242 



Dr. L. Vegard on the X-Ray Spectra 



The general equation for the frequency we get by 

 inserting into equation (5 a) the expression for V (equa- 

 tions 3). 



Instead of using the exact expression (3 a) we may 

 take (3 c), which with the first approximation takes into 

 account the variation of the mass with velocity. The 

 expression for the frequency then takes the form : 



- = "° + e 



(5 6) 



i/ is the frequency we should get when the variation of the 

 mass is disregarded, and e is the correction for variation of 



mass. ^ and € are given by the following expressions : 



R=(i-i) N2 - BN+c > 



where 



Kk 



l=k-l 



C = 



Mpw) ^p^ ~ 2 &ti>* + \ - V 2 ) 



> (5 c) 



n h ' 



l=k-l 



+ X ^te+S^-1/2). 



l=i+i n i 



The functions <f> x and $ 2 , which were introduced in my 

 previous paper, are given by the following expressions : 



<Pi{pq) = £(S 2 — s 2 _i) + s 2 _i+^ 



Upq) = ?(%>+s 2 +s 2 _ 1 )(S 2 -s 2 _ ] )-i-(^+s 2 _ 1 ) 



Finally : 



(7) 



-W N =? i )*-<'- 1 )( B ?)'] 



> (5<0 



l=k-\ 



2 ^[(»-«i) 4 -(N-a, + l)*],} 



=t+l l 



where 



a t = pi -f S 2/ , 



