442 BELL SYSTEM TECHNICAL JOURNAL 



numerical relations of the levels in a group, and to certain qualities 

 of the transitions between them, it was felt that the levels of each 

 group share some deeply fundamental quality in common. For this 

 reason we used a system of classification in which each level is repre- 

 sented b\- two symbols, one for its group and one for its place in its 

 ijroup; and we numbered the le\'els in succession, not 1 and 2 and 3 

 and 4 and 5 and so forth, but li and 2i and 22 and 3i and Sj and 3a 

 and so forth. Interpreting the groups of lines in the spectra of 

 .sodium and other atoms, we infer groups of levels. The levels in 

 one of these groups are often far apart. They may be eighteen or 

 more in number, other levels may lie between; but by reason of the 

 resemblances between the lines whence they were inferred, by reason 

 of certain numerical relations between the levels themselves, they 

 are believed to have some deeply fundamental qualit\' in common. 

 If this is vague, so also at times is the interpretation. 



The statements in the foregoing sections about the stationary 

 states of sodium are now to be understood as relating to groups of 

 stationary states. It is the groups of slatiotiary slates which are 

 (irranji^ed in parallel columns, desigJiated by numerals k, such that no 

 transition takes place unless in it k changes by one unit. It is the group 

 of stationary states which is marked by a pair of numerals, one to 

 designate its column and the other its place in its column; or by a 

 letter to designate its column and a numeral to designate its place in 

 its column. It is the group of stationary states which is denoted by 

 (32) or (l,s) or (5,rf). 



To denote a particular stationary slate we must add, to the symbols 

 for its group, a third s>-mbol for its place in its group. This s>mbol 

 is generall>' a numeral, hung on as a subscript to the letter desig- 

 nating the column (thus: (2,/'i) and {2,p2) ) or as an additional sub- 

 script to the two numerals (thus: 32i and Ssj).-' The most common 

 general symbol for this numeral is j. Geometrically, the stationary 

 states may be represented by lines or dots arranged, not in one row 

 of se\cral parallel columns as in Fig. 7, but in .se\eral rows of parallel 

 cf)himns. Readers with three-dimensional imaginations in good 

 working order may develop this idea ad libitum. The systems for 

 assigning the values of j are shifted around every few months to 

 correspond to new atom-models, and are scarcely worth memorizing. 



" The notation suggested by Saunders and Russell, evidently in concord with a 

 niiniljcr of other experts, is built in this way: Designate the column to which a 

 group lielongs by the letters suggested in section E5, capitalized (i.e., .S", P, P, F, 

 G, 11 for ^ = 1, 1, ?i, 4, .S, (>); write the serial-nunil«?r of the proup before the letter, 

 and ajipcnd the value of jf as a subscript to the letter. If it is desired to state what 

 sort of a system (cf. section ElO) a level belongs to, one may add an index to the 

 left of the letter and above it. 



