144 Proceedings of Royal Society of Edinburgh, [jan. 30 , 
I think it probable that Prof, Boltzmann has not fully appre- 
hended the meaning of the word ‘‘assumed” in this sentence. 
Otherwise I cannot understand why he is annoyed because I took 
his proof for granted. 
In taking leave, for the time, of this special question, I need 
scarcely do more, and I cannot do less, than reaffirm the assertion 
just quoted : — while adding the remark that this is very far from 
being my sole objection to Prof. Boltzmann’s very general Theorem. 
In fact Professors Burnside * and J. J. Thomson f have quite 
recently advanced other serious objections. Prof, Boltzmann’s 
Theorem, in a word, is not yet demonstrated. 
Third. As to the questions of viscosity and heat-conduction ; 
my investigations were expressly made on the assumption that 
change of permeability, due to motion, was negligible. When 
I found that I had obtained in a very simple way certain char- 
acteristic results of Clerk-Maxwell and of Clausius respectively, 
I was satisfied with the approximation I had made. Prof. Boltz- 
mann does not allude to the fact that my investigation was 
distinctly stated to be an approximate one only, and that the 
additional consideration he now adduces had been before me and 
had been rejected (rightly or wrongly) for reasons given. I said — 
“ Strictly speaking, the exponent should have had an additional 
term See the remarks in § 39 below.” 
And, in the § 39 thus pointedly referred to, one of the remarks in 
question is — 
“ We neglect, however, as insensible the difference between th-e 
absorption due to slowly moving layers and that due to the same 
when stationary.” 
And, in fact, the result which I gave for the viscosity (and which 
Professor Boltzmann, without doubt justly, claims as his own) is 
correct under the conditions by which I restricted my investigation. 
The introduction of the consideration of change of permeability 
due to the shearing motion involves an alteration of about eleven 
or twelve per cent, only in this avowedly approximate result. Of 
this I have assured myself by a rough calculation, and I will work 
it out more fully when I have leisure. It seems that I missed this 
in looking over Meyer’s book, and, according to Prof. Boltzmann, 
^ Trans, M.S.K, 1887, t Phil Trans., 1887. 
