ENERGY, ESPECIALLY IN RADIATION 97 



sible conditions are a=aP~ a , b=fiP~ l , where a and ft are 

 absolute constants, in which case (4) becomes 



e p -1 



5. To apply this expression to the case of radiation we 

 have to evaluate E n r m E,, 9 the energy transmitted per second 

 per unit range of wave-length in the neighbourhood of wave- 

 length X. We must therefore either appeal to experiment for 

 the determination of the appropriate forms to be given to 

 N m and r m in terms of X, or we must determine these by 

 means of suitable assumptions regarding ether and matter 

 and their connection. Thus if we assume that the fractional 

 rate of transmission of the energy content of each freedom 

 is identical per vibration, the fractional rate of transmission 

 per unit of time is proportional to the frequency, so that we 

 can write y8r m =yX~ 1 , y being an absolute constant. The value 

 of N m , when the frequency is not too small, is given by Ray- 

 leigh's reasoning (Sc. Papers, vol. iv. p. 484, or Phil. Mag., 

 xlix. p. 539, 1900) as A\~*, where A is a universal constant. 

 Hence 



e * -1 



an expression which, with Wien's displacement law holding, 

 gives the well-known experimental result that the maximum 

 energy is proportional to the fifth power of the absolute tem- 

 perature provided that the latter be identified with P. The 

 expression becomes identical with Planck's so long as aX is 

 negligible relatively to y. We must therefore recognise that 

 this restriction holds throughout the range of wave-length to 

 which Planck's formula is applicable. Outside that range 

 the quantity JS7 A becomes very small. 



If, within that range, Px becomes large relatively to y, 



N 



