Discussion 



139 



intercept values. A single dose of X-rays given in early adult life is 

 followed, after a latent period of 100-200 days, by a displacement of 

 the Gompertz transform parallel to itself (Fig. 1). In cases where the 

 Gompertz transform shows some curvature, it is possible to infer that 

 this displacement is a translation to the left on the time axis. The 

 interpretation is that the Gompertz transform is a linear measure of 

 the amount of ageing injury present. A single X-ray dose produces a 

 residue of permanent injury, and this is manifested by a displacement 

 of the Gompertz transform by a constant amount. 



1000- 



o 

 o 

 o 

 o* 



IT. 

 UJ 

 Q. 



o 



UJ 

 O 



o 



200 400 600 800 



TIME FROM BEGINNING OF EXPOSURE 



Fig. 1 (Sacher). Schematic representation of the long-term 

 effect of single or repeated exposure to ionizing radiations 

 on the Gompertz function (logarithm of the age- specific 

 rate of mortality) for mammals. The age-trend of mortality 

 is considered to conform to the Gompertz equation (compare 

 with equation 1 and text) 



'°s(x-f) = "'g^ + 



OCX 



where A' is the number living at age x. 

 O — unirradiated population; S^, Sg, — populations given 

 single exposures at time zero; R^, Rg — populations given 

 repeated or continuous exposure beginning at time zero. 

 Early portion of lines S^ and Sg dotted to indicate time 

 needed for displacement to attain its steady value. 



