SummaryA method of determining the upper limiting rigidity of the solar diurnal variation of the cosmic ray primaries in free space is described. It involves a comparision of the response to the anisotropy of neutron monitors at sea level and of meson telescopes underground. Making use of the model for the free-space first harmonic proposed by Rao, McCracken, and Venkatesan, the annual average value for the upper limiting rigidity (Ru) in 1958 is estimated to have been 95 GV with an error of estimate of about 10-20 GV. Changes in the observed annual mean daily variation between 1958 and 1962 indicate that Ru may have decreased by about 20-40 GV over this period, but a more refined analysis is needed to confirm this.Changes in Ru could also influence a sidereal daily variation as observed at the Earth. Evidence is presented for such an effect, from the observations underground at Hobart.It is shown that the annual average pressure-corrected solar diurnal variation observed at a depth of 40 m.w.e. must be largely under the control of the solar anisotropy. The most significant evidence presented comes from observations in three different directions underground at Hobart during 1961 and 1962. The first harmonics of the solar daily variations observed in these directions have been found to be broadly compatible with the model for the anisotropy proposed by Rao, McCracken, and Venkatesan.We also present the results of an investigation of the response of an underground telescope to generalized free-space first and second harmonics, for different approximations to the geomagnetic field and for small and large sets of arrival directions.