MONATOMIC GAS: DIFFUSION, VISCOSITY, AND THERMAL CONDUCTION. 159 
faster than the heavier, however, so that relative to the mean motion the heavier gas 
will be diffusing in the direction of increasing pressure. Such a process must go on, 
to some extent, during the passage of sound-waves in air or any mixed gas, and will 
influence the propagation of the disturbance to a degree which is probably comparable 
with that of the effects due to viscosity and thermal conduction. The effects of these 
latter have been examined by Stokes, Kirchhoff, and Rayleigh.* 
It is rather more difficult to perceive, either analytically or physically, that D T 
must be positive if the molecules 1 are the heavier (see Note E, p. 197). A discussion 
of this coefficient will be found in § 14. 
If in (10'11) we assign to u' 0 the value zero, we get the equation of condition for a 
state without diffusion. Some special cases of this equation will be considered in § 16, 
after the relative magnitudes of the various coefficients of diffusion have been 
determined. 
§ 11 . The Equation of Viscosity. 
The various pressure components p xx , p^, et cetera, for the composite gas are given 
by the following and similar equations :— 
(ll'Ol) p xz = v l m 1 V} } 2 j rv 2 m 2 \J 2 \ p xy = r 1 m 1 U 1 V 1 + r 2 m 2 U 2 V 2 . 
A reference to (5'24) or to our expressions for /(U, V, W) in §3 hence enables us to 
deduce that 
1 00 
( 1 1 *02) Pxx—Po — - ^T5 ^ Co C xx N (^Vr + ^V-rX 
(11*03) 
Pxy '6 7 5 2f t 
Cpxy N (v l y r + ly/— r ), 
We may compare these with the equations of pressure of a gas whose coefficient of 
viscosity is k 12 (c/. (2*11 ) and (2*14) for the values of c xx and c xy ):— 
(1104) 
(11*05) 
Pxx~Po — *12 
2 3uo 2 ( du 0 dv 0 9w 0 \ 
dx 3 \ dy 32 /J 
( | 3^0 \ _ 2 
p * - w~ 
xy 
It thus becomes evident that the composite gas behaves like a viscous fluid whose 
coefficient of viscosity is given by 
(11*06) 
*12 — a! J 
Co 
2 h 
2 (I'lYr + ^y-r)- 
0 
* Stokes, ‘Cambridge Transactions,’8, p. 287, 1845; Kirchhoff, ‘ Pogg. Ann.,’ 134, p. 177, 1868 ; 
Rayleigh, ‘Phil. Trans.,’ 175, p. 1883, ‘Theory of Sound,’ II., ch. XIX. 
