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.

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We analyze the sidereal daily variations observed between 1985 and 2006 at Matsushiro, Japan (MAT) and between 1993 and 2005 at Liapootah, Tasmania (LPT). These stations comprise the two hemisphere network (THN) of underground muon detectors in Japan and Australia. Yearly mean harmonic vectors at MAT and LPT are more or less stable without any significant change in phase and amplitude in correlation with either the solar activity-or magnetic-cycles. In this paper, therefore, we analyze the average anisotropy over the entire observation periods, i.e. 1985periods, i.e. -2006periods, i.e. for MAT and 1993periods, i.e. -2005 for LPT. We apply to the THN data a best-fitting analysis based on a model anisotropy in space identical to that adopted by Amenomori et al. (2007) for Tibet III data. The median energies of primary cosmic rays recorded are ~0.5 TeV for THN and ~5 TeV for the Tibet III experiment. It is shown that the intensity distribution of the best-fit anisotropy is quite similar to that derived from Tibet III data, regardless of the order of magnitude difference in energies of primary particles. This, together with the THN observations, confirms that the analysis by Amenomori et al. (2007) based on the Tibet III experiment in the northern hemisphere is not seriously biased. The best-fit amplitudes of the anisotropy, on the other hand, are only one third or less of those reported by the Tibet III experiment, indicating attenuation due to solar modulation. The rigidity dependence of the anisotropy amplitude in the sub-TeV region is consistent with the spectrum reported by Hall et al. (1999), smoothly extending to the Tibet III result in the multi-TeV region. The amplitude at higher energies appears almost constant or gradually decreasing with increasing rigidity. The rigidity spectrum indicating the solar modulation also supports the conclusion first implied by the Super Kamiokande deep underground experiment that the large scale anisotropy observed by Tibet III is due to the charged component of primary cosmic rays, and not due to high energy gamma rays to which underground muon detectors have negligible response.