184 
DR. S. CHAPMAN ON THE KINETIC THEORY OF A COMPOSITE 
(d) The Approximate Value of D T when n- 1 = <x 2 and mjm., is very large. 
The case considered in the last sub-section is realised physically in a metal or gas, 
among the molecules of which are found free electrons. Another case of physical 
importance is that in which the molecules are similar except in mass, m l jm 2 being 
large; the diameters of ordinary molecules do not differ greatly, while their masses 
may be widely different. Thus the diameters of the oxygen and hydrogen molecules 
are approximately 178.10 -8 and 1'33.10~ 8 respectively, the ratio of their masses 
being 16. If in our first approximation to D T given by (14'03) we insert the values 
of K^fO), Tc u &c., appropriate to rigid elastic spherical molecules, and write o- x = <r 2 , 
Hi — 1, Hz — 0, the result is 
D t 
15A X A 2 _3_ lmi+m 2 X 1, 
4(9 + X.,)l6^ (<Ti + <r 2 ) 2 \ hm 1 m 2 J 
approximately. 
The corresponding value of e 0 (9T5) is 3A x /(39 +X 2 ), so that 
and 
D 12 
39 + \ 2 _ 3 
4(9 + A 2 ) 16i/ u (ct- 1 + o- 2 )‘ 
'm 1 +mN l3 • , i 
- -- , approximately, 
(14'07) D t = I) 12 , approximately. 
o 9 “h A 2 
Thus when A x = X 2 = \ , D T /D 12 becomes 0'095, which is nearly equal to the 
maximum value for this particular gas. When A x or X 2 vanishes, so also does D T , 
another instance of the general theorem on which remark has already been made. 
( e ) General Remarks and Numerical Values. 
It is now evident, from the special cases treated in the preceding sub-sections, that 
the importance of the phenomenon of thermal diffusion, as compared with ordinary 
diffusion, is greater or less according as the difference between the molecular masses 
and diameters is large or small. If the mass and diameter of the one set of molecules 
are very large compared with those for the other set, D T rises to about ^ D 12 ; if there 
is a large inequality in mass, but no difference in size, D T is about xoD )2 at most # ; 
if mass and diameter are both the same for the different molecules, D T = 0, which 
is also its limiting value when X x or X 2 tends to zero, and its invariable value when 
the molecules are Maxwellian. 
The following are a few values of Dt/D^ corresponding to typical pairs of actual 
* See Note E (p. 197) for the case of nearly equal masses and very unequal sizes. 
