310 BELL SYSTEM TECHNICAL JOURNAL 



clever utilization of the law embodied in (16), for which I must refer to 

 the original papers. — When the experiment was performed on sodium, 

 it was found that the beam is split into eight components instead of 

 merely two, proving the value 4 for the factor (2/+ 1) and the 

 value 3/2 for the quantum-number of the nuclear angular momentum. 



Second, suppose an experiment done by measuring the number of 

 atoms which go through the deflecting field entirely undeflected. 

 These are the atoms for which Mz = 0, and in ideal conditions there 

 would never be any such atoms, excepting at one of the particular 

 values of field-strength for which the Mz of one (or rather, two at a 

 time) of the levels mentioned on page 309 is passing through zero; in 

 actual conditions one would expect the curve of the number-of- 

 undeflected-atoms versus the field-strength to exhibit peaks. On 

 examining equation (16) one may see that there would be one peak 

 f or / = 1 or 3/2, two for / = 2 or 5/2, three for / = 3 or 7/2, and 

 so on.^" The number of peaks by itself thus gives a partly ambiguous 

 indication, but the ambiguity can be resolved by another theorem 

 deducible from (16) : if we denote by Hi, H^, • • • the abscissae of the 

 consecutive peaks, then all the intervals {Hi — Hi-i) are equal in 

 any case, but the value of Hi is equal to the half or to the whole of their 

 common value, according as / is a full integer or a half-integer. — The 

 curve for caesium was found to display three peaks, and the second 

 criterion showed that the value of / is a half-integer, therefore 7/2. 



Third, when Mz is found by measuring the deflected beams in an 

 apparatus where field and field-gradient are accurately known (not a 

 stringent requirement in either of the two previous cases), one may 

 use equation (16) to compute b: thus determining the "hyperfine- 

 structure" separation between two states without an optical measure- 

 ment! This has been done with both varieties of hydrogen, the heavy 

 isotope and the light, because for these very important atoms the 

 separation in question is far too small to be detected by any optical 

 device: the method of magnetic deflection has proved itself the superior 

 of the long-established arts of spectroscopy, hitherto regarded as the 

 ne plus ultra of subtlety and refinement.^^ The results of these experi- 

 ments are mostly quoted for their bearing on the magnetic moment 



" Not counting the peak at H = which (it is obvious) must always appear but 

 has no bearing on the value of /. 



^' I should, however, perhaps make exception for the most delicate of these, which 

 is the derivation of hyperfine structure from observations on the resonance radiation 

 produced by polarized light acting on atoms of gases in magnetic fields, and is 

 practiced by Ellett and his school at the University of Iowa. The complexity of 

 the theory forbids a description of the method in this place, but several values of / 

 have been obtained by it. 



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