1920. No. 2. ON THE X-RAY SPECTRA. 4I 



of the deviation 



"'^•iLHilA'' 



l)0th as regard sign and absolute magnitude. On the other hand the 

 assumption I. a gave </ = o, and II. led to values ot d which were onl}- a 

 small fraction of those given by experiments. 



Now we must remember that our theory — so far it has been 

 carried — does not give an exact agreement between observed and 

 calculated values. Thus our calculations will require some small correc- 

 tions, probably due to the fact that our expression of the energy is not 

 quite currect. But if these corrections are due to errors which enters 

 into the energy, the correction terms of the frequency cannot essentially 

 alter the values which the various hypotheses give for the deviation from 

 Kossel's relation. 1 hus the assumption 1. make d identically equal to 

 zero independent of the special form of the energy funktion. And the 

 assumption II. which is merely a slight modification of I will make d 

 approximately equal to zero. 



Thus, as long as we build on the scheme here proposed for the 

 production of x-rays, / ccm see no escape from the (tssumption III, that 

 recombination takes place from secondarij circles {systems) and that alivays 

 the angular momentum of the electrons left behind in the atom is kept 

 constant during expulsion and recombination. 



If the change of energy of the electronic systems outside the broken 

 ring, which accompanies the ionisation process does not escape in the 

 form of radiation, but is utilised for the motion of the escaping electron, 

 we found the frequency of the absorption edge by putting r = co in the 

 frequency formula corresponding to III. a. And it was found that the 

 agreement between calculated and observed values was very good indeed. 



The form here given to the hypothesis of recombination from second- 

 aries cannot only explain the principal («)-linens, but we also give a 

 very close agreement for the second {ß) lines of the ÄT-series. If we 

 further assume that the L-ring has one circular and one elliptic state we 

 may say that the following lines have!been explained: A'^, iTa, Ä'„ the dou- 

 blets of the /.-series (a ß) (y ô) (Sommerfeld's denotation) and finally J/«. 



An explanation of the /-series such as the one given in Paper I. by 

 means of two L-rings is not consistent with the hypothesis of recombina- 

 tion from secondaries in its modified form ; but we shall have to find 

 some other explanation of this series of lines. 



