CONTEMPORARY ADVANCES IN PHYSICS, XXIX 305 



but now must suppose it still to be potent enough to afifect the energy 

 of the atom. It adds a third term to (14) which is supposed to be of 

 the form const. MeMn cos d:, h cos dj, h, but in any event will have 

 (27 +1) distinct values for every value of /, and is not necessarily 

 (or anyhow is not known to be) too small to account for the observed 

 separations between the members of each group. It therefore allows 

 us to estimate / by counting the members of such groups and equating 

 their number to (2/ + 1), and this (when available) is one of the most 

 acceptable ways of determining the angular momentum of the nucleus. 



With a spectroscope one counts, as always, not the number of 

 levels but the number of lines connecting them with some other 

 family of levels, and expects that the two numbers will not be the same. 

 By a rare if not unique coincidence, however, they are the same: the 

 selection-principle which is involved is such, that each group of 

 levels produces a group of an equal number of lines, or (in other words) 

 if the influence of the nucleus resolves every state of the atom in a 

 magnetic field into a group of (2/ + 1) dififerent levels, then it also 

 resolves every line connecting two such states into a group of (2/ + 1) 

 different lines. There are in the literature magnificent photographs 

 of the spectrum lines of bismuth exposed to a magnetic field, each line 

 under high resolution exhibiting ten components and proving the value 

 9/2 for /. 



It is, however, sometimes possible to count the levels directly, by 

 sending a beam of fast-moving atoms through an inhomogeneous 

 magnetic field which spreads it out into a diverging fan of smaller beams 

 or pencils, each consisting exclusively of atoms having a certain 

 distinctive value for the projection of the magnetic moment upon the 

 field-direction. This requires a great refinement of the celebrated 

 method of Gerlach and Stern, a refinement which has been achieved 

 by Rabi and his school. 



We take, as usual, sodium for our example. Consider a narrow 

 beam of sodium atoms, moving with uniform speed along the .r-direc- 

 tion into a region pervaded by a magnetic field which is parallel to the 

 z-axis, and of which the magnitude // varies as rapidly as possible with 

 z. Were it not for this variation of H with z, nothing would happen to 

 the beam, for (to make the crudest possible picture) each atomic 

 magnet would have both its north and its south pole exposed to the 

 same field-strength, and one would be pushed as hard as the other was 

 pulled, resulting in no net force upon the magnet and no deflection. 

 But when the field varies with z and the atomic magnet is oriented 

 otherwise than at right angles to the s-axis, the north and the south 

 pole will be exposed to different field strengths, there will be a resulting 



