the Emission- Spectrum of a Black Body. 215 



spectrum of a black body could be completely determined 

 from the law of the maximum of entropy. As I have shown 

 in an earlier paper, the entropy of radiation of a known 

 intensity and colour can be determined, but there is no 

 obvious physical process by which an alteration in colour 

 such as that desired can be observed to be taking place. A 

 determination of the distribution of energy is therefore im- 

 possible without hypotheses. 



An attempt has been made by E. von Lommel** and W. 

 Michelsonf to found a complete law of radiation on certain 

 premises. For this purpose the latter makes the following 

 stipulations : — 



(1) Maxwell's Law of the division of velocities among a 

 great number of molecules holds also for solids. 



(2) The period of oscillation t, which is excited by a mole- 

 cule, is connected with its velocity of propagation v by the 

 equation 



T= J 



V 



where p is a constant. (This assumption is based on a defi- 

 nite conception with regard to the excitation of the radiation.) 



(3) The intensity of the radiation sent out from a molecule 

 is proportional to the number of molecules having the same 

 time of oscillation, is further an undetermined function of the 

 temperature and a likewise unknown function of the kinetic 

 energy, which by a further hypothesis is restricted to a power 

 of v 2 . 



The law T which Michelson obtains from these assumptions 

 gives for the wave-length X m of the maximum of energy 



const. 



m V0 



where 6 denotes the absolute temperature. As for the rest, 

 this law leaves the total emission as a function of the tempe- 

 rature undetermined. 



I have now endeavoured to carry out the idea of Michel- 

 son, of making use of Maxwell's law of the division of 

 velocities as a basis for the law of radiation, and at the same 

 time to lessen the number of the hypotheses which, on account 

 of our total ignorance of the cause of the radiation, are par- 

 ticularly uncertain, by utilization of the results obtained by 

 Boltzmann and myself by pure thermodynamic treatment. 



The remaining hypotheses, however, still possess some 



* Wied. Ann. Hi. p. 251 (1877) 



t Journal de Physique [2] vi. (1887). 



