288 DR. S. CHAPMAN ON THE LAW OF DISTRIBUTION OF MOLECULAR VELOCITIES, 
Case II Q = u 2 (u 2 +v 2 +iv 2 ) s . 
§ 3 (C) Making approximations and reductions as in Case I., we have 
!M, - !(«“, - |.(jj-)'" 
dk (^Q) = dh „ {U 3 C 2s + 3w 0 U 2 C 2 * + 2sU 3 (u 0 U + r„V + ?t? 0 W) C 2(s - :) + ...} 
/d Of* /d Of* 
dx ' " ax 
d 
d- m 0 (C 2(s+1) + gsC 2(s+1) ) = 
_ 1.3.5... (2s+5) f 1 V 
ca; 
SS+1 0^ n 
2 hm dx ’ 
3 
3 
dd ( vV Q) = dd v {U 2 VC 2s + c 0 U 2 C 2s + 2sU 2 V (?/, 0 U + u„V + ?r„W) C 2(s_1) + ...} 
c# oy 
3 
= f v Vo (iC-^+A s C»^ 1 >)*= 
cy 
1.3.5... (2.s + 5) ; / 1 V +1 0Up 
15 ^ 2/wn 3?/’ 
02 
(k?rQ) - 
1 . 3 . 5 ... (2g+5) / 1 V +1 3^o 
15 \2 hm) 02 
[p) = 2UC 2 *+2sU 3 C 2(s ~ 1) 
\3 u! 
'3Q 
°> 1 >1 = °’ 
oQ' 
CJ = °- 
The equation of transfer may therefore he written 
(27) 
ALTO" = l:. 3 --A:-.(^f.3_) „ MV +I 
15 
\2 hm) L U dt 
[13 
1 3T 
5r^ + (Ul)^ 
T dt 
+ (2s + 5) ( 3 + ~~ + 
ox oy oz 
When s = 0, this becomes 
AU 2 = 
2 hm 
1 ^ t ^ rp r\ ~ 
_£di 131 . o du 0 , dv o Qjg„ 
> 3c T 3c 8x ‘ 3y 02 . 
If to this be added two similar equations giving AV 2 and AW 2 , on the left-hand 
side we have A (U 2 + V 2 + W 2 ), which is the rate of change of molecular energy due to 
encounters ; by the principle of conservation of energy this is zero, so that 
or, by (20), 
(28) 
o,l 3, 1 3T 
dt + T dt 
/ 3mo , 3r„ 
dx oy 
+ 5 + 
OWy 
~~5 
cz 
= 0, 
1 8T _ 2 ( du 0 dv 0 ' dw 0 \ _ 2 1 dv _ _2 1 dp 
T dt 3 \ 3a; dy 3 z I ^ v dt 3 p dt 
