Closing Years of the^ Nineteenth Century. 467 



^-components of velocity are comprised between u and u + du is 



^ 

 TT * a" 1 JVe * du dx, where | ma 2 = qT, 



m denoting the mass of an electron, T the absolute temperature, 

 and q the universal constant previously introduced. 



Now, an electron whose ^-component of velocity is u will 

 arrive at the interface within an interval dt of time, provided 

 that at the beginning of this interval it is within a distance u dt 

 of the interface. So the number of electrons whose ^-com- 

 ponents of velocity are comprised between u and u + du which 

 arrive at unit area of the interface in the interval dt is 



If the work which an electron must perform in order to escape 

 through the surface layer be denoted by </>, the number of 

 electrons emitted by unit area of metal in unit time is 

 therefore 



c **udu, or 

 *** 



The current issuing from unit area of the hot metal is thus 



20 30 



JirWeae'^, or N 



where t denotes the charge on an electron. This expression, 

 being of the form 



agrees with the experimental measures ; and the comparison 

 furnishes the value of the superficial discontinuity of potential 

 which is implied in the existence of 0.* 



A few years after the date of this investigation, a plan was 



* This discontinuity of potential was found to be 2*45 volts for sodium, 4-1 

 volts for platinum, and 6-1 volts for carbon. 



