5.

The distribution of energy in the radiation is in general quite arbitrary; that is, the different colors of a certain radiation may have quite different intensities. The color of a ray in experimental physics is usually denoted by its wave length, because this quantity is measured directly. For the theoretical treatment, however, it is usually preferable to use the frequency $\nu$ instead, since the characteristic of color is not so much the wave length, which changes from one medium to another, as the frequency, which remains unchanged in a light or heat ray passing through stationary media. We shall, therefore, hereafter denote a certain color by the corresponding value of $\nu$, and a certain interval of color by the limits of the interval $\nu$ and ${\nu }^{\prime }$, where ${\nu }^{\prime }>\nu$. The radiation lying in a certain interval of color divided by the magnitude ${\nu }^{\prime }-\nu$ of the interval, we shall call the mean radiation in the interval $\nu$ to ${\nu }^{\prime }$. We shall then assume that if, keeping $\nu$ constant,

we take the interval ${\nu }^{\prime }-\nu$ sufficiently small and denote it by $d\nu$ the value of the mean radiation approaches a definite limiting value, independent of the size of $d\nu$, and this we shall briefly call the "radiation of frequency $\nu$." To produce a finite intensity of radiation, the frequency interval, though perhaps small, must also be finite.

We have finally to allow for the polarization of the emitted radiation. Since the medium was assumed to be isotropic the emitted rays are unpolarized. Hence every ray has just twice the intensity of one of its plane polarized components, which could, e.g., be obtained by passing the ray through a Nicol's prism.