458 BELL SYSTEM TECHNICAL JOURNAL 



1 is extrapolated from data at T = 1650° K.; curve 2 is extrapolated 



from data at 1503 and 1650° K. The extrapolations were made by 



extending Richardson lines; curves 1 and 2 are, of course, not quite as 



certain as data taken at 1270° K. The currents at any V or F vary by 



large factors as /, the fraction of the surface covered with thorium 



varies. In order to compare the curves more effectively log i/iv=m 



has been plotted. This is equivalent to shifting the log i curves until 



they pass through a common point at V = 100 or ^J F = 60.5. A 



comparison of this family of curves with the computed curves in Figs. 



16 and 17 shows a great similarity with Fig. 17 but not with Fig. 16. 



In Fig. 17, b was constant while m was varied. From this similarity 



it follows that the experimental curves in Fig. 20 are consistent with an 



approximately constant value of b but varying /x. 



From the position and shapes of the curves in Fig. 20, we estimate 



that the value of 6 or the crystal size is about 4 X 10"^ cm. This value 



is probably too large for curve 1 and too small for curve 6 but unless 



a complete analysis were made, it is not desirable to discuss small 



variations in b. It is apparent from the figure that n changes with /. 



We have estimated the following values of n, the second significant 



figure being in doubt: 



TABLE III 



Values of /, the Fraction of Surface Covered with Thorium and Values of 

 fi in Volts (eq. 71) ju in Volts = 12O07rju/. 



/ = 0.04 0.33 0.57 0.86 1.0 1.11 



M(volts) = 0.23 0.44 0.45 0.36 0.28 0.23 



These values of n are reasonable. Furthermore, the way in which 

 H varies with/ is to be expected from the shape of the work function vs. 

 f curve which will be discussed later under adsorption. 



A particularly interesting test of the patch theory is furnished by 

 Taylor and Langmuir's ^^ electron emission from cesium on tungsten 

 because in this case the crystal size of the tungsten is known. In 

 Figs. 11,12 and 13 of their article they give log i vs. V or ^l V curves. 

 Since the diameter of the filament is given as 2 mils, it is possible to 

 convert values of V to values of F and to obtain log i vs. V F curves. 

 We have done this for the curve for d = 0.60 and have then analyzed 

 it on the basis of the hill and valley theory. This analysis gave 

 6 = 0.8 X 10-^ cm. and ju = 0.20 volt. The article states* "the 

 average grain size in these filaments was about one-fifth the diameter 

 of the wire." So that the average grain size was about 1 X 10~' cm. 

 which is about the same as the calculated value of b. 



* Taylor and Laiigmuir, reference 25, page 431. 



