178 Mr Havelock, On the continuous spectrum. 



And if 2m + 1 is even, we obtain E finally in the form 



E = CN*&-™ {A+Bu/3+...+K(ul3) 2 )e- 2a ^du...{11). 



Jo 



Changing now from frequency u to wave length \, and from /3 to 

 6, we obtain the energy in the form 



,.00 



E=\ E K d\, 



2m+l 2»i+l c 2 



where E k = ON- (\d)- 2 \ T [A (\0) T" + . . . + if J e~A* 



= 0^6 * f(kd)e Ke (18). 



Also integrating (17) with respect to u, we find that the total 

 energy of radiation varies as Q m ~%\ while if \ m be the wave 

 length for which E\ has its maximum value E m , we have 



\ m = constant; E m oc 6 m+ * (19). 



These relations are of the required form, and we notice that for 

 m = 9/2 they reduce to those which hold for black radiation. 



Indirect methods have the advantage of avoiding assumptions 

 concerning the mechanism of radiation, their results only applying, 

 of course, to black radiation ; regarding the latter as an aggregate 

 of irregular impulses, it may be possible to determine its con- 

 stitution by a theory of the statistical equilibrium of aether 

 motions. However, the direct method of summation of elementary 

 pulses serves to emphasize what is considered to be the real nature 

 of radiation giving a continuous spectrum. 



