Photoelectric and Photochemical Action. 481 



were not really essential. Equation (14) has also been ob- 

 tained by Einstein *, who bases his demonstration on the 

 assumption that radiation o£ the same frequency and equal 

 amount as that absorbed during emission is given out on 

 recombination. This hypothesis seems to be of a restrictive 

 character and results in the existence of states of radiation 

 in equilibrium with matter which are different from the 

 complete radiation characteristic of that temperature. The 

 justification urged for the existence of such states of equi- 

 librium between matter and radiation is that they would not 

 violate the second law of thermodynamics. It appears, how- 

 ever, from the foregoing considerations that the particular 

 limitation set up by Einstein is not really essential. 



In a recent paper Planck f has considered the equilibrium 

 between radiation and matter which liberates electrons under 

 its influence. He arrives thus at a consistent system which 

 includes Planck's law of distribution for the radiant energy 

 .and Maxwell's law for the energy of the electrons. The law 

 which Planck finds to govern the amount of energy ab- 

 stracted from the radiation by the liberated electrons agrees 

 with that found above in that it approaches hv as the tem- 

 perature approaches zero. This follows from equations (12) 

 •and (28) of Planck's paper. 



Einstein's demonstration leads to (14) as a limit which is 

 •true for small radiation densities. This may be regarded as 

 analogous to the result obtained above, according to which 

 (14) is necessarily valid only at low temperatures ; since low 

 temperatures correspond to small radiation densities. 



It is evident from what has been said that the functions 

 X (y-> v , T) which satisfy the equation 



x(v fl ,v ,T)dv = . . . (15) 



^0 



hv 

 EX _ l 



are of great interest in the theory of photochemical 

 action. 



It will be observed that we have not proved that (14) is 

 not true at all temperatures. All we have proved is that if 

 photochemical action is fundamentally independent of 

 temperature at low temperatures, then at such temperatures 

 (14) is true. 1 shall show in a moment that a consistent 



* Ann. der Physik, vol. xxxvii. p, 832 (1912) ; Journ. do Physique, 1913. 

 t Sitzungsber. der k. Preuss. Akad. der Wiss., Physik. -Math. Classe, 

 xviii. p. 350 (1913). 



