THEORY OF VISCOSITY AND THERMAL CONDUCTION, IN A MONATOMIC GAS. 297 
The unit term in (l+Fi + F 2 ) may be omitted. 
§ 5 (C) It is easy to show that the part of (63) which arises from the unit term of 
(1 + Fi + F 2 ) in (64) is zero. For it may be written in the form 
where 
(pi>iv 2 /ui/u 2 (AwIq/t ) 3 C R p dp de, 
0 = ffffffiQi (U'i, V'i, W'O-QiiUj, V 1; Wi)} e-^^+W dU l d\J l d\N l d\J 2 dV 2 d\N 2 
J J J J J J 
Now by (45) and (55) the latter is equal to 
(65) [jjjjj Ql (U' l5 V\, W\) e~ h(m ^‘ + ^ dU\ dvh dW\ d\j' 2 dv' 2 dW' 2 
| [Qi (Ui, Vi, Wi) e - h(mC ' 2+ ' M dlh dVi dWi d(J 2 dM 2 dW 2 . 
But the latter two integrals are equal, since they are definite integrals differing only 
in the symbols used to denote the variables. Hence (65) is zero, and the unit term 
in (1 +Fi + F 2 ) may be omitted from A 12 Qi. 
The same result can be seen also in another way : the part of A 12 Qi under 
consideration is that obtained by putting F x = F 2 = 0 in fif 2 , i.e., it is equal to the 
value of A 13 Qi in a uniform gas. In a uniform gas, however, as we may see from the 
general equation of transfer (19), AnQi = A J2 Qi = 0, whence the result follows at 
once. 
If Q(U, V, W) is of odd degree, the even part of F (U, V, W) contributes 
nothing to A 12 Q, and vice versa. 
§5 (D) We may now, therefore, write A 12 Qi. in the following form, transforming 
the variables (lb, V l5 W L ), (U 2 , V 2 , W 2 ) to (X 0 , Y 0 , Z 0 ), (x R , Y r , Z b ), by (56), (58). 
(66) A 12 Qi = 
e ftm « (c o‘ 2 + c h>(F 1 + F 2 ) C R p dp de d U t d V i h Wi d U 2 d V 2 d, W 2 
= Dr 2 (miMi) 1/2 
\ 7 T 
{Q\ — Qi)e ~ hvl ° (c ° 2+ c k 2) ( Fi + F 2 ) C R p dp dedX 0 dY 0 dZ 0 dX R dY R dZ R . 
We here suppose the functions Q (U, V, W) and F (u, V, W) expressed in terms of the 
new variables and (in the case of Qb) of e and X 12 ( or p)- are concerned both as 
regards Q and F only with terms which are integral in the variables U, V, W ; in 
reckoning their degree we shall make no distinction between Ui and U 2 , &c., or 
2 s 2 
