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



From equations (5) we see that also the assumption of preservation 

 of momentum leads to an equation of the right type; for, as we know, 

 the frequency of an A'-ray line varies with the atomic number in such 

 a way as to approximately satisfy an equation of the form : 



i'=(i-ä-"-^-^"+^- 



(8) 



At any rate this equation will hold for small atomic numbers. 



Now the quant number n- and ;?^ will be determined from the 

 coeffient of N-. 



The number of electrons in the rings must be determined from the 

 coefficients B and C. To make the final test we can by means of the 

 known (or possible) values of >?, j9, q calculate e, and thus find the 



value of ,, corrected for variation of mass. 

 h 



As mentioned in Paper I, we have first of all to find such values of 

 q that we get the right value of the coefficient B. 

 Putting as before: 



<p iq) = rp, {pq)—p ~ q {S,^ - S^_^) + -5,^- i • • • (9) 



our principal equation of condition now takes the form : 



,, „ ^iQr)+Pi ^{Qk)+Pk—Qk , sr^' 'Il 



Vq -D = 7, 5 T Zj — 



2 



10 



In the case of preservation of energy the corresponding equation of 

 condition is (See Paper I. equation 16). 



1/ r,_^(^t^-^P'- '^^ 1k)^V k 



Taking first the important case that recombination takes place 

 between successive rings, we have to put A" ^ ? -|- i, and 



l=k-l 



i = i+i ' 

 Then the equation (10) takes the simpler form: 



'^ ('/, + X.» - V, + I = \"^ ' ) [^ (7,) -+- P, 



P,+ .-''-iBn\^,..{ii^) 



