252 A Note on Thermal Diffusion. 



assumption that the gas molecules behave like rigid elastic 

 spheres. Using the formulae in the Abstract already cited, 

 the following expressions for k t are obtained*: — 



tt -, , i j. •-, j 33-1XX + 5-42X2 



Hydrogen and carbon dioxide, k t = — — — _ rN , _ go . ■. 



J s ' 47-2 + 86'5X 12 H-5-58\ 21 



67-3X 1 + 5*60X 2 



Hydrogen and sulphur dioxide, k t = 



65-7 + 168X 1 + 4'4V 



The values of k t corresponding to experiments (1), (2), (3), 

 and (5) respectively are consequently approximately equal to 



0-138, 0-101, 0-138, and 0-165. 



The corresponding values of log e T 1 /T 2 , where Tj and T 2 

 are the absolute temperatures of the hot and cold bulbs, are 

 respectively 



0-56, 0-595, 0-515, and 0'554. 



The percentage differences of composition between the 

 two bulbs, calculated from the approximate formula 

 100Jc t ]og e T 1 /T 2 , are as follows: — 



7-7, 6-0, 7-1, and 9*1. 



These correspond to the observed values 



3-6, 1-8, 2*8, and 3;5. 



The signs of! the observed differences are correct in every 

 case, but the magnitudes of the differences are not equal to 

 the theoretical values just given. The experimental results 

 are, of course, not exact, and there is perhaps room for doubt 

 (except in case 5) as to whether the steady state, corre- 

 sponding to the maximum difference of composition, was in 

 all cases attained. The excess of the calculated over the 

 observed differences, however, is easily explicable as arising 

 from the fact that the molecular model chosen as the basis of 

 the calculations is that for which k t has ijbs maximum value, 

 while it is not the model which most closely represents actual 

 gas molecules. The effect of this can be sufficiently illustrated, 

 without going into any very detailed analysis, by the example 

 of a gas in which the molecules of one kind are very small 



* The values assumed for the radii of the molecules of H 2 , C0 2 , and 

 S0 2 respectively were 1*18, T64, and 2*00, the unit being 10 _a cm. The 

 two former values are those given on p. 476, Phil. Trans. A. ccxi. ; the 

 last is assumed, as we do not know of any reliable determination of the 

 radius of the S0 2 molecule. 



