171.

Let us now try to define for the general case the state of radiation in the thermodynamic-macroscopic sense as we did above in [sect:107.] Sec. 107, et seq., for a stationary radiation. Every one of the three components of the electric field-strength, e.g., ${⋿}_z$ may, for the long time interval from $t=0$ to $t=𝖳$, be represented at every point, e.g., at the origin of coordinates, by a Fourier's integral, which in the present case is somewhat more convenient than the Fourier's series [eqn:(149)] (149): ${⋿}_z={\int }_0^{\infty }d\nu C_{\nu }\cos (2\pi \nu t-{\theta }_{\nu }),\mathrm{\backslash Label}[eqn](311)\text{upshape (311)}$ where $C_{\nu }$ (positive) and ${\theta }_{\nu }$ denote certain functions of the positive variable of integration $\nu$.

The values of these functions are not wholly determined by the behavior of ${⋿}_z$ in the time interval mentioned, but depend also on the manner in which ${⋿}_z$ varies as a function of the time beyond both ends of that interval.

Hence the quantities $C_{\nu }$ and ${\theta }_{\nu }$ possess separately no definite physical significance, and it would be quite incorrect to think of the vibration ${⋿}_z$ as, say, a continuous spectrum of periodic vibrations with the constant amplitudes $C_{\nu }$.

This may, by the way, be seen at once from the fact that the character of the vibration ${⋿}_z$ may vary with the time in any way whatever.

How the spectral resolution of the vibration ${⋿}_z$ is to be performed and to what results it leads will be shown below ([sect:174.] Sec. 174).