at every Age, in City, Town, and Country; and in different
Kingdoms of Europe: illustrated with a Chart, and with Tables.
The Comparative Mortality of the Human Species, by different
Diseases and Casualties: exhibiting a Chart, and Tables of all
the Mortal Diseases and Casualties in London during Seventy-five
Years: illustrated by and contrasted with the united Observations
of Medical Authors, with various Hospital Registers; and with a
Variety of Materials, Observations, and Comments of the Author._
That learned Physician, Dr. Arbuthnot, in his Preface to Huygen’s “_de
Ratiociniis in ludo aleæ_”, says, There are very few things which
we know, which are not capable of being reduced to a mathematical
reasoning; and when they cannot, it is a sign the knowledge of them
is very small and confused; and, when a mathematical reason can be
had, it is as great a folly to make use of any other, as to grope for
a thing in the dark when you have a candle standing by you. Medical
writers, almost universally, have neglected, or barely skimmed the
surface of the following important subjects. The public registers
of births, burials, and diseases, are overlooked by all the modern
systematick authors: they leave us equally ignorant of the aggregate,
or comparative number, or force of those fiends which haunt and ravage
the globe. To speak metaphorically, in medical books, the extensive
desolation of the most rapacious tyrants and conquerors are confounded
with the uninteresting history, and petty depredations of a robber. The
detached observations of physicians, or other literary individuals,
confined perhaps to a small town or parish, a meagre detail of village
remarks, furnish, in innumerable instances, foundations too slight for
the erection and stability of general proportions. In order to form
useful tables of the ratio of mortality at various ages, to determine
upon the absolute and relative havock by different diseases, upon
the general effects of climate, season, local situation, diet, drink,
luxuries, new customs, and manners, &c. we should extend our views far
beyond the narrow bounds of a parish, or even of a province; we should
include an interval of many years, collective numbers, and large groups
of mankind.
It appears to me, that a great number of the fundamental principles,
or of the primary orders of medical architecture, have not yet been
established, neither in Pathology, to which this Dissertation is
chiefly related; and much less in Therapeuticks. The lumber and
mountain of ponderous systems, heaped together from Galen to Stahl,
can only be compared to Egyptian pyramids. Except what has been done
by a few authors, hereafter to be mentioned, the sciences of Medical
Arithmetick and Universal Prognosticks, are new in medicine. In
emergencies, the constant appeal has been, with oracular reverence, to
aphorisms and opinions of individuals. In a word, no medical author
has yet attempted to take the gages of life and death, and of morbid
devastation, and, in one general survey, to encircle the horizon of
human existence and distempers. I have made some, at least laborious
efforts, to rescue a momentous part of active medicine from that
conjectural stigma with which the whole profession has been branded in
the lump. And, however it may be slighted as an heretical innovation, I
would strenuously recommend Medical Arithmetick, as a guide and compass
through the labyrinth of Therapeuticks.
We are now to view the human race unexpectedly arrested, and struggling
in the tragical and last stages of their terrestrial pilgrimage. The
vision of human life is soon at an end: we are ushered into the world
with lamentable exclamation; and are too often torn out of it in pain
and agony. Bills of Mortality, however defective and inaccurate, yet
sufficiently demonstrate this awful truth, that very few of the human
species die of old age, or natural decay: by far the greater proportion
are prematurely cut off by diseases. Of all the animal tribe, who
usually bring forth one at a birth, none die in such numbers, in
infancy, as the human race. In London, Vienna, Berlin, and every
other overgrown metropolis of Europe, on an average, one half of the
children born, die under three years of age. But in country towns and
villages, the proportion of infant mortality greatly abates. In some
country towns of England, of considerable magnitude and population, as
Manchester, half the children die under five; at Norwich, half under
six; at Northampton, half under ten years of age. London, therefore,
will have lost, out of equal capitals, a number in the intermediate
space, between three and ten, more than Northampton.
