The Tobolsky-Eisenberg theory serves to explain the equilibrium polymerization of sulfur in terms of the dependence of S8(ring) concentration on temperature and the dependence of number-average degree of polymerization on temperature. The predictions of the theory are completely in accord with experiment. In this paper it is shown that it is possible to take the presence of another component in the melt, Sπ, into account, using a slightly modified version of the Tobolsky-Eisenberg theory. When this is done it is found that the earlier conclusions remain valid. The molecular complexity and structure of Sπ is also discussed.