162 



heats, mentioned below, is not true unless this is so. This, apparently, is 

 not Planck's view as he seems to consider the oscillators as absorbing energy 

 continuously. 



(5) The law of emission is: The ratio of the probability that etnission 

 shall not occur, 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 K7, = the component of the electric intensity 



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

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

 determined bj^ 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 .si)ectruni of black-body radiation are completely determined. 

 Planck bases his expression for absorption on electrodynamic considerations, 

 those for emission and energy distribution upon statistical ones. 



Planck's calculations will not be rej)roduced here, the mathematical 

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

 his investigation relating to the absorption of energy upon the ecpiations 

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



Kf + L = ¥jz, Planck finds that in tlic interval of time between two 



dt = 



successive emissions the energy U increases uniformly according to the 



dU lo 



ecjuation = . 



dt 4L 



The mode of emission will obviously de])end upon the theory of proba- 

 bility. Planck finds that, when Pn is the probabilitj- that the energj- of an 

 oscillator lies between nt and (« + O* Jind r, is the probability that the 

 energy of the oscillator shall be a whole number of times f, the average energj- 

 of an oscillator is given by the equation 



U = 2P„ ln + -|£= 1 f. 



o [ 2J [r, 2J 



f 11 1 



Also U = pi + - f, or - = 1 + pi. 



3c- 

 The value of p is found to be , where c is the velocitv of light.' 



'Verh. Doutsch. Plus. Ges., 5, .3, Feb. I'JII. 



