Quantum 1 heonj of Vision. 291 



(3) Among the well ascertained facts of photo-electric 

 science the following concern the present theory, (a) The 

 electron is liberated with a velocity which, normally, 

 depends on the frequency of the light only : increasing as 

 the wave-length diminishes in such a way as to render the 

 kinetic energy a linear function of the frequency. (6) The 

 velocity is independent of the intensity (amplitude) of 

 the light. (c) For equal intensities of light of different 

 frequency, the light of highest frequency liberates most 

 electrons. (d) For lights of the same frequency, the 

 number of liberated electrons increases with the intensity. 

 (e) The electron in most cases absorbs one quantum, the 

 value of this quantum depending on the frequency according 

 to the well-known equation e = hv, where h is Planck's 

 constant ( = 6'57xl0 -27 erg. sec.) and v is the frequency. 

 In virtue of the absorbed energy, the electron acquires a 

 certain velocity and pursues a certain free path in the 

 medium till diverted by collision. 



(4) The value of the mean free path of electrons taking- 

 part in photo-electric emission from platinum has been 

 determined by Robinson (Phil. Mag. 1912, 1913). He 

 concludes that it is of the order 10 ~ 7 cm. Partzsch and 

 Hallvvachs (Ann. d. Phys. xli. p. 247, 1913) concluded that 

 99 per cent, of the photo-electrons from platinum emerge 

 from a layer thinner than 28 x 10 -7 cm. ; from which we 

 may conclude that the maximum range is about of this 

 value. Patterson (Phil. Mag. 1902, iii. p. 643, iv. p. 652), 

 dealing with the electrical conductivity of thin metallic 

 films, arrives at the conclusion that the mean free path in 

 various metals, including carbon, is of the order 10 6 cm. 

 He cites a result by Vincent (Ann. d. Chem. et d. Phys, 

 xix. p. 421, 1900) that for silver the mean electronic free 

 path is 6xl0~ 6 cm. Vincent's result also is derived from 

 measurements of resistance. 



Such of the above determinations as are based on direct 

 photo-electric measurement, using ultra-violet light, require 

 correction for the less value of the quantum associated with 

 visible wave-lengths : that is, if we assume the penetrating 

 power of the electron is dependent on its velocity. On the 

 other hand, judging by the influence of density on the co- 

 efficient of absorption of j3 electrons, a. correction for 

 density may be necessary when we venture to so far exter- 

 polate as to apply results on platinum to aqueous solutions 

 of low-density molecules such as the fluid of the retina. 

 Applying these corrections to the deductions o( Robinson 

 and to those of: Partzsch and Hallwachs, we find the mean 



U2 



