Life tables, founded upon the discovery of a numerical law regulating the existence of every human being ..

'^r^-

Cornell University Library
HG8782 .E24
+
Life tables, founded upon the discovery

3 1924 030 240 059
oiin Overs

OlorttpU Intersttg fCtbrarg

BOUGHT WITH THE INCOME OF THE

FISKE ENDOWMENT FUND

THE BEQUEST OF

ISiKard msktt

LIBRARIAN OF THE UNIVERSITY 1868-1883
1905

AM^P.^^. zUJIIJA:

Cornell University
Library

The original of this book is in
the Cornell University Library.

There are no known copyright restrictions in
the United States on the use of the text.

http://www.archive.org/details/cu31924030240059

LIFE TABLES,

FOUNDED UPON

THE DISCOVERY

A NUMERICAL LAW

REGULATING THE

EXISTENCE OF EVERY HUMAN BEING:

ILLUSTRATED BY

A NEW THEORY

CAUSES PRODUCING HEALTH AND LONGEVITY.

By T. R. EDMONDS, B.A.

LATE OF TRINITY COLLEGE, CAMBRIDGE :

AUTHOR OF

PRACTICAL MORAL AND POLITICAL ECONOMY."

LONDON: ^

PRINTED FOR

JAMES DUNCAN 37, PATERNOSTER ROW;
AND MAY BE HAD OF THE AUTHOR,

45, SOUTHAMPTON ROW, KtTSSELL SQUARE.

M.DCCC.XXXII.

E-V.

GENERAL OBSERVATIONS.

CHAPTER I.

The foundation of the science of Life Measurement rests upon the
observed relation of Dying to Living, in given intervals of age. In
constructing a Tahle of Mortality, the ordinary problem for solution
IS, — given, this relation for large intervals of age; required, to deduce
and interpolate the relation of Dying to Living, corresponding to small
intervals of age. In all Tallies which have hitherto been published,
this relation for annual intervals is continually varying. Now it is
manifest, that the same principles which have led to the conclusion,
that the variation is continued and annual, must lead to the conclusion,
that the variation is monthly, and also to the conclusion, that the varia-
tion is diurnal, and even momental. It may be assumed, therefore, that
all Tables of Mortality represent the relation of Dying to Living as
changing continuously, — that this relation is never the same for any
two successive instants of age. I have used the term "force of mor-
tality," to denote this relation at any definite moment of age. It would
evidently be improper to use this term to express the relation of Dying
to Living in yearly intervals of age ; for the force of mortality at the
beginning, at the middle, and at the end of any year of age, are all
different.

During" the succession of years and moments, measured from the
birth of any individual, the continuous change in the force of mortality
is subject to a very simple law, being that of geometric proportion.
But the same geometric progression is not observed from birth to the
ead of life. Instead of one, there are three distinct orders of pro-
gression, corresponding to three remarkable periods of animal life. The
force of mortality at all ages is expressible, — by the terms of three con-
secutive geometric series, so connected, that the last term of one series
is the first of the succeeding .defies ; — or by the ordinates of three con-
tiguous segments of three logarithmic curves. The common ratios of
the three geometric series (or the constants of the curves) appear to be

b

VI

fixed and immutable, for all human life in all ages of the world. These
three constants, now first discovered, correspond to the three grand
divisions of life, — Infancy, Manhood (or Florescence), and Old Age.
For regulating the continuous change in the force of mortality, Nature
uses one constant for Infancy, another for Manhood, and a third for Old
Age. The constant of Infancy confirms life, or indicates a continued
diminution of the force of mortality; the constants of Manhood and
Old Age indicate decay of life, or a continued increase in the force of
mortality; but the decay of life is much more rapid in the period
of Old Age than in the period of Manhood. Calling the three con-
stants pi, ps, ps, the following are their numerical values, which indicate
the rate of increase or decrease of the force of mortality, in a given time,
assumed to be one year.

In Numbers.

In Logarithms.

Period over which Constant presides.

Pi

P2

Ps

•6760830
1-0299117
1-0796923

— -1700
+ •0128
+ ^0333

Infancy (from birth to 8 years of age).
Manhood (from 12 to 55 years of age).
Old Age (from 55 to end of life).

The above constants of Manhood and Old Age are to be regarded
as much nearer approximations to the truth than the constant of
Infancy, by reason of the comparative shortness of the period of In-
fancy, in conjunction with the imperfections of all records of mortality.
The existence of the above three remarkable periods of human mortality
was long ago pointed out by Dr. Price ; but he does not appear to have
imagined that the marked distinction was expressible in numbers.
There may exist a very small fourth period, between Infancy and Man-
hood, where the force of mortality is stationary and at its minimum.
My assumption of the existence of this period, whether true or false,
can be of little or no practical consequence.

If Nature had immovably fixed the limits of the three periods of
Infancy, Manhood, and Old Age, the theory would be complete and
simple. Such, however, is not the case, either in different populations,
or in the same population at different times. An attentive examination
has impressed on my mind the belief, that the durations of the Infancy
and Manhood periods simultaneously increase or decrease. The defec-
tive existing materials may serve to establish this fact, although they
do not lead to the knowledge of the precise change in Manhood due to

Vll

a given change in Infancy. I am inclined to the opinion, that an
increase of one year in the duration of Infancy demands, under ordi-
nary circumstances, an increase of seven y^ars in the duration of Man-
hood ; under extraordinary circumstances, I believe that the diminution
of either stage may be accompanied by the prolongation of the other.
In all the best Tables, the limit of the Infancy period appears to be at
the age oi nine years, within half a year more or less; and the limit
of the period of Manhood at the age o^ fifty -five, within seven years,
more or less.

The knowledge of the cause producing this change in the position
of the limits is manifestly of very great importance, in the prediction of
future mortality from the past. This cause is identical with that which
hastens or retards the maturity of any animal : the simultaneous dimi-
nution of the stages of Infancy and Manhood is nothing more than the
shortening of the circuit from birth to death. The cause, or the ante-
cedents to change in the limits, will be found, most probably, to consist
of variations in food, in labour, or in lodging (temperature). An abun-
dant and nutritious diet, with continued repose in a pleasing tempera-
ture, contracts the stages of Infancy and Manhood ; whilst scanty and
coarse food, or hard labour, or great exposure to cold or heat, increase
the length of the two stages, by increasing the difficulties of travelling.
The proposition may be better expressed thus; — Saturation accelerates,
and Privation retards, Maturescence.

This opinion is supported by the observations on Human Mortality,
hitherto recorded, or appears to be so. But this support is, for the most
part, indirect; for the larger portion of these observations have been
made on general populations, or the representatives of various degrees
of Privation. These shew the limits of the stages of Infancy and Man-
hood to recede as privation diminishes. The only valuable and satisfactory
observations on the representatives oi Saturation are those of Deparcieux,
on a great extent of French monks and nuns ; and they all confirm the
theory, by the exhibition of the earliest known advent of the period of
Old Age (at forty-eight years). If the period of Infancy had been
observed, the corresponding limit would probably have been found very
near seven and a half or eight years of age. The unsatisfactory obser-
vations made on English and on French Government Annuitants lend
their support (whatever it may be worth) to tlie theory.

In the Table of Mean Mortality for England, I have assumed the
termination of the Infancy stage to be at the age of eight years, and
the termination of the period of Manhood to be at the age oi fifty-five.

VUl

In the selection of these limits, I have been influenced more by autho-
rities established in popular estimation than by my individual opinion.
The termination of the Infancy stage being a matter of little practical
importance, I have trusted to the guidance of my theory alone in the
fixing upon the age of eight years. I have an additional support for
selecting so early an age, in the commonly entertained opinion, that the
mortality of English infants has been diminished moi-e than that of
the rest of the population. Such diminution can be accounted for only
by the retrocession of the limit of Infancy. The mortality of infants is
a matter of very little moment to any European population, with respect
either to money or to population. The number of infants is not more
than half so great as it might be ; and the existing supply is not regu-
lated in the slightest degree by any imagined future relation of food to
surviving adults.

The termination of the Manhood period is a point of considerable
practical importance ; and I could not select an earlier age than fifty-
five, without abandoning the support of all Tables of value in the public
estimation. In the Northampton Table, this period terminates at
sixty-two ; in the Carlisle Observations, at fifty-seven years of age.
My disinclination to adopt the age of fifty-five has been diminished by
the expectation, that, in an improved state of society, this limit will be
again attained, and even exceeded. Hitherto, the stages of Infancy and
Manhood have never been increased, except in connexion with an in-
crease of mortality. Presently, I intend to shew how these stages mav
be increased, and the mortality at the same time be diminished. The
hopes of indefinite prolongation of the term of human life have now
ceased to be visionary. The limiting age of Manhood is variable for
different classes of the population. In England, I would place it, for a
city population, at fifty-five; for the general population, at fifty-two;
and for the monied population, at forty-nine years of age. Those who
have belonged to the monied class for some generations, and those who
have recently entered it from the labouring class, will probably have
different limits of the Life stages.

The following are the limits of the three periods in the five accom-
panying Tables of Mortality. In the two Tables of Mean and City
Mortality, the Infancy period terminates at eight years of age ; and the
Manhood period commences at twelve and terminates at fifty-five, where
the Old Age period- commences. In the Carlisle, or Village Table,
these limits are nine, ten, and fifty-five. In the corrected Northampton
and Stockholm Tables, they are nine, twelve, and sixty-two. In all

IX

these Tables the force of mortality is made stationary for the short
period between Infancy and Manhood : but, in the Village Table, the
force immediately after' ten differs slightly from the stationary force
immediately before. The difference is accidental, the two portions of
the Table, before and after the age of ten, having been constructed
independently of each other.

In forming a Table of Mortality, the essential point to be sought for
and ascertained is, the minimum rate of mortality, and the portion of
age to which it is applied. When this is known, the force at every
other age may be found by the help of the three constants : and knowing
the force of mortality, the numbers remaining alive at yearly intervals
may be deduced, which is the Table of Mortality required. A slight
degree of uncertainty would remain as to the exact time at which the
Old Age period commences ; because the increase in the duration of
Manhood, due to a given increase in the duration of Infancy, is not yet
precisely ascertained. As the basis of my chief Table, I have selected
a minimum rate of one death in a year out of one hundred and sixty
living. This number coincides very nearly with the minimum rate of
the Swedish population for fifty years, with the minimum rate of the
Glasgow population, and with the minimum rate of French monks and
nuns, for a very long space of time. Moreover, this base gives a gross
mortality between the ages of twenty and fifty, little differing from that
reported to have existed upon a great extent of English and French
Government Annuitants. The following are the minimum rates in
the five Tables:— Village, -005; Mean, -00636431; City, -00795539;
Northampton, -009 ; Stockholm, -0127286. (These numbers represent-
ing the quantity of death in one year from a unit of life.) The annual
rates at birth in the same five Tables are, -1612228, -1457979,
-1822474, -3049598, -4313017.

I have assumed the Carlisle Table to represent Village Mortality,
because it is a truth universally admitted, that the mortality in villages
is (in general) less than in towns, or in the country at large; and
because the Carlisle Observations express the lowest mortality ever
recorded and detailed with accuracy. The Carlisle Observations of
Dr. Heysham are not to be regarded as offering any novelty, for they
express no general fact which was not expressed long before their
existence. Every modern writer on the subject has admitted the exist-
ence of & partial rate of mortality even lower than that stated to have
once existed in the town of Carlisle ; but Mr. Milne is the first and

X

only well-qualified person who has ventured to recommend such a low
rate as a national standard.

That the Carlisle Table was ever a good measure of the mortality of
the English population in general, no sufficient proof has been, or can
be, adduced. And the establishment of such a fact would be of no
value, until a chain of connexion has been drawn between the past and
future, which has not been hitherto attempted. If the Carlisle rate has
been the general rate, the suddenness of change is inconsistent with
permanency. Under the ordinary fluctuations of given circumstances,
any temporary decrease in. the rate of mortality is invariably followed
by a temporary increase. If the circumstances of the English popu-
lation have been permanently changed for the better, the average rate of
mortality may not experience any considerable change. In a population
not subject to any high degree of privation, ordinary improvements in
food and labour may have no other effect than to diminish the fluctua-
tions from the average rate of mortality, which remains constant, and
approaches very near to that prevailing among those who have belonged
to the monied or saturated class for two or three generations. It is by
no means improbable, that a high degree of saturation, and a high
degree of privation, should be attended with the same minimum rate
of mortality. The most favourable state of life is that exposed to
alternations (within certain limits) of privation and saturation. A high
degree of privation, acting for some generations, purifies a population
of its weaker and less valuable members, and leaves only those who
possess the seeds of the best and strongest constitutions of body and
mind. When this pressure of privation is diminished, the health and
strength of succeeding generations will be proportional to the privations
previously undergone. After the pressure has diminished to a certain
point, and become stationary, the average soundness of the popula-
tion will be continually diminishing (by the accession of lives which
could not have existed under the previous higher pressure) until the
attainment of that lower degree of health, which balances the lower
degree of privation. The average rate of mortality under the high and
under the lower pressure may be the same. But a very low degree
of mortality will certainly prevail over a population in its passage from
the former to the latter state. It may be useful, as well as interesting,
here to remark, that the chronological scale adopted by Herodotus is
perfectly applicable to Europeans of modern times. In every hundred
years three generations pass away. The space of time intervening

XI

between the birth of any existing individual and the birth of his great-
grandfather rarely differs in any significant degree from one hundred
years.

The Table of City Mortality expresses what I have been induced
to believe is the measure of the mortality existing in the largest
English towns or cities. The worst kind of life, or the severest mor-
tality, is to be looked for in the poorest class of a city population, and
in the highest class of the monied, or non-labouring portion of the com-
munity ; the former representing the extreme of privation, and the latter
the extreme of saturation. It is not improbable that one Table may
represent, with correctness sufficient for any practical purpose, the
mortality of each of two classes, so widely differing in their circum-
stances. The chief objection to the making of one Table serve two
such different purposes, arises from the error made in assuming that
the periods of liifancy and Manhood are not shorter in the well-fed
than in the ill-fed portion of a community. The City Table represents
the greatest rate of mortality ever shewn to exist in any class of monied
life. Since the above remarks w^ere committed to the press, I have
arrived at the knowledge of the important confirmatory fact, that this
Table is a correct representation of the law of mortality to which the
English Peerage are subject.

It may be alleged, in objection to the use of the new Table of Mean
Mortality, that it neither is, nor professes to be, the representation of
any fact ever having had a specific existence in time, place, and popu-
lation ; but this would be no ground for esteeming it of inferior value,
compared with either the Northampton or the Carlisle Table. Admitting
the Carlisle and Northampton Observations to be perfect, they cannot
be of any considerable value, except in combination with other observa-
tions, differing in time, place, and people. In all classes of a popula-
tion, the mortality is continually varying. Observations of the past
lead to no useful result, until a chain of connexion is established
between the present, past, and future. To generalise from a single fact
is absurd ; and it is an absurdity of this kind into which those people
fall, who would apply observations made on one kind of life to all kinds
of life. It is perfectly irrational to apply the Northampton or Carlisle
Mortality to the present monied class of England, without any regard
to the utter dissimilarity of the circumstances. One combination of
circumstances may yield the same result as a different combination, but
it ought never to be assumed that it would do so.

The two Tables of Northampton and Carlisle have been presented to

Xll

the British Public by their respective authors as measures of motiied
as well as of general life. But neither Dr. Price, the promulgator of
the former Table, nor Mr, Milne, appear to have bestowed much of their
attention on the justness of the assumption, that a Table good for
labourers must also be good for people v^ho do not labour. They might
easily have observed this remarkable distinction, — that the mortality
of the labouring class was subject to very great fluctuations, whilst the
mortality of the monied class was almost invariable. They would have
found it easy to cite numerous instances o{ general mortality as high as
one (annual) death in twenty, and as low as one death in sixty ; but
they would have found it extremely difficult to cite an instance of
monied mortality differing, in any sensible degree, from one in forty.
The monied class are continually receiving recruits from the labouring
class. Fluctuations in the mortality of the monied class are probably
chiefly dependent on variations from the average recruited.

In the monied class, between the ages of twenty and fifty, there is
little ground for believing that the mortality was ever so high as that
exhibited in the Northampton Table, or so low as that exhibited in the
Carlisle Table. But there is some ground for believing that both the
Northampton and Carlisle are true expressions of rates of general
mortality existing in England at different times. In this respect, the
evidence in favour of the Northampton Table is quite as strong as any
which has yet been adduced for the Carlisle Table. The partisans of
the latter Table appear to have attached undue weight to the superior
accuracy of the narrow extent of observations on which it is founded.
For any useful practical purpose, there is no reason for believing the
Northampton Table to be a less valuable record than the Carlisle Table ;
the slight inaccuracy of adjustment of mortality to each age, in the
former Table, would be of no sensible value in practice. It is extremely
doubtful whether the principle of construction of the Carlisle Table is at
all preferable in practice to that on which the Northampton Table is
founded, when it is desired to obtain the rate of mortality prevailing
over an extensive district. If the errors in the returns are suspected to
be of considerable magnitude, the latter principle is most to be recom-
mended. The former principle is decidedly the best for indicating the
relative mortality at different ages. The trtith of the Northampton
Table is not lightly to be called in question, when it is supported by the
name of Dr. Price, although its applicability to the British population
of the present day may fairly be questioned. In confirmation of its
truth, I have to remark, that it nearly accords with the newly-discovered

Xlll

law of human mortality. In favour of its applicability, T would observe,
that the rate of mortality among English soldiers at home agrees exactly
with the Northampton rate for a population between the ages of twenty
and fifty. This fact rests upon materials of the most perfect character,
whilst the materials used by Mr, Milne, to prove the applicability of
the Carlisle Table, are of the most doubtful character. The acknow-
ledged inaccuracy of the national returns of Living and Dying is so
great, that no safe conclusion can be drawn from them. To those who
attach weight to such returns, I would observe, that the same reported
facts, which establish the applicability of the Carlisle rate to the
English population, also prove, that my new Table of Mean Mortality
is a measure of the mortality of the English population in general.
The proportion of deaths in infancy is considerably greater, according
to the Carlisle Table, than according to my Table of Mean Mortality.

It is not improbable that the partial adoption of the Carlisle Table,
as a measure of monied life, rests entirely upon the assumption, that the
class of Life Insurers is a fair sample of the monied class in general.
The correctness of this assumption may well be doubted. In every Life
Society the rate of mortality greatly depends upon the management.
The consequence of ignorance or carelessness in the management is
a mortality greater than the average, whilst a combination of illiberality
and intelligence will be attended with a mortality less than the average
of the class from which the insured are taken. Moreover, there are
reasons for believing, that the class of people who are inclined to insure
their lives are the best portion of the monied class. The great body
of insurers consist of money-making men, of men who are improving,
or have improved, their fortunes : and I believe it generally holds true,
that the most industrious, money-getting men are of " lower" birth,
and, consequently, of better constitutions than the average of the
monied class.

The new Table of Mean Mortality is the result of an extensive
comparison of the best observations, in combination with the newly
discovered Theory of mortality. Without the aid of this Theory, which
shews the connexion existing between the mortality at one age with
that at every other age, the comparison would have been of low value.
So much depending on the soundness of the Theory, I shall proceed to
make some remarks, by which the public may determine the degree of
confidence it may be entitled to. In the first place, I would state,
generally, that the Theory is best supported by the Tables which have
been always acknowledged as founded on the most complete materials ;

XIV

viz. the observations made on the populations at Carlisle, in Sweden at
different times, in French convents at different times, and in Glasgow
(by Dr. Cleland). The Tables, founded on insufficient materials, or of
questionable authority, most frequently support, and very seldom oppose,
the Theory. I know but one Table (which is of this latter kind) which
really and manifestly opposes the new Theory ; but this only at a parti-
cular portion of age, about twenty-five years in duration. It is that
lately published of the mortality of English Government Annuitants.
The value of this Table depends, in a great measure, on the truth of the
assumption, that " selection" produces no sensible effect ; in other words,
that there exist no means of distinguishing a good life from a bad one.
My opinion is entirely opposed to such a position; at the same time, I
think that the Theory would be found applicable to any class of select life,'
provided that the selection were made for all, at one and the same age.
But when the admissions take place at all ages, and at various times, as
is the case with Government Annuitants, no useful result is to be ex-
pected from a comparison in the gross of the number living and dying
in any interval of age, without any regard to the time each individual
has belonged to the society. The point on which the Government
Table opposes my theory, as well as that of every other person, consists
in declaring that, from the age of twenty to forty-five, the force of
mortality does not increase with the age; it even goes so far as to shew,
that a man's chance of living one year increases in that period. A Table
of mortality of French Annuitants presents an appearance of the same
anomaly, though less in degree ; but contemporaneous observations on
French monks and nuns were in perfect accordance with the Theory.
Possibly, the cause of this anomaly may be found in the falsification
of ages, the above period being that in which people are most tempted
to represent themselves as younger than they really are.

The reported mortality of French and of English Annuitants is not
entitled to much confidence; for the former is founded on materials
avowedly defective, and the latter rests upon the authority of a person
whose qualifications for the task undertaken are unknown to the public.
In opposition to these questionable statements, it happens very fortu-
nutely that I am able to adduce very strong additional evidence in
favour of the applicability of the new Theory. In the East Indies,
below the age of forty-five, among the civil and military European
servants of the government, the mortality increases with the age, accord-
ing to the same law as in European populations resident at home.
I state this fact as the result of very extensive and accurate observa-

XV

tions, derived, in a great measure, from official sources. A most extra-
ordinary coincidence with the Theory is to be found in the mortality
of the English officers employed in the Peninsular war. Fatigue and
battle, strange as it may appear, did not disturb the operation of the
law. The campaign increased seven-fold the previous mortality, but
left the new pressure (apparently so anomalous) adjusted to the age, in
the same manner as the natural pressuife had been. The public is left
to decide, whether these facts are not sufficient to neutralise, at least,
the effect of Government returns and calculations, so far as they lead
to the belief that the mortality between the ages of twenty and forty-five
years, among the English middling class, does not increase as the age
increases.

Even if the mortality of Government Annuitants should prove to be
correctly reported, and be independent of the effect of selection, I do
not apprehend that the stability of the new Theory of mortality will be
at all endangered thereby. The Theory is applicable only, when the
individuals compared differ in age, but resemble each other in all other
circumstances. In the labouring class, and in the middling class, there
is no remarkable change of circumstances depending on age, and, con-
sequently, to these two classes the Theory is always applicable. But
in the wealthiest class there is a most sudden and violent change made
about the age of twenty ; and it is this class which supplies, in all pro-
bability, the young life annuitants. Under the present system, the
wealthiest class are subjected to very great restraint for the five or six
years immediately succeeding the age of puberty. About the age of
twenty they are emancipated, when they indulge themselves with an
intemperance proportional to the previous abstinence. The youth of
both sexes, between the ages of twenty and thirty, are acting under the
influence of false notions of pleasure, acquired in a state of compulsory
abstinence. Possibly, the continuance of habits of intemperance in the
youthful rich is mainly to be attributed to the passion for distinction.
The appendages of wealth are of no intrinsic value, and rich people
prize them only as the means of dazzling the herd of mankind. About
the age of forty, the rich appear to discover that they have been playing
a very foolish game; and after that age, they do not (as slaves to
fashion) sacrifice their health, in order to exhibit the length of their
purse to their wondering poorer brethren.

There is a second point on which the universality of the new Theory
is subject to dispute, though of little practical consequence. In very
early infancy, or below the age of one year, the Theory in general

XVI

appears to fail ; in some cases the error is great, in others insignificant.
But the error is always on the same side ; the Theory always gives a
smaller proportion of deaths below one year of age than the observa-
tions. In most cases the difference is unimportant; in the Swedish
observations alone is the difference very great. The extraordinary
appearance presented by the Swedish Tables may be attributable to in-
accuracies in the returns of ages, or to some peculiarity in the treatment
of infants. If intervals of five years of age be taken, the Swedish agree
with other observations in infancy, made under various circumstances
on different populations. A given degree of inaccuracy in the return of
ages, which produces no sensible disturbing effect above the age often
years, may lead to very serious errors below that age, the error increasing
as the age diminishes. At present, I think that there are no observa-
tions strong enough in accuracy to contend againt the apparent univer-
sality of the Theory. Future and improved accuracy of observation may
demonstrate the inapplicability of the Theory below the age o{ seven or
eight weeks.

CHAPTER IL

The force of mortality at any age is measured by the number of deaths
in a given time, out of a given number constantly living. The given
time has been here assumed to be one year, and the given number
living to be one person ; consequently, the algebraic sign for the force
of mortality represents — the quantity of death in one year for a unit of
life at the assumed age; or rather (since the force is changing con-
tinually) represents — the quantity of death on a unit of life which
would occur by the action of this force continued uniform for the space
of one year.

The force of mortality is a simple function of the age, or time from
birth, and is always of the form {ap") during each of the three periods
of Infancy, Manhood, and Old Age ; where (p) is the characteristic of
the period, and represents the ratio of increase or decrease of force
of mortality in one year ; where (*) represents the force at some given
age ; and where (x) represents the time (in years and parts) between

xvn

that age and any other in the same period ;— for the sake of simplicity,
the given age may be assumed to coincide with that at which the period
commences.

Let, now, (y) represent the number Living or Surviving at any time (a;).
The force of mortality at that time = ap" = decrement in unit of time on unit
of life ; the finite decrement of {y) at that time = y y. a,p'; and the true decre-
ment, or the decrement in an infinitely small given time, = ya,p''dx ; that is,
— dy =: yap'dx.

Using (0 to signify hyperbolic logarithm, and (e) to denote the base of

a,

— V'-
9 ^ X ji 9 ^P

that system, we obtain by integration I- = j P and - = ^

If it be assumed that y = 1 when x = o, then g = e'P and the equation

becomes y = e^P x e '^ or y = e^P

And calling the modulus of the common system (k), and using (^) to
signify common logarithm, the equation will finally become, —

-—(I - p').

The above is the equation to the curve of Vitality, or rather is the
form of the equation to each of the three segments of that curve. In
each segment, the quantity (p) has its appropriate value. The first
segment terminates near the age of nine years ; the second near the age
of fifty-five. There may exist a very small fourth segment near the
age of ten, in which ^ = 1. The above formula will not serve to dis-
cover directly the number of survivors from hirth at any age above nine
years. Before it can be so applied, two constants must previously be
deduced from it : first, the value of (^) at the end of the first segment,
and then the value of (^) at the end of the second segment. These
constants, being used as multipliers, will give the values of (^) at any
age, corresponding to a given number born. These values of {y) at
annual intervals constitute a Table of Mortality. From the general
formula may easily be deduced an expression for the probability of
living one year, at any age ; by means of which, Tables of Mortality
may be constructed with great rapidity and security from error.

The honour of first discovering that some connexion existed between
Tables of Mortality and the algebraic expression {cfi") belongs to Mr.
Gompertz : but, to arrive at this single common point, his course of
investigation differs so widely from mine, that appearances will be found

xvm

corresponding to the reality, — that my discovery is independent of the
imperfect one of Mr. Gompertz.

The new Theory is universally true. All valuable observations made
in Europe concur in proving its truth ; and recent extensive and accu-
rate observations made on the Jamaica slave population, of African
parentage, are in conformity with it. Whence the conclusion is war-
rantable, — that the new Theory is equally applicable to the lowest as
well as to the highest grade of humanity, and to the inhabitants of tro-
pical as well as of polar regions.

The proof of the new Theory is of the strongest possible nature,
being arithmetical. By the help of the simplest rules of arithmetic,
any person may satisfy himself of the truth of the new discovery : he
has only to compare the numbers in the Tables which I have constructed
on one common principle, with the numbers in the Tables of highest
repute, formed on no principle whatever. He will find the numbers
correspond so nearly, as to give results identical for long periods, and
almost identical for short periods of time. In very few cases will he
ever find the differences to be greater than such as would have occurred
in Tables formed by different persons from the same materials.

The reader is requested to compare the Village Table with Mr.
Milne's Table for Carlisle, at all ages above two months. The Table of
Mean Mortality will be found to approach very near to the Swedish
Table of Dr. Price. But the coincidence here is accidental, as this
Cardinal Table was not intended to coincide with any existing one.
The Tables for Northampton and Stockholm will be found agreeino-
nearly with those of Dr. Price : but with respect to these two Tables,
the support derived from the agreement is reciprocated. In order to
facilitate examination, I have collected and condensed the information
contained in the chief Tables in repute. I have given the annual deaths
in intervals of ten years of age for every hundred living. By a very
simple inspection, it may be perceived whether the observations accord
with the Theory. When the decennial rate between the ages of ten and
fifty increases one-third every ten years, and when this rate, after the
age of sixty, doubles every ten years, then are the observations in near
conformity with the Theory. For the period of Infancy, a good indica-
tion of conformity with the Theory is, the proportion of three to two
between the deaths of two successive years.

Positive arithmetical coincidence is not to be looked for ; and if
any such were adduced, it would tend rather to confute, than to confirm
the Theory. The Theory informs us what are the chances of living or

XIX

of dying in a given time ; but it does not tell us how many must die.
According to the doctrine of chances, there exists a high degree of im-
probability that, in sixty throws with a six-sided die, an ace will be
thrown ten times exactly: although this number expresses the true
probability, and is more likely to happen than any other which can be
mentioned. In six hundred throws, the times of throwing an ace will
approach nearer the proportion of one-sixth than it would in sixty
throws. Similarly, with regard to the new Theory of Mortality, as the
number and extent of the observations increase, the nearer is the ap-
proach to the true measure of the probability of Dying or Living. But
perfect coincidence is never to be expected even in nature, much less in
erroneous records; and still less in Tables deduced, by the erring judg-
ments of individuals, from such erroneous records.

In a work of the present nature, arithmetical accuracy is a quality
of essential importance. In this respect, the accompanying Tables will
bear comparison with any hitherto published : at the same time, they
aim at a degree of precision never before attempted. These Tables
prove by internal evidence their own accuracy. A very simple inspec-
tion will serve to detect the existence of an error, however insignificant.
All preceding Tables are so anomalous, that irregularity is consistent
with correctness; but in these Tables, a breach of uniformity is an indi-
cation of error. As a security against errors of the press, and as a check
on errors in calculations founded on these Tables, this quality of unifor-
mity is of no inconsiderable importance.

The original calculations have all been performed in duplicate ; and
two or three days have generally intervened between the similar steps
in the parallel operations. The errors of all magnitudes detected in the
process, amounted to one in every four thousand written figures. One
half of these errors were so inconsiderable, that, if allowed to remain
unrectified, they would not have affected the printed part of the results.
They were either faults in arithmetic, in the taking out of logarith"ms,
or in copying. The two former sources were the most prolific of
error.

\

XX

CHAPTER III.

The increase of a population has a great dependence upon the number
of women at the child-bearing age, which may be assumed to extend
from the age of twenty to the age of thirty-six years. In most countries,
the proportion of such women is one-eighth of the total population. No
sensible effect, I conceive, is produced by a woman's selecting a diflfer-
ent period for the developement of her extreme prolific power. The best
child-bearing period is that in which woman enjoys her maximum of
strength and fertility. There is reason for believing that a woman does
not yield more children because she may begin to bear before the age
of twenty. That the strength of the children, as well as of the mother,
will be deteriorated by early bearing, is almost certain. The fertility,
or the chance of conception, probably decreases continually from the
age of eighteen to forty-five. In different populations, the average
extent of the child-bearing age may be expected to vary with the
vitality. In a strong, healthy, and long-lived people, this period will
certainly be longer than in a weak people. The period of sixteen years
I have considered to be the average due to ordinary European circum-
stances. There is a deduction to be made on account of total or partial
barrenness. The proportion of women totally barren has been estimated
at one in forty : to this is to be added a similar and equal barrenness of
the men ; so that one-twentieth of the women are wholly unprolific. In
the next place, an allowance more considerable is to be made for partial
barrenness, or for the loss of fertility before the expiration of sixteen
years. It would be diflBcult to make a good estimate of this quantity;
probably a deduction of one-seventh on this account will be found not
far from the truth. After making these two deductions, we arrive at
this result; — that the proportion of the effective child-bearing women
is one-tenth of the total population.

From extensive observations made by Dr. Granville on women of
Lying-in Institutions, the proportion of births to prolific years appears
subject to very little variation in all women. This proportion is one
birth every two years, until a woman ceases to bear ; the truth of which
statement the experience of most people will confirm. If, then, the
prolific power of any European population were fully exerted, every
child-bearing woman would yield one birth every two years, and the

XXI

total child-bearing women would add annually one-half their own
number to the population ; that is, the extreme prolificness of any-
European population is represented by a number of annual births, equal
to one-twentieth part of the total population.

Their extreme unchecked prolific power was probably never exerted
by any population for any considerable period of time. A very insig-
nificant portion of the earth's surface is so insalubrious, that the popu-
lation may not be increased faster than their food was ever increased.
It is even doubtful whether absolute insalubrity has any existence in
any part of the world ; for all observations hitherto made prove relative
insalubrity only. In the island of Jamaica, for example, the mortality
of Europeans is five times as great as that of Africans, which, again, is
a little greater than that of Europeans at home. This does not prove
the climate of Jamaica to be more unhealthy than that of Britain. We
are only justified in concluding, that it is a very unhealthy climate for
Europeans, and a probably unhealthy climate for Africans ; but, without
at all straining the bounds of probability, we may imagine the existence
of an indigenous population, more healthy than the African immigrants,
and as healthy as Europeans residing in their native climate.