Attend next to the small proportion of Infant Mortality in open country
districts. By Dr. Short’s registers of several small country villages
in England, the major part born live to 25, 27, 33, and 40. In many
healthy country parishes, half the inhabitants born live to mature age;
to 40, 46, and a few even to 50 and 60; and rear large families of
children. In some extensive country districts of Switzerland, similar
observations have been made by Susmilch and Muret. Here, therefore, is
an astonishing disparity between the duration of city and country life:
but particularly, let it be engraved upon the memory, in the early
stages of puerile exigence. Infants in cities resemble tender delicate
plants excluded from fresh air; or fish confined in stagnant putrid
water: they perish before acquiring a solidity and seasoning to endure
the adulterated quality of the surrounding element; and their thread of
life is then suspended by a tender cobweb.
Mortality, universally, during the first year after birth, is the most
enormous in the funeral catalogue. A London infant at birth, has but
an equal chance of living to three years old; whereas in the country,
as before observed, half born survive to maturity. Upon reaching the
third year, in cities, infants are somewhat seasoned, and the hurricane
of puerile carnage is greatly abated. There is not afterwards such
a prodigious disproportion between city and country mortality; and,
in a few years after, from seven to ten, they approach nearer to an
equality. From the London registers of burials, it appears that more
die in the metropolis under two years of age, than from two to upwards
of forty; and more under five years of age, than from five to between
fifty and sixty: yet under five, there are but an inconsiderable
number alive, compared to the latter class above that age: the deaths
are greatly disproportioned to the living numbers or capitals. A few
more die in the short interval between five and ten years of age, than
in the succeeding double interval from ten to twenty. Between eight
and sixteen years of age, one of every seventy of the Christ School
boys is computed to die. Davenant rates the decrement in these years
at only one _per cent._ After reaching the tenth year, the torrent
of mortality in city, town, and country, is subsided; and during the
next eight or ten years of adolescence, very few die. From seven to
ten, may be termed the highest pinnacle: having surmounted all the
dangers and precipices of the early preceding journey, there is no
stage wherein the future prospects of existence and longevity are so
extensive. From birth to ten, the tide of life continues in annual
gradation to increase; and from ten to the ultimate verge of existence,
vitality continues gradually to ebb. Between twenty and thirty, more
die in London than in the fifteen preceding years; and the burial list
continues turgid to sixty; at which latter stage, the mortality is
computed between four and five _per cent._
One reason, but not the only one, as I shall hereafter prove, of the
great surge in the London bills, from twenty up to forty, is, that
within this interval of life, the majority of the new settlers or
recruits, arrive; and consequently augment the burials, from twenty to
forty, beyond their natural proportion. After passing the meridian,
and in the evening of life, the seasoned inhabitants of cities are
said by Dr. Price, to have the advantage of the country, in health and
longevity: that is to say, although the number who have survived in the
country to sixty, seventy, and eighty, are greater proportionally than
in cities, yet the latter class arrived at those years in London, have,
comparatively, surer expectations of life. I do not, however, find this
assertion verified in fact; the balance, if any, vibrating alternately
on each side. The proportion of inhabitants who reach eighty years of
age are computed, in London and Vienna, at one of every forty: but in
country parishes, at one of every twenty-two; and in some, even one of
every eleven. In both city and country, the few survivors at ninety,
out of each thousand cœtaneous births, will have lost almost all their
fellow-travellers in the journey, long before reaching that goal; and
about three or four only out of each thousand, on an average, will be
then left alive.
There are a few instances of extraordinary Longevity, to 150 and 165;
such are Jenkins and Par, in this island. In Bacon Lord Verulam’s
History of Long Livers, male and female; their climate, diet, mode of
life, appetites, exercises, studies, passions, dispositions, habits,
and complexions, were exceedingly dissimilar. It is however probable,
from observation and analogy, that the indigent and laborious class
of mankind do not attain to longevity in the same proportion with the
middling and more opulent ranks. The wandering Savages of America are
notoriously short-lived. Throughout Europe, Asia, Africa, and America,
the rich, the poor, the inhabitants of city and country, with very
different complexion, climate, soil, diet, and conveniences, all seldom
exceed the usual term of life allotted to man: seventy and eighty is
mentioned in holy writ, as the brink of our earthly duration. Since the
days of Moses; that is, between three and four thousand years, human
existence has been circumscribed within the same narrow bounds. In the
London registers of mortality, during a period of thirty years, from
1728 to 1758, the total mortality is 750,332; and of all this number,
242 only reached beyond 100 years of age; one of whom arrived at 138.
