Densities of the three constituent spheroids of the same eccentricity as our earlier model of the Galaxy are assumed to be given by an analytical form of ρ i (r)= k i e − m i r u i , where k i , m i , and α i are obtained by comparing with the results of the previous model. Using three values of ρ i (r) the galactic rotation curve, mass of each spheroid and the whole Galaxy are calculated, and the three dimensional density distribution in the Galaxy is also obtained. The calculated rotation curve of the model Galaxy is in good agreement with the observed curve, and the shape of the cross section of the model Galaxy given by the computed density is very similar to the inferred shape of the spiral galaxies.

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).