A New Equation for the Distribution of Radiant Energy.

From certain considerations based on Einstein's theory of light quanta, I have recently deduced' an equation for the entropy of radiation, as a function of energy density and frequency, which is identical with the one obtained by Planck. From this expression it would seem possible to proceed immediately to Planck's equation for the distribution of radiant energy, by using a method which has hitherto been regarded as unquestionably valid. The deduction, however, rests upon a certain tacit assumption, as may be seen by a brief review of the method used in Planck's "Theory of Heat Radiation." Using the same notation as in the preceding article, U and S are the total energy and entropy of a hollow containing radiation, u and s are the corresponding densities, and u, and s, represent the rate of change of these densities with the frequency, as we proceed through. the spectrum. Thus, in the total volume V rX U= Vfuu,dv (1)