THE DETERMINATION OF THE OPTICAL DEPTH AT LARGE SOLAR ZENITH DISTANCES,

The determination of the optical depth of an atmosphere, i.e. the problem of determining the content of a column of molecules making an angle x with the zenith, is considered, particularly for large solar zenith distances. Chapmans solution for an atmosphere with constant mass, gravity and temperature is reviewed, and solutions are derived for constant scale height gradients of one-half and one. Approximations useful for numerical purposes are discussed. The earths ionosphere is studied as an example of applications. The effect of gravity is taken into account. The general conclusion is that for x or 90 degrees the Chapman Function is applicable to the ionospheric situation within an error of or -5 even though the temperature undergoes an important change in the 100-200 km region. It is emphasized that for x pi2 the optical depth must be specified in terms of the parameters at x pi2, i.e., at the maximum density point. It is shown that for ionospheric sunrise problems, the earth may be considered spherical and that one mean earth radius suffices for all optical depth calculations. Author