ORIGIN OF THE DOCTRINE OF PROBABILITIES.--ESSAY OF JOHN DE
WITT.--THE PLAGUE.--FIRST BILLS OF MORTALITY.--CAPTAIN JOHN
GRAUNT--HIS OPINIONS, LIFE, AND ESTIMATES.--CURIOUS TERMS IN THE OLD
REGISTERS--THEIR EXPLANATIONS.--LIFE OF SIR WILLIAM PETTY--HIS CAREER
AND CHARACTER.
In the early annals of this country, there was no foundation whatever
on which to form a theory of the value of life. The wars of succession,
intestine strife, and civil discord, killed their thousands. Disease,
arising from exposure to the air, from foul dwelling-places, and
from an absence of the comforts of advanced civilisation, slew its
tens of thousands. They who were spared by the sword and escaped the
pestilence, perished too often by the fire of persecution. Death came
in forms which were governed by no known laws; and, notwithstanding
the insecurity of life, there was no possibility of making a provision
for survivors. To this we owe that kind consideration for the widows
and orphans of their members, which is observable in many of the city
corporate bodies.
Commerce was yet in its infancy, and all the capital which could be
collected, was necessary to its development. It was, indeed, on this
that the wisdom of the executive was concentrated. Every half century
brought rumours of some new land which was to enrich the adventurers
who combined to explore it. The most gallant spirits of England sailed,
and not always in the stoutest vessels, to explore a new passage, or to
trade on the shores of some new country, alike indifferent where they
went or how long they remained, provided they could bring home some
attractive article of merchandise. Every energy was, therefore, devoted
to the extension of our mercantile interests; and although Lombards,
goldsmiths, Jews, and usurers, frequently granted annuities, there
appears to have been no united attempt to grant assurances on lives.
This universal spirit of commerce produced, however, marine assurance
very early, while the gradual progressive movements made in science
and philosophy, prepared the way for assurance on life. The rude
notions of an uncultivated age were succeeded by broader and more
statesmanlike views; the Roman Church, with its narrow notions and
its denunciations of progress, ceased to exist; men feared no longer
to give a free exposition of their principles; and the Provincial
Letters of Pascal prove that a new era had arrived. The doctrine
of probabilities,--originated at a gaming-table,--so curious, so
interesting, and at the same time so necessary to the present
subject, was first popularised by this great genius; but we are
indebted to Holland for its earliest application to annuities; as
when the States-General resolved to negotiate some life payments,
the pensionary, John de Witt, added one more obligation to the many
received from this distinguished man, by employing the theory which
Pascal suggested, for the requirements of his government. His report
and treatise on the terms of life annuities is the first document of
the kind, and a most important paper it is. Step by step it explains
the grounds on which the proposition of its author was based, and by
which he arrived at the conclusion that the value of a life annuity,
in proportion to one for a term of twenty-five years, was really “not
below, but certainly above, sixteen years’ purchase.” It is probable
that from political motives this paper was suppressed; but John de
Witt was certainly the first who thought of applying mathematical
calculations to political questions, and the first who attempted to fix
the rate of annuities according to the probabilities of life. The essay
of the pensionary was, however, but little known to the public, and had
no sensible influence on the subsequent progress of the science.
Leibnitz, whose hobby was to investigate the theory of chances[1],
first drew attention to this production; but though often alluded to,
its very title was not correctly given, and we are indebted to the
researches of Mr. Hendriks for its rescue from an unmerited oblivion,
and for the able translation of an essay which, had it been published
at the time it was written, would have exercised an important influence
on its subject.[2] Up to the end of the 17th century, therefore,
as there were no laws to calculate the chances of mortality, life
annuities were granted according to the caprice of the usurer, or the
ignorance of the annuitant; and there is no occasion to remind the
reader that the barbaric splendour of the Tudors witnessed customs
which, rendering the conditions of life terribly uncertain, had
a depressive effect on the science of assurance. The smallpox, a
frequent and fearful visitor, was only met by an attempt to stare it
out of countenance; for to effect a cure the patient was clothed in
scarlet, the bed was covered with scarlet, and the walls were hung
with scarlet; so simple and so ignorant were the leeches of the early
ages. Dysentery, then known by its Saxon synonyms of the “flux,”
“scouring,” and “griping,” daily carried off the unwashed artificers
of old London. Nor were dirty habits confined to the mere populace;
the banquetting-halls of the palace were rarely or ever cleansed; the
accumulations of months were left on the floors, which, to hide the
dirt and preserve an appearance of decency, were periodically covered
with rushes.[3] In such places disease was ever ready to spring into
vigorous life. Every few years, fevers which had been lurking in alleys
and ravaging obscure places, devastated the city under various names.
