-220 Dr. L. Silberstein on Dispersion and the Size of 



integer satisfying the condition (13) is k = 1. Consequently 

 we shall attribute one dispersive electron to each hydrogen 

 iitom, i. e. put 



& = e:=l-83.10 10 . , . . . . (H) 



Introducing these values of k, Jc Q into formula (12) we 

 find (as the unique positive root) 



ab = 0-4932 (15) 



Thus the condition of stability, (14), is amply satisfied. 

 Substituting this value of ab , and the above b, g for H 2 in 

 (8), we find, for the atomic coefficients of hydrogen, 



6 = 0'7719; # =0-325 5 . 10~ 10 c.G.s. . . (16) 



Thus the atomic refractivity iV of hydrogen, which may 

 conveniently be denoted by H itself, will be 



H = 0'7719+ '^~^(>^ in microns) . . (16 a) 



A- 



Notice in passing that the free wave-length \ = \h 

 belonging to a hydrogen atom is equal (#o/^o) 1/2 5 by (5), 

 that is, by (16), 



A, H = 6*494. 10~ 6 cm. = 649*4 A.U., . . (17) 



much beyond the Lyman region. 



Applications of the above atomic refractivity of hydrogen 

 will be given at a later opportunity. In the present note 

 I should like to draw the reader's attention chiefly to the 

 interatomic distance which follows from the above results. 

 From (15) and the first of (16) we have o-=a/27rR, 3 = 0-6389, 

 where a = 4*88 . 10~ 24 . This gives for the central distance 

 of the two atoms in a molecule of hydrogen 



R= 1-067. 10" 8 cm (18) 



Now, the remarkable thing about this distance is that it 

 approaches very nearly the values of the semidiameter of 

 a molecule of hydrogen (considered as an elastic sphere), 

 obtained by various methods based on the kinetic theory of 

 gases. In i'act, these values are *, 



Deviation from Heat- 



Boyle's Law. Viscosity, conduction. Diffusion. 



Semidiameter = 1-025 1*024 0'995 1-01. 10" 8 cm. 



If we were to judge from this single case the coincidence 

 could claim to be one of the order of magnitude only. But 

 the following two cases, of oxygen and nitrogen, will show 

 that there is more than this. 



* Cf. J. H. Jeans's < Dyn. Theory of Gases,' p. 840 (1904). 



