302 BELL SYSTEM TECHNICAL JOURNAL 



Insert in (13) the permitted values of F, which are (2/ + l)or(2/-|- 1) 

 in number according as / is or is not greater than 7, and are spaced at 

 unit intervals from (/ + /) downwards (page 299) ; call them, in order 

 of descending magnitude, F„,, Fm-y, Fm-2 • • ■ Form the 2/ or 2/ con- 

 secutive first differences between the so-computed permitted values of 

 Wf; call them AWm, AWm-^, AWm-2, • • • Then as is readily worked 

 out, 



AW„, : AWr.-i : AW,,,^. • • • : : F,,^ : F._i : F„,_2 • • • 



::(/ + /):(/+/- !):(/ + /- 2) •••. 



The successive energy-differences or intervals should stand to one 

 another as the successive members of the chain of integers (or half- 

 integers, as the case may be) stepped oft" at unit intervals and stretch- 

 ing from (/ + /) downwards.^ 



This is an interval-rule based on a specific notion of the intra-atomic 

 forces (the sine-law aforesaid), and having analogues in the parts of 

 atomic theory having to do with the interactions between electrons 

 the extra-nuclear electrons only. If verified, it enables one to deter- 

 mine (/ -f /) and therefore / from the analysis of a single cluster of 

 states with a single value of /, even when / is smaller than / and the 

 preceding method would fail. Much use has been made of this 

 method, and there are a few cases in which a fairly accurate measure- 

 ment of a chain of intervals has shown that it closely agrees with a 

 chain of consecutive integers or half-integers, though more usually the 

 intervals are small and the measurements rough and it is merely as- 

 sumed that there is perfect agreement with that particular succession 

 of half-integers or integers with which there is the nearest apparent 

 agreement. 



(c) The relative intensities of the members of a line-duster are capable 

 of giving information about the quantum-numbers of the states which 

 they connect, provided one adapts quantum-mechanical formulae 

 developed for transitions into which the nuclear angular momentum 

 does not enter. The formulae are of appalling complexity, while 

 intensity-measurements, especially when one is working so near the 

 limits of the possible as when hyperfine-structure is being measured, 

 are notoriously liable to error. This method is probably to be classi- 

 tied as by far the least reliable, for the present at any rate. 



'' The biggest interval may be that between the highest and the next-to-highest 

 energy-value, or that between the lowest and the next-to-lowest; whichever case is 

 realized gives a clue to the "sign" (page 318) of the magnetic moment; usually the 

 former corresponds to a positive, the latter to a negative moment, but features of 

 the extra-nuclear electron-system may cause this statement to be reversed. Inci- 

 dentally, relative intensities of lines also have a bearing on the sign of the moment. 



