In this article, we reexamine and extend a relationship proposed earlier between entanglement density and chain dimensions in polymer melts. The power-law equation presented in the earlier work, relating the entanglement molecular weight M-e, melt chain density rho, and the packing length p is tested with additional polymer species. Now included are additional polydienes and their hydrogenated derivatives, the isotactic forms of polypropylene and polystyrene, the essentially syndiotactic form of poly(methyl methacrylate), along with poly(tetrafluoroethylene), poly(vinylmethyl ether), various poly(methacrylates), and polymeric sulfur. We find that within experimental uncertainties, M-e/rho and p are related through an equation (M-e/rho = 218p(3)) that is insensitive to temperature (25 degrees C less than or equal to T less than or equal to 380 degrees C) and which seems to be universal for flexible Gaussian chains in the melt state.