CONTEMPORARY ADVANCES IN PHYSICS, XX IX 299 



turns out that the last condition is the one which prevails. Suppose 

 then that / compounds itself with J according to the following rule, 

 repeated word-for-word with appropriate changes of symbol from the 

 rule for compounding ^ and / into j: 



Rtde for compounding I and J into F. If / is greater than J, start 

 with the numerical value of (/ + /) and write down the sequence of 

 numbers spaced at unit intervals from (/ + /) to (/ — /) inclusive: 

 to wit, (/ + /), (/ + /-1), (/ + /- 2), •••(/- /). These 

 (2/ -+- 1) numbers are the permitted values of the quantum-number 

 F. If / is greater than /, start with the numerical value of (/ + I) 

 and write down the sequence of numbers spaced at unit intervals from 

 (/ + 7) to (/ — /) inclusive. These (2/ + 1) numbers are the per- 

 mitted values of the quantum-number F. 



The quantum-number F refers to a vector of magnitude ylF{F -f- 1) 

 (h/lir), which has taken over from / the role of the angular momentum 

 of the atom-as-a-whole, being the resultant of / and of the nuclear 

 angular momentum /. 



Now if all these suppositions are correct, we may expect to find not 

 individual states, but whole serried clusters of states, corresponding to 

 individual values of /. If out of the manifold term-system of an 

 atom we select a state for which J = 1/2, one for which / = 3/2, one 

 for which / = 5/2 and so on as far upward as our knowledge extends, 

 we may expect on close scrutiny to find that these apparent states are 

 actually clusters, each cluster comprising a number of states which for 

 one or two or more of the lowest values of / may be equal to (2/ -f 1), 

 but for higher values reaches and remains at a limit which we identify 

 as (21 -f 1). 



What is observed with the spectroscope, though, is not the indi- 

 vidual state, but the line which reveals a transition between two 

 different states. \^'hat in a feeble spectroscope appears as a single 

 line, and is attributed to a transition between two states with resultant 

 electronic angular momenta (I fear no shorter term will serve hence- 

 forth) j' and j", should in an excellent spectroscope appear as a cluster 

 of lines due to transitions between the several members of two clusters 

 of states. 



This again is exemplified by the principal series of sodium. As I 

 said earlier, this appears in a feeble spectroscope as a series of single 

 lines, each of which is resolved by a good spectroscope into a doublet. 

 This structure, by the way, is called the "fine structure" of the lines; 

 and this it is which indicates that the P-states of sodium are close 

 pairs, and which thus invites and requires the introduction of the 

 quantum-numbers j and 5 and the spin-momentum of the electron. 



