THERMIONIC ELECTRON EMISSION 463 



identical with equation (75) above if his Fo = Stt/T/, his 2j -\- \ — N 

 and his 2k -\- \ = K. His equation is not quite as general as ours 

 since he deals only with the case for which p = yu. 



Compton and Langmuir * in 1930 presented an interesting discussion 

 of the poor saturation in composite surfaces. They, too, proposed a 

 checkerboard or patch distribution like the one we are discussing, 

 and on page 151 of their paper they give an equation for the potential 

 above such a surface. Unfortunately there is an error in this equation 

 which was pointed out by Linford.*^ They use only a single summation 

 whereas a checkerboard distribution requires a double summation. 

 However, since they use only the first term of their summation and 

 since this first term is the same as the first term of the correct equation, 

 this error is not serious in their case. Their formula, too, is less 

 general than equation (75) since they deal only with the case p = ji; 

 this is equivalent to assuming that the white squares are clean tungsten 

 and only the black squares are covered. 



They reject their patch theory because (1) "to obtain departures 

 from the Schottky curve comparable to those observed, the patches 

 must be assumed to contain many thousands of atoms," and (2) 

 "the patch theory predicts a departure from the Schottky curve which 

 is small with small fields and increases with large fields, whereas 

 exactly the reverse is the actual case." f From what has been said 

 above it is clear that their second objection is really tied up with their 

 first one, for if larger patch sizes are assumed their statement is 

 incorrect and quite good agreement is found with experiment. They 

 assumed a value oi h = 10~® cm. whereas the experimental curves 

 require h ~ 10~^ cm. They feel that such "extremely non-uniform 

 distributions" or "such large clusters of adsorbed atoms" are "very 

 improbable." One reason for this belief is that "Becker has shown, 

 for example, that a thorium layer at emission temperatures behaves 

 like a two-dimensional gas on the surface." 



In my opinion these objections to the checkerboard or patch theory 



are not well founded. It seems quite natural to me that various 



crystals on the surface or various crystal facets may have somewhat 



different adsorptive properties and that consequently different crystals 



would be covered to different extents with thorium and would thus 



have different work functions. It is probable that the size of the 



squares should be comparable to the crystal size which is of the order 



of 10~^ cm. This is still true if thorium migrates over the surface 



of the tungsten. The successes of the patch theory presented above 



far outweigh these objections. 



* Reference 1, especially pp. 146-160, 

 t Reference 1, p. 157. 