The check on the exertion of the prolific power is scarcity of food.
The more the prolific power is exerted, the greater is the difficulty of
obtaining food. When the extreme power is put forth, famine and
pestilence are seldom far absent. The severe moral and physical penal-
ties attached (by the customs of all nations) to child-bearing, without
the consent of the supporting relatives, would never have existed, if the
supply of food had been unlimited. By restraining fecundity, there is
no class of men, however poor, who may not become rich, and command
all the real enjoyments of life. As a society improves in knowledge,
the prospect of poverty, or semi-starvation, operates with increasing
force. The degree of poverty of the bulk of a nation is one of the best
tests of its intelligence, — taking scantiness and coarseness of food as
the proper measure of poverty. . Brutes, and the lowest order of men,
sacrifice their future happiness (in which that of their offspring is in-
volved) for the sake of a present selfish gratification: a wise man is
influenced by the remote probable consequences of his actions, and he
will refrain from doing any thing which will add to his present enjoy-
ment, by diminishing disproportionately his future enjoyment.

The observations of Dr. Granville were made on the worst class
of London Life; for it is reasonable to expect that the applicants for
charitable aid belong to the most suffering , class of the community.

d

XXI 1

The great mortality of the children, of the women observed, supports
this opinion. This mortality is not less than it was a century ago for
the total London population, which then could barely maintain its
numbers by the extreme of propagation. Either these people observed
were (contrary to Dr. Granville's opinion) representatives of the worst
class of London Life, or the increased duration of life in London is
a fable. If they are supposed to belong to the class of severest mor-
tality, it might be doubted whether the interval between two successive
births would be the same in the general population as in this class. It
might be expected that the births would be quicker in the general
population, because subject to a lower degree of privation and mortality.
In answer to an objection of this nature, I would urge, that the degree
of privation is not so great as to affect considerably the chance of con-
ception ; and that any effect thus produced would be balanced by the
mortality of the suckling infants, which is greatest when the chance
of conception is least. The minimum interval between two successive
births is probably one year and eight months ; which minimum is appli-
cable to the two extremes of the English population, — to the portion
enjoying the strongest frames and the most robust health, and to the
portion whose health and strength have been undermined and enfeebled
by luxurious living; the latter portion (consisting of the wealthiest
part of the community) not being accustomed to complete the function
of child-bearing, by suckling their infants.

The ordinary average annual mortality of a European population
may properly be estimated at one death to every forty living. This pro-
portion is subject to little variation on account of any common increase
or decrease of population. The possible annual births having been
shewn to amount to one-twentieth part of the population, we shall
have, on deducting the deaths from the births, the annual possible
increase of a European population equal to one-fortieth part, or to two
and a half per cent. This gives twenty-eight years as the period in
which a population may double its numbers. This rate of increase
apparently agrees with that which has prevailed for a long space of
time over the British American population. In most parts of Europe,
population increases at the rate of one per cent per annum. The pos-
sible prolificness of the British American population is undoubtedly
much greater than that of the kindred British population at home. In
all probability no people were ever so favourably circumstanced as the
inhabitants of the United States for the development of health, strength,
and prolificness. They obtain an abundance of plain and nutritious

XXIU

food by means of a moderate portion of labour, in a pure atmosphere.
In England, the bulk of the population acquire a scanty supply of
coarse food by incessant labour, in a confined and consequently impure
atmosphere. In America, a large quantity of food is given in exchange
for a small quantity of useful healthy labour: in England, unceasing
toil frequently fails to purchase a sufficiency of the coarsest food. This
superiority is, however, of a temporary nature. Every increase of density
of the American population is another step towards the state of misery
and privation at present existing in Europe.

Whether it is desirable that any European population should in-
crease, is an important question for philanthropists, the proportion of
food to population being supposed to remain unchanged. The question
resolves itself into this, — Does an increase of human beings add any
thing to the national stock of happiness ? For any European population,
I would, without hesitation, answer in the negative, and say, that an
addition to the numbers was an addition to the general mass of misery.
In the best state of society, pain and pleasure will balance each other;
in the existing state of society in Europe, ten times as much pain as
pleasure is spread over a man's life. There is but one advantage
attending an increase of population worthy of consideration; it is this,
— that knowledge increases with the density of a population. This
will be manifest to any one who considers that additions to the common
stock of knowledge are made by individuals ; as the number of indivi-
duals increases, the additions increase, or knowledge more rapidly ad-
vances. In the moral, as in the physical world, the effect of each man's
labour increases, as the number of individuals with whom he acts in con-
cert increases.

There is another important question, — Is it desirable that a nation
should exert its utmost powers of increase, when the supply of food is
unlimited ? As happiness does not depend on abundance of good food
alone, I would again answer in the negative. The' average soundness
and robustness of health in a nation is one of the most important con-
stituents of its happiness. Now, it is perfectly certain that the health
of children closely resembles that of their parents. A person's stock of
health and strength may be increased or diminished by education, but
it will be mainly dependent on the source whence it is derived. It is,
therefore, manifestly desirable that no weak or diseased person should
transmit his defects to posterity. Even if his life were a blessing to an
unhealthy person, it can never be so to the society in which he lives :
he will defile every thing he touches — all his objects of attachment will

XXIV

be injured by his love. When food is secured, procreation ought to be
so directed as to yield the highest amount of health, strength, velocity,
and intelligence, which are the elements of every thing good and
beautiful.

It is a fact, capable of demonstration, that the population of Britain
may be 'mcressed^ve-fold, — that the soil and agricultural knowledge
possessed by Britain are capable of yielding an abundant supply of
good food for five times the existing number of inhabitants, without
increasing the proportion of agricultural labour due to each individual.
The knowledge of this fact has induced many well-meaning people to
exert themselves strenuously in support of the doctrine,— that all actions
tending to increase the population are deserving of national encourage-
ment. The benevolence of such men gives additional force to their
erroneous and mischievous opinions. Every man, who is intelligent as
well as benevolent, will regard the increase or decrease of a population
as an object of secondary importance; such a man will direct his chief
exertions towards the increase of the proportion of food to population.
He will endeavour to accelerate the increase of food, and to retard the
increase of the population. If the population of Britain were to exert
their extreme prolific. power, and at the same time were to receive an
abundance of food, they would quickly degenerate from their high rank
among European nations. All the existing bodily and mental defects
and diseases would then be transmitted to the next generation ; whilst,
under the existing pressure of privation, not more probably than one-
half are transmitted (although new ones are created). In the struggle
for existence in which all European populations are engaged internally,
the weak in body and mind are commonly last in the race ; they become
impoverished, are shunned by others, and leave behind them no progeny
or heirs to their defects. In all classes of all countries there are re-
strictions on the exertion of the extreme prolific power, and all these
restrictions are more or less beneficial. Strength, beauty, and intel-
ligence, will retain their hold upon the affections of man as long as
he endures ; and the force of these virtues will greatly neutralise the
effect of money, in the struggle for giving life to the future generation.
In a perfect state of society, the good qualities of mind and body will
alone form the grounds of attachment or preference between individuals.
At present, the possession of money, by inheritance or descending con-
sanguinity, exerts a great disturbing and deteriorating influence on
European populations. The greatest defects of body or mind, conjoined
with money, are secure of transmission to posterity.

XXV

A good system of hereditary distinctions is much to be desired.
Talent is hereditary ; and it is desirable that the possessors should bear
distinguishing marks, which may operate as premiums on the propaga-
tion from a good stock. The chances are much in favour of the exist-
ence of talent in the children of people of great natural endowments,
and as much against the existence of talent in the children of parents
who have never possessed any corporeal or mental virtues. Taking the
untried progeny of 1 00 horses, of various ascertained degrees of swift-
ness, and supposing them to run a race; — the chances of reaching the
goal first would be more in favour of the foal of the swiftest horse than
in favour of any other foal j but some one of the 99 opponents is likely
to outstrip this foal of the swiftest horse. If the same equality pre-
vailed among men as among horses, it would not be very difficult to
assign to each man his order of merit. But under the existing unequal
distribution of the advantages of education, it is not easy to distinguish
the endowments of nature from the adventitious accomplishments of
art. The pre-eminence of any individual (under the existing system)
is generally the result of natural talent of no high order, combined
with extrinsic, fortuitous, and extraordinary advantages of cultivation.
In all probability there lived contemporary with Newton hundreds^f
Englishmen his superiors in mathematical discernment, or in the power
of drawing j ust conclusions from a given quantity of facts, relating to
space, time, weight, or number.

Assuming that a child inherits one-half of the aggregate qualities
of his father and mother, or (less correctly) that he inherits one-half
of the qualities of each parent; the grandchild will inherit l-4th, the
great-grandchild l-8th, of the qualities of either first parent. The child
from the fifth generation will possess no more than l-32d part of the
blood of the original parent. If a distinction were conferred on the first
parent, and transmitted to his descendants in such a manner that the
honours diminished as the original blood diminished, no evil would
ensue, if the honours were reckoned on the side of one parent only.
But if the honours are reckoned on both sides, and if the father and
mother bear equal distinguishing honours, the children would be entitled
to the same honour as their parents. To obviate this absurdity, of
accounting a man of presumed excellence equal to a man of tried
excellence, a decree of this kind should be made; — that two-thirds,
instead of one-half, of any hereditary honour shall be extinguished at
each generation. In this case, the child from the fifth generation
would possess only l-243d part of the honour of either first parent.

XXVI

If males and females of similar honours are always paired, then l-3d
of an honour is extinguished at each generation, and the child from
the fifth generation would possess about l-8th part of the original
honour.

CHAPTER IV.

In all countries, and in all classes, there is a manifest difference in
the mortality of the two sexes ; and the difference is always in favour
of female life at all ages. Taking a gross average, it may be said,
that female life is better than male life, in the proportion of eleven
to ten. This superiority is not occasioned by any difference in the
■occupation of the two sexes ; for, in Infancy, it is as conspicuous as
at any other period of life. With improved accuracy of observation,
a comparison of male with female mortality may lead to some very
useful results ; principally, perhaps, in shewing the dependence of the
first and second periods of mortality on the age of puberty. So far
as the existing imperfect observations can be trusted to, there is a
strong appearance of the periods of " Infancy " and " Manhood " termi-
nating at an earlier age among females than among males. No existing
Table affords any foundation for the belief, that child-bearing produces
any disturbing effect on the female rate of mortality. The sensible
mark, indicating that a woman has arrived at the termination of her
child-bearing age, is probably closely dependent on the year of life at
which the period of " Old Age" commences in her class.

The remote cause of the difference in the mortality of the two sexes
is yet hidden among other secrets of nature. There is known, however,
a proximate cause to which it is probably referable. Throughout the
animal kingdom, this general law appears to prevail, — that males are
more excited by given circumstances than females are. Now, all sick-
ness is occasioned by excessive excitement (positive or negative) of
some particular organ ; and sickness will be most severe in the sex
subject to the higher degree of moral and physical excitement. Let any
one institute a comparison between his male and female acquaintance ;
he can hardly fail to come to the conclusion, that activity is as much
the characteristic of the male, as passiveness is of the female sex. In

xxvu

the outward signs of feeling, women outdo men, and children outdo
women ; but neither women nor children are, on that account, to be
esteemed as capable of more intense pleasurable or painful excitement.
The most violent internal commotion is generally accompanied by a
forced calmness of exterior. Those who are most ready to give vent to
their feelings in words, rarely exhibit much feeling or resolution in their
actions. The passions of women more quickly rise, and also more
quickly subside, than those of men; but the intensity and duration
of excitement is much inferior. The nervous energy t)f the female is
much less than that of the male ; and her superior quickness of excite-
ment may be accounted for on the principle, that a small mass is more
easily set in motion than a large mass. There is one passion about
which some doubt might be entertained, on account of the peculiar
organisation of the female, — I mean the sexual. Is this passion
stronger in the female than in the male? The reverse is manifestly
the case among the inferior animals; and appearances do not oppose
the expectation, that the human race, in this respect, obey the law
to which other animals are subject. In the shape of proof, may be
adduced the records of suicide in Paris, which shew that love kills
much more males than females. It is now time that the decision of
the ancient Greeks in this matter should be reversed. I allude to the
fabled sportful dispute between Jupiter and Juno, wherein the judge is
made to award the palm to Jupiter's opinion, that woman had the larger
half of the pleasure shared between the two sexes.

CHAPTER V.

The rate of mortality in large towns is greater than in small towns,
and greater in the small towns than in the villages of any nation.
This truth has been long known ; but no satisfactory reason has yet
been advanced, why a country population should live longer than a
town population. The excessive mortality of large towns has most
commonly been attributed to intemperance and debauchery ; that is to
say, a population known to be suffering a high degree of privation, are
supposed to kill themselves by excessive indulgence. In gratifications
of inferior moment, it frequently happens, that a man inconsiderately

XXVIU

purchases one pleasure by the sacrifice of one more valuable. But it
may safely be denied, that any considerable body of men are content to
exchange their necessary food for any other gratification. No enjoy-
ment can co-exist with the pain of hunger. The proportion of people
having the power and the disposition to kill themselves by excessive
indulgence is so inconsiderable, compared with the total population
of any city, that where there is one death from having too much, there
are one hundred deaths from having too little. The popular notion,
that intemperance causes death, is true, indirectly ; but the evil arises
from the institutions of society, which sanction the slavish subjection
of children to the male parent. There are few fathers of families who
do not endeavour to increase their own enjoyments, by diminishing the
just gratifications of their wives and children. If the man is poor, this
tyrannical disposition is displayed by spending on gin for himself, what
ought to be expended in allaying the hunger of his family. Proportioned
to the strength of this disposition, is the degree of hunger, and the
degree of mortality.

There are two principal causes to which I would ascribe the exces-
sive mortality of large towns, viz. to excessive poverty, and to excessive
impurity of air inspired. In other words, these causes are two kinds of
privation, — first of food, and then of space. At first sight, it appears
improbable that there should be more poverty in cities than in villages ;
because it is a well-known fact, that money wages are considerably
higher, and real wages a little higher, in cities than in villages. If
all labourers obtained constant employment, there would be less poverty
in cities than in villages; but this is not the case. Some labourers
receive no wages, and very little victuals, for one month every year,
some for two months, some for three, and so on. But there is a certain
average of unemployed time, in every class of labourers in every place,
which might be ascertained without much difficulty. This average
waste starving time I imagine to be much greater in cities than in
villages; and the reader will agree with me, if he admits that labourers
and capitalists have similar principles of action. It is a well-known
fact, that the expectation of a high prize, either in a mine or in a
lottery, will exchange for much more than the true value of that ex-
pectation. In the hopes of getting a high prize in the lottery, many
sensible men have paid £16 for a chance, which, on sure mathematical
grounds, they knew not to be worth £8. On the same principle opera-
tives proceed : they are all ready to sacrifice twenty shillings a week
(nearly) constant employment, for twenty-five shillings a week uncer-

XXIX

tain employment. Now, if the lottery principle be correctly applied,
the receivers of twenty-five shillings will acquire less money in a given
long time than the receivers of twenty shillings. Operatives will endure
more to obtain a sum of money distributed in twenty-five shilling prizes,
than they would endure for the same sum distributed in twenty shilling
prizes. Hence high wages, unconnected with high talent, is an indica-
tion of great poverty ; of course, the places selected for comparison must
have free communication with each other. In a city, a man obtains
more food for a day's labour than he does in a village ; but, in the
course of the year, he will have obtained less food in the city than in
the village, by reason of the excess of unemployed time in the city.
Inequality of employment is also a cause of death, at least it is so
when combined with that improvidence or ignorance, whicli is the
necessary attendant upon a system which degrades and confines the
labourer to the lowest animal gratifications. There is another reason
why the want of food should be felt more severely in cities than in
villages. It is this; — that in cities, the sufferers are generally among
strangers, whilst in villages they are at home among relatives. It is
not so easy to undergo a process of starvation among relatives as among /
strangers/ " "..

The second cause of excess of mortality in cities, is impurity of the -
air respired. This impurity arises chiefly from privation of space. The
purity of confined air increases as the space allotted to each individual
increases. About one thousand cubic feet is the proper lodging space
for each individual. Perfectly pure air is that which is inhaled in fields;
the air in broad streets, or between two parallel walls, is of nearly equal
purity. The first stage of sensible impurity may be represented by a
cubical vessel having its sixth side removed. In such a vessel, all
direct motion is prevented, and the included air will be stagnant, unless
acted upon by the motion of the external air, in contact with the open
side. If the sixth side of the cube be added, we shall arrive at the
second stage of impurity, in which all human habitations are to be
classed.' If the joinings of the cubic apartments in which men live
were air-tight, we should obtain perfectly impure, or irrespirable air.
In connexion with this subject, the close alliance existing between
" civilisation " and pulmonary consumption is well worthy the most
serious attention.

The function of the lungs is of equal importance with the function
of the stomach. Good air is as necessary for health as good food. The
inhabitants of villages enjoy better health than those of cities, because

XXX

they inhale purer air. The circumstances of the villager impel him
to pass the chief portion of his time in free, unconfined air ; whilst the
circumstances of the citizen cause him to spend all his time in a con-
fined space of impure air : the employment of the former is out' of doors,
of the latter in-doors. This is applicable to only one-half of a man's
life, — to twelve hours out of the twenty-four; there remains for consi-
deration, the manner in which the two kinds of labourers are lodged at
night. In this respect, also, it will be found that the villager is greatly
superior to the citizen. The average cubical space allotted to the lodg-
ing of each individual is much greater in villages than in cities. The
crowded state of the poorest class of city labourers is a well-known
fact. That the general bulk of city labourers are more crowded than
the general bulk of village labourers, results from the undeniable fact,
that space is much more valuable in cities than in villages. The rent
of a given sized room is much higher in cities than in villages ; and a
city labourer's inducement to live in impure air is proportionally in-
creased.

CHAPTER VI.

The circumstances most favourable to vitality, consist in alternations
of privation and saturation, — in changes between tension and relax-
ation. The best bodily ec^ucation is that which elicits the endurance
of the greatest oscillation between privation and saturation. There is
a certain degree of elasticity in the organs on which life depends,
which is capable of unlimited increase or diminution. The elasticity
of any organ may be destroyed by either of two opposite causes, — long-
continued excitement, or long-continued repose. These two causes
of destruction are in constant operation in all " civilised " countries.
Most Europeans belong to one of two classes, — either to that of con-
tinued privation, or to that of continued saturation. The labouring
class suffer continually a high degree of excitement, and enjoy vei-y
little relaxation from hunger or labour; the monied, or non-labouring
class, are surfeited with repose which they cannot enjoy, because they
have not been previously excited. But experience proves that satura^
tion impairs health and strength much more than privation does.

XXXI

Those men who possess what are esteemed the advantages of wealth
and birth combined, are almost invariably distinguished by feebleness
of body.

The labourer is continually subject to the evils of exhaustion ; the
monied class are continually subject to the evils of repletion. Food
and repose ought always to be preceded by hunger and labour; this
law of Nature is not to be infringed with impunity. All labour consists
in the exertion of the contractile force of a certain muscle for a certain
time. A weak force of contraction may be continued for a long time,
a strong force can be maintained only for a short time; the former
constitutes gentle labour, the latter hard labour. The compressing
effect of hard labour is much greater than that of gentle labour; and
the elasticity or health of any organ appears to be proportional
to compression, accompanied by adequate repose. The health and
strength of a man who labours eight hours a-day may be greatly in-
creased by making him do in a day of six hours what he was pre-
viously accustomed to do in seven hours. By combining privation and
saturation in the same individual, and increasing both to their extreme
limits by insensible degrees, I believe that the health and force of man
may be 'rendered superior to that of any existing animal. I shall
borrow an illustration of this opinion from the phenomena occurring
among brutes.

It holds true generally, that the wildest animals are also the
strongest. Ferocity and strength, docility and weakness, are most
commonly combined. The lion may be considered as the representa-
tive of ferocity and intractability ; the horse, of timidity and docility.
Consequently, in comparison with the lion, the horse's strength is
weakness ; that is, a given mass of muscle of a horse will produce an
effect much inferior to that of a lion. That a lion is stronger than
a horse, in sudden momentary muscular exertions, will hardly be dis-
puted ; but it might be denied that a lion would effect more in a day than
a horse, although it might be admitted that he would effect much more
in a minute. But I believe that there exist no grounds for supposing
that one animal, whose extreme muscular tension is greater than that of
another, should not maintain a given moderate degree of tension longer
than the weaker animal. It is, however, extremely probable that, by
increasing the time of action, the relative superiority of one animal
over another may be diminished indefinitely. The total muscular action
of any animal is closely dependent on the quantity of food consumed •
and as the stronger animals do not consume much more food than the

xxxu

weaker, it is not to be expected that the muscles of motion should pro-
duce a much greater continued effect in the former than in the latter.
Animal strength may be nothing more than the faculty of compressing
a given quantity of muscular action into a small space of time. If the
experiment could be tried, I imagine that the strength of the lion and
of the horse would be found related in this way ; — that, for impulse or
instantaneous effect, a lion is three times as strong as a horse; but
that, in a day, the total extreme development of strength in a lion
would only be twice as great as that of a horse ; and that, in two days,
the superiority would be less than in one day. The best indication of
strength consists, I believe, in the density and compactness of the
structure of bones and muscles.

The cause of this superiority remains to be considered. I believe
the lion to be stronger than the horse, because the former is exposed
to greater alternations of privation and saturation. The food of the
horse is distributed in small parcels, which may be collected by very
easy exertion, continued for a short time in a rich pasture, and for a
long time in a scanty pasture. The food of the lion is distributed in
large masses, not to be obtained except at the expense of the most
violent effort. Before the lion enters into action, the pain arising from
the privation of food must preponderate over the pain of extreme
muscular exertion: before a horse acts, it is only necessary that the
privation of food should be great enough to balance the pain of a very
low degree of muscular action. Nature requires of the lion great mus-
cular tension, continued for a short time ; and she requires of the horse
weak muscular tension, continued for a long space of time. The differ-
ence in strength between a horse and a lion rests, I imagine, entirely on
this remarkable distinction. This opinion (of incalculable importance,
if practically adopted), when expressed in general terms amounts to
this, — that muscular strength increases as the average muscular tension
is increased. The power of any muscle may be increased, bi/ diminish-
ing the time, and increasing the force of tension.

The above remarks relate particularly to the muscles by which
animals operate upon external objects, or to the muscles of motion;
but they are indirectly applicable to the minute muscles presiding over
the complex internal atomic movement existing in every animate body.
The organs of digestion, like the muscles of motion, are the strongest
when they are accustomed to the greatest tension for a short time,
followed by a long interval of repose. No tame animal could survive
the gorging of a ravenous beast of prey, any more than it could endure

XXXUl

the long previous fasting. In a long given time, as one year, a horse
will probably move over the same space of ground, and consume the
same quantity of food, as a lion : but in eating and in moving, the lion
will probably effect in four hours what a horse requires twelve hours to
efiFect. The extreme shortness of the alimentary canal in beasts of prey
is probably consequent upon the extreme strength of the digestive
organs.

Like the muscles of motion and digestion, are the organs or muscles
by means of which animals resist or adapt themselves to changes of
external temperature : those which are habituated to encounter the
greatest changes are invariably the best and strongest. In support of
this opinion may be adduced the well-known fact, that the English
people are better able to endure sudden changes between cold and heat
than any other civihsed nation. The variable climate of England
demands of the muscles of temperature the most energetic action,
continued for a short space of time; whilst other climates are so equable
in their variations, that a languid action of long continuance is re-
quired of these muscles. For the muscles of motion and digestion, the
point of saturation is ascertainable, and subject to little variation; but
for the muscles of temperature, this point varies greatly. It is easy
to determine, by experiment, the quantity of labour and the quantity of
food which will produce the greatest health and strength ; but the most
advantageous temperature is not so easily to be determined. I believe
the natural and the best point of saturation to be, — the mean tem-
perature of the climate. The human body ought to be so disciplined,
as to feel most comfortable without clothing in motionless air of the
mean temperature of the climate.

The phenomena occurring among the human race are in perfect
accordance with the phenomena observed to exist among the inferior
animals. The wild men (called savages) are greatly superior to the
tame ones (calling themselves civilised), in every physical advantage.
There is hardly a European in existence who could compete (with any
chance of success) with an ordinary North American Indian hunter,
in either of the three grand tests of animal power, — marching or run-
ning the greatest distance in a given time; enduring the greatest
hunger or thirst ; and bearing the greatest extremes of heat and cold.
The astonishing indolence of savages is a mark of affinity to the charac-
ter of the lion, which knows no medium between perfect repose and
most violent action.

It is a fact, too well known to be disputed, that the hardiest

XXXIV

constitutions are to be found among the people who have to endure
the severest privations. The tenacity of life is greater among the
survivors of great privation than among the survivors of lesser priva-
tion. But muscular strength is proportional to the degree of privation
and saturation combined, and not to the degree of privation alone.
The majority of European labourers suffer moderate privation con-
tinually, with little or no admixture of saturation. The effect of in-
cessant privation is, to prune a population of its weaker branches, and
to leave only the very best lives. These lives, however, have not been
improved by passing through this ordeal ; but, on the contrary, have
suffered injury proportioned to the privation. Excessive labour, with
insufficient food and repose, exhausts and debilitates the strongest
frame. If the process of exhaustion has been of long continuance, the
suffering individual will never be able to recover the health and strength
which he has lost; but his offspring may, by judicious treatment, im-
prove their health, so as to attain the rank from which their parent fell.
The men of the strongest and most robust frames are not found among
those who labour hardest, but they are generally found among those
who labour moderately, and are well fed. The best elements of life
and strength are to be sought for among the hardest-faring men ; and
in performing experiments to elicit the greatest human muscular action,
the individuals ought to be selected from this class. The children
of the selected individuals may be rendered greatly superior to their
parents, and, in a few generations, a greater degree of muscular strength
may be elicited than was ever known among men. There is no apparent
limit to the increase of the muscular force of man ; he may render
himself stronger than a lion. The causes of strength and weakness
are placed out of the reach of the lion, but within the reach of the
intelligence and regulations of man. Strength depends on the length
of the oscillations between privation and saturation. Strength is im-
paired by too great, as well as by too small, oscillations. Man possesses
the exclusive privilege of commanding the length or extent of oscilla-
tion ; which privilege, hitherto, has been worse than useless to him.
Instead of using it to increase his strength, \vhich he might do, by
insensible additions to the length of the average oscillations, he impairs
his strength by extreme and unnatural diminutions in the extent of
oscillation.

In the making of war, the strength, velocity, and hardiness of the
soldier are of the utmost importance. The effect of courage and disci-
pline may be more than doubled by the careful cultivation of qualities

XXXV

which have been hitherto totally neglected. An English soldier under-
goes no preparation for improving his capacity of enduring long
marches, extreme hunger, or extreme cold. On the contrary, there
is the strongest ground for believing, that the treatment he experiences
is positively inj urious, and tends daily to diminish his power of with-
standing the effects of fatigue, cold, and hunger. It is a remarkable
fact, that the mortality and the sickness of English soldiers at home
are very much greater than among the English labouring population
of the same age. The proportion of three to two will nearly express
the relative mortality and sickness for a soldier and for a labourer.
When it is considered that all soldiers are picked men, the difference is
still more surprising ; and it is very probable that soldiers suffer twice
as much death and sickness as labourers of equally good constitutions.
As soldiers are under the absolute control of government regulations
of health, which have never been excepted against, this fact indicates
the value of the knowledge in England respecting the laws of health.

The error in the treatment of soldiers consists, I imagine, in the
suddenness of passage from a state of continued privation to a state of
continued saturation. An English recruit suddenly exchanges coarse
and scanty fare, hard labour, and cold lodging, — for good food, warm
lodging, and the exercise of drilling. The previous hard labour is but
slightly compensated by the fatigue of drilling. In the former, the
great muscles are exerted ; in the latter, the exertion is chiefly confined
to the smaller muscles of motion. It is not improbable that the ordi-
nary muscular action of a day labourer is ten times as great as that of
a soldier, although the fatigue on both sides may be equal. It is never
expected that a man who has lived in luxury can suddenly descend to
privation, without serious injury : it ought no more to be expected, that
a body formed under privations can with safety be suddenly transferred
to a state of satiety. The excessive mortality of soldiers cannot reason-
ably be ascribed to their superior freedom from moral restraint ; for it is
difficult to conceive that any considerable quantity of intemperance and
debauchery can be purchased for half-a-crown a-week, which is the limit
of the English soldier's spending money.

As a remedy for the existing evil, I would suggest, — the exercising
of thie soldier in walking, running, and leaping, — the diminution of
harassing and unprofitable drillings, — and the reduction of the average
temperature of the soldier's skin, by changes in clothing and lodging.
From every soldier, let ten miles of running be exacted every day, or

XXXVl

rather one hundred miles every ten days. The kind and quantity of
food might remain unchanged, but the frequency of meals should be
diminished. The adoption of a plan of this nature would, I conceive,
quickly restore the health of soldiers to the level of that pf labourers ;
and in a few years soldiers would become what they ought to be, — the
healthiest and strongest part of the community. The experiment pro-
posed may very easily be tried, and the correctness of the principle
be proved or disproved, by its application to two or three regiments.
If the average rate of sickness be not considerably reduced in a few
months, then is the principle to be abandoned, and some new cause
of the pernicious consequences of the existing mode of treatment is to
be sought for. There is nothing, probably, more deserving the deepest
attention of the army government than plans for the diminution of sick-
ness. At home, or in a short campaign, the injurious eflPects of sickness
are not very important ; but in a long campaign, and in all great effotts,
at least one-half of the army expenditure is to be placed to the account
of sickness. It is an important fact, that an English army cannot long
continue active operations before one-third of its power becomes paralysed
by sickness (exclusive of inefficiency from wounds in battle). The
enormous proportion of sick is attended with a corresponding mortality,
which occasions a vast expenditure in the recruiting and transport
departments. Simply by reducing the rate of sickness one-half, it is
not improbable that the expense may be reduced one-half, of main-
taining an active army of a given efficiency in a foreign country.

The monied class of England are greatly inferior to the labouring
class in corporeal advantages. Those who live in a state of continued
saturation, cannot compete in bodily exercises with the suflFerers of
continued privation. But the monied cIeiss have it in their power
to reverse this relation ; they have only to adopt a system of voluntary
privation, alternating with their ordinary state of saturation. The
readiest means of attaining the desired object, would be to subject
themselves to a system of military regulations. They would be no
losers in present happiness by so doing : the pain from fasting, from
hard labour, or from exposure to cold, is very inconsiderable, when we
have in close and certain prospect the unbounded gratification of the
desire excited. The pleasure of gratifying a new want is an indis-
putable gain, to which is to be added the distant pleasures inevitably
attendant upon improvements in health and strength. Privation is
an ingredient of pleasure more indispensable than saturation ; for the

xxxvu

place of the latter is often supplied by the imagination. Pleasure
may be defined to be, the meeting together of privation and saturation;
in the same manner as the electric shock is the rushing together,
commingling, and neutralisation of two antagonist fluids ; the shock, in
either case, being proportional to the previous degree of tension.

CHAPTER VII.

There exist§ a popular notion, that the mortality of the English popu-
lation has been diminishing for the last century. This notion is founded
upon National Returns of Living and Dying, acknovyledged on all sides
to be very imperfect. Any approach to correctness in these returns,
rests entirely on the principle which impels a man — to tell the truth
(if known), when nothing is to be gained by the trouble of falsification.
But there exists no principle impelling a man to incur the irksome
labour of closely investigating and accurately reporting a truth or fact
in which his own immediate interests are not concerned. Any consi-
derable body of men, having a certain duty to perform, never do it
carefully when they receive the same amount of praise or money for
doing it negligently. These Returns cannot lead to any safe conclusion
as to the absolute rate of mortality at any time ; although they may
indicate the relative rate of mortality at different times ; and they are
to be considered as strong evidence of a temporary diminution of English
mortality. The force of this evidence would be very great, if any satis-
factory reason had been alleged to account for this diminution ; but so
far is this from being the case, that the strongest arguments can be
adduced to shew that English mortality ought to have been increasing
during the last century. Mortality varies inversely as food, and food
varies as wages. Now, it is an undeniable fact, that wages have been
continually decreasing during the last century : the day-labour of a man
now will excbajige for one-third less com than it used to do ; conse-
quently there is strong ground for believing the mortality to have been
increasing. This seeming paradox, of a population improving its health
by diminishing its food, may be accounted for by change of circum-
stances so great, that wages do not afford any good measure of the food

f

xxxvin

consumed in times so distant. The English labourers of former times
were small farmers or cottagers, like those of Ireland now ; they de-
pended more upon the produce of their plot of ground than upon
the produce of their labour in the service of others. Even if the
same kind of food were consumed, we could not safely institute any
comparison as to the amount consumed, founded upon the wages
of such labourers and the wages of labourers of the present day, who
depend entirely on their labour-earnings and on the poor's rate.
But what I apprehend to be the true solution of the diflSculty is, the
substitution, to a very great extent, of potatoes for com. It is very
probable that more nutriment is obtained by English labourers of the
present day, by the expenditure of two shillings on a mixture of corn
and potatoes, than could be obtained from three shillings expended on
corn alone.

