CONSTITUTED OF SPHERICALLY SYMMETRICAL MOLECULES. 483 



for mixtures as well as for simple gases indeed, the formula has been more often 

 tested for air than for any simple gas. SCHMITT* and others have shown that 

 experimental results fully bear out this conclusion.! 



* 'Ann. d. Phys.,' 30, p. 393, 1909; TANZI.ER (' Verb. Deutech. Phys. Ges.,' 8, 12, p. 122, 1906). 



t THIESKN ('Verb. Deutech. Phya. Gea.,' 8, 12, p. 236, 1906) states that SUTHERLAND'S formula and 

 his own law (see 18 of this paper) are incompitible, although TANZLER'S experiments demonstrate the 

 contrary. 



Note addtd February 15, 1912. 



Later investigation shows that the neglect of the terms of higher degree than the third, in the 

 expression for the function F (p. 441), is not easily justifiable by rigorous analysis. The omitted terms 

 have been considered by ENSKOCJ (' Phys. Zeitschrift,' xii., 58, 1911); his work suffices to show that the 

 fi>n!ml;i' in this paper are correct except as regards a factor which in general is a function of the 

 temperature (only), and in particular cases is a numerical constant. The latter cases include the case of 

 elastic spherical molecules (as pointed out by ENSKOG), and also of point centres of force varying inversely 

 as the n th power of the distance. Thus Lord RAYLEIGH'S theorem (p. 474) can be rigorously established. 



I have endeavoured to form a numerical estimate of the correction factors to be applied to the formulae, 

 but the analytical difficulties involved have thus far proved unsurmountable. The expressions obtained 

 do not converge rapidly, and the calculations are very laborious ; but the problem is now perfectly definite, 

 and improved analysis may remove the difficulties. 



The present theory must therefore be regarded as approximate only. In conjunction with ENSKOG'S 

 work, however, it provides rigorous proofs of the relations connecting viscosity and conductivity with the 

 pressure and molecular diameter and mass, and in special cases also with temperature; the relations 

 themselves are well known in the case of simple gases, but not in that of compound gases. The numerical 

 constants are not rigorously determined, and are subject to correction ; but the agreement with experiment 

 seems to show that the approximation is a good one. 



Lastly, it should be remarked that the theory of diffusion is unaffected by the terms omitted, so that 

 the above statements do not apply to it. 



