160 Dr. W. Wilson on the 



with experimental results. It demands a photo-electric 

 " accumulation period." The experiments of Marx and 

 Lichtenecker* seem to show, however, that this period (if it 

 exists at all) must be much shorter than that calculated from 

 the principles of Planck and Ishiwara. 



The later theory of Planck and that of Ishiwara are not, 

 and cannot be, extended to aether vibrations, since such an 

 extension would involve the consequence that the aether 

 would possess energy at the absolute zero of temperature. 

 In fact, Planck, in developing his theory, has been at some 

 pains to leave the aether within the domain of ordinary 

 dynamical methods. In consequence of this, he is forced 

 to load his theory with a highly arbitrary additional hypo- 

 thesis connecting the probability of an emission of an 

 oscillator and the intensity of the radiation of like frequency 

 in its neighbourhoodf. 



These objections cannot be advanced against the form of 

 Quantum Theory I have suggested, while it has the advan- 

 tage over those of Planck, Ishiwara, and Bohr that only one 

 hypothesis is used which goes bevond ordinary dynamics. 

 This is the hypothesis (3) stated above, which lays certain 

 restrictions on the interchange of energy between material 

 systems and between such systems and the aether. It is not 

 claimed that this hypothesis goes far enough, or that it is 

 sufficiently complete to lead in all cases to unambiguous 

 results ; but it leads, I believe, to all those results of the 

 other theories mentioned which are in agreement with 

 experimental facts. Some of these have been dealt with 

 in my previous paper J. It leads to Einstein's law without 

 requiring an " accumulation period." This can be shown in 

 the following way : — The average energy of the vibrations 

 in the illuminated solid is given by 



hv 



hv 



e kT -l 



if we only consider vibrations perpendicular to a fixed plane. 

 Now, for the whole range of temperatures within which 

 photo-electric measurements have been made, and for values 

 of v in the ultra-violet or even in the visible part of the 

 spectrum, this expression reduces to an exceedingly small 

 fraction of hv. Most of the vibrations therefore in this 

 range of frequencies have no energy at all. The number 

 having the energy of hv will be a very small fraction of the 



* E. Marx & K. Licktenecker, Ann. d. Phys. xli. p. 124 (1913). 

 f M. Planck, loc. cit. p. 159. 

 I W. Wilson, loc. cit. 



