The capture cross section measured by the neutron lifetime and thermal decay time well logs depends largely on the amount of high capture cross section elements present in the rock and may be affected by neutron diffusion between the borehole and rock. The effect of both could be checked by a universally applicable method for measurement of capture cross section in small core samples. The goal of this investigation is to develop such a method. Reduction in the thermal flux with time, following a burst of 14 Mev neutrons, depends on the capture cross section and relative volume of each of the elements present. The capture process produces gamma-rays in numbers proportional to the neutron flux at any given time. The slope of a semi-log plot of gamma-rays versus time is proportional to the capture cross section. Gamma-rays from rock samples are masked by background due to physical limitations of the room in which the neutron generator is housed, even with the shielding designed to reduce the background. Water could be measured since it is mostly hydrogen which establishes a higher thermal flux and produces a recognizable count rate above background. The slope for water indicated a lower cross section than the true value due to net diffusion into the sample from the room. In the absence of a thermal flux from the room the indicated cross section of a small sample would be higher than the true value due to diffusion out of the sample. Capture cross section can only be measured directly by this method when the sample size is very large. As the sample becomes smaller the increase in indicated cross section becomes larger due to increased diffusion. Diffusion can probably be corrected for by use of uniform sample sizes and shapes, and by varying the correction for different major rock classifications.