Molecules of Hydrogen, Oxygen, and Nitrogen. 217 



The simple problem to be treated in the present note, as 

 an application o£ the general ideas laid down in the paper 

 quoted above, will be this : 



Given the molecular ref ractivity N of the diatomic sub- 

 stance, that is, given its coefficients b, g, find the atomic 

 coefficients b , g , and therefore the atomic refractivity i\ 7 0? 

 and also the interatomic distance R involved in a. 



These are three unknowns, while we have in (8) but two 

 equations *. Thus far, therefore, the problem is indeter- 

 minate. In order to convert it into a determinate one, we 

 shall have to make some assumption about the relation 

 between b and g in each atom. For this purpose let us 

 choose the obvious assumption that the value of b 2 /g be- 

 longing to each " dispersive particle " or atomic resonator 

 is equal to an exact multiple of the electronic value of the 

 right hand member of (6). More definitely, if e be that 

 electronic value, let us assume that, for any atom, 



h 2 



~°- = «e, (9) 



9o 



where k is in each case the smallest integer compatible with 

 the conditions of the problem. By "electron" we mean 

 here the electron proper. Remembering that our charges e 

 are in rational units, and taking for the specific charge 



1 etc 



, — . — that value, 1*77 . 10 7 C.G.S., which suits best the 

 \A±7r ru 



observed typical cases of the Zeeman phenomenon and 

 represents, at the same time, the mean of the more recent 



* Theoretically one could say that b , g , a are to be determined from 

 three observed values of N, corresponding to three different wave- 

 lengths. But having once neglected higher powers of g j\ z and having 

 therefore adopted the form (7), linear in X -2 , we have eo ipso reduced 

 any number of observations to two independent data only, b and g. The 

 same would be the case if instead of the straight line (7), representing 

 iVas function of A -2 we had taken a hyperbola analogous to (3). For 

 this would again involve only two independent data. The rigorous 

 curve of N is, by (25 6) he. cit., the superposition of two hyperbolae, 

 viz. 



so that, theoretically speaking, the three unknowns y , B, R could be 

 determined from three observed values of N. The actually available 

 observations, however, are, notably in the case of the gases to be treated 

 here, quite insufficient to distinguish the dispersion curve from a straight 

 line. Thus, for the time being, we are driven by necessity to the linear 

 form (7), amounting to two independent experimental data only, and the 

 third datum must be supplied by some plausible assumption. 



