The incidence of bone sarcomas among 3055 female radium-dial workers who entered the dial industry before 1950 was used to determine dose-response relationships for the induction of bone sarcomas by radium. Two subpopulations were analyzed: all measured cases who survived at least 5 yr after the start of employment and all cases who survived at least 2 yr after first measurement. The first constituted a group based on year of entry; it contained 1468 women who experienced 42 bone sarcomas; the expected number was 0.4. The second comprised a group based on first measurement; it contained 1257 women who experienced 13 bone sarcomas; the expected number was 0.2. The dose-response function, I = (C + alpha D + beta D2)e-gammaD, and simplifications of this general form, were fit to each data set. Incidence (I) was in units of bone sarcomas per person-yr; (D) was the quantity (muCi) of radium that entered the blood. Two functions, I = (C + alpha D + beta D2)e-gammaD and I = (C + beta D2)e-gammaD, fit the data for year of entry (p greater than or equal to 0.05); both these functions and I = (C + alpha D) fit the data for first measurement. The function I = (C + beta D2)e-gammaD was used to predict the number of bone sarcomas in all other pre-1950 radium cases (medical, laboratory and other exposures); fewer were actually observed than the fit of this function to the female dial workers predicted.