some Constants of the Inert Gases. 71 



In the case of gases, where /lc — 1 is small, 



2 



g=z -(/jL — 1) approximately. 



The refractivities of the inert gases given in the paper 

 quoted above are shown in the sixth column of the table, 



2 



multiplied by ^, and in the last column are shown the ratios 



of the molecular volumes as determined from the viscosities 

 to those derived from the refractivities. The constancy of 

 the ratio in the cases of argon, krypton, and xenon is re- 

 markable, and, considering the dissimilarity of the two 

 methods and the number of assumptions upon which they 

 rest, the concordance between the two sets of values in 

 absolute measure is not less surprising. 



Relation between the Number of Electrons in the 

 Atom and the Radius of the Sphere of Action. 



Till recently the refraction and dispersion of gases have 

 usually been expressed in terms of Cauchy's formula 



1 K • B , C 



^ 1==A _^ + _ 



But in view of the success which had attended the use of 

 a formula of Sellmeier's type 



N 



p-l = 



n — n 



in explaining the observed facts of dispersion in other cases, 

 it was thought better to express the refractivities of the inert 

 gases in this form in the paper quoted above. 



Here N is a constant, n is the frequency of the free 

 vibration of the parts of the atom (assuming there to be only 

 one) and n that of the light whose refractivity is measured. 

 When this equation is transformed into the shape it assumes 

 on the electronic theory, as developed by Drude, N becomes 

 proportional to the number of electrons in the molecule which 

 are effective in influencing dispersion. 



Table II. shows the values of the constants N and n q 

 obtained experimentally *. 



* In the paper quoted above the values for N were doubled for com- 

 parison with similar figures for diatomic gases. The numbers here pfiven 

 are those calculated from the actual observations by the method of least 

 squares. 



