Another Essay (Petty 1683)

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Another Essay in Political Arithmetick (1683)
by William Petty

Another Essay is first published in 1683. This edition is from the The Economic Writings of Sir William Petty, edited by Charles Henry Hull, and published in 1899.

2532267Another Essay in Political Arithmetick1683William Petty




Political Arithmetick,

Concerning the Growth of the





Measures, Periods, Causes,
and Consequences there-
of. 1682.

BySirWilliam Petty, Fellow of the


Printed by H. H. for Mark Pardoe, at the Black
, over against Bedford-House, in the Strand. 1683.


Another Essay in Political Arithmetick was probably written in Ireland about 1681[1], but was not sent to press until after Petty came to London in June, 1682[2]. Three years after the first edition, which is dated 1683, there appeared, under a changed title[3], a "second edition, revised and enlarged." The revision extends only to a few verbal changes which are recorded in the footnotes of this reprint. The enlargement was affected by the addition of the stationer's address to the reader and the "extract of a letter" which are reprinted on pages 453 to 455. Aside from these pages the ensuing text conforms to that of the original edition issued in 1683. The Essay is reviewed in the Journal des Sçavans, 15 Mars, 1683.



To the Reader.

THe ensuing Essay concerning the Growth of the City of London was entituled [Another Essay][4] intimating that some other Essay had preceded it, which was not to be found, I having been much importuned for that precedent Essay[5], have found that the same was about the Growth, Encrease, and Multiplication of Mankind, which Subject should in Order of Nature precede that of the Growth of the City of London, but am not able to procure the Essay itself, onely I have obtained from a Gentleman[6], who sometimes corresponded with Sir W. Petty, an Extract of a Letter from Sir William to him, which I verily believe containeth the scope thereof; wherefore, I must desire the Reader to be content therewith, till more can be had.

The Extract of a Letter concerning the scope of an Essay intended to precede Another Essay concerning the Growth of the City of (London), &c. An Essay in Political Arithmetick, concerning the Value and Encrease of People and Colonies.

THE scope of this Essay, is concerning People and Colonies, and to make way for Another Essay concerning the Growth of the City of London. I desire in this first Essay to give the World some light concerning the Numbers of People in England, with Wales, and in Ireland; as also, of the || number of Houses, and Families, wherein they live, and of Acres they occupy.

2. How many live upon their Lands, how many upon their Personal Estates, and Comerce, and how many upon Art, and Labour; how many upon Alms, how many upon Offices and Publick Employments, and how many as Cheats and Thieves; how many are Impotents, Children, and decrepit Old men.

3. How many upon the Poll-Taxes in England, do pay extraordinary Rates, and how many at the Level[7].

4. How many Men and Women are Prolifick, and how many of each are Married or Unmarried.

5. What the Value of People[8] are in England, and what in Ireland at a Medium, both as Members of the Church or Commonwealth, or as Slaves and Servants to one another; with a || Method how to estimate the same, in any other Country or Colony.

6. How to compute the Value of Land in Colonies, in comparison to England and Ireland.

7 How 10 thousand People in a Colony may be, and planted to the best advantage.

8. A Conjecture in what number of years England and Ireland may be fully peopled, as also all America, and lastly the whole habitable Earth.

9. What spot of the Earths-Globe were fittest for a general and universal Emporium, whereby all the people thereof may best enjoy one anothers Labours and Commodities.

10. Whether the speedy Peopling of the Earth would make

1. For the good of Mankind.
2. To fulfil the revealed Will of God.
3. To what Prince or State the same would be most advantageous. ||

11. An exhortation to all thinking Men to salve the Scriptures and other good Histories, concerning the Number of People in all Ages of the World, in the great Cities thereof, and elsewhere.

12. An Appendix concerning the different Number of Sea-fish and Wild-fowl, at the end of every thousand years, since Noah's Flood.

13. An Hypothesis of the use of those spaces (of about 8,000 miles through) within the Globe of our Earth, supposing a shell of 150 miles thick.

