716 BELL SYSTEM TECHNICAL JOURNAL 



the predicted value of c" gives the reciprocal of the factor by which 

 the field-strength must be multiplied. 



This explanation has the disadvantage of being not only plausible 

 but much too easy. So long as there is not any independent evidence 

 about the area of the effective spots or the field-strength prevailing 

 over them, the theory simply delivers an equation with two disposable 

 constants, which is not very valuable for testing the underlying 

 assumptions. It appears from the data examined by Nordheim, 

 however, that the ratio of the predicted to the observed value of c'' 

 is always between 10 and 20, and the ratio of the observed to the 

 predicted value of c' is always about 10~'° (at least for tungsten). 

 This uniformity of the two quantities which figure in the theory as 

 the disposable constants may be taken as a confirmation of some 

 weight. 



Photoelectric Effect 



According to the former theory, the elementary process of the 

 photoelectric effect runs thus: a quantum dives into a metal, and gives 

 its whole energy (say Ea) to an electron initially at rest, which then 

 may escape from the metal after suffering a reduction of kinetic 

 energy equal at least to Wa and possibly more (more, that is to say, 

 if the electron loses kinetic energy on its way to the surface). Even 

 if we suppose that the electron originally belonged to an electron-gas 

 conforming to the classical statistics, its initial energy would almost 

 always be quite negligible compared to that which the quantum gives 

 it. But if the electron-gas obeys the new statistics, it comprises 

 electrons with energy-values ranging up to Wi. However if the new 

 statistics is valid, then the reduction of kinetic energy at the boundary 

 is also greater by Wi than we have hitherto supposed. The net 

 result is, that by the new statistics as by the old we derive Einstein's 

 equation for the maximum kinetic energy of the electrons expelled 

 by quanta of frequency v. 



£n,ax = £o + Wi - Wa = llV + COUSt. (79) 



only the additive constant is now {Wi — Wa) instead of (— Wa)- 

 This additive constant should as before agree with the thermionic 

 constant b. 



The new theory has one marked distinction, probably an advantage, 

 over the old: it implies a sharply definite maximum kinetic energy — 

 that is to say, the distribution-in-energy function of the escaping 

 electrons should jump suddenly from zero to some definitely higher 

 value at the energy-value E = -E,„a.x prescribed by (79) ; the slope of 



