THEORY OF VISCOSITY AND THERMAL CONDUCTION, IN A MONATOMIC GAS. 309 
(122) c 12 (r 2 +) = 
*4 e- ( ** + * 2 >' + '£*' (-1 )* [# 12 (r i2 y) {p v B k (r + 2, s) + fB*(r+l, s+l) 
+ + 21 B 4 (r, s+2) — 4:(fx 1 fx 2 )~' l 'y 2 (/n^'B 4 (r+1, s) 
+ fj- 2 1 ^'B 4 (?*, s +1 )J + 4 1 B / (?■, s)} 
— 8 {fj-\fJ-o)' l2 y 2( p f,c i 2 {^ny) i^i^B 4 (r +1, s) 
-2 W-VF(r, sJ + ^B^r, s+l)} 
- 16 ,ui//,?/ 4 0 //4 i 2 (t 12 ?/) B 4 ' (r, s)] 2112 «Y clx dy. 
The symbol r in 0* 12 (r I2 ?/) is defined by the equation 
(123) 
T12 
Vh 
vm. 
The integration with respect to a? in the above expressions is of a quite elementary 
nature, but it will not be executed in general terms owing to the complexity of the 
polynomials B 4 (r, s ), which are integral in x 2 . Any individual term in the integrands 
of (119) to (122) is of the form (so far as concerns x) 
[ e~ x 'x 2{m+ ' ) dx = 
Jo 
The integration with respect to y will similarly not be executed in general; in any 
case, owing to the unspecified functions </> 4 12 (ry), this integration could be only 
formally completed, and until we come to consider special types of molecular models 
we shall be content to leave b (r, s) and c (r, s ) in the above form. 
+■ ' fe (m + i)„ 
(124) 
The Complete Expression for A 12 Q L . 
§ 7 (H) On referring back to § 7 (A), and the definition of b (r, s ), c (r, s), it is clear 
that we are now able to write down the complete expressions for A 12 Qi in the two cases 
we have considered. This involves taking into account all the terms (r = 0 to co) in 
F(U, V, W), with their appropriate coefficients, as in (78), (80); and in order tc 
make the expressions more symmetrical, it is convenient to change the values of Q x 
slightly, by multiplying them by certain numerical factors (cf 26, 30). Thus 
writing 
(125) 
A. 
-l.S-1 
~~ 1.3.5. 
_ 1 _ 
(2r + 3) r . 1.3.5... (Zs + Sjs’ 
“1.3.5... (2r+ 5) .1.3.5... (2s+ 5)’ 
( 126 ) 
