Using the Angstrom principle, a new apparatus for measuring the thermal diffusivity of soil was designed. In order to give the sinusoidal boundary condition, the apparatus was constructed to change the applied voltage of a heater. A simple auto transformer and a special cam were used for this purpose. Using this apparatus, the thermal diffusivity of frozen soil as well as wet soil was measured. In the case of frozen soil, the samples were prepared under the conditions similar to natural frost formation. Thermal conductivity was computed from the diffusivity thus obtained and the volume specific heat of the soil. Moisture relationship of the thermal diffusivity and the thermal conductivity of frozen soils are represented by an empirical formula of exponential form. The formula holds only in the range of moisture content below the saturation. These relationships are shown graphically. Similar measurements were carried out with wet soil at room temperature. In nature, we often observe the segregation of ice in frozen soil. Such a frozen soil usually contains more water than that of saturation. Samples of various modes of segregation of ice were artificially prepared and their thermal diffusivity was measured. For the moisture ratio above saturation, the rate of increase of the thermal diffusivity with respect to moisture ratio is smaller than that expressed by the above formula. The variation of the thermal diffusivity of the frozen soil in relation to the direction of heat flow is comparatively small.