260 Prof. J. J. Thomson on the Emission of 



the metal of thickness c next the surface: as soon as a cor- 

 puscle enters this layer it will be acted upon by a force 

 directed away from the surface ; if the corpuscle has only a 

 small amount of kinetic energy it will soon be stopped, and 

 will turn back without ever reaching the surface, one with 

 greater velocity will get nearer to the surface, and those 

 moving above a certain speed will be able to reach the surface 

 and escape from the metal. If the distance c is comparable 

 with the thickness of metal required to absorb the radiation 

 of the type produced by the impact of the molecules against 

 the corpuscles, then the rate of emission of radiation from the 

 metal will depend chiefly upon the more rapidly moving- 

 corpuscles. For not only do these possess greater energy, 

 and therefore when in collision produce the more intense 

 pulses, but they travel nearer to the surface so that the 

 radiation which they emit has not to travel through so great 

 a thickness of metal, and is consequently not so much 

 absorbed. 



To calculate the rate at which energy is radiated from the 

 metal by the electromagnetic waves produced by the collisions 

 between the corpuscles and the molecules, we require to know 

 the attraction exerted by the molecules on the corpuscles; 

 for without this knowledge we cannot tell how near to the 

 surface a molecule moving with a given velocity will pene- 

 trate ; we also require to know how much of the radiant 

 energy produced by the collision is absorbed in passing from 

 the place of collision to the outside of the metal. In default 

 of information on these points let us calculate the rate of 

 emission of radiant energy on the assumption that only those 

 corpuscles whose velocity is greater than v x get near enough 

 to the surface for any of their radiation to escape, and that 

 all the radiation from those moving with a velocity greater 

 than v x escapes without absorption. Assuming Maxwell's 

 law of distribution, and that the energy in the electromag- 

 netic pulse produced by the collision is proportional to the 

 square of the velocity, we find that the rate at which energy 

 is emitted from the metal is proportional to 



ij . 



0-fl v 5 6 dv 3 



where 6 is the absolute temperature. If mv{ 2 is large com- 

 pared with 6, this expression increases very rapidly with 6. 



The collision of free corpuscles with the molecules will not 

 be the only source of radiation — indeed if it were only con- 

 ductors of electricity would radiate — similar radiation will be 



