120 
DR. S. CHAPMAN ON THE KINETIC THEORY OF A COMPOSITE 
The corresponding component equations, involving X, Y, Z or u, v, w with 
appropriate suffixes, are similar and will not be written down here. 
By inverting the above equations we obtain the following expressions for the 
original in terms of the derived quantities :— 
( 1*08) 
, m Q 
m x = m 0 + — , 
Ai 
Pa 
= ^Po + 
m 0 
P'o 
Xi’ 
Ci = c u + ^ 
A 1 
(109) 
m' o 
m 2 = m 0 -- , 
^2 
P 2 
_ ^^2 T) 
— P 0 
m 0 
F 0 
X 2 ’ 
C'o 
= C 0 -— 0 
x 2 
( b) The Interpretation of the Derived Quantities. 
Corresponding to (l'08) and (l'09), the motion of the gas can be analysed into (a) 
a steady motion of the composite gas as a whole with velocity c 0 , together with (b) a 
motion of interdiffusion in which the mean velocities of the two streams are 
respectively c'J X x and — c'jx 2 . In this latter motion equal numbers of molecules are 
transferred per unit time in each direction, the number (per unit area normal to the 
direction of the vector c' 0 ) being j/ 0 c' 0 , since by (1'01) 
(no) vic'JXi = v 2 c'J x 2 = v 0 c' 0 . 
The momentum of the common motion (a) is clearly p 0 c 0 per unit volume, while that 
of the motion of interdiffusion is v 0 (m 2 — m 2 ) c\ or, by (1 '05), p' 0 c ' 0 ; in general this is 
not zero, owing to the inequality of mass of the molecules, although the diffusing 
streams convey equal numbers of them in any interval of time. This analysis of 
momentum corresponds to the equation 
(l ll) P]C] + p 2 c 2 — v x m x c x + v 2 m 2 c 2 — p$Cq + p p 0 . 
The equations (1*06) differ from the others by involving the molecular masses as 
well as and v 2 . This resolution of the forces P 2 and P 2 may be considered as 
follows : the first terms (cf 1’08 and 1'09), viz.,— 1 P 0 on m l and — P 0 on m 2 , represent 
w 0 m 0 
forces which will impart a common acceleration P 0 /m 0 to each group of molecules (we 
may regard this variation as affecting their common velocity of streaming, c 0 ); the 
remaining components, T'jx l on m x and — P \jx 2 on m 2 , when summed up over the 
v x , v 2 molecules of the corresponding groups, afford equal and opposite total forces 
i/oP'o, vqP'o. In connection with this we may remember that two such interdiffusing 
groups of molecules as we have considered will exert equal and opposite actions on 
one another, and that equal and opposite forces must be applied to the two groups if 
their motion of interdiffusion is to be maintained, or modified without imparting any 
common velocity to them. 
