The general problem of interpreting granulation data, in particular Edmonds' r.m.s. intensity fluctuation distribution against heliocentric angle 0, is discussed.
A inethod is developed for investigating a variety of models of inhomogelaeous departures fi'om radiative equilibrium using two dimensional solutions of the equation of radiative transfer, and theoretical r.m.s, intensity fluctuation distributions are computed. It is found that only a very narrow range of models yields distributions which exhibit the essential features of Edmonds' distribution (a center-of-disk value of 14 % and a maximum value of 20.5 % at a heliocentric angle of 53:'). The feature of these models is a maxilaaum in the temperature fluctuations of about 660 K r.m.s., which represents a temperature difference belwecn hot and cold regions of 2000K, at a depth of about 250 km below r:-.000 ~ 0.03. Below this the temperature fluctuations decrease rapidly in the next 70 kin.
These results are interpreted in terms of convective and radiative transport of energy. Velocities of the order of 8 kin/see arc deduced in the essentially convective regime near 320 kin, decreasing through 4 km/scc near the temperature fluctuation inaxinaum to negligible values in the radiative region above 200 kin.
These features are shown to be consistent with modern theoretical and laboratory studies of convection in incompressible fluids. Further, these studies indicate that a second temperature fluctuation should occur at the bottom of a convective layer. For this reason, further photospheric models are studied in which, below the region of small temperature fluctuations near 320 kin, the fluctuations incrcase sharply. For one of these models a theoretical intensity r.m.s, distribution is obtained which closely fits not only the maximum at 0 --53 ' ira Edraonds' observed distribution but also the initial decrease and smallcr minimum near 24".