798 Dr. L. Silberstein on Radiation from 



When the first and second terms only are retained (which 

 even for i = Q or 7 is sufficiently correct), then (47 a) 

 becomes of a similar type to the Moggendorff-Hicks formulae 

 for sodium, lithium, &c. But assuming that i is as large as r 

 say, 15 or 20, we can reject even the second term, writing 



77" 



simply U{= (2i -f 1) — . Then we have, from (47 a), 



H^-ww}' ■ ■ ■ <«•> 



where 9 , 



R =i~- («> 



that is a frequency formula of the Balmer type. 



Thus, the simple typical dispersion (44 a), or the corre- 

 sponding simple series (47), approaches Balmer' slaw asympto- 

 tically, with increasing i. In view of this property it seems 

 legitimate to assert that this dispersion formula expresses 

 something which is essential about spectra, and as such 

 deserves some particular attention. 



Again, the structure of the coefficient E in (47 b) has a suggestive 

 meaning. As has already been stated, it is not the purpose of 

 these investigations to enter upon any intra-atomic mechanisms. 

 But, incidentally, the reader may find some interest in interpreting 

 our formulae electronically. Now, according to either Drude's or 

 Planck's electronic theory of ordinary (molar) dispersion (cf. Drude's 

 Lehrbuch der OptiJc, 2nd ed. 1906, pp. 376-377), the coefficients B 

 in K = K + 3B/(\ 2 — y 2 ) have the physical meaning 



where q is the charge, in ordinary (irrational) electromagnetic units^ 

 and m the mass of the " electrons," or more generally of the 

 electrified particles responsible for the particular term B/(\ 2 — y 2 ), 

 and N the number of these particles per unit volume. In our 

 case, remembering that the part of B is taken over by £>/47r 2 a 2 , 

 the electronic interpretation would give 



y m 



Now, our coefficient E contains, besides a purely numerical 

 factor, precisely the combination b/y 4 which has such an intrinsic 

 and simple meaning on any electronic theory. To wit, by (48), 



7T m 

 where a is the radius of the spherical (atomic) source, or, if 9? be 