In order to ascertain the rate of mortality to which a nation is
subject, there is no method to be placed in competition with that of
decennial enumerations of the living, classed in decennial intervals of age.
This method is greatly superior to any other, because the result sought
will be affected in the lowest possible degree by errors in the enumera-
tion of the total population. The absolute mortality will be made to
depend almost entirely on correctness of proportion in the distribution
of the population in classes of decennial age. This is a kind of correct-
ness on which the greatest reliance can be placed, in operations of mag-
nitude, as there exists the highest mathematical probability that any
errors of distribution in one return will be neutralised by opposing errors
in some other return.

The English Population Returns for 1831 have been published
whilst the present work is passing through the press. Their form is
very unsatisfactory, and is an indication that the science of life measure-
ment has made a retrograde movement. The best, and perhaps the only,
opportunity which ever existed of determining with accuracy the abso-
lute mortality of an extensive and varied population has just been
thrown away. If the ages of the living population had been returned
in the present, as they were in the Report of 1821, we should now
be informed of the rate of mortality prevailing in every district of
England. From the English Population Returns no valuable informa-
tion is to be derived, respecting either the relative or the absolute
mortality at different ages.

From a statement made in the Returns of 1831 of the ages of the

XXXIX

dying population of the county of Essex, I entertain a strong suspicion
that the apparent diminution of the gross English mortality arises entirely
from the retrogression of the limit of infancy from the age of nine to the
age of seven years.

CHAPTER VIII.

There subsists the most intimate connexion between Sickness and
Death ; and, in the order of nature, the latter is preceded by the
former as its cause. That death and sickness simultaneously increase
and decrease, is a proposition which few people will be inclined to
dispute. From a great extent of observations, I have collected the
important fact, that death is proportional to duration of sickness alone,
and is independent of intensity. These observations have been made
on military masses of the greatest magnitude, under the widest variety
of circumstances. They serve to establish the fact, that in any con-
siderable quantity of men, placed for a given time under peculiar
circumstances, there exists a fixed proportion between the number of
deaths and the aggregate duration of sickness ; and, what may appear
extraordinary, the definite proportion which is applicable to one set
of circumstances, agrees nearly with the definite proportion which is
applicable to any other combination of circumstances. Two years
of sickness to each death appears to be the law of nature, from which
little deviation is allowed, except in very unhealthy climates. This
proportion has been observed to rule over the English army employed in
the Peninsular war, the European troops in the East Indies, and the
native troops in the East Indies. In the English army, at home and
inactive, there are 2^ years of alleged sickness to each death. In the
English West India army, there is 1^ year of sickness to each death.
In the East Indies, the proportion, more correctly stated is, 2^ years
for the native troops, and If years for the European troops. The
experience of Benefit Societies shews that this proportion for the English
working population approaches very near to two years. In any popu-
lation between the ages of 20 and 55, if the numbers constantly sick
amount to four per cent on the living, then it may be safely inferred
that the annual deaths amount to two per cent on the living.

xl

At different ages, the rate of sickness increases as the rate of morta-
lity increases. The expectation that it ought, is so reasonable, that
Dr. Price long ago acted upon it in the construction of his Tables
of Sickness, which are in universal use. The opinion is confirmed
by the report of sickness in Scotland, made by the Highland Society,
at least with the exception of old age. But the opposition here is a very
questionable fact, and of no practical importance.

In constructing the Tables for provision in sickness and in old age,
I have been influenced by the general principle, — that all savings from
the earnings of labour ought to be made before the age of fifty-five
years; that between the ages of 55 and 65 a man should expend the
labour barely sufficient for his maintenance ; and that for the portion
of life which may be enjoyed after the age of Q5, he should subsist
entirely on previous savings. According to these Tables, the allowance
during old age commences at 65, but the weekly payments given in
exchange for it cease at the age of 55. The Health Assurance Table is
confined to periods terminating at the age of 55 ; at least it is so when
the price paid is an even weekly payment, continued from the age of
admission to the end of the term of insurance. But I have given a
second Table, wherein the contributions are variable and increasing,
which shews the value of health insurance for the term of one year,
at all ages below 70. By the help of -this second Table, the even
weekly payment for health insurance, commencing at 55 and termi-
nating at 65 years of age, may be obtained sufficiently near for practical
purposes.

The basis assumed of my Tables of Sickness, is intermediate between
that reported by the Highland Society, and that said to be assumed by
Dr. Price. But the basis really assumed by Dr. Price in his Tables
differs from mine in a very insignificant degree. Dr. Price appears
to have fallen into the error of confounding an assurance for a long
term with an assurance for a short term. He seems to have assumed,
that the weekly payment for health insurance for thirty years does not
differ from the weekly payment for a term of ten years. It is, however,
not improbable that the error was known at the time, — that Dr. Price
preferred making an incorrect statement, to the exposing of difficulties
of calculation, which neither he nor any other person has succeeded in
surmounting. By the help of the new discovery, I have been able
to overcome the difficulty in one case only ; and, most fortunately, this
case is the only one of great practical importance.

I would here observe, that a Life and Health Association may act in

xli

such a manner as to exhibit results differing widely from my Tables
of Mean Mortality and Sickness; and yet there may be no reason
for calling in question the correctness of the assumed averages. For
I present these Tables as the best standard of truth for a long space
of time, on the supposition that the management of the Society is liberal
and intelligent in an average degree. By liberality, I would be under-
stood to mean, the disposition to admit rather exceptionable lives, pro-
vided that the inducement to seek admission has not been founded on
the knowledge of this exception. The profitable effect of a Life and
Health Association greatly depends on the Tables selected ; but it is still
more dependent on the general management.

ILLUSTRATIONS OF THE TABLES.

Tab. a. 1. Out of 146,472 born alive, 100,000 attain the ^e of 12 years,
50,224 attain the age of 60, and 1702 die in their 61st year of age.

Tab. a. 3. The value of annuity of £1 on a single life, aged 60 years,
when the rate of interest is 4 per cent, is 9*0179 ; the payments being made at
the end of annual intervals, and no allowance being due for the fractional time
lived in the year of death.

Tab. A. 6. The present value of annuity of £ 1 on the joint continuance of
two lives, aged 20 and 30 years, is 15*6890 ; the annual payments cease on the
failure of either of the two lives.

Tab. A. 21. The average duration of life from and after any age, is termed
the expectation. A person aged 35 years has an expectation of living 28'1617
complete years. To obtain the total expectation, about half a-year is to be added
to the numbers in this Table for fractional years of existence.

Tab. a. 22. Of two lives, aged 30 and 40 respectively, — the probability
that the younger will die first, is represented by -37259 ; that of the elder by
•62741 ; — the sum of these probabilities, or certainty, being represented by
unity.

Tab. a. 30. In a stationary population, wherein 100,000 attain the age of
12 every year, there are 903,374 constantly living between the ages of 20 and
30, and 8445 annually dying in the same interval of age. For 100,000 living
at all ages, 42,073 are between the ages of 20 and 50.

Tab. A. 31. In a population increasing ten per cent every ten years (but
stationary during each decennial interval), wherein the living, between the ages
of 20 and 30, belong to the stationary population of the adjoining Table; — out
of a total population of 6,055,290, there are 1,480,766 living below the age of
10, which is equivalent to 244,541 out of one million.

Tab. a. 32. Health insurance for the term of one year. For lOOd. a week
during sickness, a person who has just completed his 30th year will be required
to pay 2d. (2"0137) per week. The benefit and the weekly payments terminate
at the age of 31, when another annual engagement may be made.

Tab. a. 33. Health Insurance during the effective stage of Human Life.
A person who has lived exactly 25 years will be required to pay 2^d. (2-4927)

xlii

per week for 30 years, in order that he may receive lOOd. per week during the
portion of that time in which he may happen to he sick. For ten years' insur-
ance, from 55 to 65, the even weekly payment is about 6|rf.

Tab. a. 34. A person aged (precisely) 25 years will be required to pay
a weekly premium of 7d. (6-9257) for 30 years, as an equivalent for lOOd. per
week, after 40 years, or for the time he may live beyond the age of 65 years.

Tab. a. 35. A person aged 25 will be required to pay 6d. (5*9530) every
quarter of a year, in order that his representative may receive £5 on the day of
his death.

Tab. a. 36. The present value of a deferred annuity of £10, payable to B,
now aged 30 years, in case of surviving another person, A, now aged 40,
is £52-001 in a single payment, and £3-6002 in yearly payments, during the
joint lives, the first payment being made now. If the deferred annuity is to
commence growing from the death of A, and not from the date of the last
annual payment, the numbers in this Table will then be a trifle too high.

Tab. a. 37. At the age of 40 years precisely, the force of mortality is such,
that 1-4526 would die in one year out of 100 constantly living.

Tab. B. 23. Village Mortality. For £100 payable on the deafh of A,
aged 40, provided that another person, B, aged 50, be then alive; — the single
payment is £19-954, and the annual payment during the joint lives is £ 1-689.

Tab. B. 24. For £100 payable at the end of the year, in which a person,
now aged 35, may happen to die. If the assurance extends over the whole of
life, the equivalent annual payment for life is £2-0300 ; if the assurance is only
for the term of one year, the payment is £ 1-0140.

Tab. C. 6. Comparative view of three Tables of Mortality, assuming as a
common base, that 100,000 annually attain the age of 12 years. According to
the Table of Mean Mortality, between the ages of 20 and 30, the sum of the
living at the beginning of each of the ten annual intervals is 907,597 ; the
annual deaths amount to 8445; and the proportion of annual deaths to 100
annual survivors is -9305. The number of annual survivors exceeds the number
constantly living by half the annual deaths nearly, which excess is generally
very small.

Tab. C. 7. Between the ages of 20 and 50, with the Mean rate of Morta-
lity; — for 100,000 annually attaining the age of 12, there are living (annually
surviving) 2,429,331, and dying annually 30,393, being at the rate of 1-2511
per cent. In a stationary population of one million at all ages, there are living
417,892 between the ages of 20 and 50, and 5228 dying between those ages;
and out of 100,000 deaths at all ages, 20,751 happen between 20 and 50 years
of age.

\* The accompanying Tables, since being in type, have been read over by the Author
four times; ouce before, and three times after going to press; two readings with the
manuscript, and two readings with the original calculations. In the first reading, one
error of the press was found in every five pages, or one error in ten thousand figures ; an
extremely small amount, and an index of printing talent of a high order. The first alone
of the two under-mentioned erroi-s was not marked for correction before going to press.

ERRATA.

Tad. a. 5. Column 7, line 24, should be 3-1447'.
Tab. C. 6. _ 10 _ IQ, _ 38-f 118.

TABLES.

MEAN MORTALITY.

Tab. A. 1.

Tab. a. 2.

Shewing, at the end of any number of
years from birth, — the Living out of a
given number born, — also the Dying
in the year succeeding.

Shewing, at every age of life, in logarithms, — the
probability of living one year, (x,fl), — and the
Living out of a given number born (a. a).

1

<

Living.

Dying.

4

Living.

Dying.

146472-1

16647-2

50

64027-2

1255-0

1

129824-9

10169-2

51

62772-2

1266-8

2

119655-7

6420-0

52

61505-4

1278-0

3

113235-7

4144-1

53

60227-4

1288-5

4

109091-6

2715-5

54

58939-0

1298-2

5

106376-1

1797-5

55

57640-8

1338-3

6

104578-6

1198-0

56

56302-5

1410-1

7

103380-6

802-2

57

54892-4

1482-8

8

102578-4

650-8

58

53409-6

1556-0

9

101927-6

646-6

59

51853-6

1629-2

10

101281-0

642-5

60

50224-4

1701-6

11

100638-5

638-5

61

48522-8

1772-6

12

100000-0

643-8

62

46750-2

1841-2

13

99356-2

658-8

63

44909-0

1906-6

14

98697-4

673-8

64

43002-4

1967-7

15

98023-6

689-3

65

41034-7

2023-6

16

97334-3

704-8

66

39011-1

2073-0

17

96629-5

720-5

67

36938-1

2114-7

18

95909-0

736-5

68

34823-5

2147-5

19

95172-6

752-6

69

32676-0

2170-2

20

94420-0

768-9

70

30505-8

2181-6

21

93651-1

785-3

71

28324-2

2180-6

22

92865-8

801-9

72

26143-5

2166-3

23

92063-8

818-7

73

23977-2

2137-9

24

91245-1

835-6

74

21839-3

2094-8

25

90409-6

852-5

75

19744-6

2036-7

26

89557-0

869-7

76

17707-8

1963-8

27

88687-4

886-8

77

15744-0

1876-5

28

87800-5

904-1

78

13867-5

177.5-8

29

86896-4

921-4

79

12091-7

1662-9

30

85975-0

9388

80

10428-8

1539-6

31

85036-2

956-1

81

8889-2

1408-2

32

84080-1

973-5

82

7481-0

1271-0

33

83106-6

990-8

83

6210-0

1131-0

34

82115-8

1008-1

84

5079-0

991-1

35

81107-6

1025-3

85

4087-9

854-1

36

80082-3

1042-5

86

3233-8

723-0

37

79039-8

1059-5

87

2510-8

600-3

38

77980-4

1076-3

88

1910-5

488-1

39

76904-1

1093-0

89

1422-5

388-0

40

75811-1

1109-4

90

"1034-5

301-0

41

74701-6

1125-6

91

733-5

227-5

42

73576-0

1141-6

92

506-0

167-1

43

72434-4

1157-2

93

338-9

119-1

44

71277-2

1172-5

94

219-8

8-2-1

45

70104-7

1187-4

95

137-8

54-6

46

68917-2

1201-9

96

83-2

34-9

47

67715-3

1216-0

97

48-2

21-4

48

66499-3

1229-5

98

26-8

12-6

49

65269-8

1242-5

99

14-2

7-0

1

2

3

4

5

.6

7

8

9

10

11

12

13

14

15

16

17

1

19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49

A,a

[-9476032
-9645754
•9760500
•9838078
•9890528
•9925988
•9949961
•9966170
-9972360
-9972360
•9972360
•9972360
•9971949
•9971110
•9970246
•9969356
•9968439
-9967495
-9966523
-9965521
-9964490
-9963428
-9962334
-9961207
-9960047
-9958852
-9957621
-99563|
-99551
-9953705
-9952318
-9950892
-9949423
-9947910
-9946352
-9944748
-9943095
•9941393
•9939640
-9937834
-9935975
-9934060
-9932087
-9930056
•9927964
•9925809
•9923590
•9921304
-9918950
-9916526

AO

•1657549
•1133581
•0779335
•0539835
•0377913
•0268441
•0194429
•0144390
•0110560
-008-2920
-0055280
-0027640
-0000000
[-9971949
-9943059
•9913305
•9882661
•9851100
•9818595
•9785118
■9750639
•9715129
•9678557
•9640891
•9602098
■9562145
•9520997
•9478618
•9434971
•9390019
•9343722
•9296040
■9246932
•9196355
•9144265
•9090617
•9035365
•8978460
•8919853
•8859493
•8797327
•8733302
•8667362
•8599449
•8529505
•8457469
•8383278
•8306868
•8228172
•8147122

50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99

A,a

9914029
9911458
9908809
9906082
9903272
9897978
9889848
9881070
9871592
9861359
9850310
9838381
9825501
9811595
9796581
9780370
9762867
9743969
9723566
9701536
9677751
9652070
9624343
9594406
9562083
95-27184
9489504
9448822
9404897
9357472
9306268
9250983
9191292
9126844
9057260
8982131
8901015
8813434
8718874
8616778
8506546
8387529
8259028
8120285
7970487
7808750
7634125
7445582
7242015
7022225

A a

r8063648
•7977677
•7889135
•7797944
•7704026
•7607298
•7505276
■7395124
-7276194
-7147786
-7009145
-6859455
-6697836
-6523337
-6334932
-6131513
-5911883
-5674750
-5418719
-5142285
•4843821
•4521572
•4173642
•3797985
•3392391
•2954474
•2481658
•1971162
•1419984
•0824881
•0182353
?-9488621
-8739604
-7930896
-7057740
-6115000
•5097131
-3998146
-2811580
-1530454
-0147232
r-8653778
-7041307
-5300335
-3420620
■1391107
;-9199857
-6833982
-4279564
•1521579

MEAN MORTALITY.

Tab. a. 3.
Shewing the present valiie of an Annuity of £l depending on a single life at any age.

<

3 f cent

4^cent

5Fcent

6^cent

1

3 f cent

4^cent

5Vcent

e^cent :

18-0508

14-9621

12-7061

11-0074

50

13-2921

12-0276

10-9518

10-0295

1

19-9764

16-5558

14-0522

12-1640

51

12-9646

11-7588

10-7293

9-8438

2

21-3244

17-6814

15-0088

12-9896

52

12-6285

11-4811

10-4978

9-6494

3

22-2094

18-4312

15-6527

13-5497

53

12-2834

11-1937

10-2566

9-4454

4

22-7447

18-8966

16-0597

13-9083

54

11-9285

10-8959

10-0049

9-2310

5

23-0250

19-1541

16-2931

14-1191

55

11-5631

10-5870

9-7417

9-0052

6

23-1234

19-2627

16-4018

14-2235

56

11-1931

10-2722

9-4720

8-7725

7

23-0931

19-2654

16-4215

14-2516

57

10-8250

9-9576

9-2010

8-5377

8

22-9719

19-1927

16-3774

14-2248

58

10-4593

9-6433

8-9293

8-3012

9

22-8122

19-0878

16-3060

14-1746

59

10-0964

9-3300

8-6571

8-0633

10

22-6465

18-9781

16-2307

14-1210

60

9-7366

9-0179

8-3848

7-8244

11

22-4749

18-8632

16-1510

14-0638

61

9-3804

8-7075

8-1128

7-5847

12

22-2969

18-7430

16-0668

14-0028

62

9-0281

8-3992

7-8414

7-3446

13

22-1146

18-6190

1^-9795

13-9392

63

8-6802

8-0933

7-5711

7-1044

14

21-9301

18-4930

15-8904

13-8742

64

8-3370

7-7902

7-3021

6-8646

15

21-7433

18-3650

15-7997

13-8077

65

7-9989

7-4903

7-0348

6-6254

16

21-5541

18-2348

15-7071

13-7398

66

7-6662

7-1940

6-7697

6-3872

17

21-3627

18-1025

15-6128

13-6704

67

7-3393

6-9016

6-5071

6-1504

18

21-1689

17-9680

15-5166

13-5995

68

7-0186

6-6135

6-2474

5-9153

19

20-9727

17-8314

15-4185

13-5271

69

6-7042

6-3301

5-9909

5-6823

20

20-7740

17-6924

15-3184

13-4530

70

6-3966

6-0517

5-7379

5-4517

21

20-5729

17-5512

15-2164

13-3772

71

6-0960

5-7785

5-4889

5-2239

22

20-3693

17-4076

15-11-24

13-2998

72

5-8026

5-5109

5-2441

4-9993

23

20-1631

17-2616

15-0062

13-2206

73

5-5166

5-2492

6-0038

4-7780

24

19-9544

17-1131

14-8979

13-1396

74

5-2383

4-9935

4-7683

4-5605

25

19-7429

16-9622

14-7873

13-0567

75

4-9679

4-7442

4-5378

4-3470

26

19-5288

16-8086

14-6745

12-9718

76

4-7055

4-5015

4-3128

4-1378

27

19-3119

16-6523

14-5593

12-8850

77

4-4512

4-2655

4-0932

3-9331

28

19-0922

16-4933

14-4417

12-7960

78

4-2051

4-0364

3-8795

3-7333

29

18-8695

16-3315

14-3216

12-7049

79

3-9674

3-8144

3-6717

3-5384

30

18-6439

16-1668

14-1988

12-6115

80

3-7380

3-5995

3-4700

3-3488

31

18-4152

15-9991

14-0733

12-5158

81

3-5170

3-3918

3-2746

3-1645

32

18-1834

15-8283

13-9450

12-4176

82

3-3044

3-1915

3-0856

2-9858

33

17-9483

15-6542

13-8138

12-3168

83

3-1001

2-9985

2-9029

2-8127

34

17-7098

15-4768

13-6795

12-2134

84

2-9042

2-8129

2-7268

2-6454

35

17-4678

15-2960

13-5420

12-1071

85

2-7165

2-6347

2-5573

2-4840

36

17-2222

15-1115

13-4012

11-9979

86

2-5370

2-4638

2-3943

2-3285

37

16-9728

14-9232

13-2568

11-8855

87

2-3656

2-3001

2-2380

2-1789

38

16-7195

14-7310

13-1088

11-7698

88

2-2021

2-1437

2-0882

2-0353

39

16-4621

14-5346

12-9569

11-6506

89

2-0464

1-9944

1-9449

1-8976

40

16-2004

14-3340

12-8009

11-5276

90

1-8983

1-8521

1-8080

1-7659

41

15-9343

14-1287

12-6405

11-4008

91

1-7577

1-7167

1-6776

1-6401

42

15-6634

13-9187

12-4756

11-2697

92

1-6244

1-5881

1-5534

1-5201

43

15-3875

13-7036

12-3058

11-1342

93

1-4982

1-4661

1-4354

1-4059

44

15-1065

13-4831

12-1309

10-9938

94

1-3788

1-3506

1-3235

1-2974

45

14-8199

13-2569

11-9506

10-8484

95

1-2662

1-2414

1-2174

1-1944

46

14-5275

13-0248

11-7642

10-6974

96

1-1601

1-1383

1-1172

1-0969

47

14-2289

12-7862

11-5717

10-5405

97

1-0602

1-0411

1-0226

1-0048

48

13-9238

12-5408

11-3724

10-3773

98

-9664

•9497

-9335

•9178

4S

13-6117

12-2881

11-1660

10-2071

9S

•8785

•8639

-8497

•8360

MEAN MORTALITY.

Tab. a. 4.

Shewing the values of Annuity of £l depending on the co-existence or joint

continuance of two lives oi equal ages.

Ages.

Secant

4 ^ cent

5^ cent

6<P'£ent

Ages.

accent

4^ cent

5 y cent

6!t?^cent

0-0

1-1

2-2
3-3
4-4
5-5
6-6
7-7
8-8
9-9
10-10
11-11
12-12
13-13
14-14
15-15
16-16
17-17
18-18
19-19
20-20
21-21
22-22
23-2.3
24-24
25-25
26-26
37-27
28-28
29-29
30-30
31-31
32-32
33-33
34-34
35-35
36-36
37-37
38-38
39-39
40-40
41-41
42-42
43-43
44-44
45-45
46-46
47-47
48-48
'49^9

11-5474
14-1396
16-1444
17-5678
18-4957
19-0356
19-2864
19-3281
19-2205
19-0507
18-8736
18-6888
18-4961
18-2987
18-1001
17-9003
17-6993
17-4972
17-2939
17-0895
16-8839
16-6771
16-4692
16-2601
16-0497
15-8382
15-6254
15-4114
15-1960
14-9793
14-7611
14-5415
14-3203
14-0975
13-8730
13-6466
13-4182
13-1877
12-9550
12-7197
12-4818
12-2410
11-9970
11-7494
11-4980
11-2424
10-9822
10-7168
10-4456
10-1682

9-8586
12-0509
13-7537
14-9718
15-7761
16-2555
16-4918
16-5513
16-4836
16-3626
16-2351
16-1008
15-9593
15-8135
15-6663
15-5178
15-3678
15-2165
15-0639
14-9098
14-7544
14-5976
14-4393
14-2796
14-1185
13-9559
13-7918
13-6262
13-4589
13-2901
13-1195
12-9472
12-7731
12-5970
12-4190
12-2388
12-0564
11-8716
11-6842
11-4941
11-3010
11-1048
10-9050
10-7015
10-4939
10-2818
10-0647
9-8422
9-6136
9-3784

8-5738
10-4593
11-9283
12-9851
13-6899
14-1177
14-3375
14-4053
14-3631
14-2744
14-1802
14-0799
13-9733
13-8627
13-7508
13-6375
13-5229
13-4070
13-2896
13-1709
130508
12-9292
12-8063
12-6819
12-5560
12-4286
12-2997
12-1692
12-0371
11-9033
11-7678
11-6305
11-4914
11-3503
11-2071
11-0618
10-9143
10-7643
10-6117
10-4563
10-2980
10-1364
9-9714
9-8026
9-6297
9-4522
9-2698
9-0819
8-8879
8-6872

7-5726

9-2175

10-5019

11-4301

12-0539

12-4378

12-6412

12-7120

12-6863

12-6198

12-5483

12-4716

12-3892

12-3033

12-2162

12-1278

12-0382

11-9473

11-8552

11-7617

11-6670

11-5709

11-4734

11-3746

11-2745

11-1729

11-0698

10-9652

10-8591

10-7514

10-6421

10-5311

10-4183

10-3036

10-1870

10-0683

9-9475

9-8243

9-6986

9-5703

9-4392

9-3049

9-1673

9-0261

8-8808

8-7312

8-5768

8-4170

8-2513

8-0790

50-50
51-51
52-62
53-63
54-54
55-55
56-56
57-57
58-58
59-59
60-60
61-61
62-62
63-63
64^64
65-65
66-66
67-67
68-68
69-69
70-70
71-71
72-72
73-73
74-74
75-75
76-76
77-77
78-78
79-79
80-80
81-81
82-82
83-83
84-84
85-85
86-86
87-87
88-88
89-89
90-90
91-91
92-92
93-93
94r-94
95-95
96-96
97-97
98-98
99-99

■8837
•5913
•2902
•9793
■6576
•3234
•9855
•6530
•3264
■0059
■6918
■3844
0841
7910
5054
■2274
■9573
■6952
■4412
■1955
■9581
■7290
■5083
■2961
0921
8965
7092
5300
3589
1957
0403
8925
7622
6192
4933
3742
2619
1560
0564
9628
8761
7930
7163
6448
5782
6165
4594
4066
3581
3136

9-1358

8-8849

8-6249

8-3546

8-0728

7-7781

7-4784

7-1822

6-8900

6-6021

6-3189

6-0407

5-7677

5-5003

5-2388

4-9834

4-7344

4-4919

4-2562

4-0274

3-8057

3-5911

3-3837

3-1837

2-9910

2-8057

2-6277

2-4571

2-2937

2-1376

1-9886

1-8466

1-7115

1-5831

1-4614

1-3461

1-2371

1-1343

1-0373

•9462

•8605

•7803

•7063

•6352

•5700

•6094

•4533

•4014

•3537

-3098

8-4790

■2625

8-0367

7-8005

7-5525

7-2914

7-0242

6-7592

6-4967

6-2371

5-9807

5-7279

6-4790

6-2344

4-9942

4-7590

4-5288

4-3039

4-0846

3-8711

3-6635

3-4621

3-2669

3-0781

2-8957

2-7199

2-6506

2-3880

2-2319

2-0823

9393

1-8027

1-6725

1-5486

1-4308

1-3191

1-2133

1-1133

1-0190

■9301

■8465

■7680

'6946

■6260

■5620

■6025

•4473

■3963

■3493

•3061

7-8993

7-7114

7-6143

7-3068

7-0875

6-8550

6-6158

6-3777

6-1410

5-9060

5-6730

5-4426

5-2149

4 9904

4-7692

4-5519

4-3385

4-1295

3-9250

3-7264

3-5307

3-3413

3-1573

2-9788

2-8059

2-6389

2-4777

2-3224

21730

2-0297

1-8922

1-7608

1-6352

1-5154

1-4014

1-2931

1-1904

1-0931

1-0012

•9145

•8328

-7561

-6842

-6169

-5542

-4958

-4416

•3913

-3450J

-30251

MEAN MORTALITY.

Tab. a. 5.
Shewing the values of Annuity on the joint continuance of two lives.
Difference of age Five years.

Ages. 3 V cent 4 ^ cent

0-5
1-6
2-7
3-8
4-9
5-10
6-11
7-12
8-13
9-14
10-15
11-16
12-17
13-18
14-19
15-20
16-21
17-22
18-23
19-24
20-25
21-26
22-27
23-28
24-29
25-30
26-31
27-32
28-33
29-34
30-35
31-36
32-37
33-38
34-39
35-40
36-41
37-42
38-43
39-44
40-45
41-46
42-47
43-48
44-45
45-50
46-51
47-51

14-8036

16-4985

17-6514

18-3619

18-7566

18-9389

18-9691

18-8907

18-7367

18-5516

18-3624

18-1688

17-9707

17-7697

17-5675

17-3642

17-1596

16-9539

16-7469

16-5388

16-3294

16-1188

15-9069

15-6938

15-4793

15-2635

15-0463

14-8276

14-6074

14-3856

14-1621

13-9368

13-7097

13-4805

13-2491

13-0154

12-7791

12-5401

12-2981

12-0529

11-8041

11-5514

11-2944

11-0326

10-7656

10-4929

10-2137

9-9273

5 F cent

12-6406
14-0868
15-0796
15-7015
16-0581
16-2361
16-2854
16-2425
16-1346
15-9998
15-8612
15-7185
15-5716
15-4218
15-2707
15-1182
14-9642
14-8089
14-6521
14-4939
14-3342
14-1730
14-0104
13-8462
13-6804
13-5130
13-3439
13-1731
13-0005
12-8260
12-6496
12-4711
12-2904
12-1075
11-9221
11-7341
11-5432
11-3494
11-1523
10-9516
10-7471
10-5384
10-3252
10-1069
9-8830
9-6531
9-4163
9-1721

6 ^cent

10-9855
12-2375
13-1030
13-6518
13-9740
14-1433
14-2021
14-1814
14-1041
14-0034
13-8991
13-7913
13-6796
13-5652
13-4495
13-3324
13-2139
13-0940
12-9726
12-8498
12-7256
12-5998
12-47251
12-3436
12-2131
12-0810
11-9472
11-8116
11-6742
11-5349
11-3936
11-2502
11-1046
10-9567
10-8063
10-6533
10-4974
10-3386
10-1764
10-0106
9-8411
9-6673
9-4888
9-3054
9-1163
8-9211
8-7190
8-5094

9-6899
10-7875
11-5504
12-0387
12-3304
12-4894
12-5523
12-5456
12-4891
12-4119
12-3317
12-2482
12-1613
12-0720
11-9814
11-8895
11-7963
11-7018
11-6060
11-5088
11-4102
11-3102
11-2087
11-1058
11-0014
10-8954
10-7877
10-6784
10-5674
10-4546
10-3398
10-2231
10-1043
9-9832
9-8598
9-7338
9-6052
9-4736
9-3388
9-2007
9-0588
8-9129
8-7624
8-6071
8-4463
8-2795
8-1059
7-9249

3 f cent

48-53

49-54

50-55

51-56

52-57

53-58

54-59

55-60

56-61

57-62

58-63

59-64

60-65

61-66

62-67

63-68

64-69

6^70

66-71

67-72

68-73

69-74

60-75

71-76

72-77

73-78

74-79

75-80

76-81

77-82

78-83

79-84

80-85

81-86

82-87

83-88

84^89

85-90

86-91

87-92

88-93

89-94

90-95

91-96

92-97

93-98

94-99

95-100

4^cent

S^cent 6'P'cent

6331

3299

0170

6983

3787

0579

7356

4113

0892

7734

46436

16215

'86705

■57945

0272|4-
76304
50694
25904
01943

9-

9

9-

8-

8-

8-

7-

7'

7-

6-

6'

6-

5-

5

5"2994'5

5-

4-

4-

4

4'

3

7882
5653
3508
1447

2,

2-9470:2
2-7575,2
2

57622
40292

2377
0802
9305
7882
6533
52561

4047
2906
1831
0819
9867
■8975
8139
•7358
■6630
•5952
•5322
■4739
•4200
■3704

9195
6576
3854
1066
■8255
■5420
•2557
■9661
•6771
•3926
■1130
•8386
•5698
•3067
•0497
•7990
•5548
•3173
-0867
-8630
6465
4373
2353
0407
8535
6736
5011
•3358
•1778
•0269
•8831
•7462
•6161
-4926
-3757
-2651
-1606
-0622
-9695
-8824
■8008
-7244
•6531
-5866
-5248
-4675
-4146
-3658

8-2913 7-7355
8

X

06387-5367
8257|7-3274
5805i7-1106
33216-8901
0803,6-6656
8249 6-4366
5652'6-2028
3048!5-9673
04755-7338
5-7938'5-5027
5-5438'5-2742

2980 5-0488
0567 4-8268
82014-6084
58854-3940
4-36224-1838
4-14153-9781

;i.

3-92643-7772
3-71733-5812

3-514213-3904
3

,1;

2-4299,2-3625

2-

2-

1'

.1.

3174'3-2049
■12693-0250
-94292-8506
765312-6821
59432-5193

27212-2116
1208 2-0666

9761
8378
7060
5804
4611
3478
2405
1390
0431
9528
■8678
■7881
■7133
•6435
•5783
■5176
•4614
-4093
-3612

1-9276

1-7946

1-6675

1-5462

1-4307

1-3210

2168

1181

0248

9367

8537

7757

7026

•6341

5702

•5106

•4553

•4041

■3568

MEAN MORTALITY.

Tab. a. 6,

Shewing the values of Annuity on the joint continuance of two lives.

Difieience of age Ten years.

■Ages.

