Re fr activity and Atomic Interaction. 531 



radius r. The equation is of a rather complicated kind. It 

 is, however, conveniently solved by the process of successive 

 approximations which leads very rapidly to a more than 

 sufficiently correct result. In this manner*, and substituting 

 for a the values (J.) and for R the values (20), I find from 

 {22), for the atomic radii of hydrogen, oxygen, and nitrogen, 

 respectively, 



r H = 1-085, r = 1-501, ^=1-534 . 10~ 8 . . (23) 



These radii of the atomic spheres are based upon R and the 

 free-path diameters equalled, approximately, to 2/y. 



Let us still consider the Boyle-diameters of the molecules. 

 These diameters enter through the volume of the molecules 



and will thus be given by — ( -~ 1 = volume of the two 



atomic spheres minus that of the lenticular region of over- 

 lapping. The latter could be easily calculated. Having, 

 however, once replaced the diatomic molecule by the ellipsoid 

 of revolution (21), let us keep to this substitute. Thus we 

 shall have 



ia B = (ab^ = (r + ^nyi s r 2/B . . . . (24) 



By means of this formula, and using the interatomic dis- 

 tances R, we can predict what the Boyle-radii of the 

 molecules should be. Let us take for this purpose the set 

 (23) of atomic radii r which we have obtained a moment 

 ago. Then, with R substituted from (20), formula (24) 

 gives 



H 2 o» N 2 



i-<7 B = 1-260 1-711 1-785. 10" 8 , . . . (25) 



while the values actually deduced from the deviation from 

 Boyle's law are (Jeans, p. 342, not containing 2 ) : 



!<7 B = l-26 1-77. 10" 8 . . . . (J.) 



The agreement is surprisingly good. Thus the free-path 

 values a appear connected with the Boyle-values cr B through 

 the dispersion theory. 



In view of this result we shall adopt, for the kinetic radii 

 of the atoms of hydrogen, oxygen, and nitrogen our above 

 set (23), retaining ultimately but two decimal figures, i. e. 

 r ? = l-09, r o = l-50, ?y=l-53.10- 8 . . (23a) 



The reader will have noticed that the interaction-theory 

 of dispersion is entirely independent of these radii, and, in 

 fact, of any concepts of size or shape of the molecules and 

 of their component atoms. For in this theory the atom 

 plays only, thus far, the part of an (optical) centre or point, 

 * Using- a five figure table of log F a . 



