The sarcastic criticism which M. Bertrand (Comptes Rendus, May 4 and 18, 1896) again bestows on Clerk-Maxwell's earliest solution of the fundamental problem in the Kinetic Theory of Gases, together with Prof. Boltzmann's very different, but thoroughly depreciatory, remarks (ib., May 26), have led me to reconsider this question, already discussed by me at some length before the Society. Both of these authorities declare Maxwell's investigation to be erroneous:—but, while Prof. Boltzmann allows his result to be correct, M. Bertrand goes further, and bluntly calls it absurd. He had, in his Calcul des Probabilités, (1888), already given Maxwell's proof as an example of illusory methods. I have the misfortune to agree with Maxwell, and to hold that his reasoning, though not by any means complete, is (like his result) correct. (Trans. R.S.E., vol. xxxiii. pp. 66 and 252.)

I have not found anything in these communications of mine (so far at least as the present question is concerned) which I should desire to retract; but they can be considerably improved; and I think that, by the introduction of the Döppler- (properly the Römer-) principle, the true nature of a part of the argument can be made somewhat more immediately obvious. Also I will venture to express the hope that Prof. Boltzmann may at last recognise that I have, in this matter at least, not deserved the reproach of having reasoned in a circle.