136 
DR, S. CHAPMAN ON THE KINETIC THEORY OF A COMPOSITE 
It may readily be deduced from the above equations that 
(4 35) /°12 ( r iOl) = P 21 Pl 2 (^Ol) = — 'P21 (^Ak)) 
(4 36 ) = P2P12 P1P21 (diS 2 ) = M2P21 ( 0 o 5 2 ). 
Also, in the case of Maxwellian molecules, for which k t = 1 and k\ 2 = k° 12 
(whatever the value of t) we shall have 
(4'37) p 12 (liSj) — 5 p r2 (OjSi) - f7ri/ 1 i/ 2 M 2 2*s(s+f), +1 K'j 2 (o) (Sp-i+^ + ^pJc 0 ^), 
(4‘38) PiaiMi) - 5 /)i 2 (0 2 «i) = — |7rr 1 j/ 2 /x 1 // 2 2 2 s S (s+f) J+1 K' 12 (o) (4 + fF 12 ). 
§ 5. The Symbolic Solution for the Coefficients in / (U, V, W). 
(a) The- Linear Equations for a, /3, y. 
We now refer back to the two corresponding sets of equations (2‘07)-(2'10) and 
(4’0l)-(4'04). For the two members of each pair of corresponding equations the left- 
hand side is the same, so that we may equate the right-hand sides. Also, as regards 
the first two pairs, we may separately equate the parts which contain as factors the 
0T 
independent quantities and —— . Thus we have 
si 'll* 
1 W 
(5'01) — A 0 2 N rs [nqoq { Pn (r^ + p^ (r^)} + m 2 a._ rPl2 (r^)] = 1, (s = 0 to s = c°), 
p 0 r = 0 
1 00 
(5'02)-A 0 2 N rs [m 1 a. r p 21 (r 1 s 2 ) + m 2i u_ r {p 2a (r 2 s 2 ) + p 2 i{r' i S 2 )}] = 1, (s — 0 to 5 = 0 °), 
Pq r = 0 
1 
(5T3) — B 0 2 N \ s [mffp n (r 1 s 1 ) + Pr j(r 1 s 1 )}+m 2 p_ r p 12 (r 2 s 1 )'] = 1, {s = 1 to s = 00 ), 
xv 
VXi r = 0 
(5*04) B 0 2 N',. s [mf rP21 (r ]S 2 ) + m 2 (3_ r {p 22 {r 2 s 2 ) + p 21 (r 2 s 2 )}] = 1, (5 = 1 to 5 = 00 ), 
JXV 2 T= 0 
(5‘05) 
1 00 
B 0 2 sN' rs [m^ rPl2 (r l Sy)+m 2 p_ rPl2 (r^)] = 0, (5 = 0), 
r = 0 
1 00 
(5T6) — C 0 2 N"„[y r {/ 11 (r 1 s 1 ) + /0 'i 3 (r 1 s 1 )}+y_ r/ o , 13 (?’ a s 1 )}] = 1, (s = 0 to s = 00 ), 
Pl r = 0 
(5*07) -C 0 2 N "rsbrp 21 (^ 82 )+ y_ r {p' 22 {r 2 s 2 )+p' 2 X (r 2 s 2 )}~] = 1, (s = 0 to 5 = 00 ). 
V 2 r — 0 
By virtue of (4‘26) and (4’35) the equations (5'0l) and (5'02) are identical when 
5 = 0, while (5'03) and (5‘04) then assume the same special form (5*05); we may 
