MONATOMIC GAS: DIFFUSION, VISCOSITY, AND THERMAL CONDUCTION. 187 
of the gas is steady—and expressing the result in terms of X, and X 2 instead of X 0 
and X'„) 
(16-02) 
(16’03) 
Since 
(16-04) 
^ = 2AX,X 2 (X,-X J )-i T 02|T j 
= 2/,x l \,(X = -X l )4/- T 'V«i. 
dx dx 
±U\ = _0_AA = L _ h 0x -2 = 
dx\vj dx\\J \ 2 dx dx 
we may re-w r rite (16"02) or (16"03) in the form 
(16-05) A(V) = 2A'J(X,-X 2 )-i*, 
or 
(16-06) 
A] T - X 2 0A, 1 0A| 
2 n 2 
Xo 2 0# Xo 2 dx ’ 
V 2 
^2 
0X 
8 log (vjv 2 ) _ 2/^ (X — X )— ^ ^ 
0# 12 gaj 
If the temperature and external forces are uniform, from ( 16*06) and the two 
similar y and z equations we may deduce the integral 
(16-07) 
— ( V -l \ e 2 A {(Xi-X 2 )i+(Y,-Y,)y+(Z 1 -Z 2 )^} i 
* v 2 Vo 
which is a well-known result directly deducible from the statistical theory of 
distribution of density in a gas. # If the external forces are gravitational, the z axis 
being vertically upwards, 
X = Y = 0, Z, = —m x g, Z 2 = —m^g. 
and, if g be regarded as constant, we have 
D _ / D \ g-2 hgz(mi — m?) 
v 2 \vj 0 
The heavier gas, naturally, is relatively denser in the lower strata, the amount of the 
effect being greater the greater the inequality of ma,ss and the smaller the temperature. 
In the case of the atmosphere, since the molecular masses of oxygen and nitrogen are 
nearly equal, the magnitude of this imperfection of diffusion is but small. It is found 
that the change in the value of vjv 2 would amount only to about ^ per cent, per 
kilometre, t 
* Cf. Jeans’ ‘Dynamical Theory of Gases ’ (2nd. ed.), p. 91 (234, 235). 
t Cf. Jeans’ treatise, § 369. 
2 D 
VOL. CCXVII.-A. 
