WEBSTER. — PIANCK'S RADIATION FORMULA. 145 



We have been guided thus far by the necessity of correlating experi- 

 mental facts. Let us therefore judge these assumptions by the 

 number of experimental facts for which they account. 



It would undoubtedly be possible to set up numerous models and 

 sets of equations which would account, in a more or less complex way, 

 for this law of emission, but it would not be profitable at present, as 

 the laws would not be simple, and probably not very instructive. 

 Therefore we shall not attempt to do so here. 



The Derivation of Planck's Law. Planck's formula may now 

 be derived by an argument almost like his, except as follows: 



First, for the proof, Part IV, Chapter II, that the rate of absorption 

 is constant with respect to time and proportional to the intensity of 

 the light, we may substitute the fact that this is a well known result 

 of an equation of the type of (3) when the intensity of the light is 

 constant. The proportionality factor, as we have seen, is the same 

 as in Planck's theory, though since it cancels out during the proof of the 

 law of radiation, this fact is of no importance here. 



Second, in Part III, Chapters III and IV, since the energy of a 

 magneton can never get below the amount it has just after emission, 

 the excess over this amount is what must be considered in the calcula- 

 tion of the entropy of the system. 



Third, in the calculation of the distribution of energy among the 

 oscillators, Part IV, Chapter III, we must divide them into two classes, 

 those which are not emitting at the instant in question, and those that 

 are; for the former, Planck's argument on the fraction of them in any 

 energy interval at any time applies without change. Then since each 

 one emits exactly as much energy as it absorbs, and at a constant rate, 

 the distribution of the emitting ones, and therefore of both classes 

 together, must be exactly like that of the absorbing ones. The 

 transfer of energy to and from the molecular motions, being inde- 

 pendent of the amount of energy in the steady current, cannot affect 

 this distribution. 



Thus we have Planck's law, derived by an argument almost identical 

 with his, from assumptions which, although they are not so simple as 

 his, are inconsistent with the classical dynamics only in the internal 

 structure of the magneton. Being consistent with the classical 

 electrodynamics, they correlate the phenomena of heat radiation with 

 those of optics and electricity, at the same time giving an account of 

 the law r s of photo-electric and photo-chemical phenomena. Finally, 

 being based on Parson's magneton, they correlate all these phenomena 

 with those of chemical combinations. 



