RECENT STATISTICAL THEORIES 



721 



equal to the number of atoms. The values of x computed with this 

 last assumption should then be not less than the actual susceptibility; 

 they may be somewhat greater, because of the diamagnetic effect 

 which is opposed in sign to the paramagnetic effect and therefore 

 neutralizes it in part. Of this diamagnetic effect we can predict the 

 order of magnitude, and we may expect that it will be greater, the 

 higher the atomic number of the metal. 



The value of x proposed above is the value for absolute zero; for 

 higher temperatures a closer approximation can be obtained by using 

 two terms of the expansion in (66), instead of the first term only. 

 It appears, however, that the alteration is slight. Like the average 

 energy and the pressure, the susceptibility of the electron-gas should 

 be very nearly the same at all temperatures from absolute zero up 

 through room-temperature and far beyond. Now it is a fact that the 

 susceptibility of the alkali-metals is independent of temperature — a 

 fact so surprising, that the desire to explain it seems to have been 

 Pauli's principal incentive in undertaking this research. For if the 

 electron-gas were governed by the classical statistics, and the electrons 

 were as many as the atoms, the susceptibility of a metal would increase 

 as the temperature diminished and attain enormous values near the 

 absolute zero. 



When Pauli published the theory to which this section is devoted, 

 the experimental data indicated that the susceptibilities of potassium 

 and sodium were somewhat lower, those of rubidium and caesium 

 markedly lower than the predicted values — divergences which might 

 be charged to the diamagnetic effect or to faults in the theory. Recent 

 Canadian work, coming out very much a propos, has improved the 

 situation remarkably. This tabulation (taken from E. S. Bieler, 

 to whose article I refer for the sources) shows the comparison: 



(All numerical values to be multiplied by 10 •*) 



Singularly enough, the agreements are too good! one would expect 

 the diamagnetic effect to be more considerable than the very slight 

 discrepancies between the experimental and the theoretical values for 

 sodium, potassium, and caesium. Perhaps further work on the theory 

 of the diamagnetic effect would now be desirable. 



