428 BELL SYSTEM TECHNICAL JOURNAL 



thermionic cathodes. For the present it would seem best to consider 

 S as an unknown whose value lies somewhere between 1 and 10 for 

 rough surfaces such as those on oxide coated filaments, and between 

 1 and 2 for relatively smooth surfaces such as tungsten. The exact 

 value will no doubt depend on the exact treatment of each surface. 



Fortunately the uncertainty of our knowledge of 5 does not seri- 

 ously affect our correlation made above. It is necessary to divide 

 values of i and A in the empirical equations by 5 to reduce to the basis 

 of true surface area before comparing them with theoretical equations. 

 The observed values of i and A should thus be reduced by 25 to 50 

 per cent for smooth surfaces and by larger values for rough surfaces. 

 Thus in the case of surfaces, such as tungsten, molybdenum and 

 tantalum, for which A has the value 60, the true A should be between 

 about 30 and 45 as compared with a theoretical value of 120. Since 

 the deviations from 120 are due to a temperature dependence of the 

 work function, it means that we must postulate a somewhat larger 

 value of a in equation (34) than otherwise. 



On the Reflection Coefficient 

 There is still another topic that enters into the correlation of experi- 

 ment and theory, namely the reflection coefficient. Thus far we have 

 assumed that every electron whose normal component of velocity 

 exceeded a certain value escaped while those having less than this value 

 failed to escape. On the classical viewpoint this assumption is jus- 

 tified but on the quantum-mechanical viewpoint there is a finite prob- 

 ability that the electron considered as a wave will be reflected at the 

 surface even though its velocity is such that it could escape ; also a 

 wave electron has a finite probability of passing through a potential 

 peak when classically its velocity is not large enough to permit it to 

 pass over the top of the peak. Consequently we should include an 

 average transmission coefficient D in the theoretical emission formula. 

 D = \ — r where 7 is the average reflection coefficient. Equation 

 (22) then becomes 



i= U{\ - r)r- exp. (- w/T). (38) 



A number of writers ^- ^ have attempted to explain the deviations 

 between A and U by postulating such values of r that A = U{\ — r). 

 This explanation is possible only for cases for which A < U since 

 < r < 1. Even when A < U the numerical values turn out to be 

 such that the difference between A and U cannot be accounted for by 

 computed probable values of r. These values of r are determined 

 chiefly by the shape of the curve giving the work an electron must do 



