soMii coxiLMroK.iRy .ii>r.i.\Li:s i\ rinsics—r m9 



in it the idea that there is a rert.iiri fixed |)olential-(litTereiire helweeii 



the interior of a metal and the region outside of it, resulting ii% a 



potential-drop localized in a thin stratinii ai the surface, which an 



electron within the metal must surmount in order to escape from 



the ntetal into a contiguous vaciumi. Such a potential-drop woulfl 



for instance result from a "double layer" alt)iiic the surface of the 



met.d. a sheet of positi\e charges within and a sheet of negative 



charges opposite, parallel, and close to the positive sheet on the 



outside. It has Im-ou jiointed out that, since proliably half of the 



tirbiial electrons In-longing to the atoms at the frontier of a metal 



lie outside the plane containing the nuclei of these atoms, the>' with 



the nuclei constitute a sort of double-layer; it has also been suggested 



that after a certain number of electrf)ns issue from the metal, the\ 



are held as an electron-atmosphere above it by the forces due to the 



distribution of residual positive charge within the metal (Kelvin's 



electrical-image conception), and the electron-atmosphere with the 



positive surface-charge together form a double-layer. However we 



may conceive this double-layer, it is obvious that if we postulate 



free electrons within the metal, we must also postulate a barrier 



in the shape of an opposing potential-drop between the metal and 



the exterior world to keep the electrons from wandering awa\ . 



Designate this potential-drop by b, so that el> is the energy which 



an electron must give up in traversing it from inside to outside. 



.Assume further (disregarding the old specific-heat difiticulty) that 



the velocities of the electrons inside the metal are distributed iso- 



tropically in direction, and according to Ma.xwcH's distribution-law 



3 

 ill s]Hitl, with the mean kinetic energy-— -^7' ajjpropri.itc to the tini- 



IR-rature 7' of the metal. Imagine the metal surface to occupy the 

 plane .v = 0, metal to the left and vacuum to the right. Consider 

 the electrons which come from within the metal and strike unit area 

 of the boundary in unit time; those of them which have velocities 

 of which the .v-compoiunl lio i)ctwicii /( .md ii-\-ilit an- in number 

 equal to 



ill = , e 2*r<f«, ((i) 



V2wkT m 



n meaning as heretofore the number of electrons per innt volume of 

 metal. The total numl>er which strike unit area of the boundary 

 from within is equal to the integral of this expression from «=() to 

 »< = « , which is 



Io = ny/kT/27rm. (') 



