Books: Essays on Mankind and Political Arithmetic
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Sir William Petty >> Essays on Mankind and Political Arithmetic
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1604 and 1605 . . . 5,135. A.
1621 and 1622 . . . 8,527. B.
1641 and 1642 . . . 11,883. C.
1661 and 1662 . . . 15,148. D.
1681 and 1682 . . . 22,331. E.
Wherein observe, that the number C is double to A and 806 over.
That D is double to B within 1,906. That C and D is double to A and
B within 293. That E is double to C within 1,435. That D and E is
double to B and C within 3,341; and that C and D and E are double to
A and B and C within 1,736; and that E is above quadruple to A. All
which differences (every way considered) do allow the doubling of
the people of London in 40 years to be a sufficient estimate thereof
in round numbers, and without the trouble of fractions. We also say
that 669,930 is near the number of people now in London, because the
burials are 22,331, which, multiplied by 30 (one dying yearly out of
30, as appears in the 94th page of the aforementioned observations),
maketh the said number; and because there are 84,000 tenanted houses
(as we are credibly informed), which, at 8 in each, makes 672,000
souls; the said two accounts differing inconsiderably from each
other.
We have thus pretty well found out in what number of years (viz., in
about 40) that the city of London hath doubled, and the present
number of inhabitants to be about 670,000. We must now also
endeavour the same for the whole territory of England and Wales. In
order whereunto, we first say that the assessment of London is about
an eleventh part of the whole territory, and, therefore, that the
people of the whole may well be eleven times that of London, viz.,
about 7,369,000 souls; with which account that of the poll-money,
hearth-money, and the bishop's late numbering of the communicants,
do pretty well agree; wherefore, although the said number of
7,369,000 be not (as it cannot be) a demonstrated truth, yet it will
serve for a good supposition, which is as much as we want at
present.
As for the time in which the people double, it is yet more hard to
be found. For we have good experience (in the said page 94 of the
aforementioned observations) that in the country but 1 of 50 die per
annum; and by other late accounts, that there have been sometimes
but 24 births for 23 burials. The which two points, if they were
universally and constantly true, there would be colour enough to say
that the people doubled but in about 1,200 years. As, for example,
suppose there be 600 people, of which let a fiftieth part die per
annum, then there shall die 12 per annum; and if the births be as 24
to 23, then the increase of the people shall be somewhat above half
a man per annum, and consequently the supposed number of 600 cannot
be doubled but in 1,126 years, which, to reckon in round numbers,
and for that the aforementioned fractions were not exact, we had
rather call 1,200.
There are also other good observations, that even in the country one
in about 30 or 32 per annum hath died, and that there have been five
births for four burials. Now, according to this doctrine, 20 will
die per annum out of the above 600, and 25 will be born, so as the
increase will be five, which is a hundred and twentieth part of the
said 600. So as we have two fair computations, differing from each
other as one to ten; and there are also several other good
observations for other measures.
I might here insert, that although the births in this last
computation be 25 of 600, or a twenty-fourth part of the people, yet
that in natural possibility they may be near thrice as many, and
near 75. For that by some late observations, the teeming females
between 15 and 44 are about 180 of the said 600, and the males of
between 18 and 59 are about 180 also, and that every teeming woman
can bear a child once in two years; from all which it is plain that
the births may be 90 (and abating 15 for sickness, young abortions,
and natural barrenness), there may remain 75 births, which is an
eighth of the people, which by some observations we have found to be
but a two-and-thirtieth part, or but a quarter of what is thus shown
to be naturally possible. Now, according to this reckoning, if the
births may be 75 of 600, and the burials but 15, then the annual
increase of the people will be 60; and so the said 600 people may
double in ten years, which differs yet more from 1,200 above-
mentioned. Now, to get out of this difficulty, and to temper those
vast disagreements, I took the medium of 50 and 30 dying per annum,
and pitched upon 40; and I also took the medium between 24 births
and 23 burials, and 5 births for 4 burials, viz., allowing about 10
births for 9 burials; upon which supposition there must die 15 per
annum out of the above-mentioned 600, and the births must be 16 and
two-thirds, and the increase one and two-thirds, or five-thirds of a
man, which number, compared with 1,800 thirds, or 600 men, gives 360
years for the time of doubling (including some allowance for wars,
plagues, and famines, the effects thereof), though they be terrible
at the times and places where they happen, yet in a period of 360
years is no great matter in the whole nation. For the plagues of
England in twenty years have carried away scarce an eightieth part
of the people of the whole nation; and the late ten years' civil
wars (the like whereof hath not been in several ages before) did
not take away above a fortieth part of the whole people.
