7.

turbid media just described. No space is optically void in the absolute sense except a vacuum. Hence a chemically pure substance may be spoken of as a vacuum made turbid by the presence of molecules.

A typical example of scattering is offered by the behavior of sunlight in the atmosphere. When, with a clear sky, the sun stands in the zenith, only about two-thirds of the direct radiation of the sun reaches the surface of the earth. The remainder is intercepted by the atmosphere, being partly absorbed and changed into heat of the air, partly, however, scattered and changed into diffuse skylight. This phenomenon is produced probably not so much by the particles suspended in the atmosphere as by the air molecules themselves.

Whether the scattering depends on reflection, on diffraction, or on a resonance effect on the molecules or particles is a point that we may leave entirely aside. We only take account of the fact that every ray on its path through any medium loses a certain fraction of its intensity. For a very small distance, $s$, this fraction is proportional to $s$, say ${\beta }_{\nu }s\mathrm{\backslash Label}[eqn](3)\text{upshape (3)}$ where the positive quantity ${\beta }_{\nu }$ is independent of the intensity of radiation and is called the "coefficient of scattering" of the medium. Inasmuch as the medium is assumed to be isotropic, ${\beta }_{\nu }$ is also independent of the direction of propagation and polarization of the ray. It depends, however, as indicated by the subscript $\nu$, not only on the physical and chemical constitution of the body but also to a very marked degree on the frequency. For certain values of $\nu$, ${\beta }_{\nu }$ may be so large that the straight-line propagation of the rays is virtually destroyed. For other values of $\nu$, however, ${\beta }_{\nu }$ may become so small that the scattering can

be entirely neglected. For generality we shall assume a mean value of ${\beta }_{\nu }$. In the cases of most importance ${\beta }_{\nu }$ increases quite appreciably as $\nu$ increases, i.e., the scattering is noticeably larger for rays of shorter wave length;Lord Rayleigh, Phil. Mag., 47, p. 379, 1899. hence the blue color of diffuse skylight.

The scattered radiation energy is propagated from the place where the scattering occurs in a way similar to that in which the emitted energy is propagated from the place of emission, since it travels in all directions in space. It does not, however, have the same intensity in all directions, and moreover is polarized in some special directions, depending to a large extent on the direction of the original ray. We need not, however, enter into any further discussion of these questions.