At last, that awful sickness which, even at the present day, chills the
blood but to think of it, seemed to be naturalised in this country,
under the name of the plague; but to it we owe that the initiative step
was taken in England, in founding the first principles which govern
life assurance, for to it we owe our earliest Bills of Mortality.
Within a period of seventy years, London had been visited by it five
separate times; 145,000 having died from its collective attacks. As the
visitation had been governed by no known system, as it came without any
apparent cause and disappeared quite as capriciously, the Londoners
never felt safe from its re-appearance. It seemed always hovering
over them; and as the intervals between its departure and return were
sometimes only eleven years, and had never exceeded twenty-nine, its
harassing impressions were constantly on the minds of the citizens.
Its visits did not allow time even to soften or subdue the painful
remembrances connected with it; and were it necessary, a reference to
the letters, diaries, and chronicles of the day, would show that the
name of the plague turned men pale, and predisposed their constitutions
for its reception; that the very thought made the merchant regardless
of ’Change and of counting-house; and that the tradesman shuddered at
the memory of a disease which slew his children, depopulated London,
and destroyed his business.
The reports of the approach of the plague were, then, a positive and
practical evil; and in 1592, when 30,561 died of the disease, the
rumours of its horrors, appalling as these were in reality, were
enormously exaggerated. An attempt to quiet public feeling by correctly
indicating its progress was, therefore, made in the Bills of Mortality;
and though they were not at first maintained consecutively, they were
afterwards found so useful as to be continued from 29th December, 1603,
to the present time.[4] The mode of their production was simple. When
any one died it was indicated either by tolling or ringing a bell, or
by bespeaking a grave of the sexton. The sexton informed the searchers,
who hereupon “repair to the place where the dead corpse is, and by
view of the same and by other inquiries they examine by what disease
or casualty the corpse died. Hereupon they make their report to the
parish-clerk; and he, every Tuesday night, carries in an account of all
the burials and christenings happening that week, to the parish-clerks’
hall. On Wednesday, the general account is made up and printed; and on
Thursday, published and disposed of to the several families who will
pay 4_s._ per annum for them.” In 1629, two editions of the weekly
bills were printed, one with the casualties and diseases, and the
other without. For a long time these papers were made but little use
of by the public. A writer of the day says they were examined at the
foot, to see whether the burials increased or decreased; they were
glanced at for the casualties, as a matter of gossiping interest; and
in the plague time, the progress of the pest was closely watched by
the courtiers and the nobles, that they might escape its ravages; and
by the citizens, with that morbid feeling which is as much attached
to extraordinary calamities as to great crimes. But though this might
be the case ordinarily, such was not the view with which a citizen of
London, by name John Graunt, thought they should be regarded. This
man was the author of the first English work on the subject, entitled
“Natural and Political Observations on the Bills of Mortality.” Little
is known of his antecedents, save that he was the son of one Henry
Graunt of Lancaster, that he was born in “Birching Lane,” and that he
had the ordinary education granted to the sons of tradesmen. He came
early into business, passed through the chief offices of his ward with
reputation, and became captain and major of the train-bands, when such
an office involved danger as well as honour.
All that has hitherto been said of Graunt might be said of many. But
Graunt’s genius was far from being confined within these limits.
It shone through all the disadvantages of mean birth and doubtful
breeding. It broke down the barriers of rank and the limits of
position, and gave him the first thought of a design, which was
the earliest movement in economical arithmetic, and the closest
approximation to the data on which life assurance is founded.
