THEORY OF VISCOSITY AND THERMAL CONDUCTION, IN A MONATOMIC GAS. 313 
where c n , c ]2 , &c., are given by (72). The coefficients j8 r and y„ for r = 0 to r = oo, 
are given by (140), where (cf (136), (137), (130), (131)), 
(143) b rs = 32B 0 ,X« We-*'* 2 f k (ry) 
[r,s] 
& = 1 
B 2/t (r + 2 , s +1) + B 2/t (r + 1 , s + 2 ) 
+2 ^1ifTT B!it,(, ' +1 ’ s+1)+ 4Tn B ”' ,(, ' +1 ’ s+1) 
x y 2 dx dy , 
— B 2A (r + 1 , s + 1 ) 
(144) c rs = 72C 0 A , w jje-^ 2%* (r^)[B 2 * (r+ 2 , sJ + fB 2 * (r + 1 , s+l) + B* (r, 6 + 2 ) 
2Jc + l 
W 
4&+1 
2 h 
B 2A+1 (r+ 1 , s) + B 2k+1 (r, 5 + l) 
+ (B 2k ~\r +1,6') + B*- 1 ^, s -1) j - (W*(r +1,6) + B 2A (r, 5 +1) 
+ 4+ )' , (2^ + 2) (2k + l) b^+2 / \ 
V t(4& + 3) (4& + 1) [V,S) 
4F + lW*(r,5) 
+ 
( 2 £+l ) 2 
(4&+3) (4A+1) (4/c+ 1) (47c— 1) 
where (cf (123)) 
(145) 
and, by (ill), 
(146) 
2lc (2k —l) a/ \ 
(31+1+4++ B (r ’ s) 
- 2 (!TT b w +) +4 | i b *- 1 +) 
= (2Am) ,/2 , 
x 2 ?/ 2 dxdy 
f k (z) = 2 (4A+ 1 ) 2 {l-P 2/£ (cos x )} B 
J 0 
where P* (cos x) is the usual Legendre’s coefficient, and y is a function oi p and 2 
which depends (§ 4 (D)) on the law of inter-action between two molecules at an 
encounter. The factors A rs and \' rs are defined by (125), (126), while the functions 
B* (r, 6 ), which are integral polynomials in x and y, with merely numerical coefficients, 
are defined by (129) and (96). In the upper limit of Jc, [r, 6] denotes the integral 
part of the lesser of the two quantities \r + 1 , 3-5 + 1 . 
The factors B 0 , C 0 are, as yet, arbitrary; we now assign to them the values 
determined by the equations 
(147) 
K — 1) 
C 00 — 1 * 
This makes B 0 and C 0 each equal to v~ 1 multiplied into a function of ( 2 Am), i.e.f of 
2 u 2 
