124 
DR. S. CHAPMAN ON THE KINETIC THEORY OF A COMPOSITE 
If we write Q = 1, since AQi = 0, and 
to 
3 Qi 
d(u\ 
= 0, the equation of transfer reduces 
( 2 ‘ 011 ) 
9*! , 9(riWi) , d(vyVy) , d{vyWy) _ A 
dt + dx ai^ 3s _ 0 
which is the equation of continuity for the first component of the composite gas. By 
adding to this the corresponding equation for the second component, we obtain the 
equation of continuity for the gas as a whole, in the form 
or 
( 2 - 012 ) 
3 (t'j 4~ r 2 ) 9 (vyUy 4~ r^Ug) i 9 (VyVy ^ 2 ^ 2 ) . 9 (VyWy 4~ V 2 IV 2 ) q 
9 t dx 3 y 9 2 
9fo , 9(r 0 M 0 ) 3 (v 0 y 0 ) 9 (v 0 W 0 ) _ Q 
dt dx dy dz 
If at the point under consideration the mean velocity of the gas is zero, the last 
equation may be written 
(2-013) 
1 9 
— 
"o 3Z 
9^0 , dv 0 3 w 0 
dx 3 y 9 z )' 
(b) Qy = UyCy*. 
If in the equation of transfer (2"0l) we assign to Qi the value (w) x (e)i 2s , and omit 
all terms which in a gas of ordinary density are of the second order, we find that 
(2-02) AlfiCW = 1 - 3 - 5 — ( >2g + 3 ) 
vy 
(2 kyniy ) S 
du 0 
3 1 
2h 1 m 1 yy dx m 1 dx\2hymy/A 
We have here used the convention that c 0 = 0 at this particular point and time, 
so that (c)i and C x are identical, and, except in differential coefficients, c 0 can be 
neglected. 
If we multiply both sides of (2"02) by m 1; and add the corresponding equation for 
the second group of molecules, in the case when s = 0 we obtain the result 
A (m.U. + m.U,) = (* + «) + (^ | + 
(nX,+, 2 x 2 ) + Ui S-(A -)+* 
dx\2hy) 2 dx\2h u 
du a 
in "v" , d 1 v, Vo 
(2-03) 
