THERMODYNAMICS OF RADIATION. 341 



Let the energy density of the radiation in the range of wave-length 

 from X to X + dX. be denoted by ed\; e may be termed the energy per 

 unit range about the wave-length A. By the expansion let A., A + t/A 

 change to A', A' + dM, while edX, changes to e'dX,'. 



As shown above 



But dX' = -d\ 



r 



then er 5 = eV 6 



r & 

 or since ~ 



or, comparing e, the energy per unit range, or in equal ranges rfA, in two 

 full radiations at different temperatures and taking corresponding wave- 

 lengths given by \0 = constant we see that e is proportional to the fifth 

 power of the temperature. 



Q 



Suppose, then, at any one temperature we plot 25 as ordinate against 



A# as abscissa, we shall obtain a curve which will be identical for full 

 radiation at all temperatures. 

 Then we may put 



or e 



where / is a function of the product A/9 only. 



Maximum Value of Energy for Given Range of Wave-Length. 



a 



For a given temperature, when e is a maximum, is a maximum. 



Then writing the maximum value of e as e m , ~ is the same for all 



temperatures, and therefore X m O is the same for all temperatures, where 

 A m is the wave-length for maximum energy per unit range. 



Form of the Function expressing the Distribution of Energy 



in the Spectrum. The methods used up to this point do not afford us 

 any information as to the form of the curve expressing the distribution 

 of the energy in the radiation spectrum, except that it must be 

 represented by 



At present it appears to be necessary to introduce some hypothesis as to 

 the way in which radiation is produced, in order to find the form of 