According to which account or measure of doubling, if there be now
in England and Wales 7,400,000 people, there were about 5,526,000 in
the beginning of Queen Elizabeth's reign, A.D. 1560, and about
2,000,000 at the Norman Conquest, of which consult the Doomsday
Book, and my Lord Hale's "Origination of Mankind."
Memorandum.--That if the people double in 360 years, that the
present 320,000,000 computed by some learned men (from the measures
of all the nations of the world, their degrees of being peopled, and
good accounts of the people in several of them) to be now upon the
face of the earth, will within the next 2,000 years so increase as
to give one head for every two acres of land in the habitable part
of the earth. And then, according to the prediction of the
Scriptures, there must be wars, and great slaughter, &c.
Wherefore, as an expedient against the above-mentioned difference
between 10 and 1,200 years, we do for the present, and in this
country, admit of 360 years to be the time wherein the people of
England do double, according to the present laws and practice of
marriages.
Now, if the city double its people in 40 years, and the present
number be 670,000, and if the whole territory be 7,400,000, and
double in 360 years, as aforesaid, then by the underwritten table it
appears that A.D. 1840 the people of the city will be 10,718,880,
and those of the whole country but 10,917,389, which is but
inconsiderably more. Wherefore it is certain and necessary that the
growth of the city must stop before the said year 1840, and will be
at its utmost height in the next preceding period, A.D. 1800, when
the number of the city will be eight times its present number,
5,359,000. And when (besides the said number) there will be
4,466,000 to perform the tillage, pasturage, and other rural works
necessary to be done without the said city, as by the following
table, viz.:-
A.D. Burials People in People in
London England
1565 2,568 77,040 5,526,929
As in the } 1605 5,135
former table } 1642 11,883
} 1682 22,331 669,930 7,369,230
1722 44,662
1762 89,324
1802 178,648 5,359,440 9,825,650
1842 357,296 10,718,889 10,917,389
Now, when the people of London shall come to be so near the people
of all England, then it follows that the growth of London must stop
before the said year 1842, as aforesaid, and must be at its greatest
height A.D. 1800, when it will be eight times more than now, with
above 4,000,000 for the service of the country and ports, as
aforesaid.
Of the aforementioned vast difference between 10 years and 1,200
years for doubling the people, we make this use, viz.:- To justify
the Scriptures and all other good histories concerning the number of
the people in ancient time. For supposing the eight persons who
came out of the Ark, increased by a progressive doubling in every
ten years, might grow in the first 100 years after the Flood from 8
to 8,000, and that in 350 years after the Flood (whereabouts Noah
died) to 1,000,000 and by this time, 1682, to 320,000,000 (which by
rational conjecture are thought to be now in the world), it will not
be hard to compute how, in the intermediate years, the growths may
be made, according to what is set down in the following table,
wherein making the doubling to be ten years at first, and within
1,200 years at last, we take a discretionary liberty, but
justifiable by observations and the Scriptures for the rest, which
table we leave to be corrected by historians who know the bigness of
ancient cities, armies, and colonies in the respective ages of the
world, in the meantime affirming that without such difference in the
measures and periods for doubling (the extremes whereof we have
demonstrated to be real and true) it is impossible to solve what is
written in the Holy Scriptures and other authentic books. For if we
pitch upon any one number throughout for this purpose, 150 years is
the fittest of all round numbers; according to which there would
have been but 512 souls in the whole world in Moses' time (being 800
years after the Flood), when 603,000 Israelites of above twenty
years old (besides those of other ages, tribes, and nations) were
found upon an exact survey appointed by God, whereas our table makes
12,000,000. And there would have been about 8,000 in David's time,
when were found 1,100,000, of above twenty years old (besides
others, as aforesaid) in Israel, upon the survey instigated by
Satan, whereas our table makes 32,000,000. And there would have
been but a quarter of a million about the birth of Christ, or
Augustus's time, when Rome and the Roman Empire were so great,
whereas our table makes 100,000,000. Where note, that the
Israelites in about 500 years, between their coming out of Egypt to
David's reign, increased from 603,000 to 1,100,000.
