A highly accurate, fully compensated, high spatial resolution, wave propagation system for measuring dielectric constant and resistivity of fluids or solids in a cylindrical enclosure and method for measuring well core characteristics in-situ or in a laboratory. One embodiment of the invention relies on waves propagated from transmitters above and below two spaced receivers which transmit and receive electromagnetic waves via slots on the inner periphery of a cylinder structure. The data is then processed with a CPU either down hole for later retrieval or on the surface for real-time monitoring.