A series of experiments on cosmic-ray air showers is described. Four "fast" ionization chambers, with electronic coincidence and photographic recording of pulse height, were used to investigate the structure of these showers in detail, at mountain altitudes. The experiments show that the showers have the structure characteristic of electron cascades. There is no evidence for unusually narrow showers. If the showers originate from the decay of neutral mesons, these mesons must be produced either singly, or in groups whose total angular divergence is not greater than ~10-4 radian. The frequency of occurrence of showers which have particle density greater than ρ-particles per square meter at the point of observation is shown to be 1.05(460ρ)1.5 hr.-1, 300<ρ<2000 particles/m2, at 3050-m elevation. This frequency is also given for two points of observation with various distances separating them. Data on the angular distribution of the showers at 3050 m and the altitude variation between 3050 m and 4300 m are presented. The results of some theoretical calculations on altitude and angular variation are given, but they are not sufficiently accurate to indicate clearly the nature of the primary event which causes these showers. Absolute rates for the number of showers of a certain size, and for the number of primary events, are presented. Twenty-seven showers of more than 1016-ev total energy were recorded.