342 DR. S. CHAPMAN ON THE LAW OF DISTRIBUTION OF MOLECULAR VELOCITIES, 
between p and T agrees much more closely with Sutherland’s law p T l/s (l+S/T) -1 
than with any other; for example, Schmitt* has found that the law is valid for 
hydrogen and helium from — G0° C. to 185° C., and Barus has shown that it holds 
good for air over a wide range of temperature. The law has not been tested, for the 
former gases, above 185° C. 
This seems to indicate that for the kinetic theory of gases at ordinary temperatures 
the best molecular model is an attracting sphere, and it is interesting to notice that 
this model is the one used by van der Waals with such success in deducing his 
famous law. Further confirmation is supplied by the excellent agreement between 
the values of the molecular diameters deduced on this hypothesis from the constant 
b of van der Waals’ law and from the viscosity by means of my formula (250)— 
cf. § 12 (F). 
At low temperatures Schmitt*, BESTELMEYERf, Vogel* and others have shown 
that the observed values of p are greater than those predicted by Sutherland’s 
law. This may be compared with the rise in the value of p when the pressure is 
greatly increased, both effects probably having a like cause ; in these states, when the 
mean free path of the molecule is much reduced, the molecular paths may cease to be 
approximately rectilinear between collisions, and multiple encounters will grow in 
importance. Since our theory rules out. these contingencies, its results cease to be 
applicable, and a modification of the theory and its postulates is necessary if a proper 
account of these phenomena is to be given. In regard to this, one point which should be 
noticed is that in § 9 (E) a term f 2k (y) in f k ( rij ) was neglected (cf. (211)) which, if 
retained, would cause the law connecting p and T to take the form 
r p7a 
'“*1+(S/T)+/(T) 
where f (T) can be expanded in the form AT -2 + BT~ 3 + .... This term is due to the 
effect of the attractive forces in producing deflections without the occurrence of 
collisions, and is probably always small; but it may readily be seen that it is always 
positive, and that this correction would lead to a diminution in the theoretical value 
of p at low temperatures. Clearly, therefore, the observed discrepancies cannot be 
attributed to our neglect of this small quantity.§ 
* Schmitt, ‘Ann. d. Phys.,’ 30, p. 399, 1909. 
t Bestelmeyer, ‘Munich dissertation,’ 1903. 
\ Vogel, ‘Berlin dissertation,’ 1914, where full references, and an interesting discussion of low 
temperature work on viscosity, are given. 
§ Vogel, in his dissertation, suggests as possible causes of the failure of the theory to represent the 
observed variation of y with T at low temperatures (i.) a failure of the ordinary mechanics, such as is 
contemplated in Planck’s theory of quanta; (ii.) that the attracting sphere model no longer represents 
the molecule; (iii.) that 1+S/T should be replaced (according to my suggestion in ‘Phil. Trans.,’ A, 
vol. 211, p. 474, 1912) by 1 + (S/T) ± (C'/T) 2 . By the latter means a better accordance with observation 
is obtained, but the new term has the minus sign, and is therefore illegitimate. 
