We develop a more general theory of the two-component system of galaxies by treating the galaxies as extended structures. We make use of the softened potential (r² + ∊²)^-1/2, with ∊ as a measure of the finite size of the galaxies, to evaluate the partition function, various thermodynamic properties of the system and the distribution function. Our analysis shows that the distribution function is not too greatly altered by the softening, thus vindicating our earlier claim¹ besides making the theory more elaborate as all the earlier results^1,2 are retrieved exactly from the new distribution function. Also, an attempt is made to account for the dark matter in the universe.

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