196 
DR. S. CHAPMAN ON THE KINETIC THEORY OF A COMPOSITE 
last factor in I A is nearly equal to unity, so that we shall neglect it in our approximate 
calculations. In this case, therefore, 
T) 0 
T — 1 1Jn 
-*-A. 3 T) / * ' 
Jbi/m 
For oxygen the value of D u ° is approximately 0'19 (cf Jeans’ treatise, p. 335), 
while Tt/m = 260 . 10 4 ( loc . cit., p. 131). Hence I A = 0'24. 10 -7 approximately. 
Thus if the density-ratio of the two gases is changing by 1 per cent, per second, the 
difference of temperature, if they are equally mixed (i.e., X 1 — X 2 = |-), is approxi¬ 
mately one thousand-millionth of a degree centigrade.* The hotter gas is the 
one which is diminishing in relative concentration. In fact, we may perhaps regard 
the slightly excess speed of the molecules of this gas as the cause of its relative 
expansion and consequent rarefaction. It is clear from these figures, however, that 
the phenomenon is likely to be of very minute dimensions in ordinary cases. 
* Thus T' 0 = AjA 2 (T t - T s ) = J (Tj - T 2 ) = - 0 • 24. KP 7 ~° = -0*24.10~ 9 , so that T, - T 2 = - 10"® 
ot 
approximately. 
Note A. (To p. 118, line 3.) 
[Since this paper was communicated to the Royal Society, this part of the theory has been 
experimentally tested and confirmed, at least qualitatively. An account of the preliminary qualitative 
experiments, made by Dr. F. W. Dootson, will be found in the ‘ Philosophical Magazine,’ xxxii i , 
p. 248.— Note added February 22, 1917.1 
Note B. (To p. 118, middle.) 
[Recently I have succeeded in proving the identity of u and sin ttx with the determinants referred 
to, using elementary algebraical methods. The construction of a formal justification of the analytical 
methods used in the present paper is also being proceeded with, and I hope to be able later to deal 
with the questions of convergence raised here, and to bring the present theory into satisfactory relation 
with that based on Boltzmann’s equation.— Note added February 22, 1917.\ 
Note C. (To p. 129, line 2.) 
[In a later paper it will be shown that considerations of convergence require a re-grouping of the terms 
in these expansions, so that they become series of polynomials in C 2 . The expansions are really used in 
this form in the present paper, the re-grouping of the terms being effected by means of the difference- 
transformations described in § 5 (d).—-Note added February 22, 1917 .] 
Note D. (To p. 189, line 12.) 
[Since the above was written the indicated result has been qualitatively confirmed in the case of three 
pairs of gases. The time taken to attain the steady state was only a few hours in the experiments 
referred to; they are described in a Note by Dr. F. W. Dootson and the author in the ‘ Philosophical 
Magazine,’ xxxiii, p. 248 .—Note added February 22, 1917.] 
