432 BELL SYSTEM TECHNICAL JOVR\AL 



accentuati' this conlrast, and l.Ui-r to a certain extent aid to explain 

 it away. I commence with the atoms other than hydrogen, and take 

 sodium as the specific instance. 



A few of the stationary' states of the sodium atom are exhibited in a 

 single column on the left of Fig. 6. The energ>-value of each IcncI, 

 measured from the energy of the ionized atom as zero, is affixed at 

 the left ; but the practice of drawing the le\e!s at distances proportional 

 to their energy-values has had to be discarded for the sake of lucidity. 

 In this case, the distances are proportioned to the differences Ijetween 

 the logarithms of the energy-values. Drawing arrows from each of the 

 levels to every other, and ascertaining which of them correspond to 

 actual and which to missing lines, we find that the missing lines are 

 such that the stationary states can be sorted out into several families, 

 to be arranged in parallel columns as on the right of Fig. 6. There are 

 at least seven of these, but it is of no advantage to us to consider more 

 than the first four. The feature of this arrangement is, that transitions 

 between stationary states in adjacent columns correspond to actual tines; 

 but the lines corresponding to all other transitions are missing. 



This is a principle of selection. It may be phrased in an equixalent 

 but pregnant way, in this maniuT. Let me attach to the several 

 columns the numerals 1, 2, 1^, 4 . . . , as they are indicated at the 

 bases; and let me use k as the general symbol for each and all of these 

 numerals. Then this particular selection-principle ma\' be i)lirased 

 thus: 



The only transitions which correspond to actual spectrum 

 lines are those in which k changes by unity; Ak = ±l. 



The numeral k bears the ponderous name of azimuthal quantum- 

 number. This is a name dcri\-ed from theory and not from experience, 

 as will be made clear in due time. The principle of selection which 

 has just been stated is the .selection-principle for the azimuthal (juan- 

 tum-number. 



Kxceptions to this rule occur; tiu' verbolcn lint's, like oilier vcrholen 

 things, occasionalh' c\ade the prohibition. This happens particu- 

 larly when the atoms are subjected to intense electric fields, or to 

 violent spasmodic electrical discharges in which strong transient 

 fields are produced: in these circumstances great numbers of the 

 missing lines leap suddenK' into sight. In Fig. 11 some of these lines 

 appear elicited by a strong electric field. Some lines corresjKJnding 

 to changes of k by two units or by none, which by the foregoing rule 

 should be absent, do actually occur even when there is no obvious 



