The electrical resistivity and magnetic susceptibility of allotropically pure β-Ce and γ-Ce and some two-phase (α+β or β+γ) samples, which were predominantly β-Ce, were measured from 2 to 300 K. Because β-Ce transforms to α-Ce between 15 and 50 K, several unusual experimental techniques were used to obtain reliable data. Our results show that the electrical resistivity of β-Ce remains unusually large, > 50 μΩcm down to 40 K and below this temperature it drops an order of magnitude. The magnetic-susceptibility data show that β-Ce obeys the Curie-Weiss law down to near its Néel temperature, ~ 12.5 K. Low-field susceptibility data, < 800 Oe, show a Néel temperature at 12.5 K and that the magnetic susceptibility near the ordering temperatures decreases with increasing field. X-ray metallographic data indicate that when β-Ce transforms to α-Ce the initial growth occurs at the surface and grows inward. The unusual temperature dependence of the electrical resistivity of β-Ce could not be explained by several existing models (band-spin fluctuation or crystalline field) which have been used to explain large increases in the resistivity for other materials. However, a recently developed model based on Kondo scattering which is quenched by magnetic ordering appears to account for the observed results.