Statistical Theories of Matter, Radiation and Electricity ^ 



By KARL K. DARROW 



The atomic or " kinetic " theory of gases, with its interpretations of such 

 qualities as temperature, pressure, viscosity and conductivity, has ranked 

 forniore than half a century as a very important part of theoretical physics. 

 A corresponding thepry for radiation and for negative electricity is much 

 to be desired, since it is known that in many ways each of these entities 

 behaves as though it were atomic. There are, however, differences among 

 the three, and only within the last five years have these been formulated 

 suitably. This article is devoted to the resulting statistical theories. 



THE major subjects of this article are two extensions of what 

 formerly was called atomic theory — that is to say, the attempt 

 to explain as many as possible of the properties of pieces of matter 

 large enough to be visible and tangible and ponderable, by visualizing 

 these as swarms of tiny particles each endowed with only a very few 

 and simple qualities. Among the properties of gases, for example, 

 are pressure and viscosity and entropy and temperature. Conceivably 

 one might invest the ultimate atoms with all four. The atomic theory 

 of gases as it stands today, however, is the outcome of a very different 

 procedure. It is the achievement of an effort to interpret these four 

 properties and several more as features of a hypothetical assemblage 

 of very many corpuscles all alike, and not possessing them nor 

 any others except position and velocity and mass (and moment of 

 inertia, sometimes) and the liability to make elastic impacts with 

 each other. On the whole the effort has been remarkably successful. 

 Therefore viscosity and temperature and entropy are not attributed 

 to single atoms, but pictures and expressions for them are derived as 

 qualities of the assemblage. The theory which leads to these results 

 is called statistical; it is based on certain assumptions which, in the 

 form in which they were originally made, constitute the classical 

 statistics. The successes of the classical statistics are a part of the 

 evidence that matter is corpuscular. Once they were nearly the 

 whole of the evidence, for they antedated the striking demonstrations 

 of individual atoms which now spring to the mind whenever one is 

 asked to state the reasons for accepting the atomic theory. 



Radiation resembles a gas in some respects. Entropy and temper- 

 ature and pressure, for example, are properties displayed by radiation 

 when enclosed in a space surrounded by a wall of even temperature, 

 just as they are by a gas in a like situation. It seems quite natural 

 that one should try to interpret them in the same way as for a gas 

 they are interpreted by the atomic theory: imagining the radiation 



1 Physical Review Supplement, Vol. 1, July 1929, pp. 90-155. 



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