The usual assumption of the pressure equilibrium between the convective elements and the surrounding fluid has been dropped, and the effects of the pressure perturbation of the convective element on its velocity and T perturbation have been estimated.

Effect of the ratio of mixing length to the pressure scale-height α =l/HP on the effective temperature has been investigated under some simplifying assumptions. The result is compared with that of the existing model calculations. The role of convection zone in the stellar evolution is briefly summarized.

We have investigated the structure of the general relativistic polytrope(G.R.P.) of n=5. The numerical solutions of the general relativistic Lane-Emden functions υ a n d θ for the ratio of the central pressure to the central density σ = 0.1 , 0.3, 0.5 and 0.8333 are plotted graphically. We may summarize the results as follows: 1. As the invariant radius ¯ ξ increases, the numerical value of the mass parameter υ does not approach toward the assymptotic limit, as it does in the classical case ( υ ∼ √ 3 ) , but it increases continuously with progressively smaller rate as compared with the classical case. 2. When ¯ ξ is less than ∼ 5.5 , the value of the density function θ drops more rapidly than the classical one, whereas when ¯ ξ is greater than ∼ 5.5 , θ becomes greater than the classical value. For the greater values of σ these phenomena become significant. 3. From the above results it is expected that the equilibrium mass of the G.R.P. of n=5 must be larger than the classical masse ( √ 3 ) and the mass is more dispersed than the classical configuration (i.e. equilibrium with infinite radius).