where I is the daily exposure in roentgen, dose-rate [f and bo t* is the mean after-survival at the mean after-survival of controls. tive of this function, called the impulse lethality function, The first derivaSy 5 allowed the identification of four distinct phases of injury with peaks at 0.5, 5, 13 and }O days and these times could be related to different modes of injury to the nervous system, the intestinal epithelium, the leukopoietic and the erythropoietic marrow, respectively (see Figure V). For mean after-survivals in excess of 60 days a plot of the log mean after-survival versus the daily dose was found to be very nearly linear: this procedure allowed the assessment of life-shortening coefficients with small uncertainties. The paper by Sacher and Grahn [S4]) con- tains a full discussion of the mathematical formalism underlying the cumulative lethality functions. This represents an advancement in the identification of the phenomenology of radiation injury and lethality. 17. Lesher et al. [L9] reported on the pathology of these animals, in an at~ tempt to establish the cause of death. The daily exposures of 5 and 12 R/day were considerably more carcinogenic than higher exposure rates, and the lower carcinogenic efficiency of the higher dose rates was tentatively attributed either to the earlier death of the more heavily irradiated animals or perhaps to a "therapeutic" effect on the potentially transformed cells as the dose-rate increased. It was found, in general, that the duration-of~life exposure yielded less tumours per R of accumulated exposure than single or terminated irradiation regimes. Tumours of the genital tract and a higher incidence of lymphoma were responsible for the much higher tumour incidence in the female mice; also, some diseases were accelerated in the irradiated mice and some were not. 118. Sacher and Trucco [513] analysed a model for mammalian radiation letha- lity and recovery, based essentially on the kinetic characteristics of selfrenewing cell populations. The model assumes that population growth proceeds at a rate proportional to cell number but that growth is constrained, so that each cell population attains a given stationary size. The rate of growth is therefore the product of two terms, one of which is a monotone function of the size of the population and the other is a monotone function of the difference between actual size and limiting size at any given time. Based on these simple assumptions Sacher and Trucco produced a complex phenomenological theory which was applied to radiation data on survival after split doses, multiple fractionation and protracted continuous exposure and showed some qualitative agreement between the curves obtained experimentally and those predicted by the model.