582 Mr. Gompertz on the nature of the function 
According to the Carlisle table of mortality at 3 per cent, 
to assure 100/. at the 
Age .... 
For 7 years, the annual ' 
premium, by common 
modes of calculation . 
For one year, the premium 
For 10 years, the annual 1 
premiu-m, by common I 
modes of calculation . J 
For one year, at an age"\ 
5 years older ... .j 
10 
20 
30 ■ 
40 
50 
£0 10 5 
0 13 10 
0 19 10 
00 
III 0 
0 10 5 
0 13 9 
0192 
186 
I 12 I 
0 II 3 
0 14 7 
104 
» 7 7 
1 14 11 
012 0 
0 14 2 
0 19 11 
190 
I 14 10 
6o 
3 *3 8 
3 15 9 
3 17 8 
3 *9 9 
Moreover, because^ 
T 
1 a, h, c, 
I im « 
&C. 
, or the single premium for the 
assurance of unity, on the joint lives a, h, c, &c. for m 
years, is =«^i 
L 
a,b,c. Sec. ^ \\a,h,c,Scc. 0I2, J, c, &c. , 
. / ——m ' m-v *r 1 — — 
I. 
m : a, b, c, & c. m ® ; a, b, c. See. « 
— r r — izr: 1 — — — — r (1— 
a,b,c. Sec. • 
a,b,c,S^c. ^a,b,c,Sec. 
if this be divided by we shall have the annual 
r r 
premium for such assurance ; that is,”^ — 
^~m:a,b,c,Sec. »» 
L 
a, b,c. Sec. — aniiual premium maybe ex- 
pressed by 
1 
0 
a, 6, c, &c. 
( 1 — a, i, c, &c. J" ,( 1 &c _ a-i, c-i,&c.'\ ^ , 
—j— — .rj— \ . X T~ ^ 
a, b, c, Sec. ' a, b, c, Sec. ' 
This last mode is 'well adapted to logarithms in the use of 
our general tables ; and this method, supposing the annuities 
were accurately determinable by our general tables, would 
be accurate. The last formula is derived from that imme- 
r 
6 & 
diately before, in consequence of ! — L_i — being identical 
r 
L 
a-l,6-l,c-l,&c. u-l,b-\,c~li Sec. 
with ^ piTT 7 
(If Cf &c» 
