We have analyzed data obtained with 39 globally distributed detectors, with median primary rigidity of response (Rm) in the range: 10 GV≤Rm≤330 GV, for the period 1953 to 1992. The time interval covers several epochs of solar activity maxima, minima, and polar field reversals. Data are sparse for earlier period but adequate after 1970. We have investigated long-term changes in the parameters applicable to the annual mean solar semidiurnal variation. We show that its dependence on the median asymptotic latitude of viewing (&lgr;m) is given by cos2&lgr;m. The data are consistent with a double power law fit in rigidity for the entire period of our study. The power law exponents are given by &ggr;1=0.7¿0.3 (if R≤Rp) and &ggr;2=-0.4¿0.2 (if R>Rp), where Rp is the peak primary rigidity. The values of Rp near maximum for even solar activity cycles (20,22) are quite large (~125 GV) compared to other periods. These large values lie close to the epochs of magnetic polarity reversals from negative (qA0) in the northern hemisphere of Sun. During these times, the exponent &ggr;2 acquires large negative values. Near solar activity minima, the values Rp are among the lowest at about 40 GV. We have also computed the mean limiting primary rigidity (Rc) for each year. The values of Rc lie close to 50 GV for solar activity minima and near 100 GV for maxima. In other words, the values of Rc are very close to those of Rp. Moreover, the correspondence between them is good. Both exhibit solar as well as Hale cycle variations. ¿ American Geophysical Union 1996