Since some of the earliest evolutionary calculations it has been found that post main sequence stars become red giants (e.g. Sandage and Schwarzschild, 1952). However the exact physical processes that lead to and determine the rate of redward evolution are not completely understood. We hypothesized that the redward evolution might be due to an increase in radiation pressure somewhere in the star that causes the layers above it to be pushed outward, resulting in an expanded envelope and a cooler surface temperature. If the radiative luminosity somewhere in the star approached the Eddington limit, the outer layers would obviously expand. However, due to the presence of gas pressure, the critical value for expansion would be somewhat less than the Eddington limit.