140 



Discussion 



If each X-ray dose produced a constant displacement of the 

 Gompertz function, and if they added with one another as well as 

 with the basic ageing trend, then a cohort exposed daily throughout 

 adult life should show a constant divergence from controls, and a set 

 of different daily doses should produce a fan of Gompertz curves. 

 This is in fact seen (Sacher, 1956). The parameters of the daily dose 

 response are consistent with those of the single dose response. 



o 



> 



cc 



If) 



I- 



o 

 < 

 a: 



200 



400 



600 



800 



TIME FROM BEGINNING OF EXPOSURE 

 Fig. 2 (Sacher). Survivorship curves corresponding to the 

 schematic Gompertz functions in Fig. 1. The "single dose" 

 curves can be superimposed on the "control" curve by 

 sliding them to the right. The "repeated exposure" curves 

 can be superimposed on the "control" by multiplications 

 of their time scales by scaling factors. 



This mode of analysis therefore gives a parsimonious description of 

 radiation mortality, and relates it to the ageing process in terms of a 

 life-table function, the Gompertz function, where properties are 

 consistent with the hypothesis that the function is a linear measure 

 of the amount of ageing injury present in the population. A theoreti- 

 cal justification of this hypothesis can be given in terms of the con- 

 cepts of physiological fluctuations and probability of failure that 

 were introduced in the text (Sacher, 1956). 



In view of the earlier point, that any one of the life-table functions 

 contains the same information as the others, it follows that any 

 other desired quantities, such as expectations, medians, deciles, 



