SURFACE CHEMISTRY 57 



By substituting in this equation the values of F from Eq. (23), Va can 

 be calculated in terms of M. Actually we have reversed the process. From 

 the experimentally determined values of Va as functions of and T, we 

 have calculated F by Eq. (24) and from these by Eq. (23) have obtained 

 M, These values of M are found to be functions of but are not appreciably 

 dependent on T, although a slight dependence is indicated by the form of 

 Eq. (23). 



A test of this theory can be made since the values of M obtained from 

 Va may be compared with values of M obtained from the contact potential 

 which may in turn be obtained from measurements of Vg. The contact 

 potential V of the surface covered with an adsorbed film as compared with 

 that of a pure metal surface is given by 



V = 27TaM. (25) 



Furthermore the electron emission Ve is related to the contact potential 

 V by the Boltzmann equation 



VeK = exp (Ve/kT) , (26) 



where Vw is the electron emission from pure tungsten at the same tempera- 

 ture. The full line curve in Fig. 2 gives values of V calculated by Eq. (25) 

 from M as determined from Va. The points shown by small circles represent 

 values of V obtained from Va by Eq. (26). 



The values of V obtained by these two independent methods agree 

 nearly perfectly when 0<o.5. The deviations at higher values of seem 

 to indicate that for high values of the short range forces are somewhat 

 greater than those given by the factor i — 0, the denominator of the first 

 term of the second member of Eq. (23). Calculation shows that for a value 

 of = 0.75, that part of the spreading force which is due to the short 

 range forces is actually 45 percent greater than is given by the first term in 

 the second member of Eq. (23). 



It is also possible to calculate the contact potential from data on Vp, the 

 rate of evaporation of ions from the surface. The values of Va, Ve and Vp 

 must be so related to one another that they give concentrations of atoms, 

 electrons and ions in the vapor space near the filament which agree with 

 the thermodynamical requirement for equilibrium among these particles. 

 We may thus put 



nenp/na = K, (27) 



where K is the equilibrium constant that can be determined from the ioniz- 

 ing potential in accordance with the Saha equation. When this is done, 

 and we combine with the Boltzmann equation and the Dushman equation 



