RECENT STATISTICAL THEORIES 673 



as an assemblage of innumerable particles, a swarm of photons or 

 corpuscles of light. Nowadays at least the idea seems quite natural; 

 but of course, in the years when no one as yet had broken away from 

 the tradition that light is altogether wavelike, it would doubtless 

 have been thought a very wild one. Even after Einstein had ventured 

 such a breach with the past, nearly a score of years elapsed before 

 there was developed out of the theory of quanta an adequate conception 

 of the "radiation-gas." The historical sequence in the growth of 

 the atomic theory of matter was here inverted: there was abundant 

 evidence for the corpuscular theory of light, in phenomena such as 

 the Compton effect and the photoelectric effect showing the work of 

 individual photons, before the statistical theory of these corpuscles 

 was perfected. We now see that the trouble was, that even when 

 one accepts the notion of corpuscles of light without reserve, and even 

 when one knows the proper values of energy and momentum to be 

 assigned to these corpuscles, it still is not correct to apply to them the 

 same statistics as gives such good results when applied to the atoms 

 of matter. Bose discovered how to remodel the statistics, in order to 

 construct a competent atomic theory of the radiation in thermal 

 equilibrium in an enclosure. 



The other of the new extensions of atomic theory is partly a revival 

 ■ — the resurrection of the theory, first proposed some thirty years ago, 

 that part at least of the negative electricity within a metal acts like 

 a swarm of freely-flying corpuscles which collide now and again not 

 with each other but with the atoms. It was of course the classical 

 statistics which was always used in developing this theory. Moribund 

 because of several incurable discordances with fact, the theory was 

 resuscitated by Pauli and by Sommerfeld with a revision of the 

 statistics. It was not quite the same revision as enabled Bose to set 

 up an atomic theory of radiation, but a very similar one, invented 

 first by Fermi and later independently by Dirac. One cannot say 

 that the so-renovated "electron-gas theory" is a perfect explanation 

 of all the multifarious phenomena of the flow of electricity and heat 

 inside of metals and outward through the boundaries of metals. Its 

 initial successes, however, are so auspicious as to suggest that the 

 hope of further progress lies not in renouncing it (as seemed to be 

 almost inevitable before the alterations) but in amending it in its 

 details. 



Is the atomic theory of material gases to remain untouched by 

 these novel ideas? Apparently all three forms of statistics, the classical 

 and the two recent types, lead to very nearly the same conclusions 

 when applied to material gases. Only at remarkably low temperatures 

 and remarkably high densities do their predictions diverge; and under 



