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



where we have written 



p JL. 



^11 T2T 



~rT~ 



In this case, therefore, the constants k are no longer independent of the 

 temperature. It must not be forgotten that these last equations do not apply to 

 vapxmrs. 



PAKT III. DISCUSSION OF THE THEORETICAL RESULTS, AND COMPARISON WITH 



EXPERIMENTAL DATA.* 



16. The principal formulae arrived at in the first part of this wprk are (33)-(4l); 

 they are quite general and involve no hypothesis as to the mode of interaction 

 between molecules (it being always understood that these are spherically symmetrical). 

 Although these formulae indicate certain general laws, which require no knowledge 

 of the nature of the encounters, for the most part the equations can be reduced to a 

 useful form only when the quantities symbolically denoted by P' n , P' 12 , E/ n , k, k lt and 

 k 2 are properly evaluated. This can be done only in certain special cases ; and in 

 Part II. these calculations have been performed for three kinds of molecules, viz., 

 rigid elastic spheres, point centres of force repelling or attracting one another 

 according to the inverse n ih power law, and rigid elastic spheres surrounded by fields 

 of attractive force. The results of these calculations are given in equations (44)-(46), 

 (48), and (52) respectively. 



When the formulae are thus completed, by comparison with experimental data we 

 may find which of these three representations of the molecules best explains the facts, 

 though, as all of them are somewhat artificial and ideal, it is not necessary that any 

 one should excel the others in all respects. We shall find, however, that the third 

 hypothesis (that the molecules are rigid elastic attracting spheres) is, on the whole, 

 much the best of the three. It is, indeed, remarkable that so simple a mechanism can 

 explain so much. 



As it might be considered that the choice of formula allowed by the general 

 nature of our theory may possibly conceal errors due to some weakness in the 

 foundations of the analysis, I shall first consider the cases wherein this latitude of 

 choice is least, beginning with the case where there is none at all. I refer to 

 equation (34), viz., 



which is a perfectly definite relation between three measurable quantities. I shall 



* Part III. has been entirely rewritten in October-November, 1911; much new matter, not in the 

 original Part III., has been added, this consisting chiefly (at Prof. LARMOR'S suggestion) of further 

 comparisons of the theory with experiment. Wherever possible I have used recent data, and I have in 

 particular nude great use of the results obtained by the pupils of Prof. DORN, of Halle, from a well- 

 directed series of experiments on viscosity, diffusion, and conduction. I am indebted to Prof. DORN for 

 tha loan of many reprints and dissertations relating to these experiments. 



