Statistical Theory of Heat Radiation. 123 



indefinitely small on Larmor's theory any more than on 

 Planck's*. 



The total number of elements of energy per c.c. (^/ ; ) is 

 given by the equation 



Hence 



^ = r^uuiyv 



Jo Ac\° \ / 



'"-(Sfc* 1 ,* *+■■■■> 



The series in brackets is equal to 1*20 

 The total energy per c.c. is 



48wwA¥ 



= a sav 



E = 



c 3 h 



where *=1 + ~ + ^ 4 +. . . . = 1-0823. 



Let e denote the average energy per element so that 



Now 3kt/2 is the average translational energy of a molecule 

 ot a gas, and 



= 2-, = l-80.... 



3fo 



It appears, therefore, that the average energy per element 

 of disturbance in the radiation is equal to 1*80 times the 

 energy of a monatomic gas molecule. This result, it will be 

 observed, is independent of the absolute values of the constants 

 in Planck's formula. 



The pressure (p) of the radiation is equal to E/3, so that 



x a 



For a gas we have p — SVkt if 9V now denotes the number of 

 molecules per c.c. Thus for a given pressure and tempe- 

 rature a gas contains 0*90 times as many molecules per c.c. 

 as full radiation contains elements of energy. The elements 

 of disturbance have on the average as much energy as if eacli 

 possessed 5*4 degrees of freedom and equipartition held good. 

 For a gas each molecule of which has six degrees of freedom 



* The value of e for any wave-length is of course given by e = ^c/A, 

 using the value of h required by the observed values of e K . 



