Mortality & Life
creation of the first mortality
tables permitted annuities to be put on a firmer foundation. Thus
begins works devoted to the computation of such. We
include here selections from Aubrey's Brief Lives
to provide glimpses of
some personages. These lives are published as Volume
(A-H) and Volume
(I-Y) under the editorship of
Andrew Clark in 1898.
was a celebrated Roman jurist. He constructed a table of the remaining
years of life to be assigned to an individual of a given age. The
purpose of this rule was to assist in the evaluation of
duration of a usufruct in the matter of succession of inheritances.
Dio Cassius in writing of the events of 40 BC (Roman History
says that the lex Falcidia
was enacted by Publius Falcidius while he was Tribune of the Plebes.
Its terms are that if an heir feels burdened in any way he may secure a
fourth of the property bequeathed him by surrendering the remainder.
Prior to the l. Facidia heirs to an insolvent estate were liable for
all debts without limit. The essential feature of this law was that
legacies or bequests could not exceed three-quarters of the total
estate. Equivalently, a testator could not deprive his legal heir of
more than three-fourths of the estate. Legacies in excess of
three-fourths were scaled down pro
The l. Facidia was applied separately to each heir. A legatee may be
required to give security for return of what might be paid in excess of
what was due under the l. Facidia or for return of the legacy
the supposed heir was evicted. Security was also given so that the full
value of a usufruct may be returned at the expiration of the usufruct.
This law remained in force into the sixth century since it was
incorporated in the Institutes
John Graunt & William
on the Bills of
Mortality, written by John
Graunt, was published in 1662. A
first edition may be found at
the website of Ed Stephan.
was a close friend of
Graunt (See Aubrey's Brief Life
who wrote on any number
topics. He coined the term "political arithmetic." His essay Political arithmetic
begun in 1671 but its completion not earlier than 1676. This work
concerns the extant and value of lands, people, buildings of Great
Britain and how this relates to neighbors of Holland, Zealand and
France. It was printed in 1690. Political arithemetic as a discipline
was developed by Petty, Gregory King (1648-1712) and Charles
Davenant (1656-1714) in England, Vauban (Sébastien Le Prestre,
Seigneur de Vauban, 1633-1707)
nick-named the French "Petty,"
Nicolas Struyck (1687-1769) in the Netherlands, and Johann Peter
(1707-1767) in Germany. For links to several works see the section on Political Arithmetic below.
was, in fact, debate as to
authorship with some asserting that it was the product of Petty rather
than Graunt. For this reason, it is natural that it be Included among
his collected works. Readily available is a reprinting of
the fifth edition of the
For this see the
Writings of Sir William Petty
edited by Charles Henry Hull (1899). In Volume
may be found the material on
the life of Graunt. Volume
contains the Observations
The brothers Huygens
Christiaan and Ludwig, engaged in correspondence regarding life
expectancy derived from Graunt's table.
- Greenwood, Major, "Graunt
and Petty," Journal of the Royal
Vol. 91, Issue 1 (1928), pp. 79-85.
- Greenwood, Major, "Graunt
and Petty--A Re-statement," Journal
of the Royal
Vol. 96, Issue 1 (1933), pp. 76-81.
- Willcox, Walter, "The
Founder of Statistics," Revue de
Statistique, Vol. 5, No. 4
(1938), pp. 321-328.
Johann Van Hudde &
Johan (Jan) de Witt
originally written by Jean-Étienne Montucla and
published with additions by J. de la Lalande (See
Volume 3, Part V, Book I, page
407 (1802)) it is mentioned that Johann Hudde, Burgomeister of
Amsterdam, (1628-1704) had written on annuities but the title
unknown. The work however mentions Waardye van Lyf-renten
van Losrenten or The
Value of life-annuities in proportion to redeemable annuities
Jan de Witt (The Hague, 1671).
De Witt's treatise was essentially lost until recovered by Frederick
Hendricks among the papers in the state archives of Holland around
1850. He published a translation of it in The Assurance Magazine
and Journal of the
Institute of Actuaries as
part of a larger study
entitled "Contributions to the History of Insurance and the
of Life Contingencies." These appear in Vol.2 (1852) pp.
222-258, and Vol. 3 (1853), pp. 93-120. The second section contains the
treatise of de Witt and the third section, containing the
correspondence of de Witt with Hudde as recovered by Hendricks, is the
source of our knowledge of the role played by him.
speaking of the study of games of chance:
Pensionnaire de Wit
cela encore davantage, & applique à d'autres usages
plus considérables par rapport aux rentes de vie: &
m'a dit, que Mr. Hudde
a encore eu d'excellentes
méditationes là-dessus, & que c'est
dommage qu'il les
ait supprimées avec tant d'autres. Ainsi les jeux
mériteroient d'étre examinés:
& si quelque
là-dessus, il y trouveroit beaucoup d'importantes
considérations; car les hommes n'ont jamai montré
d'esprit que lorsqu'ils ont badiné."
Pensionner de Witt has pushed this
yet further, & applied to some other uses more considerable
respect to annuities: & Mr. Huygnes has said to me, that Mr.
has yet had excellent thoughts on that subject, & that it is a
that he has suppressed them with so many others. Thus the same games
would merit to be examined: & if some shrewd Mathematician
meditate on that subject, he would find many important considerations;
for me have never shown more spirit than when they have play."
In addition, among the correspondence of Jakob Bernoulli
we find the futile attempt by Leibniz to obtain a copy of the treatise
of de Wit.
