398 Di. N. Bohr on the Quantum Theory of 



mechanics in general does not lead to periodic orbits. An 

 exception to this, however, occurs if the electrons are 

 arranged in rings and rotate in circular orbits, and from 

 simple considerations of analogy the following assumption 

 was proposed (see I. p. 24). 



E. In any atomic or molecular system consisting of 



positive nuclei and electrons in which the nuclei are 

 at rest relative to each other, and the electrons move 

 in circular orbits, the angular momentum of each 

 electron round the centre of its orbit will be equal 

 to h\2ir in the " normal " state of the system, 

 i. e. the state in which the total energy is a 

 minimum. 



It was shown that in a number of different cases this 

 assumption led to results in approximate agreement with ex- 

 perimental facts. In general, no stable configuration in which 

 the electrons rotate in circular orbits can exist if the problem 

 of stability is discussed on ordinary mechanics. This is no 

 objection, however, since it is assumed already that the 

 mechanics do not hold for the transition between two 

 stationary states. Simple considerations led to the following 

 condition of stability. 



F. A configuration satisfying the condition E is stable 



if the total energy of the system is less than in 

 any neighbouring configuration satisfying the same 

 condition of angular momentum of the electrons. 



As already mentioned, the foundation for the hypothesis E 

 was sought in analogy with the simple system consisting of 

 one electron and one nucleus. Additional support, however, 

 was obtained from a closer consideration of the formation of 

 the systems. It was shown how simple processes could be 

 imagined by which the confluence of different rings of elec- 

 trons could be effected without any change in the angular 

 momentum of the electrons, if the angular momentum of 

 each electron before the process was the same. Such 

 considerations led to a theory of formation of molecules. 



It must be emphasized that only in the case of circular 

 orbits has the angular momentum any connexion with the 

 principles of the Quantum theory. If, therefore, the applica- 

 tion of ordinary mechanics to the stationary states of the 

 system does not lead to strictly circular orbits, the assumption 

 E cannot be applied. This case occurs if we consider con- 

 figurations in which the electrons are arranged in different 

 rings which do not rotate with the same frequency. Such 

 configurations, however, are apparently necessary in order 



