Mr Havelock, On the continuous spectrum. 175 



On the continuous spectrum. By T. H. Havelock, B.A., 

 St John's College. Communicated by Professor Thomson. 



[Read 4 May 1903.] 



The continuous spectrum may be regarded as produced by 

 radiation constituted of an irregular sequence of impulses; in 

 other words, it arises from the analysis of purely heat radiation. 

 The problem of the constitution of the radiation has generally 

 been limited to the case of the hypothetical black body, this 

 radiation being defined more strictly as the equilibrium state of 

 the radiation within an enclosure maintained at constant tem- 

 perature. Then from thermodynamic considerations it can be 

 shown that 



EaO 4 -; \,„0 = constant (1), 



where E = density of total energy of the radiation, 



= absolute temperature of the walls of the enclosure, 



\ m = wave length for which the energy is a maximum. 



Also if the energy E can be written in the form 



E 



/•ao 



= E k d\ (2), 



Jo 



it follows that E K is of the form 



E K = \- 5 (f>(\0) (3), 



and the problem has been to determine the correct form of the 

 function (/>. 



Some years ago Lord Rayleigh (Phil. Mag. 1889, p. 460) gave 

 a simple form of average impulse which was capable of represent- 

 ing the complete radiation of a substance at a given temperature ; 

 he obtained in this way the formula of H. F. Weber, viz. 



c. 



E K = Cl X~ 2 e * (4), 



which represented approximately the experimental results known 

 at that time. It may be of interest to show how this method can 

 be extended so as to include the temperature factor and give 

 results similar in form to those indicated by recent experiments 

 and by the indirect theoretical methods. 



12—2 



