Observations made by the two-hemisphere network of surface-level, multidirectional muon telescopes at Hobart (Tasmania, Australia) and Nagoya (Aichi, Japan) are used to examine the origin of the solar semidiurnal variation in cosmic ray intensity. The network allows us to precisely determine the asymmetry of the variation across both hemispheres. It is shown that the variation is consistent with the north-south (NS) symmetric distribution of cosmic ray intensity in space. The phase of the space harmonic vector responsible for the variation is consistent with both the second-order anisotropy expected from a bidirectional latitudinal density gradient (type I) and also one arising from pitch angle scattering (type II). The network also observed a purely NS antisymmetric, antisidereal diurnal variation with the maximum phases differing by 12 hours between the two hemispheres. This is consistent with an antisidereal diurnal variation arising from annual modulation of the solar diurnal variation produced by a second-order anisotropy. The phase of the space harmonic vector responsible for the antisidereal diurnal variation is consistent with the phases predicted from both type I and type II anisotropies. It is shown, however, that the ratio of the amplitude of the space harmonic vector of the antisidereal diurnal variation to that of the solar semidiurnal variations is consistent with the type II anisotropy but not with the type I anisotropy. This result implies that the solar semidiurnal variation and the antisidereal diurnal variation observed during the period 1992--1995 mainly arise from the type II anisotropy and cannot be explained solely as arising from the type I anisotropy. ¿ 1998 American Geophysical Union