268 Dr. L. Vegard on the X-Ray Spectra 



Putting : 



Pj-1 =c. 



d = [N(c + {qj - 1)6 - qja) + qjO 2 - (q, - l)b 2 - c 2 ] 1/n/ . (26 6) 

 In the case o£ K^. K a , and L a we get : 



<KiX + (r\ - © K , = °' 413 N - 3>53 - (26 ») 



This formula shows that the quantity d is not constant 

 but increases with atomic number. The formula is not 

 exact, because the variation o£ mass is disregarded. 



Having previously calculated the frequencies for the three 

 lines, we can from these values find d. Now, on the other 

 hand, the frequencies derived from observations do not fulfil 

 Kossel's relation identically. They show, in fact, a deviation 

 which is too great to be due to errors of experiment. 



In the Table XVIII. are given calculated and observed 

 values of the deviation d for the lines K^, K a , and L a . 





Table XVIII. 





N. 



<W 



*«L 



30 



4- 5-5 



4-110 



40 



+ 12-8 



4-14-8 



50 



4-23-6 



4-22-5 



60 



4-44-6 



4-379 



It appears from the table that the calculated and observed 

 values of d, both as regards sign and absolute magnitude, 

 agree in a very striking manner. The observed values of d 

 increase with atomic number in the way required by theory. 



This fact, that our theory is able to explain the deviation 

 from KossePs relation, is a matter of the greatest importance 

 and weighs heavily in favour of the assumption of recom- 

 bination from secondaries in its modified form. 



A third Modification of the Hypothesis of Recombination 

 from Secondaries. 



§ 14. In our previous treatment of recombination from 

 secondaries we assumed the electron before starting re- 

 combination to be moving in a stability circuit of its own 

 with quant-number t. We further assumed the secondary 



