CONTEMPORARY ADVANCES IN PHYSICS, XXIX 307 



were it not for one more feature of the laws of the behavior of atoms 

 and their internal angular momenta in the magnetic field. 



I have described at length how, in magnetic fields of the field- 

 strengths customary in spectroscopy, where the angular momenta / 

 and J of nucleus and electron-system are "decoupled" and orient 

 themselves independently in the field, each state with a given value of 

 / is converted into (2/ -f 1) groups of (2/ -f 1) levels apiece. But in 

 no field at all, I and /are "coupled" into a resultant F, or rather into 

 one or another of several such resultants; and I mentioned that there is 

 reason to suppose that, in fields very much weaker than the customary 

 ones, this coupling subsists and the atom orients itself as a single 

 entity in the field. I emphasized then (page 303) that different as are 

 these two extremes, they have one feature in common: the total 

 number of the levels corresponding to a single value of /, which at 

 both extremes is (27 + 1) (2/ -+- 1). The practical usefulness of this 

 theorem is diminished by the fact that some of these levels may have 

 identical values of ct ^^"^^ but in the atom-model they are nevertheless 

 distinct. 



One naturally gt^ hat as the field -strength is increased from 



"very weak" to "c^ ary," each level of the one extreme passes 



over into a level of .her extreme, so that for any field-strength 



low, intermediate or there are always just (2/ 4- 1) (2/ -f 1) of 



them. There arise t! he lesser problem of ascertaining the "cor- 



relation," i.e. which If 3f the one extreme goes over into which of the 

 other; and the grea ' roblem of ascertaining just how, for each of 

 these continuously-d i^ce levels, the energy -value and the component 

 of the magnetic mo, ent along the field-direction — which latter de- 

 termines the deflection, and which let us call Mz — vary with the field- 

 strength H. Formidable theoretical articles have been written on 

 both of these problems, culminating in rules for the former and formulae 

 for the latter. They were worked out originally for the behavior of the 

 vectors L and 5 in applied magnetic fields, but are translated into 

 rules and formulae available for our present interests by simply re- 

 placing these vectors with / and / and making corresponding changes 

 in the g-factors.^ For such an atom as hydrogen or sodium in its 

 normal state, for which J = ^, I will quote the formula from Breit 

 and Rabi. 



^ Strictly one should take into account the influence of the magnetic field on the 

 interrelations between L and 5 and on those between / and J simultaneously, but it 

 usually happens that when H is increased to a magnitude which already suffices to 

 decouple / and / pretty thoroughly, it is not yf , great enought to do much to the 

 coupling between L and 5. I have spoken of is range of magnitudes as "cus- 

 tomary," on the ground that it is usual in ex, -ments on the Zeeman effect; but 

 there is no good single word for qualifying it, inj auch as it is simultaneously weak 

 with respect to the (L, S) coupling and strong w h respect to the (/, J) coupling. 



