MONATOMIC GAS : DIFFUSION, VISCOSITY, AND THERMAL CONDUCTION. 1 37 
recall that in § 4 ( b ) the value of sN'„ was defined to be r -1 N^ when s = 0 (or N„ 
when r is also zero). Moreover, from (4’26) and (4'36), it is clear that in (5'01)-(5’05) 
the ratio of the factors of a 0 and a_ 0 , or of /3 0 and ft_ 0 has the constant value — 1. 
Consequently, the above equations do not enable us to determine the separate values 
of a 0 and a_ 0 , or /3 0 and (3_ 0 , but only of a 0 — a_ 0 and /3 0 —/5_ 0 , which form single 
unknowns. When these and all the other values of a r and /3 r (r ^ 0) have been 
determined, the separate coefficients a 0 , a_ 0 , /%, /3_ 0 may be deduced with the aid 
of (313) and (314). 
In order to simplify the notation of our formal solutions for the coefficients a, y > 
it is convenient to re-write (5'0l)-(5’07) in the form 
-i 
r = 1 
/3'o 
s + 2 b r _ hs _jj8 r =1 (5 = — 00 to s = 00 , excluding s = 0), 
AjA 2 r = 1 
(5'08) 2 a rs a. r +a 0s (a 0 —a_ 0 ) + 2 a rs a r =1 (s = — 00 to s = co 5 including s — 0), 
f — — 00. 
(5-09) 2 b r+hs+i /3 r -b 
X — — co 
(510) 
(511) 2 c rs y r =1 (±r, ±s range from 0 to co). 
2 b r+ i/3 r — b ~~r~ + 2 b r _ 1 (3 r — 0, 
= — co AiA 2 r = 1 
In obtaining (5'09), (510) from (5'03)-(5'05) we have eliminated f3 0 and /3_ 0 by 
means of (314), and in order to preserve symmetry we have subtracted l/sAi or 
l/sA 2 times the equation (5'05) from (5‘03) or (5’04) respectively. The new symbols 
are defined as follows :— 
(512) s>0 a ot = -a_ 0s = — A 0 N 0s /) 12 (0 1 Si), a rs = — A 0 N„{p 11 (?’ 1 s 1 ) + /> ia (r 1 s 1 )} r>0, 
r 0 
(513) s<0 a 0s = -a_o, = - — K^osp 2 i{OiS 2 ), a„ = - — A 0 N rs {p 22 (r 2 5 2 )+p 21 (r 2 s 2 )} r< 0, 
v 0 
m, 
Vo 
(514) r<0, s>0 a rs = ^A 0 N„p 12 (r 2 s 1 ), a rs = - — A 0 N rs p 21 (ns 2 ) r>0, s<0, 
"0 
m 1 
(515) r>0 b r = —y-K+i.o-^oo), b = -Sr«oo, b r = ^(a r _i, 0 -a_oo) r<-0, 
A 0 U r +1 A 0 xv AylA T +1 
(516) s>0 b s = - 
1_JB0_J_/ X 7 1 B n 1 
Al A (J It s 1 
(^o.s+i - a oo)> ARs + l^ 0 '*" 1 
b - 1 B ° 
\i A 0 R (v +1) {s +1) 
1 B, 
{^r + l.s + l °t>,s + l <^r+l, 0 + ^00) 
. , '" _ \ 1 A 0 K(r+l)( S +l) {ar - , ’ ,+,_O - 0 ' ,+ ‘ + r < °’ 
(517) s> 0 
