SOME CONTEMPORARY ADVANCES IN PHYSICS— X 123 



hut by \aryini2, the relative orientation of the two. Althoiip;h this 

 theory has not been harmonized with tiiose which I have hitherto 

 recited, it is competent in its own held; and for that reason I present it. 

 We will imagine that the atom is represented by a combination of 

 two flywheels, two whirling objects, endowed each with angular 

 momentum. These angular momenta are vectors, pointing along 

 the directions of the axes of rotation of the respective flywheels, and 

 having certain magnitudes. I will designate them temporarily as Py 

 and Pr, each symbol standing for a vector generally and also (when 

 in an equation) for its magnitude. The angular momentum of the 

 entire atom, which is necessarily constant in magnitude and in direc- 

 tion so long as the atom is left to itself, is the resultant of Pv and 

 Pr; a vector, pointing along the direction of the so-called "invariable 

 axis" of the atom. I designate it by Pa- The following equation 

 shows the relation between the magnitudes of these three angular 

 momenta and the angle between the two first-named, the angle 

 which describes the relative orientation of the axes of rotation of the 

 two flywheels: 



P\=P\.^P\ + 2Pv Pr cos (6) 



Remembering the successes which in dealing with the spectrum of 

 hydrogen ha\-e resulted from assuming that the angular momentum 

 of the entire atom is constrained to take only such values as are 

 integer multiples Jh/2Tr of the quantity h/2Tr, we make the same as- 

 sumption here. We further make the same assumption for each of 

 the flywheels separately; the magnitudes of the angular momenta Pv 

 and Pr are supposed to take only such values F/?/2x and Rh/2Tr as 

 are integer multiples of the same quantity /? 27r.^ These particular 

 assumptions, frankly, are foredoomed to failure; but the failure will 

 be instructi\e. 



Making all these assumptions together, we see that in effect we 



have laid constraints upon the angle which measures the relative 



orientation of the two flywheels. For if Py is an integer multiple of 



h/2T, and Pr is an integer multiple of h/2Tr, then Pa which is fully 



determined by equation (6) cannot be an integer multiple of h/2ir 



unless is very specially adjusted. To illustrate this by an instance 



(which will be clearer if the reader will work it out with arrows on a 



sheet of paper) : if Pr and Pr are each equal to the fundamental 



quantity h/2T, and if Pa must itself be an integer multiple of h/2ir: 



then cos must take only the values, +1, —h, —1, which yield the 



5 All that is actually being assumed is, that Py and Pr and P^ are all integer 

 multiples of a common unit; nothing in this section will indicate either h/lir or any 

 other value as the precise amount of that common unit. 



