Spectra and Planck's Law. 427 



on the magnetic boundary of the atoms in (2). In other 

 words, 



[m. + ^y (1 + S) 2 ' 

 so that the series (3) could be written in the form 



The difference between the limiting frequencies of the 

 series (1) and (4) is thus 



C \(m + 8')*~(l + 8) 2 ) 



and this, as we see from (1), is the gravest frequency of the 

 principal series. 



Comparing this result with the Rydberg- Schuster law 

 that the gravest frequency of the principal series is equal 

 to the difference in the limits of the principal and first 

 subordinate series, we infer that the series (4) represents the 

 first subordinate series. Just as in the previous case we may 

 have atoms which are neutral, i. e. which contain the normal 

 number of electrons, and also atoms which have lost one 

 electron and thus have unit positive charge. The positions 

 of equilibrium for these are not the same as for the neutral 

 atom, and the frequencies will therefore be represented by 





ot) (5) 



This has the same limit as (4), and therefore corresponds to 

 the second subordinate series. If there are atoms which 

 have two positive charges there would be another series with 

 the same limits as (5), but with a different step between the 

 various lines ; or, again, if instead of being positively charged 

 the atom were negatively charged, I. e., had got one more 

 electron than the normal, and in some gases (such as, for 

 example, hydrogen and the electronegative gases oxygen, 

 chlorine, and iodine) these, as Positive Ray Analysis shows, 

 are plentiful, there might yet be another series again with 

 the same limit but with a different step from any of the 

 preceding series. Thus, on this view, one of the subor- 

 dinate series, the one connected with the principal series, 

 would be emitted by uncharged atoms, while other subor- 

 dinate series would be emitted by charged ones. 



