Work Function of .Electron escaping from Hot Body* 197 



so that dz/dwcz %?(X—a)~P. It is required of ^that it be a 

 curve-factor having linear range from f= — qo to ? = a, 

 angular range pir, and such that | $?(£—a)~ p | is constant 

 for negative values of f. 



Forms of If known to satisfy these conditions are 



(r+«T^i and rX where 



^sKr+^r-a" 2 )}'-!^")/?}^ . . (is) 



^ 1 =(? V2 +a lyz ) <f+ ° )/at (?-a) (f -'" /4a exp(-|2* 3 a- 1/8 ). (19) 



Other forms of curve-factor which can be used in this 

 way may be got by assigning convenient forms to / in the 

 formula 



Exp tt-'J/ (&) log {(r+ o/tr-0 I/2 ) }<», . 



(20) 



or by using another formula given in article 40 of the 

 previous paper on the subject. In each case the form of the 

 nozzle depends upon the selected form of ^ The difficulty 

 of integrating the (c, f) relation may be formidable. 



XXIX. The Determination of the Work Function when an 

 Electron escapes from the Surface of a Hot Body. By 

 Horace H. Lester *. 



THE equation for the thermionic emission from a hot 

 metal in a vacuum has been deduced by Richardson f 

 and others from theoretical considerations involving the 

 assumption that the potential energies of an electron inside 

 and outside of the surface are different, so that an escaping 

 electron must do work against an equivalent adverse 

 potential difference. This difference in potential is repre- 

 sented in equivalent volts by the symbol <f>. The work 

 done by an escaping electron is represented in the well- 

 known Richardson equation 



i -- 

 i = ad' 2 e d 



by the constant b. 



In order to justify completely the assumption involved 

 in b, such a work function should be found to exist, and its 

 magnitude should be identical with that of b. 



In 1903 Richardson J showed that the escape of electrons 



* Communicated by Prof. H. L. Cooke, M.A. 

 t Proc. Camb. Phil. Soc. 1901, p. 2S6. 

 X Phil. Trans. A. vol. cci. p. 497. 



