177 



h 



"'■■•="■2^ + 



n, may be positive or negative; this depends on the direction of 

 motion of the electron. 



In the principal part «„ of a only the absolute value |7?8| occurs. 



B>om (18) the spectral formula may be deduced in the same way 

 as above. The following groups of lines (corresponding to those 

 called B and E in § 4) are of special interest: 



a). Take : n^ = — n^' =2—71^; n^ = n^' == n^ ; the valnes of ?i,, 11^ 

 change in an arbitrary manner. The frequencies emitted then are: 



If n^ has always the same value, different positive and negative 

 values of n^ give a set of equidistant lines, accompanying the line 

 \\; the distance of two consecutive satellites will be: 



2n..A 



h). Take: 11^= -71^'=^ — n^; n^' ::=7i^" =:7i^ (as was done above 

 under a); while the values of n^ and ri, do not change. In this case: 



«„ (n/ w; w,') = «„ (?i/' w," n,") ; 

 hence the frequency emitted becomes : 



Vtt = 4 — = rr — I'n . . . . . . (11) 



The structure of these systems is in some respects analogous to that 

 of the absorption bands of water vapour ; (1) corresponds to the barid 

 observed near : I = 6,26;t ; (II) to the lines in the far distant infra-red. 



It must not be forgotten, however, that this example has been 

 chosen arbitrarily, so that no great value can be attached to the absolute 

 magnitude of Ar. 



Summary. 



An attempt is made to show that it is possible to deduce from 

 the theory of quanta spectral formulae for rotating systems, which 

 may explain the structure of the bands, observed in the infra-red 

 absorption spectra of certain gases. 



At the same time a formula has been found which might be 

 useful in the explanation of the band spectra and which is an 

 extension of one already given by Schwarzschild. 



In order to simplify the problem it has been assumed that the 

 system rotates about a fixed axis; hence the question arises whether 

 it is not possible to give a more general treatment, in which account 

 is taken of the precessional motion of the molecule. 



