Apparent thermal conductivity ka, measured with a line source lying between two dissimilar media, equals the mean conductivity of the two media, ka=(k2+k2)/2. This theoretically derived formula is substantiated by data in the literature. With reference to a medium of known conductivity k1, the relation justifies the development of an inexpensive, simple, rapid, and reliable method to determine conductivity k2 of samples which cannot be penetrated with a conventional needle probe. Measurements by methods of half-space needle probe or half-space line source have been made in the past by discarding the contribution of k1, resulting in overestimation of conductivity if correction through calibration is not made. For example, with respect to an epoxy half-space probe, a sample of fused silica (k2=1.36 W m-1 K-1) could be overestimated by 6.5% if the finite conductivity of epoxy (k1=0.087, W m-1 K-1) is neglected. ¿ American Geophysical Union 1989