S^cent

4^cent

5 W'cent

6#'oent

3 f cent

4 'f cent

5#'cent

6 f cent

0-10

1-11

2-12

3-13

4-14

5-15

6-16

7-17

8-18

9-19

10-20

11-21

12-22

13-23

14-24

15-25

16-26

17-27

18-28

19-29

20-30

21-31

22-32

23-33

24-34

25-35

26-36

27-37

28-38

29-39

30^0

31-41

32-42

33-43

34-44

35-45

36-46

37-47

38-48

39-49

40-50

41-51

42-52

43-53

44-54

7132
■2070
■2276
■8720
■2349
■3938
■4078
■3196
■1596
'9695
■7752
5766
3736
1676
9604
■7519
■5420
■3308
■1183
■9044
■6890
■4723
■2540
•0341
■8126
5893
3643
1374
■9084
■6773
■4439
2080
9694
7280
4834
2355
9838
7281
4679
2029
9325
6562
3734
0832
7851

12-6177
13-8995
14-7842
15-3526
15-6838
15-8426
15-8781
15-8265
15-7129
15-5730
15-4292
15-2814
15-1294
14-9745
14-8180
14-6601
14-5007
14-3396
14-1770
14-0128
13-8469
13-6793
13-5099
13-3387
13-1656
12-9905
12-8134
12-6341
12-4525
12-2684
12-0819
11-8925
11-7002
11-5048
11-3060
11-1035
10-8970
10-6861
10-4705
10-2498
10-0233
9-7905
9-5509
9-3035
9-0477

11-0016
12-1161
12-8912
13-3959
13-6974
13-8508
13-8981
13-8698
13-7874
13-6820
13-5730
13-4604
13-3440
13-2248
13-1041
12-9820
12-8583
12-7330
12-6062
12-4777
12-3475
12-2156
12-0820
11-9465
11-8091
11-6697
11-5282
11-3845
11-2385
11-0901
10-9391
10-7853
10-6286
10-4687
10-3053
10-1383
9-9673
9-7919
9-6118
9-4264
9-2352
9-0378
8-8333
8-6210
8-4002

9-7284

10-7086

11-3945

11-8457

12-1204

12-2662

12-3193

12-3061

12-2452

12-1639

12-0795

11-9918

11-9006

11-8070

11-7120

11-6156

11-5178

11-4185

11-3177

11-2154

11-1115

11-0060

10-8988

10-7898

10-6791

10-5664

10-4518

10-3351

10-2162

10-0950

9-9714

9-8450

9-7159

9-5837

9-4482

9-3092

9-1663

9-0191

8-8673

8-7105

8-5480

8-3793

8-2037

8-0204

7-8285

45-55
46-56
47-57
48-58
49-59
50-60
51-61
52-62
53-63
54-64
65-65
56-66
57-67
58-68
59-69
60-70
61-71
62-72
63-73
64-74
65-75
66-76
67-77
68-78
69-79
70-80
71-81
72-82
73-83
74-84
75-85
76-86
77-87
78-88
79-89
80-90
81-91
82-92
83-93
84-94
85-95
86-96
87-97
88-98
89-99

■4780
•1666
•8560
-5464
-2377
-9301
•6234
-3177
-0128
-7083
-4040
•1031
•8096
•5234
-2450
•9744
•7118
•4573
-2110
•9730
•7434
•5222
•3094
•1050
■9088
■7210
■5413
■3696
2059
■0500
9018
7610
6275
5011
3816
2689
1626
0626
■9686
■8805
7981
7210
6492
5824
5203

•7825
•5120
•2410
•9697
•6980
•4261
•1538
•8811
•6078
•3337
•0583
•7850
•5173
•2554
•9996
•7502
•5073
•2711
•0419
•8197
•6046
•3968
•1963
■0031
■8173
■6389
'4678
3040
1474
9979
8555
7199
5912
4690
3533
2439
1407
0434
9518
8659
7853
7099
6396
5740
5132

8-1697
7-9334
7-6957
7-4566
7-2163
6-9748
6-7319
6-4876
6-2417
5-9940
5-7440
5-4949
5-2499
5-0095
4-7739
4-5434
4-3181
4-0985
3-8846
3-6767
3-4748
3-2792
3-0900
2-9072
2-7310
2-5613
2-3982
2-2417
2-0917
1-9483
1-8113
1-6807
1-5563
1-4382
1-3261
1-2199
1-1196
1-0248
9356
■8517
■7729
■6991
6302
■5659
■5062

7-6270
7-4194
7-2098
6-9981
6-7846
6-5690
6-3514
6-1317
5-9097
5-6850
5-4573
5-2294
5-0047
4-7833
4-5657
4-3521
4-1428
3-9380
3-7380
3-5431
3-3533
3-1689
2-9901
2-8169
2-6494
2-4878
2-3322
2-1824
2-0387
1-9009
1-7690
1-6431
1-5229
1-4086
1-2999
1-1968
1-0992
1-0069
9199
8379
■7609
'6887
6211
'5581
'4994

MEAN MORTALITY.

Tab. a. 7.

Shewing the values of Annuity on the joint continuance of two lives.

Difference of age Fifteen years.

Ages.

0-15
1-16
2-17
3-1
4-19
5-20
6-21
7-22
8-23
9-24
10-25
11-26
12-27
13-28
14-29
15-30
16-31
17-32
18-33
19-34
20-35
21-36
22-37
23-38
24-39
25-40
26-41
27-42
28-43
29-44
30^5
31-16
32-47
33-48
34-49
35-50
36-51
37-52
38-53
39-54
40-55
41-56
42-57

3#'cent

14-2776

4#'cent

15-7092
16-6836
17-2948
17-6334
17-7745
17-7753
17-6774
17-5099
17-3132
17-1123
16-9071
16-6974
16-4846
16-2703
16-0544
15-8370
15-6179
15-3972
15-1746
14-9503
14-7240
14-4957
14-2652
14-0325
13-7973
13-5596
13-3191
13-0757
12-8290
12-5788
12-3250
12-0670
11-8045
11-5371
11-2644
10-9858
10-7008
10-4086
10-1086
9-7998
9-4872
9-1762

dV'cent

12-3063

13-5420

14-3920

14-9351

15-2473

15-3916

15-4161

15-3557

15-23.50

15-0886

14-9383

14-7839

14-6251

14-4633

14-2998

14-1345

13-9674

13-7984

13-6276

13-4547

13-2797

13-1025

12-9231

12-7413

12-5570

12-3700

12-1801

11-9872

11-7911

11-5915

11-3881

11-1807

10-9689

10-7523

10-5306

10-3031

10-0694

9-8288

9-5807

9-3242

9-0585

8-7880

8-5178

6#'cent

10-7721
11-8514
12-6000
13-0851
13-3717
13-5134
13-5515
13-5157
13-4270
13-3157
13-2008
13-0821
12-9595
12-8340
12-7068
12-5778
12-4470
12-3144
12-1799
12-0433
11-9047
11-7639
11-6209
11-4754
11-3274
11-1768
11-0233
10-8668
10-7070
10-5438
10-3768
10-2057
10-0302
9-8499
9-6644
9-4731
9-2755
9-0710
8-8588
8-6381
8-4080
8-1725
7-9362

9-5544
10-5072
11-1723
11-6081
11-8709
12-0072
12-0527
12-0332
11-9669
11-8804
11-7908
11-6978
11-6012
11-5020
11-4012
11-2987
11-1946
11-0888
10-9811
10-8716
10-7601
10-6466
10-5310
10-4130
10-2927
10-1698
10-0443
9-9158
9-7843
9-6494
9-510§
9-3684
9-2218
9-0704
8-9139
8-7519
8-5836
8-4085
8-2258
8-0347
7-8341
7-6278
7-4201

43-58

44-59

45-60

46-61

47-62

48-63

49-64

50-65

51-66

52-67

53-68

54-69

55-70

56-71

57-72

58-73

59-74

60-75

61-76

62-77

63-78

64-79

65-80

66-81

67-82

68-83

69-84

70-85

71-86

72-87

73-88

74-89

75-90

76-91

77-92

78-93

79-94

80-95

81-96

82-97

83-98

84-99

8a-loo

S^cent

-8670

-5598

•2548

■9523

-6523

•3550

-0606

'7690

■4804

■1946

■9115

•6309

3523

0786

8129

5552

3057

0645

8317

6072

3911

1834

9841

7930

6102

4354

2686

1097

9585

8148

6785

5494

4273

3119

2031

1007

0044

9141

8295

7503

6765

6078

5439

4$" cent

-2479

-9787

•7103

-4429

•1767

•9118

•6484

•3865

-1262

-8674

■6100

■3537

■0983

•8464

•6009

3621

•1302

9052

6873

4767

2733

0773

8887

7074

5334

3668

2074

0552

9100

7718

6404

5157

3975

■2857

1801

0805

■9867

•8986

•8160

7386

6663

5989

5363

5 lucent

-6993

■4621

-2247

■9872

■7499

•5129

■2762

■0401

8044

5693 _

3344 5

•0998
•8649
6323
4050
1832
9670
7568
5525
3545
1628
9775
■798712

62652

■4608 2

■3017

■1492

■0033

■8638

■7307

6039

■4834

3690

2605

1579

0610

■9696

■8837

■8029

■7272

•6564

5904

5289

■2110

■0009

■7898

■5779

■3654

■1524

•9390

■7-253

■5112

■2968

-0820

-8664

-6498

-4346

■2236

■0170

■8152

■6182

■4264

•2399

•0589

■8835

•7138

■5499

■3920

•2399

•0938

•9537

•8196

■6913

■5689

■4523

■3415

•2362

■1365

■0422

■9531

■8692

7903

7162

6468

5821

5217

MEAN MORTALITY.

Tab. a. 6.

Shewing the values of Annuity on the joint continuance of two lives.

Difference of age Twenty yeaxs.

Ages.

accent

4^ cent

accent

6 #* cent

Ages.

accent

4#'cent

0-20

1-21

2-22

3-23

4-24

5-25

6-26

7-27

8-28

9-29

10-30

11-31

12-32

13-33

14-34

15-35

16-36

17-37

18-38

19-39

20-40

21--tl

22-42

23-43

24-44

25-45

26-46

27-47

28-48

29-49

30-50

31-51

32-52

33-53

34-54

35-55

36-56

37-57

38-58

39-59

7874
1535
0778
6515
9623
0827
0680
9582
7813
5761
3665
1525
9336
7115
4874
2614
0332
•8028
■5702
■3351
■0974
■8569
■6135
■3670
■1171
■8635
•6060
■3442
•0778
•8064
•5294
•2464
■9568
■6600
■3552
•0417
•7243
•4089
•0955
•7845

9520
1390
9513
4655
7558
8832
8944
8234
6938
5391
3803
2172
0495
■8784
■7052
•5297
■3520
■1718
■9891
■8038
•6155
•4243
■2299
■0321
■8307
■6253
•4157
•2015
•9824
7580
5276
2909
0472
7958
5360
2669
9929
7194
4466
■1747

10-5086

11-5511

12^2708

12^7334

13-0025

13-1305

13-1575

13-1125

13-0160

12-8971

12-7745

12-6479

12-5170

12-3830

12-2469

12-1086

11 •9680

11^8250

lb6794

11^5313

ir3803

11-2263

11-0692

10-9087

itff7445

10^5764

10^4042

10-2273

10-0455

9-8583

9-6651

9-4656

9-2589

9-0444

8-8214

8-5888

8-3508

8-1122

7-8732

7^6341

9-3533

10-2776

10-9201

ir3381

ir5869

11^7120

11 •7483

11^7211

11 •6480

ir5550

11-4586

11-3586

11-2548

11-1480

11-0393

10-9286

10-8157

10-7005

10-5830

10^4630

10-3404

10-2149

10^0865

9^9548

9^8196

9^6806

9^5377

9^3903

9^2381

9-0806

8-9174

8-7479

8-5714

8-3871

8-1943

7-9920

7-7839

7-5745

7-3640

7-1526

40-60
41-61
42-63
43-63
44-64
45-65
46-66
47-67
48-68
49-69
50-70
51-71
52-72
53-73
54-74
55-75
56-76
57-77
58-78
59-79
60-80
61-81
62-82
63-83
64-84
65-85
66-86
67-87
68-88
69-89
70-90
71-91
72-92
73-93
74-94
75-95
76-96
77-97
78-98
79-99

4763
1709
8688
5701
■2751
9840
6971
4144
1362
8625
5935
3291
0693
•8139
•5627
•3153
■0738
■8406
■6158
■3994
•1914
•9917
■8003
■6171
■4420
•2750
■1158
■9643
■8203
■6837
•5543
•4319
-3163
-2073
-1046
-0081
-9175
-8327
•7533
-6793

7-9040
7-6348
7-3673
7-1018
6-8386
6-5779
6-3198
6-0647
5-8126
5-5638
5-3182
5-0761
4-8372
4-6016
4-3690
4-1391
3-9138
3-6957
3-4848
3-2811
3-0848
2-8959
2-7143
2-5401
2-3732
2-2135
2-0610
1-9156
1-7771
1-6454
1-5205
1-4020
1-2900
1-1841
1-0843
-9903
-9020
8191
7415
6690

3951
1565
9186
6815
4456
2111
9781
7470
5178
2907
0660
8435
6234
4055
■1896
9754
•7648
•5604
•3621
•1702
•9846
•8056
•6331
•4672
•3078
•1550
•0088
•8691
•7357
•6087
•4880
•3733
•2646
•1618
•0647
-9731
■8869
•8060
•7301
•6591

9406
7281
5155
3029
0905
8787
6676
4574
2484
0406
8342
6293
4258
2238
0229
8230
6258
4338
■2471
0659
■8902
■7203
•5562
•3980
■2457
0994
9591
■8247
■6962
■5736
•4568
•3457
■2402
■1403
•0457
-9565
-8724
•7932
•7190
•6495

MEAN MORTALITY.

Tab. a. 9.
Shewing the values of Annuity on the joint continuance of two lives.
Difference of age Twmty-five years.

Ages.

3#'cent

4#'cent

5#'cent

6$" cent

Ages.

S^cent

4^ cent

S^cept

0-25

1-26

2-27

3-28

4-29

5-30

6-31

7-32

8-33

9-34

10-35

11-36

12-37

13-38

14-39

15-40

16-41

17-42

18-43

19-44

20-45

21-46

22-47

23-48

24-49

25-50

26-51

27-52

28-53

29-54

30-55

31-56

32-57

33-58

34-59

35-60

36-61

37-62

13-2444
14-5374
15-4054
15-9366
16-2155
16-3119
16-2787
16-1543
15-9654
15-7491
15-5280
15-3021
15-0710
14-8359
14-5983
14-3579
14-1146
13-8681
13-6182
13-3648
13-1076
12-8462
12-5803
12-3096
12-0336
11-7519
11-4640
11-1693
10-8672
10-5569
10-2376
9-9146
9-5934
9-2745
8-9582
8-6446
8-3342
8-0272

11-5549

12-6871

13-4563

13-9374

14-2020

14-3095

14-3048

14-2205

14-0796

13-9141

13-7440

13-5692

13-3894

13-2056

13-0190

12-8294

12-6366

12-4404

12-2407

12-0371

11-8294

11-6173

11-4004

11-1784

10-9508

10-7172

10-4769

10-2295

9-9742

9-7102

9-4367

9-1583

8-8804

8-6033

8-3271

8-0522

7-7790

7-5076

10-2110

11-2114

11-8977

12-3342

12-5828

12-6944

12-7079

12-6514

12-5447

12-4160

12-2831

12-1458

12-0038

11-8580

11-7094

11-5579

11-4032

11-2452

11-0837

10-9183

10-7489

10-5750

10-3965

10-2127

10-0234

9-8280

9-6259

9-4165

9-1991

8-9729

8-7370

8-4956

8-2535

8-0111

7-7687

7-5264

7-2846

7-0435

9-1247

10-0163

10-6326

11-0298

11-2620

11-3736

11-3987

11-3616

11-2797

11-1780

11-0725

10-9630

10-8493

10-7320

10-6121

10-4895

10-3639

10-2351

10-1030

9-9673

9-8276

9-6838

9-5354

9-3820

9-2231

9-0584

8-8871

8-7086

8-5222

8-3271

8-1222

7-9115

7-6994

7-4862

7-2722

7-0575

6-8424

6-6272

38-63

39-«4

40-65

41-66

42-67

43-68

44-69

45-70

46-71

47-72

48-73

49-74

50-75

51-76

52-77

53-78

54-79

55-80

56-81

57-82

58-83

59-84

60-85

61-86

62-87

63-88

64-89

65-90

66-91

67-92

68-93

69-94

70-95

71-96

72-97

73-98

74-99

75-100

•7239
•4246
•1296
-8392
-5535
•2729
-9975
•7275
•4632
■2047
9520
■7054
4648
2302
0015
7785
5610
3485
1424
9448
7554
■5742,2
•401012
2359 2
07852
■9288 1
78671
6518J1
■5242 1
•40341
2894 1
181911
0807 1
•9857
•8965
•8130
■7350
6622

•2384
■9718
-7079
■4471
•1896
•9357
•6856
4396
1979
9607
7281
■5003
2773
0592
8459
6373
4332

6-8035
6-5648
6-3277
6-0926
5-8596
5-6290
5-4012
5-1763
4-9546
4-7363
4-5215
4-3106
4-1034
3-9002
3-7009
3-5054
3-3135

3
3-233l'3-1248

-0386
-8514
-6716
•4992
-3340
■1761
■0253
■8815
■7447
•6147
•4913
■3744

2-9408
2-7634
2-.5924
2-4281
2-2704
2-1192
1-9745
1-8363
1-7045
1^5790
1-4598
1-3465

2639 1-2393
1595J1-1379
061M-0421

-9685
•8815
•7999
•7236
■6523

•9518
•8669
-7872
•7125
•6427

6^4122
6-1977
5-9838
5-7709
5^5593
5-3493
5-1410
4-9348
4-7308
4-5294
4-3306
4-1348
3-9419
3-7522
3-5655
3819
3-2012
3-0230
2^8487
2-6802
2^5175
2-3607
2^2099
2^0650
r9261
1-7931
16661
1-5449
1-4295
1-3197
1-2156
1-1170
1-0237
•9357
•8528
•7749
•7018
•6334

MEAN MORTALITY. 9

Tab, a. 10. Annuity on two joint lives. Difference of age Thirty years.

Ages..

3 f cent

4^ cent

accent

■

6^ cent

Ages.

3 f cent

4^cent

5#'cent

6#'cent

0-30

12-6436

11-1094

9-8733

8-8635

35-65

7-2435

6-8102

6-4201

6-0676

1-31

13-8550

12-1792

10-8255

9-7170

36-66

6-9483

6-5454

6-1816

5-8519

2-32

14-6595

12-8991

11-4730

10-3025

37-67

6-6580

6-2841

5-9453

5-6375

3-33

15-1423

13-3417

11-8788

10-6750

38-68

6-3731

6-0265

5-7116

5-4247

4-34

15-3844

13-5762

12-1027

10-8871

39-69

6-0936

5-7729

5-4808

5-2139

5-35

15-4524

13-6597

12-1943

10-9820

40-70

5-8198

5-5237

5-2531

5-0052

6-36

15-3968

13-6352

12-1908

10-9926

41-71

5-5520

5-2790

5-0288

4-7991

7-37

15-2541

13-5342

12-1195

10-9427

42-72

5-2903

5-0391

4-8082

4-5956

8-38

15-0497

13-3783

11-9992

10-8488

43-73

5-0350

4-8042

4-5915

4-3952

9-39

14-8185

13-1982

11-8570

10-7351

44-74

4-7861

4-5745

4-3790

4-1980

10-40

14-5820

13-0130

11-7100

10-6169

45-75

4-5439

4-3502

4-1708

4-0043

11-41

14-3398

12-8222

11-5578

10-4940

46-76

4-3084

4-1315

3-9672

3-8144

12t42

14-0917

12-6255

11-4000

10-3659

47-77

4-0798

3-9185

3-7683

3-6283

13-43

13-8388

12-4239

11-2375

10-2334

48-78

3-8581

3-7113

3-5743

3-4462

14-44

13-5820

12-2183

11-0709

10-0971

49-79

3-6433

3-5100

3-3853

3-2684

15-45

13-3212

12-0084

10-9002

9-9567

50-80

3-4354

3-3146

3-2013

3-0949

16-46

13-0561

11-7938

10-7248

9-8120

51-81

3-2343

3-1251

3-0224

2-9257

17-47

12-7863

11-5743

10-5445

9-6625

52-82

3-0399

2-9414

2-8485

2-7610

18-48

12-5115

11-3495

10-3589

9-5079

53-83

2-8520

2-7633

2-6796

2-6004

19-49

12-2312

11-1189

10-1675

9-3477

54-84

2-6703

2-.5907

2-5153

2-4440

20-50

11-9450

10-8820

9-9698

9-1813

55-85

2-4941

2-4229

2-3553

2-2912

21-51

11-6523

10-6383

9-7652

9-0084

56-86

2-3247

2-2610

2-2005

2-1430

22-52

11-3527

10-3872

9-5532

8-8279

57-87

2-1631

2-1063

2-0523

2-0009

23-53

11-0454

10-1280

9-3329

8-6394

58-88

2-0093

1-9588

1-9106

1-8647

24-54

10-7298

9-8600

9-1036

8-4419

59-89

1-8630

1-8182

1-7754

1-7344

25-55

10-4050

9-5823

8-8644

8-2345

60-90

1-7243

1-6845

1-6465

1-6100

26-56

10-0763

9-2996

8-6196

8-0211

61-91

1-5927

1-5575

1-5238

1-4915

27-57

9-7496

9-0172

8-3741

7-8063

62-92

1-4682

1-4372

1-4073

1-3787

28-58

9-4251

8-7357

8-1282

7-5903

63-93

1-3505

1-3232

1-2969

1-2715

29-59

9-1033

8-4551

7-8822

7-3734

64-94

1-2395

1-2155

1-1923

1-1699

30-60

8-7843

8-1758

7-6363

7-1558

65-95

1-1350

1-1138

1-0934

1-0738

31-61

8-4685

7-8982

7-3910

6-9378

66-96

1-0366

1-0181

1-0002

•9829

32-62

8-1562

7-6225

7-1463

6-7197

67-97

-9443

-9281

-9124

-8973

33-63

7-8477

7-3491

6-9028

6-5018

68-98

•8577

-8436

-8299

-8167

34-64

7-5434

7-0782

6-6606

6-2843

69-99

-7767

•7644

-7525

-7409

Tab. A. 11. Annuity on two joint lives. Difference of age I%irty.^ue years.

3 f cent

6 f cent

6#'cent

Ages.

3 ^ cent

'cent

accent 6^ cent

0-35

1-36

2-37

3-38

4-39

5-40

6-41

7-42

8-43

9-44

10-45

11-46

12-47

13-48

11-9776
13-0971
13-8296
14-2566
14-4554
14-4893
14-4059
14-2397
14-0145
13-7630
13-5050
13-2401
12-9680
12-6894

6070
6052
2679
6651
8634
9173
8678
■7447
5687
3685
1618
9484
7276
5003

4876
3832
9850
3538
5475
•6137
•5882
•4969
•3579
•1968
•0296
■8558
•6750
■4877

8-5619

9-3705

9-9190

10-2612

10-4481

10-5215

10-5129

10-4453

10-3345

10-2035

10-0668

9-9240

9-7745

9-6188

14-49
15-50
16-51
17-52
18-53
19-54
20-55
21-56
22-57
23-58
24-59
25-60
26-61
27-62

4052
1149
8179
5138
2018
8813
5515
2178
8859
5564
2294
■9054
'5846
•2673

2669
0271
7803
5259
2632
9914
7098
4231
■1368
■8511
■5665
■2832
■0015
•7217

2944 9'

0946'9'

8878'9'

6733"

4504

2184

9762

7282

4795

2304

9811

7320

4833

2353

4573
2895
1149
9327
7422
5426
3329
1171
8998
6812
4617
2414
0207
7999

10

MEAN MORTALITY.
Tab. a. n.—{Continwd.)

Ages.

Sfcent

4^ cent

5 #"06111

6^ cent

Age*.

accent

4^ cent

5f cent

erceat

28-63

7-9540

7-4443

6-9884

6-5792

47-82

3-0S29

2^9818

2-8866

2^7969

29-64

7-6449

7-1694

6-7429

6-3589

48-83

2-8953

2^8041

2-7181

2-6368.

30-65

7-3403

6-8975

6-4991

6-1394

49-84

2-7149

2-6328

2-5553

2-4818

31-66

7-0404

6-6288

6-2573

5-9209

50-55

2-5417

2-4680

2-3982

2'3320

32-67

6-7457

6-3636

6-0178

5-7037

51-86

2-3756

2-3095

2-2468 ^•1872|

33-68

6-4563

6-1023

5-7809

5-4882

52-87

2-2163

2-1572

g'lOlO

2-0475

34r-69

6-1726

5-8451

5-5469

5-2746

53-88

2-0637

2-0110

1^9607

1-9128

35-70

5-8947

5-5923

5-3161

5-0633

54-89

1-9173

1-8704

1^8256

1-7828

36-71

5-6229

5-3441

5-0888

4-8545

55-90

1-7767

1-7351

1-6952

16571

37-72

5-3574

5-1009

4-8653

4-6485

56-91

1-6424

1-6055

1-5702

1^53e3

38-73

5-0985

4-8628

4-6458

4-4456

57-92

1-5152

1-4826

1-4514

1-4213

39-74

4-8462

4-6301

4-4306

4-2460

58-93

1-3949

1-3662

1-3386

1-3120

40-75

4-6007

4-4029

4-2198

4-0500

59-^94

1-2814

1-2561

1-2318

1^2083

41-76

4-3622

4-1815

4-0138

3-8579

60-95

1-1744

1-1522

1-1307

MlOl

42-77

4-1309

3-9661

3-8127

3-6698

61-96

1-0737

1^0542

1-0354

1^0172

43-78

3-9067

3-7567

3-6167

3-4860

62-97

•9790

•9620

•9455

•9295

44-79

3-6898

3-5534

3-4260

3-3067

63-98

•8903

•8754

•8610

•8470

45-80

3-4801

3-3565

3-2407

3-1319

64-99

-8072

•7942

•7816

•7694

46-81

3-2779

3-1659

3-0608

2-9620

65-100

•7295

•7182

■7073

•6967

Tab. a. 12. Annuity on two joint lives. Difference of age Forti/ years.

0-40

1-41

2-42

3-43

4-44

5-45

6-46

7-47

8-48

9-49

10-50

11-51

12-52

13-53

14-54

15-55

16-56

17-57

18-58

19-59

20-60

21-61

22-62

23-63

24-64

25-65

26-66

27-67

28-68

29-69

3®" cent

•2352
•2501
8994
2609
4078
3994
■28'J5
■0830
•8292
•5490
■2604
-9629
-6559
-3398
0150
-6807
-3424
■0060
-6718
•3403
•0118
-6865
•3649
-0472
•7338
-4249
•1209
-8221
-.5288
-2412

4#'cent

10

10

11

11

12

12

11

11

11

11

11

10

10

10-

10-
9-
9'
9-
8-
8'
8
8
7'
7
7
6
6
6
6
5

0357
■9504
5453
■8878
0414
■0575
•9751
■8220
■6176
■3885
■1510
-9044
-6481
-3822
-1072
-8222
-5319
-2420
-9527
-6644
3775
0922
8088
5277
2493
■9738
•7016
•4330
■1683
■9078

d#'cent

6^ cent

9-0414

9-8699

10-4161

10-7392

10-8945

10-9274

10-8721

10-7530

10-5870

10-3981

10-2009

9-9949

9-7791

9-5539

9-3194

9-0745

8-8238

8-5723

8-3203

8-0681

7-8160

7-5643

7-3134

7-0635

6-8150

6-5682

6-3235

6-0810

5-8412

5-6044

3#'cent

8-2085

8-9625

9-4653

9-7692

9-9232

9-9676

9-9324

9-8394

9-7035

9-5464

9-3814

9-2079

9-0250

8-8328

8-6313

8-4i95

8-2016

7-9820

7-7612

7-5393

7-3166

7-0935

6-8702

6-6470

6-4242

6-2022

5-9812

5-7615

5-5435

5-3275

30-70

31-71

32-72

33-73

34-74

35-75

36-76

37-77

38-78

39-79

40-80

41-81

42-82

43-83

44-84

45-85

46-86

47-87

48-88

49-89

50-90

51-91

52-92

53-93

54-94

55-95

56-96

57-97

58-98

69-99

4^isent

5f cent

9595

6841

4151

1527

8971

6485

4070

1728

9458

7263

5142

3097

1126

9230

7409

5663

•3990

•2389

■0860

•9402

•8013

■6691

•5434

-4240

-3105

-2025

-1001

-0038

•9135

•8289

e^cenl

6517

4004

1540

9129

6773

4474

2233

0052

7934

5878

3886

1960

0099

8304

6576

4914

3318

•1788

■0323

■8923

•7587

•6312

•5099

•3943

-2844

■1794

•0799

•9862

•8981

•8155

5-3708

5-1407

4-9145

4-6923

4-4745

4-2613

4-0529

3-8495

3-6512

3-4583

3-2710

3-0892

2-9132

2-7431

2-5788

2-4204

2-2681

2-1216

1-9812

1^8466

1-7179

1-5950

1-4777

1-3658

1^2592

M573

r0604

•9691

•8831

j ^8024

5^113?

4f902k

4-6941

4-488S

4-2870

4-0888

3-8945

3-7043

3-5185

3-3372

3-1606

2-9889

2-8222

2-6606

2-5042

2-3532

2-2075

2-0672

9324

1-8030

6789

1-5602

1 4468

1-3384

1-2349

1-1359

1-0416

•9526

•8687

■7898

12

MEAN MORTALITY.
Tab. a. 14. — Continued.

Ages.

3f cent

4#'cent

S^-ceiit

6^ cent

Ages.

3#'cent

4#'cent

accent

6^ cent

20-70

6-0661

5-7494

5-4606

5-1965

35-85

2-6034

2^5268

2-4543

2^3855

21-71

5-7846

5-4928

5-2259

4-9812

36-86

2-4331

2^3645

2-2993

2^2375

22-72

5-5097

5-2413

4-9952

4-7689

37-87

2-2703

2^2089

2-1505

2^0949

23-73

5-2416

4-9952

4-7686

4-5598

38-88

2-1149

2-0600

2-0078

1^9580

24-74

4-9806

4-7548

4-5465

4-3541

39-89

1-9667

1-9178

1-8711

1^8266

25-75

4-7267

4-5201

4-3291

4-1522

40-90

1-8256

1-7821

1-7405

1^7007

26-76

4-4801

4-2915

4-1167

3-9543

41-91

1-6915

1-6529

1-6159

r5804

27-77

4-2410

4-0691

3-9093

3-7606

42-92

1-5642

1-5300

1-4971

1^4656

28-78

4-0094

3 8530

3-7073

3-5713

43-93

1-4436

1-4133

1-3842

1-3562

29-79

3-7855

3-6435

3-5108

3-3867

44-94

1-3294

1-3026

1-2769

1^2521

30-80

3-5692

3-4405

3-3200

3-2069

45-95

1-2215

1-1979

M752

1-1533

31-81

3-3607

3-2442

3-1349

3-0322

46-96

1-1197

1-0990

1-0790

1-0597

32-82

3-1598

3-0546

2-9557

2-8625

47-97

1-0239

1-0057

-9881

•9711

33-83

2-9667

2-8719

2-7825

2-6981

48-98

•9337

•9178

•9024

•8874

34^84

2-7812

2-6959

2-6153

2-5391

49-99

•8491

-8352

•8217

•8086

Tab. a. 15.

Shewing the values of Annuity on the joint continuance of two lives.
Difference of age Fifty-five years.

Ages.

accent

4fcent

5^cent

6^ cent

Ages.

accent

4^cent

5#'cent

6#'cent

0-55

8-3250

7-6647

7-0902

6-5873

23-78

4-0354

3-8773

3-7302

3-5928

1-56

8-9042

8-2072

7-5990

7-0652

24-79

3-8096

3-6661

3-5322

3-4068

2-57

9-2064

8-4988

7-8794

7-3343

25-80

3-5916

3-4616

3-3399

3-2258

3-58

9-2984

8-5992

7-9852

7-4432

26-81

3-3814

3-2638

3-1534

3-0498

4-59

9-2395

8-5614

7-9641

7-4353

27-82

3-1790

3-0728

2-9730

2-8789

5-60

9-0762

8-4274

7-8540

7-3448

28-83

2-9844

2-8887

2-7985

2-7134

6-61

8-8427

8-2278

7-6826

7-1970

29-84

2-7976

2-7115

2-6302

2-5533

7-62

8-5628

7-9842

7-4696

7-0099

30-85

2-6184

2-5412

2-4680

2-3987

8-63

8-2531

7-7116

7-2285

6-7956

31-86

2-4470

2-3777

2^3120

2-2496

9-64

7-9342

7-4291

6-9770

6-5707

32-87

2-2830

2-2211

2^1622

2-1061

10-65

7-6188

7-1485

6-7262

6-3455

33-88

2-1265

2-0712

2^0185

1-9683

11-66

7-3072

6^8700

6-4763

6-1204

34-89

1-9773

1-9280

1-8810

1-8361

12-67

6-9995

6-5939

6-2275

5-8954

35-90

1-8353

1-7915

1-7495

1-7094

13-68

6-6969

6-3213

5-9810

5-6716

36-91

1-7004

1-6614

1-6241

1-5884

14-69

6-4002

6-0529

5-7374

5-4497

37-92

.1-5723

1-5378

1-5047

1-4729

15-70

6-1097

5-7893

5-4972

5-2302

38-93

1-4509

1-4204

1-3910

1^3628

16-71

5-8257

5-5305

5-2607

5-0133

39-94

1-3360

1-3091

1-2831

r2582

17-72

5-5483

5-2769

5-0281

4-7994

40-95

1-2275

1-2038

1-1809

1-1588

18-73

5-2779

5-0288

4-7997

4-5886

41-96

1-1252

1-1043

1-0841

1-0647

19-74

6-0146

4-7863

4-5759

4-3814

42-97

1-0288

1-0104

•9927

-9756

20-75

4-7586

4-5498

4-3568

4-1780

43-98

•9381

•9221

•9065

•8915

21-76

4-5099

4-3193

4-1426

3-9786

44-99

-8531

•8391

•8255

•8123

22-77

4-2688

4-0951

3-9337

3-7834

45-100

•7734

-7612

•7493

•7378

MEAN MORTALITY.

