82 BIOLOGY OF DEATH 



was published in 1693, although thirty years before that 

 time Pascal and Fermat (c/. Levasseur) had laid down 

 certain mathematical rules for the calculation of the 

 probabilities of human life. Since Halley's time a great 

 number of such tables have been calculated. Dawson 

 fills a stout octavo volume with a collection of the more 

 important of such tables, computed for different coun- 

 tries and different groups of the population. Now they 

 have become such a commonplace that elementary classes 

 in vital statistics are required to compute them (see for 

 example Dublin's New Haven life table). 



CHANGES IN EXPECTATION OF LIFE 



I wish to pass in graphic review some of these life 

 tables in order to call attention in vivid form to an impor- 

 tant fact about the duration of human life. In order to 

 bring out the point with which we are here concerned it 

 will be necessary to make use of another function of the 

 mortality table than either the / or d x lines which are 

 shown in Figure 18. I wish to discuss expectation of 

 life at each age. The expectation of life at any age is 

 defined in actuarial science as the mean or average number 

 of years of survival of persons alive at the stated age. 

 It is got by dividing the total survivor-years of after life 

 by the number surviving at the stated age. Or, if we let 

 e.x denote what is called the curtate expectation of life 



lx + lx+l + lx+2 + -Mz-fn 



ex = 



To a first approximation, sufficiently accurate for our 

 present purposes, the total expectation of life, called e x , 

 may be obtained from the curtate expectation by the 

 simple relation 



= ** + 1/2 



