1888 .] 
Prof. Tait’s Reply to Prof. Boltzmann. 
143 
genau dieselben Voranssetziingen zu Grunde gelegt, welclie aucli 
Herr Tait maclite, nur dass icli liber die relative Grosse der Durcli- 
messer X und A der Molecule beider Gase, sowie liber den Grossen- 
werth des Verlialtnisses : H2 niclit die mindeste Annahme 
gemaebt babe.” 
Tliis is so far from being tbe case, that it was precisely bis assump- 
tions, and not bis proof, wbicb I disputed. My remark was; — 
“I tbink it will be allowed that Prof. Boltzmann’s assumptions, 
wbicb (it is easy to see) practically beg tbe whole question, are 
tbemselves inadmissible, except as consequences of the mutual im- 
pacts of the particles in each of the two systems separately. 
Of course, with bis assumptions, Prof. Boltzmann obtains tbe 
desired result : — baving in them virtually begged tbe question. He 
now blames me for not having said a word in refutation of bis proof, 
for I bad professed my willingness to allow its accuracy without even 
reading it. There was no discourtesy in that remark : — nothing but 
a cheerful admission that, in tbe hands of Prof. Boltzmann, such 
premises could not fail to give tbe result sought. My comments 
were in fact necessarily confined to the assumptions. For, as I 
could not admit them, the proof founded on them had no interest 
for me. Professor Boltzmann assumed that two sets of particles, 
even if they have no internal collisions, will by their mutual collisions 
arrive at a state of uniform distribution in space, and of average 
behaviour alike in all directions. This may possibly be true, but it 
is certainly very far from being axiomatic, and thus demands strict 
proof before it can be lawfully used as a basis for further argument. 
In quoting my remarks on this point Prof. Boltzmann very signi- 
ficantly puts an “&c.” in place of tbe following words: — “it is 
specially to be noted that this is a question of effective diameters only 
and not of masses : — so that those particles wbicb are virtually free 
from the self-regulating power of mutual collisions, and therefore 
form a disturbing element, may be much more massive than tbe 
others.” It was of this preliminary matter, of course, that I spoke 
when I wrote the following sentence, which seems to have annoyed 
Prof. Boltzmann : — 
“ I have not yet seen any attempt to prove that two sets of 
particles, which have no internal collisions, will by their mutual 
collisions tend to the state assumed by Prof. Boltzmann,” 
