MONATOMIC GAS: DIFFUSION, VISCOSITY, AND THERMAL CONDUCTION. 189 
absence of external forces; the density, on the other hand, will vary inversely as the 
temperature. 
These numbers are based on the hypothesis that the molecules are rigid elastic 
spheres; for n tb power centres of force the effect would be somewhat less, vanishing 
altogether if n — 5. It seems very desirable that the theory should be experimen¬ 
tally tested ; the effect predicted is of easily measurable amount, and could be further 
magnified by taking a greater temperature range. The magnitude of the concen¬ 
tration gradient is so large as to seem improbable, and it is possible that some 
circumstance has been overlooked which would modify the theory, but I have been 
unable to detect any such flaw. It is difficult to say how long a time it would take 
to reach the steady state, or what influence the constant flow of heat through the 
gas, from the hot plate to the cold, would have upon the phenomenon. (See Note D, 
p. 196.) 
§ 17. The Coefficient of Viscosity. 
The general expression for the coefficient of viscosity is (cf. (11‘06)) 
(17*01) 
C OD 
*i2 — -sirs ^ Z [nyr + ^y-r)■ 
We shall not trouble here to go beyond a first approximation to this expression, 
even this being somewhat complicated. Referring to (9'27), we obtain the following 
result as our first approximation :— 
(17'02) 
5RT CiI'd "t" 2Cj2 J/ l* ; 2 “t C. 2 V 2 
TtK 12 (o) k n C 1 V l + 2 k 12 C I2*'l ,, 2't k 22^2^2 
The values of c 1} c 2 , c 12 , c\ 2 are defined by (9'28)-(9'30). The equation (17'02) is 
identical, except as regards notation, with that given in my first memoir on the 
kinetic theory ( loc. cit., p. 451). When v 2 = 0, the formula reduces to 
(17*03) 
5RT 1 _ 5RT 
TtK'^O)^ 0 xK n 2 (0)’ 
which is the first approximation to the coefficient of viscosity of a simple gas 
composed entirely of molecules of the first kind. Some idea of the accuracy of 
(17‘02) as a first approximation may be gained from the fact that for a simple gas 
the error (i.e., of (17'03)) amounts to only 1'6 per cent, for rigid elastic spherical 
molecules, and less for n th power centres of force (cf. my second memoir, loc. cit., § 11), 
the first approximation being too small. How the error varies with v 1 : v 2 cannot be 
stated without carrying the calculation further, but it is probable that it is always 
of the same order of magnitude, 1 or 2 per cent. A second approximation to k V2 
would replace the last factor of (17'02) by the quotient of one homogeneous quartic 
2 d 2 
