470 MR. S. CHAPMAN ON THE KINETIC THEORY OF A GAS 



satisfactory,* it nevertheless forms a useful interpolation formula. The expression is 



(mp + m'pT (PULUJ) 



- s ''-* l2 ' 3 i 



SUTHERLAND, by an argument which though not rigorous is very interesting and 

 suggestive, arrives at the formula 



r H ^ . , (SUTHERLAND, THIESEN), 



1 + Ap ip 1 + 



which THIESEN also obtained by a different method of proof. While, however, 

 THIESEN left the formula as an empirical one, SUTHERLAND strove to find expressions 

 for A and B in terms of molecular constants. He found such expressions, but did so 

 half empirically by a study of GRAHAM'S data. In the case of the gases which he 

 considered, a very fair agreement was obtained. 

 My own formula (39) can be written 



(53) 



M 



where E, F, G, F l are given by equation (39) in terms of /x, //, D 12 (the coefficient of 

 diffusion), and a constant k which depends on the particular law of action between 

 the molecules ; k is unknown, but may be expected to lie near or between the values 

 already found for it in special cases (O'GO for elastic spheres, 0771 for Maxwellian 

 molecules). 



Of the above formulae, that by PULUJ is the only one which is perfectly explicit. 

 THIESEN'S expression is completely empirical, and is useful only as an interpolation 

 formula. PULUJ'S relation shares the virtues and defects of the theory on which it is 

 founded, and therefore prescribes a law of variation with temperature inconsistent 

 with the facts for most gases. THIESEN'S law, on the other hand, does not give any 

 information concerning variation with temperature, and the constants A and B must 

 be empirically determined for each case. 



The formula (34) or (53), as we shall see later, completely expresses the relation 

 between /x 12 and the temperature, but, being quite general, it specifies a different law for 

 each molecular hypothesis ; and while, conversely, the determination of k and the law 

 of temperature variation from experimental data may lead to further knowledge as to 

 the best molecular hypothesis, this very generality gives the formula a semi-empirical 

 character. 



On theoretical grounds it is desirable that the success of equation (34) as an 

 interpolation formula should be tested. Excellent experimental material exists for 

 the purpose. ScHMiTrt has lately given a resumd of an extensive series of experi- 



h Thus it tacitly implies that the viscosity varies as the square root of the absolute temperature (since 

 the theories on which it is based lead to this law). 



t 'Ann. d. Phys.,' 30, p. 393, 1909. Full references to the original sources of the data are there given. 

 SCHMITT was apparently unaware of SUTHERLAND'S formula, but, of course, it is the same as THIESEN'S, 

 if treated empirically. 



