THEORY OF VISCOSITY AND THERMAL CONDUCTION, IN A MONATOMIC GAS. 287 
neglecting in each case quantities of the second order. Since Q is of the first order, 
to the same degree of accuracy as in the above equations, we have 
^ (rQ) = 0. 
Again, writing u = U, v — V, w = W after differentiation, we have 
|Q) = C“ + 2sU , C s, '- u = i (2s+ 3) C“ = L 3 - 5 ---(2s + 3) / 1 
duJ 3 \2hm 
Here we have omitted UVC 2(s_1) and UWC 2(i_1) , since when multiplied by X, which 
is of the first order, the result is of the second order, and hence negligible. 
Similarly 
= 0 . 
The equation of transfer consequently takes the form 
(24) AUC 2s 
1 . 3 . 5 ... (2.9 + 3) / 1 V f 1 
3 2 hm) 1.2 hm 
dv 9/ 1 \_Lv + 9/ 1 \\ 
dx V dx\2hm! m SV dx\2lim)\ 
When s = 0, this becomes 
AU 
2 hm dx dx \2 hmj m 
Now mAU is the rate of change of momentum per unit volume due to the 
molecular encounters, and, since action and re-action are equal and opposite, this 
change is zero. Hence we have, remembering that ( 2h)~ x — ItT = p/v, 
(25) 
which is one of the equations of pressure of the gas. 
On substituting the value of X given by (25) into (24), the latter may be written 
(26) 
(2 hm)' +1 3 A 0 o, 1 9T 
1 .3.5... (2s + 3) s v T dx 
where we have used the equation (cf. 8) 
9 / 1 
2 hm 
dx \2hm 
1_ 9T 
T dx ' 
There are two equations similar to (26) giving AVC 2s and AWC 2s in terms of dT/dy 
and 9T/9z. 
2 E 
VOL. CCXVI.— A. 
