MONATOMIC GAS: DIFFUSION, VISCOSITY, AND THERMAL CONDUCTION. 135 
</>, Y r > X (depending on the functional relation between 0 12 and p, y) the integration 
with respect to y can only be made formally , however, and for this purpose we shall 
use the notation 
(4-24) 
K*(«) = 4x /,J 
(t + k + jjr ) 
t + k *'0 
e ,J *<f> k {y) y 2{t+k l) dy. 
The suffix 11, 12, or 22 is to be appended to K* (t) to correspond with the suffix 
of <j> k (y) on the right. The notation is chosen so as to make K* (t) equal to </>* (y) 
when this is independent of y, as in the case of molecules which obey Maxwell’s 
fifth-power law. # 
For small values of r and s it is convenient to simplify our formulae by writing also 
7, = K ; 13 (0 p _ K a u (t) ¥ _ K 2 12 jt) ¥ _ Kf(t) 
(4 25) ^- K ' 12 ( 0 )’ A ' 11 -K' 12 (o)’ A ' 12 -K' 12 (0)’ Aj ”-K / ia (0)’ 
In terms of the above notation we may now give the following results:— 
(4 26) Pn{ r i0i) = pn{^i s i) = 0, Pn(Sili) = Pn (1 1 *^ 1 ) = Lg 7rJ/ f ,5 (' 5 +2")i+i-^ 12 (d) 
n> 
(4-27) 
(4-28) 
(4‘29) 
Pl2 (^ldi) — P 12 (dl^l) — 9 7rl/ l 1/ 2/ u 2-^ ( S “t 2)5 + 1 ^ 12 ( 0 ) ^sh'tP-l 1 P-2 ht 
0 
p\2 — l 7ri/ i 1/ 2Mi2’(^'+|) r+ i K 12 ( 0 ) 2 j .C' (/ u 2 ’ WTc t , 
0 
P 12 (0 2 ^i) — y 7n' 1 v 2 Pi2 (s + -§-) s+1 K ]2 ( 0 ) —i s Qj t p.i t p. 2 t h t , 
(4'30) Pi 2 (sili) = P 12 (li^i) = |™i^2 2s (s + f)5+iK' 12 (o) f2 s CVi‘ V (pA+pA + i) 
0 
s-l 
+ s S^iC^i P 2 (3 Pi h t -\- fx 2 ht +2 T ^>PiPf 12 ) 
( 431 ) ^ 12 (b 2 ^ 1 ) — i) 7vv i v 2 p'f ,s 4 - !) s+ i K' 1S (0) 
(4-32) 
2 “ J S h'tP\ P 2 i^pft ~t pft+l) 
0 
s-l U 
+ spip 2 2 s _ 1 G i/ u 1 fx 2 ( 3 h t -\-Jc t+2 5^*12 > 
P n(di s i) — P 11 (sffii) = f-^v{ (s + -|) s+ 2 K ' 12 (0) 
(4 33) p 12 (Oi^i) — P ]2 {sfi) — 4 g7n / 1 r 2 /X22 S (s + |)i + 2 K- i 2 ( 0 ) WgC^i* P 2 (pft “t 1 \pf l 12)} 
0 
(4 34) ^^(ffiSl) — '4§7r* / 1 l/ 2 /X 2 2 S (s + -f) s+ 2 K-^2 ( 0 ) SjCjytlf V/( pft + fopfhyf 
* Cf. ‘Phil. Trans.,’ A, vol. 216, §9 (C), p. 323. 
