RECENT STATISTICAL THEORIES 715 



ginnings of a theory of the effects of surface-conditions on thermionic- 

 emission, and of the cold discharge. 



The Cold Discharge 



Suppose that a potential-difference is now applied between the 

 metal and a neighboring electrode, such that near the metal the 

 resulting field-strength is very great. Does it penetrate the region 

 which I have just been describing? Assume that it does penetrate as 

 far as the "surface" just defined. Then, everywhere beyond the 

 surface, the actual field is the resultant of this "applied" and the 

 previously-mentioned "intrinsic" field. The shape of the field- 

 strength-vs-distance curve is thus changed, in a way which is calculable 

 if we have postulated some particular original shape; and in certain 

 simple cases it is possible to calculate the consequent change of the 

 coefficient r, and therefore the electron-current — or the additional 

 electron-current — which the applied field causes to emerge from the 

 metal. This is the current known as the "cold discharge." 



Nordheim adopted for the field-strength-vs-distance curve, in the 

 absence of applied P. D., the shape which is most commonly proposed 

 — the inverse-square curve, the law of the "image-force" which a 

 charge in the vicinity of a conductor experiences because of its "elec- 

 trical image " in the conductor. For the current i of the cold discharge 

 he then derived this approximate formula: 



i = c'SF'-Qxp{- c"IF), (78) 



in which 7^ stands for the applied field, 5 for the surface-area of the 

 metal exposed to it, c' and c" for constants which can be calculated 

 when Wi is known. 



There are certain experiments (for an account of which I refer to 

 Nordheim's paper in the Physikalische Zeitschrift) which indicate 

 that the actual relation between the current and the field-strength 

 agrees in form with (78), but that the predicted values of c' and c" 

 are too large — too large by a factor of the order of ten in the latter 

 case, by several orders of magnitude in the former. However it is 

 possible to explain away these contradictions. One may assume, 

 for instance, that the actual surface concerned in the discharge is a 

 collection of small spots which altogether have but a small fraction 

 of the total area of the metal surface; and that over these small spots, 

 the field-strength is much higher than it would be if the metal were 

 everywhere uniform and smooth. The ratio of the observed to the 

 predicted value of c' then gives the fraction of the total surface which 

 is covered by these "active" spots, and the ratio of the observed to 



