﻿and its Relation to the Quantum Theory. 8G9* 



the angular momentum about the axis of symmetry be an 



7 



integral multiple of £1 - *, and that the motion be adiabati- 



° 1 27T ' 



cally derivable from an unperturbed orbit for which the 

 action integral has the value given in (24) . Bohr's conditions 

 are therefore in agreement with the application of the 

 Ehrenfest adiabatic hypothesis given above. 



Jefferson Physical Laboratory, 



Harvard University. 



March 13, 1922. 



Note. — Since this paper was written^ an article by Bohr 

 has appeared in the Zeitschrift fur Physik, vol. ix. (1922),. 

 p. 1, in which he conjectures that the Kemble model with 

 axial symmetry and with crossed orbits (studied in the 

 present paper) may be the correct solution of the normal 

 helium atom. It is therefore to be regretted that calcula- 

 tion has given an ionization potential of 20*7 volts instead 

 of 25*4 demanded by experiment. 



According to Bohr the normal helium atom is capable of 

 formation from a free electron and ionized helium atom by 

 continuous transition through a series of intermediate orbits. 

 The family of orbits in the present by varying the constants 

 of integration p and iv furnish a means of transition from the 

 Kemble model to a stationary state of lower energy given by 



10=0 and jo= — , which gives the coplanar circular orbits 



of the original Bohr helium model. According to Bohr 

 (p. 32) this model cannot be formed by a continuous 

 transition from the stationary states found in the orthohelium 

 model (coplanar orbits of unequal size), but the statement 

 which I have just made makes it appear capable of formation 

 by continuous transition from the stationary states of the 

 parhelium series. The instability which may result from 

 the possibility of degeneration into coplanar orbits of lower 

 energy makes it plausible that the normal state of the helium 

 atom may not be characterized by crossed orbits with axial 

 symmetry. 



* Bohr's conditions demand that the resultant angular momentum of 

 a single electron about the axis of symmetry be -~— , while in our con- 

 ditions this value was taken for the resultant angular momentum of both 

 electrons, a quantity twice as great. This, however, is probably not a 

 contradiction, as Bohr's method was derived for systems with only one 

 electron. 



