A CENTURY'S PROGRESS IN PHYSICS 383 



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 

 inexact to any such extent as the divergence between 

 theory and experiment would indicate, is inconceivable; 

 that they are insufficient when applied to motions of elec- 

 trons in such intense fields as occur within the atom 

 seems no longer open to doubt. In order to obtain a 

 radiation formula in accord with experiment Planck has 

 found it necessary to extend the atomic idea to energy, 

 which he conceives to exist in multiples of a fundamental 

 quantum hv, v being the frequency and h Planck's con- 

 stant. That some such hypothesis of discontinuity is 

 essential in order to obtain any law that will even 

 approximately fit the experimental facts has been proved 

 by Poincare. But the precise spot at which the quantum 

 is introduced differs for every new derivation of Planck's 

 law. As deduced most recently by Planck himself, the 

 quantum shows itself in connection with the emission of 

 energy by the material oscillators with which the radi- 

 ation field is in equilibrium. These oscillators are sup- 

 posed to act quite normally in every respect except 

 emission; here the radiation demanded by the electro- 

 dynamic equations is cast aside, and an oscillator is 

 supposed to emit at once all its energy after it has accu- 

 mulated an amount equal to some integral multiple of hv. 

 A form of the theory which does not contain this improb- 

 able contradiction of the firmly established facts of 

 electrodynamics introduces the quantum into the specifi-. 



