THEORY OF VISCOSITY AND THERMAL CONDUCTION, IN A MONATOMIC GAS. 
339 
hypothesis as to the values of /3 0 , y 0 , which were determined from AUC 2 and AU 2 as in 
this paper ; in effect, the later coefficients were neglected, while /3 } and y 0 were obtained 
from the equations (138), (139) corresponding to s — 0. Viewed otherwise, my 
co 
previous formulae were equivalent to (237), (248) divided respectively by 2/c r y r //c 0 
and 2/c 
Br/: 
*r y-r 
Thus the neglected factors in /u. and f were 
2 , 
■ K o7r 
and 
2/3 r 2/c,.y r 
o . o_ 
2 . 
K r y r 
2y r 2 K r fi r 
0 0 
which evidently reduce to unity if we neglect all the [3' 0 and y, after r — 0, without 
any assumption as to the values of /% and y 0 . 
One of the main results of the former paper was that f = -| for all monatomic gases, 
and not only for those composed of Maxwellian molecules. This is now seen to require 
modification, but the values here found for f in the special cases which have been 
considered in §§ 9, 10 show that the correction needed to make the equation accurate 
is very small; it appears probable that for all likely molecular models f is very 
slightly greater than 2‘5, and that it is nearly but not quite constant with change 
of temperature (except when the molecules are elastic spheres or centres of force 
proportional to r~ n ). 
Comparison of the Formula for n and b tvith the Results of other Theories. 
§ 11 (F) The only kinetic theory of viscosity a,nd thermal conductivity which could 
hitherto lay claim to numerical accuracy (within the limits imposed by the initial 
postulates) is? Maxwell’s theory* of a gas composed of molecules of the kind dealt 
with in § 9 (C). The results of his theory are special cases of the general formulae of 
this paper. 
The theory of a gas composed of molecules which are point centres of force varying 
inversely as the n th power of the distance had not been discussed in detail, previous 
to my own former paper. Rayleigh, t however, from considerations of dimensions 
alone, had deduced the law of variation of viscosity with temperature, and the same 
argument would also show that for such a gas f is an absolute constant (for any given 
value of n). Nothing was known as to the value of this constant, or of the numerical 
coefficient in the expression for /a, and it is a surprising result, which could hardly 
have been guessed a priori, that as n ranges from 5 to oo the value of f should vary 
only from 2'500 to 2'525 approximately. 
The theory for molecules which are rigid elastic spheres exerting attractive forces 
was equally undeveloped. Sutherland £ had taken an important step, however, in 
* Maxwell, ‘Collected Papers,’ vol. II., p. 23. 
t Rayleigh, ‘Roy. Soc. Proc.,’ vol. 6, p. 68, 1900. 
X Sutherland, ‘Phil. Mag.,’ (5), 31, 1893. 
