334 I)R. S. CHAPMAN ON THE LAW OF DISTRIBUTION OF MOLECULAR VELOCITIES, 
In the case of the actual gases for which S has been determined, it has an extreme 
range from about 50 to 250, while the range of absolute temperature over which 
experiments are usually made is from about 50° C. to 500° C. Thus the limits 5 and A 
are rather extreme values of S/T, but from the above table it appears that the variation 
in 2/3„ 2y r or their quotient hardly exceeds 1 per cent, over this range. The variation 
is especially slow in the neighbourhood of S/T = 1. 
§11. Viscosity and Thermal Conduction. 
We now proceed to apply the expression for the velocity-distribution function 
(§ 8 (B)) to the determination of the coefficients of viscosity and thermal conduction. 
We shall first obtain general formulae for these coefficients, true for any monatomic 
gas, afterwards considering special molecular models in conjunction with the results 
of §§ 9, 10. 
The Coefficient of Viscosity. 
§ 11 (A) The system of pressures at any point of a gas is given by the equation 
(231) T xx = P \f, P, y = pUV, &c. 
By means of (5) and the velocity-distribution function (142), we find that 
(232) p„ = pi? = + 
= ^~i£^i CnG °^ yr ' 
(233) 
Since, by (74), 
we have 
P — _ 1 
xy 30 hm " 12 
CioC 0 2y,. 
Cxi + C 2 2+C 3 3 — 0, 
(234) 
+ P +P 
: 1 yy 1 z 
3 p 
2hm 
= P> 
p being the hydrostatic pressure as usually defined. 
By comparing (232), (233) with the equations giving the system of pressures in a 
viscous fluid having a coefficient of viscosity p, viz., with 
(235) 
P _ ~ 2/o duo dv 0 dw 0 
xx 1 3M ' dx dy dz 
P 
(236) 
P = 
xy 
-p 
dv 0 du, 
dx dy 
= ~amc 12 
