704 BELL SYSTEM TECHNICAL JOURNAL 



tory, A is indeed very small. The new statistics leads to a result 

 indistinguishable from that of the old statistics. To discriminate 

 between the two by experiments on material gases, one would have 

 to work with temperatures so low and densities so high that the 

 gases would probably either be liquefied already, or at least would 

 be in a condition very different from that "ideal" state to which the 

 statistics is tacitly supposed to apply. Perhaps though it is not 

 impossible to make the test with helium or hydrogen. 



A this point apparently Fermi stopped. But it occurred to Pauli 

 that if the new statistics were applied to an electron-gas as dense as 

 that which Riecke and Drude had supposed to pervade the interiors 

 of metals, the deviations from the classical distribution would be 

 much more pronounced. For, in the first place, the mass m of the 

 individual electron is smaller by several orders of magnitude than the 

 mass of the atoms or molecules of any material gas. And, in the 

 second place, if the number N of free electrons in a piece of metal 

 is as great as or greater than the number of atoms, then it is thousands 

 of times as great as the number of particles in an equal volume of a 

 material gas. Now the quantity equated to A in equation (64) 

 contains N in the numerator and w^'^ in the denominator, and for the 

 hypothetical electron-gas within the metals it is no longer small. 

 The expression (64) for A is then no longer acceptable. 



While the statement just made about m is based on a fact of experi- 

 ence, the statement about N is not so firmly grounded. We have no 

 direct knowledge of the number of free electrons in a given volume, 

 say the number n {= NjV) in unit volume, of a metal. This as I 

 said above is a disposable constant of the theory. One of the tests 

 of the theory is whether one can obtain correct numerical values of 

 half-a-dozen properties of a metal by choosing a single value of n 

 for that metal. So long as the classical statistics was applied to the 

 electron-gas, this was impossible. If the value of n was put as high 

 as the number of atoms in unit volume, the predicted value of specific 

 heat (and we may now add, the predicted value of susceptibility) 

 turned out to be too large; if n was lowered sufficiently to avoid this 

 particular discordance, other predictions were impaired. It was 

 however the general impression, that one should put n equal to the 

 number of atoms or a small multiple thereof. I suspect that this 

 decision was largely due to a feeling that since the free electrons are 

 detached from atoms, and since all the atoms are alike, any atom 

 should supply as many free electrons as any other. However that 

 may be, it was natural though not inevitable for Pauli and for Sommer- 

 feld to link the Fermi statistics with the postulate that there are as 



