is proportional to the amount of injury present and is independent of age; death occurs when the sum of all injuries reaches a given value, called the lethal bound; radiation injury is additive to the injury accumulating because of age; and age-cumulative injury is postulated to be linear with age. 31. Stover and Fyring [S15] and Eyring and Stover E1] developed a steady- state theory of mutation rates and applied it to the survival data of beagle dogs injected with 239 py an d 2206p 4. The fits of the experimental data obtained by the use of this model were good and they allowed the identification of various mechanisms of death operating with the two nuclides. The formalisms developed in this series of papers, in addition to describing the experimen- tal data adequately, were thought to be of potential use for their interpretations. 32. Sato, Nakamura and Eto [S16] performed calculations of the life-shortening effects of radiation as a function of dose and dose-rate under the assumption of linearity of the Gompertz function for both acute and continuous exposure. They showed that within the range of doses usually employed with mice the values of percentage life-shortening are not appreciably changed if the survival time is measured as mean, median or mode. 33. Iberall [13] examined in great detail the various models of radiation lethality and attempted a unitary description of the various modes of death from the very high acute doses to the low chronic treatments through an analysis of much experimental data. In so doing he illustrated the level of com- plexity required by a careful mathematical description of the actuarial pro- perties of a population. This description pointed towards the isolation of five or six possible factors affecting lethality at the various irradiation regimes and supplemented the studies of Sacher and Grahn [S4] by a widespread examination of the entire problem from a mathematical point of view. 3h. Another model for life-shortening by late effects of ionizing radiation was developed by Scott and Ainsworth [S47]. It applies to data in the mouse and it is specific for doses much below the LD 50/30° It focuses on the num- ber of individuals with life-shortening injury and their variation on dose, dose-rate and quality of radiation. For these individuals the survival time distribution differs and shows earlier times to death as compared to other members of the population not showing life-shortening injury. The results of MO