344 PHENOMENA, ATOMS, AND MOLECULES 



Subtracting 6n from ^obs in accordance with Eq. (12) we obtain the 

 values of 6a given in the 7th column. The 8th column contains 0', the frac- 

 tion of the active surface occupied by adatoms : 



The 9th column contains values of B' calculated from Eq. (16) from 

 the values of [i, da, and T in the table. These results fully justify our as- 

 sumption that B' is independent of 6a and indicate that the adatoms in the 

 active areas are so far apart that they do not influence one another and 

 therefore are to be regarded as isolated active spots. Eq. (16) becomes 



logio [m(1 - d')/d''] = 28.58 - 19,300/r. (17) 



These "active" spots may be located at any reentrant angle between crystal 

 planes or at irregularities in the lattice which may cause a Cs atom to be 

 held more tightly than at other points. Thus the active area 6ax will probably 

 vary in extent depending on the grain size of the filament and on the heat 

 treatment given. However, the properties of the normal surface will be 

 unaffected. It is to be noted that Eq. (17) is in such a form as to be valid 

 even if 6ai should change. 



VII. EQUATION OF STATE AND EVAPORATION EQUATION 

 FOR THE ADSORBED Cs FILM 



The equation of state of the two dimensional gas making up the adsorbed 

 film was found theoretically ^ for molecules which repel as dipoles, by 

 means of the Clausius virial. The forces are repulsive forces varying as the 

 inverse 4th power of the distance (r) between adatoms. This equation gave 

 the spreading force F in terms of 6, T, and the dipole moment M. By use of 

 Gibbs' equation for the adsorption isotherm, the rate of evaporation of 

 atoms Va could be expressed in terms of 6, T, and the spreading force F. 

 These equations were of the form required by the experimental data. 

 Therefore F and hence M could be calculated as functions of ^ entirely 

 from data on the evaporation of atoms. 



The contact potential of the surface against that for pure tungsten 

 could also be calculated from the relation. 



Vc = 27rM(T(c.g.s.) - 1885^/c-:^ volts. (18) 



After obtaining Vc, the electron emission Ve was calculated for any value 

 of 6 from the Boltzmann equation, 



vJv,, = exp{V\e/kT) (19) 



and Dushman's equation for v^, the electron emission from clean tungsten. 



