METHOD OF FORMING TABLES OF EXPECTATION OF LIFE. 121 
hi+V. ± An 4- 3 + ~h • • • • ~4~ tm+t 
c 
0 
c - = 2 + 
hence the following rule for finding the expectation of life: 
“ Divide the sum of the number who complete each age above the 
given one, by the number living at the given age, and to the quotient 
add half unity.” 
123. In forming a table of expectations for every age, we begin with 
the living at the oldest, adding thereto the living at the oldest but one, 
then to this sum the living at the oldest but two, and to this sum again 
the living at the oldest age but three; proceeding in this manner with 
each age throughout the table, we have the requisite dividends and 
divisors for finding the expectations. 
The following calculations by the Northampton Rate of Mortality 
show the mode of forming a table of expectations ; 
Expectation. 
Additions checked. 
1 
4 
9 
16 
24 
34 
88 = sum of living 
above 90. 
/«= 24 24 ' 
54 * * 
L = 34 
-J* .5=2.41 — e go 
124. The present expectation of life after t years is 
the remaining part of the expression is the expectation of life at the age 
of (m + t) years; the expression may therefore be written e m+t .p m> 
125. Hence the duration of life that a person has the present expec-