RADIATION OF ENERGY. 359 



By combining equation (1) with an expression (3) for the mean intensity of radi- 

 ation, for the steady state, R p , resulting from an oscillator of mean energy, U 

 and frequency, v, 



(3) 



**-? U > 



Planck obtained a formula for the energy density, w, in a space completely 

 surrounded by black walls, 



(4) 



u 



8rhv* 1 



c 3 e h " lkT - 1 



One of the results of Planck's theory is that an elementary oscillator 



only radiate energy in multiples of a definite unit «, for if it did otherwise its 

 total energy would not remain always equal to a multiple of «. . 



The strongest evidence in favor of this remarkable theory is that it gives a 

 theory of the radiation of a black body which agrees with the results of experi- 

 ment. Other theories such as that of Lorentz 1 based upon the Theory of Elec- 

 trons, and the Rayleigh-Jeans 2 theory based upon the Theorem of the Equipar- 

 tition of Energy are incomplete, being true only for the long wave-lengths of the 

 spectrum. 



Another remarkable development of this theory is its application by Nernst 1 

 to the theory of specific heats. In this domain it gives results which are in 

 wonderful accord with the results of experiment. 



Combined with the gas laws it also gives values for the mass and charge of 

 the electron which agree closely with experimental values. 



In his earlier development of the theory, Planck assumed that both the 

 emission and absorption of energy by the oscillators could only take place in 

 definite multiples of the quantum, €. In his more recent papers, however, he has 

 modified his views, and he now assumes that an oscillator can emit energy only 

 in definite multiples of «, but that it can absorb it continuously.* He also points 

 out in his recent writings that this discontinuous emission can only be com ived 

 of as taking place in an oscillating system, and cannot be conceived of as taking 

 place when a body is moving continuously in a straight line. 



He also draws attention to the fact that it is the elements of disturbance, 

 rather than the elements of energy, which are distributed according to the law 

 of probabilities, 6 and that h, the action constant, is introduced by the necessity 

 of using a statistical method. 



1 Lorent*, Theory of Electrons, pp. 80-90. 



•Rayleigh, Nature, vol. 72, pp. 54, 55, 1905; Jeans, Philosophical Magazine, vol. 10, pp. 91-98, 1905. 



• ZeiUehr. f. Elektrochemie, Bd. 17, pp. 265-275, 1911. 



*Annalen der Physik, Bd. 37, pp. 142-G56, 1912: Phytikalische ZeiUchrift, Jfthrg. 13, pp. 174 175, 

 1912. 



• Larmor, Proc. Roy. Soc., vol. 83, A, pp. 82-95, 1909. 



