Experiments on the tunneling of electrons through a thin dielectric layer separating two superconducting metals are reported. Data are presented for the pairs AI-Pb, Sn-Pb, and In-Sn. Particular attention is paid to the form of the tunneling current vs voltage characteristics and to the changes observed as a function of temperature. Experimental details relative to the measurement techniques, the preparation of the samples, and the preparation of the dielectric layers are presented. An analysis of the problem is presented which is based on the simple, one-dimensional model of the electron energy spectrum of a superconductor given by the theory of Bardeen, Cooper, and Schrieffer. Close quantitative agreement is obtained between the results of the calculations and the observed characteristics.