t 96 ] 
variation, be exadly the fame with the expeBation 
of thofe lives at the time when their exiffence com- 
menced. Thus; was it found that a 19th part of 
all the marriages among any body of men, whofe 
numbers do not vary, are diflblved every year by the 
deaths of cither the hufband or wire, it would ap- 
pear that 19 was, at the time they were contracted, 
the expeclatio?! of thefe marriages. In like manner; 
was it found in a fociety, limited to a fixed number 
of members, that a 28th part dies annually out 
of the whole number of members, it would appear 
that 28 was their common expectation of life at the 
time they entered. So iikewife ; were it found in 
any town or diftriCt, where the number births and 
burials are equal, that a 20th or 30th part of the in- 
habitants die annually, it would appear that 20 or 
30 was the expeBation of a child juft born in that 
town or diftriCt. Thefe expeBatmis, therefore, for 
all Jingle lives, are eafily found by a Table of Ohferva- 
tionsy ftiewing the number that die annually at all 
ages, out of a given number alive at thole ages ; 
and the general rule for this purpofe is “ to divide 
“ the fum of all the living in the Table at the age 
“ whofe expeClation is required, and at all greater 
“ ages, by the fum of all that die annually at 
“ that age, and above it; or, which is the fame, by 
“ the number in the Table of the living at that age ; 
“ and half fubtraCted from the quotient will be the 
“ required expeBationP Thus, in Dr. Halley’s 
Table, the fum of all the living at 20 and upwards 
is 20,724. The number living at that age is 598 ; 
and the former number divided by the latter, and 
half 
