124 BELL SYSTEM TECHNICAL JOURNAL 



values 0, 27r/3, tt for 9, which yield the values 2/^/27r, h/2'K, for Pa. 

 Any other integer values for PA/{h/2Tr) are unattainable by any 

 value of whatsoever; any value of 9 not among these three would 

 yield a value for Pa not an integer multiple of h/2Tr, which is con- 

 trary to the assumptions. Thus, the assumptions that the atom 

 is a conjunction of two whirling parts, and that the atom altogether 

 and each of its two parts separately whirl with angular momenta 

 which are constrained to be integer multiples of a common factor — 

 these assumptions lead to the conclusion that the relative inclination 

 of the two revolving parts is constrained to take one or another of a 

 strictly limited set of values. 



This essentially is the model devised by Lande to account for the 

 complexity of the Stationary States. The several Stationary States 

 which form a group belonging to a sequence — in other words, which 

 share a common value of n and a common value of k, like the 2pi and 

 2/>2 states of sodium or the Mi, 3^2, 3^3 states of mercury — are supposed 

 to resemble one another in this, that each of the whirling parts sep- 

 arately has the same angular momentum in every case; and to differ 

 from one another in this, that in the several cases the two whirling 

 parts are differently inclined to one another, so that the angular 

 momentum of the entire atom differs from one state to the next. 

 The different Stationary States which share common values of n and 

 k are supposed to correspond to different orientations of the two 

 parts of the atom and to different values of its angular momentum. 



I will now no longer disguise the fact that these whirling parts are, 

 or at any rate have been, supposed to be precisely the valence-electron 

 and the residue. To the former we should therefore assign these values 

 for the angular momentum Py: the value }i/2Tr for every state be- 

 longing to an 5-sequence, the value 2/?/27r for every /?-state, ?,h/2ir 

 for every J-state, and so on. Then to the angular momentum Pr 

 of the residue we should assign a suitable constant value; a "suitable" 

 value in this case being such a one, as would yield the proper grouping 

 of terms in the various sequences of the system which the atom under 

 consideration is known to have. Thus, for an atom-model to represent 

 sodium with its doublet system we require a value for the angular 

 momentum of the residue, such as will yield one permitted orientation 

 when the atom is in an 5-state {Pv = h/2Tr), and two when it is in any 

 state for which Pv = kh/2T and k is any integer greater than unity. 

 No such value can be found. The value PR = h/2ir will not do; 

 for, as was shown in the illustrative instance a couple of pages back, 

 it yields three permitted orientations when Pv = h/2iT, and (as can 

 easily be shown) three for each and every other value of Pv which 