On the other hand, if we pitch upon a less number, as 100 years, the
world would have been over-peopled 700 years since. Wherefore no
one number will solve the phenomena, and therefore we have supposed
several, in order to make the following table, which we again desire
historians to correct, according to what they find in antiquity
concerning the number of the people in each age and country of the
world.
We did (not long since) assist a worthy divine, writing against some
sceptics, who would have baffled our belief of the resurrection, by
saying, that the whole globe of the earth could not furnish matter
enough for all the bodies that must rise at the last day, much less
would the surface of the earth furnish footing for so vast a number;
whereas we did (by the method afore mentioned) assert the number of
men now living, and also of those that had died since the beginning
of the world, and did withal show, that half the island of Ireland
would afford them all, not only footing to stand upon, but graves to
lie down in, for that whole number; and that two mountains in that
country were as weighty as all the bodies that had ever been from
the beginning of the world to the year 1680, when this dispute
happened. For which purpose I have digressed from my intended
purpose to insert this matter, intending to prosecute this hint
further upon some more proper occasion.
A TABLE SHOWING HOW THE PEOPLE MIGHT HAVE DOUBLED IN THE SEVERAL
AGES OF THE WORLD.
A.D., after the Flood.
Periods of { 1 8 persons.
doubling { 10 16
{ 20 32
{ 30 64
{ 40 128
In 10 years { 50 256
{ 60 512
{ 70 1,024
{ 80 2,048
{ 90 4,096
{ 100 8,000 and more.
{ 120 years after
In 20 years { the Flood. 16,000
{ 140 32,000
{ 170 64,000
30 {
{ 200 128,000
40 240 256,000
50 290 512,000
60 350 1,000,000 and more.
70 420 2,000,000
100 520 4,000,000
190 710 8,000,000
290 1,000 16,000,000 in Moses' time.
400 1,400 32,000,000 about David's time.
550 1,950 64,000,000
750 2,700 128,000,000 about the birth of
Christ.
1,000 3,700 256,000,000
300 {
In { 4,000 320,000,000
1,200 {
It is here to be noted, that in this table we have assigned a
different number of years for the time of doubling the people in the
several ages of the world, and might have done the same for the
several countries of the world, and therefore the said several
periods assigned to the whole world in the lump may well enough
consist with the 360 years especially assigned to England, between
this day and the Norman Conquest; and the said 360 years may well
enough serve for a supposition between this time and that of the
world's being fully peopled; nor do we lay any stress upon one or
the other in this disquisition concerning the growth of the city of
London.
We have spoken of the growth of London, with the measures and
periods thereof; we come next to the causes and consequences of the
same.
The causes of its growth from 1642 to 1682 may be said to have been
as follows, viz.:- From 1642 to 1650, that men came out of the
country to London, to shelter themselves from the outrages of the
Civil Wars during that time; from 1650 to 1660, the royal party came
to London for their more private and inexpensive living; from 1660
to 1670, the king's friends and party came to receive his favours
after his happy restoration; from 1670 to 1680, the frequency of
plots and parliaments might bring extraordinary numbers to the city;
but what reasons to assign for the like increase from 1604 to 1642 I
know not, unless I should pick out some remarkable accident
happening in each part of the said period, and make that to be the
cause of this increase (as vulgar people make the cause of every
man's sickness to be what he did last eat), wherefore, rather than
so to say quidlibet de quolibet, I had rather quit even what I have
above said to be the cause of London's increase from 1642 to 1682,
and put the whole upon some natural and spontaneous benefits and
advantages that men find by living in great more than in small
societies, and shall therefore seek for the antecedent causes of
this growth in the consequences of the like, considered in greater
characters and proportions.
