6 B. Benjamin 



ages, i.e. that the modal span of hfe was invariant; he re- 

 jected the possibihty as "intangible speculation" outside the 

 practical framework of his study, namely the relatively short- 

 term trend of mortality. Deaths were then divided into two 

 categories, namely those which happened because the term 

 of the lifespan had run out — senescent deaths — , and all others, 

 whether from accident or disease, which were in fact a cutting 

 short of the lifespan — anticipated deaths. He first obtained, 

 therefore, a limiting curve of deaths by constructing a table 

 of mortality in which the q^ (probability of death between age 

 X and age x -[- 1) column would consist of values (g|) appro- 

 priate only to causes of death which could be regarded as 

 senescent. The next stage was to predict the pace at which 

 actual rates of mortality would in a given future period 

 approach those of the limiting table. It is not necessary to 

 discuss this aspect here. 



Clarke originally intended to define "senescent" deaths by 

 choosing certain degenerative diseases (e.g. cerebral vascular 

 lesions, myocardial diseases, angina pectoris, arteriosclerosis, 

 other diseases of the circulatory system, bronchitis, nephritis), 

 but he naturally found it difficult to select disease groups with 

 sufficiently specific reference to degeneration. Ultimately 

 therefore he arbitrarily assumed ratios of qljq^ rising from 

 0-05 at age 20 to 0-10 at age 40, 0-20 at age 50, 0-70 at age 

 70, 1-00 at ages 80 and above. 



His limiting curve of deaths was not symmetrical. There 

 was a sharp peak at age 80 with a tailing off rapidly on one 

 side to age 100 or so and on the other side a rapid decline to 

 about age 60 and then a much slower tailing off to age 20. 



The present approach 



The present author's approach has been even more arbitrary 

 and pragmatic. In a particular life-table the values of d^ 

 (deaths between age x and x -\- 1) have been plotted for 

 every value of x in the table (Figs. 1-3), thus producing an 



