Mr. Morgan on Survhorjhips . 
r — "r . V CC - 2 . r T . CC-CCC it r-l 
5 ° 
'ir 
andL = — x V — 2 CC - 2CCC. 
or ^ 
Q. E. D. 
Were we poffeffed of complete tables of the values of annui- 
ties on two and three joint lives, the preceding rules would give 
an eafy and exact folution of this problem in all cafes. But 
as fuch tables, computed for every age, would be a work of 
immenfe difficulty, efpecialiy in regard to the values of three 
joint lives, Mr. Simpson’s rule for approximating to thefe 
from the given values of the two joint lives, has hitherto been 
adopted, and it feems upon the whole to anfwer the purpofe 
very well. In the prefent problem it is attended with no other 
inconvenience than incr'eafing the labour of the computations; 
for the values of the reverfions derived from it appear in gene- 
ral to be perfectly correft. This is more fully afcertained by 
a table which Dr. Price has given in his Treatife on Rever- 
fionary Payments (Vol. If. Table 37.), of the values of three 
equal joint lives computed at 4 per cent . from the probabilities 
of life at Northampton. By the affiftance of this table, 
when the lives are of the fame age, it is evident, from what 
has been already obferved, that the exaft value of the reverfion 
may be eafily obtained. The few following fpecimens com- 
puted from it, and compared with the values of the reverfions 
deduced from the firft and fecond of the preceding rules, de- 
monftrate the accuracy of thofe rules : for, notwithftanding 
the approximated values of the three joints lives have been ufed 
in every inftance in which the rules have been employed, yet 
the refults approach fo near the truth, even in the laft ftages 
of life, when the decrements are moft irregular, that, though 
derived from thefe approximations, there can be little doubt of 
their corredtnefs in almoft every other period of life. 
& 
Common 
