INSOLATION 85

that were present even before the outer atmosphere was reached. The minima, indicating strong absorptions in the solar atmosphere, constitute the well-known Fraunhofer lines.

In addition to the vast number of intensity deficiencies, absorption or Fraunhofer lines, as they are called, inherent in solar radiation, there are many similar deficiencies resulting from its passage through the oxygen, carbon dioxide, water vapor, ozone, and possibly other substances of the atmosphere. Carbon dioxide, water vapor, and ozone also strongly absorb the long wave-length earth radiation. Oxygen and water vapor absorb in many exceedingly restricted regions, so restricted, indeed, that in mere appearance they are indistinguishable from the narrow Fraunhofer lines. And in addition to these numerous narrow lines there are a number of broad absorption bands, certainly of water vapor, ozone, and carbon dioxide. Oxygen, too, seems to have a broad band in the region of exceedingly short wave lengths. Presumably all these bands are simply aggregates of large numbers of individual lines.

Whatever the actual process of absorption, it is certain that to within observational errors the amount of energy absorbed increases arithmetically with the intensity of the incident radiation and, for monochromatic radiation, geometrically with the quantity of the absorbing material passed through, provided it is all under the same physical condition. Thus, if /ox is the initial intensity of a parallel beam of monochromatic radiation, and a/ox its intensity after passing normally through a homogeneous layer of absorbing material of unit thickness, then its intensity after traversing a distance of m units in the same material is given by the equation,

/x = 7oxam.

In the case, also, of scattering of monochromatic radiation, the extinction progresses according to the same laws that apply to absorption. That is to. say, it is always a constant fraction of the remaining radiation that gets through a unit quantity of the scattering material.

The coefficients both of direct absorption and of extinction by scattering (see Chap. VII, Part IV) are radically different for radiations of different wave lengths. But if /ox is the initial intensity of the radiation of a given wave length and <2/nx its intensity after it has passed normally through a layer of absorbing material of unit thickness, then after normal transmission through layers m and n units thick, respectively,

am, and 7nX =

Hence,

_i

/w\Y"~" ___17 T /^*nX

i T T

; ana /ox = l

m\