Jan De Witt also contributed in 1650 the mathematical work Elementa linearum curvarum. Leyden. Reproduced (1659) in Geometria, à Renato Des Cartes anno 1637 gallicè edita...
(Amstelaedami: L. & D. Elzevirios), 2, 153-340. An English
translation by Albert Grootendorst is published by Springer . Book I,
2000, Book 2, 2010.
The life table of Graunt was certainly unsatisfactory and many saw the
need for one constructed from real data. Halley,
(Aubrey's Life of Halley)
for whom the
comet is named, made use of the Breslau (Wroclaw, Poland) tables in the
important memoir "An
estimate of the Degrees of the Mortality of Mankind, drawn from the
curious Tables of the Births and Funerals at the City of Breslaw; with
an Attempt to ascertain the Price of Annuities on Lives."
This is followed by "Some
further Considerations on the Breslaw Bills of Mortality."
papers were published in the Philosophical
Transactions of the Royal Society
Vol. XVII (1693) pp. 596-610
and 654-656 respectively. The links are to the University of York site.
One observation should be noted here and that is that some debate arose
over the initial population. Graunt speaks of 100 quick conceptions.
with a population of 1000, but it is not clear if this is the number of
births or the number who arrive to age 1 year.
We mention in passing that Abraham de
Moivre and Thomas Simpson
after him wrote on Annuities on Lives.
Finally, there is Johann Peter Süssmilch (1707-1767) whose Die Göttliche
published in 1741, its full title being Die Göttliche
Ordnung in den Veränderungen des menschlichen
Geburt, dem Tode und der Fortpflanzung desselben erwiesen
divine order proved in the changes of
the human sex, from the birth, death and the reproduction of the same.
A second edition of two volumes expanded from an original of
pages to 576 and 625 pages respectively and exclusive of tables
appeared in 1761-2. A third edition from the author appeared
1765. The edition for which links appear below is that revised by
Süssmilch's son-in-law and edited by Ch. J. Baumann in 3
A study of Süssmilch's statistical work by Frederick S. Crum,
Statistical Work of Sussmilch," appeared in Publications of the
Association, Volume VII,
No. 55, pp 1-46. On page
42, the preface to the first edition by Süssmilch is quoted in
part and that is reproduced here:
remarks were new to me, a desire was awakened for further
investigation, and as the great utility of these truths was plainly
evident, I became attentive to everything which might strengthen them.
When I came back to Berlin from the University there fell into my hands
some additional lists, both from Berlin and for the whole country. To
my great satisfaction I observed an almost complete agreement of our
countries with England in these matters. I got together everything that
I could find. The contributions which had been made for some years in
Breslau to medicine, physics, and other sciences contained many lists
... which in great measure confirmed the order observed by the
Englishmen... As I was gradually led ever farther, the writings of the
Lord-Mayor Graunt and of the Knight Petty fell into my hands... To
Graunt belongs the highest praise, for he first broke the ice over
these new truths, and he first tried, in the search for them, to make
use of the London lists. Petty soon followed, and in his attempts in
political arithmetic not only accepted and confirmed many of Graunt's
propositions but also clearly demonstrated their utility in politics
II, and Volume
III of 1775-6. The text of 1741 has been rendered into French by
Jean-Marc Rohrbasser and published as L'Ordre
Divin by L'Institute National d'Études
Démographiques (INED) in 1998.
Political arithmetic is the collection of statistical data on states. Several
early examples of these are:
 Pasquier, Étienne. Des recherches de la France, livre premier, Plus un pourparler du Prince. Paris: J. Longis et R. Le Magnier. Augmentees par l'Autheur ceste derniere Edtion (1617), Augmentées en cette derniere Edition (1643).
 Sansovino, Francesco. Del Governo e amministrazione di diversi regni e republiche. Venice. Vol. XXI of 1578, Volume XXII of 1583.
 d'Avity, Pierre. Les
Estats, Empires Royaumes, Seigneuries, Duchez et Principautez du Monde;
representez ... par la description & situation des pays... Par le sieur D.V.T.Y. Paris. Followed by several other editions: e.g. 1621, 1625, 1630, 1659, and 1665.
 von Seckendorff, Veit Ludwig. Teutscher Fürsten Staat. Hanaw. Later editions exist. E.g. 1687, 1720, and 1754.
The more important writers are:
-  Another
essay in political arithmetick, concerning the growth of the city of
London, with the measures, periods, causes and consequences thereof. London. (See Volume II, 1899.)
-  Five Essays in Politcal Arithmetick (English and French) London: H. Matlock. Printed in Several Essays in Political Arithmetick. 4th ed. London: D. Brown (1755).
-  Political arithmetic, or a discourse concerning the... value of lands, people. London: R. Clavel & H. Mortlock.
-  The
politcal anatomy of Ireland, with the establishment for that kingdom
when the late Duke of Ormond was Lord Lieutenant... To which is added,
Verbum sapienti, or an account of the wealth and espences of England,
and the method of raising taxes in the most equal manner. 2 pt. London: D. Brown & W. Rogers. (See Volume I, 1899.)
-  The Economic Writings of Sir William Petty. Volume I and Volume II (1899) Edited by Charles Henry Hull..
- Charles Davenant
- King, Gregory.
Natural and political observations and conclusions upon the state and condition of England.
- Sébastien Le Prestre de Vauban, . Projet d'une dixme royale.
(1707) Paris. English translation (1708). A project for a royal tythe, or general tax. London: G. Strahan.