174 



If the election passes from a state of motion characterized by the 

 numbers n^' nj n, nj to another, characterized by n^" n^" n^" n^", the 

 energy decreasing from a' to a", according to Bohr's hypothesis the 

 system emits liglit of the frequency : 



. = '-^'1 (10) 



Hence the spectrum lines of the molecule under consideration are 

 given by the formula: 



V 



h 27x1 ' ' ' ' 'S.i'I 



With the aid of this expression it is possible to show the influence 

 of the rotation on the spectrum. 



§ 4. Discussion of the spectrum. 



The spectrum lines given by formula (U), which are characterized 

 by 8 numbers, may be grouped in different ways. In order to show 

 the influence of the rotation of the molecule as clearly as possible 

 we will consider a definite change n,' nj n,' -^ n^" 7i," 71^" (henc^ the 

 values of «„' cr„" «/ «/' are fixed); then by giving different values 

 to the numbers n,',n^", different eystenis of lines are obtained. 



A. First consider the case 7i,' = ??," = (in both states of motion 

 the rotation of the molecule as a whole is zero) ; then the frequency is: 



• v^ = '^l—^ (12) 



n 



B. If n,' and ?i," are equal, and different from zero, the frequency 



will be found to be: 



a' — a" 



' (13) 



'^-"^ "^ 2:tl 



Hence the original line i\ appears to be accompanied on both 

 sides by equidistant satellites, in the same way as in Bjehrum's 

 theory. The distance of the satellites is equal to: 



Ar = ^^p;^' (U) 



In general the value given by (14) is not the same as that given 

 by Bjerrum's theory which is : 



Ar=:-V, (14«) 



4 jt J 



The expressions (14) and (14a) may give the same value if for 



