In a homologous series of compounds, internal cohesive forces correlate with densities, boiling points, heats of vaporization, refractive indexes, and surface tensions but do not correlate with the puzzling behavior of melting points. Rotational symmetry is the neglected major factor as a determinant of melting points. A symmetrical molecule with a high-symmetry number sigma has increased order and reduced rotational entropy by the amount of R ln(sigma), which elevates the melting point but has no effect on the boiling point. This opens the prospect that melting points can be predicted by group contribution methods plus molecular symmetry.