In some races and families of men, longevity seems to be hereditary;
and his age, though little more than a dream, exceeds that of all other
living creatures, a few only excepted. Amongst the quadruped creation,
the elephant surpasses man in longevity: amongst the birds, the Swan,
and a few others, have survived upwards of a century. The age of fishes
is determined with more ingenuity than certainty: some seem to rival
man in years. Among the numerous vegetable tribes, the Oak, Chestnut,
and some other great trees, survive centuries.
On contrasting the mortality of Males and Females, it appears, that,
notwithstanding the surplus of male births, the perils of childbearing,
the many vexatious diseases peculiar to the fair sex, and that
physicians and apothecaries have many more patients of the latter; yet
the total aggregate number of living females exceeds that of males,
in most European kingdoms. Upon a numerical inquest in Edinburgh, and
some other great cities, it was found, that females were to males as 4
to 3: in London, as 13 to 10; and in some other cities and towns, as
9 to 8. But in country districts, Graunt and Susmilch agree, that the
two sexes approach nearer to an equality. In the province of Jersey, in
North America, the males were found the majority. From 1702 to 1752;
that is, during a period of fifty years, I find the proportion of male
and female mortality in London as follows: Male deaths, 618,076; Female
deaths, 626,692. Whence, therefore, does it happen, that female deaths
preponderate over the male, when more of the latter are born, and, as
calculators assert, the mortality of males, at all ages, is greater
than that of females? As a solution of this difficulty and partial
exception, I should suggest a greater exportation and transportation
of males to the sea and land service, to nautical commerce, and to
unhealthy climates.
Even in the Marriage State, the chance of survivorship seems
considerably in favour of the wife. In Breslaw, during eight years,
five married men died to three married women. Susmilch, on a scrutiny
through several kingdoms and principalities of Germany, found, that
three married men died to two married women. Dr. Price estimates
the chance in favour of the wife being the survivor in marriage, as
3 to 2: and this calculation is confirmed by the experience of the
general Clerical Society in Scotland, who have long established funds
to support their widows. From their records, it appears that twenty
married clergymen have died to twelve wives; or, as 5 to 3. By an
accurate survey of several principalities and cities in Germany, and
collected by Susmilch, the widows were to the widowers as 3, and
even 4 to 1. At marriage, it should be observed, there is generally
a disparity of age; the bridegroom is from six to twelve years older
than the bride; and therefore should, in the course of nature, die
sooner: and perhaps also more widowers, comparatively with the other
sex, enter into a second marriage; which tends to reduce their numbers.
Besides, husbands are more exposed to the vicissitudes of the weather
and seasons, to excessive labour and noxious trades, and to many
other causes of diseases. Dr. Price finds, that the sexes respectively
commence to be widowers and widows about 52 and 44; that is, men and
women entering into matrimony, on a general average, at the age of 33
and 25, will become widowers and widows at 52 and 44: consequently,
that each marriage will be dissolved by the death of one of them, in
nineteen years; which is the ultimate term and probability of the
husband and wife being both alive. For although some marriages may be
protracted forty and fifty years, yet others may be dissolved in one
year, or in a shorter time.
We have not yet sufficient information to determine the comparative
chances of Female Longevity in the married and single state. At Berlin,
indeed, calculators have remarked, that there were more married women
alive at great ages, than of those who remained single. But such result
might naturally be expected from a greater proportion in the decline of
life of widows and wives, compared to antiquated virgins. From the ages
of fifteen to twenty-five, married women likewise are said to have the
advantage of the single, in whom the dictates of nature are frustrated
and violated.
Comparing the mortality of the Seasons, Dr. Short found, from a variety
of country-registers, that mortality generally begins its reign
in December; that at March it is in its zenith; and at May in its
declension. In twenty-five country towns and parishes, he found the
winter to the summer mortality as 50 to 41. At Manchester, a country
town of England, Dr. Percival found the winter to the summer mortality
as 11 to 8. At Vevey, in Switzerland, during sixty years, Mr. Muret
found the burials, during the four winter months, as 5 to 4 to those of
the summer. Another proof of this is recorded in the _Recherches sur
la Population, par Messance_: The total sick admitted into the _Hotel
Dieu_ hospital in Paris, from 1724 to 1763 (forty years) were, in the
four winter months, December, January, February, and March, 314,824;
and in the four summer months, June, July, August, September, 238,522;
or as 4 to 3. In London too, the undertaker’s, harvest is in winter.
