468 BELL SYSTEM TECHNICAL JOURNAL 



In the preceding sections the thermionic work function W was 

 shown to be equal to P — K where P is the difference in potential 

 energy between an electron at rest inside and outside of the metal 

 and K is given by equation (16). If we assume that there is one free 

 electron per atom in the metal for all elements, then 



Kje = 2S.9{DIM)\ (77) 



where D is the density of the metal and M the atomic weight. 



From values of Kje given by equation (77) and experimental values 

 of Wje, Rother and Bomke calculated Pje for a number of elements. 

 Their values of Pje were said to be in accord with the empirical 

 equations 



Pie = 12.6{DzJMy^ for some elements (78) 



and 



Pje = \6.3{Dz/M)i for all other elements, (79) 



where z is the maximum chemical valence of the element. 



We have computed values of K/e from equation (77) and with the 

 most probable values of W/e from Table IV have determined the 

 probable values of P/e. Since the work function and the heat func- 

 tion differ by only small amounts, it is justifiable to use the heat func- 

 tions for W/e. To test equations (78) and (79) we have plotted log 

 P/e vs., log (Dz/M) in Fig. 23. According to equations (78) and (79), 

 the points should fall on two straight lines in this plot. The two lines 

 are shown in the figure and have a slope of f . The values of z used in 

 this plot are those given by Rother and Bomke. The points lie in the 

 general neighborhood of the lines but there is no clear indication of a 

 division into two groups. The deviations in about half of the cases are 

 larger than the possible experimental error. 



Bomke ^^ has recently found that his values of P/e (from calculated 

 K/e and experimental W/e) plotted against the compressibility gave a 

 smooth curve. The equation of this curve was 



P/e = 0.30k-K (80) 



where k is the compressibility. Unfortunately he plotted his data on a 

 linear scale and most of the points on his plot were clustered near one 

 axis where the curve was steep, making it difficult to estimate the 

 deviations. A plot of log P/e vs. k which is similar to Fig. 23 showed 

 that the deviations were of the same order of magnitude as the devia- 

 tions in Fig. 23 previously discussed. Hence values of P/e calculated 



