146 Proceedings of Royal Society of Pdinhurgh. [jan. 30 , 
Fifth, As to my proof (so designated) of the Maxwell Law of 
distribution of velocities : — I have already explained that this part of 
my paper was a mere introductory sketch, intended to make into a 
connected whole a series of detached investigations, and therefore 
contained no detailed and formal proofs whatever. Maxwell’s 
result as to the error-law distribution of velocities, being universally 
accepted, was thus discussed in the briefest manner possible. I said 
also that a detailed proof can be given on the lines of § 21 of my 
paper. Prof. Boltzmann* at first accused me of reasoning in a circulus 
vitiosus, and went the extreme length of asserting that the inde- 
pendence of velocities in different directions can do no more than 
prove the density (in the velocity space diagram) to be dependent 
on the radius vector only. Now, when I have taken the trouble 
to point out briefly and without detail what I meant by the state- 
ments he misunderstood, he says I have admitted that my proof is 
defective ! For my own part, I see no strong reason wholly to reject 
even the first proof given by Maxwell ; and it must be observed 
that although its author said (in 1866) that it depends on an 
assumption which “ may appear precarious,” this did not necessarily 
imply that it appeared to himself to be precarious. The question 
really at issue was raised in a very clear form by Prof. Newcomb, 
who was the earliest to take exception to my first sketch of a 
proof. He remarked that it seemed to him to possess too much of 
a geometrical character {i.e. to prove a physical statement by mere 
space-reasoning), while Maxwell’s seemed to involve an unauthorized 
application of the Theory of Probabilities. In consequence of this 
objection I examined the question from a great many points of 
view, but I still think my original statement correct. What I said 
was “ But the argument above shows further, that this density must 
be expressible in the form 
f{r)f{y)f{z) 
whatever rectangular axes be chosen passing through the origin.” 
In my second paper I said (in explanation of this to Prof. Boltz- 
mann), that the behaviour parallel to y and 2 (though not the 
* This addition to Prof. Boltzmann’s first attack on me seems to have 
appeared in the Phil. Mag. alone. It is not in either of the German copies 
in my possession (for one of which I am indebted to the author), nor do I 
find it in the Sitzungsbericlite of the Vienna Academy 
