THEORY OF VISCOSITY AND THERMAL CONDUCTION, IN A MONATOMIC GAS. 321 
Molecules which are Point Centres of Force varying as r~ n . 
§ 9 (B) When the molecules are point centres of force varying inversely as the 
power of the distance, the angle y in the expression (146)— cf. § 4 (D)—is given by 
the following integral* :— 
n 
(181) 
X 
V- 
— 9 
( [l x ] v ‘dr]. 
Jo 
Here % is the least positive root of the equation [l — >/ 2 — (>//«)" x ] = 0, and a is a 
multiple of p, thus, 
(182) 
fn —1 y-Von \-zt In— 1V _ V, 
a ~ P \4K?J ~ P ( Km ) ' K "~ ’ 
where K is a constant which measures the intensity of force between two molecules 
at unit distance. Hence {cf (ill)) 
where n A /c is a constant depending on n and k, but not on y or h (i. e. , not on the 
absolute temperature). 
When this value of f k (r y) is substituted in our expressions for h rs and c rs , it 
becomes possible to execute the integration with respect both to x and to y in terms 
of gamma-functions. Thus {cf (165)) 
(184) I e y 'f k {ry) ?/ 2(ra+1) dy = {m+%) m K 
Jo 
m — 2k, k 
n -5 
/ 1 \a i) / 2 
-Way r K 2 -^ 
so that 
(185) 
— TV — _-V2 A 
— xv 0,1 — 1 5” n 1 *-! 
'll - 5 
X \2 (n— 1) 
2 hm) 
r U 
n— 1 
* Cf. § 14, p. 454, of my former memoir, ‘Phil. Trans.,’ A, vol. 211 (1911). The V 0 of the formula 
there given is the relative velocity of two molecules, which in our notation is (/^iaW ^Cr = 2C E when the 
gas is simple. 
2x2 
