CONTEMPORARY ADVANCES IN PHYSICS 331 



I must, however, admit that all these cases of which I have been 

 speaking are special, and comparatively rare. Both the cases in 

 which the spins neutralize each other perfectly, and the cases in which 

 the orbital moments neutralize each other perfectly — both types are 

 unusual. Still more unusual, and yet occurring here and there, is the 

 most special of all cases — that in which all of the moments and all 

 the momenta, both those of the spins and those of the orbits, balance 

 one another perfectly so that the sums are zero. An atom in such a 

 state is completely devoid both of magnetism and of spin; such atoms 

 are those of helium, of neon, of argon and the other noble gases, when 

 in their normal states. Usually, however, we find ourselves confronted 

 with some example of the general case, in which neither the spins nor 

 the orbits are completely neutralized. The atom has an angular 

 momentum which is a sort of composite or resultant of the angular 

 momenta of the spins and the orbits, and it has a magnetic moment 

 which also is a sort of composite or resultant. 



If I were to embark on the description of the general case this 

 lecture might go on interminably, and at its end you would probably 

 not remember anything except what you had already known at its 

 beginning. The laws of the composition of spins and orbits are so 

 foreign to our customary ways of thinking, and the formulae which 

 express them are so curiously built, that to work once only through 

 them is not sufficient: one has to memorize the derivations and the 

 results alike, and go over them incessantly until they are imprinted 

 on the brain. I think you will agree to this readily enough, when I 

 remind you that this theory is none other than the general theory of 

 spectra; for even quite outside the ranks of physicists, the theory of 

 spectra is beginning to be notorious for its complexity. I shall not 

 venture even to give the formulae, much less their derivations; it must 

 suffice to fill out the two lists of ^-values and /^-values on which I 

 have already begun, and the list of w-values or numbers-of-permitted- 

 orientations. 



The spinning atom is a congeries of electrons, all of them always 

 possessing spin, most of them usually possessing orbital motions; and 

 these motions are compounded with each other in such ways, that: 



First, the angular momentum of the spinning atom has one of the 

 values, 



p^ (0, i 1,1,2,1,3 ■■■)hl2ir. 



Second, the number of beams in the Gerlach-Stern experiment, or 

 the number of permitted orientations of the atom in the field, has 

 one of the values, 



w = 1, 2,3,4, •••. 



