The investigation in question, which was published by Maxwell in the 12th volume of the Cambridge Philosophical Transactions only a short time before his death, has been the subject of some adverse criticism at the hands of Sir W. Thomson and of Mr Bryan. The question is indeed a very difficult one; and I do not pretend to feel complete confidence in the correctness of the view now to be put forward. Nevertheless, it seems desirable that at the present stage of the discussion some reply to the above-mentioned criticisms should be hazarded, if only in order to keep the question open.

The argument to which most exception has been taken is that by which Maxwell (Scientific Papers, ii. p. 722) seeks to prove that the mean kinetic energy corresponding to every variable is the same. In the course of it, the expression (T) for the kinetic energy is supposed to be reduced to a sum of squares of the component momenta, an assumption which Mr Bryan characterizes as fallacious. But here it seems to be overlooked that Maxwell is limiting his attention to systems in a given configuration, and that no dynamics are founded upon the reduced expression for T. The reduction can be effected in an infinite number of ways. We may imagine the configuration in question rendered one of stable equilibrium by the introduction of suitable forces proportional to displacements.