11.

All the distinctions and definitions mentioned in the two preceding paragraphs refer to rays of one definite color only. It might very well happen that, e.g., a surface which is rough for a certain kind of rays must be regarded as smooth for a different kind of rays. It is readily seen that, in general, a surface shows

decreasing degrees of roughness for increasing wave lengths. Now, since smooth non-reflecting surfaces do not exist ([sect:10.] Sec. 10), it follows that all approximately black surfaces which may be realized in practice (lamp black, platinum black) show appreciable reflection for rays of sufficiently long wave lengths.

[12.]12. Absorption.–-Heat rays are destroyed by "absorption." According to the principle of the conservation of energy the energy of heat radiation is thereby changed into other forms of energy (heat, chemical energy). Thus only material particles can absorb heat rays, not elements of surfaces, although sometimes for the sake of brevity the expression absorbing surfaces is used.

Whenever absorption takes place, the heat ray passing through the medium under consideration is weakened by a certain fraction of its intensity for every element of path traversed. For a sufficiently small distance $s$ this fraction is proportional to $s$, and may be written ${\alpha }_{\nu }s.\mathrm{\backslash Label}[eqn](4)\text{upshape (4)}$ Here ${\alpha }_{\nu }$ is known as the "coefficient of absorption" of the medium for a ray of frequency $\nu$. We assume this coefficient to be independent of the intensity; it will, however, depend in general in non-homogeneous and anisotropic media on the position of $s$ and on the direction of propagation and polarization of the ray (example: tourmaline). We shall, however, consider only homogeneous isotropic substances, and shall therefore suppose that ${\alpha }_{\nu }$ has the same value at all points and in all directions in the medium, and depends on nothing but the frequency $\nu$, the temperature $T$, and the nature of the medium.

Whenever ${\alpha }_{\nu }$ does not differ from zero except for a limited range of the spectrum, the medium shows "selective" absorption. For those colors for which ${\alpha }_{\nu }=0$ and also the coefficient of scattering ${\beta }_{\nu }=0$ the medium is described as perfectly "transparent" or "diathermanous." But the properties of selective absorption and of diathermancy may for a given medium vary widely with the temperature. In general we shall assume a mean value for ${\alpha }_{\nu }$. This implies that the absorption in a distance equal to a single wave length is very small, because the distance $s$, while small, contains many wave lengths ([sect:2.] Sec. 2).