284 
Mr. Gompertz’s analysis applicable to the 
r t T 
+ T la, t, C, &C. =f+ 7 a, b , c, &C. nearly ; and similarly is ^ 
1 i — — — — 1 0 
a,b,c, Sec. 
r 
= nearly; that is a momentary income, 
1 1 
which in a year certain without interest would amount to one 
pound, will, if it is to be received on the joint lives a, b, c, &c. 
reckoning interest, be worth £ -j- the life annuity of one 
pound payable on the joint lives a, b, c, &c. 
q 
Art. 2. Moreover, because (Art. 3, Section 1) » 
a, b, c, Sec 
r 
"IT 
— *—? 
m — q 
r 
i 
a, b, c, See. • n 
— m 
a, b, c, See. — n 
— ■ m 
a,b,c,se c. . + : &c - 
a, 5 , C, &c. 
m-\-q m: a,b, c, &c. q 
'‘a, b, c, &c. 
a, b, c, &c. — T n . 
L , D _ r m + ? L 
r n n—q - Cl, b, c, &c. 
m : a, b, e, &c. 
J a, b, c, &c. 
q 
■ — (t — r 0 * n a, b, c . Sec . , it is therefore from above = 
L 
n—q : a, b, c, Sec. 
______ 
Til 4* q t c n ~ _i_ q 
r • m+g: a, b, c. Sec. ^ J T ‘ i> + q ,L n:a,b,c,Se c.~~ r H L m:a,b 
, b, c, Sec. y \ 2 P • tj r & c . 
a, b, c, &c. 
1 
■ r I, Tf 
+ n+p a ,b,c,& c. j. It />== i, 0=0, «=o, m infinite, since 1 — r* 
m I — _ — _ j 
will be equal to q hyp. log. of A we shall have ~o\a, b, c, &c. = 
o 1 ■ 
nearly i—ihyp. log. of A — hyp. log. of A x and 
if for — hyp, log. of A 0 r its equal hyp. log. of 1 — (1— r) we 
write — ( i r) — - & Ci the expression will 
* 3 
