DR. S. CHAPMAN ON THE KINETIC THEORY OF A COMPOSITE 
194 
where 
(20-04) 
( r , 
s) = fj 
e -m+y 2) x 2yi 
(20’05) 
rl 
C4/1212 
( r , 
s) = N r _ 1 .._ 1 K 1 v a j 
| e~ (x2+y2) x 2 y 2 
(20-06) 
d 
Uj 2U2 
(r, 
s ) — N r _i iS _i^ 1 r 2 j" 
j" e -n a +r) x 2y2 
k = 0 
k = 0 
k = 0 
There are similar equations in which the suffixes 1, 2 are interchanged, which need 
not be written down. 
From a comparison of (20'01) with (20'02), (20‘03) we obtain the following 
equations for S T , S _ r :— 
(20'07) 32D 0 — 2 [{dnn{r, s) + d 1212 (r, s)} S r + d 2 U 2 {r, s) §_ r ] = 1, 
V 0 0 
(20*08) 32D 0 — 2 [d 1221 (r, s) S r + {d 2222 (r, s) + d 2121 (r , s)} <L r ] = -1. 
"o o 
In these equations s ranges from 1 to co (that the zero value is excluded may be 
readily seen from § 2 (c), (e)). Similarly r effectively ranges over the same values, 
since it is clear from (20'04)-(20'06) that d( 0, s) — 0 in all cases.* Hence the 
equations (20'07), (20‘08) do not enable us to determine S 0 and S_ 0 , which are given 
by (3’10l), (3'102) in terms of the remaining cTs. Indeed, to obtain T' 0 in terms of 
qw / oo oo 
~ ~, by means of (3*151), we need only to calculate 2 rS r or 2 rS_ r ( cf. (3'122)). 
ct 1 1 
Symmetrical determinantal expressions for these can be deduced as in § 5, if desired, 
but we shall be content here to determine S' Q to a first approximation only. 
The two central terms of the two central equations of type (20'07), (20’08) are 
(20'09) 32D 0 i[R„i(l, l)+dm,(l, 1)} \+d m2 (1, l)i_J = 1, 
(20-10) 32D 0 —d 1221 (l, lR+{0 2222 (l, l) + d 2121 {l, l)}«Li]=-l, 
"0 
and it may readily be seen that 
(20-11) <Wl, 1)= TTjVK'.ao), 
144 
(20-12) <4»( 1, 1) = ./K' 32 (0), 
(20 13) di2n (l, 1)— ^]22l (l, l) = ^2121 (l) 1 ) ~ ^2112 ( 1) 0 = ^ ]2 (0)- 
When r or s is zero, k = 0, and = 0. Cf. (4 - 17), 
