THEORY OF VISCOSITY AND THERMAL CONDUCTION, IN A MONATOMIC GAS. 3 1 7 
The ratio of these two expressions is given by 
b rs + 1 ) _ A 
C rs (^ S + 1 ) S + 1 
where A is a quantity independent of r and s. When s = 0, as we have seen, 
b rs +1) and c rs (|-s + 1) become identical with b rs and c rs respectively. Hence 
K = A 
C r0 
and since B 0 and C 0 have been chosen so that b m = 1 , c 00 = 1 , the value of A must be 
unity. Hence, when s is even and r ^ s, 
(s+l)b rs (^s+l) = c rs (|s+l), 
with the consequence that 
^r0 — C r0 
as a special case. 
It is convenient to introduce the notation 
(165) 
f e (ry) y‘ 1 "* 0 dy = fir‘'*(m+|)»K,,_ ai , to 
->0 
so that if <p 2k (ry) had the value unity, the value of K m _ 2t-A . would also be unity, by 
(159). In terms of this notation (163) and (164) may be written as follows : — 
(166) 
(167) 
Mio+1) = 2~ (r+s+3) B 0 .t t S s + V\i Z r _.C 
K. 
2 ^ r- s v -'t- lv r—s—1, |s+l) 
S+ 1 {(s + -f) s+2 } 2 « = o 
«»(*»+1) = 9 ■ 2- (r + ,tB C 0 w, ; r _»C,K,_,_«,„ + ,. 
U S +^b + 2 J- 1 = 0 
By writing t = r—s — t' it is evident that 
(168) 2 „_,C ( K r _,_ a , +1 = 2 r _.C,K,, h+1 . 
1=0 1=0 
By giving to r and s in (166), (167) the value zero, we have 
(169) b 00 = ^ 5 B 0 rxK 0il , c 00 = ^ 5 C 0 J> 7 rK 01 , 
whence, remembering that (cf. (147)) B 0 and C 0 are so defined as to make b M and c, 
each equal to unity, we have 
(170) 
ft — 2.25. 
-L>n — a. 
1TV 
K 0>1 ’ 
On = 25- 
1TV. 
K 0il ’ 
T} — iiP 
-Dq — 4^0* 
