Encyclopaedia Britannica > Volume 3, Anatomy-Astronomy

228
History.
ANNUITIES.
Explanation of Table A.
The sign (-|-) after the number of lives and of deaths
in column a signifies that the real number was greater
than is there stated. Those stated were the numbers of
the nominees in the two tontines which commenced in
1689 and 1696, the particulars of which have been given
by M. Deparcieux; but he also made all the use he could
of the tontine which commenced in 1734 (less than eight
years before his observations terminated), without stating
any of the numbers in his essay. And whatever may
have been the whole number of nominees, or of their
deaths, which he availed himself of in this tontine, M.
Deparcieux’s observations were actually made on so many
more than 9260 nominees, and 7933 deaths, among them.
The number of persons living in the two Carlisle pa¬
rishes at the end of the observations was 8677; but be¬
sides them, the observations were made upon the 1840
persons who died in the place in the term of nine years
during which they were continued; and these numbers
together amount to 10,517, the greatest number stated in
column b. But the real number the observations were
made upon was greater still, by the number who left the
place and did not return during the observations, which
is the reason of the mark ( + ) being put after 10,517 in
column b.
For information respecting the number of lives insured,
and of deaths, in the Equitable Assurance Society, given
at the head of column c, the reader is referred to the note
at the end of this historical introduction.
The better to enable the reader to judge of the compa¬
rative extent of the observations made upon the nominees
in tontines, and other annuitants, by M. Deparcieux and
Mr Finlaison, and of those made upon the population of
the two Carlisle parishes, the lives insured in the Equi¬
table Society, and the population of Sweden and Finland,
the mean number of living annuitants has been assumed
to have been an arithmetical mean proportional between
the numbers of them at the commencement and at the end
of the term, which can only be precisely true if they died
off by equal numbers in equal times ; and that is the
reason why the double sign (=tz) has been placed after
the mean number of the nominees or other annuitants in
each column. Thus 2860=h: in column d shows that the
mean number of living nominees of that description was
2860 wore or Zess. Ihe deviation from precision in this
case is of no importance.
The values in column a have been taken from the work
on Annuities of Mr Baron Maseres; those in columns d
and e from Mr Finlaison’s report (obs. 4 and 5); that in
column f at each age to 50 inclusive is a mean between
those m columns d and e;—after 50 they are taken from
Mr Tmlaisons 5th observation. The value in column q
at each age is a mean between the two against the same
age in columns e and/of table B; the values in column i
are from Mr hinlaison’s first observation.
Of Table B.
♦u TonIalUe! '10 v0lTnS e and / have been taken from
tne ^Otti and 13th observations respectively in Mr Fin
laison’s report, and were calculated from the rates of
mortality for the two sexes, which have been adopted for
use by government.
They were deduced from observations on the mortality
among the nominees in the three Irish tontines which
commenced in 1773, 1775, and 1778 respectivelv, on the
tontine of 1789, and those of the sinking fund from 1808
to 1822.
It will be observed that the excess of the value of an
annuity on a female life above that of a male is, accordino-
to the table for Sweden, in many cases not half, and in Historv
some less than one third as much as according to Mr'^^v\
Finlaison’s, derived from the government annuitants. The
cause of this cannot but be an object of interest, and de¬
serves further investigation. It may arise in great mea¬
sure from the ages of many females being stated below
the truth in the Swedish returns, while they were accu¬
rately ascertained among the government annuitants.
Of Tables M, N, and O.
The values according to Demoivre’s hypothesis were
taken from Dodson’s Mathematical Repository (vol. ii. p.
169); those in column d of table M, founded upon Duvil-
lard’s table of mortality for France before the Revolution,
published in his work on the Mortality from Small-Pox
(4to, Paris, 1806), were taken from The Doctrine of Com¬
pound Interest by M. Corbaux (8vo, London, 1825); the
values according to Dupre and St Cyran from the Cal-
culs des Rentes Viageres of the latter.
The authorities for the rest appear sufficiently from the
preceding historical sketch.
The values of annuities according to M. Kersseboom’s
table of mortality are not given here, that table being of
doubtful character, as he neither published the whole of
the data from which he formed it, nor explained the man¬
ner of its construction.
It would have been desirable to include the values ac¬
cording to the tables of Dr Halley for Breslaw, and Dupre
de St Maur for the Parisian and French country parishes
in table M; but as the values of annuities have not been
calculated from these tables at four per cent., we have
added tables N and O, and have given in each of them the
values from the Northampton table, with the view of fa¬
cilitating the comparison of the values in N and O with
those in M and A.
Observations on the above Tables.
All the tables of mortality from which the values of an¬
nuities in tables M, N, and O, have been deduced, were
calculated from bills of mortality alone of places where the
population was variable, and the numbers of the people at
the different ages were not ascertained. And therefore,
notwithstanding the attempts to supply their defects,
which were made by the eminent mathematicians who
constructed them, none of them represented truly the laws
of mortality in the places where the respective obser¬
vations were made; as will be evident to those who un¬
derstand the article on the Law of Mortality in this work,
and pay the necessary attention to the materials and man¬
ner of construction of those tables. Consequently the va¬
lues ot annuities derived from them cannot be correct,
but will in general be considerably less than the truth,
even for the general average of the whole population of
the places in which the observations were made.
But those values of annuities are also objectionable on
this ground—that the places they were intended for, and
understood to be adapted to, were generally populous
towns, containing a large proportion of poor persons de¬
pendent upon their daily labour for their supply of food
from day to day, often with little forethought, and many
of them engaged in unwholesome employments, amongst
whom great distress is often endured by the comparatively
high prices of bread and potatoes, or the low rate of wages,
when the unwholesome and scanty food they are reduced
to produces typhus fever, and sometimes the dysentery
among them, which carry them off in great numbers.
And these visitations were much more common at the
times when the observations were made from which most
of those tables were constructed, than they have been of
late years.