S(hMH ahwuMriU.'.iKy .ini-.txcrs ix /'insics riii' 447 



Mk-nients of tlu- first roluiiin of tlu* pt-rioclir tal)l«' possi-ss a (loiil)li'l 

 syslt'in of s(.ilion.ir\' slali-s; i-IimiumUs of llu- tliird (-oliiiun, a (loiil)l(.-t 

 systfin .111(1 ill addition a (|viarli.'l systi'in. It is infiTn-d tlial flrnu-nts 

 of tlu' fifth column possess tlu-sf and a sextt-t system in addition; 

 i-k'UK-nts of tlu- svvi-nlli. tlu-si- tlirt-f and an octi-t systi-m in addition. 

 Kli-ntents of tlu- soi-ond roliimn of tlu- periodic tahle |M)ssess a singk-l 

 system and in atklilion a tripk-t system. Il is inferreil that eknnents 

 of tlie fourth column possess the.se two and ,i i|iiintet system in arldi- 

 tion; ek'inents of the sixth cokimn, these three and a septet system; 

 ek-ments of the einhth. the.se four and a nonet system. These infer- 

 ences h.ue been partialK' \erilie<i. I'or titanium, in the fourth rokimn 

 of the (leriodic table, the triplet and (juintet systcn^s have been dis- 

 coNereti; for vanadiimi (fifth cohmin) the (|uartcl and sextet; for 

 chromium (sixth) the quintet and sejitet ; for manganese (seventh) the 

 quartet, sextet, and octet; for iron (eiglith) the triplii. (|iiinlet. and 

 septet. Apparently it is by no means certain tli.it tlu- unicuniinncd 

 systems are really missing, as the dilVu iiliies of anal\/.in^ these com- 

 plex spectra are terrific. 



There are certain rules governing the number of le\els in a grouj), 

 and the effect of a magnetic tiekl upon these le\els. These rules 

 were tliscovered chiefly by I.ande; I give them in his iKil.iiioii. I 

 recall, to begin, that we ha\e designated each group <it lc\tN li\ ,i 

 numeral it, which is 1 for all the groups in the s-column, 2 for all 

 groups in the /)-column, 3 for all groups in the rf-column, and so forth. 

 We have further distinguished the different le\els in a group by 

 assigning them ditTercnt values of another numeral _/; the manner in 

 which these values of j arc cho.sen was described in section KX. Lande 

 introduces a numeral K which is smaller than ^ by I; K thus is \ for 

 all groups in the 5-column, 1.'. for all groups in the />-column, and so 

 forth. He also introduces a numeral J which is greater than 7 by 5; 

 and a numeral R which is ^ for every level belonging to a singlet 

 system, 2 2 for every level belonging to a doublet system, 3 2 for 

 every level belonging to a triplet system, anfl so fr)rth. 



These are Land^''s rules: 



(1) The total number of le\'els in a grf)up characterized by the 

 numeral K, belonging to a system characterized by the numeral R, 

 is twice the smaller of the two numerals R and K (that is, it is '2R if 

 R<K, 2K if R>K: 2R = 2K if R = K). 



(2) In the formula (8) for the Zecman effect, the factor a? is equal 

 to e -iiriic multiplied by a factor g, which depends on the numerals 

 R. K. and J for the level in question in the following manner: 



g = 3/2+(/?=-A:')/2(y^-i) (9) 



