294 Mr. Gompertz's analysis , 
that that portion of the annuity is payable to the assignees 
of those persons; its value will be equal to \ 
m 
i, b, c, Sec. -{- 
ir 
1 
n — i 
m — i 
— L 
7t + t , tt+ 1 : a, b t c, &c. i , • r t v 
r T . t . x f ! , but if L , . , . „ be 
L r o 71 + 1 : a, b, c , See. 
a, b , c, &c. ’ 
considered sufficiently approximated by the expression 
: a, l, c, &c. ^«r: a,b, c, &c. ^ + I : a, b, c, &c. 
J a,b > c, &c. 
'a, c, &c. 
and as a sufficient 
approximation for r nT+t we write r w+I , the expression will be- 
come 
r 
T) 
n la, c, &c. 
m'— — — 
— M*™ I 
m — » 
r : a, b, c, ” I : a, &, c. &c. 
. _ _ 
a, 6, c 
r r 
n ti 
«|a, b,c,&.c. _j_ JL* w ja, b, c, &c. and will agree with Mr. Baily’s 
observations on page 344, of his Doctrine of Life Annuities, as 
far as it goes. Note, we might with a similar proximity have 
omitted the t in the exponent of r ; and as a nearer approxi- 
mation have written r” +1 for r a+t 
(not deeming it necessary 
to go nearer), and the expression will be * 
r 
a, b, c, &c. ~f- r 1 • X 
■■ " 2 
nja,b,c,& c. . I might make some farther observations on the 
m I 
comparison of the different methods pointed out, with respect 
to their proximity, but I fear that the length of this Paper has 
already caused me to occupy too large a portion of the pre- 
sent volume. 
