326 PHENOMENA, ATOMS, AND MOLECULES 



d^. Since, however, our knowledge of o depends upon our postulated value 

 of Oi, as given by Eq. (2), it is preferable to express these properties as 

 functions of the covering fraction $ defined by .. 



= Ga/oai. (4) 



All the values of 6 in this paper have been calculated in this way from Ga 

 by using the value of Oai given by Eq. (3). It should be noted that 6 is 

 also equal to o/oi. 



We must also have clearly in mind the relation of 5 and Sa to our 

 definitions of \i and v. We shall define [.lo as the number of incident atoms 

 per unit time per unit area of apparent surface Sa- Thus from the kinetic 

 theory 



|i.o =^ p(2KmkT)'^'^' = 3.796/'T"*/2 atoms cm"^ sec."^ (5) 



where p is the pressure in baryes and T is the temperature of the caesium 

 vapor. 



In a similar way we define v,, as the number of atoms which escape from 

 the filament by evaporation per unit time per unit area of apparent surface 

 (Sa). 



We wish, however, to know the rate of evaporation per unit area of 

 true surface 5" for this alone should be an intrinsic property of the adsorbed 

 film. 



In the steady state to which Eq. (i) applies, the condensation on and 

 evaporation from each element of area must balance. The atomic flux 

 density in the neighborhood of the filament must therefore be isotropic 

 just as is the heat radiation within an enclosure at uniform temperature. 

 The values of |x and v over the surface of S, in Fig. i, must thus be the 

 same as over the surface Sa- 



Consider now the irreversible evaporation of adatoms from a filament 

 in a space in which |x = o. We see from 5 in Fig. i that a large fraction 

 of the atoms that evaporate from the valleys (and a smaller fraction from 

 the peaks) are intercepted by the surface of the opposing peaks before they 

 can escape. The concentration of adatoms thus decreases near the peaks 

 faster than in the valleys unless surface mobility equalizes their con- 

 centration. 



If mobility does maintain a uniform 6 and if a = i so that all incident 

 atoms condense, it follows from the reversibility principle (see Section 

 XII) that the emission occurs in accord with Lambert's cosine law. The 

 situation is exactly analogous to that in optics where the brightness of an 

 incandescent black body is independent of its contour. 



During irreversible condensation from a vapor with a given \i, the 

 concentration at the peaks should increase faster than in the valleys, assum- 