Tab. a, 16.

Shewing the values of Annuity on the joint continuance of two lives!

Difference of age Sixty years.

13

Ages.

3f cent

4 f cent

S^'oent

6#'cent

Ages.

S^cent

4^ cent

Sfcent

6*" cent

0-60

7-1091

6-6150

6-1782

5-7899

20-80

3-6111

3-4800

3-3572

3-2422

1-61

7-5510

7-0340 6-5756

6-1671

21-81

3-3995

3-2809

3-1696

3-0651

2-62

7-7584

7-2380 6-7751

6-3616

22-82

3-1957

3-0887

2-9880

2-8932

3-63

7-7905

7-2804

6-8254

6-4178

23-83

2-9998

2-9034

2-8125

2-7267

4^4

7-6983

7-2077

6-7687

6-3744

24-84

2-8118

2-7250

2-6431

2-5656

5-65

7-5216

7-0560

6-6381

6-2616

25-85

2-6315

2-5537

2-4799

2-4101

6-66

7-2891

6-8516

6-4576

6-1016

26-86

2-4590

2-3892

2-3230

2-2601

7-67

7-0210

6-6127

6-2440

5-9098

27-87

2-2941

2-2316

2-1723

2-1159

8-68

6-7308

6-3519

6-0087

5-6968

28-88

2-1366

2-0809

2-0278

1-9773

9-69

6-4355

6-0851

5-7667

5-4765

29-89

1-9866

1-9369

1-8895

1-8443

10-70

6-1455

5-8220

5-5272

5-2578

30-90

1-8438

1-7996

1-7574

1-7170

11-71

5-8609

5-5629

5-2905

5-0408

31-91

1-7080

1-6688

1-6313

1-5953

12-72

5-5820

5-3080

5-0568

4-8259

32-92

1-5793

1-5445

1-5112

1-4792

13-73

5-3096

5-0580

4-8268

4-6138

33-93

1-4572

1-4265

1-3970

1-3686

14r-74

5-0443

4-8138

4-6014

4-4052

34-94

1-3418

1-3146

1-2886

1-2634

15-75

4-7864

4-5756

4-3808

4-2005

35-95

1-2327

1-2088

i-1858

1-1636

16-76

4-5359

4-3435

4-1653

3-9998

36-96

1-1298

1-1088

1-0886

1-0690

17-77

4-2931

4-1178

3-9549

3-8034

37-97

1-0330

1-0146

■9967

•9795

18-78

4-0579

3-8985

3-7500

3-6115

38-98

•9419

•9258

-9102

•8951

19-79

3-8306

3-6859

3-5508

3-4244

39-99

-8565

•8424

-8287

•8155

Tab. a. ir.

Shewing the values of Annuity on the joint continuance of two lives.

Difference of Age Sixty-Jive years.

Ages.

a^eetA

4f cent

5 f cent

6^ cent

Ages.

3f cent

4#'cent

5#'cent

efcent

0-65

5-9277

5-5724

5-2533

4-9655

18-83

3-0133

2^9161

2-8246

2^7382

1-66

6-2457

5-8776

5-5461

5-2463

19-84

2-8242

2-7368

2-6543

2-5763

2-67

6-3715

6-0044

5-6729

5-3723

20-85

2-6429

2-5645

2-4903

2-4200

3-68

6-3558

5-9993

5-6764

5-3830

21-86

2-4695

2-3992

2-3326

2-2693

4-69

6-2418

5-9020

5-5933

5-3120

22-87

2-3036

2-2408

2-1811

2-1243

5-70

6-0622

5-7425

5-4513

5-1852

23-88

2-1454

2-0893

2-0359

1-9851

6-71

5-8406

5-5428

5-2707

5-0214

24-89

1-9946

1-9446

1-8970

1-8515

7-72

5-5931

5-3177

5-0653

4-8335

25-90

1-8511

1-8067

1-7642

1-7236

8-73

5-3305

5^0772

4-8445

4-6301

26-91

1-7147

1-6753

1-6375

1-6014

9-74

5-0664

4-8342

4-6203

4-4227

27-92

1-5853

1-5504

1-5169

1-4847

10-75

4-8089

4-5965

4-4003

4-2186

28-93

1-4627

1-4318

1-4022

1-3736

11-76

4-5581

4-3642

4-1846

4-0178

29-94

1-3468

1-3195

1-2933

1-2680

12-77

4-3142

4-1375

3-9734

3-8207

30-95

1-2372

1-2132

1-1901

1-1677

13-78

4-0776

3-9169

3-7674

3-6278

31-96

1-1339

1-1128

1-0924

1-0728

14-79

3-8489

3-7030

3-5669

3-4396

32-97

1-0367

1-0181

1-0002

•9829

15-80

3-6281

3-4959

3-3723

3-2565

33-98

-9452

-9290

•9133

•8981

16-81

3-4152

3-2957

3-1837

3-0784

34-99

-8595

•8453

-8315

•8182

17-82

3-2103

3-1024

3-0010

2-9056

35-100

•7791

•7668

•7548

•7432

14 MEAN MORTALITY.

Tab. a. 18. Annui^ on two joiftt li^es. Difference of age Seventy years.

Ages.

3$" cent

4^ cent

6#'cent

6^ cent

Ages.

3#'ceBt

4$'cent

decent

6^ cent

0-70

4-8166

4-5717

4-3483

4-1440

15-85

2-6528

2-5740

2-4993

2-4286'

1-71

5-0284

4-7774

4-5480

4-3376

16-86

2-4785

2-4079

2-3409

2-2773

2-72

5-0881

4-8404

4-6134

4-4048

17-87

2-3120

2-2488

2-1888

2-1317

3-73

5-0382

4-8000

4-5812

4-3795

18-88

2-1530

2-0966

2-0430

1-9918

4-74

4-9138

4-6889

4-4817

4-2904

19-89

2-0016

1-9513

1-9034

1-8577

6-75

4-7411

4-5315

4-3379

4-1587

20-90

1-8574

1-8128

1-7701

1-7293

6-7f5

4-5386

4-3452

4-1660

3-9997

21-91

1-7205

1-6809

1-6429

1-6066

7-77

4-3188

4-1415

3-9769

3-8238

22-92

1-5906

\-5655

1-5218

1-4895

8-78

4'0898

3-9283

3-7779

3-6377

23-93

1-4675

1-4365

1-4066

1-3780

9-79

3-8620

3-7153

3-5784

3-4504

24-94

1-3511

1-3237

1-2973

1-2720

10-80

3-6415

3-5086

3-3843

3-2677

25-95

1-2411

1-2170

1-1938

1-1713

11-81

3-4285

3-3083

3-1956

3-0897

26-96

1-1375

1-1162

1-0958

1-0760

12-82

3-2229

3-1144

3-0124

2-9164

27-97

1-0398

1-0212

1-0033

-9859

13-83

3-0249

2-9272

2-8351

2-7482

28-98

•9481

-9318

•9160

■9008

14-84

2-8349

2-7470

2-6641

2-5856

29-99

-8620

-8478

-8340

-8207

Tab. a. 19.

Annuit)

1 on two

joint lives. Difference of age SeoeTrfy^oe

years.

Ages.

S^'eent

4^tieiit

Sfcent

e^^ccnt

Ages.

3#'cdit

Woeta

S^oeni

6 f cent

0-75

3-8065

3-6448

3-4953

3-3567

13-88

2-1597

2-1030

2-0491

1-9977

1-76

3-9322

3-7686

3-6169

3-4761

14-89

2-0076

1-9572

1-9090

1-8631

2-77

3-9425

3-7828

3-6345

3-4965

15-90

1-8630

1-8181

1-7752

1-7342

3-78

3-8716

3-7197

3-5783

3-4463

16-91

1-7255

1-6857

1-6476

1-6111

4-79

3-7471

3-6052

3-4726

3-3488

17-92

1-5952

1-5599

1-5261

1-4936

5-80

3-5892

3-4582

3-3356

3-2207

18-93

1-4717

1-4405

1-4105

1-3818

6-81

3-4117

3-2920

3-1796

3-0741

19-94

1-3548

1-3273

1-3009

1-2754

7-82

3-2239

3-1152

3-0130

2-9168

30-95

1-2445

1-2203

1-1970

1-1745

8-83

3-0316

2-9335

2-8410

2-7538

21-96

M406

1-1192

1-0987

1-0788

9-84

2-8423

2-7540

2-6707

2-5919

22-97

1-0426

1-0239

1-0059

•9884

10-85

2-6605

2-5813

2-5063

2-4352

23-98

-9506

-9342

-9184

-9031

11-86

2-4862

2-4152

2-3479

2-2840

a4r-99

•8643

-8500

-8361

-8227

12-87

2-3192

2-2567

2-1954

2-1381

' 25-100

•7834

-7709

-7589

•7472

Ta

B. A. 20

. Annuity on two joint lives. Difference

of age Eighty years.

Ages.

S^cent

4^cent

5#'cent

e^cent

Ages.

3$* cent

4^cent 5$" cent

fi^cent

0-80

2-9189

2-8168

2-7212

2-6315

10-90

1-8671

1-8221

1-7791

1-7379

1-81

2-9795

2-8776

2-7820

2-6921

11-91

1-7297

1-6898

1-6515

1-6149

2-82

2-9565

2-8582

2-7659

2-6789

12-92

1-5991

1-5637

1-5298

1-4972

3-83

2-8764

2-7840

2-6970

2-6148

13-93

1-4752

1-4440

1-4139

1-3850

4-84

2-7601

2-6746

2-5940

2-5177

14-94

1-3581

1-3305

1-3039

1-2784

5-85

2-6223

2-5442

2-4703

2-4004

15-95

1-2475

1-2232

1-1997

1-1772

6-86

2-4730

2-4023

2-3353

2-2717

16-96

1-1432

1-1218

1-1012

1-0813

7-87

2-3186

2-2551

2-1947

2-1373

17-97

1-0450

1-0262

1-0081

-9907

8-88

2-1631

2-1063

2-0522

2-0007

18-98

-9527

-9363

-9205

-9051

9-89

2-0H5

1-9609

1-9126

1-8666

19-99

•8662

-8618

-8380

-8246

MEAN MORTALITY.

15

Tab, a. 21.

The Expectation of complete years, at all ages; or the value of Annuity of £1, when

there is no interest of money.

1

Expect".

i

Expect".

Expect".

i

Expfct".

i

Expect".

<

Expect".

38-6889

17

40-1971

34

28-8037

51

18-1134

68

8-5296

85

2-9926

1

42-6499

18

39-4991

35

28-1617

52

17-4864

69

8-0902

86

2-7830

2

45-2746

19

38-8048

36

27-5223

53

16-8575

70

7-6657

87

2-5844

3

46-8415

20

38-1141

37

26-8853

54

16-2260

71

7-2562

88

2-3964

4

47-6209

21

37-4270

38

26-2505

55

15-5915

72

6-8614

89

2-2186

6

47-8365

22

36-7435

39

25-6179

56

14-9621

73

6-4813

90

2-0507

6

47-6587

23

36-0635

40

24-9873

57

14-3464

74

6-1158

91

1-8923

7

47-2110

24

35-3871

41

24-3584

58

13-7447

75

5-7646

92

1-7431

8

46-5802

25

34-7141

42

23-7310

59

13-1572

76

5-4277

93

1-6027

9

45-8776

26

34-0446

43

^3-1050

60

12-5840

77

5-1047

94

1-4707

10

45-1705

27

33^3785

44

22-4802

61

12-0253

78

4-7955

95

1-3468

11

44-4589

28

32-7156

45

21-8561

62

11-4812

79

4-4997

96

1-2307

12

43-7427

29

32-0560

46

21-2327

63

10-9519

80

4-2172

97

1-1219

13

43-0262

30

31-3996

47

20-6096

64

10-4375

81

3-9476

98

1-0203

14

42-3133

31

30-7462

48

19-9865

65

9-9380

82

3-6907

99

•9253

15

41-6042

32

30-0958 49

19-3630

66

9-4535 83

3-4461

16

40-8988

33

29-4484 50

18-7387

67

8-9841 84

3-21351

Part the Second of Tab. A. 3.
Shewing the values of Annuity on a single life at any age.

<

7#'cent

accent

<

7 f cent

8 ^ cent

1

7f cent

8 f cent

7#'cent

5#'cent

9-6931

8-6518

25

11-6571

10-5084

50

9-2331

8-5408

75

4-1700

4-0057

1

10-7016

9-5421

26

11-5918

10-4571

51

9-0770

8-4085

76

3-9752

3-8238

2

11-4238

10-1813

27

11-5249

10-4044

52

8-9124

8-2682

77

3-7840

3-6448

3

11-9165

10-6192

28

11-45(52

10-3503

53

8-7386

8-1191

78

3-5967

3-4690

4

12-2351

10-9044

29

11-3856

10-2946

54

8-5547

7-9604

79

3-4137

3-2968

5

12-4257

11-0774

30

11-3132

10-2373

55

8-3597

7-7908

80

3-2351

3-1282

6

12-5240

11-1692

31

11-2388

10-1784

56

8-1575

7-6141

81

3-0610 2-96361

7

12-5560

11-2025

32

11-1622

10-1177

57

7-9528

7-4345

S2

2-8918

2-8032

8

12-5400

11-1933

33

11-0835

10-0551

58

7-7457

7-2521

83

2-7276

2-6471

9

12-5034

11-1660

34

11-0024

9-9905

59

7-5366

7-0674

84

2-5685

2-4955

10

12-4641

11-1362

35

10-9189

9-9239

60

7-3258

6-8803

85

2-4145

2-3486

11

12-4217

11-1039

36

10-8328

9-8550

61

7-1135

6-6913

86

2-2659

2-2064

12

12-3761

11-0688

37

10-7440

9-7838

62

6-9000

6-5007

87

2-1227

2-0691

13

12-3283

11-0318

38

10-6523

9-7100

63

6-6857

6-3085

88

1-9848

1-9367

14

12-2793

10-9938

39

10-5575

9-6336

64

6-4709

6-1153

89

1-8525

1-8093

15

12-2292

10-9550

40

10-4594

9-5543

65

6-2559

5-9212

90

1-7256

1-6870

16

12-1779

10-9151

41

10-3577

9-4719

66

6-0410

5-7267

91

1-6041

1-5697

17

12-1254

10-8743

42

10-2523

9-3862

67

5-8266

5-5319

92

1-4881

1-4574

18

12-0716

10-8325

43

10-1429

9-2968

68

5-6131

5-3372

93

1-3775

1-35Q2

19

12-0166

10-7896

44

10-0291

9-2036

69

5-4007

5-1430

94

1-2722

1-2480

20

11-9602

10-7457

45

9-9106

9-1061

70

5-1899

4-9496

95

1-1722

1-1507

21

11-9025

10-7006

46

9-7870

9-0040

71

4-9809

4-7573

96

1-0773

1-0584

22

11-8434

10-6544

47

9-6580

8-8970

72

4-7741

4-5665

97

•9875

•9708

23

11-7828

10-6070

48

9-5230

8-7844

73

4-5698

4-3774 98

-9027

•8880

24

11-7207

10-5583

49

9-3816

8-6659

74

4-3684

4-1904 99

-8227

•8099

16

MEAN MORTALITY.

Tab&. a. 22 — 29. Shewing the probability of the Younger or the Elder of two lives being Jirst in the

order of Decease.
A. 22. A. 23.

Difference of age Ten years. Difference of age Twenty yeaia.

Ages.

Younger

Elder.

Ages.

Younger

Elder.

0-10

•55552

•44448

45-55

•33932

•66068

1-11

•50211

•49789

46-66

•33594

•66406

2-12

•46300

•53700

47-57

•33271

•66729

3-13

•43555

•56445

48-58

•32966

•67034

4-14

•41699

•58301

49-59

•32683

•67317

5-15

•40496

•59504

50-60

•32425

•67575

6-16

•39759

'60241

51-61

•32199

•67801

7-17

•39350

•60650

52-62

•32010

•67990

8-18

•39171

•60829

53-63

•31864

•68136

9-19

•39085

•60915

54-64

•31769

•68-231

10-20

•39007

•60993

55-65

•31736

■68264

11-21

•38938

•61062

56-66

•31738

•68262

12-22

•38876

•61124

57-67

•31739

•68261

13-23

•38818

•61182

58-68

•31740

•68260

14-24

•38758

•61242

59-69

•31742

•68258

15-25

•38694

•61306

60-70

•31744

•68256

16-26

•38627

•61373

61-71

•31746

•68254

17-27

•38558

•61442

62-72

•31748

•68252

18-28

•38485

•61515

63-73

•31750

•68250

19-29

•38408

•61592

64-74

•31753

•68247

20-30

•38328

•61672

65-75

•31757

•68243

21-31

•38244

•61756

66-76

•31761

•68239

22-32

•38155

•61845

67-77

•31765

•68235

23-33

•38062

•61938

68-78

•31770

•68230

24-34

•37964

•62036

69-79

•31776

•68224

25-35

•37862

•62138

70-80

•31782

•68218

26-36

•37763

•62247

71-81

•31789

■68211

27-37

•37639

•62361

72-82

•31798

■68202

28-38

•37519

•62481

73-83

•31807

•68193

29-39

•37392

•62608

74-84

•31818

•68182

30-40

•37259

•62741

75-85

•31831

•68169

31-41

•37117

•62883

76-86

•31846

•68154

32-42

•36968

•63032

77-87

•31862

•68138

33-43

•36810

•63190

78-88

•31881

•68119

34-44

•36642

■63358

79-89

•31903

■68097

35-45

•36465

•63535

80-90

•31929

■68071

36-46

•36276

•63724

81-91

•31958

■68042

37-47

•36077

•63923

82-92

•31991

■68009

38-48

•35864

•64136

83-93

•32029

■67971

39-49

•35639

•64361

84-94

•32072

•67928

40-50

•35398

•64602

85-95

•32120

•67880

41-51

•35142

•64858

86-96

•32173

•67827

42-52

•34869

•65131

87-97

•32231

•67769

43-53

•34578

•65422

88-98

•32294

•67706

44-54

•34266

•65734

89-99

•32362

•67638

Ages.

0-20

1-21

2-22

3-23

4-24

5-25

6-26

7-27

8-28

9-29

10-30

11-31

12-32

13-33

14-34

15-35

16-36

17-37

18-38

19-39

20-40

21-41

22-42

23-43

24-44

25-45

26-46

27-47

28-48

29-49

30-50

31-51

32-52

33-53

34-54

35-55

36-56

37-57

38-58

39-59

Younger

•48833

•42672

•38155

•34975

•32814

•31398

•30515

■30006

•29760

•29620

■29487

■29361

•29242

•29125

■29001

•28872

■28736

28593

■28443

28285

28119

27944

27759

27564

27358

'27141

26911

26668

26411

26138

25849

25542

25216

24869

24499

24105

23698

23292

22886

22482

Elder.

•51167

•57328

•61845

•65025

•67186

•68602

•69485

•69994

•70240

•70380

•70513

•70639

•70758

■70875

•70999

■71128

■71264

■71407

•71557

■71715

■71881

'72056

72241

72436

72642

72859

73089

73332

73589

73862

74151

74458

74784

75131

75501

75895

76302

76708

77114

'77518

Ages.

Younger

40-60

41-61

42-62

43-63

44-64

45-65

46-66

47-67

48-68

49-69

50-70

51-71

52-72

53-73

54-74

55-75

56-76

57-77

58-78

59-79

60-80

61-81

62-82

63-83

64-84

65-85

66-86

67-87

68-88

69-89

70-90

71-91

72-92

73-93

74-94

75-95

76-96

77-97

78-98

79-99

Elder.

•22081

•21684

•21292

•20905

•20527

•20159

•19802

•19460

•19135

•18831

•18552

•18304

•18094

•17930

•17822

•17785

•17788

•17792

•17797

•17801

•17807

•17813

•17820

•17829

•17838

•17849

•17861

•17876

•17892

•17911

•17932

•17957

•17985

•18018

•18055

•18098

•18147

•18202

•18263

•18329

■77919
■78316
•78708
79095
79473
79841
80198
80540
•80865
•81169
•81448
•81696
•81906
•82070
•82178
•82215
•82212
•82208
•82203
•82199
•82193
•82187
•82180
•82171
■82162
•82151
•82139
•82124
•82108
•82089
■82068
■82043
■82015
•81982
•81945
•81902
•81853
■81798
•81737
•81671

MEAN MORTALITY.

17

Tabs. A. 22 — 29. Shewing the probability of the Younger or the Elder of two lives being^rrf in the

order of Decease.

A. 24.
Difference of age Thirty years.

Ages.

Younger

Elder.

Ages.

Younger

Elder.

0-30

•43362

•56638

35-65

•14682

•85318

1-31

•36569

•63431

36-66

•14328

•85672

2-32

•31581

•68419

37-67

•13976

■86024

3-33

•28060

•71940

38-68

•13626

■86374

4-34

•25656

•74344

39-69

■13279

•86721

5-35

•24069

•75931

40-70

•12936

•87064

6-36

•23066

•76934

41-71

•12596

•87404

7-37

•22475

■77525

42-72

•12262

•87738

8-38

•22171

■77829

43-73

■11934

•88066

9-39

■21982

•78018

44-74

•11611

•88389

10^0

•21798

•78202

45-75

•11297

•88703

11-^1

•21620

•78380

46-76

•10991

•89009

12-42

•21448

•78552

47-77

•10696

•89304

13-43

•21274

■78726

48-78

•10413

•89587

14-44

•21091

•78909

49-79

•10145

•89855

15-45

•20898

•79102

50-80

•09896

•90104

16-46

•20694

•79306

51-81

■09669

•90331

17-47

•20479

•79521

52-82

■09473

■90527

18-48

•20252

•79748

53-83

•09314

■90686

19-49

•20012

•79988

54-84

•09208

■90792

20-50

•19758

•80242

55-85

•09173

■90827

21-51

■19490

•80510

56-86

•09181

•90819

22-52

•19205

•80795

57-87

■09189

•90811

23-53

■18903

•81097

58-88

•09199

•90801

24-54

•18582

•81418

59-89

•09210

•90790

25-55

•18242

•81758

60-90

■09224

•90776

26-56

•17890

•82110

61-91

■09239

•90761

27-57

•17536

■82464

62-92

■09257

•90743

28-58

•17181

•82819

63-93

■09278

•90722

29-59

•16825

■83175

64-94

•09302

•90698

30^0

•16468

■83532

65-95

•09329

•90671

31-61

•16110

•83890

66-96

•09359

•90641

32-62

•15752

•84248

67-97

■09392

•90608

33-63

•15395

•84605

68-98

•09428

•90572

34-64

•15038

•84962

69-99

•09467

•90533

A. 25.
Difference of age Forty years.

Ages,

0-40

1-41

2-42

3-43

4-44

5-45

6-46

7-47

8-48

9-49

10-50

11-51

12-52

13-53

14-54

15-55

16-56

17-57

18-58

19-59

20-60

21-61

22-62

23-63

24-64]

25-65

26-66

27-67

28-68

29-69

Younger

•38746

■31446

•26077

•22275

•19667

•17932

•16821

•16149

•15784

•15539

•15297

•15058

•14821

•14579

•14322

■14050

•13770

•13488

•13204

•12920

■12636

•12351

•12066

•11781

•11497

•11213

•10930

■10649

■10369

■10091

Elder.

•61254

■68554

■73923

■77725

•80333

•82068

•83179

•83851

•84216

•84461

•84703

•84942

•85179

■85421

■85678

■85950

■86230

■86512

■86796

■87080

■87364

■87649

■87934

■88219

88503

88787

89070

89351

89631

89909

Ages.

30-70

31-71

32-72

33-73

34-74

35-75

36-76

37-77

38-78

39-79

40-80

41-81

42-82

43-83

44-84

45-85

46-86

47-87

48-88

49-89

50-90

51-91

52-92

53-93

54-94

55-95

56-96

57-97

58-98

59-99

Younger

■09815

•09541
•09270
•09001
•08736
•08474
•08215
■07961
•07710
■07464
■07223
■06986
■06754
■06527
06305
06090
05880
05678
05482
05295
05117
04952
04804
04680
04594
04573
04598
04633
04678
04738

Elder.

90185
90459
•90730
•90999
•91264
■91526
■91785
■92039
■92290
■92536
■92777
■93014
■93246
■93473
■93695
■93910
•94120
■94322
•94518
•94705
•94883
•95048
•95196
•95320
•95406
•95427
•95402
•95367
•95322
•■95262

18

MEAN MORTALITY,

Tabs. A. 22 — 29. Shewing the probability of the Younger or the Elder of two lives being first in the

order of Decease.
A. 26. A. 27.

Difference of age Fifty years. Difference of age Sixti/ years.

Ages.

Younger Elder.

0-50

1-51

2-52

3-53

4-54

5-55

6-56

7-57

8^8

9-59

10-60

11-61

12-62

13-63

14-64

15-65

16-66

17-67

18-68

19-69

20-70

21-71

22-72

23-73

24-74

•34716
•27000
•21311
•17268
•14475
•12598
•11379
•10633
•10221
•09947
•09686
•09440
•09210
•08989
•08768
•08547
•08328
•08110
•07893
•07677
•07464
•07252
•07042
•06835
•06630

•65284
•73000
•78689
•8-3732
•85525
■87402
•88621
•89367
•89779
•90053
•90314
•90560
•90790
•91011
•91232
•91453
•91672
•91890
■92107
•92323
•92536
•92748
•92958
•93165
•93370

Ages.

Younger

25-75
26-76
27-77
28-78
29-79
30-80
31-81
32-82
33-83
34-84
35-85
36-86
37-87
38-88
39-89
40-90
41-91
42-92
43-93
44-94
45-95
46-96
47-97
48-98
49-99

•06428
•06229
•06033
•05840
•05651
•05465
•05282
•05104
•04929
•04759
•04592
•04430
•04272
•04119
•03970
•03826
•03686
•03551
•03421
•03296
•03177
•03064
•02957
•02856
•02762

Elder.

•93572
•93771
•93967
■94160
•94349
■94535
■94718
•948''6
■95071
•95241
•95408
■95570
•95728
•95881
•96030
•96174
•96314
•96449
•96579
•96704
•96823
•96936
•97043
•97144
•97238

Ages.

Younger

Elder.

Ages.

Younger

Elder.

0-60

•30734

•69266

20-80

■04120

•95880

1-61

•22843

•77157

21-81

•03981

•96019

2-62

•17065

•82935

22-82

•03845

•96155

3-63

•12986

•87014

23-83

•03713

•96287

4-64

•10194

•89806

24-84

•03583

•96417

5-65

•08341

•91659

25-85

•03457

•96543

6-66

•07161

•92839

26-86

•03334

•96666

7-67

•06459

•93541

27-87

•03214

•96786

8-68

•06099

•93901

28-88

•03097

•96903

9-69

•05882

•94118

29-89

•02984

•97016

10-70

•05680

•94320

30-90

•02875

•97125

11-71

•05493

■94507

31-91

•02769

•97231

12-72

•05325

•94675

32-92

•02667

•97333

13-73

•05166

•94834

33-93

•02569

•97431

14-74

•05009

•94991

34-94

•02474

•97526

15-75

•04855

■95145

35-95

•02384

•97616

16-76

•04703

•95297

36-96

•02299

•97701

17-77

•04553

•95447

37-97

•02220

•97780

18-78

•04406

•95594

38-98

•02146

•97854

19-79

•04262

•95738

39-99

•02076

•97924

A. 28.
Difference of age Seventy years.

Ages.

0-70

1-71

2-72

3-73

4-74

5-75

6-76

7-77

8-78

9-79

10-80

11-81

12-82

13-83

14-84

Younger

Elder.

•26705
•19134
•13638
•09788
■07169
■05444
■04357
■03726
■03429
■03272
•03128
•03000
■02889
■02788
•02690

•73295
•80866
•86362
•90212
■92831
■94556
•95643
•96274
•96571
•96728
■96872
■97000
■97111
■97212
■97310

Ages.

Younger

15-85
16-86
17-87
18-88
19-89
20-90
21-91
22-92
23-93
24-94
25-95
26-96
27-97
28-98
29-99

■02595
•02502
■0-2411
■02323
•02238
■02156
•02076
•01999
•01925
•01854
•01786
•01721
■01662
•01608
•01558

Elder.

■97405
■97498
■97589
■97677
■97762
■97844
■97924
■98001
■98075
■98146
•98214
■98279
■98338
■98392
■98442

A. 29.
Difierence of age Eighty yeare.

Ages.

0-80
1-81
2-82
3-83
4-84
5-85
6-86
7-87
8-88
9-89

Younger

•22206
•15460
•10633
•07286
•05025
■03540
•02606
■02070
•01837
•01735

Elder.

•77794
•84540
•89367
•92714
•94975
•96460
•97394
•97930
•98163
•98265

Ages.

10-90
11-91
12-92
13-93
14-94
15-95
16-96
17-97
18-98
19-99

Younger

•01642
•01561
•01496
•01440
■01387
■01336
•01287
•01242
•01201
•01164

Elder.

•98358
•98439
•98504
•98560
•98613
•98664
•98713
•98758
•98799
•98836

MEAN MORTALITY.

19

Tabs. A. 30 and 31.
Shewing the relations of constantly Living, and annually Di/ing, to large intervals of age, in a
Stationary Population, and in a Population increasing (suddenly) ten per cent in the succes-
sive decennial intervals of age.
A. 30. Stationary Population. A. 31. Increasing Population.

Ages.

Living.

Dying.

Rate
#■ cent.

Living.

0—5
5-10
10-20
20-30
30-40
40-50
50-60
60-70
70-80
80-90
90-100

596227
516294
979612
903374
810346
700415
574669
408033
199907
46556
2578

40096

5095

6861

8445

10164

11784

13803

19719

20077

9394

1027

6-7250

•9869

•7004

•9348

r2543

h6824

2^4019

4-8326

10-0432

20-1783

39-8503

10391

8998

17072

15744

14122

12207:

10015

7111

3484

811

45

0-100

5738010

146465

2-5525

100000

0-20
20-50

50-100

2092133
2414135
1231743

52052
30393
64020

2-4880
1-2590
5-1975

36461
42073
21466

Ages.

Living.

Dying.

Living.

Dying.

0-10

1480766

60150

244541

9933

10-20

1185330

8302

195751

1371

20-30

993712

9290

164106

1534

30-40

810346

10164

133824

1679

40-50

636741

10713

105154

1769

50-60

474933

11407

78433

1884

60-70

306561

14815

50627

2447

70-80

136539

13713

22549

2265

80-90

28908

5833

4774

963

90-100

1455

580

240

96

0-100

6055290

144966

1000000

23940

0-20

2666096

68452

440292

11304

20-50

2440798

30166

403085

4982

50-100

948396

46348

156623

7654

Tabs. A. 32 and 33.

Health Insurance. Weekly payments equivalent to a benefit during Sickness of 100 pence per
week, wiien the Insurance is for the term of one year, and when it is for the term compre-
hended between the age of admission and the age of Fifty-Jive years. Rate of interest
3 per cent.

A. 32. Insurance for one year. A. 33. Insurance until aged 55.

Between
ages.

Weekly
payment
in pence.

Between

ages.

Weekly
payment
in pence.

Between

ages.

Weekly
payment
In pence.

20-21
21-22

22-23
23-24
24-25
25-26
26-27
27-28
28-29
29-30
30-31
31-32
32-33
33-34
34-35
35-36
36-37
37-38

1-4997
1-5445
1-5907
1-6383
1-6873
1-7378
1-7898
1-8433
1-8985
1-9552
2-0137-
2-0740
2-1360
2-1999
2 2657
2-3335
2-4033
2^4751

38-39
39-40
40-41
41-42
42-43
43-44
44-45
45-46
46-47
47-48
48-49
49-50
50-51
51-52
52-53
53-54
54-55

2-5492
2-6254
2-7040
2-7848
2-8681
2-9539
3-0423
3-1333
3-2270
3-3235
3-4229
3-5263
3-6308
3-7394
3-8512
3-9664
4-0851

55-56
56-57
57-58
58-59
59-60
60-61
61-62
62-63
63-64
64-65
65-66
66-67
67-68
68-69
69-70
70-71

4-4106

4^7621

5^1416

5^5514

5-9938

6-4714

6-9871

7-5440

8-1452

8-7943

9-4951

10-2518

11-0688

11-9509^

12-9033

13-9316

Age.

Weekly
payment
in pence.

Age.

Weekly
payment
in pence.

