SOME CO.WTF.MfOR.tRy .IPr.lNCES IN riivsics—y Ml 



Ix-ing in fact tin- M.iwvrll (lislril)iiti<)n-fiincti()n with tin- s.inic iiu'.in 



kiruMic i'iu'ri;>- ',^ A'/'. Tin- .irniiiiu-nt as i^Wvn proNcs tlit- point only 



lor the cii.slrihution in the velocit\ -component ;/; but the flistrihu- 

 lion-fiinitions in v and «•, the \eloeity-coinp(>iunts parallel to the 

 Ifoumlary of the metal, are unaffected by the double-layer, since v 

 and K' for any particular electron are unafTcctetl by the passage 

 through it; and since it is the essential feature of the Maxwell dis- 

 tribution-law that the distributions in v and u' arc identical for each 

 and e\er>' value of ii, the coiulusioii follows as stated. Xe\ertheless 

 it does sound paradoxical. 



This conclusion has been verified repeatedly by experiment. 

 Richardson began by simulating the simple mathematical conditions 

 of infinite plane electrodes as closely as practicable; he inserted a 

 small flat incandescent surface in an aperture in the middle of a large 

 flat cold plate, charged the two to the same potential, and placed op- 

 posite and parallel to them a large flat collecting-electrode. Charging 

 this latter to various potentials \' inferior to the potential of the emit- 

 ting surface, he plotted the electron-current which it received as func- 

 tion of l'; this is the distribution-function of the speed ii of equation 

 (6) and the following equations translated into terms of the correspond- 

 ing kinetic energy i mu- as independent variable. To ascertain the 

 distribution-functions in v and to he isolated a small area of the collec- 

 ing-electrode, moved it to and fro in a plane parallel to the plane of the 

 emitting surface, and measured the current into it in its various posi- 

 tions. Many measurements have since been mtide upon the currents 

 into cjlindrical collectors from hot wires stretched along the axes of 

 the cylinders; it is somewhat more difficult to w'rite out the formula 

 for the expected relation between current antl retarding-potential, but 

 the experimental conditions are much more under the experimenter's 

 control. All these investigations have confirmed the theorem, except 

 a single discordant one which was later explained away; the strongest 

 verification is furnished by the experiments of Ciermer, whose pre- 

 cautions of preparation and accuracy of measurements far surpassed 

 everything that had gone before. 



The evidence thus is quite favorable to the idea of an electron- 

 gas within the metal with its electrons moving with velocities as 

 prescribed by Maxwell's distribution-law, and kept from diffusing 

 away by a double-layer covering the surface. Other evidence for 

 the existence of a double-layer is furnished by the photoelectric 

 effect and by the existence of contact-potential-difTerences. When 



