178 On some Questions in the Kinetic Theory of Gases. 



to Prof. Boltzmann) that the behaviour parallel to y and z 

 (though not the number) of particles whose velocity compo- 

 nents are from x to x + dx, must obviously be independent of 

 x, so that the density of " ends " in the velocity-space diagram 

 is of the form f(x). F(y,z). The word I have underlined 

 may be very easily justified. No collisions count, except 

 those in which the line of centres is practically perpendi- 

 cular to x (for the others each dismiss a particle from the 

 minority ; and its place is instantly supplied by another, 

 which behaves exactly as the first did), and therefore the 

 component of the relative speed involved in the collision.-! which 

 ice require to consider depends wholly on y and z motions. 

 Also, for the same reason, the frequency of collisions of various 

 kinds (so far as x is concerned) does not come into question. 

 Thus the y and z speeds, not only in one x layer but in all, 

 are entirely independent of x ; though the number of par- 

 ticles in the layer depends on x alone. Prof. Boltzmann's 

 remark about my quotation from De Morgan will now be 

 seen to be somewhat irrelevant so far as I am concerned, 

 though he may (perhaps justly) apply it to some of his own 

 work. 



Sixth. As to the Mean Path, though 1 still hold my own 

 definition to be the correct one, I would for the present 

 merely say that Prof. Boltzmann entirely avoids the state- 

 ment I made to the effect that those who adopt Maxwell's 

 definition, which is not the ordinary definition of a " mean," 

 must face the question " Why not .... define the mean 

 path as the product of the average speed into the average 

 time of describing a free path ?" The matter is, however, of 

 so little moment, that a very great authority, whom I con- 

 sulted as to the correct definition of the Mean Free Path, told 

 me that the preferable one was that which lent itself most 

 readily to integration. 



Seventh. In his remarks upon the effect of external poten- 

 tial, Prof. Boltzmann does not defend his proof to which I 

 objected, but gives a new and fearfully elaborate one. And 

 he quotes, as a remark of mine on this entirely different 

 proof, the phrase "this remarkable procedure" which Iliad 

 applied to his objectionable old one ! He also treats in a dis- 

 paraging manner the assumption on which my very short in- 

 vestigation is based ; viz. " When a system of colliding par- 

 ticles has reached its fund slate, ire may assume that on the 

 average for every particle which enters^ and undergoes collision 

 in, a thin layer, another goes out from the other side of the 

 layer precisely as the jirst would have done had it escaped col- 

 lision.'" Of course it would be easy to make a 20 page proof 



