MONATOMIC GAS: DIFFUSION, VISCOSITY, AND THERMAL CONDUCTION. 145 
Also in V (b mn ) and V r (& mn ) we may in this case omit the central row and column, all 
the elements of which are zero (if r^O) except the central element, which is the 
same in each (b ); we suppose that this is done, so that V and V, become determinants 
which possess no single central row or column, just as with V (c mn ). We will consider 
the two central columns of V (b mn ) and V (c mn )j corresponding to m = ± 0. We have, 
by (512)-(518), (4-35>-(4’38), and (6'03), 
(6-06) 
s > 0, 
7 . _ 1 B 0 1 
^0s A T) „ , l ®0,i + l/ 
Aj AlqJAi S + I 
= (0) {n +5 W2 (3 Ml s +^+^, w A 2 »)}, 
(6'07) 
s < 0, 
&-os — Q 75 P> B 0 K 12 (0) {v 2 + 5^1^ (3m 2 +Mi + l/“iM 2 &i 2 °)}> 
(6-08) 
s>0, 
b -“ = ~ TiHf (0) (1 + »*■ A 
(6-09) 
■s < 0, 
h, = i^B 0 K' 12 (o) ft V 2 (i+WU 
(6'10) 
s> 0, 
qO 
C 0J - ^C 0 K' 12 0) [3^ k n °+2w 2 {lO^+SM)], 
15 
(6'11) 
5> 0, 
qo 
C_o s = ^ ^3 27T/A 2 1/ 2 C 0 K 12 (0) ( 1 Omi + 3/A^io ), 
(6'12) 
s < 0, 
qo 
c 0s = — s 27T ) a 1 J/ 1 C u K' 12 (0) ( — 10^2 + 3^12°), 
15 
(6'13) 
s < 0, 
c_ 0s = ||7rC 0 K' 12 (0) [3r 2 ft 2 ° + 2^,1 (10^2 + 3^°)]. 
15° 
All these quantities, it will be noticed, are independent of s; thus we see that in 
V (b mn ) and V (c mn ) the elements of the two centre columns take only four distinct 
values, all the elements of these columns which are in the same quadrant having 
the same value. 
By using the method of differencing by rows it is easy to prove, as a consequence 
of the property of V (b mn ) and V (c mn ) which we have just established, that 
(614) ft = 0 (r>2, r<—2), y r = 0 (r>l, r<-l), 
while (cf. (6-05), (614), (314)), 
(615) 
(616) 
7o 
ft = -ft - 
C-oo C Q-o 
C_qoCq_o Cq O C_ 0 _q 
*>-0-0 ^-00 ; 
&_oo^o~o ^oo^-o-o 
7-0 
G)0 ^0-0 
A-o — A-i — 
CoqC_o-o C 0 _ 0 C_oq 
b,a—b, 
CO u 0-0 
&0—0^-00 ^OO^-O-O 
