APPENDIX III 
PLANCK'S RADIATION FORMULA 
Formulae for determining the distribution of energy throughout 
the spectrum may be expressed either in terms of the wave-length 
A, or the frequency v. 
We give below formulae for the space density of the energy of 
uniform monochromatic unpolarized radiation on the classical theory 
(Rayleigh), and on the quantum theory (Planck). To find the 
corresponding expressions for plane-polarized radiation, the results 
must be divided by 8tz/c, where c is the velocity of light. 
In terms of wave-length : 
Ea.dA — 8nkTA~*dA, 
Rayleigh ; 
Planck. 
In terms of frequency : 
Rayleigh ; 
Planck. 
In these formulae, k is Boltzmann’s constant and T is the absolute 
temperature. If we write x for hv/kT, Planck’s formula differs from 
Rayleigh’s through the presence of the factor %/{e x — i). For large 
values of AT Planck’s formula becomes identical with Rayleigh’s. 
For small values of AT it becomes ^^t e -ch/k\r which expresses 
Wien’s law of energy distribution.