159.

On the other hand, for large values of $\lambda T$ [eqn:(276)] (276) becomes $E_{\lambda }=\frac{ckT}{{\lambda }^4},\mathrm{\backslash Label}[eqn](283)\text{upshape (283)}$ a relation which was established first by Lord RayleighLord Rayleigh, Phil. Mag. 49, p. 539, 1900. and which we may, therefore, call "Rayleigh's law of radiation."

We then find for the specific intensity of radiation $𝖪$ from [eqn:(274)] (274) $𝖪=\frac{k{\nu }^{2}T}{c^2}\mathrm{\backslash Label}[eqn](284)\text{upshape (284)}$ and from [eqn:(275)] (275) for the space density of monochromatic radiation we get $𝗎=\frac{8\pi k{\nu }^{2}T}{c^3}.\mathrm{\backslash Label}[eqn](285)\text{upshape (285)}$

Rayleigh's law of radiation is of very great theoretical interest, since it represents that distribution of energy which is obtained for radiation in statistical equilibrium with material molecules by means of the classical dynamics, and without introducing the hypothesis of quanta.J. H. Jeans, Phil. Mag. Febr., 1909, p. 229, H. A. Lorentz, Nuovo Cimento V, vol. 16, 1908. This may also be seen from the fact that for a vanishingly small value of the quantity element of action, $h$, the general formula [eqn:(276)] (276) degenerates into Rayleigh's formula [eqn:(283)] (283). See also below, [sect:168.] Sec. 168 et seq.