Precision-measurements in the X-Ray Spectra. 611 



where S represents the Bohr function 

 p ' 



i—p — 1 



x sin i 

 P 



The basis of this formula may be briefly related : — 

 Debye considers an atom where the first inner electron 

 ring of one quantum holds n electrons. When one of these 

 n electrons is brought to an outer orbit with two quanta and 

 then falls back to the inner ring the a-line will be the result. 

 The best agreement with the empirical values is obtained 

 when n is taken as 3. In the normal state all the atoms 

 (from Na) would therefore have an inner electron ring with 

 this number of electrons 



A somewhat better representation is arrived at when the 

 above assumptions are slightly modified, as has been shown 

 by J. Kroo *. If the two innermost electron rings before 

 replacing are characterized by 



The first ring (1 quantum) with 2 electrons, 

 and the second ring (2 quanta) ,, 9 „ 



-and after replacing by 



the first ring (1 quantum) ,. 3 ,, 



and the second ring (2 quanta) ,, 8 „ 



The calculation of the radiated frequency accompanying 

 this change gives the formula 



r_«i*-i)./i-^ir , 2('+i: 



H, a. 



*/!-*••% +^qp i/i-**F s 



-^1-^-^1-^ .... (5) 



a- 



where Z=3, Z = 8, 



F,=i(N-* + l-S l+1 )», 



F 3 =(N-S,)>, 



F 4 =i(N-£-S ; ) 2 . 



There is only a slight difference between the equations (4) 

 and (5), but the comparison with the measurements speaks 

 decidedly in favour of the Kroo formula. 



* J. Kroo, Phji. Zs. 1918, p. 307. 



