Mr. Morgan on Survivorships. 
c. 
Ages of 
B. A. 
Annuity of £ 1 . 
True value. 
Approximation. 
78 
'5 
75 
.138 
.146 
70 
20 
65 
.406 
00 
0 
1 
81 
7° 
80 
•53° 
•55° 
'5 
85 
10 
t 3- 8 33 
13.782 
15 
75 
15 
- 11 -385 
- - 11.230 
35 
75 
15 
8.968 
8.834 
'5 
65 
20 
- 8.485 
- 8.379 
80 
70 
9 9 3 
9-529 
*5 
10 
85 
.647 
- .698 
15 
15 
75 
1.038 
'-'93 
35 
15 
75 
- .786 
- *920 
'5 
20 
65 
1.769 
1.876 
15 
70 
80 
4.307 
4.671 
From these examples it appears, that when C or A is the 
oldest of the three lives, the approximated and the true values 
agree sufficiently near for any useful purpose ; and that even 
when B is the oldest, the difference is almost as inconsiderable. 
It should likewise be observed, that these examples are cases 
in which the difference is likely to be greatest, and therefore a 
nearer approximation need not be required. Both Mr. Simp- 
son and myself have given solutions offthis problem, and in 
most of the foregoing examples the values derived from them 
are more correct than could have been expected; but these 
solutions being founded on a wrong hypothesis, are not so 
correct as the present, except when C is the oldest of the 
