Thermodynamics of Radiation . 877 



by integrating the partial pressure pdv from to infinity at 

 constant T, is 



P = 2CT 4 /6 3 = 4Q/3c = lo-T 4 /3c (7) 



Whence the value o£ the constant C is 2ab*/3c. Substituting 

 this value of the constant C in the equation for the latent heat 

 Idv per unit volume, we obtain the equation for the latent 

 heat of emission per second, per sq. cm., in terms of the 

 radiation constant a, 



2T{dq/dT) l/ dv=crbh 2 T(l + bv/T)e-^dv, . . (8) 



which represents the curve of distribution of energy, as 

 experimentally observed, plotted against the frequency as 

 abscissa. The corresponding curve with the wave-length X as 

 abscissa is obtained by substituting v = e/\, and dv=- — ed\/X 2 . 

 The curve plotted in terms of wave-length has a maximum at 

 the point where XT = ( V2~- V)bc/2 = -2071k. The mean of 

 various experimental determinations puts the maximum of 

 the wave-length curve at XT = '290, when the wave-length 

 is measured in cms. Whence the value of the constant 

 be = 1*400. The curve obtained with this value of the 

 constant be gives very good agreement with experiment, both 

 for the distribution curve at constant temperature, and for 

 the variation with temperature of the energy of a particular 

 frequency, both of which are included in the same formula 

 (8) by putting either T or v constant, 



It is at once evident that a formula of the type shown 

 in (8) must be capable of representing the distribution curve 

 with considerable accuracy, since it reduces to the same type 

 as Wien's when XT is small or bv/T large, and to the same type 

 as Kayleigh's when XT is large or bv/T small. It would be 

 tedious and unnecessary to analyse all the observations 

 (though this has been done) since it is generally admitted 

 that Planck's formula fairly represents the experimental 

 data. It may be of interest, however, to give curves showing 

 the differences between the formulae, if only to illustrate the 

 limitations of experimental verification. The formulae com- 

 pared are those of Wien, Planck, Rayleigh, Walker and 

 Callendar. The value of the distribution constant l> is 

 calculated for each formula from the position of the maximum 

 by taking the same value of X W T, namely, *290, for all. If 

 the same absolute value of the Stefan constant a were also 

 taken for all, the absolute value of the maximum would be 

 different for each formula. But since only relative values 

 are obtainable experimentally in the distribution curve, the 

 maximum for each formula has been reduced to 100, and the 



