Eddington's approximation was employed to compute the irradiances passing through atmospheres consisting of several different, albeit internally homogeneous, layers, as a function of solar zenith angle, albedo for single scatering, the asymmetry factor of the phase function, and the albedo of the underlying surface. Results computed for a single layer atmosphere were found to agree with more exact computations within a few percent. Irradiances within several vertically inhomogeneous three-layer model atmospheres were computed. Effects caused by the vertically inhomogeneous structure are considered. It is noted, for example, that the irradiance within an atmosphere can be greater than that incident upon the atmosphere bemuse radiation may he partially trapped within the atmosphere. The Eddington approximation affords a means to rapidly compute irradiances within realistic inhomogeneous atmospheres with an accuracy of several percent.