soMi- coxrr..\tr(}K iKv .inr.ixirs ix riivsns- iiii -m 



imri'latrd liiu-s forliiitously rlosi- to>;fther, l)Ut a pair of lines shariiiR 

 sonu- (li'tply limd.imiMital {|uality in common. This is indiralt-H 

 rhii'tly by the fai'ts tliat tlu- distance (me.isiired in fre(]iiency) between 

 the components of a doublet is the same for all the doublets, and very 

 sm.dl comparml with the distance between consecutive doublfls. 

 For this re.ison the tloublets are treatetl as entities, and they retiilire 

 .1 n.ime: which is what physicists have preser\ed for them, in con- 

 tinuing to call them "lines." "Doublet" would be better than "line", 

 .md "group" would be better yet; but we cannot ever be sure that 

 even the apparently-single lines are not very close groups, and yet 

 it would be silly to call every line a group. Sirius appears as a df)uble 

 star in a few of the most powerful telescopes, but nobody would 

 insist on calling it a double star when pointing it out in the night sky. 



.All this is not so trivial as it sounds. It is easy enough to speak 

 of doublets when looking at lines which appear single except when 

 viewed in the most powerful spectroscope, and then are resoKed 

 into components much closer together than the nearest similar line 

 is to either. Such lines occur not in the spectra of hydrogen and 

 ioniKed helium only, but in the spectra of sodium and other elements 

 generally. But the spectroscopist is constantly applying such names 

 as "doublet" and "triplet" and "quadruplet", and the inclusive 

 name "multiplet" to groups of lines which lie far apart in the spec- 

 trum, with scores of others inter\ening. Here his function is not 

 to split apparent lines into narrow groups, but to unite widely-scat- 

 tere<i lines into wide groups. This he does not because of propinquity 

 of the lines, but because of resemblances or analogies or fixed intensity- 

 relations between them, or because he finds it possible to construct 

 a series of such groups with identical frequency-differences between 

 corresponding lines within them, or because of analogies with other 

 elements with more perspicuous spectra, or theoretical predictions, 

 or intuitions or clairvoyance. Ciroups such as these are not generally 

 termed lines, except in very abstract discussions; it is difficult to 

 call a group a line, when it is clearly resolved b%- any instrument 

 worthy the name of spectroscope. But they are like the lines of the 

 Balmer series, treated as entities because their lines are believed to 

 share some deeply fundamental quality in common. 



What I have said about lines and groups of lines is transferable in 

 substance to stationary states and groups of stationary states. What 

 we had originally called the levels of hydrogen and ionized helium, 

 with their energy-values -Rli'n^ and -ARh/n} (w = l, 2, 3 . . . ), 

 were resolved into groups of levels in order to interpret the fine 

 structure of the lines. But owing to the propinquity and to certain 