The exact time is not known when he began to collect and to consider
the Bills of Mortality; but he says his thoughts had been turned
that way for several years, before he had any design of recording
certain notions he had formed. Until he published his volume, a more
than Egyptian darkness was on the eyes of the people, and he had to
combat some very singular notions. Among others, that London was to be
reckoned by millions, that the proportion of women to men was three
to one, and that in twenty-six years the population had increased two
millions. “Men of great experience in this city talk seldom under
millions of people to be in London.” To grapple with these and similar
errors was Graunt’s object; and it is easy to comprehend, that his
readers rebelled against assertions which lowered the pretensions of
their favourite city. It is probable that he made some enemies by his
book; as when the fire of London occurred, he was accused of having
gone to the reservoir of the New River Company, and of cutting off
the supply of water. As, however, he had changed, or was on the point
of changing his creed from puritanism to papistry, and the papists
had the credit of originating the fire; the accusation was possibly
a party one, and is of little importance now. It is with his work on
the population we have to deal, and this, which contained “a new and
accurate thesis of policy, built on a more certain reasoning than had
yet been adopted,” was first published in 1664; meeting with such an
extraordinary reception that another edition was called for in the
following year, the book being spoken of wherever books then made
their way. It formed a taste for these studies among thinking men; and
the fact is greatly to the author’s credit, that he made a bold, if
fruitless, attempt to deduce the law of life from bills of mortality
which did not record the ages as well as the deaths of the people.
In addition to the London bills, he gave one for a country parish
in Hampshire; and in the later editions he added one for Tiverton,
and another for Cranbrook. Charles II. recommended the Royal Society
to elect him one of their members, charging the Fellows “that if
they found any more such tradesmen, they should admit them all;” and
immediately after the appearance of the work, Louis XIV. ordered the
most exact register of births and deaths to be kept in France, that
was then known in Europe. A few extracts from this rare and curious
work will at once indicate its character, and show the simplicity
of the existing information; but in their perusal the reader will do
well to consider, that Graunt was the first who wrote on the subject;
that he had but slight foundations for his calculations; and that with
all these difficulties, he was very successful in his conclusions. He
says:--
“There seems to be good reason why the magistrate should himself
take notice of the number of burials and christenings: viz., to see
whether the city increase or decrease in people, whether it increase
proportionably with the rest of the nation, whether it be grown big
enough. But,” he adds, “why the same should be known to the people,
otherwise than to please them as with a curiosity, I see not.
“Nor could I ever yet learn from the many I have asked, and those not
of the least sagacity, to what purpose the distinction between males
and females is inserted, or at all taken notice of; or why that of
marriages was not equally given in. Nor is it obvious to every body why
the account of casualties is made. The reason which seems most obvious
for this latter is, that the state of health in the city may at all
times appear.” In another page he writes that “7 out of every 100 live
in England to the age of 70.” “It follows from hence that, if in any
other country more than 7 of the 100 live beyond 70, such country is to
be esteemed more healthy than this of our city.” It must be remembered,
however, that this was very conjectural. “We shall,” he says, when
leading to this conclusion, “come to the more absolute standard and
correction of both, which is the proportion of the aged; viz. 15,757
to the total 229,250, that is, of about 1 to 15, or 7 per cent.; only
the question is, what number of years the searchers call aged, which I
conceive must be the same that David calls so, viz. 70. For no man can
be said to die properly of age, who is much less.”
Out of the above 229,250 he estimates that 86 were murdered; and,
alluding to a peculiar disease which had arisen, intimates that the
proportion of males was greater than that of females, in the words,
“for since the world believes that marriage cures it, it may seem
indeed a shame that any maid should die unmarried, when there are
more males than females; that is, an overplus of husbands to all that
can be wives.” “In regular times when accounts were well kept, we
find not above 3 in 200 died in childbed; from whence we may probably
collect that not 1 woman of 100, I may say of 200, dies in her labour,
forasmuch as there may be other causes of a woman’s dying within the
month.” He then attempted to show the population of London, from which
he had been a long time prevented by his religious scruples; but his
arithmetical mind was provoked by a “person of high reputation” saying
there were “two millions less one year than another.” To ascertain the
number he made many very interesting calculations, and came to this
conclusion:--“We have, though perhaps too much at random, determined
the number of the inhabitants of London to be about 384,000.” He then
gave the following table, which is perhaps one of the most remarkable
we have, the period and the material being taken into consideration:--
Of 100, there die within the first six years 36
The next ten years, or decad 24
The second decad 15
The third ” 9
The fourth ” 6
The fifth ” 4
The sixth ” 3
The seventh ” 2
The eighth ” 1