the Kinetic Theory of Gases. 177 



tingency which might possibly occur by collision even with a 

 particle of the gas, certainly by collision with the containing 

 vessel. There is a common proverb, "All roads lead to 

 Rome." It seems it ought now to be amended by the addi- 

 tion, " whether you go backwards or forwards along them." 



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, in- 

 tended 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 dis- 

 tribution 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 independence 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 with- 

 out detail what I meant by the statements 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 as- 

 sumption which " may appear precarious," this did not neces- 

 sarily 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 ob- 

 jection 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 shoivs further, that this 

 density must be expressible in the form 



/(•) /GO/CO 



whatever rectangular axes be chosen passing through the 

 origin/' In my second paper I said (in explanation of this 



* This addition to Prof. Boltzniann'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 Sitzungsberichte of the Vienna Academy. 



