142 Proceedings of Boy al Society of Bdinhurgli. [jan. 30 , 
keep constantly in view was to make my papers at least easily intel- 
ligible. 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 Foundations of the Kinetic Theory (for to these 
alone do my papers profess to extend) in a form which renders 
them easily apprehended, 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 discrepancies 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, repre- 
sented 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 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 
jMaxwell’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 Phil. Mag. of April 1887; and of it he says: — 
“Bei Ableitung dieser Gleichung habe ich dort im Ubrigen 
