estimation of the value of life contingencies . 
evidently, since r is near unity, be nearly equal to i- 
285 
x — r 
2 
i 1 — r 
(1— r) . 1 + (VT • ~\ a > b > c > &c - = nearl y r —■ tt* ; | a,B, c ,&c. 
r r* r 1 
but 1 L, h,c,kc. = r— (l r) i\ a> b,c, &c. .'. • 0 Jar, b, c, &c. — ^7 
xTL c , &c. nearly ; that is the value of one pound to be re- 
1 1 
ceived at the discontinuance of the joint lives of the ages 
a, b, c, &c. is equal nearly to -h x the value of one pound to be 
r z 
received at the first anniversary from the present time, which 
shall happen after the discontinuance of the same lives. Also 
h b,c,8t c. . r 2 or which is the same thing, the value of one 
pound to be received a half year after the discontinuance of the 
r 
joint lives is nearly =± Y|a, b, c, &c, > or the value of one pound 
1 i. . - 
to be received at the first anniversary from the present time, 
which shall happen after the discontinuance of the joint lives; 
and 7L&, Cj & c . • r is nearly = 7 a, b, c ,&c. • r*; that is the value 
o 1 - I 
of one pound to be received one year after the discontinuance 
of the joint lives of the ages a, b, c, & c. is nearly equal to ri x 
the value of the same contingency on one pound to be re- 
ceived at the first anniversary which shall happen after the 
discontinuance -of the joint lives. 
Art. 3. Again with respect to the calculation of the value 
of the expresion q . q n 
b m 
MDCCCXX. 
a, b — q 
m 
J a — q S , 
t • » \b, a—q from the 
p P 
