MONATOMIC GAS: DIFFUSION, VISCOSITY, AND THERMAL CONDUCTION. 125 
by (1'18). In this equation the left-hand side is the rate of change of the momentum 
per unit volume of the whole gas at (x, y , z, t) which is produced by encounters 
between the molecules. Since, however, an encounter between two molecules leaves 
their combined momentum unchanged, A (wijlh +m 2 U 2 ) is zero, and consequently 
(2'04) 
0W O 
Jt 
= — X„ 
ffln 
1 
dx 
v 0 m a 
This and the two similar equations in y and z are the equations of mean motion of 
the gas. 
• • • 0^4 
We will now apply (2'04) to the elimination of -r- 2 from (2'02). At the same time 
ct 
we shall neglect the difference between and h 0 , T x and T 0 in products or 
derivatives, since our equations are to be carried only to the first order of accuracy. 
Then (2'02) becomes 
(2-05) - AU.C “ = A 1 y + - X.-X, - xh. +(s+ 1)A( 1' 
1.3.5...(2s + 3) v x 2h 0 v 1 ox m 0 v 0 m 0 dx dx\2h 0 
_ 1 ( 1 + I iW\ + JL /_L\ _ L x' 0 - ^ Po i j — l— 
2/^ 0 Vj/j dx vq dx) dx\2hj \ 0 j/ 0 m 0 dx dx\2h ( 
1 
Xi 
1 d\ n y/ TTl 0 dp I 
o~7 'N ^ 0 -N 
2 hn dx 
r 0 m 0 dx . 
+ Rs 
STo 
dx ' 
Thus, if we write 
(2-06) 
£/ — 1 0^- o _vy _ o ^Po 
* 0 — 2/i/n 0x 0 v 0 m 0 dx ’ 
the equation (2‘05) and the corresponding equation for the second set of molecules 
become 
(2-07) 
(2’08) 
3 (2 hfpm))* 
1.3.5... (2s+ 3) 
3 (2 h 0 m 2 ) s 
3T 0 
dx 
m 
,AU 2 C 2 2i — — v 0 £' 0 T- E>Sr 2 
9T„ 
1.3.5... (2s + 3) ”'' 2 “~ 2 ~ 2 u ' "“' 3 0a: ' 
To this order of approximation, therefore, these equations do not involve T' 0 . 
(c) Q, = U^C*. 
When Q x = U^C! 2 *, the equation of transfer takes the form (cf. § 3 (C) of my second 
paper, loc. cit.) 
(2 ' 09) - 5 »fit + ( * +1)2 *4fe 
+ 
T 2 
