348 L. Page — A Century's Progress in Physics. 



the radiation itself, meaning by this the temperature of 

 the material body with which it would be in equilibrium. 



The problem of black radiation is to find the distribu- 

 tion of energy among the waves of different frequencies 

 at any given temperature. The first step toward a solu- 

 tion was made when Stefan showed experimentally, and 

 Boltzmann as a deduction from thermodynamics and 

 electrodynamics, that the total energy density summed 

 up over all wave lengths varies with the fourth power of 

 the absolute temperature. If the energy density is 

 plotted as ordinate against the wave length as abscissa, 

 the experimental curve for any one temperature rises 

 from the axis of abscissas at the origin, reaches a maxi- 

 mum, and falls to zero again as the wave length becomes 

 infinitely great. Now Wien's displacement law, the 

 second important step toward the determination of the 

 form of this curve, shows that as the temperature is 

 raised the wave length to which its highest point cor- 

 responds becomes shorter, — in fact this particular wave 

 length varies inversely with the absolute temperature. 

 This theoretical conclusion is entirely confirmed by 

 experiment. (J. W. Draper, 4, 388, 1847.) 



Farther than this general thermodynamical princi- 

 ples are unable to go. Statistical mechanics, however, 

 asserts that when a large number of like elements are in 

 thermal equilibrium, the average kinetic energy asso- 

 ciated with each degree of freedom is equal to a universal 

 constant multiplied by the absolute temperature. This 

 " principle of equi-partition of energy" has been applied 

 in various ways to obtain a radiation law. The most 

 straightforward method is based on the equilibrium 

 which must ensue between radiation field and material 

 oscillators when the latter emit, on the average, as much 

 energy as they absorb. From whatever aspect the prob- 

 lem is treated, however, the radiation law obtained from 

 the application of the equi-partition principle is the same. 

 And while this law agrees well with the experimental 

 curve for long wave lengths, it shows an energy density 

 that becomes indefinitely great for extremely short 

 waves, which is not only at variance with the facts, but 

 actually leads to an infinite value of this quantity when 

 integrated over the entire spectrum. 



The Energy Quantum. — Now the principle of equi- 

 partition of energy rests securely on most general 

 dynamical principles. That these dynamical laws are 



