Mr . Morgan on Sttrvivorjhips . 
Common age. Exaft value* of too. Value of £. too. com- Value of £. ioo. computed 
computed from Dr. Price’s puted from the firfl of the from the fecond of the fore- 
Tables of the values of two foregoing rules, and from going rules, and from Mr. 
and three equal joint lives. 
Mr. Simpson’s approxi- 
mation Co the values of 
three joint lives. 
S 1 m p s 0 n’s approximation to 
the values of three joint 
lives. 
70 
*12.000 
I2.OO5 
- 
12.000 
75 
12.944 
I2.943 
- 
12.943 
80 
“ I3.84O 
I3.81O 
- 
13.880 
85 
I4.43O f 
14,670 
- 
14.340 
Mr. 
Dodson j, and Mr 
. Simpson §, are 
the 
only writers 
who have folved, or rather who have approximated to the 
folution of this problem. But the former, by deducing his 
rules immediately from a wrong hypothefis, having rendered 
* That is, one-Jixth part of the whole reverfion. 
f The feveral reverfions in this column, when computed from Simpson’s 
approximation to the values of the three joint lives, are 12.012, 12.933, 13.8479 
and 14.803 refpedtively ; which upon the whole differing nearly as much from 
the real values as thofe in the two other columns afford a convincing proof, 
that the very fmall deviation from the truth in thefe latter values proceeds not 
from any inaccuracy in the rules themfelves, but folely from having ufed the 
approximated inflead of the real values of the three joint lives. And this alfo 
will account for the difference in the values by the firfl and fecond rules. Were 
thofe values computed from tables which give the correct values of two and three 
joint lives at all ages, they would come out exadtly the fame. In the two firfl 
examples, where the values by one rule are true, it appears, that the values by 
the other rule are equally fo. In the two lafl examples, where the values are not 
quite fo accurate, it may be obferved, that they differ as much in excefs by one 
rule as they do in defedt by the othtr ; which mufl in general be the cafe from 
the very nature of thofe rules ; for if L (or the value by the firfl rule) be 
~ j V cc 
greater than the truth, the difference between - — — and aL (or the 
2r 
value by the fecond rule) mufl be lefs than the truth; and, on the contrary, if 
L be lefs, this difference will be greater than the truth. 
% See Dodson’s Mathematical Repofitory, Vol. IIL Queflions 42, 43, &c. 
§ See Simpson’s Seledl Exercifes, Prob. 38* 
H 2 raoft 
