RECENT STATISTICAL THEORIES 713 



or thereabouts, and the quantity to be added to the observed constant 

 b is larger than h itself. 



Is there then any other way of determining the work-function than 

 out of this apparently ambiguous current-vs-temperature curve? If 

 there is a direct and independent way, it may serve not only to decide 

 between the two statistics, but also — if it favors the new by yielding 

 a value for Wa greater than the thermionic b — to give an experimental 

 value for {W,, — b) = Wi and hence for the disposable constant n 

 which is the one uncertain quantity in the theoretical formula for Wi. 

 It may, that is to say, serve to determine the number of electrons 

 per unit volume of the electron-gas. 



Now it seems that the diffraction of electrons by crystals provides 

 an independent and direct way of determining the work-function. 

 For in the phenomena in which negative electricity behaves as a 

 wave-motion, the work-function figures in the index of refraction; 

 and the index of refraction of a metal may be determined from the 

 diffraction-patterns which it forms when irradiated with slow electrons. 

 Ample data concerning one metal — nickel — have already been acquired 

 by Davisson and Germer, and from these it transpires that the work- 

 function is much in excess of the thermionic constant b — so much 

 indeed, that the corresponding value of Wi implies that there are 

 twice as many free electrons as atoms in the metal, or even more.^ 

 The values deduced for the work-function from the refractive index 

 vary however with the speed of the electrons; and it is evident that 

 much remains to be understood. 



The factor which multiples T^ exp £— (Wa — Wi)/kT^ in the 

 right-hand member of (76) involves universal constants only (sup- 

 posing that G is such) and is therefore the same for all metals — a 

 principle derived by Richardson from the first and second laws of 

 thermodynamics twenty years ago, without any assumptions at all 

 about the distribution of the electrons. Its actual value lirk-meG/h^ 

 differs only by the factor G from the value derived by Dushman, 

 which is numerically equal — in the customary units — to 60.2 amperes 

 per cm.^ per degree squared. There are several metals for which the 

 experimental value of this quantity — commonly known as ^, a 

 symbol which in this article is monopolized by another meaning — 

 agrees well with 60.2. One might infer that G must be unity, a 

 choice which would demolish the theory of paramagnetism; but there 

 is another recourse; one may suppose that half the electrons which 



^ L. Rosenfeld, E. E. Witmer (/. c. infra). From Rupp they cite values of re- 

 fractive index for six other metals (Al, Cr, Cu, Ag, Au, Pb) and compute values of n. 

 In considering these, however, the reader should assess G. P. Thomson's criticism 

 of Rupp's values. 



