thus to the end of the table, 15 nominees attain the
age of 95, 5 of whom die before the age of 96, so that 85 payments will
be paid in respect of these 5 lives. Of the survivors all die before
attaining the age of 97, so that the annuities on these lives will be
payable for 86 years. Having previously calculated a table of the values
of annuities certain for every number of years up to 86, the value of
all the annuities on the 10,000 nominees will be found by taking 40
times the value of an annuity for 2 years, 35 times the value of an
annuity for 3 years, and so on--the last term being the value of 10
annuities for 86 years--and adding them together; and the value of an
annuity on one of the nominees will then be found by dividing by 10,000.
Before leaving the subject of De Witt, we may mention that we find in
the correspondence a distinct suggestion of the law of mortality that
bears the name of Demoivre. In De Witt's letter, dated the 27th of
October 1671 (_Ass. Mag_. vol. iii. p. 107), he speaks of a "provisional
hypothesis" suggested by Hudde, that out of 80 young lives (who, from
the context, may be taken as of the age 6) about 1 dies annually. In
strictness, therefore, the law in question might be more correctly
termed Hudde's than Demoivre's.

De Witt's report being thus of the nature of an unpublished state paper,
although it contributed to its author's reputation, did not contribute
to advance the exact knowledge of the subject; and the author to whom
the credit must be given of first showing how to calculate the value of
an annuity on correct principles is Edmund Halley. He gave the first
approximately correct mortality table (deduced from the records of the
numbers of deaths and baptisms in the city of Breslau), and showed how
it might be employed to calculate the value of an annuity on the life of
a nominee of any age (see _Phil. Trans_. 1693; _Ass. Mag_. vol. xviii.).

Previously to Halley's time, and apparently for many years subsequently,
all dealings with life annuities were based upon mere conjectural
estimates. The earliest known reference to any estimate of the value of
life annuities rose out of the requirements of the Falcidian law, which
(40 B.C.) was adopted in the Roman empire, and which declared that a
testator should not give more than three-fourths of his property in
legacies, so that at least one-fourth must go to his legal
representatives. It is easy to see how it would occasionally becom