[en] Measurements near the endpoint of the tritium beta-decay spectrum using a gaseous molecular tritium source yield an essentially model-independent upper limit of 27 eV on the /ovr ν//sub e/ mass at the 95% confidence level. Since demonstrating from this initial measurement the successful operation of a gaseous source based system, most of our effort has been concentrated towards the upgrade and optimization of the experimental apparatus. The emphasis of this work has been to eliminate or further reduce effects that generate systematic errors. Based on realistic projections from our initial measurement, an ultimate sensitivity to neutrino mass of 10 eV is expected. 12 refs., 1 fig