2 49 
estimation of the value of life contingencies. 
results ; making the division by 2 L a b for the sake of conveni- 
ence on the sum of numerators, we obtain in the same for- 
mula excepting the notation, with the ingenious Mr. Morgan 
first, and Messrs. Baily and Milne after him, the value of 
the contingency for any part or the whole of life, that the 
age a shall survive h. If we use the second form, the part due 
L » | L L i . 
to the interval between n and n-\-i, will stand — — - -- - - - 
L a, b 
this form, at least if the tables of mortality have the 
number of living inserted for every half year, would be easier 
in practice than the other. If a less accurate solution would 
answer our purpose, we might take t much larger ; if it were 
taken ten years we should soon get through the work, and 
frequently with sufficient accuracy, either from the article 
now quoted, or from Art. 13. of the same section ; that due 
to the interval between n and n + t, is b ± n+t '> ' 
2 L , 
L a, ° 
^ b+n b—n+nt T 
° r L 7 * L a+n + lt • 
a , b 
Art. 2. That A and B whose present ages are a and b , both 
die during the time ; but that B dies last, is from a similar 
L L, , 
argument = — fluent of (1 ftf) x = correction — 
L b 
+ fluent of — L +1 ; and this case may be therefore 
b a ,b 
found immediately from the other; or the other case imme- 
diately from this. But if from the period x=n to x—n+m, 
the decrements of each life be proportional to the times, 
however different the decrements of A's life and of B’s life 
