19, Gompertz in 1925 found that the age-specifie mortality rate in man as a function of age increased exponentially over a considerable portion of life and assumed that this phenomenon reflected an exponential decline with age of some vital system. In the field of radiation research Brues and Sacher [B1| first introduced a mathematical approach to long-term mortality based on the observation of Gompertz and this was followed later as a basis for the analysis of experimental data and for much theoretical formulations. According to this approach, the survival characteristics of a group of individuals may be described by actuarial functions. One of the most widely used is the Gompertz function. 20. The Gompertz function is the logarithm of the age-specific rate of where Q(t) = - eB Q(t) z\a mortality which is defined as is the age-specific mortality and surviving up to the time t. (1) N is the number of animals Linearity of the Gompertz function with time implies that (t) where Py and P. = P_el are positive constants. (2) Experience shows that a single acute dose of radiation is followed (after a period of latency) by an upward displacement of the Gompertz function without change in slope, the amount of displacement with respect to control being a function of dose. tion would change the constant Po in equation (2), without affecting single exposures would affect median survival, t where a (D) In other words, acute irradia- = t med’ linearly with dose a- bD is the median survival time of the control group and dent constant. P 1° If D, then (3) b a dose-depen- Chronic irradiation, on the other hand, characteristically in- creases the slope of the Gompertz function proportionally to intensity of irradiation, so that med