860 
DE. EAEE OX THE COXSTELX'TIOX OF LIFE-TABLES. 
their living 58 years, as they are 50,861 to 49,149 ; upon the other hand, the chances 
of their living 69 years (49,895) are less than the chances 50,105 of their dying before 
attaining that age. Upon trial it will be found that the chances of living to and the chances 
r T • IP rna^i rn . 50,851 — 50,000 » , 851 , , „ „ 
ot dying belore 58f|^ years = 58-}- ^ ‘ 9 ^ years, or about ohf years 
are nearly equal ; hence this is called the probable lifetime, or vie probable by French 
writers, for ^=i. At the age 20 the probable lifetime is 47 ];||| , nearly 48 years. 
The probable lifetime at every age is immediately seen by inspection. 
(22.) V. THE THEEEEOLD LIFE-TABLE— PEESOXS, MALES^ FF AIAL FS 
The Life-Table is threefold. A Table having the six columns is made for males ; 
another Table is separately made for females. The several columns of the two Tables 
incorporated together form the Table of persons which has 100,000, and may have any 
other number for its basis. The basis of the Male Table in the illustration is 51,125, 
while the basis of the Female Table is 48,875. In that proportion males and females 
were born in the districts. Under this arrangement the number of contemporaneous 
males and females living at each age in columns is slio-wn: thus 38,388 males and 
37,212 females attain the age of 20; 17,145 males attain the age of 70, and 17,133 
females attain the same age ; at all ages under 71 the number of males exceeds the 
females; at the age of 71 and upwards the females exceed the males in number: and 
upon referring to the columns it will be seen that the males die off in greater 
numbers than females after the age of 42. The age after the second year at which the 
greatest number of deaths occurs is 75 in males, 76 in females. 
These numbers all refer to the Life-Table for healthy districts. 
Some of the other properties of the Life-Tables, admitting of innumerable applica- 
tions in the solution of social phenomena, will appear in the following formulae, which 
will be found useful in practice. 
VI. HSEFUL FOEMHLAl. 
The following formula will facilitate the use of the Life-Table. The figures must be 
taken from the Tables of Persons, of males or females, applicable to the case. The for- 
mulae are general, and are applicable to any other Life-Table. 
(23.) ^=:m^=the rate of mortality in the year of age following the precise age .r. 
(24.) y ^^’ = 1— ^' = the probability that a person A of the age x, in average 
health, will die in the following year. 
(25.) = l — ^ = the probability that A, a person of the age x\ will hve 
a year; .'. 1— ^^=the probability that A, age x, will die in the year following, as cer- 
tainty of life =1. 
