24 Prof. F. A. Lindemann on the 



the value (27r) 3/2 being that derived by Sackur, Tetrode, 

 Nernst and others. Since Stephan's constant 



_2tt b 1&_ 

 (J ~ 15 cW 



one may therefore write, as mu J s=3iT in a monatomic gas, 



4aT 4 



Now — — = P is the radiation pressure o£ complete 



OC 



radiation of temperature T on the walls of a containing 

 vessel,, so that the vapour pressure 



f T *o-/(T) 



*=- s?-?*-* K ' r 



■dT 



where v is the velocity of the molecules in the gas. 



If the velocity of sound Y = v\/ ? = t, Vo is introduced 



this becomes 



or /on- 3 r T x -/(T) 7 



X A 



623-LPe RT 



at low temperatures at which /(T) is small. If any frequency 

 v is considered, the wave-length of the elastic w^ave in the 



. V . . c 



gas is -- and of the corresponding electromagnetic wave - . 



Therefore the energy residing in the gas in a cube whose side 

 is one wave-length divided by the corresponding energy in 



the radiation is 1*246 e , i.e. 1*246 times the fraction of 

 molecules whose energy is greater than the potential energy 

 acquired when they are removed from the solid to infinity. 

 This relation is strongly reminiscent of a well-known theorem 

 in the theory of radiation, namely, that complete radiation is 

 in equilibrium in any two dielectrics when the energy in a 

 wave-length cube in one, is equal to the energy in a wave- 

 length cube of the same frequency in the other. In com- 

 paring the energy in the gas to that in the radiation at 

 reasonably low temperatures the corresponding theorem 

 would be, that radiation pressure is in equilibrium with 

 vapour pressure when the energy per molecule capable of 