There is one obvious reason why, in every metropolis, the winter
mortality should exceed that of summer, from the greater concourse of
inhabitants of all ranks: but, independent of additional population
in winter, the same law seems to prevail in country places. In a
subsequent part I shall attempt to throw some collateral illustration
upon the subject.
Let us close this humiliating scene with a general abstract of human
carnage. If we scan the dolorous mansions of disease, we find, on an
average, 1 death, annually, out of every 5 families in cities: but in
country towns, and open districts, 1 of 7, 8, 9; and in a few healthy
places, 1 of every 10 families. Including the whole assemblage of
inhabitants in city, town, and country, from birth to the extreme of
existence, they are computed to die in the following annual proportion
to the living: In London, 1 of 21; Dublin, 1 of 22; Edinburgh, 1 of
21; Vienna, 1 of 20; Amsterdam, 1 of 22; Berlin, 1 of 26. This is
nearly Dr. Price’s calculation; but Halley and Susmilch compute only
1 of 22 to 29 to die annually in cities. In smaller cities and towns,
such as Norwich and Northampton, the general average of deaths is 1
of 24 to 26; but in several provinces and healthy country villages, 1
of 32 and 33, up to 45, 50, and even 60, is the annual drain: 1 of 43
to 50 was the average in upwards of a thousand country parishes on the
continent; and recorded in Susmilch. Within the above short intervals
of time, there will have died in the respective cities and country
places enumerated, a number equal to the whole inhabitants. But the
annual decrease of the oppressed Negroes, in the West India islands, is
estimated at 1 of 7.
The ancient Egyptians allotted 3 generations to a century, which is
bordering upon the truth; at this day, 1 of 32 and 33 up to 35, is near
the measure of a generation, and to the general decrease of a community
throughout Europe, comprehending all the inhabitants in city, village,
and country: that is, mankind share amongst them from about 32 and 33
to 35 years each of existence: and within this fugitive interval of
time, a number equal to all the present inhabitants of this island, or
of the whole earth, will be exterminated. If we extend this estimate
to the whole human race, eight hundred million will die in 33 years;
about twenty-eight million annually; seventy or eighty thousand daily;
about three thousand hourly; and from fifty to sixty every minute. It
is perhaps superfluous to add, that, in the same intervals, an equal or
superior number will be born.
According to De Moivre and Dr. Price, “the probabilities or expectation
of life, decrease as we advance from childhood to old age, in an
arithmetical progression; that is, in such a manner that the difference
is always the same between the number of persons living at the
beginning of any one year, and the number living at the beginning of
the following year.” Or, in other words, less enveloped in mathematical
obscurity, out of any specified number, an hundred or a thousand, the
same proportion will continue to die every year until near 80 years of
age and upwards: consequently, the probabilities of life are constantly
decreasing; because notwithstanding the progressive annual drain from
the capitals, yet the deaths continue throughout equal. But this
proportion is certainly erroneous in the first stages of life, and
until about 10. View the above proposition in another light.
From any given number there will be an equal drain annually, until
what De Moivre terms the _complement_ or _maximum_, or utmost probable
extreme of life, which he fixes at 86, all are dead. The probability,
therefore, that the whole of any limited number whatsoever, or age,
will all be exterminated is the number of years between 86 and the year
such a number are all alive. Of 56 persons alive at 30, they should all
be dead in 56 years, because 56 added to 30 amounts to 86, the maximum:
of 46 persons alive at 40 years of age, they should all be dead in 46
years: and 36 persons alive at 50 years of age, should be dead in 36
years; for 50 and 36 complete the maximum. Again, the expectation of
any single life is only half the maximum or complement, or half the
space between that age and the ultimate term of existence: but here we
must repeat the former exception, and draw the line after 10 years of
age. The expectation of two equal joint lives, according to De Moivre,
is one third of the complement of life. Example: two lives, aged 40,
have an even chance or probable prospect of continuing together in
exigence only 15 years; which is the third of the complement, reckoning
from 40 to 86: the expectation of the survivor is also 15. Or, suppose
a lot of marriages of persons at 40 years of age, they will, on an
average, continue together 15½ years; and the survivors the same time
after. This expectation, therefore, is the probable duration of each
marriage, and the share of each person’s life. But it may be proper
to add, that the duration of marriages, and the value of single and
joint lives, will, on a promiscuous calculation, be different from
the registers of annuitant and insurance offices; because they are
scrupulously vigilant to exclude all diseased and unhealthy persons
from becoming members.
