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To help resolve uncertainties as to the most appropriate weighting factor for tritium β rays, a large experiment was carried out to measure the relative biological effectiveness (RBE) of tritiated water compared to X rays for the induction of myeloid leukemia in male mice of the CBA/H strain. The study was designed to estimate the lifetime incidence of myeloid leukemia in seven groups of about 750 mice each; radiation exposures were approximately 0, 1, 2 and 3 Gy both for tritiated water and for X rays. The lifetime incidence of leukemia in these mice increased from 0.13% in the control group to 6-8% in groups exposed to higher radiation doses. The results were fitted to various equations relating leukemia incidence to radiation dose, using both the raw data and data corrected for cumulative mouse-days at risk. The calculated RBE values for tritium β rays compared to X rays ranged from 1.0 ± 0.5 to 1.3 ± 0.3. A best estimate of the RBE for this experiment was about 1.2 ± 0.3. A $w_{{\rm R}}$ value of 1 would thus appear to be more appropriate than a $w_{{\rm R}}$ of 2 for tritium β rays.