446 RADIATION INJURY AND LETHALITY 



cal for the two species. The ensuing discussion imphes that the trans- 

 formation has been made straightforwardly between mouse data and 

 man, and is to be regarded only as a working hypothesis whose implica- 

 tions are such that it is very important to seek ways and means of 

 testing its validity. 



By way of introducing a simplified picture of the effect of radiations 

 on the Gompertz function, we present in Fig. 1 the effect of fractionated 

 exposure in early life and constant exposure throughout life in mice. 

 The effect of single exposure is an upward displacement of the function 

 without change in slope, whereas that of constant exposure is to increase 

 the slope of the subsequent function (Fig. 1). A further property of 

 the Gompertz functions is that they summate, both superimposing ex- 

 posures and superimposing an exposure pattern on normal aging 

 (Fig. 2). 



It may be said that the long-term effect of a schematized single dose 

 received at age x is to decrease the after-expectation to that for an age 

 X + q, where g is a function of dose and other variables. The depend- 

 ence of q on dose is not simple, especially in the region of acute frac- 

 tionally lethal doses or where we are concerned with fractionation of 

 dosage. The physiological factors here involved will be discussed later; 

 we assume as a further working hypothesis that at sufficiently low dos- 

 ages the upward displacement of the Gompertz functions becomes pro- 

 portional to dose. 



Approaching the question of species comparison on this basis, we will 

 consider the case that two species have equal sensitivity as measured 

 by the Gompertz function. Then, if the normal life expectations of the 

 unknown and known species are in the ratio l/K, the reduction of life 

 expectation by a single exposure at the actuarially equivalent age in the 

 unknown species will also be changed by the factor l/K; hence the per 

 cent reduction of life expectation by a single dose will be equal for the 

 two species. 



Since the effect of continuous exposure at low dose rates is to increase 

 the slope of the Gompertz function, we can derive this relationship: to 

 induce equivalent per cent reduction of the life span in the two species 

 by duration-of-life exposure we must expose the unknown species at 

 dose rate KI. For example, if the respective expectations are 2 and 40 

 years, equivalent shortening of life in the two species would be accom- 

 plished by 5 and 0.25 r per day, respectively. 



We have made four assumptions here, for all of which there is experi- 

 mental evidence : 



1. The Gompertz function for natural aging increases linearly with 

 age. 



