rs by means of a
series of arithmetical calculations. The mortality table here given is
an example of modern use.

The first writer who is known to have attempted to obtain, on correct
mathematical principles, the value of a life annuity, was Jan De Witt,
grand pensionary of Holland and West Friesland. Our knowledge of his
writings on the subject is derived from two papers contributed by
Frederick Hendriks to the _Assurance Magazine_, vol. ii. p. 222, and
vol. in. p. 93. The former of these contains a translation of De Witt's
report upon the value of life annuities, which was prepared in
consequence of the resolution passed by the states-general, on the 25th
of April 1671, to negotiate funds by life annuities, and which was
distributed to the members on the 30th of July 1671. The latter contains
the translation of a number of letters addressed by De Witt to
Burgomaster Johan Hudde, bearing dates from September 1670 to October
1671. The existence of De Witt's report was well known among his
contemporaries, and Hendriks collected a number of extracts from various
authors referring to it; but the report is not contained in any
collection of his works extant, and had been entirely lost for 180
years, until Hendriks discovered it among the state archives of Holland
in company with the letters to Hudde. It is a document of extreme
interest, and (notwithstanding some inaccuracies in the reasoning) of
very great merit, more especially considering that it was the very first
document on the subject that was ever written.

TABLE OF MORTALITY--HM, HEALTHY LIVES--MALE.

_Number Living and Dying at each Age, out of 10,000 entering at Age 10._

+------+---------+--------+------+---------+--------+
| Age. | Living. | Dying. | Age. | Living. | Dying. |
+------+---------+--------+------+---------+--------+
| 10 | 10,000 | 79 | 54 | 6791 | 129 |
| 11 | 9,921 | 0 | 55 | 6662 | 153 |
| 12 | 9,921 | 40 | 56 | 6509 | 150 |
| 13 | 9,881 | 35 | 57 | 6359 | 152 |
| 14 | 9,846 | 40 | 58 | 6207 | 156 |
| 15 | 9,806 | 22 | 59 | 6051 | 153 |
| 16 | 9,784 | 0 | 60 | 5898 | 184 |
| 17 | 9,784 | 41 | 61 | 5714 | 186 |
| 18 | 9,743 | 59 | 62 | 5528 | 191 |
| 19 | 9,684 | 68 | 63 | 5337 | 200 |
| 20 | 9,616 | 56 | 64 | 5137 | 206 |
| 21 |