440 Mr. J. H. Jeans on the 



the frequency equation through its square, and expressions 

 which contain odd powers of p must not be regarded as con- 

 tinuous functions of r. Hence the lines in the spectrum- 

 series corresponding to values of n other than n = co , cannot 

 be regarded as forming continuous bands of light *". 



It will be seen that such a group of lines may be regarded 

 as forming two striated bands of light. A line will fall into 

 one band or the other according to the sign of p for the shell 

 with which it is associated, the dark places in one band corre- 

 sponding to the bright places in the other. 



In the case of the real atom, this will give two separate 

 groups of spectrum-series. Each group will consist of a 

 number of adjacent spectrum- series, and the two groups will 

 have (approximately) a common head. The various series 

 correspond to the various shells of ions in the atom ; those in one 

 group correspond to shells of negative ions, those in the other 

 to shells of positive ions. We may imagine the vibrations 

 associated with the innermost shells of ions to be of less 

 energy than those associated with the outer shells, and in 

 this case the lines of a given order (n) in either group will 

 themselves form a series of lines of diminishing brightness, 

 until the lines become so faint as to be invisible. 



The spectrum-series of the real atom which correspond to 

 the ideal spectrum-series of which the heads are given by 

 equation (2±) will similarly fall into two groups, but the series 

 of any groups will be adjacent only if W varies continuously 

 from ion to ion as we pass inwards from the surface of the 

 atom. 



§ 25. It will be at once seen that the arrangement of 

 spectrum-series just found is sufficiently general to describe 

 the arrangement which is known to exist in an actual atom. 

 The adjacent series forming a single group may be supposed 

 to form the series of triplets, double or single lines which 

 occur in observed spectra. The two classes of series corre- 

 sponding to equations (24) and (25) will be the principal 

 and subordinate (or else subordinate and principal) series of 

 the classification of Kayser and Runge. The two sets of 

 subordinate series (the first and second according to Kayser 

 and Runge ; the ' nebuleux' and ' etroit' according to Rydberg) 

 will be the two groups of one of the two classes given by 

 (either) equation (24) or (25). It does not seem possible to 

 identify the various series of our theory with observed series 

 without carrying our theory much further than has been 



* Otherwise thus : — The continuity in the ideal spectrum, in the case 

 of every value of n except w = oo , is effected by the vibrations associated 

 with the thin transition-layers, and these have no actual existence. 



