Data covering a complete solar cycle (1965 1976) have been analyzed in a comprehensive investigation of the nature of transient modulations of relativistic galactic cosmic rays associated with interplanetary magnetic field intensity excursions in the vicinity of the earth. It had been recognized earlier that the correlation coefficient between the cosmic ray intensity and the IMF magnitude is small. In fact, it remains less than 0.5 throughout the solar cycle. In order to understand the nature of field-related modulations and to minimize the complications arising from the effects of other features of solar plasma, the data are here analyzed by the method of superposed epochs. Following newly developed procedures for evaluating the statistical significance of the results obtained with this type of analysis, it is demonstrated that, while the days characterized by high IMF magnitude B are associated with intensity decreases, the IMF rarefactions (low B) cause an increase in the flux. In contrast to the case of geometric disturbances, which respond more rapidly, maximum cosmic ray intensity variations associated with both high and low B occur 1 day after the key days characterized by field departures from average values. This indicates that the modulation mechanism becomes efficient only when the plasma engulfment of the earth extends at least a gyroradius beyond 1 AU. Finally, while the geomagnetic index Ap follows the interplanetary magnetic field changes rather closely, the polar nucleonic intensity shows a prolonged recovery time (7--10 days) following magnetic enhancements as well as rarefactions. These results suggest that, on average, interplanetary magnetic field intensity variations which are presumably related to disturbances traveling from the sun are effective transient modulators of the relativistic particles and that the corotation of the modulating region plays a significant role in the recovery of the cosmic ray intensity. An investigation of the spectra of the cosmic ray intensity variations produced by interplanetary magnetic field enhancements and rarefactions, respectively, over the rigidity range covered by ground-based nucleonic intensity detectors has revealed that a power law of the form Kp-1 fits the data in both cases. This result is relevant to further theoretical studies of cosmic ray modulation processes.