MONATOMIC GAS: DIFFUSION, VISCOSITY, AND THERMAL CONDUCTION. 161 
or (cf. § 1 and (11*01)) as 
0 0 
(12'05) r 0 Xo = - {poUo + p'y,) + — {p 0 U 0 2 + 2p' 0 u 0 u' 0 +p xx } 
+ ^ {p 0 U 0 V 0 + p'o (u 0 v' 0 + u' 0 V o) +p zy } 
+ ^ {p 0 U 0 W 0 + p'o {u 0 w' 0 + u' 0 W 0 ) +P 
\ 
X if 
= v 0 ^ {m 0 u 0 + (m : -m 2 ) u' 0 } + p 0 u 0 ( 
cu' o , , 0wV 
dx dy dz 
I / r pxx I ( Pxr/ I | / q ,t ^P 0 U 0 | o w o . „„/ f, P o^n 
+ I "5- r “5-1- -5— ) + \ U 0 ~5-r v 0 —5-t W 0 -v~ 
dx dy dz J \ dx dy dz 
In deducing the third equation, the equation of energy, it is convenient, first of all, 
to write out the following equations giving the appropriate special values of the 
various quantities which occur in (I2'0l):— 
(12 '06) ^Qi + r 2 Q 2 = \v{rrii (c 0 3 + 2 1,u 0 u' 0 + Ci) + \v 2 m 2 j c 0 2 - 2 'Zu 0 u r 0 + C 2 
— ?Po c o “t p q2'U 0 'M 0 + jRj^oT, 
(12 07) D (^)j Qi "F v 2 (^)a Qa — ^0 ( 2 Po^o "t p q^jUqU q ~t tjTUoT) + zjyj Q U 0 C 0 
+ { U 0 Pxx + V 0 Pxy + W oPxz) + (|-^lUiCi 3 + 1^U 2 C 2 3 ), 
(12-08) -a-xhA-l + ix^A) = .-.w.x.+^x, = 
Wi . \3 (w)i/ m 2 \3 (w) 2 / 
On substitution of these values in (12 *01), this becomes 
(l2 - 09) v 0 {^m 0 c 0 *+(?n 1 “ma) 2w 0 w' 0 + fKT} +^2 (p' 0 c 0 V (0 ) 
^ 0 
+ 2 x— (u 0 p xx + v 0 p zy + Wy,p xz ) — (a/ 3 iUiOi 2 + 2 p 2 U 2 C 2 2 ) 
0a? 
003 
Va£u 0 (X^ X 2 ) — 0. 
This equation can be simplified by eliminating i/ 0 2w 0 X 0 ; thus from (12‘05) we 
deduce that 
( 12 - 10 ) x„z« 0 X 0 = .'.j yj, (*»i—»»j)«'o+(>W( 4 ‘d (l + fr" 
0a; 0?/ 02 
