1895-96.] Prof. Tait on Clerk-Maxwell's Lain of Distribution. 123 
Note on Clerk-Maxwell’s Law of Distribution of Velocity 
in a Group of Equal Colliding Spheres. By Prof. Tait. 
(Read June 15, 1896.) 
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 Cases, 
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 Probability, (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 Doppler- (properly the 
Rbmer-) 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.* 
1. The following quotation from my first paper (in which I have 
italicized the greater part of one sentence) shows the general 
ground of my reasoning, which was expressly limited to a very 
numerous group of equal, perfectly hard, spherical particles. 
“Very slight consideration is required to convince us that, unless 
* Phil. Mag., xxv. (1888), pp. 89, 177. 
