SOME COXTEMPOR.IKV .inr.lWr.S /.V rilYSlCS nil 44.? 



The host of tlieni, however, are adjusted so as to express a new and 

 additional selertioii-principle, which is roec|iial with the other selcr- 

 tion-prinrii>le we met a few pages above. 



This principle is derived in the .same way as the first one. Tin- 

 groups of levels are established by inference from tiie groups of lines; 

 then arrows are drawn from every level to e\ery other, the corrc- 

 s|H)nding spectrum-lines are sought, and most of them arc not foimd. 

 .Some of these missing lines are those which would contravene the 

 first selection-principle, as they correspond to transitions in which 

 the numeral k changes by more than one unit, or not at all. Putting 

 these aside, there are still a number of missing lines, to which the 

 first selection-principle has offered no objection. Now it is found 

 possible to chcHKse the numeral j in such a manner that the only 

 transitions which correspond to actual spectrum lines are those in 

 which 7 changes by one unit or not at all iSj = 0,±l). Furthermore 

 it is possible to adjust the values of _; in such a manner that the lines 

 corres^Kinding to transitions, in which j is initiall\- zero and remains 

 unchanged, are missing. 



This is the selection- principle for the inner quantum number; for 

 the numeral j. when adjusted in this manner, is known as the inner 

 quantum number. This again is a name imposed b\- theoni- and not 

 by the data of experience. 



As the two selection-principles arc etTective concurrently, the pair 

 of them may be fused into this one: 



Of the three numerals n, k and j, which specify a stationary stale com- 

 pletely, two (k and j) may be so chosen that the only transitions which 

 correspond to actual lines are those in which : first, Ak = ± 1 ; second, 

 S]=0, ± 1 ; third, j is not zero both before and after the transition. 



This complicated rule is evidently the sign of some very important 

 principle, the full nature of which thus far escapes us. It will prohahh' 

 seem dithcult to grasp and fix in mind; but difficulty of this sort is 

 likely to alH)und in the physics of the near future. Not so many 

 years ago the physicist's path lay among differential equations; the 

 defter he was in integrating hard specimens of these, the better he 

 was fitted for his profession. I should not care to say that this is no 

 longer true; but he will probably have to cultivate a sense for prob- 

 lerps such as this. 



It remains to give some idea aliout the number of stationary states 

 in the various groups. P'or sodium, as laid out in Fig. 6, the groups 

 in the j-column are merely single levels (this sounds like a contra- 

 diction in terms, but may be borne for the sake of the generality): 

 the groups in the other columns are pairs of levels, or "doublet terms." 



