THEORY OF VISCOSITY AND THERMAL CONDUCTION, IN A MONATOMIC GAS. 289 
On integration this gives T p~" <3 - constant, or, since p = BET, it is equivalent to 
= constant; this is the law of adiabatic expansion for a gas which possesses only 
translational energy. 
Eliminating - Q- and ^ ^ from (27) by means of (20) and (28), we have 
(29) AU 2 C 2s = 
v at T at 
1 . 8 . 5 ... (2s + 3) ( 1 V +1 
15 
2 h m 
cu n . dv „ . dw ,. 
+ (2* + 5)(3p + ^ + 
ox cy c>z 
. 1 • 3 . 5 ... (2s+5) 9 /_1 V+1 ' ~ 
or 
(30) 
45 \ 2 hm / 
(2 hm ) s+1 45 
o cro u 9 f u dw 0 
"N 'N / 5 
ox cy cz 
^ ^ 
I .8.5... (2.v-j-5) 2i J = 2 -"-- 
ox cy oz 
By transformation of axes, or otherwise, we may deduce the equation 
(31) 
■ '"N '"N 
- cr,, . oiv, 
-- — A2VWC- S = 3 (+ 
1 . 3.5 ... (2s + 5) 2 v ■ \cz di 
§ 4. The Effect of Molecular Encounters. 
§ 4 (A) In this paper our primary concern is with simple gases containing molecules 
of one kind only ; the difficulties are much enhanced when molecules of two kinds are 
present, especially as regards the equations of transfer, and the final determination 
of the coefficients of F when AQ has been calculated. These matters will be dealt 
with in a future paper, on diffusion and the general theory of composite gases. In 
the calculation of AQ, however, there is scarcely any advantage in making the 
restriction to one kind of molecule only, and it is convenient to carry out the 
calculation for a composite gas in order that the results may be quoted without 
repetition in the later, more general, investigation. 
The notation of § 2 may be adapted to the case of a composite gas without further 
change than the addition of suffixes 1, 2 to denote to which group of molecules 
a sjunbol such as v , to, U, V, W , f, F refers. The mean velocity of the two groups 
will be supposed the same, so that (u 0 , v 0 , w 0 ) is the same for both, either 
separately or together ; similarly, their temperature or mean energy, and their 
relative densities (pjv-?) are supposed constant. All the remarks made concerning 
f and F hold both for J\ and F l5 and f 2 and F 2 , these being functions respectively 
of (U l5 Vj, W[) and (U 2 , V 2 , W 2 ); they may each now be expected to involve v x : v 2 
and m x : m 2 in addition to the quantities mentioned in § 2. A further important 
consideration which did not arise there is that J\ and f 2 , or F x and F 2 are similar , 
