Chopper measurements have been made of neutron spectra in either D2O, H2O, or D2O-H2O mixtures within a container that has been placed inside a uranium tube in the reactor R1. The fluid layer was 11.3-mm thick and its temperature either 22 or about 80°C. The neutron energy ranged from 0.008 to 1000 eV. With D2O in the container, the spectrum was only slightly softer than in the empty container. When the D2O was replaced by H2O, the spectrum changed considerably. The experiment had a clean geometry, which makes it possible to apply calculational methods. We have used the THERMOS transport theory code to compute the neutron spectra. The computed thermal spectra were slightly softer than the chopper spectra—the difference is not important for reactor calculations. All calculations underestimated the neutron flux in the joining region (≈0.3 eV). This effect can be important in calculations on reactors with plutonium.