20

2-2702

38

3-1481

21

2-3134

39

3-2029

22

2-3572

40

3-2583

23

2-4017

41

3-3143

24

2-4469

42

3-3708

25

2-4927

43

3-4279

26

2-5392

44

3-4854

27

2-5864

45

3-5435

28

2-6342

46

3-6021

29

2-6827

47

3-6611

30

2-7318

48

3-7205

31

2-7816

49

3-7803

32

2-8321

50

3-8405

33

2-8832

51

3-9010

34

2-9349

52

3-9619

35

2-9873

53

4-0229

36

3-0403

54

4-0842

37

3-0939

20

MEAN MORTALITY.

Tab. a. 34. Maintenance in old age. Benefit
100 pence per week, after the age of Sixty-
Jive. Weekly payments to cease at the age of
Fifty-Jive.

Tab. a. 35. Benefit 100 shillings
on the day of death. Equiva-
lents in quarterly and in single
present payments.

Weekly

Single

Weekly

Single

Quarterly

Single

Age.

payment
la pence.

payment
in pounds.

Age.

payment
in pence.

payment
in pounds.

Age.

payment
in pence.

payment

20

5-2352

21-2206

28

8-3021

28-9082

20

5-2347

37-1211

21

5-5259

22-0366

29

8-8431

30-0853

25

5-9530

40-1687

22

5-8380

22-8897

30

9-4336

31-3200

30

6-8038

43-4170

23

6-1737

23-7817

35

13-3987

38-4873

35

7-8295

46-8932

24

6-5354

24-7150

40

20-3183

47-7346

40

9-0966

50-6391

25

6-9257

25-6917

45

34-6910

59-8418

45

10-7154

54-7195

26

7-3478

26-7144

50

79-0212

75-9579

50

12-8846

59-2352

27

7-8052

27-7856

55

—

97-8125

55
60

16-0023
20-4397

64-3456
69-7441

Tab. A. 36. Shewing the values in single and in annual payments of a deferred Annuity
of £10, payable on the death of A, during the future portion of life which may be
enjoyed by another person, B. Interest 3 per cent.

B.

A.

Single
payment.

Annual
payment.

B.

A.

Single
payment.

Annual
payment.

B.

A.

Single
payment.

Annual
payment.

20

20
30
40
50
60
70
80

38-901

50-850

66-766

88-291

117-622

147-079

171-629

2-1752

3-0469

4-4224

6-8205

11-7484

20-8146

37-2210

40

20
30
40
50
60
70
80

21-031
27-566
37-188
52-679
77-242
103-806
126-862

1-3930

1-9085

2-7583

4-4147

"8-1511

15-2213

28-1027

60

20
30
40
50
60
70
80

7-248
9-523
12-603
18-065
30-448
47-622
65-452

-7239
-9733
1-3300
2-0230
3-9585
7-9711
15-6159

30

20
30
40
50
60
70
80

29-549
38-828
52-001
71-145
98-597
126-844
150-747

1-7705

2-4635

3-6002

5-6783

10-0771

18-2260

32-9918

50

20
30
40
50
60
70
80

13-471
17-627
23-596
34-084
53-620
76-986
98-567

1-0407
1-4068
1-9774
3-1317
6-0045
11-6760
22-2230

70

20
30
40
50
60
70
80

3-305

4-371

5-768

8-031

14-222

24-385

36-756

-4677
•6280
8458
1-2180
2^3805
4^9183
9^8781

Tab. a. 37. Shewing, at quinquennial intervals of age, the force of mortality, or the
number of Deaths which would occur in one year, upon 100 constantly living.

Age.

Rate
V cent.

Age.

Rate
spi cent.

Age.

Rate
^ cent.

Age.

Rate
!|fwcent

Age.

Rate
^cent

Age.

Rate
^cent.

5
10
15

14-5798

2-0595

•6364

•6953

20
25
30
35

-8057

■9336

1-0818

1-2536

40
45
50
55

r4526
1-6833
1-9505
2-2602

60

65
70
75

3-3163

4-8658

7-1392

10-47'49

80
85
90
95

15-3692
22-5502
33-0865
48-5458

100

105
110
115

71-2281
104-5084
153-3386
224-9838

VILLAGE MORTALITY.

21

Tab. B. 1.

Tab. B. 2.

Shewing, at the end of any number of
years from birth, — the Living out of a
given number born, — also the Dying
in the year succeediag.

Shewing, at every age of life, in logarithms, — the
probability of living one year (x,a),- — and the
Living out of a given number born (x a).

i

Living.'

Dying.

Living.

Dying.

151403-0

18909-6

50

68966-3

1128-4

1

132493-4

11427-5

51

67838-0

1142-8

2

121065-9

7162-1

52

66695-2

1156-9

3

113903-8

4600-6

53

65538-3

1170-5

4

109303-2

3004-6

54

64367-8

1183-7

5

106298-6

1984-4

55

63184-1

1224-9

6

104314-1

1320-6

56

61959-2

1295-8

7

102993-5

883-3

57

60663-4

1368-7

8

102110-2

592-9

58

59294-7

1443-1

9

101517-3

481-9

59

57851-6

1518-7

10

101035-4

511-4

60

56332-8

1595-0

11

100524-0

5240

61

54737-8

1671-5

12

100000-0

536-8

62

53066-4

1747-4

13

99463-2

549-8

63

51319-0

1822-1

14

98913-3

563-1

64

49496-8

1894-8

15

98350-2

576-6

65

47602-1

1964-4

16

97773-6

690-4

66

45637-7

2030-0

17

97183-3

604-2

67

43607-6

2090-6

18

96579-0

618-4

68

41517-0

2144-8

19

95960-6

632-8

69

39372-2

2191-5

20

95327-9

647-3

70

37180-7

2229-4

21

94680'5

662-1

71

34951-4

2257-2

22

94018-4

677-1

72

32694-1

2273-7

23

93341-4

692-2

73

30420-4

2277-7

24

92649-2

707-5

74

28142-7

2268-2

25

91941-6

723-1

75

25874-5

2244-1

26

91218-5

738-8

76

23630-4

2205-0

27

90479-8

754-6

77

21425-4

2150-3

28

89725-2

770-6

78

19275-2

2080-0

29

88954-6

786-7

79

17195-2

1994-5

30

88167-8

803-0

80

15200-7

1894-5

31

87364-8

819-4

81

13306-1

1781-3

32

86545-5

835-8

82

11524-8

1656-5

33

85709-6

852-4

83

9868-3

1522-3

34

84857-2

869-0

84

8346-0

1381-1

35

83988-2

885-8

85

6964-9

1235-7

36

83102-4

902-5

86

5729-2

1089-3

37

82200-0

919-2

87

4639-9

944-8

38

81280-8

936-0

88

3695-1

805-3

39

80344-8

952-7

89

2889-8

673-7

40

79392-1

969-4

90

2216-2

552-2

41

78422-7

986-0

91

1664-0

442-8

42

77436-7

1002-6

92

1221-2

346-8

43

76434-1

1019-0

93

874-4

264-8

44

75415-2

1035-2

94

609-6

196-6

45

74379-9

1051-4

95

413-0

141-8

46

73328-5

1067-3

96

271-2

99-0

47

72261-2

1083-0

97

172-2

66-7

48

71178-3

1098-4

98

105-5

43-3

49

70079-9

1113-5

99

62-2

27-1

A.a

[-9420598
•9608276
-9735162
-9820948
-9878946
•9918157
•9944668
•9962591
•9974708
-9979336
•9977962
-9977303
-9976624
-9975925
-9975205
-9974463
•9973699
-9972913
•9972102
•9971268
•9970408
•9969523
•9968612
-9967673
-9966706
-9965710
•9964684
•9963628
•9962540
•9961419
•9960265
•9959077
•9957853
-9956592
•9955293
•9953956
•9952579
•9951160
•9949700
•9948195
•9946645
•9945050
-9943406
-9941713
-9939970
-9938174
•9936325
•9934420
•9932458
•9930438

Aa

•1801345
•1221943
•0830219
■0565381
•0386329
-0265275
•0183432
•0128100
•0090691
•0065399
•0044735
•0022697
•0000000
[■9976624
•9952549
•9927754
•9902217
•9875916
•9848829
•9820931
•9792199
-9762607
-9732130
•9700742
•9668415
•9635121
•9600831
•9565515
•9529143
-9491683
•9453102
•9413367
•9372444
•9330297
•9286889
•9242182
•9196138
•9148717
■9099877
•9049577
•8997772
-8944417
-8889467
•8832873
-8774586
•8714556
-8652730
-8589055
-8523475
■8455933

A.a

:-9928358
-9926215
•9924007
•9921735
•9919392
•9914982
•9908207
•9900891
•9892993
•9884466
•9875259
•9865318
•9854585
•9842996
•9830484
•9816975
•9802389
•9786641
•9769638
•9751280
•9731459
-9710058
•9686952
•9662005
■9635069
■9605987
•9574587
•9540685
•9504081
■9464560
■9421890
■9375819
■9326076
■9272370
■9214383
■9151775
■9084178
■9011194
■8932395
■8847314
■8755455
■8656274
-8549189
-8433570
-8308738
-8173958
-8028436
-7871318
•7701679
•7518520

Pia

[•8386371
•8314729
•8240944
•8164951
•8086686
•8006078
•7921060
•7829267
•7730158
•7623151
•7507617
•7382876
•7248194
•7102779
•6945775
•6776259
•6593234
•6395623
•6182264
•5951902
-5703182
-5434641
•5144699
•4831651
•4493656
•4128725
-3734712
-3309299
-2849984
-2354065
•1818625
-1240515
-0616334
1-9942410
-9214780
-84-29163
-7580938
-6665116
-5676310
-4608705
•3456019
•2211474
•0867748
! -9416937
-7850507
•6159245
•4333203
•2361639
■0232957
i^7934636

22

VILLAGE MORTALITY.

Tab. B. 3. The Expectation of complete years, at all ages; or the value of Annuity
of £1, when there is no interest of money.

-

Expecto.

Expect",

4

Expect".

1

Expect".

i

Expect".

4

<

Expect". J>

Expect".

39-4556

15

44-5490

30

33-8378

45

23-7501

60

13-9704!

75

6-6232

90

2-4662

1

44-0867

16

43-8117

31

33-1488

46

23-0906

61

13-3775

76

6-2522

91

2-2846

2

47-2481

17

43-0779

32

32-4627

47

22-4317

62

12-7989

77

5-8956

92

2-1130

3

49-2190

18

42-3474

33

31-7792

48

21-7730

63

12-2347

78

5-5533

93

1-9511

4

50-2906

19

41-6203

34

31-0984

49

21-1142

64

11-6850

79

5-2251

94

1-7984,

5

50-7121

20

40-8966

35

30-4202

50

20-4552

65

11-1502

80

4-9107

95

1-6547

6

50-6769

21

40-1762

36

29-7445

51

19-7954

66

10-6301

81

4-6099

96

1-5196

7

50-3267

22

39-4591:

37

29-0710

52

19-1346

67

10-1250

82

4-3224

97

1-3927

8

49-7620

23

38-7454-

38

28-3998

53

18-4724

68

9-6348

83

4-0480

98

1-2737

9

49-0527

24

38-0348

39

27-7306

54

17-8083

69

9-1597

84

3-7863

99

1-1622

10

48-2866

25

37-3275

40

27-0634

55

17-1419

70

8-6996

85

3-5371

11

47-5323

26

36-6234

41

26-3979

56

16-4808

71

8-2545

86

3-3000

12

46-7813

27

35-9224

42

25-7341

57

15-8328

72

7-8243 87

3-0747

13

46-0338

28

35-2246

43

25-0716

58

15-1983 73

7-4092 88

2-8609

14

45-2«97

29

34-5297

44

24-4104

59

14-5774 74

7-0088 89

2-6582

Tab. B. 4. Shewing the present value of Annuity of £l, depending on a single life.

3#'cent

4^ cent

5 Vcent

3 f cent

4 ^ cent

5 V cent

accent

4^ cent

5^ cent

8833
0487
5993
6462
3073
6851
8598
8907
8202
6781
'5048
■3331
■1590
■9825
■8036
6222
■4383
■2518
0627
8711
■6767
■4797
■2799
■0772
■8718
■6634
■4520
■2375
0200
■7992
■5752
3477
1168
8823

14-7461
16-5247
17-8079
18-6847
19-2500
19-5859
19-7569
19-8106
19-7812
19-6926
19-5780
19-4648
19-3494
19-2320
19-1124
18-9907
18-8668
18-7407
18-6123
18-4815
18-3483
18-2127
18-0746
17-9340
17-7907
17-6447
17-4959
17-3443
17-1898
17-0322
16-8716
16-7077
16-5406
16-3699

12-4756
13-9690
15-0519
15-7983
16-2864
16-5841
16-7445
16-8072
•16-8002
16-7433
16-6643
16-5865
16-5071
16-4260
16-3432
16-2586
16-1722
16-0839
15-9938
15-9017
15-8076
15-7115
15-6132
15-5128
15-4101
15-3052
15-1978
15-0880
14-9756
14-8606
14-7429
14-6223
14-4988
14-3722

34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67

6442
4022
1563
9063
6521
3934
1302
8622
5893
3110
0274
7380
4425
1407
8322
5166
1936
8625
5230
1746
8166
■4484
0754
■7033
3326
■9638
5972
2331
8721
5145
1607
8111
4661
1260

16-1957

16-0179

15-8361

15-6504

15-4605

15-2662

15-0674

14-8638

14-6551

14-4413

14-2218

13-9966

13-7651

13-5272

13-2823

13-0301

12-7701

12-5018

12-2247

11-9381

11-6414

11-3339

11-0202

10-7059

10-3911

10-0763

9-7619

9-4482

9-1356

8-8246

8-5154

8-2085

7-9043

7-6032

2424
1093
9726
8323
6882
5401
3877
2308
0693
9027
7309
5535
3702
1805
9841
7806
5693
3498
1215
8837
6357
3767
1110
8433
5740
3035
0320
7600
■4877
2155
9439
6731
■4035
■1356

68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99

7-7912
7-4621
7-1390
6-8222
6-5120
6-2087
5-9125
5-6238
5-3426
5-0692
4-8037
4-5463
4-2971
4-0562
3-8237
3-5995
3-3837
3-1763
2-9772
2-7865
2-6039
2-4294
2-2629
2-1043
1-9533
1-8099
1-6739
1-5450
1-4231
1-3080
1-1995
1-0973

7-3055
7-0116
6-7218
6-4366
6-1563
5-8811
5-6113
5-3473
5-0894
4-8377
4-5924
4-3539
4-1222
3-8974
3-6798
3-4694
3-2663
3-0706
8822
7012
5275
3611
2020
2-0500
1-9051
1-7671
1-6359
1-5115
1-3935
1-2819
1-1765
1-0771

6-8696
6-6060
6-3452
6-0874
5-8331
5-5825
5-3360
0940
4-8566.
4-6243
4-16972
4-1755
3-9596
3-7495
3-5455
3-3477
3-1562
2-9711
2-7926
2-6206
2-4551
2-2963
2-1440
1-9982
1-8590
1-7261
1-5996
1-4793
1-3651
1-2568
1-1544
1-0577

VILLAGE MORTALITY.

23

Tabs. B. 5, 6, and 7. Shewing the values of Annuity depending on the co-existence or joint continuance of
two lives, whose common difference of age is 0, 5, or 10 years.

B. 5.

B. 6.

B. 7.

Equal ages.

Ages.

cent

1

2—2
3—3
4—4
5—5
6—6
7—7
8—8
9—9
10-10
11-11
12-12
13-13
14-14
15-15
16-16
17-17
18-18
19-19
20-20
21-21
22-22
23-23
24-24
25-25
26-26
27-27
28-28
29-29
30-30
31-31
32-32
33-33
34-34
35-35
36-36
37-37
38-38
39-39
40-40
41-41
42-42
43-43
44-44
45-45
46-46
47-47
48-48
49-49

9-4836
11-8791
13-7966
15-2097
16-1777
16-7893
17-1316
17-2767
17-2799
17-1817
17-0398
16-9022
16-7629
16-6221
16-4798
16-3358
16-1902
16-0430
15-8941
15-7436
15-5914
15-4376
15-2820
15-1247
14-9656
14-8047
14-6419
14-4773
14-3107
14-1421
13-9714
13-7986
13-6236
13-4462
13-2664
13-0841
12-8991
12-7112
12-5204
12-3263
12-1289
11-9278
11-7228
11-5137
11-3000
11-0814
10-8575
10-6278
10-3918
10-1489

Ages.

'cent

50-50
51-51
52-52
53-53
54-54
55-55
56-56
57-57
58-58
59-59
60-60
61-61
62-62
63-63
64-64
65-65
66-66
67-67
68-68
69-69
70-70
71-71
72-72
73-73
74-74
75-75
76-76
77-77
78-78
79-79
80-80
81-81
82-82
83-83
84-84
85-85
86-86
87-87
88-88
89-89
90-90
91-91
92-92
93-93
94-94
95-95
96-96
97-97
98-98
99-99

8984

9-6397

9-3718

9-0938

8-8046

8-5031

8-1963

8922

7-5912

7-2937

6-9999

6-7104

6-4253

6-1452

5-8702

5-6007

6-3369

5-0792

4-8277

4-5828

4-3445

4-1130

3-8886

3-6713

3-4612

3-2584

3-0629

2-8748

2-6941

2-5207

2-3546'

2-1958

2-0441

1-8994

1-7617

1-6308

1-5066

1-3889

1-2776

1-1724

1-0733

-9799

-8922

-8100

•7330

-6611

-5941

•5318

-4740

-4205

Difference of age Five years.

Ages.

0—5

1—6

2—7

3—8

4-9

5-10

6-11

7-12

8-13

9-14

10-15

11-16

12-17

13-18

14-19

15-20

16-21

17-22

18-23

19-24

20-25

21-26

22-27

23-28

24-29

25-30

26-31

27-32

28-33

29-34

30-35

31-36

32-37

33-38

34-39

35-40

36-41

37-42

38-43

39-44

40-45
41-46
42-47
43-48
44-49
45-50
46-51
47-52

12-5945
14-2525
15-4297
16-2034
16-6634
16-9X348
17-0066
17-0075
16-9371
16-8159
16-6726
16-5305
16-3868
16-2414
16-0944
15-9457
15-7954
15-6434
15-4897
15-3342
15-1770
15-0180
14-8571
14-6944
14-5297
14-3630
14-1944
14-0236
13-8506
13-6753
13-4977
13-3176
13-1350
12-9496
12-7613
12-5700
12-3755
12-1775
11-9758
11-7701
11-5603
11-3458
11-1264
10-9016
10-6709
10-4339
10-1899
9-9383

Ages.

4#'oent

48-53

49-54

50-55

51^6

52-57

53-58

54-59

55-60

56-61

57-62

58-63

59-64

60-65

61-66

62-67

63-68

64-69

65-70

66-71

67-72

68-73

69-74

70-75

71-76

72-77

73-78

74-79

75-80

76-81

77-82

78-83

79-84

80-85

81

82-87

83-88

84-89

85-90

86-91

87-92

88-93

89-94

90-95

91-96

92-97

93-98

94-99

95-100

9-6783

9-4091

9-1297

8-8437

8-5549

8-2631

9682

7-6697

7-3712

0765

6-7858

6-4995

6-2180

5-9417

5-6707

5-4054

5-1461

4-8930

4-6463

4-4062

4-1730

3-9467

3-7275

3-5155

3-3108

1134

2-9234

2-7407

2-5654

2-3974

2-2366

2-0831

1-9366

1-7971

1-6645

1-5385

1-4191

1-3061

1-1994

1-0987

1-0038

-9147

-8310

•7527

-6794

-6112

-5476

-4887

Difference of age Ten years.

Ages.

0-10

1-11

2-12

3-13

4-14

5-15

6-16

7-17

8-18

9-19

10-20

11-21

12-22

13-23

14-24

15-25

16-26

17-27

18-28

19-29

20-30

21-31

22-32

23-33

24-34

25-35

26-36

27-37

28-38

29-39

30-40

31-41

32-42

33-43

34-44

35-45
36-46
37-47
38-48
39-49
40-50
41-51
42-52
43-53
44-54

4 #"0601

12-6734
14-1381
15-1758
15-8658
16-2905
16-5207
16-6117
16-6040
16-5265
16-3993
16-2504
16-1025
15-9529
15-8016
15-6485
15-4935
15-3368
15-1782
15-0176
14-8552
14-6907
14-5242
14-3555
14-1847
14-0116
13-8361
13-6582
13-"4778
13-2946
13-1086
12-9197
12-7276
12-5321
12-3331
12-1303
11-9235
11-7123
11-4964
11-2754
11-0490
10-8166
10-5777
10-3318
10-0782
9-8161

45-55
46-56
47-^7
48-58
49-59
50-60
51-61
52-62
53-63
54-64
55-65
56-66
57-67
58-68
59-69
60-70
61-71
62-72
63-73
64-74
65-75
66-76
67-77
68-78
69-79
70-80
71-81
72-82
73-83
74-84
75-85
76-86
77-87
78-88
79-89
80-90
81-91
82-92
83-93
84-94
85-95
86-96
87-97
88-98
89-99

'cent

9-5447
9-2679
8-9899
8-7109
8-4308
8-1498
7-8679
7-5849
7-^009
7-0156
6-7288
6-4435
6-1630
5-8877
5-6178
5-3537
5-0956
4-8437
4-5983
4-3596
4-1277
3-9028
3-6850
3-4744
3-2712
3-0752
2-8867
2-7055
2-5316
2-3650
2-2057
2-0536
1-9085
1-7704
1-6390
1-5144
1-3963
1-2845
1-1790
1-0794
-9857
-8977
-8151
-7378
-6655

24

VILLAGE MORTALITY.

Tabs. D. 8, 9, 10. Shewing the value of Annuity depending on the co-existence or joint continuance of two
lives, whose common difference of age is IS, iOy^ot 25 years.

B. 8.

B. 9.

Difference of age Fifteen years.

Ages.

4#'cent

Ages.

4#'cent

0-15

12-3809

43-58

9-0039

1-16

13-8006

44-59

8-7274

2-17

14-8028

45-60

8-4509

3-18

15-4653

46-61

8-1747

4-19

15-8689

47-62

7-8990

5-20

16-0828

48-63

7-6239

6-21

16-1608

49-64

7-3496

7-22

16-1426

50-65

7-0762

8-23

16-0564

51-66

6-8037

9-24

15-9217

52-67

6-5.321

10-25

15-7655

53-68

6-2614

11-26

15-6102

54-69

5-9915

12-27

15-4529

55-70

5-7220

13-28

15-2936

56-71

5-4556

14-29

15-1324

57-72

5-1951

15-30

14-9690

58-73

4-9408

16-31

14-8035

59-74

4-6929

17-32

14-6358

60-75

4-4515

18-33

14-4658

61-76

4-2170

19-34

14-2935

62-77

3-9894

20-35

14-1188

63-78

3-7688

21-36

13-9415

64-79

3-5554

22-37

13-7615

65-80

3-3493

23-38

13-5788

66-81

3-1505

24-39

13-3932

67-82

2-9591

25-40

13-2046

68-83

2-7750

26-41

13-0127

69-84

2-5983

27-42

12-8175

70-85

2-4289

28-43

1-2-6186

71-86

2-2668

29-44

12-4159

72-87

2-1119

30-45

12-2091

73-88

1-9641

31-46

11-9979

74-89

1-82.32

32-47

11-7819

75-90

1-6893

33-48

11-5610

76-91

1-5621

34-49

11-3345

77-92

1-4414

35-50

11-1022

78-93

1-3272

36-51

10-8634

79-94

1-2193

37-52

10-6177

80-95

1-1174

38-53

10-3644

81-96

1-0215

39-54

10-1029

82-97

-9313

40-55

9-8322

83-98

-8466

41-56

9-5566

84-99

•7672

42-57

9-2804

85-100

•6930

Difference of age Twenty years.

Ages.

4#'cent

Ages.

4 f cent

0-20

12-0498

40-60

8-6546

1-21

13-4182

41-61

8-3776

2-22

14-3797

42-62

8-1015

3-23

15-0105

43-63

7-8267

4-24

15-3895

44-64

7-5535

5-25

15-5842

45-65

7-2820

6-26

15-6468

46-66

7-0125

7-27

15-6159

47-67

6-7453

8-28

15-5188

48-68

6-4804

9-29

15-3744

49-69

6-2182

10-30

15-2090

50-70

5-9586

11-31

15-0439

51-71

5-7019

12-32

14-8766

52-72

5-4480

13-33

14-7068

53-73

5-1969

14-34

14-5346

54-74

4-9485

15-35

14-3599

55-75

4-7024

16-36

14-1825

56-76

4-4608

17-37

14-0023

57-77

4-2260

18-38

13-8192

58-78

3-9981

19-39

13-6331

59-79

3-7773

20^0

13-4438

60-80

3-5636

21-41

13-2511

61-81

3-3572

22-12

13-0549

62-82

3-1581

23-43

12-8550

63-83

2-9664

24-44

12-6511

64-84

2-7821

25-45

12-4429

65-85

2-6051

26-46

12-2302

66-86

2-4354

27-47

12-0126

67-87

2-2730

28-i8

11-7899

68-88

2-1178

29-49

11-5615

69-89

1-9697

30-50

11-3272

70-90

1-8286

31-51

11-0863

71-91

1-6944

32-52

10-8383

72-92

1-5669

33-53

10-5827

73-93

1-4460

34-54

10-3187

74-94

1-3316

35-55

10-0456

75-95

1-2234

36-56

9-7675

76-96

1-1213

37-57

9-4891

77-97

1-0251

38-58

9-2106

78-98

-9347

39-59

8-9324

79-99

•8497

B. 10.

1

1

1 Difference of age Tweniy-five years.

Ages.

4^ cent

Ages.

4#'cent

0-25

11-6757

38-63

7-9698

1-26

12-9857

39-64

7-6938

2-27

13-9006

40-65

7-4199

3-28

14-4949

41-66

7-1483

4-29

14-8453

42-67

6-8794

5-30

15-0171

43-68

6-6134

6-31

15-0612

44-69

6-3506

7-32

15-0147

45-70

6-0913

8-33

14-9033

46-71

5-8356

9-34

14-7466

47-72

5-5839

10-35

14-5690

48-73

5-3363

11-36

14-3912

49-74

5-0929

12-37

14-2104

50-75

4-8539

13-38

14-0267

51-76

4-6194

14-39

13-8397

52-77

4-3894

15-40

13-6494

53-78

4-1638

16-41

13-4556

54-79

3-9425

17-42

13-2581

55-80

3-7251

18-43

13-0567

56-81

3-5131

19^4

12-8511

57-82

3-3085

20-45

12-6411

58-83

3-1112

21-46

12-4264

59-84

2-9213

22-47

12-2067

60-85

2-7387

23-48

11-9816

61-86

2-5634

24-49

11-7508

62-87

2-3955

25-^0

11-5137

63-88

2-2349

26-51

11-2699

64-89

2-0814

27-52

11-0188

65-90

1-9350

28-53

10-7600

66-91

1-7956

29-54

10-4926

67-92

1-6630

30-55

10-2159

68-93

1-5371

31-56

9-9341

69-94

1-4] 78

32-57

9-6521

70-95

1-3049

33-58

9-3700

71-96

1-1982

34-59

9-0883

72-97

1-0976

35-60

8-8071

73-98

1-0028

36-61

8-5267

74-99

-9137

37-62

8-2475

75-100

•8301

VILLAGE MORTALITY.

25

Tabs. B. 11, 12, 13, and 14. Shewing the Talues of Annuity depending on the co-existence or joint continuance

of two lives, whose common difference of age is 30, 35, 40, or 45 years.

B. 11. B. 12.

Difference of age ThWty years.

Ages.

4 # cent

Ages.

4 ^ cent

Ages.

4^ cent

0-30

11-2519

24-54

10-6400

48-78

4-2470

1-31

12-4950

25-55

10-3596

49-79

4-0288

2-32

13-3561

26-56

10-0741

50-80

3-8162

3-33

13-9077

27-57

9-7882

51-81

3-6094

4-34

14-2242

28-58

9-5023

52-82

3-4082

5-35

14-3687

29-59

9-2167

63-83

3-2126

6-36

14-3900

30-60

8-9316

54-84

3-0223

7-37

14-3239

31-61

8-6474

55-85

2-8370

8-38

14-1957

32-62

8-3643

56-86

2-6578

9-39

14-0227

33-63

8-0828

57-87

2-4859

10-40

13-8290

34-64

7-8032

58-88

2-3213

11-41

13-6340

35-65

7-5256

59-89

2-1640

12-42

13-4352

36-66

7-2505

60-90

2-0137

13-43

13-2323

37-67

6-9782

61-91

1-8705

14-44

13-0250

38-68

6-7090

62-92

1-7342

15-45

12-8132

39-69

6-4432

63-93

1-6047

16-46

12-5965

40-70

6-1810

64-94

1-4819

17-47

12-3746

41-71

5-9228

65-95

1-3655

18-48

12-1471

42-72

5-6688

66-96

1-2554

19-49

11-9137

43-73

5-4193

67-97

1-1515

20-50

11-6739

44-74

5-1746

68-98

1-0536

21-51

11-4272

45-75

4-9348

69-99

-9614

22-52

11-1730

46-76

4-7001

70-100

-8748

23-53 10-9109

47-77

4-4708

Difference of age Thirty-five years.

Ages.

4 f cent

Ages,

4^ cent

Ages.

4 f cent!

0-35

10-7709

22-57

9-9060

44-79I4-O770I

1-36

11-9369

23-58

9-6165

45-80

3-8632

2-37

12-7354

24-59

9-3272

46-81

3-6556

3-38

13-2368

25-60

9-0385

47-82

3-4542

4-39

13-5128

26-61

8-7506

48-83;3-2593|

5-40

13-6240

27-62

8-4639

49-84

3-0707

6-41

13-6169

28-63

8-1787

50-85

2-8886

7-42

13-5258

29-64

7-8954

51-86

2-7128

8^3

13-3747

30-65

7-6142

52-87

2-5434

9-44

13-1799

31-66

7-3356

53-88

2-3800

10-45

12-9642

32-67

7-0598

54-89

2-2226

11-46

12-7457

33-68

6-7871

55-90

2-0706

12-47

12-5217

34-69

6-5178

56-91

1-9247

13-48

12-2921

35-70

6-2523

57-92

1-7858

14-49

12-0563

36-71

5-9909

58-93

1-6537

15-50

11-8140

37-72

5-7338

59-94

1-5283

16-51

11-5646

38-73

5-4814

60-95

1-4094

17-52

11-3076

39-74

5-2338

61-96

1-2970

18-53

11-0423

40-75

4-9913

62-97

1-1907

19-54

10-7682

41-76

4-7542

63-98

1-0905

20-55

10-4844

42-77

4-5227

64-99

•9961

21-56

10-1954

43-78

4-2969

65-100

-9074

B.

13.

Difference of age Forty years.

Ages.

4#'oent

Ages.

4^ cent

Ages.

4 #■ cent

0-40

10-2205

20-60

9-1319

40-80

3-8979

1-41

11-2965

21-61

8-8408

41-81

3-6882

2-42

12-0210

22-62

8-5508

42-82

3-4850

3-43

12-4623

23-63

8-2623

43-83

3-2884

4-44

12-6887

24-64

7-9757

44-84

3-0983

5-45

12-7582

25-65

7-6913

45-85

,2-9149

6-46

12-7148

26-66

7-4093

46-86

2-7382

7-47

12-5907

27-67

7-1303

47-87

2-5682

8^8

12-4086

28-68

6-8544

48-88

2-4049

9-49

12-1837

29-69

6-5820

49-89

2-2482

10-50

11-9371

30-70

6-3135

50-90

2-0981

11-51

11-6853

31-71

6-0490

51-91

1-9544

12-52

11-4257

32-72

5-7890

52-92

1-8171

13-53

11-1577

33-73

5-5336

53-93

1-6859

14-54

10-8807

34-74

5-2833

54-94

1-5606

15-55

10-5939

35-75

5-0381

55-95

1-4407

16-56

10-3018

36-76

4-7983

56-96

1-3265

17-57

10-0092

37-77

4-5643

57-97

1-2186

18-58

9-7164

38-78

4-3361

58-98

1-1168

19-59

9-4239

39-79

4-1139

59-99

1-0209

B. 14.

Difference of age Forty-five years.

Ages.

4^ cent

Ages.

4 f cent

Ages.

4 #■ cent

0-45

9-5833

19-64

8-0460

38-83

3-3123

1-46

10-5523

20-65

7-7587

39-84

3-1206

2-47

11-1877

21-66

7-4739

40-85

2-9356

3-48

11-5550

22-67

7-1920

41-86

2-7574

4r-49

11-7192

23-68

6-9133

42-87

2-5861

5-50

11-7349

24-69

6-6382

43-88

2-4215

6-51

11-6433

25-70

6-3669

44-89

2-2636

7-52

11-4744

26-71

6-0997

45-90

2-1125

8-53

11-2491

27-72

5-8371

46-91

1-9680

9-54

10-9814

28-73

5-5792

47-92

1-8301

10-55

10-6901

29-74

5-3263

48-93

1-6986

11-56

10-3952

30-75

5-0787

49-94

1-5735

12-57

10-0997

31-76

4-8366

50-95

1-4546

13-58

9-8042

32-77

4-6002

51-96

1-3418

14-59

9-5088

33-78

4-3698

52-97

1-2349

15-60

9-2139

34-79

4-1455

53-98

1-1337

16-61

8-9198

35-80

3-9275

54-99

1-0379

17-62

8-6269

36-81

3-7158

55-100

-9471

18-63

8-3356

37-82

3-5108

26

VILLAGE MORTALITY.

