340 DR. S. CHAPMAN ON THE LAW OF DISTRIBUTION OF MOLECULAR VELOCITIES 
deducing the correction to the law connecting p and T (i.e., p oc T 1/-2 ) for molecules 
which are rigid elastic spheres without attraction ; he showed, without attempting 
numerical accuracy, but by a method which is correct in its main outlines, that the 
attractive forces necessitate an additional factor (l+S/T) -1 , as in (249). The law 
p cc T' /2 (l +S/T) -1 is more successful than any other in representing the observed 
relation between p and T over a considerable range of temperature, and S is deservedly 
known as Sutherland’s constant. 
The theory of a gas composed of molecules which are rigid elastic spheres, which 
was taken by Sutherland as the basis of his modified formulae, has been developed 
along lines different from those of this paper by Clausius, Maxwell, Boltzmann, 
Meyer, Stefan, Jeans, and others. Their method was less analytical than the 
present one, and while it gave correctly the general relationships between p, 3-, p, p, 
and T, its results do not possess numerical precision. Jeans* notably improved 
certain of the formulae due to earlier authors by taking into account the tendency 
of a molecule to persist, after a collision, in the general direction of its original course. 
For this reason his expression for the viscosity, viz., 
(252) 
Q'88 m /R t \ iy * 
4 x tt 12 a- 3 \m ) 
(Jeans) 
approaches more nearly to the correct expression (249) than does the formula of any 
other authorf. A comparison of (249) with (252) indicates that the latter is still too 
small by 12 per cent.; the error of the- original formula, without Jeans’ correction, 
was 30 per cent. 
The numerical inaccuracy of the earlier prevailing theory of conductivity, which 
was due to Meyer }, was very great. Its result was generally given as 
S- = fpC v where f — 1‘6027, 
but Prof. L. V. King, of McGill University, has pointed out to me by letter that 
Meyer’s argument really leads to the result 
/= 1-4161, 
a numerical mistake having crept into his work which had not previously been 
detected. The correct value of f for rigid elastic spheres is given in (249), i.e., 
f = 2A25. 
This large error in Meyer’s theory indicates the difficulty of arriving at numeri¬ 
cally accurate formulae by the older “ mean free path ” method, and diminishes 
* Cf. Jeans’ ‘ Dynamical Theory of Gases.’ 
t Apart from that in my former paper, which was 1 • 6 per cent, too small. 
| Meyer’s ‘ Kinetic Theory of Gases,’ 2nd English edition, chap. IX. 
