so.\ir. coMF.Mfoh-.iKy .iKi.ixcr.s i\ i:iiysn.s- i iii m 



iiif\ ital)l\' In' .irr.iiiKi'd in •> single coluinn. as il was doiu- in Vi^. *>. 

 Hill in this arraniii-nuMit the si'k'rtion-priiu'ipli' of thi- fori'noinjj p.ira- 

 Kraph is app.iri-iitly rontravt-ni'd. lM>r, when tlie Ie\els of the scKliiiin 

 atom were arranjjiHl into <-oliiniiis, the transitions lu-tween levels 

 l>eloni;iiiK to one and the same column were amonn the inhil>itefl 

 transitions, the lines corresponding to these were amon^ the missing 

 lines. But the transitions between the levels in the single column 

 which contains all of them for the hydroijen atom, correspond to the 

 actual lines which constitute the entire Indrogen spectrum. 



This ili.scord is only ap[)arent. It vanishes when we recall the fact, 

 already once mentionetl as a forewarning and then neglected for ease 

 of e.xposition, that the stationary states of the hydrogen atoms are 

 compound — that what has been called a "stationary state" in the 

 precetling pages is really an ensemble of adjacent stationars' states. 

 Kvery line of the Balmer series, the series R(l nr— 12^), is actually a 

 close doublet; the frec|uency -differences between the components of 

 all the doublets are approximately the same. Interpreted in the 

 new fashion, this means that what we have called the stationary state 

 of energy —Rii/-i is actually a pair of "component" stationary states 

 very close together — so close together, that if the energy of one were 

 exactly —R)t 4, the energy- of the other would depart from that 

 value by less than one part in forty thousand. Further in analyzing 

 the sf)ectrum of hydrogen we cannot go, probably because the minute 

 details (if there are any) of the structure of its lines overtax the 

 resolving-power of our spectroscopes. The spectrum of ionized 

 helium, however, is spread out in a more generous scale; and some 

 of its lines were analyzed by Paschen. Among these were the lines 

 of frequency 4/?(l, 3=- 1/4=); 4/?(l/3=- 1/5=); and 4/?(l/3=- 1/6=). 

 They were resolved respectively, into six, fi\c, and three components; 

 and the line 4/?(l '4=— 1 5=) resolved into four. 



Interpreted in the new manner, these data mean that what we have 

 called the stationary states of energy-values —4Rli 9, — 4/?/;,'16, 

 — ARh 2.5, and — Rh 'i<o, are really ensembles of "component" sta- 

 tionary states lying very closely together. It would scarcely be 

 possible to infer from these data, independently and without ex- 

 traneous guidance, just how many "com[)onents" belong to each of 

 the four ensembles. Fortunately or unfortunateK', Paschen's measure- 

 ments were preceded and inspired by a specific prediction of the 

 number of components in each ensemble — a prediction that what 

 we have called the «th stationary state should be a group of n "com- 

 ponent" stationary states. This prediction is graphically set forth 

 in the second column of Fig. 8, in which the level of energy-value 



