NOVEMBER 10, 1899. ] 
named the statement above assumption A shows 
that he has in mind an assumption B. This 
latter, however, he does not attribute to Boltz- 
mann. It is his own, and is of a character to 
show that he is entirely undismayed by the diffi- 
culties of the Kinetic Theory in its ordinary 
form. Assumption B is proposed as asubstitute 
for assumption A, and it runs as follows: 
‘The chance of a given molecule having at 
any instant assigned velocities is not independent 
of the positions and velocities of all the other 
molecules at the instant. On this assumption 
B, instead of deducing the chance of the mem- 
bers of a group of 7 molecules having respec- 
tively at any instant the velocities wy --- uv, + dw, 
etc., from the assumed chances for individual 
molecules, we must reverse the process.’’ Ac- 
cording to this assumption ‘‘the chance that 
the x velocity of the first molecule shall lie be- 
tween u, and uw, + du,, whatever be the positions 
and velocities of the other n—1 molecules, is 
+ oo 
i f (da, dary  d2n dv,dw, du, dwn ) 
KF yy Uy Wn)? 
He does not introduce this complication out of 
pure wantonness, nor is he in this particular 
ease making an effort to get, in his own phrase, 
‘as near an approach to chaos as is possible in 
an imperfect world.’ It is his hope by means 
of assumption B so to generalize the Kinetic 
Theory as to make it fit the case of a vapor ap- 
proaching liquefaction. A few quotations will 
indicate some of the aims and results of his 
discussion. Thus on p. 46 under the heading 
Finite Forces, by which phrase he means to 
exclude the case of ‘rigid elastic bodies,’ which 
exert infinite force upon each other at collision, 
he writes, ‘‘I propose to prove in this and the 
next chapter that in a system consisting of 
molecules of finite dimensions in stationary mo- 
tion, it is not true for molecules very near to 
one another, that the chances of their having 
velocities between assigned limits are inde- 
pendent, as condition A assumes; but, on the 
contrary, if the forces be repulsive, they tend to 
move on the average in the same direction,’’ etc. 
In 399, under the heading ‘Concerning the 
Maxwell-Boltzmann Law m,a,2—m,a,? = ete.,’ 
that is, the law which asserts that the mean 
_ SCIENCE. 
687 
kinetic energy of the molecules of one species 
of particles is equal to that of the molecules of 
any other species at the same temperature, we 
have, ‘‘It seems therefore to follow that the 
law m,c,2—=™m,q,2, etc., cannot hold universally. 
It can be accepted only on the authority of the 
great physicists by whose name it is known.”’ 
In 3107, ‘‘It follows from this result that”’ 
** *® ‘(the system would tend more and more, 
with increasing number of molecules in a given 
space, to assume the form of a number of 
denser aggregates, say clouds, moving through 
a comparatively rare medium.’’ On p. 112, 
after a passage similar to that just quoted, but 
containing other particulars, we have ‘‘ Such is 
the process which our analysis leads us to ex- 
pect. Physicists may consider how far it cor- 
responds with what is known to take place in 
gases under condensation, or on what (if any) 
farther hypothesis it may be made to corre- 
spond with it.’ This last quotation is espe- 
cially significant as to the point of view from 
which the whole book is written. 
The last chapter (X.) is devoted to Thermo- 
dynamical Relations. It contains, with con- 
siderable matter descriptive of the speculations 
of others, the author’s kinetic ‘proof of the 
second law’ of thermodynamics in accordance 
with ‘assumption B.’ His proof with assump- 
tion A was published in 1876, and Mr. G. H. 
Bryan,* who has made an exhaustive study of 
such efforts, declares it to be the simplest proof 
based on the ‘ Boltzmann-Maxwell law of dis- 
tribution of speed.’ But the wayfaring physi- 
cist who is seeking an excuse for avoiding an 
encounter with the new and more general proof 
offered by Mr. Burbury will find it in another 
remark made by Mr. Bryan in the conclusion 
of his report.+ ‘‘Although many of the re- 
searches mentioned in this report are not infre- 
quently called dynamical proofs of the Second 
Law, yet to prove the Second Law, about which 
we know something, by means of molecules, 
about which we know much less, would not be 
in consonance with the sentiments [judge the 
unknown from the known] expressed at the 
end of the last paragraph. The most conclu- 
sive evidence for regarding Carnot’s principle 
*B. A. Report, 1891, p. 85. 
{ Idem, p. 121. 