The following Chart and Tables, present a distinct prospect of the
fates clipping the mortal thread, from birth to old age, in city and
country. But we are not to suppose that in every instance there will be
annually a regular arithmetical diminution, as marked in the different
tables: some years will be more fatal than others; and we are to form
estimates from an average of several years. The first column points
out the age, the second the number living at that age, the third the
number who die during the year; and so on to the end of the table. But
observe, that the number of infants, at the beginning of the second
column, are supposed to be all born together on the first day of that
year; and this rule applies throughout all the remaining ages. The two
short tables of 15 and 30 years mortality in London, demonstrate the
gradations at longer intervals than a single year. From these different
tables may be estimated the annual waste, out of any specified number,
at all ages, the ultimate prospects of existence, and the odds or
probability of a person in health surviving a stated number of years.
A GENERAL CHART, with different Tables,
Exhibiting the Gradations of Mortality in City and Country.
Shewing the Probability of the Duration of Life in LONDON, deduced by
Mr. Simpson, from Observations on the Bills of Mortality in London
for Ten Years, from 1728 to 1737. The total Number of Inhabitants,
probably, about 650,000 in Winter. One Half born died under Three
Years of Age.
-------+-----------+----------
Ages. | Persons | Decr.
| living. | of life.
-------+-----------+----------
0 | 1000 | 320
1 | 680 | 133
2 | 547 | 51
3 | 496 | 27
4 | 469 | 17
-------+-----------+----------
5 | 452 | 12
6 | 440 | 10
7 | 430 | 8
8 | 422 | 7
9 | 415 | 5
-------+-----------+----------
10 | 410 | 5
11 | 405 | 5
12 | 400 | 5
13 | 395 | 5
14 | 390 | 5
-------+-----------+----------
15 | 385 | 5
16 | 380 | 5
17 | 375 | 5
18 | 370 | 5
19 | 365 | 5
-------+-----------+----------
20 | 360 | 5
21 | 355 | 5
22 | 350 | 5
23 | 345 | 6
24 | 339 | 6
-------+-----------+----------
25 | 333 | 6
26 | 327 | 6
27 | 321 | 6
28 | 315 | 7
29 | 308 | 7
-------+-----------+----------
30 | 301 | 7
31 | 294 | 7
32 | 287 | 7
33 | 280 | 7
34 | 273 | 7
-------+-----------+----------
35 | 266 | 7
36 | 259 | 7
37 | 252 | 7
38 | 245 | 8
39 | 237 | 8
-------+-----------+----------
40 | 229 | 7
41 | 222 | 8
42 | 214 | 8
43 | 206 | 7
44 | 199 | 7
-------+-----------+----------
45 | 192 | 7
46 | 185 | 7
47 | 178 | 7
48 | 171 | 6
49 | 165 | 6
-------+-----------+----------
50 | 159 | 6
51 | 153 | 6
52 | 147 | 6
53 | 141 | 6
54 | 135 | 6
-------+-----------+----------
55 | 129 | 6
56 | 123 | 6
57 | 117 | 5
58 | 112 | 5
59 | 107 | 5
-------+-----------+----------
60 | 102 | 5
61 | 97 | 5
62 | 92 | 5
63 | 87 | 5
64 | 82 | 5
-------+-----------+----------
65 | 77 | 5
66 | 72 | 5
67 | 67 | 5
68 | 62 | 4
69 | 58 | 4
-------+-----------+----------
70 | 54 | 4
71 | 50 | 4
72 | 46 | 4
73 | 42 | 3
74 | 39 | 3
-------+-----------+----------
75 | 36 | 3
76 | 33 | 3
77 | 30 | 3
78 | 27 | 2
79 | 25 |
-------+-----------+----------
Shewing the Probabilities of Life in LONDON for all Ages. Formed from
the Bills for Ten Years, from 1759 to 1768. By Dr. Price.