DE. FAEE ON THE CONSTEUCTION OE LIFE-TABLES. 
861 
(26.) 4 ''^"= the probability that A, age x, will die in the next n years. 
(27.) the probability that A, of age x, will live n years. 
(28.) Put— and when is taken at such an age as to fulfil the conditions of 
the equation, then n is i\ie probable lifetime=vie probable=ih.e time that it is an even 
chance a person of the age x will live. 
“^^Aji^the mean after lifetime^ or as it is often called, the expectation of life — 
an incorrect expression, which is rather applicable to the probable lifetime. 
Upon Demoivee’s hypothesis, the probable lifetime, that is the time that a 
person may fairly expect to live, his expectation, was the same as the mean after lifetime. 
(30.) G^=.r--j-A^=the mean age at death of persons who have already lived exactly 
X years. 
(31.) S=c -^=the number of members of any Society between the ages x and x-\-n, 
which will be permanently sustained by c ... annual admissions at the age x. 
s/ 
(32.) c=Q-^=annual recruits of the Society (S). 
members leaUng the Society (S) on attaining the age x-{-n. 
(34.) ^-^=annual deaths in such a Society (S). 
*x I n 
Q'x+n 
(35.) SQ^=the aggregate number of persons living, who have left such a Society, 
as pensioners or otherwise. 
In the following formulae it is assumed that the population is normally constituted 
Yj, 
Q'=A',=the mean after lifetime of all persons of the age x and upwards. 
Y^— Y Y 
(37.) Q^~Q^^”=Q^=the mean after lifetime of all persons of the age of x and 
under the age of x-\-n. 
Y 
number of persons of which a Society will ultimately consist, 
recruited by c annual additions of members in the tabular proportions between the age 
X and x-\-n. 
Y.,„-Y. 
(o9.) c * ' — ^he number of persons to which a Society joined by c persons 
of the tabular ages x and under x-]-m would amount in n years. When x-{-n>u; this 
formula will be reduced to the same form as equation (38.). And when x-{-m, as well as 
x+n >&>, the equation becomes the same as (36.). 
5 X 
MDCCCLIX. 
