M?- James, Theoretical Value of Sutherland's Constant, etc. 447 



The Theoretical Value of Sutherland's Constant in the Kinetic 

 Theory of Gases. By C. G. F. James, Trinity College, Cambridge. 

 (Communicated by Mr E,. H. Fowler.) 



[Received 28 April: read 2 May 1921.] 



§ 1. In any attempt to deduce, from observations on viscosity 

 and diffusion for gases, facts as to the nature of the intermolecular 

 forces, it is necessary to find the theoretical relation that holds 

 between the so-called Sutherland's constants, and any assumed 

 intermolecular force. It is assumed that the molecule behaves as 

 a perfectly elastic sphere surrounded by a field of attractive force. 

 This is in fact the only known model, capable of satisfactorily 

 predicting the observed laws of variation with temperature of these 

 quantities, at least at ordinary temperatures. The relations in 

 question have been worked out by Professor Chapman in various 

 papers*. His formulae for Sutherland's constants are given on 

 p. 459 of his first paper on the subject. 



It appears however that the formulae in question are affected 

 by a certain error explained below. This mistake affects the rela- 

 tions between Sutherland's constant S for a single gas, and analogous 

 quantities, and the potential of the intermolecular field. It must 

 be definitely understood however that this in no way aft'ects the 

 rest of his theory, or the numerical values of <t, the molecular 

 diameter, obtained. These are in fact deduced directly from observed 

 values of ;S. It is only when theoretical values of ;S become im- 

 portant, that this mistake is of any significance. 



It was suggested to me by Mr Fowler that the correct theoretical 

 determination of this constant is of considerable importance. This, 

 then, forms the subject of this paper. 



It is known, that with fair accuracy the relation between the 

 viscosity [x oi a, single gas and the temperature T is, when T is 

 sufficiently large, 



/xoc Ti/{1 + S/T), 



where S is Sutherland's constant; and can be calculated in terms 

 of the forces in action. Thus if (f) (r) is the potential of the force 

 between two molecules whose distance apart is r. Prof. Chapman's 

 result was 



S = cf> {c7)l3R, 



R being the usual gas constant for one molecule (1-372 x 10~^). 



* Phil. Trans. (A), vol. 211 (1912), p. 432; vol. 216 (1915), p. 276; vol. 217 

 (1917), p. 115. 



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