162 



heats, Jiiciit ioiicd Ix'hnv, is not true unless this is so. This, ai)i);ircntly, is 

 not Phmck's \i('\v ;is ho seems to consider the (jsciUators us absorbing energj' 

 continuously. 



(5) ''J'he law of emission is: The ratio of l/ic pn/hdhiUti/ (liat emission 

 shall not oeeur, to the probability that emission shall occur, is proportional to the 

 intensity of the vibration exciting the oscillator. This intensity is defined by the 



Ivdv, where Ez = the component of the electric intensity 



in the direction of the axis of the oscillator, and as before v = freciuency of 

 the vibration. The constant of proportionality for any given period may he 

 determined by means of Rayleigh's law of energy distribution. 



By means of these assumptions the properties of the stationary state, the 

 entropy and temperature of a system of oscillators as well as the distribution 

 of energy in the spectrum of black-body radiation are completely determined. 

 Planck bases his expression for absorption on electrodj-namic considerations, 

 those for emission and energj^ distribution upon statistical ones. 



Planck's calculations will not be rejjroduced here, the mathematical 



processes being merely indicated and some of the results stateci. Basing 



his investigation relating to the absorption of energy upon tlie ecjuations 



given under assumptions (3) and (5) and the additional eciuation 



d-f 



Kf + L = Ez, Planck finds that in tlie interval of time between two 



dt^ 



successive emissions the energy L incri'ases imiformly accortling to the 



dU lo 



ccjuation = . 



dt 4L 



The mode of emission will obNiously (le])end upon tin- theory of proha- 



bilit}'. Planck finds that, when Pn is the probabilit}' that the energy of an 



oscillator lies between nr and (/? + l)f and t; is the probability that the 



energy of the oscillator shall ))(> a w hole number of t imes ; , the average energy 



of an oscillator is given by the eciuation 



i 1| I'l ll 



U = ^1\ \n+ -\e = I 1.-. 



'' [ 2J h 2J 



f 1^ 



Also U = pi + - 



2 



1 

 , or- = 1 + pi. 



fi 



.3c- 



riie value of p is found to be , where c is t he \ clocit v of light . 



32i:-'v'h 



'Vpih. Duulscli. Phvs. GcM., 5. :!, I'rii, I'.Ul. 



