THEORY OF VISCOSITY AND THERMAL CONDUCTION, IN A MONATOMIC GAS. 
335 
(remembering the meaning of c n , c 12 , &c., as defined in (72)), it appears that the two 
are identical if we write 
(237) 
M = 
1 
10 
hm 
C„2y r . 
Hence, according to the kinetic theory, a gas behaves like an ordinary viscous 
fluid having a coefficient of viscosity defined in terms of the molecular data by (237). 
By (170), (173) we have 
f 
(238) C, = —, 
7 TVKy 
whence, also, 
(239) 
M = 
_5_ 
2 7r JlK 0 
oo 
0 
As we have seen in § 8 (B), k 0 and 2y r are functions of the temperature (or h) only, 
0 
and v does not appear at all in the formula for //. Hence, within the limits of 
applicability of our theory (cf § 2), the coefficient of viscosity of a gas is independent 
of its density, varying only with the temperature. The law of this variation depends 
on the law of inter-action between two molecules at encounter, this being involved 
through ff-ry). As this function has remained unspecified, the expression in (237) 
is perfectly general and valid for any nearly perfect monatomic gas. 
The Equation of Energy for a Simple Monatomic Gas. 
§ 11 (B) In the discussion of the equation of transfer in § 3, we consistently neglected 
such second order quantities as products of differentials, or differentials of small 
quantities like UV, C 2 —3U 2 , and so on. In this way we have obtained an expression 
for the velocity-distribution function which is correct to the first order. By means 
of this function we can now determine the values of UV, C 2 —3U 2 , UO 2 , and similar 
expressions which are of the first order of small quantities, and by substitution in the 
equation of transfer obtain this in a form accurate to the second order. This we shall 
do for the special case Q = (u) 2 + (v) 2 + (w ) 2 , in order to get a second approximation to 
the equation of energy. 
From the velocity-distribution function, using the formula (237) for the coefficient 
of viscosity, we have 
(240) C 2 = 3 (/mi) -1 = SUrT/m. 
(241) 3U 2 —C 2 - -2 ftp) ( 2 ^ 
(242) =-EM (H+!§»). 
2 z 
VOL. OCXV1.-A. 
