wh, At higher dose-rates the life-shortening continues to increase but, owing to the progressive reduction of life, the dose accumulated decreases and the curve bends over towards the origin. described by Lorenz et al. {B5| and Sacher [S1]. Such an effect had previously been [L6] and may be predicted by the theories of Blair Although this observation is not immediately apparent from Figure X it may be noted that all along the curve the data obtained at approximately similar dose rates are reasonably well clustered together. This immediately points to a relationship between the three quantities under study in the graph: dose, dose-rate and life-shortening effect. 145. Simply in order to describe the data with a maximum of precision, an attempt was made to fit a curve where the three quantities cited would all contribute to determine the final shape of the relationship. The following equation was assumed to interpolate the phenomenon reasonably where y is the percentage of life-span-shortening, dose-rate, b and ce D being proportionality constants. the dose and A the Such a relationship could not be fitted adequately in the absence of some function relating dose and dose-rate. In order to find such a function the simplifying assumption of an exponential decrease of the life-span with increasing dose-rate was made for any given total absorbed dose r= pt ° eA, (2h) Since the total absorbed dose is given by the product of the duration of life and the dose-rate D= AT (25) it follows that D= AT enA/A, (26) A plot of total absorbed dose versus dose-rate for data belonging to the same experiments in Figure IX was found to agree reasonably well with an expression of the above type. Therefore, the previous relationship was fitted to the ex- perimental data, yielding D with an Re = 0.98. = 664.11 Ae -0.0351 (27)