Direct observations of primary cosmic rays are compared with the predictions of alternative theoretical models of the long term intensity modulation. The experimental data used are those of the satellites Explorer VII and Ariel I for heavy primary cosmic rays in the high rigidity region and those of balloons and IMP I for protons and alpha particles in the low rigidity regions. The solar wind and the electric field modulation models are considered in greater detail after it is found that the character of the predictions of the general solar dipole magnetic field theory is similar to that of the solar wind theory in the low rigidity region. A new quantity, In R, is introduced to characterize the modulation. R is the ratio, j( P or T; t)/ j( P or T; t′), between the differential rigidity or energy spectra at two different times. The log-log representation of In R vs. rigidity or kinetic energy/nucleon is advantageous for the comparison of observations with theoretical models and for eliminating the arbitrariness inherent in the conventional representation of the intensity changes. It is found that the most decisive criterion for the comparison is the ratio R(P) = 1 n R p(P) 1 n R α(P) , where the suffixes denote proton and alpha particles, whereas the quantities j p(T,t)/jα(T,t), 1 n R and R(T) , etc., cannot serve as a selection criterion if the modulation coefficient, M, for the solar wind model and the energy loss, δE, for the electric field model are rigidity dependent. Because of the dearth of experimental values of R(P) , a definite conclusion as to whether one of the two models is preferable cannot be reached. However, the present analysis reveals that M and δE, respectively, must be rigidity dependent for the theoretical predictions to fit the experimental results. Thus, for example, the electric field model based on a simple electrostatic potential in the interplanetary space is excluded. Some implications of and restrictions on the two alternative models are discussed. Especially in the case of solar wind modulation theory, many fruitful consequences can be quantitatively deduced. For example, the analysis reveals that the rigidity dependence of M appeared to differ during the ascending and descending phases of the last solar cycle. The spectrum of M was flatter during 1954–1958 than during 1958–1963, but apparently did not vary drastically during these intervals. The absolute value of M is estimated, in order to compute the unmodulated spectra, and the results indicate that even during the solar minimum period, modulation of the cosmic ray intensity still occurs.