On some Questions in the Kinetic Theory of Gases, 173 



request, I undertook an examination of Clerk-Maxwell's 

 first proof of his own Theorem. But it is still of a very 

 fragmentary character. I had, years ago, read papers by 

 Maxwell and by Clausius, and had glanced at the treatises of 

 0. E. Meyer and Watson. I had also made a collection of 

 various papers by Prof. Boltzmann. But I found that, with- 

 out much expenditure of time and labour, it would be impos- 

 sible to master the contents of the three last-named works, 

 mainly because the methods employed seemed to me altogether 

 unnecessarily intricate. [I have already stated the impression 

 produced on me by such of Prof. Boltzmann's papers as I 

 have tried to read, and I need not recur to it.] I therefore 

 set to work for myself, having certain definite asserted results 

 in view, but little knowledge of the processes which their dis- 

 coverers or propounders had used. After obtaining a demon- 

 stration of Clerk-Maxwell's Theorem, I was led to pursue my 

 investigations into other matters, such as the rate of restora- 

 tion of the special state, the size of molecules, &c. I brought 

 before the Society such of these investigations as I had more 

 fully developed ; and I hope to communicate others. One 

 object which I tried to keep constantly in view was to make 

 my papers at least easily intelligible. Intelligibility is not too 

 common a characteristic of papers or treatises on this subject. 

 But if I have succeeded in putting some parts of the Founda- 

 tions of the Kinetic Theory (for to these alone do my papers 

 profess to extend) in a form which renders them easily appre- 

 hended, I shall have done a real service to students of Physical 

 Science. The other object at which I aimed was, of course, 

 the verification of Maxwell's Theorem ; and of the extension 

 of it (to all degrees of freedom of complex molecules) which 

 was made by Prof. Boltzmann. Sir William Thomson and 

 myself were., in fact, called to the question by the discre- 

 pancies between the observed behaviour of gases and the 

 behaviour which Prof. Boltzmann's Theorem would have led 

 us to expect. To test this excessively general theorem, I 

 determined to examine certain special cases, and (that these 

 might be, however imperfectly, represented by systems of free 

 particles) it was necessary to assume want of freedom for 

 collision, though confessedly as one step only. I could not, 

 of course, in this way put limits on the excursions or the 

 admissible speeds for different degrees of freedom. 



Second. While examining, and seeking to improve, the 

 proof which Clerk-Maxwell originally gave of his Theorem, I 

 found it impossible to begin without the assumption of a 

 certain regularity of distribution of masses and velocities ; 

 and of course I sought how to justify such an assumption. I 