Tabs. B. 15, 16, 17, 18, and 19. Shewing the values of Annuity depending on the co-existence or joint
continuance of two lives, whose common difference of age is 50, 55, 60, 65, or 70 years.

B. 15.

B. 16.

Difference of age Fifty years.

Ages.

4^ cent

Ages.

4#'cent

Ages.

4$* cent

0-^0

8-8332

17-67

7-2460

34-84

3-1399

1-51

9-6723

18-68

6-9649

35-85

2-9535

2-52

10-1973

19-6916-6873

36-86

2-7740

3-53

10-4710

20-70

6-4136

37-87

2-6014

4-54

10-6545

21-71

6-1441

38-88

2-4356

5-55

10-4984

22-72

5-8791

39-89

2-2766

6-56

10-3460

23-73

5-6189

40-90

2-1244

7-57

10-1306

24-74

5-3639

41-91

1-9789

8-58

9-8723

25-75

5-1141

42-92

1-8401

9-59

9-5848

26-76

4-8699

43-93

1-7078

10-60

9-2857

27-77

4-6316

44-94

1-5819

11-61

8-9891

28-78

4-3992

45-95

1-4623

12-62

8-6936

29-79

4-1730

46-96

1-3489

13-63

8-3997

30-80

3-9532

47-97

1-2415

14-64

8-1076

31-81

3-7399

48-98

1-1399

15-65

7-8178

32-82

3-5332

49-99

1-0441

16-66

7-5305

33-83

3-3332

SO-100

•9538

Difference of age Fifty-five years.

Ages.

4$" cent

Ages.

4^cen(

Ages.

Aiffeeax

0-55

7-9297

16-71

6-1828

32-87

2-6147

l-,56

8-6102

17-72

5-9158

33-88

2-4478

2-57

9-0092

18-73

5-6537

34-89

2-2879

3-58

9-1886

19-74

5-3966

35-90

2-1348

4-59

9-2068

20-76

5-1450

36-91

1-9885

5-60

9-1111

21-76

4-8990

37-92

1-8488

6-61

8-9372

22-77

4-6589

38-93

1-7157

7-62

8-7103

23-78

4-4249

39-94

1-5891

8-63

8-4482

24-79

4-1971

40-95

1-4689

9-64

8-1628

25-80

3-9757

41-96

1-3549

10-65

7-8694

26-81

3-7608

42-97

1-2469

11-66

7-6798

27-82

3-5527

43-98

1-1449

12-67

7-2932

28-83

3-3513

44-99

1-0485

13-68

7-0099

29-84

3-1568

43-100

-9578

14-69

6-7302

30-85

2-9691

15-70

6-4544

31-86

2-7884

B. 17.

B. 18.

B. 19.

Difference of age Sixty years.

Ages.

.

0-60

1-61

2-62

3-63

4-64

6-65

6-66

7-67

8-(

9-69

10-70

11-71

12-72

13-73

14-74

15-75

16-76

17-77

18-78

19-79

4^ cent

6-9156
7-4582
7-7560
7-8654
7-8381
7-7156
7-5289
7-2996
7-0429
6-7687
6-4899
6-2166
5-9478
5-6839
5-4252
5-1720
4-9244
4-6827
4-4472
4-2180

Ages.

20-80
21-81
22-82
23-83
24-84
25-85
26-86
27-87
28-88
29-89
30-90
31-91
32-92
33-93
34-94
35-95
36-96
37-97
38-98
39-99

4^ cent

-9952

-7791

■5697

-3671

-1714

-9827

•8010

-6263

-4585

•2977

■1438

•9967

■8564

■7226

5954

4746

3601

2516

1491

0524

Difference of age Sixty-fioe years.

Ages.

4#'cent

Ages.

4#'cent

0-65

5-8949

18-83

3^3808

1-66

6-3073

19-84

3-1842

2-67

6-5129

20-85

2-9945

3-68

6-5618

21-86

2-8119

4-69

6-4989

22-87

2-6363

5-70

6-3596

23-88

2-4678

6-71

6-1697

24-89

2-3062

7-72

5-9474

25-90

2-1516

8-73

5^705 1

26-91

2-0039

9-74

5^4510

27-92

1-8629

10-75

5^1954

28-93

1-7286

11-76

4^9465

29-94

1-6009

12-77

4^7035

30-95

1-4796

13-78

4^4666

31-96

1-3646

14-79

4^2362

32-97

1-2567

15-80

4-0122

23-98

1-1528

16-81

3-7949 34-99

1-0557

17-82

3^5844 35-100

•9643

Difference of age Seventy years.

Ages.

4^cenf

Ages.

4^ cent

0-70

4-9008

16-86

2-8214

1-71

5- 1958

17-87

26451

2-72

5-3219

18-88

2-4758

3-73

6-3225

19-89

2-3136

4-74

5-2363

20-90

2-1584

5-75

5-0894

21-91

2-0101

6-764-9059

22-92

1^8686

7-77

4-6993

23-93

1-7338

8-78

4-4796

24-94

r6056

9-79

4-2527

25-95

1-4839

10-80

4-0270

26-96

1-3685

11-81

3-8087

27-97

1-2593

12-82

3-5973

28-98

M560

13-83

3-3927

29-99

1-0586

14-84

3-1952

30-100

-9669

15-86

3-0047

VILLAGE MORTALITY.

27

Tabs. B. 20 and 21 . Shewing the values of Annuity depending on the co-existence or joint continuance of

two lives, whose common difference of age is 75, or 80 years.

B. 20. B. 21.

Difference of age Seventy-five years.

Ages.

4#'cent

Ages.

4 f cent

Ages.

4 #' cent

0-75

3-9652

9-84

3-2054

18-93

1-7383

1-76

4-1599

10-85

3-0136

19-94

1-6097

2-77

4-2220

11-86

2-8296

20-95

1-4876

3-78

4-1875

12-87

2-6526

21-96

1-3719

4-79

4-0873

13-88

2-4828

22-97

1-2623

5-80

3-9446

14-89

2-3200

23-98

1-1588

6-81

3-7755

15-90

2-1643

24-99

1-0611

7-82

3-5916

16-91

2-0155

25-100

•9691

8-83

3-4000

17-92

1-8735

Difference of age Eighty years.

Ages.

4 f cent

Ages.

4^ cent

Ages.

4^ cent

0-80

3-1152

7-87

2-6469

14-94

1-6133

1-81

3-2293

8-88

2-4865

15-95

1-4909

2-82

3-2436

9-89

2-3260

16-96

1-3748

3-83

3-1874

10-90

2-1694

17-97

1-2650

4-84

3-0845

11-91

2-0202

18-98

1-1612

5-85

2-9526

12-92

1-8778

19-99

1-0633

6-86

2-8040

13-93

1-7422

Tab. B. 22. Shewing the values of a Temporary Assurance of £100, — in one single present
payment, or in annual payments continued during the term of years insured.

Age.

Annual Premium.

Single Premium.

Age.

Five

Tea

Fifteen

Twenty

Five

Ten

Fifteen

Twenty

yean.

years.

years.

years.

years.

years.

years.

years.

20

•6911

•7394

-7877

■8355

31572

6-0494

8-6826

11-0628

20

25

•8004

•8560

•9115

•9662

3-6484

6-9701

9-9726

12-6643

25

30

•9268

•9909

P0546

1-1169

4-2143

8-0237

11-4387

14-4708

30

35

1^0730

1-1468

1^2198

1-2908

4-8653

9-2270

13^0996

16-5001

35

40

1^2421

1-3270

1-4105

1-5278

5-6137

10-5982

14^9749

19-2233

40

45

1^4377

1-5352

1-6879

1-9060

6-4730

12-1567

17^6739'23-4674

46

50

1^6638

1^8767

2-1762

2-5055

7-4579|l4-6973'22-2863,29-7409

50

65

2^16]6

2-5751

3-0162

3-4479

9-6139,19-6920 29-6916 38-4353

56

60

3-1498

3-7249

4-3016

4-8089

13-7528 27-2621 39-330248-7192

60

65

4-6753

5-3544

6-0654

6-5964

19-4606 36-8263 50-3446 58-9504

1 1 1

65

Tab. B. 23. Contingent Assurance. Benefit £lOO. on the death of (A), provided that this person (A)
dies before another person (B). Interest 4 per cent.

A.

B.

single
payment.

Annual

payment.

A.

B.

Single
payment.

AnDual
payment.

A.

B.

Single
payment.

Annual
payment.

A.

B.

Single
payment.

Annual
payment.

20

20
30
40
50
60
70
80

18-093

15-936

13-537

10^958

8^061

5^408

3-313

1-090
1-016'
-937
-865
•796
•729
-663

40

20
30
40
50
60
70
80

30-910
28-386
24-752
19-954
14-341
9-499
5-845

2-140
2-039
1-885
1-689
1-485
1-323
1-193

50

20
30
40
50
60
70
80

40-295
38-102
34-597
29-042
21-372
13-855
8-191

3-179
3-091
2-928
2-665
2-336
1-991
1-701

60

20
30
40
60
60
70
80

52-971
51-198
48-526
43-437
34-616
24-002
14-708

6-228
5-165
5-026
4-747
4-327
3-778
3-223

30

20
30
40
60
60
70
80

23-715
21^210
18-077
14-486
10-603
7-147
4-407

1-511
1-417
1-299
1'176
1-068
•977
•890

45

15
25
36
46
65
65
75

36-140
34-198
31-226
26-766
20-658
14-040
8-803

2-616
2-544
2-416
2-216
1-959
1-695
1-483

55

15
25
36
45
55
65
75

47-087
45-394
42-959
38-785
31-725
22-029
13-739

4-061
3-996
3-889
3-678
3-338
2-860
2-409

70

20
30
40
50
60
70
80

66-077
64-724
62-882
59-381
51-562
39-722
26-785

8-913
8^850
8^757
8^534
8-115
7^432
6-573

28

VILLAGE MORTALITY.

Tab. B. 24. Shewing the Annual Payments equivalent to £100. in the year of death,—
when the Assurance is for one year, and when it extends over the whole of life. Rate
of interest 4 per cent.

Age.

One year.

For life.

Age.

One year.

For life.

Age.

One year.

For life.

Age.

One year.

For life.

12-0092

2^5046

25

•7562

1-5173

50

1-5731

3-4159

75

8-3395

11-9085

1

8-2932

l^8601

26

•7787

1-5604

51

1^6198

3-5602

76

8^9721

12-5759

2

5'6884

1-4708

27

•8019

1^6051

52

1^6678

3-7155

77

9^6500

13-2840

3

3-8836

1^2339

28

•8258

1-6514

53

1-7173

3-8830

78

10^3761

14-0352

4

2-6432

b0921

29

•8504

1-6995

54

1-7682

4-0644

79

11-1531

14-8319

5

1-7950

P0115

30

•8757

1-7493

65

1-8640

4-2616

80

11-9842

15-6769

6

1-2173

•9715

31

•9018

1-8011

56

2-0110

4-4731

81

12-8723

16^5727

7

-8247

•9591

32

•9286

1-8549

57

2-1694

4-6966

82

13-8208

17^5221

8

•5583

-9659

33

•9563

1-9109

58

2-3402

4-9326

83

14-8327

18^5280

9

•4564

-9865

34

•9847

1-9692

59

2-5242

5-1821

84

15-9112

19-5931

10

•4867

1-0134

35

VOUO

2-0300

60

2-7225

5-4459

85

17-0597

20-7203

11

•5012

1-0403

36

1-0442

2-0934

61

2-9361

5-7249

86

18^2813

21-9125

12

•5161

1-0680

37

1-0753

2-1597

62

3-1662

6-0200

87

19-5790

23-1724

13

•5315

1-0965

38

1-1072

2-2290

63

3-4140

6-33-24

88

20-9558

24-5027

14

•5474

1-1259

39

1-1401

2-3016

64

3^6808

6-6631

89

22-4147

25-9060

15

•5637

1-1562

40

1-1741

2-3776

65

3-9680

7-0133

90

23-9580

27-3847

16

•5805

1-1874

41

1-2089

2-4575

66

4^2771

7-3843

91

25-5881

28-9410

17

•5978

1-2195

42

1-2448

2-5415

67

4-6096

7-7774

92

27^3067

30-5765

18

•6157

1-2527

43

1-2818

2-6300

68

4-9674

8-1941

93

29-1154

32-2929

19

•6340

1-2869

44

P3199

2-7234

69

5-3520

8-6358

94

31^0149

34-0910

20

•6529

1-3222

45

1-3591

2-8220

70

5-7655

9-1041

95

33-0054

35-9713

21

•6724

1-3587

46

1-^995

2-9265

71

6-2098

9-6008

96

35-0863

37-9335

22

•6924

1-3964

47

1^4410

3-0375

72

6-6870

10-1276

97

37-2561

39-9767

23

•7130

1-4354

48

1-4:838

3-1555

73

7-1995

10-6865

98

39-5124

42-0990

24

•7343

1-4756 49

1-5278

3-2814

74

7-7495

1 1-2794

99

41-8515

44-2975

Tab. B. 25. Values of Annuity on the joint continuance of three lives, whose differences
of age are and 30 years.

Ages.

4 ^ cent

Ages.

4^ cent

Ages.

4#'cenl

Ages.

4#'cent

0-30-30

9-5190

18-48-48

9-7004

36-66-66

5-0200

54-84-84

1^6768

1-31-31

10-5216

19-49-49

9-4742

37-67-67

4-7809

55-85-85

1-5509

2-32-32

11-2031

20-50-50

9-2415

38-68-68

4-5476

56-86-86

1-4308

3-33-33

11-6266

21-51-51

9-0015

39-69-69

4-3200

57-87-87

1-3172

4-34-34

11-8550

22-52-52

8-7533

40-70-70

4-0985

58-88-88

1-2098

5-35-35

11-9414

23-53-53

8-4960

41-71-71

3-8832

59-89-89

M085

6-36-36

11-9265

24-54-54

8-2286

42-72-72

3-6742

60-90-90

1-0131

7-37-37

11-8400

25-55-55

7-9497

43-73-73

3-4716

61-91-91

•9234

8-38-38

11-7026

26-56-56

7-6660

44-74-74

3-2756

62-92-92

•8392

9-39-39

11-5287

27-57-57

7-3848

45-75-75

3-0861

63-93-93

•7603

10-40-40

11-3379

28-58-58

7-1064

46-76-76

2-9033

64-94-94

•6866

11-41-41

11-1462

29-59-59

6-8313

47-77-77

2-7272

65-95-95

•6178

12-42-42

10-9514

30-60-60

6-5596

48-78-78

2-5577

66-96-96

■5538

13-43-43

10-7533

31-61-61

6-2918

49-79-79

2-3948

67-97-97

•4944

14-44-44

10-5516

32-62-62

6-0280

50-80-80

2^2385

68-98-98

•4394

15-45-45

10-3458

33-63-63

5-7687

51-81-81

2-0887

69-99-99

•3886

16-46-46

10-1357

34-64^64

5-5141

52-82-82

1-9453

17-47-47

9-9207

35-65-65

5-2644

53-83-83

1-8081

CITY MORTALITY.

29

TaBvC. 1.

Tab. C. 2.

Shewing, at the end of any number of
yeais from birth, — the Living out of a
given number bom, — also the Dying
in the year succeeding.

Shewing, in logarithms, at every age of life, — the

Probability of living one year (\,a),~also the
living out of a given number bom (xo).

t* Liviuff.

Dying.

<

Living.

Dying.

1

A,a

Aa

4
<

Xfl

Aa

0161136-45

22557-3

50

57273-8

L399-8

T-9345040

•2071936

50

1-9892535

r-7579557

1 138579-0

13433-1

51

55873-9

1405-9

1

•9557193

•1416976

51

-9889322

•7472092

2 125146-0

8336-1

52

54468-0

1411-0

2

•9700626

•0974169

52

•9886012

•7361414

3 116809-8

5319-0

53

53057-0

1415-0

f

•9797598

■0674795

53

•9882602

■7247426

4111490-9

3458-2

54

51642-0

1417-9

[ -9863159

•0472393

54

•9879090

•7130028

5 108032-7

2277-0

55

50224-1

1453-3

•9907484

•0335552

55

•9872473

•7009118

6 105755-6

1512-2

56

48770-7

1522-0

•9937452

•0243036

56

•9862310

•6881591

7 104243-5

1010-1

57

47248-7

1590-0

•9957712

•0180488

57

-9851337

•6743901

8 103233-3

818-0

58

45658-7

1656-7

( ^9965450

•0138200

58

•9839490

•6595238

9 102415-3

811-5

59

44002-0

1721-3

) ^9965450

•0103650

59

•9826699

•6434728

10101603-8

805-1

60

4-2280-7

1783-0

) -9965450

-0069100

60

•9812888

■6261427

11 100798-7

798-7

61

40497-8

1840-7

•9965450

-0034550

61

-9797977

•6074315

12 100000-0

804-1

62

38657-1

1893-6

. -9964936

-0000000

62

-9781877

■5872292

13 99195-9

821-4

63

36763-5

1940-5

! ^9963887

1-9964936

63

-9764494

■5654169

14 98374-4

838-9

64

34823-0

1980-3

1 ^9962807

-9928823

64

-9745726

■5418663

15 97535-5

856-5

65

32842-7

2011-9

5-9961694

-9891630

65

-9725462

•5164389

16 96679-1

874-2

66

30830-8

2034-1

3 ^9960549

-9853324

66

-9703584

■4889851

17 95804-8

892-1

67

28796-7

2045-8

7 ^9959369

-9813873

67

-9679962

•4593435

18 94912-7

910-1

68

26751-0

2046-0

3 ^9958 153

-9773242

68

-9654457

■4273397

19 94002-5

928-2

69

24705-0

2033-7

3 ^9956902

-9731395

69

-9626920

•3927854

20 93074-3

946-4

70

22671-3

2008-2

2

3 -9955612

•9688297

70

-9597188

•3554774

21 92127-8

964-7

71

20663-1

1969-0

2

1 -9954285

•9643909

71

-9565088

■3151962

22 91163-2

983-0

72

18694-1

1915-8

2

2 -9952917

•9598194

72

-9530428

■2717050

23 90180-2

1001-3

73

16778-3

1848-7

2

3 -9951509

-9551111

73

-9493007

■2247478

24 89178-9

1019-6

74

14929-6

1768-0

2

4 -9950059

•9502620

74

•9452604

■1740485

25 88159-2

1037-9

75

13161-6

1674-6

2

5 -9948565

-9452679

75

-9408980

■1193089

26 87121-3

1056-2

76

11487-0

1569-7

2

8 -9947026

-9401244

76

-9361881

■0602069

27 86065-1

1074-4

77

9917-3

1454-9

2

7 -9945442

-9348270

77

-9311027

^9963950

28 84990-7

1092-5

78

8462-5

1332-2

2

8 -9943810

-9293712

78

-9256122

■9274977

29 83898-1

1110-5

79

7130-3

1203-9

2

9 -9942129

•9237522

79

-9196840

•8531099

30 82787-6

1128-4

80

5926-4

1072-7

3

-9940398

-9179651

80

-91328.35

•7727939

31 81659-2

1146-1

81

4853-7

941-3

3

1 -9938615

-9120049

81

-9063728

•6860774

32 80513-1

1163-6

82

3912-5

812-5

3

2 -9936779

-9058664

82

-8989115

■5924502

33 79349-5

1180-8

83

3100-0

688-9

, 3

3 -9934888

-8995443

83

-8908555

■4913617

34 78168-7

1197-7

84

2411-1

573-0

' 3

4 -9932940

-8930331

84

-8821575

•3822172

35 76971-0

1214-4

85

1838-1

466-8

3

5 -9930934

■8863271

85

-8727664

■2643747

36 75756-6

1230-7

86

1371-3

371-9

3

6 -9928869

•8794205

86

-8626268

■1371411

37 74525-9

1246-6

87

999-5

289-2

3

7 -9926741

■8723074

87

-8516792

3^9997679

38 .73279-3

1262-1

88

710-3

219-1

3

8 -9924550

-8649815

88

-8398592

■8614471

39 72017-2

1277-1

89

491-2

161-3

3

9 -9922293

-8574365

89

-8270972

•691 3063

40 70740-1

1291-7

90

329-9

115-3

4

-9919968

•8496658

90

-8133182

■5184035

41 69448-5

1305-6

91

214-6

79-7

4

1 ^9917575

•8416626

91

-7984412

■3317217

42 68"142-8

1319-1

92

135-0

53-2

4

2 •99151-09

•8334201

92

•7823784

[ ^1301629

43 66823-8

1331-8

92

81-8

34-2

4

3 -9912570

•8249310

93

-765035'/

4-9125413

44 65492-C

1343-9

94

[ 47-6

21-1

4

4 -9909955

•8161880

94

-7463108

■677577C

45 64148 1

1355-3

91

26-5

12-4

4

5 ^9907261

-8071835

95

-7260937

■4238878

46 62792-8

1365-9

9t

14-1

7-0

4

6 ^9904487

•7979096

96

•704265C

) •149981£

47 61426-9

1375-7

9^

7-1

3-7

4

7 •990163C

-7883583

97

•680697?

Sr 8542471

48 60051-2

1384-7

98

3-4

1-9

4

8 •989868g

-7785213

9S

•6552519 -534944^

49 58666-5

1392-7

9£

1-5

•9

4

9 •989565£

•7683902

9£

•6277781 •190196J

30

CITY MORTALITY.

Tab, C. 3. The Expectation of complete yeaw, at all ages of life; or the value of Annuity
of £1, when there is no interest of money.

<

Expect".

1

Expect".

<

Expect".

1

Expect".

4

Expectn.

1

Expect".

1

Expect".

33-0085

15

37-9929

30

28-4525

45

19-6183

60

10-9988

75

4-8227

90

1-6150

1

37-3815

16

37-3295

31

27-8457

46

19-0417

61

10-4831

76

4-5257

91

1-4822

2

40-3940

17

36-6701

32

27-2420

47

18-4652

62

9-9823

77

4-2420

92

1-3576

3

42-2767

18

36-0148

33

26-6415

48

17-8882

63

9-4964

78

3-9713

93

1-2408

4

43-2936

19

35-3635

34

26-0440

49

17-3104

64

9-0256

79

3-7133

94

1-1314

5

43-6795

20

34-7162

36

25-4492

50

16-7313

65

8-5698

80

3-4676

95

1-0291

6

43-6200

21

34-0728

36

24-8572

51

16-1505

66

8-1290

81

3-2339

96

-9336

7

43-2527

22

33-4334

37

24-2676

52

15-5674

67

7-7032

82

3-0120

97

•8446

8

42-6759

23

32-7978

38

23-6805

53

14-9814

68

7-2923

83

2-8014

98

•7617

9

42-0168

24

32-1661

39

23-0955

54

14-3919

69

6-8963

84

2-6018

99

•6847

10

41-3524

25

31-5381

40

22-5124

55

13-7982

70

6-5149

85

2-4128

11

40-6827

26

30-9138

41

21-9311

56

13-2094

71

6-1480

86

2-2341

12

40-0076

37

30-2932

42

21-3513

57

12-6349

72

5-7956

87

2-0654

13

39-3320

28

29-6762

43

20-7728

58

120749

73

5-4574

88

1-9062

14

38-6604

29

29-0626

44

20-1952

59

11-5295

74

5-1331

89

1-7561

Tab. C. 4. Shewing the present value of Annuity

of £1, depending on a single life.

1

3 ^ cent

4#'cent

5^ cent

4

3 ^ cent

4 ^ cent

5 W cent

S^" cent 4 #■ cent

S^cent

16-0590

13-4264

11-4802

34

16-5180

14-5447

12-9387

68

6-1227

5-8028

5^6111

1

18-2332

15-2364

13-0163

35

16-2783

14-3619

12-7971

69

5-8286

5-5347

5^2659

2

19-7960

16-5468

14-1341

36

16-0354

14-1758

12-6523

70

5-5420

5^2724

5^0251

3

20-8450

17-4367

14-9000

37

15-7892

13-9863

12-5043

71

5^2630

5-0162

4^7892

4

21-4946

17-9993

15-3913

38

15-5395

13-7932

12-3529

72

4^9919

4-7664

4-5583

5

21-8482

18-3185

15-6782

39

15-2862

13-5963

12-1978

73

4^7287

4^5230

4-3327

6

21-9882

18-4614

15-8166

40

15-0291

13-3954

12-0390

74

4-4737

4^2864

4-1127

7

21-9763

18-4784

15-8484

41

14-7678

13-1903

11-8760

75

4-2269

4-0567

3^8984

8

21-8571

18-4056

15-8036

42

14-5023

12-9808

11-7087

76

3-9884

3-8340

3^6901

9

21-6926

18-2947

15-7263

43

14-2322

12-7665

11-5368

77

3-7582

3-6185

3-4879

10

21-5219

18-1785

15-6445

44

13-9573

12-5471

11-3600

78

3-5365

3-4102

3-2919

11

21-3446

18-0566

15-5579

45

13-6772

12-3224

11-1779

79

3-3231

3-2092

3-1022

12

21-1605

17-9289

15-4663

46

13-3916

12-0919

10-9901

80

3-1181

3-0156

2^9190

13

20-9720

17-7972

15-3713

47

13-1000

11-8552

10-7962

81

2-9214

2-8293

2-7423

14

20-7815

17-6636

15-2746

48

12-8022

11-6119

10-5958

82

2-7330

2-6504

2-5722

15

20-5891

17-5281

15-1763

49

12-4974

11-3614

10-3881

83

2-5528

2-4788

2-4087

16

20-3946

17-3908

15-0763

50

12-1854

11-1032

10-1728

84

2-3806

2-3145

2-2517

17

20-1982

17-2514

14-9745

51

11-8654

10-8366

9-9490

85

2-2164

2-1574

2^1013

18

19-9996

17-1101

14-8710

52

11-5368

10-5609

9-7161

86

2-0600

2-0076

1^9575

19

19-7991

16-9668

14-7658

53

11-1989

10-2755

9-4732

87

1-9113

1-8646

1^8201

20

19-5964

16-8215

14-6587

54

10-8510

9-9793

9-2194

88

1-7700

1-7286

1-6890

21

19-3917

16-6741

14-5497

55

10-4920

9-6715

8-9537

89

1-6360

1-5994

1-5643

22

19-1848

16-5245

14-4389

56

10-1288

9-3581

8-6816

90

1-6092

1-4768

1-4458

23

18-9757

16-3728

14-3261

57

9-7687

9-0459

8-4093

91

1-3893

1-3607

1-3333

24

18-7645

16-2189

14-2113

58

9-4122

8-7353

8-1372

92

1-2761

1-2509

1-2267

25

18-5509

16-0628

14-0944

59

9-0596

8-4268

7-8658

93

1-1694

1-1473

1-1260

26

18-3351

15-9043

13-9755

60

8-7112

8-1206

7-5953

94

1-0689

1-0496

1-0309

27

18-1169

15-7434

13-8543

61

8-3676

7-8173

7-3262

95

•9746

•9577

-9413

28

17-8963

15-5802

13-7309

62

8-0290

7-5171

7-0588

96

-8861

•8713

-8570

29

17-6733

15-4144

13-6052

63

7-6958

7-2204

6-7934

97

-8033

•7904

-7779

30

17-4476

15-2460

13-4771

64

7-3684

6-9277

6-5306

98

-7259

•7147

•7038

31

17-2194

15'0750

13-3465

65

7-0471

6-6392

6-2706

99

•6537

■6440

•6346

32

16-9884

14-9011

13-2133

66

6-7322

6-3554

6-0138

33

16-7547

14-7244

13-0774

67

6-4239

6-0765

6-7605

31

Tab. C. S. Comparative vifew of the preceding Tables of Mortality. Quinquennial stages. Common
basis, 100000 aged 12 years. Sliewing, — the Survivors at the beginning, and the Dying, during
each stage; — also the Sum of the Survivors at the beginning of each of the five years of tlie stage.

Sum of Annual Survivors.

Dying.

Survivors incepting.

q

Between
Ages.

!^

Village.

Mean.

City.

Village.

Mean.

City.

Village.

Mean.

City.

s

0—5

628169

618280

653162

45104

40096

53103

151403

146472

161136

6-10

517234

518841

523680

5264

5095

6429

106299

106376

108033

5

10-15

499936

499973

499973

2685

3257

4069

101035

101281

101604

10

15-20

485847

483069

478935

3022

3604

4461

98350

98024

97535

15

20-25

470017

464246

455724

3386

4010

4915

95328

94420

93074

20

25-30

452320

443351

430234

3774

4435

5371

91942

90410

88159

25

30-35

432645

420314

402478

4180

4867

5817

88168

85975

82788

30

35-40

410916

395114

372550

4596

5297

6231

83988

81108

76971

35

40-45

387101

367800

340647

5012

5706

6592

79392

75811

70740

40

45-50

361228

338506

307085

5414

6078

6874

74380

70105

64148

45

50-55

333406

307471

272315

5782

6386

7050

68966

64027

57274

50

55-60

302953

274099

235904

6851

7417

7943

63184

57641

50224

55

60-65

264953

233409

193022

8731

9189

9438

56333

50224

42281

60

65-70

217737

184483

143926

10421

10529

10172

47602

41035

32843

65

70-75

163389

130790

93736

11306

10761

9509

37181

30506

22671

70

75-80

107401

79156

50159

10674

9316

7236

25875

19745

13162

75

80-85

58246

38088

20204

8236

6341

4088

15201

10429

5926

80

85-90

23919

13165

5410

4749

3053

1508

6965

4088

1838

85

90-95

6585

2833

809

1803

897

304

2216

1035

330

90

95-100

1024

310

53

378

131

25

413
35

138

7

26

1

95
100

0-100

6125026

5813298

5480006

151368

146465

161135

Tab; C. 6. Comparison continued. Decennial stages. Common basis 100000 annually attaining the age
of 12 years. Shewing the relations of Annual Deaths and Annual Survivors.

» Sum of Annual Survivors.

Annual Deaths.

Deaths from 100 years of Life.

Between
Ages.

Between

Ag s.

Village.

Mean.

City.

Village.

Mean.

City.

Village.

Mean.

City.

e

0-10

1145403

1137121

1176842

50368

45191

59533

4-3974

3-9742

5-0587

0-10

10-20

985783

983042

978907

5708

6861

8530

•5790

•6979

•8713

10-20

20-30

922337

907597

885959

7160

8445

10287

•7763

•9305

1-1611

20-30

30-40

843561

815428

775028

8776

10164

12048

1-0403

1-2464

1-5545

30^0

40-50

748329

706307

647733

10426

11784

13466

1-3932

1-6684

2-0790

40-50

5,0-60

636359

581570

508219

12633

13803

14993

1-9853

2^3734

2-9501

50-60

60-70

482689

417892

336948

19152

19719

19609

3-9678

4-7186

5-8197

60-70

70-80

270790

209946

143895

21980

20077

16745

8-1170

9-5629

11-6369

70-80

80-90

82165

51253

25614

12984

9394

5596

15-8030

18-3292

21-8492

80-90

90-100

7610

3143

862

2181

1027

329

28-6628

32-6887

32-8118

90-100

0-100

6125026

5813299

5480007

151368

146465

161136

2-4713

2-5195

2-9404

0-100

32

Tab. C. 7. Comparison continued. Exhibiting, in three large intervals of age, the relations of Annual
Survivors and Annual Deaths. Assuming two additional bases — a total Population of 1,000,000 —
and 100,000 as the total yearly deaths.

Between
Ages.

Living.

Dying.

Rate of Death to Life,
and to Age.

Between
Ages.

Village.

Mean.

City. ■

Village.

Mean.

City.

ViUage.

Mean.

City.

0-20
20-50
50-100

2131186
2514227
1479612

2120164
2429331
1263804

2155750
2308719
1015538

56075
26362
68931

52052
30393
64020

68062
35801
57273

2-6312
1-0485
4-6587

2-4551
1-2511
5-0657

3-1572
1-5507
5-6397

0-20
20-50
50-100

0-100

6125025

5813299

5480007

151368

146465

161136

2-4713

2-5195

2-9404

0-100

0-20
20-50
50-100

347947
410485
241568

364709
417892
217399

393385
421298
185317

9155

4304

11254

8954

5228

11013

12420

6533

10451

37045
17416
45539

35539
20751
43710

42239
22218
35543

0-20
20-50

50-100

0-100

1000000

1000000

1000000

24713

25195

29404

100000

100000

100000

0-100

Tab. C. 8. Comparison continued. Shewing, at quinquennial intervals, the Expectation of complete
years, and the values of Assurance of £100. in Single Payments, and in Annual Payments. Rate
of interest 3 per cent.

Age.

For Assurance of £100 in the year of Death.

Age.

Expectation.

Annual Premium for Life.

Single Premium.

Village.

Mean.

City.

ViUage.

Mean.

City.

Village.

Mean.

City.

