786 Mr. R. H. Fowler on the 



§ (2) . Sutherland's S and van der Waals a.— It is well 

 known that both the constant S introduced by Sutherland* 

 into the formula for the viscosity of a gas, and the constants 

 of van der Waals' or Dieterici's equations of state f express 

 the effects ofintermolecular attractions. On the assumption 

 of "spherically symmetrical" molecules — i.e., that the 

 molecules are spheres and that the attractive force <j>(r) 

 between two molecules depends only on the distance r 

 between their centres and acts along the line joining them — 

 Chapman % has shown how to obtain an exact expression for 

 S in terms of cj)(r) and known constants. The most complete 

 determination of a in terms of </>(r) with which I am 

 acquainted has been made by Keesom §, but no attempt 

 appears to have been made to compare together both 

 theoretical and experimental values of a and S. This is the 

 more to be regretted as the quantities a and S may be taken 

 to refer to gases in identical physical states. A strict 

 comparison of theory with the experimental values of a and 

 S is then legitimate, and should lead to results of interest as 

 to the nature of the law of intermolecular attraction under 

 these conditions. 



When we come to compare a with experiment, we must 

 remember that our theoretical calculations only apply to gases 

 at reasonably large dilutions, that is to cases in which the 

 departures from the perfect gas laws are moderately small. 

 In order to make a reliable comparison between theory and 

 experiment we must therefore be certain that the observations 

 and calculations do actually apply strictly to one and the 

 same state of the gas. The calculations used really always 

 present the equation of state of a gas in the form 



pv =mT+lf(T)+ofy l] , (1) 



* Sutherland, Phil. Mag. ser. 5, vol. xxxvi. p. 507 (1893) and suc- 

 ceeding vols. 



t Jeans, ' The Dynamical Theory of Gases,' ed. 3, chap. 6 (19^1). 



+ Chapman, Phil. Trans. A, vol. 211. p. 460 (1912). The actual 

 formula given by Chapman is affected by an algebraical slip. The 

 correct expressions have been given by C. G. F. James, Proc. Camb. 

 Phil. Soc. vol. xx. p. 447 (1921), and previously in part by D. Enskog, 

 Inaugural-Dissertation, Uppsala 1917, p. 95. 



§ Keesom, Proc. Sect, of Sciences, Amsterdam, vol. xv. (1) pp. 240, 

 256, 417, 643 (1912). 



|| 0(-^) is a convenient and comprehensive notation for "terms ot 



order 1/y 2 , which may therefore be neglected for values of v which are 

 sufficiently large." This is a satisfactory paraphrase of the strict 

 mathematical definition of 0, to which of course I adhere throughout. 



