Two-group neutron diffusion theory has been applied to two concentric cylindrical regions representing borehole and formation to show that the ratio of thermal neutron flux at two appropriately large distances along the axis is virtually identical to the epithermal flux ratio, and is a measure of a single epithermal parameter of the formation, viz., the slowing down length. The slowing down length is most strongly dependent on hydrogen content. It is shown that variations in salinity of the liquid in the formation or the borehole and uncertainties in borehole size have relatively little effect on the flux ratio. Experiments in a borehole model showed that the thermal flux ratio does not depend on eccentricity of location of the logging tool in the borehole. Fits of theory to experiment allowed determination of slowing down lengths for Pu-Be neutrons in salt water filled sandstone at two porosities for which experimental values have not previously been available. These investigations suggest that an improved porosity log can be obtained by use of 70- and 90-cm source-detector spacings with a neutron source of 5 X 10 8 neutrons/sec or greater. Proportional counters containing He 3 are recommended as detectors. Such a system employing flux ratios is expected to be insensitive to casing and cement in cased holes.