The empirical regularities in the appearance of superconductivity in the periodic system discussed by Matthias are considered in the light of the microscopic theory of superconductivity proposed by Bardeen, Cooper, and Schrieffer. A simple model of electrons and ions interacting via screened Coulomb forces is used to describe the electron-lattice interaction. With the aid of this model, it is shown how the theory of Bardeen, Cooper, and Schrieffer provides both a satisfactory criterion for the appearance of superconductivity and a good qualitative account of the variation in transition temperature from one metal to another.