We report on an experimental method to measure the electrical conductivity of cortical tissue. We use a pair of 5mm diameter Ag/AgCl electrodes in a perspex sandwich device that can be brought to a distance of 400 microns apart. The apparatus is brought to uniform temperature before use. Electrical impedance of a sample is measured across the frequency range 20 Hz - 2.0 MHz with an Agilent 4980A four-point impedance monitor in a shielded room. The equipment has been used to measure the conductivity of mature mouse brain cortex in vitro. Slices 400 microns in thickness are prepared on a vibratome. Slices are bathed in artificial cerebrospinal fluid (ACSF) to keep them alive. Slices are removed from the ACSF and sections of cortical tissue approximately 2 mm times 2 mm are cut with a razor blade. The sections are photographed through a calibrated microscope to allow identification of their cross-sectional areas. Excess ACSF is removed from the sample and the sections placed between the electrodes. The impedance is measured across the frequency range and electrical conductivity calculated. Results show two regions of dispersion. A low frequency region is evident below approximately 10 kHz, and a high frequency dispersion above this. Results at the higher frequencies show a good fit to the Cole-Cole model of impedance of biological tissue; this model consists of resistive and non-linear capacitative elements. Physically, these elements are likely to arise due to membrane polarization and migration of ions both intra- and extra-cellularly.