James Clerk Maxwell and Modern Physics

by Richard Glazebrook

If we can never go further—and it must be admitted that the difficulties in the way of further advance are enormous—it may, I think, be claimed for Maxwell that the progress already made is greatly due to him. Both these laws, for the case of elastic spheres, are contained in his first paper of 1860; and while it is to the genius of Boltzmann that we owe their earliest generalisation, and in particular the proof of the uniqueness of the solution under proper restrictions, Maxwell’s last paper contributed in no small degree to the security of the position. Not merely the foundations, but much of the superstructure of molecular science is his work.

The difficulties in the way of advance are, as we have said, enormous. Boltzmann, in one of his papers, has considered the properties of a complex molecule of a gas, consisting maybe of a number of atoms and possibly of ether atoms bound with them, and he concludes that such a molecule will behave in its progressive motion, and in its collisions with other molecules, nearly like a rigid body. But to quote from Mr. Bryan: “The case of a polyatomic molecule, whose atoms are capable of vibrating relative to one another, affords an interesting field for investigation and speculation. Is the Boltzmann distribution still unique, or do other permanent distributions exist in which the kinetic energy is unequally divided?”

Again, the spectroscope reveals to us vibrations of the ether, which are connected in some way with the vibrations of the molecules of gas, whose spectrum we are observing. It seems clear that the law of equal partition does not apply to these, and yet, if we are to suppose that the ether vibrations are due to actual vibrations of the atoms which constitute a molecule, why does it not apply? Where does the condition come in which leads to failure in the proof? Or, again, is it, as has been suggested, the fact that the complex spectrum of a gas represents the terms of a Fourier Series, into which some elaborate vibration of the atoms is resolved by the ether? or is the spectrum due simply to electro-magnetic vibrations on the surface of the molecules—vibrations whose period is determined chiefly by the size and shape of the molecule, but in which the atoms of which it is composed take part? There are grave difficulties in the way of either of these explanations, but we must not let our dread of the task which remains to be done blind our eyes to the greatness of Maxwell’s work.

One other important paper, and a number of shorter articles, remain to be mentioned.

The Boltzmann-Maxwell law applies only to cases in which the temperature is uniform throughout. In a paper published in the Philosophical Transactions for 1879, on “Stresses in Rarefied Gases Arising from Inequalities of Temperature,” Maxwell deals, among other matters, with the theory of the radiometer. He shows that the observed motions will not take place unless gas, in contact with a solid, can slide along the surface of the solid with a finite velocity between places where the temperature is different; and in an appendix he proves that, on certain assumptions regarding the nature of the contact of the solid and the gas, there will be, even when the pressure is constant, a flow of gas along the surface from the colder to the hotter parts.

Among his less important papers bearing on molecular theory must be mentioned a lecture on “Molecules” to the British Association at its Bradford meeting; “Scientific Papers of Clerk Maxwell,” vol. ii., p. 361; and another on “The Molecular Constitution of Bodies,” Scientific Papers, vol. ii., p. 418.

In this latter, and also in a review in Nature of Van der Waals’ book on “The Continuity of the Gaseous and Liquid States,”[56] he explains and discusses Clausius’ virial equation, by means of which the variations of the permanent gases from Boyle’s law are explained. The lecture gives a clear account, in Maxwell’s own inimitable style, of the advances made in the kinetic theory up to the date at which it was delivered, and puts clearly the difficulties it has to meet. Maxwell thought that those arising from the known values of the ratio of the specific heats were the most serious.

In the articles, “Atomic Constitution of Bodies” and “Diffusion,” in the ninth edition of the Encyclopædia Britannica, we have Maxwell’s later views on the fundamental assumptions of the molecular theory.

The text-book on “Heat” contains some further developments of the theory. In particular he shows how the conclusions of the second law of thermo-dynamics are connected with the fact that the coarseness of our faculties will not allow us to grapple with individual molecules.

The work described in the foregoing chapters would have been sufficient to secure to Maxwell a distinguished place among those who have advanced our knowledge; it remains still to describe his greatest work, his theory of Electricity and Magnetism.