’ (Phil. Trans. 1866). Some of his conclusions he had attempted to verify by direct experiments, which are described in the Bakerian lecture ‘On the Viscosity of Air and other Gases’ (Phil. Trans. 1866).
The theorem as to the distribution of velocity in a gas was extended by Boltzmann (Vienna Proceedings, 1871–2), and still further by Maxwell in a paper ‘On Boltzmann's Theorem’ (Camb. Phil. Soc. Trans. 1878). Various objections have been urged against the theorem, and it seems now to be established that in the most general form given to it in his last paper, it does not hold (see Bryan, ‘On our Knowledge of Thermodynamics,’ Brit. Assoc. Report, 1891, where the points at issue are clearly stated). Another paper on the same subject, ‘On Stresses in Rarefied Gases arising from Inequalities in Temperature’ (Phil. Trans. 1879), deals among other things with the theory of Mr. Crookes's beautiful instrument, the radiometer.
In Maxwell's collected papers are to be found many others which have a bearing on the constitution of matter and on the theory of gases. Among them may be mentioned his lecture before the British Association at Bradford (Nature, vol. viii.) on ‘Molecules;’ and another lecture before the Chemical Society (ib. vol. xi.) on the ‘Dynamical Evidence for the Molecular Constitution of Bodies;’ his articles in the ‘Encyclopædia Britannica’ on ‘Atom,’ ‘Attraction,’ ‘Capillary Action,’ ‘Diffusion,’ ‘Constitution of Bodies,’ and other subjects; together with his review of Van der Waal's important work ‘On the Continuity of the Gaseous and Liquid States’ (Nature, vol. x.)
But the researches for which Maxwell is best known are those dealing with electricity and magnetism. These commenced with the paper in 1856 on Faraday's lines of force. The next published paper of importance was that on ‘Physical Lines of Force’ (Phil. Mag. 1861, 1862). It was Maxwell's view that electrical and magnetic effects do not arise from the attractions of electric or magnetic matter distributed over the surfaces of conductors or magnetic bodies, but are the means by which changes of some unknown description in the ether which fills space or in some of its properties become known to us. In consequence of these changes energy is stored up in the ether, and electrical or magnetic forces are one form of the manifestation of changes in the distribution of the energy. The experiments of Quincke on electric stress and of Kerr on electro-optics have shown the reality of this stress in the ether, while the theory of Poynting enables us to understand one method by which the energy may travel from place to place. The paper we are now considering describes a mechanism which would have properties in many respects analogous to those possessed by the electro-magnetic medium, though it does not pretend to be a complete representation of the actual condition of the ether.
Similar ideas, though in a far more general form, are developed in the great paper ‘On a Dynamical Theory of the Electro-magnetic Field,’ read before the Royal Society, 8 Dec. 1864 (Phil. Trans. vol. clv.). In it Maxwell took the important and novel step of applying dynamical equations in the generalised form given to them by Lagrange to the problems of electro-magnetism, in dealing with which ‘we are led to the conception of a complicated mechanism capable of a vast variety of motions, but at the same time so connected that the motion of one part depends, according to definite relations, on the motion of other parts. … Such a mechanism must be subject to the laws of dynamics.’ Electro-magnetic action is shown to travel through space at a definite rate in waves, and these waves consist of disturbances which are transverse to the direction in which the waves are propagated. In this respect then they resemble waves of light. Moreover, it is found by experiment that the velocity of the electro-magnetic waves in air and in many other media is the same as that of light, and thus the electro-magnetic theory of light becomes possible. The experiments in Maxwell's time were indirect, though so far as they went conclusive enough. We owe it to the genius of Hertz that we are now able to measure directly the velocity of electro-magnetic waves and to show that they are propagated, and can undergo reflection, refraction, and polarisation exactly like waves of light, and we now feel able to say that the two are the same in character; they differ merely, as do the bass and treble notes of a musical instrument, in the rapidity with which they are executed. In light waves periodic changes in the ether are taking place at the rate of some five hundred billions per second; the most rapid electro-magnetic changes we have yet produced are some few millions per second. The laws of these vibrations, when they are completely known, will give us the secret of the ether, and will enable some disciple of Clerk Maxwell to
