174 Prof. Tait on some Questions in 



was thus led to believe that collisions, not merely of particles 

 of the two kinds with one another but among those of each 

 kind, are absolutely necessary for this justification. Then I 

 saw that, in complex molecules, perfect freedom of collisions 

 of all kinds of "degrees of freedom" could not possibly be 

 secured, and that this might, in part at least, account for the 

 discrepance between Prof. Boltzmann's Theorem and the 

 observed behaviour of gases. I saw also that, for the truth 

 even of Maxwell's Theorem, it was necessary that neither of 

 the two gases should be in an overwhelming majority. Thus 

 these two things, which Prof. Boltzmann now speaks of as 

 "physically less important/' are from my point of view vital 

 to the general truth of his Theorem. 



Prof. Boltzmann commences his recent paper by citing a 

 " general equation " from the Philosophical Magazine of 

 April 1887 ; and of it he says : — 



" Bei Ableitung dieser Gleichung habe ich dort im Ubrigen 

 genau dieselben Voraussetzungen zu Grunde gelegt, welche 

 auch Herr Tait machte, nur dass ich iiber die relative Grosse 

 der Durchmesser X und A der Molecule beider Gase, sowie 

 iiber den Grossenwerth des Verhaltnisses N, : N 2 nicht die 

 mindeste Annahme gemacht babe/' 



This is so far from being the case, that it was precisely his 

 assumptions, and not his proof, which I disputed. My remark 

 was : — 



" I think it will be allowed that Prof. Boltzmann's assump- 

 tions, which (it is easy to see) practically beg the whole 

 question, are themselves inadmissible, except as consequence* of 

 the mutual impacts of the particles in each of the two systems 

 separately.'''' 



Of course, with his assumptions, Prof. Boltzmann obtains 

 the desired result : — having in them virtually begged the 

 question. He now blames me for not having said a word in 

 refutation of his proof, for I had professed my willingnesa to 

 allow its accuracy without even reading it. There was no 

 discourtesy in that remark: — nothing but a cheerful admission 

 that, in the hands of Prof. Boltzmann, such premises could not 

 fail to give the result sought. My comments were in fact 

 necessarily confined to the assumptions. For, as 1 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 axio- 

 matic, and thus demands strict proof before it can be lawfully 



