PROCEEDINGS OF SECTION G. 



529 



If we asume 100,000 births of each sex, the figures given in the 

 last table enable us to write down at once the numbers out of 

 100,000 of each sex born, who, according to the experience under 

 review, will survive to each of the succeeding ages up to 5. These 

 results are as follows, the probability of surviving a year at each 

 tige being also given: — 



Table IV. 



The number of suvivors at each age has been obtained by 

 multiplying the results in Table III. by 100,000, and subtracting 

 the products successively from 100,000. 



The probability of surviving one year at age x has been ob- 

 tained by dividing the number of survivors at age (x + 1) by the 

 number at age x. 



6. The Makeham-Gompertz Formula. 



In a paper contributed to the Royal Society in 1825, Benjamin 

 Gompertz shewed that for a considerable ranj^e of values the survivors 

 at successive ages in a Life Table could be represented by the expres- 

 sion kg'' , where k, g, and c were constants for the table under review 

 and the variable x denoted the age, but that to represent the whole 

 range of adult life, it was necessary to change the values of the 

 (•onstants between ages 50 and 60. In 1860, in a puper submitted to 

 the Institute of Actiaries, W VI. Makeham shewed tiiat by adding a 

 farther constant a closer representation with one set of constants could 

 be obtained from about age 20 onwards to the oldest age. The 



formula which Makeham fir^t gave was in the form Ij. = ks^'g'^ , though 

 later he suggested the addition of still another constant, and gave an 



expression of the form l^ = ks^h^'^g'''^,wheTe ^a: denotes the number who 

 reach age x according to the experience under review. The former of 



