147 
Prof. Tail’s Reply to Prof. Boltzmann. 
number) of particles whose velocity components are from xiox-\- 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,i2). The 
word I have underlined may be very easily justified. No collisions 
count, except those in which the line of centres is practically 
perpendicular 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 collisions which we require to consider 
depends wholly on y and 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 2 speeds, not only in 
one X layer but in all, are entirely independent of x ; though the 
number of particles in the layer depends on x alone. Prof. Boltz- 
mann’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 v/ork. 
Sixth. As to the Mean Path, though I still hold my own 
definition to be the correct one, I would for the present merely say 
that Professor Boltzmann entirely avoids the statement 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 T The matter 
is, however, of so little moment, that a very great authority, whom 
I consulted 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 potential, 
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 I had applied to his objectionable 
old one ! He also treats in a disparaging manner the assumption 
on which my very short investigation is based; viz. “When a 
system of colliding particles has reached its final state, ive may 
assume that {on the average) for every particle ivhich enters, and 
undergoes collision in, a thin layer, another goes out from the other 