Now, whereas in arithmetic, out of two false positions the truth is
extracted, so I hope out of two extravagant contrary suppositions to
draw forth some solid and consistent conclusion, viz.:-
The first of the said two suppositions is, that the city of London
is seven times bigger than now, and that the inhabitants of it are
4,690,000 people, and that in all the other cities, ports, towns,
and villages, there are but 2,710,000 more.
The other supposition is, that the city of London is but a seventh
part of its present bigness, and that the inhabitants of it are but
96,000, and that the rest of the inhabitants (being 7,304,000) do
cohabit thus: 104,000 of them in small cities and towns, and that
the rest, being 7,200,000, do inhabit in houses not contiguous to
one another, viz., in 1,200,000 houses, having about twenty-four
acres of ground belonging to each of them, accounting about
28,000,000 of acres to be in the whole territory of England, Wales,
and the adjacent islands, which any man that pleases may examine
upon a good map.
Now, the question is, in which of these two imaginary states would
be the most convenient, commodious, and comfortable livings?
But this general question divides itself into the several questions,
relating to the following particulars, viz.:-
1. For the defence of the kingdom against foreign powers.
2. For preventing the intestine commotions of parties and factions.
3. For peace and uniformity in religion.
4. For the administration of justice.
5. For the proportionably taxing of the people, and easy levying
the same.
6. For gain by foreign commerce.
7. For husbandry, manufacture, and for arts of delight and
ornament.
8. For lessening the fatigue of carriages and travelling.
9. For preventing beggars and thieves.
10. For the advancement and propagation of useful learning.
11. For increasing the people by generation.
12. For preventing the mischiefs of plagues and contagious. And
withal, which of the said two states is most practicable and
natural, for in these and the like particulars do lie the tests and
touchstones of all proposals that can be made for the public good.
First, as to practicable, we say, that although our said extravagant
proposals are both in nature possible, yet it is not obvious to
every man to conceive how London, now seven times bigger than in the
beginning of Queen Elizabeth's reign, should be seven times bigger
than now it is, and forty-nine times bigger than A.D. 1560. To
which I say, 1. That the present city of London stands upon less
than 2,500 acres of ground, wherefore a city seven times as large
may stand upon 10,500 acres, which is about equivalent to a circle
of four miles and a half in diameter, and less than fifteen miles in
circumference. 2. That a circle of ground of thirty-five miles
semidiameter will bear corn, garden-stuff, fruits, hay, and timber,
for the 4,690,000 inhabitants of the said city and circle, so as
nothing of that kind need be brought from above thirty-five miles
distance from the said city; for the number of acres within the said
circle, reckoning two acres sufficient to furnish bread and drink-
corn for every head, and two acres will furnish hay for every
necessary horse; and that the trees which may grow in the hedgerows
of the fields within the said circle may furnish timber for 600,000
houses. 3. That all live cattle and great animals can bring
themselves to the said city; and that fish can be brought from the
Land's End and Berwick as easily as now. 4. Of coals there is no
doubt: and for water, 20s. per family (or 600,000 pounds per annum
in the whole) will serve this city, especially with the help of the
New River. But if by practicable be understood that the present
state may be suddenly changed into either of the two above-mentioned
proposals, I think it is not practicable. Wherefore the true
question is, unto or towards which of the said two extravagant
states it is best to bend the present state by degrees, viz.,
Whether it be best to lessen or enlarge the present city? In order
whereunto, we inquire (as to the first question) which state is most
defensible against foreign powers, saying, that if the above-
mentioned housing, and a border of ground, of three-quarters of a
mile broad, were encompassed with a wall and ditch of twenty miles
about (as strong as any in Europe, which would cost but a million,
or about a penny in the shilling of the house-rent for one year)
what foreign prince could bring an army from beyond seas, able to
beat--1. Our sea-forces, and next with horse harassed at sea, to
resist all the fresh horse that England could make, and then conquer
above a million of men, well united, disciplined, and guarded within
such a wall, distant everywhere three-quarters of a mile from the
