RADIATION INJURY AND LETHALITY 445 



of a "somatic mutation" causing a single cell to behave in a special man- 

 ner. The unicentric origin of cancer is obvious, and under heavy stimu- 

 lation of mice with radiostrontium the victim animals show multiple 

 bone tumors which are distributed in the treated population in good 

 correspondence with the Poisson theorem. If the center is a single cell, 

 then carcinogenesis is in all cases a rare event, for with an incidence of 

 0.1-1.0 per animal lifetime and 10^ susceptible cells the incidence per 

 cell is on the order of 10~^ per lifetime or perhaps 10~^ per cell genera- 

 tion, which places it in the statistical range of many genetic mutations. 



Here we at once strike a difficult problem in extrapolation. Since 

 man may have 10^ times as many cells of a given type as the mouse, 

 one would expect, other things being equal, a corresponding increment 

 in fre(iuency, which is obviously not true for either spontaneous or in- 

 duced cancer. Other things are clearly not equal, and we may rest on 

 the thought that the cells of a man must have a correspondingly lower 

 susceptibility in order to survive. Possibly this is a useful concept in 

 cancer research which has not been utilized. 



Besides the size factor there is also the time factor. Since man lives 

 30 or 40 times as long, cancer seems in this and other ways to be tied 

 in some way to the aging process, which leads us to the next section of 

 our discussion. 



The characteristics of the survival of groups of individuals are de- 

 scribed by means of the actuarial functions (27). These are related 

 mathematically; the mean survival time is a single point on one of these 

 functions. The most useful for our purposes was described by Gom- 

 pertz about a century ago (28). It is a well-established fact that the 

 logarithm of the rate of mortality, which we call the Gompertz function, 

 has an approximatel}^ linear dependence upon age in adult life for all 

 species of mammals investigated and for many other metazoan forms 

 (29). The Gompertzian plot of cancer mortality rates follows a similar 

 pattern (30) but appears in most cases to saturate in old age. This satu- 

 ration might appear to be due to relatively faulty diagnosis in the senile 

 human being, but appears also in our studies in spontaneous mouse lym- 

 phoma in two strains (31). 



Data on the incidence of cancer in human beings subject to carcino- 

 genic chemical insults have been collected by Kennaway (32), and it is 

 possible to infer that the Gompertz function for these groups is quite 

 parallel to the function observed in the general population. 



If we assume that the linear dependence for log of mortality rate on 

 age holds strictly for two species of different life span, each of the ac- 

 tuarial functions has the same analytical form, and an origin and a time- 

 scaling factor may be chosen such that all the functions become identi- 



