EVAPORATION OF ATOMS 367 



periments of Figs. 23 and 24 we have constructed, by the data of Table I, 

 a curve giving v as a function of dn in the range near 600 and from this 

 curve have read off the value of $„ by taking v = ao\ia as given by the steady 

 ion current method. 6(x, (by Eq. (12)) is then equal to ^„ + 0.005. The 

 horizontal portions of the full line curves in Figs. 23 and 24 have been 

 drawn by using these calculated values of ^qo- The close agreement of these 

 horizontal lines with the limiting values of $ given by the experimental 

 points is an illustration of the accuracy of our general equations for Va in 

 terms of 6 and T, and serves to justify our use of the surface phase postu- 

 late. 



Calculation of transient curves 



By expressing v as a function of 6 and T, we can, by integration of 

 Eq. (38), theoretically obtain ^ as a function of t. The experimental de- 

 terminations of Va have shown that Vq at constant T increases very rapidly 

 with 0, so that within any narrow range of values of 6, say between Oi and 

 02, we may put 



v^Kexp(He), (39) 



where K and H are constants within the range 61 to 62, but depend on the 

 values of 61 and 62. More strictly, we may define H by diflferentiation of 



Eq. (39) 



H = d\n v/dO. (40) 



In Fig. 25 the ordinates are values of H calculated in this way by 

 differentiation of the expression we have derived for In Va as functions of 

 and T. It is seen that except for very small and very large values of 6, 

 H changes relatively slowly with 6, so that the use of Eq. (39) is justified 

 if the range di to 62 is not very great. 



Inspection of the experimental data of Fig. 24 shows that the transition 

 between the sloping straight line (o = \yt) and the horizontal straight lines 

 {6 = ^00) is very rapid. Because of the large magnitude of H, a very small 

 decrease in 9 below 00 lowers v^ to a value which is negligible compared 

 to |i, so that dO/dt becomes constant. Thus, to calculate the whole curve, we 

 need only to have an expression for v which applies to a narrow range of 6. 



Introducing the value of v from Eq. (39) into Eq. (38), we find that 

 the final stead}' value B^ is given by 



v= A'exp (//^oo) =^- (41) 



Case I. If we start with a completely coated filament at f = O we obtain 

 by integration 



exp (-/i////cr.4i) = l-exp [-//(0-O]. (42) 



