175 



h 



instance a, z=:n^~; for certain systems this may be approximately 



the case ^). 



C. If 7i^=\=n^', so that the general formula (11) has to be 

 retained, each line \\ appears to possess a double infinite system of 

 satellites, the distances of which are given by a quadratic formula. 

 This formula is of the same type as the one given by Deslandres 

 and others for the band spectra'). A formula of this kind has been 

 derived from the theory of quanta for the first time by Schwarzschild '); 

 ScHWARZscHiLD has also pointed out that if the moment of inertia / 

 is calculated from the coefficient of the term of the second degree, 

 the values obtained are of the proper order of magnitude. 



Other groups of lines. 



D. If n\ n\ 7i\ are equal to n'\n'\n", respectively, so that only 

 7l^ changes in the transition from the first state of motion to the 

 second, a set of lines is obtained, vi'hich may be denoted by the 

 name of "rotation spectrum" : 



Vr=-(nJ-n:').^4-{n,'^-n:^)-^ . . .(15) 



From the order of magnitude of the coefficients it may be inferred 

 that these lines are to be found in the infra-red (they stretch out 

 as far as r = oo, ).z=cc). 



E. Rubens and Hettner *) have observed in the absorption spectrum 



1) The difference between formula (14) and (14a) becomes of importance if it 



is desired to calculate the value of the moment of inertia from the distance of 



h 

 the lines. (In Bjerrum's theory --T7 is sometimes given for Av instead of the 



value (14a); cf. H. Rubens and G. Hettner, 1. c. p. 168). 



A more important difference between formula (14) and Bjerrum's theory is 

 that the value given by (14) depends on a/— «i", and hence on the numbers 

 ^11%%%'%'%". This makes the value of A" in general different for different 

 .lines vo, whereas on Bjerrum's theory /.v is independent of vq. 



Compare also the example given in § 5. 



2) Cf. H. M. Konen, Das Leuchten der Gaseund Dampfe, (Braunschweig, 1913), 

 p. '214, seq. 



3) K. ScHWABZSCHiLD, 1. c. p. 566. — ScHWARZSCHiLD supposcs that the 

 rotation of the molecule and the motion of the electron do not exert any influence 

 upon each other; the opposite supposition is essential to the theory given above. 

 This is the cause of the term which is linear in w^ and %" being absent in 

 Schwarzschild's formula. 



*) H. Rubens and G. Hettner, 1. c- 



