The primary cosmic radiation has been measured with a Cerenkov scintillation counter at various times in the solar cycle at locations having nominal cutoff rigidities of 0.8, 1.6, and 2.7 bv. Results are used here to delineate spectral features of low rigidity protons and α particles and to examine the rigidity and charge dependence of the eleven‐year solar modulation. Details of particle transmission near the geomagnetic cutoff are also examined. The measurements indicate: (1) The observed nonsharp cutoff appears to be primarily due to expected transmission effects in a dipole‐like field and to instrumental effects, and the actual cutoff is quasi‐sharp in the Störmer sense. This is true even though the observed cutoff may be reduced to half that to be expected from the internal field, presumably because of external current systems flowing in the magnetosphere and its boundary. (2) The rigidity dependence of the eleven‐year modulation of protons and that of α particles are closely similar above ∼1.2 bv. None of the presently proposed models for this modulation agree with our results. The implications of this lack of agreement are discussed, and it is concluded that certain general features of particle motion in the interplanetary medium not considered in present models may be of importance. One such general feature may be diffusive deceleration in the radially expanding interplanetary medium, which is shown to have the same effect as a static heliocentric electric field. (3) The differential spectrum of galactic cosmic rays near sunspot minimum at about 1‐bv rigidity is either flat or falling slightly toward lower rigidities. The measurements in the rigidity range below 1 bv are compared with recent observations in this range.