The method and results of the study of the outer ionosphere based on the ' rise' and ' set' of radio signals of the sputnik are given in full in the paper of which this is an abstract. Results of the theoretical calculations of the maximum horizontal distance rM of signalreception, which are needed for the treatment of experimental data, are also described. Calculations were carried out for a spherical Earth, and the resulting elliptic integral was tabulated by means of the high-speed electronic computer of the Academy of Sciences of the U.S.S.R. A parabolic model of the lower ionosphere and an exponential decline of electronic concentration in its outer part were accepted.