158 



temperature, or E = k(T'' — Tu). The law has been amply verified for a 

 black body by the experiments of Lummer and Pringshoim', but is not strictly 

 Inic for other bodies. Holtztnann deduced the law theoretically in the fol- 

 lowing manner. 



According to tlie electromagnetic theoi'v of light, light exei-ts a i)ressure 

 on any perfectly reflecting plane surface which is jierpendic iilar to the direc- 

 tion of the light numerically ecpuil to the energy density of the radiation. 

 When light is incident in all directions we may assume one-third of it travel- 

 ing in each of three mutually perpendicular directions, and so the pressure 

 exertcfl upon the walls of a perfectly reflecting vessel filled with radiation 

 would be etiual to cme-third of the energy density. Let AC (Fig. 1) be a 

 cylinder of unit cross-section and length a, having perfectly reflecting sides 

 and a perfectly reflecting piston P, but the end AB is a perfectly black body 

 at a temperature T. Then the space between AB and P will be filled with 

 radiation of energy density u corresponding to the temperature T. When 

 equilibrium is established replace AB by a perfectly reflecting plate, and 

 push the piston P in from a point distant x from AB to a point distant (j — di). 

 The total amount of energy supplied, dQ, is ecjual to the increase of the in- 

 ternal energy, dl\ plus the external work performed, d\V . Therefoi'c 



4 

 dQ = dli -F d\V = d(xu) + p dx = x du + -;j- dx. 



If '^ is the entropy, then 



dQ X 4u dtp d^ 



d? = = — du -| dx = 



T T 3T 



X t^'^ 4u dcf, 6"- 



T -u .'5T f^x div 



Since T is independent of . 



1 4fl udT 



du 4dT 



T 3tT T-duJ u T 



(1) u = kT"", where /,• is a conslant. 



Sujjpose that instead of the case above considered we take the case of a 

 small radiating body at the center of a liollow sphere having perfectly re- 



(Icctiiig walls. 'i'hen ///••' will !)(• constaiil, where /• is the distance fnini t he 



/"'■ 

 center ol tlie sphei-e. Then l' = 4x I ur-'dr = 4xr-'u. // being in this case the 



• () 



energy density al tiie surface ol" the spliere. Tlie r;idiatiiin pressui'c on the 



"Ann. (let- Pliysik, fi:{, p. Hi)."), 1S!I7. 



