174 Profs. Richardson and Cooke on the Heat developed 



potential difference of a fraction of a volt. The precise value 

 of the fraction depends, of course, on the absolute temperature, 

 to which it is proportional. The first loss appears to be small 

 compared with the second at all available temperatures. 



The heating effect which should occur, on this view, when 

 electrons enter a metal is made up similarly of two parts : 

 one proportional to the kinetic energy, l\ which the electrons 

 possess immediately before entering the metal, and two, a 

 part which depends upon the difference of potential energy 

 of the electron when inside and outside of a metal. This will 

 be equal to the work, w = e<p, done by the surface forces on 

 the entering electrons. Here e is the charge on an electron 

 and <f> is the difference of potential energy per unit charge. 

 Hence, if n electrons enter the metal in unit time, the rate 

 at which kinetic energy is transported into the metal will be 

 equal to n(e$-\-k). In general, k will consist of two parts, 

 the first due to the energy, a#, of thermal agitation of the 

 hot metal from which they are emitted, and the second, due 

 to the potential difference, V, driving them from the hot 

 metal to the cold. If the conditions are steady, the current 

 will be continuous and there will be a flow of an equal number 

 of electrons out of the cold metal, each of which will trans- 

 port on the average an amount of kinetic energy a0 o with it, 

 where is the temperature of the cold metal. The total 

 quantity of heat developed by the n electrons when they flow 

 into the cold metal is, therefore, equal to 



»(<?<£ + eV+*(0 1 -0 o )), 



so that the rate of production of heat by a current, i, will be 

 equal to 



i(4>+v+ ± (0,.-0 o ) j. 



For constant values of 6 l and O the rate of production of 

 heat will thus be a linear function of V which takes the value 



$ + -(0^6,), when V = 0. 



This development of heat is clearly analogous to the heat 

 liberated during the condensation of a vapour to a liquid. 



2. Method of Experimenting. 



To detect and measure this heating effect an electrical 

 method was used. The electrons were obtained by heating 

 osmium filaments which were kindly presented to us by the 

 Deutsche Gasglilhlkht Aktiengesellschaft of Berlin, to whom 



