The intensities of the primary cosmic-ray alpha particles and protons at geomagnetic latitude 55°N are determined from measurements of the ionization and range of the charged cosmic-ray particles observed at atmospheric depths of 8 g/cm2 and deeper. The measurements were made with a balloon-borne Geigerproportional counter telescope which contained absorbers of mercury or lead. Showers of particles in the telescope were detected by out of line counters and eliminated. The particles having residual ranges between 1.5 g/cm2 and 43 g/cm2 are shown to be secondary electrons and secondary protons. The penetrating particles having range greater than 43 g/cm2 divide into singly and doubly charged particles. Extension of the penetrating particle intensity curves to zero depth yields values for the primary intensities of 0.19 (cm2 sec sterad)-1 for protons and 0.032 (cm2 sec sterad)-1 for alpha particles. The alpha particles are absorbed exponentially in the atmosphere and the slope of the absorption curve yields the value 35+/-7 g/cm2 for their mean free path in air. Data obtained by removing the absorbers in flight indicate that the net results are free of shower effects. Other systematic uncertainties in the values of the primary intensities are estimated to be +/-10%, which is larger than the statistical uncertainties.