576 Prof. E. 0. C. Balyon Light 



the existence of frequencies far slower than the rotational 

 frequencies. It is difficult to conceive of any vibrations 

 exhibited by a molecule, as a whole, which are far less rapid 

 than its rotations. 



Kriiger * has proposed an alternative theory in that he 

 substitutes precessional motions for the rotational velocities. 

 He gives the following expression for the frequency of 

 precession : 



V _ 27rA X cos<£' 



where N is the angular momentum of the electron spin, 

 A is the moment of inertia of the atom nucleus perpendicular 

 to the figure axis, and (j> is the angle swept out by the figure 

 axis as the result of the precession. By the absorption of 

 one energy quantum the angle <£ is increased and the value 



of — r is doubled. Kriioer himself saw the difficulty 

 cos <p ° . 



connected with the width of the absorption-bands due to the 

 precessional motions. He was led to the conclusion that for 

 a given precession the values of cj> cannot be exact, but must 

 lie between broad limits. But, as stated above, the cogent 

 criticism must be made that in order to explain the observed 

 phenomena it is necessary to postulate a difference between 



the extreme limits of a given mean value of -, which is 



fo cos <£' 



equal to or greater than the difference between two con- 

 secutive mean values of — r. Then, again, it is difficult to 



cos <f> ° 



conceive of motions of a gyrostatic system far slower than 

 its precessions. 



But the most important fact to be considered in discussing 

 these two theories is that the so-called molecular frequencies 

 are due to small groups of atoms within the molecule, and 

 that they are the least common multiples of the frequencies 

 characteristic of those atoms. Further, the same atomic 

 frequencies are shown by the same elementary atoms in 

 different compounds — for example, oxygen in sulphur dioxide 

 and water, and sulphur in hydrogen sulphide and sulphur 

 dioxide. When two or more atoms enter into chemical 

 combination, the resulting molecule is endowed with a 



* F. Kriiger, Ann. der PMjsik, vol. 1. p. 346, li. p. 450 (1916). 