5
10
15
20
25
30
35
40
45
50
55
60
65
70
75
80
85
90
95

39-4556

50-7121

48-2866

44-5490

40-8966

37-3275

33-8378

30-4202

27-0634

23-7501

20-4552

17-1419

13-9704

11-1502

8-6996

6-6232

4-9107

3-5371

2-4662

1-6547

38-6889

47-8365

45-1705

41-6042

38-1141

34-7141

31-3996

28-1617

24-9873

21-8561

18-7387

15-5915

12-5840

9-9380

7-6657

5-7646

4-2172

2-9926

2-0507

1-3468

33-0085

43-6795

41-3524

37-9929

34-7162

31-5381

28-4525

25-4492

22-5124

19-6183

16-7313

13-7982

10-9988

8-5698

6-5149

4-8227

3-4676

2-4128

1-6150

1-0291

2-3831

1-1384

1-1682

1-3207

1-4972

1-7035

1-9476

2-2414

2-6030

3-0618

3-6691

4-5232

5-7102

7-2799

9-3739

12-1845

15-9655

21-0320

27-7348

36-3798

2-3365

1-2497

1-3163

1-4843

1-6800

1-9083

2-1780

2-5022

2-9012

3-4085

4-0843

5-0472

6-4013

8-1999

10-6071

13-8436

18-1934

23-9942

31-5905

41-2137

2-9494

1-4641

1-5275

1-7194

1-9426

2-2022

2-5081

2-8750

3-3260

3-9007

4-6715

5-7891

7-3847

9-5142

12-3733

16-2192

21-3703

28-1777

36-9407

47-7305

45-0001
28-1016
28-6268
31-1975
33-9513
36-9028
40-0724
43-4887
47-1935
51-2487
55-7470
60-8298
66-2219
71-4240
76-2941
80-7075
84-5715
87-8360
90-4963
92-5873

44-5121
30-0241
31-1266
33-7575
36-5806
39-5837
42-7847
46-2103
49-9017
53-9226
58-3726
63-4085
68-7284
73-7897
78-4565
82-6177
86-2000
89-1752
91-5584
93-3994

50-3137
33-4519
34-4024
37-1192
40-0104
43-0555
46-2690
49-6749
53-3134
57-2508
61-5960
66-5281
71-7148
76-5618
80-9457
84-7760
88-0055
90-6318
92-6916
94-2487

5
10
15
20,
25
30
35
40
45
50
55
60
65
70
75
80
85
90
95

NORTHAMPTON MORTALITY.

33

Tab. D. 1.

Tab. D. 2.

Shewing, at the end of any number of
years from birth, — the Living out of a
given number born, — also the Dying
in the year succeeding.

Shewing, at every age of life, in logarithms, — the
probability of living one year (x,o),— also the
Living out of a given number born (xo).

4
<

liiving*

Dying.

4

Living.

Dying.

218820-2

48803-7

50

53232-0

1469-5

1

170016-5

26667-4

51

51762-5

1471-1

2

143349-1

15617-1

52

50291-5

1471-4

3

127732-0

9582-7

53

48820-1

1470-4

4

118149-3

6067-9

54

47349-7

1468-1

5

112081-4

3924-9

55

45881-6

1464-4

6

108156-4

2575-4

56

44417-2

1459-4

7

105581-1

1706-3

57

42957-8

1453-0

8

103874-8

1138-0

58

41504-8

1445-1

9

102736-8

920-5

59

40059-8

1435-7

10

101816-3

912-3

60

38624-1

1424-9

11

100904-0

904-0

61

37199-2

14126

12

100000-0

909-2

62

35786-6

1431-8

13

99090-8

927-8

63

34354-8

1481-7

14

98163-0

946-5

64

32873-2

1528-1

15

97216-5

965-2

65

31345-1

1570-2

I6

96251-3

984-1

66

29774-9

1607-1

17

95267-2

1003-0

67

28167-7

1638-0

18

94264-1

1022-0

68

26529-8

1661-7

19

93242-2

1041-0

69

24868-0

1677-5

20

92201-2

1060-0

70

23190-5

1684-4

21

91141-2

1078-9

71

21506-1

1681-5

22

90062-3

1097-9

72

19824-6

1668-2

23

88964-5

1116-7

73

18156-4

1643-9

24

87847-8

1135-5

74

16512-5

1608-2

25

86712-4

1154-1

75

14904-2

1561-0

26

85558-3

1172-6

76

13343-2

1502-4

27

84385-7

1190-8

77

11840-8

1432-8

28

83194-9

1208-9

78

10408-1

1353-0

29

81986-1

1226-7

79

9055-1

1264-0

30

80759-4

1244-2

80

7791-1

1167-4

31

79515-2

1261-4

81

6623-7

1064-9

32

78253-8

1278-2

82

5558-8

958-4

33

76975-7

1294-6

83

4600-4

850-1

34

75681-0

1310-5

84

3750-3

742-4

35

74370-5

1326-0

85

3007-9

637-6

36

73044-5

1341-0

86

2370-4

537-5

37

71703-5

1355-4

87

1832-9

444-4

38

70348-1

1369-1

88

1388-5

359-7

39

68978-9

1382-2

89

1028-9

284-5

40

67596-7

1394-6

90

744-4

219-5

41

66202-0

1406-3

91

524-8

165-0

42

64795-7

1417-1

92

359-9

120-4

43

63378-6

1427-1

93

239-5

85-2

44

61951-5

1436-2

94

154-2

58-3

45

60515-2

1444-4

95

95-9

38-5

46

59070-8

1451-6

96

57-4

24-4

47

57619-2

1457-7

97

33-0

14-9

48

56161-5

1462-8

98

18-2

8-6

49

54698-8

1466-7

99

9-5

4-8

A.ffl

r- 8904037
•9259038
-9499048
-9661315
-9771021
-9845191
-9895336
-9929239
-9952159
-9960914
-9960913
-9960914
-9960332
-9959145
-9957923
-9956665
-9955368
-9954033
-9952658
-9951242
-9949784
-9948282
-9946735
-9945142
•9943501
-9941811
•9940070
-9938278
-9936431
-9934530
•9932572
-9930555
•9928477
-9926338
•9924135
•9921866
-9919528
-9917121
■9914642
-9912089
■9909460
■9906751
-9903962
-9901089
-9898131
-9895084
•9891946
-9888713
■9885385
•9881956

Aa

•3400875
•2304912
•1563950
•1062998
•0724313
•0495334
-0340525
-0235861
-0165100
-0117259
-0078173
-0039086
-0000000
r-9960332
-9919477
-9877400
-9834065
-9789433
-9743466
-9696124
-9647366
-9597150
-9545432
-9492167
•9437309
■9380810
■9322621
■9262691
■9200969
•9137400
•9071930
•9004502
•8935057
•8863534
•8789872
••8714007
•8635873
■8555401
■8472522
•8387164
•8299253
•8208713
•8115464
•8019426
•7920515
•7818646
•7713730
•7605676
•7494389
•7379774

A, a

r9878426
•9874789
•9871044
•9867186
•9863214
•9859122
•9854908
•9850568
•9846099
•9841495
•9836754
■9831871
•9822670
•9808538
•9793280
■9776806
•9759019
•9739814
•9719080
•9696693
•9672521
-9646424
-9618246
-9587824
•9554976
•9519511
•9481220
-9439877
-9395240
•9347045
•9295010
•9238827
•9178168
•9112674
•9041961
•8965613
•8883180
■8794178
■8698083
■8594331
•8482310
■8361362
■8230775
•8089781
■7937552
•7773190
•7595730
•7404129
•7197258
•6973901

;ia

r7261730
•7140156
•7014945
•6885989
•6753175
•6616389
•6475511
•6330419
•6180987
■6027086
•5868581
•5705335
•5537206
•5359876
•5168414
•4961694
•4738500
•4497519
•4237333
•3956413
•3653106
•3325627
•2972051
•2590297
■2178121
•1733097
•1252608
•0733828
■0173705
r- 9568945
•8915990
•8211000
•7449827
•6627995
•5740669
•4782630
•3748243
•2631423
•1425601
•0123684
r8718015
•7200325
•5561687
•3792462
-1882243
i-98 19795
-7592985
•5188715
•2592844
^9790102

34

STOCKHOLM MORTALITY.

Tab. D. 3.

Tab. D. 4.

Shewing, at the end of any number of years
from birth, — the Living out of a given
number born, — also the Dying m the year
succeeding.

Shewing, in logarithms, at every age of life, — the
probability of living one year (».,o), — also the
Living out of a given number bom (x a).

<

Living.

Dying.

Living.

Dying.

/,a

A a

1

Aa

X a

302679-3

90852-2

50

40994-S

1591-3

T-844998S

•4809828

50't^9828058

T^6 127296

1

211827-1

45413-8

51

39403-6

1574-4

1

-8962064

•32,59817

61

•9822915

■5966354

2

166413-3

25049-3

52

37829-2

1556-7

2

•9291608

•2211881

52

•9817618

•5778269

3

141364-C

14762-4

53

36273-4

1535-4

3

•9521001

•1503389

53

•9812163

•5695887

4

126601-6

9097-0

64

34738-C

1613-4

4

•9676167

•1024390

54

•9806544

•5408050

5

117504-6

5777-0

65

33224-6

1489-8

5

•9781055

•0700547

55

•9800758

•5214594

6

111727-6

3744-0

56

31734-8

1464-6

6

-9851976

•0481602

56

•9794798

•5015352

7

107983-6

2459-9

57

30270-2

1437-8

7

-9899923

•0333577

57

•9788660

•4810150

8

105523-7

1631-3

68

28832-4

1409-4

8

•9932340

•0233500

58

•9782339

•4598810

9

103892-4

1314-0

59

27423-0

1379-6

9

•9944720

•0165840

59

•9775828

■4381149

10

102578-4

1-297-4

60

26043-4

1348-3

10

•9944720

•0110560

60

•9769123

■4156977

11

101281-0

1281-0

61

24695-1

1315-7

11

•9944720

•0055280

61

•9762217

■3926100

1,2

100000-0

1283-5

62

23379-3

1311-9

12

•9943898

-0000000

62

•9749203

■3688317

13

98716-5

1304-7

63

22067-4

1333-9

13

•9942219

1-9943898

63

•9729217

•3437520

14

97411-8

1325-7

64

20733-6

1349-8

14

-9940491

•9886117

64

■9707637

•3166737

15

96086-1

1346-5

65

19383-7

1358-9

15

-9938711

•9826608

65

■9684338

•2874374

16

94739-7

1367-0

66

18024-8

1360-4

16

-9936878

-9766319

66

■9659182

•2.558712

17

93372-6

1387-3

67

16664-4

1353-8

17

-9934990

-9702197

67

•9632022

•2217894

18

91985-4

1407-3

68

15310-6

1338-6

18

•9933046

•9637187

68

■9602697

•1849916

19

90578-1

1426-8

69

13972-1

1314-1

19

•9931043

•9570232

69

•9571035

•1452613

20

89151-3

1446-0

70

12658-0

1280-4

20

•9928980

•9501275

70

•9536850

■1023648

21

87705-2

1464-7

71

11377-6

1237-4

21

•9926856

•9430255

71

•9499940

•0560498

22

86240-5

1483-0

72

10140-1

1186-4

22

•9924668

•9357111

72

•9460089

•0060438

23

84757-5

1500-7

73

8954-7

1124-8

23

•9922414

•9281779

73

•9417063

2-9520527

24

83256-7

1517-8

74

7830-0

1056-3

24

•9920094

•9204193

74

•9370607

■8937590

25

81738-9

1534-3

75

6773-6

981-1

25

■9917703

•9124287

75

•9320449

•8308197

26

80204-6

1550-1

76

5792-5

900-4

26

■9915242

•9041990

76

•9266294

■7628646

27

78654-4

1565-2

77

4892-1

816-7

27

-9912707

•89.57232

77

•9207823

■6894940

28

77089-3

1679-5

78

4076-4

728-7

28

•9910095

•8869939

78

•9144693

■6102763

29

75509-8

1592-9

79

3347-7

641-3

29

•9907406

•8780034

79

■9076532

•5247456

30

73916-9

1605-4

80

2706-4

555-2

30

•9904637

•8687440

80

•9002939

•4323988

31

72311-5

1617-0

81

2151-3

472-3

31

•9901784

-8592077

81

•8923480

•3326927

32

70694-6

1627-5

82

1679-0

394-2

32

•9898846

-8493861

82

•8837690

•2250407

33

69067-0

1637-1

83

1284-7

322-4

33

•9895821

•8392707

83

•8745064

•1088097

34

67429-9

1645-5

84

962-3

267-9

34

•9892705

-8288628

84

•8645054

^•983316 1

35

65784-5

1652-8

85

704-4

201-4

35

•9889495

-8181233

85 •8637075

•8478215

36

64131-7

1658-8

86

503-0

153-3

36

•9886190

■8070728

86

•8420492

•7015290

37

62472-9

1663-6

87

349-6

113-5

37

-9882786

■7956918

87

•8294617

•5435782

38

60809-4

1667-0

88

236-1

81-6

38

■9879280

■7839704

88

■8158711

•3730399

39

,59142-3

1669-1

89

154-5

56-7

39

-9875669

■7718984

89

■8011975

•1889110

40

57473-2

1669-8

90

97-7

38-1

40

•9871950

■7594653

90

■7853645

4-9901085

41

55803-4

1669-1

91

59-6

24-7

41

-9868119

■7466603

91

■7682489

-7754630

42

54134-3

1666-8

92

35-0

15-3

42

•9864176

■7334722

92

■7497800

-5437119

43

52467-4

1663-1

93

19-7

9-1

43

•9860112

■7198897

93

■7298394

-2934919

44

50804-3

1657-7

94

10-6

5-2

44

•9855928

•7059009

94

■7083097

•0233313

45

49146-6

1650-8

96

5-4

2-8

45

•9851618

•6914937

96

•6850643

5-7316410

46

47495-8

1642-2

96

2-6

1-4

46

•9847180

•6766555

96

•6599663

•4167053

47

45853-6

1632-0

97

1-2

-7

47

-9842609

■6613735

97

•6328683

-0766716

48

44221-6

1620-1

98

-5

-3

48

-9837900

■6456344

98

■6036107

ff-7095399

49

42601-4

1606-6 99

-2

•1

49

-9833052

■6294244 99

■5720216

•3131506

35

Tab. D. 5. Comparison of the preceding Northampton and Stockholm Tables (which are those of Dr. Price,
adapted to the New Theory) under the heads,— Expectation of complete years,— Survivors at successive
ages— Annual Deaths, and Constantly Living in a Stationary Population, resulting from 1 00,000 annually
attaining the age of 12 years.

Age.

Expectation.

Survivors.

.

Northampton

Stockholm.

Northampton

Stockhohn.

24-1582

15-7839

218820

302679

5

41-1753

34-1583

112081

117505

10

40-1980

33-9452

101816

102578

15

37-0044

31-1028

97216

96086

20

33-9064

28-3644

92201

89151

25

30-9239

25-7530

86712

81739

30

28-0538

23-2646

80759

73917

35

25-2897

20-8919

74371

65784

40

22-6214

18-6232

67597

57473

45

20-0328

16-4401

60515

49147

50

17-4990

14-3142

53232

40995

55

14-9821

12-2000

45882

33225

60

12-4233

10-0232

38624

26043

65

9-8351

7-7786

31345

19384.

70

7-5785

5-8578

23190

12658

75

5-6928

4-2920

14904

6774

80

4-1596

3-0510

7791

2706

85

2-9478

2,-094S

3008

704

90

2-0172

1-3783

744

98

95

1-3255

-8387

96

5

Between
Ages.

■ Living.

Dying.

Rate
^cent.

0—5

724698

106739

14-7287

5-10

527298

10265

1-9467

10-20

971408

9615

-9898

20-30

866334

11442

1-3207

30-40

743049

13163

1-7715

2

40-50

604808

14365

2-3751

1

50-60

458973

14608

3-1827

60-70

311806

15434

4-9497

^

70-80

151042

15399

10-1954

80-90

34430

7047

20-4669

•

90-100

1867

740

39-6197

0-100

5395713

218816

4-0554

20-50

2214191

38969

1-7600

0—5

856298

185175

21-6250

5-10

539169

14926

2-7684

10-20

960036

13427

1-3986

20-30

816691

15234

1-8654

30^0

657539

16444

2-5008

40-50

491762

16478

3-3508

50-60

333248

14951

4-4866

60-70

193582

13385

6-9146

3

70-80

70867

9952

14-0425

80-90

9427

2609

27-6726

90-100

184

98

53-2193

0-100

4928803

302679

6-1410

20-50

1965992

48156

2-4495

Tab. D. 6. Exhibiting the coincidence, for long portions of time, of the Table of Village Mortality with
the Carlisle Table of Mr. Milne ; the former being under .the regulation of the New Theory, and the latter
expressing an imagined decrement for short periods of the greatest irregularity. Rate of interest 4 per cent.

Age.
5

Survivors.

Expectation. j

Life Annual Premium for 1
Assurance of £ LOO. 1

Premium for one year's
Assurance of £lOO.

Life Annuity of f 1.

Age.

5

Milne*

Theory.

Milne.

Theory.

Milne.

Theory.

Milne.

Theory.

Mitae.

Theory.

10522

10521

51-25

51-21

1-0096

1-0115

1-7117

1-7950

19-594

19-586

10

10000

10000

48r82

48-79

1-0117

1-0134

-4316

•4867

19-585

19-578

10

15

9762

9734

45^00

45-05

1-1648

1-1562

-5952

-5637

18-956

18-991

15

20

9427

9435

41-46

41-40

1-3183

1-3222

•6789

•6529

18-363

18-348

20

25

9101

9100

37-86

37-83

1-5172

1-5173

-7032

-7562

17-645

17-645

25

30

8734

8726

34-34

34-34

1-7554

1-7493

-9714

-8757

16-852

16-872

30

35

8300

8313

31-00

30-92

2-0220

2-0300

-9863

1-0140

16-041

16-018

35

40

7856

7858

27-61

27-56

2-3750

2-3776

1-2504

1-1740

15-074

15-067

40

45

7317

7362

24-46

24-25

2-774'6

2-8220

1-4239

1-3591

14-104

13-997

45

50

6807

6826

21-11

20-96

3-3641

3-4159

1-2902

1-5731

12-869

12-770

50

55

6305

6254

17-58

17-64

4-2839

4-2616

1-7233

1-8640

11-300

11-334

55

60

5639

5576

14-34

14-47

5-5320

5-4459

3-2201

2-7225

9-663

9-762

60

65

4672

4711

11-79

11-65

6-8984

7-0133

3-9506

3-9680

8-307

8-208

65

70

3717

3680

9-18

9-20

9-1257

9-1041

4-9658

5-7654

6-709

6-722

70

75

2593

2561

7-01

7-12

12-1820

11-9085

9-1848

8-3395

5-239

5-347

75

80

1475

1504

5-51

5-41

15-4476

15-6769

11-7039

11-9842

4-183

4-122

80

85

689

689

4-12

4-04

20-4551

20-7203

16-8539

17-0597

3-115

3-071

85

90

220

219

3-28

2-97

25-4278

27-3847

25-0541

23-9580

2-416

2-^202

90

95

46

41

3-53

2-15

23-3721

35-9713

22-4359

33-0054

2-674

1-511

95

36

Tab. D. 7. The Observations made on the Populations of Sweden, Glasgow, Carlisle, and Stockholm,
compared with the New Table of Mean Mortality. Expressing the annual Death from 100 con-
stantly Living.

Between

Glasgow.

CarUsle.

The New
Table. •

Sweden.

Stockholm.
9 Years. 1756—63.

Between
Ages.

Ages.

6 Yean.
1821—26.

9 Years.
1779-87.

21 Years.

17SS-7.'i.

20 Years.
I776-«5.

5 Years.
1801—6.

Hales.

Females.

0—5
5-10
10-20
20-30
30-40
40^0
50-60
60-70
70-80
80-90

Al>ove90

7-7300

1-2937

-7147

1-0500

1-3101

1-7057

2-8802

5-1932

11-4978

19-2833

37-1515

8-2282

1-0226

-5854

•7541

P0588

1-4345

1-8267

4-,1249

8-2992

17-5627

28-4444

6-7250

•9869

•7004

•9348.

1-2543

1-6824

2-4019

4-8326

10-0432

20-1783

39-8503

9-0089

1-4165

•7086

•9181

1^2200

1-7409

2-6412

4-8095

10-2320

20-7769

39-4096

8-5027

1-3648

•6530

•8910

1-1560

1-6063

2-3868

4-9340

10-4115

19-7391

35-1325

7-3889

1-0701

-5370

-7415

•9712

1-4602

2-5115

4-8940

11-1768

23-2119

41-9837

26-9579

2-8926

1-3041

2-6260

3-5419

4-6711

6-4587

10-0992

15-8654

31-9444

37-5000

22^8428

2-5641

•9353

1-5035

2-4115

3-3909

4-0532

6-6732

14-6809

34-1708

44-4444

0—5
5-10
10-20
20-30
30-40
40-50
50-60
60-70
70-80
80-90
90-100

AU Ages.

2-5557

2-5000

2-5525

2-8898

2-6786

2-4449

5-9312

4-7772

0-100

Tab. D. 8. Deparcieux's French Monks, Nuns, and Tontine.
Expressing the relation of annual Deaths to 100 annual
Survivors.

Between
Ages.

Tontine.

Benedict.
Monies of
St. Maur.

Other Be-
nedictine
Monks.

Monks

of St.

Gteeri^Te

Many
other
Monks.

Many

Nuns

in Paris.

20-30

1-03

-74

-83

-87

•78

-80

30-40

1-10

1-12

-95

1-36

•94

1-04

40-50

1-22

1-58

1-53

2-03

r5i

1-40

50-60

2-22

2-98

2-91

3-11

2-72

2-34

60-70

3-83

5-48

5-67

5-89

5-20

4-59

70-80

8-65

12-30

12-88

11-20

10-93

9-10

80-90

18-23

23-77

24-14

24-54

24-03

18^84

90-100

44-00

33-33

33-33

33-33

42-86

26^67

20-100

2-46

2-57

2-56

2-70

2-51

2-46

Tab. D. 9. Shewing the relation of Sickness
to Life, at different ages, according to the
Report made by the Highland Society.

Between
Agefc

Years
of Life.

Weeks of
Sickness.

Sick
Weeks in
a Year.

Rate of
Sick time

to ISO of
Lifetime.

17-20
20-30
30-40
40-50
50-60
60-70

AboTe70

1056

23509
36261
25119
12598
4548
1127

401
13907
24894
25806
23691
25622
18642

•3797

•5916

•6865

1-0273

1-8805

5-6337

16-5413

•7611

•7278
M337
r3157
1-9689
3-6041
10-7970
31-7016

20-^0

84889

64607

1^4586

Tab. D. 10. Shewing the Annual Rate of Mortality per cent, on Six Classes of Government Annuitants, for
periods terminating in the year 1826, so for as can be collected from the published " Statement."

Between
Ages.

Nos. 1.

2.

3.

4.

5.

6.

2, 3, 4, and 5. |

Male.

Female.

Male.

Female.

Male.

Female.

Male.

Female.

Male.

Female.

Male.

Female.

Hate.

FemBl&

0-11
11-21

21-31
31-41
41-51
51-61
61-71
71-81
81-91

•95
1-21
2-61
2-21
2-57
3-33
6-29
11-91
21-05

1-44
-78
1-57
1-88
2-02
3-42
4-49
9-95
25-22

-54

-50

1-16

1-17

1-29

2-91

6-64

11-72

20-66

-68
;52
1-12
1-28
1-63
2-49
5-03
9-14
14-76

-70
-85
1-36
1-25
1-35
2-40
4-27
8-59
20-12

-59

•67

■97

1-15

1"24

1^52

3-53

8-78

14-93

-79
-96
1-31
1-30
1-17
2-18
4-07
8-08
11-59

-65

•78

•76

1-00

1^30

1-71

2-73

7-50

19-19

-84
-87
1-30
1-12
1-46
3-05
5-34
9-35
21-97

-78
-89
-81
-93
•97
1-63
4-35

1-65
2-20
4-27
8-37
15-17

-76

1-44

2-80

6-85

13-98

-77
-85
1-30
1^20
1^34
2^69
5-30
9-73
18-95

-67

•75

•89

1^07

1-31

1-94

4-20

8-78

15-30

Total 1
nuatlu.l

594

408

892

1504

911

1082

637

678

1243

580

593

955

3683

3844

Number 1

ll'ing i-

olIginBll^.j

594

408

928

1624

1486

2071

1498

2020

2764

2067

2077

4815

6676

7782

obiern. f
tlon In f

90 years.

80

51

37

. 37

9

40 1

37

Tab. D. 11. Shewing the present value of
£100 certain, to be received at the end of
any number of years, from one to fifty.

Tab. D. 12. Shewing the present value of
Annuity of £l, for a fixed term of years,
payments being made at the end of each year.

Years.

S^-cent.

l#'cent.

5 f cent.

6 #' cent.

Years.

3 #■ cent.

4 #■ cent.

5 #" cent.

6 ^ cent.

1

97-0874

96-1538

95-2381

94-3396

1

-9709

•9615

-9524

-9434

2

94-2596

92-4556

90-7029

88-9996

2

1-9134

1-8861

1-8594

1-8334

3

91-5142

88-8996

86-3838

83-9619

3

2-8286

2-7751

2-7232

2-6730

4

88-8487

85-4804

82-2702

79-2094

4

3-7171

3-6299

3-5460

3-4651

5

86-2609

82-1927

78-3526

74-7258

5

4-5797

4-4518

4-3295

4-2124

6

83-7484

79-0315

74-6215

70-4961

6

5-4172

5-2421

5-0757

4-9173

7

81-3092

75-9918

71-0681

66-5057

7

6-2303

6-0021

5-7864

5-5824

8

78-9409

73-0690

67-6839

62-7412

8

7-0197

6-7327

6-4632

6-2098

9

76-6417

70-2587

64-4609

59-1898

9

7-7861

7-4353

7-1078

6-8017

10

74-4094

67-5564

61-3913

55-8395

10

8-5302

8-1109

7-7217

7-3601

11

72-2421

64-9581

58-4679

52-6788

11

9-2526

8-7605

8-3064

7-8869

12

70-1380

62-4597

55-6837

49-6969

12

9-9540

9-3851

8-8633

8-3838

13

68-0951

60-0574

53-0321

46-8839

13

10-6350

9-9856

9-3936

8-8527

14

66-1118

57-7475

50-5068

44-2301

14

11-2961

10-5631

9-8986

9-2950

15

64-1862

55-5265

48-1017

41-7265

15

11-9379

11-1184

10-3797

9-7122

16

62-3167

53-3908

45-8112

39-3646

16

12-5611

11-6523

10-8378

10-1059

17

60-5016

51-3373

43-6297

37-1364

17

13-1661

12-1657

11-27-41

10-4773

18

58-7395

49-3628

41-5521

35-0344

18

13-7535

12-6593

11-6896

10-8276

19

57-0286

47-4642

39-5734

33-0513

19

14-3238

13-1339

12-0853

11-1581

20

55-3676

45-6387

37-6889

31-1805

20

14-8775

13-5903

12-4622

11-4699

21

53-7549

43-8834

35-8942

29-4155

21

15-4150

14-0292

12-8212

11-7641

22

62-1893

42-1955

34-1850

27-7505

22

15-9369

14-4511

13-1630

12-0416

23

50-6692

40-5726

32-5571

26-1797

23

16-4436

14-8568

13-4886

12-3034

24

49-1934

39-0121

31-0068

24-6979

24

16-9355

15-2470

13-7986

12-5504

25

47-7606

37-5117

29-5303

23-2999

25

17-4131

15-6221

14-0939

12-7834

26

46-3695

36-0689

28-1241

21-9810

26

17-8768

15-9828

14-3752

13-0032

27

45-0189

34-6817

26-7848

20-7368

27

18-3270

16-3296

14-6430

13-2105

28

43-7077

33-3477

25-5094

19-5630

28

18-7641

16-6631

14-8981

13-4062

29

42-4346

32-0651

24-2946

18-4557

29

19-1885

16-9837

15-1411

13-5907

30

41-1987

30-8319

23-1377

17-4110

30

19-6004

17-2920

15-3725

13-7648

31

39-9987

29-6460

22-0359

16-4255

31

20-0004

17-5885

15-5928

13-9291

32

38-8337

28-5058

20-9866

15-4957

32

20-3888

17-8736

15-8027

14-0840

33

37-7026

27-4094

19-9873

14-6186

33

20-7658

18-1476

16-0025

14-2302

34

36-6045

26-3552

19-0355

13-7912

34

21-1318

18-4112

16-1929

14-3681

35

35-5383

25-3415

18-1290

13-0105

35

21-4872

18-6646

16-3742

14-4982

36

34-5032

24-3669

17-2657

12-2741

36

21-8323

18-9083

16-5469

14-6210

37

33-4983

23-4297

16-4436

11-5793

37

22-1672

19-1426

16-7113

14-7368

38

32-5226

22-5285

15-6605

10-9239

38

22-4925

19-3679

16-8679

14-8460

39

31-5754

21-6621

14-9148

10-3056

39

22-8082

19-5845

17-0170

14-9491

40

30-6557

20>8289

14-2046

9-7222

40

23-1148

19-7928

17-1591

15-0463

41

29-7628

20-0278

13-5282

9-1719

41

23-4124

19-9931

17-2944

15-1380

42

28-8959

19-2575

12-8840

8-6527

42

23-7014

20-1856

17-4232

15-2245

43

28-0543

18-5168

12-2704

8-1630

43

23-9819

20-3708

17-5459

15-3062

44

27-2372

17-8046

11-686!

7-7009

44

24-2543

20-5488

17-6628

15-3832

45

26-4439

17-1198

11-1297

7-2650

45

24-5187

20-7200

17-7741

15-4558

46

25-6737

16-4614

10-5997

6-8538

46

24-7754

20-8847

17-8801

15-5244

-

47

24-9259

15-8283

10-0949

6-4658

47

25-0247

21-0428

17-981C

15-5890

48

24-1999

15-2195

9-6142

6-0998

48

25-2667

21-1951

18-0772

15-650C

49

23-495C

14-6341

9-1564

I 5-754€

49

25-5017

.21-3415

,18-1687

.15-7076

50

22-8107

14-0713

8-7204

[ 5-428S

50

25-729S

i 21-4822

18-255£

» 15-761E

60

16-9732

9-506C

5-353e

) 30314

60

27-675e

) 22-623£

18-929C

1 16-1614

70

12-6297

6-421S

3-286f

> 1-6927

70

29-123^

t 23-394£

> 19-3427

16-384£

80
90

9-3977
6-9928

4-3384
2-930£

\: 2-0177

' -9455

80

30-200?

! 23-9154

[ 19-5961

) 16-5091

> 1-2387

' -527f

Perpe
tual.

33-3331

i 25-OOOC

20-OOOC

) 16-6667

38

The few following Formulce will be found to embrace all cases of common occurrence in
the Practice of Life Assurance. I have adopted the Notation used by Mr. Milne, in
his " Treatise on Life Annuities^

The different letters of the alphabet denote distinct lives of specified ages. The
manner of writing each letter denotes the kind of contingency. For a specified life or
age, the Saxon large character denotes an Assurance of £1, or the value of £1, payable
at the expiration of the year of death ; the common Roman capitals denote the value of
£ 1, payable annually during life ; the small Italic characters denote the tabular Survivors
at the given age out of a given number born. The last characters, with small figures
added to the left and lower corner, express the probability of surviving one, two, or more
years. The expression for any specific contingency on a given life is made to serve for a
life older or younger by a known number of years : if older, this number is placed at the
higher and left corner ; if younger, at the lower and right corner.

The present value of £ 1 , payable certain, at the end of one year := v.

A=iaD(l+iA): i. e. value of Annuity of £1 on given life = r— ) probability of

living one year x « X (1 + Annuity on life one year older).

AB=A4-B— AB: i. e. Annuity on longest of two lives=Annuity on A+ Annuity
on B — Annuity on the joint lives.

-j-rA^A — ,a ««'A : i. e. life Annuity for (f) years=Annuity for whole of life — probabi-
lity, of living (<) years x v' x Annuity on life {t) years older.

I — lav'

Annual payment for Assurance of £1 for (t) years = , . 'n -4-'A '>"*""~^

Single payment for same = Annual payment x {1 -t-A — ,ai;'(l +'A)}^-yM

Single payment for £ 1, payable on the ) 1 ( ^« , ^ ^ ) -Annual nav
death of (A), provided (B) then alive j " 2 1 +^^~ A 5 ~*°''"^' P^^'

ment x (1 + AB).

Value of Annuity on longest of three lives, or A B C = ( A + B + C) — (AB + AC + BC)
+ABC.

Value of £ 1, payable if A, B, and C are all alive at the end | _'a'b'c ', , , . ,

of (0 years 5 ~ 'Si^'' ~'^^ ^^^

Value of absolute reversion of Life Annuity =

l—v

Value of Life Reversion to B after A =B — AB.
Value of Life Annuity of £ 1 , payable weekly = A + •S.

Constants.

Interest.

V.

x«.

X 1 — c).

3 per cent.

4 per cent.

5 per cent.

6 per cent.

•97087379
•96153846
•95238095
•94339623

t987 16277
•98296666
•97881070
•97469413

^•4642840
•5850267
•6777807
•7528454

T7J ^ '^ The three values of >i p

j/=io ^

h, or modulus of common logarithms='434294482.

Ml

—•1700.
0128.
0333.

And A A = T^6377843.

LONDON:
J. M0YE9, CASTLE STREET, LEICESTER SQUARE.