housing, to elude the granadoes and great shot of the enemy? 2. As
to intestine parties and factions, I suppose that 4,690,000 people
united within this great city could easily govern half the said
number scattered without it, and that a few men in arms within the
said city and wall could also easily govern the rest unarmed, or
armed in such a manner as the Sovereign shall think fit. 3. As to
uniformity in religion, I conceive, that if St. Martin's parish (may
as it doth) consist of about 40,000 souls, that this great city also
may as well be made but as one parish, with seven times 130 chapels,
in which might not only be an uniformity of common prayer, but in
preaching also; for that a thousand copies of one judiciously and
authentically composed sermon might be every week read in each of
the said chapels without any subsequent repetition of the same, as
in the case of homilies. Whereas in England (wherein are near
10,000 parishes, in each of which upon Sundays, holy days, and other
extraordinary occasions there should be about 100 sermons annum,
making about a million of sermons per annum in the whole) it were a
miracle, if a million of sermons composed by so many men, and of so
many minds and methods, should produce uniformity upon the
discomposed understandings of about 8,000,000 of hearers.
4. As to the administration of justice. If in this great city
shall dwell the owners of all the lands, and other valuable things
in England; if within it shall be all the traders, and all the
courts, offices, records, juries, and witnesses; then it follows
that justice may be done with speed and ease.
5. As to the equality and easy levying of taxes. It is too certain
that London hath at some time paid near half the excise of England,
and that the people pay thrice as much for the hearths in London as
those in the country, in proportion to the people of each, and that
the charge of collecting these duties have been about a sixth part
of the duty itself. Now in this great city the excise alone
according to the present laws would not only be double to the whole
kingdom, but also more equal. And the duty of hearths of the said
city would exceed the present proceed of the whole kingdom. And as
for the customs we mention them not at present.
6. Whether more would be gained by foreign commerce? The gain
which England makes by lead, coals, the freight of shipping, &c.,
may be the same, for aught I see, in both cases. But the gain which
is made by manufactures will be greater as the manufacture itself is
greater and better. For in so vast a city manufactures will beget
one another, and each manufacture will be divided into as many parts
as possible, whereby the work of each artisan will be simple and
easy. As, for example, in the making of a watch, if one man shall
make the wheels, another the spring, another shall engrave the dial-
plate, and another shall make the cases, then the watch will be
better and cheaper than if the whole work be put upon any one man.
And we also see that in towns, and in the streets of a great town,
where all the inhabitants are almost of one trade, the commodity
peculiar to those places is made better and cheaper than elsewhere.
Moreover, when all sorts of manufactures are made in one place,
there every ship that goeth forth can suddenly have its loading of
so many several particulars and species as the port whereunto she is
bound can take off. Again, when the several manufactures are made
in one place, and shipped off in another, the carriage, postage, and
travelling charges, will enhance the price of such manufacture, and
lessen the gain upon foreign commerce. And lastly, when the
imported goods are spent in the port itself, where they are landed,
the carriage of the same into other places will create no further
charge upon such commodity; all which particulars tend to the
greater gain by foreign commerce.
7. As for arts of delight and ornament. They are best promoted by
the greatest number of emulators. And it is more likely that one
ingenious curious man may rather be found out amongst 4,000,000 than
400 persons. But as for husbandry, viz., tillage and pasturage, I
see no reason, but the second state (when each family is charged
with the culture of about twenty-four acres) will best promote the
same.
8. As for lessening the fatigue of carriage and travelling.
The thing speaks for itself, for if all the men of business, and all
artisans, do live within five miles of each other, and if those who
live without the great city do spend only such commodities as grow
where they live, then the charge of carriage and travelling could be
little.
9. As to the preventing of beggars and thieves.
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