Current vs voltage measurements have revealed two different conduction zones in a NLC sample. A standard sandwich type sample was filled with K18 (6CB) which was aligned (approximately) homeotropically by the two ITO surfaces previously cleaned in orthochromic mixture. On two opposite sides of the cell, the NLC was limited by two Mylar stripes acting as spacers. The other two sides were left open, and the liquid crystal had two free surfaces (limited only by air) in the form of a cylindrical meniscus. The overall conductivity of the cell depended strongly on the length of the free surface. For the same area, samples with a larger free surface experienced a higher overall conductivity. In the absence of an electric field, we considered the order in the free surface zone to be planar with n being normal to LC-air interface. For small electric fields the conduction along director n in the bulk is less than the conduction perpendicular to n on the free zone. At higher fields, the Freedericksz transition which operates on the free zone reduces the overall conductivity. This reduced conductivity was practically equal to that obtained when ITO electrodes were completely immersed in liquid crystal; that is, the free surfaces do not contribute to the conduction. Considering the measured values, we have concluded that the order in the free surface zone was planar for a depth of about 50 mum.