the Emission- Spectrum of a Black Body. 217 



where a denotes a constant, which can be deduced from the 

 mean velocity * v by means of the equation 



The absolute temperature is therefore proportional to a 2 . But 

 the vibrations sent out by a molecule whose velocity is v are 

 completely unknown in their dependence on the condition of 

 the molecule. A now-a-days generally accepted view is that 

 the electric charges of the molecules can excite electro- 

 magnetic waves. 



We make the hypothesis, that each molecule sends out 

 vibrations of a wave-length which only depends on the 

 velocity of the molecule moved and whose intensity is a 

 function of this velocity. 



It is possible to obtain this deduction by several different 

 special hypotheses with regard to the process of radiation ; 

 as, however, such premises at this preliminary stage are com- 

 pletely arbitrary, it appeared to me to be the safest method to 

 make the necessary hypothesis as simple and general as 

 possible. 



As the wave-length A, of the radiation sent out by any 

 molecule is a function of v, v is also a function of X. 



The intensity (j)\ of the radiation whose wave-length lies 

 between X and (X-f dX) is therefore proportional 



(1) To the number of molecules which send out radiations 

 of this period ; 



(2) To a function of the velocity v, therefore also to a 

 function of X. 



Consequently 



<£ A = F(X)* <T; 



where F and /denote two unknown functions, and 6 denotes 

 the absolute temperature. 



Now the change of radiation with temperature is composed, 

 according to the theory given by Boltzmannf and myself J, 

 of an increase of total energy in proportion to the fourth 

 power of the absolute temperature and of a change of wave- 

 length of the whole energy comprised between X and (X-hdX) 

 in such a direction that the wave-length belonging to it 

 alters in inverse ratio to the absolute temperature. If we 

 imagine the energy at any temperature plotted as a function 

 of the wave-length, then the curve obtained would remain 



* v is the square root of mean square of velocity. — Transl. 



t Wied. Ann. xxii. p. 291 (1884). 



X Wien, Ber. d. Berlin. Akad. 9th Feb., 1893. 



Phil. Mag. S. 5. Vol. 43. No. 262. March 1897. S 



