714 BELL SYSTEM TECHNICAL JOURNAL 



come up to the bounding surface from within with energy sufficient 

 to escape are nevertheless reflected. A factor (1 — r) — r being 

 called the coefficient of reflection, and being put equal to | — then 

 enters into the formula, and balances out the factor 2 introduced by 

 giving the preferred value to G. Moreover one may explain values 

 of the constant still smaller than 60.2, or between 60.2 and 120.4, 

 by adjusting r accordingly. But there are also recorded values 

 enormously greater than 120; so evidently something remains to be 

 understood. ^° 



The methods of wave-mechanics have been applied by Fowler and 

 Nordheim to the problem of evaluating this coefficient of reflection. 

 They have attained some notable results in the fields of thermionics, 

 cold discharge, and photoelectric effect. These however are conse- 

 quences not of the new statistics only, but of a combination of the 

 new statistics with the new way of considering the transmission and 

 reflection of electron-waves at surfaces. There is not space for me 

 to deal with the latter, beyond indicating its point of departure and 

 its chief results. 



Thus far I have been speaking of a metal as an equipotential region 

 surrounded by a surface at which there is a sharp potential-drop, 

 and beyond which there is the equipotential region of outer space. 

 Fowler and Nordheim however, like Schottky and others before 

 them, conceive a metal as an equipotential region surrounded by a 

 surface, beyond which lies a region in which there is a field (or at all 

 events an image-field) the strength of which is a function of the 

 distance from the surface. The quantity Wa appears as the integral 

 of this field-strength, from the surface to infinity. Electrons of a 

 given kinetic energy being supposed to fall against the surface from 

 within, the fraction which fails to pass completely through the region 

 of the field depends upon the kinetic energy of the electrons and 

 upon the shape (not solely upon the integral) of the field-strength-vs- 

 distance curve. The average value of this fraction for all the electrons 

 of all speeds coming up to the surface from within — the average 

 being taken with due regard to the relative proportions of the electrons 

 of various speeds, that is to the distribution-in-velocity — is the 

 coefficient r aforesaid. For certain simple shapes of the field-vs- 

 distance curve it may be calculated. One thus arrives at the be- 



1" If the empirical equation is of the form i = aT" exp (— hjT), then whatever 

 may be the values of the constants a and b, one can always claim that it agrees with 

 the foregoing theory provided one assumes that Wi or r or both vary with temperature 

 in just the proper way. But, as Fowler puts it: "the variety of possible uncon- 

 trollable hypotheses (if such assumptions are to be admitted) becomes too large 

 for profitable discussion." 



