MON ATOMIC GAS: DIFFUSION, VISCOSITY, AND THERMAL CONDUCTION. 119 
The density of the gas is supposed to be such that the mean free path of a molecule 
is large compared with the distance at which molecules appreciably affect one 
another’s trajectories : this we express concisely by terming the gas “ nearly 
perfect.” 
Similar quantities relating to the two groups of molecules will be represented 
by similar symbols, with distinguishing suffixes 1, 2; it is convenient to adopt the 
convention that the first gas is that which has the greater molecular mass. The 
molecular masses will be denoted by m x , m 2 , while the notation for various other 
characteristics of the gas at ( x , y , 2 , t)* is explained by the following list: 
r l5 v 2 = the number of molecules of the first and second kinds 
per unit volume. 
Xu A 2 EE the proportion of molecules of each kind at ( x, y , 2, t). 
Pi, p 2 EE the densities of the constituent gases. 
P l5 P 3 = the external forces (in vector notation) acting on each 
molecule m 2 . 
(Xi, Yj, Zj), (X 2 , Y 2 , Z 2 ) = the same forces in Cartesian notation. 
Ci, c 2 or (ui, Vi, Wi), ( u 2 , v 2 , w 2 ) = the mean velocities of the two groups of molecules in 
vector or Cartesian notation. 
We define further quantities of the same nature, in terms of the above, as 
follows :— 
(l'Ol) r 0 = i'i + i'q, so that \ = vj(v x + v.^) = vjv 0 , A 2 = ^/(u + 'a) — A x + A 2 = 1. 
(l 02) 2A 0 — Aj A 2 , Aj 2 A 1 /A 2 , A 21 ~ Ao/A], so that Ai 2 A 2 j — 1. 
(1'03) m 0 = A 1 w 1 + \ 2 m 2 , m' 0 = X x (m 1 —m 0 ) = -A 2 (m 2 -m 0 ) = AX 2 (mi-wi 2 ). 
Now we have 
(1 *04) P i = vyih, 
so that, by (l'Ol) and (1*03), 
P‘2 — 
(105) Pl) — p x + p 2 — v 1 mi + v 2 m 2 = v 0 m 0 , /fi 0 — ^ Li ' 
AiA 2 
Also, in vector notation P, c, we shall write 
= v 0 (m 1 —m 2 ). 
(1-06) P, = A.P. + A*, F. = \,(p,-ap e ) = -X 2 (P 2 -^P.) = X^(2»p, 
771 0 
rth 
,m v m 0 
(l 07) c 0 — \ x Ci + A 2 c 2 , c 0 — Aj (cj c 0 ) — A 2 (c 2 c 0 ) — AjA 2 (cj c 2 ). 
I.e., at the point ( x, y, z) and at time t. 
