132 BELL SYSTEM TECHNICAL JOURNAL 



We have supposed, in dealing with multiplets, sometimes that the 

 angular momentum of the entire atom is constrained to take such 

 values as are integer values of ^/2x, and sometimes that it is con- 

 strained to take such values as are odd-integer multiples of ^ (h/2ir).'^^ 

 In either case the permitted values of the angular momentum are 

 spaced at equal intervals; and as the rule for the component of the 

 angular momentum along the direction of the field bears the form 

 which it does, we may well suppose that something in the order of 

 nature constrains both the angular momentum and its projection to 

 accept only values which form a sequence spaced always at that 

 curious interval /?/2x. 



The total number of permitted orientations will obviously be 

 limited by the actual magnitude P of the angular momentum. This 

 being supposed always to be an integer multiple of | h/2ir, let it be 

 written P = 2/(^ h/2Tr). The permitted orientations are those which 

 yield a series of values for the projection Pcos a spaced at intervals 

 h/2Tr; let these be written 



P cos a=Ao, Ao-h/27r, Ao-2h/2T Ao-mh/2T (15) 



Nothing in the experiments thus far described gives the least notion 

 of the value which should be assigned to Ao. AH we know at present 

 is that Ao cannot exceed P and that {Ao — mh/2Tr) cannot be alge- 

 braically less than —P. Suppose in the first place that^o = P; that 

 is to say, that the atom may orient itself with its axis parallel to the 

 magnetic field. Then the permitted orientations are those which 

 yield this series of values of the projection : 



P cos a = P, P-h/2Tr, P-2h/2T P-mh/2T (16) 



= 2JiUi/2Tr), (2J-l)ihh/2Tr), (2J-2)(}h/2T, ..... 



of which there are (2/+1) in all. On the other hand, it may be that 

 the atom is prevented from orienting itself parallel to the field; that 

 the least permitted angle between the axis of the atom and the direc- 

 tion of the field is some angle yielding a projection Ao intermediate 

 between P and {P — h/2-K). Then there are 2 J permitted orientations 

 altogether. 



Summarizing the results of this last paragraph : if the angular 

 momentum of the atom is an integer multiple 2/(| h/2ir) of the fun- 

 damental unit \ {h/2-n), then according to the orientation theory 



" It was remarked at the beginning of Section S that the evidence to be presented 

 in that Section would support neither h/lir nor any other particular numerical value 

 for the fundamental unit of angular momentum; here, however, we have evidence 

 for that value. 