14. What may be the meaning of Glorified Bodies, in case the place of the Blessed shall be without the Convex of the Orb of the fixed Stars, if that the whole System of the World was made for the use of our Earths-men. ||

The Principal Points of this

1. THAT London doubles in Forty Years, and all England in Three hundred and sixty Years.

2. That there be, Anno 1682. about Six hundred and seventy Thousand Souls in London, and about seven Millions four hundred Thousand in all England and Wales, and about twenty-eight Millions of Acres of Land.[9]

3. That the Periods of doubling the People, are found to be in all Degrees, from between Ten, to Twelve hundred Years.

4. That the Growth of London must stop of its self before the Year 1800.

5. A Table helping to understand the Scriptures, concerning the Number of People mentioned in them. ||

6. That the World will be fully Peopled within the next Two Thousand Years.

7. Twelve Touch-stones[10], whereby to Try any Proposal, pretended for the Publick Good.

8. How the City of London may be made (Morally speaking) Invincible.

9. An Help to Uniformity in Religion.

10. That 'tis possible to increase Mankind by Generation four times more than at present.

11. The Plagues of London is the Chief Impediment and Objection against the Growth of the City.

12. That an Exact Account of the People is Necessary in this Matter. ||

Of the Growth of the CITY of LONDON: And of the Measures, Periods, Causes, and Consequences thereof.

BY the City of London, we mean the Housing within the Walls of the Old City, with the Liberties What is meant by London. thereof, Westminster, the Borrough of Southwark, and so much of the built Ground in Middlesex and Surrey, whose Houses are contiguous unto, or within Call of those afore-mentioned. Or else we mean the Housing which stand upon the Ninety seven Parishes within the Walls of London; upon the Sixteen Parishes next, without them; the Ten Parishes of Westminster, and the Seven Parishes |6| without them all; all which One hundred and thirty Parishes[11] are comprehended within the Weekly Bills of Mortality[12].

The Growth of this City is Measured,What is meant by the Growth of London.1.By the Quantity of Ground, or Number of Acres upon which it stands.2.By the Number of Houses, as the same appears by the Hearth-Books and late Maps.3.By the Cubical Content of the said Housing. 4.By the Flooring of the same.5.By the Number of Days-work, or Charge of Building the said Houses.6.By the Value of the said Houses, according to their Yearly Rent, and Number of Years Purchase.7.By the Number of Inhabitants; according to which latter sense only, we make our Computations in this Essay.

Till a better Rule can be obtained, we conceive that the Proportion |7| of the People may be sufficiently Measured by the Proportion of the Burials in such Years as were neither remarkable for extraordinary Healthfulness or Sickliness.

That the City hath Increased in this latter sense, appears In what Measures the City hath Increased. from the Bills of Mortality, represented in the two following Tables, viz. One whereof is a continuation for Eighteen years, ending 1682, of that Table which was Published in the 117th. pag. of the Book of the Observations upon the London Bills of Mortality, Printed in the Year 1676. The other sheweth what Number of People dyed at a Medium of two Years, indifferently taken, at about Twenty Years distance from each other. |8|

The first of the said two Tables.
1 7761 is a misprint for 761, which is the reading of the second edition and corresponds to the footing.
According to which latter Table, there dyed as followeth. |9|
The latter of the said two Tables.
There dyed in London, At a Medium between the Years.
1604 and 1605 5135. A.[13]
1621 and 1622 8527. B.
1641 and 1642 11883. C.
1661 and 1662 15148. D.
1681 and 1682 22331. E.

Wherein Observe, That the Number C. is double to A. and 806 over. That D. is double to B.[14] within 1906. That C. and D. is double to A. B. within 293. That E. is double to C. within 1435. That D. and E. is double to B. and C. within 3341. And that C. and D. and E. are double to A. and B. and C. within 1736[15]. And that E. is above Quadruple to A. All which differences (every way considered) do allow the doubling of the People of London in forty Years, to be a sufficient estimate thereof in round |10| Numbers, and without the trouble of Fractions. We also say, That 669930 is near the Number of People now in London, because the Burials are 22331. which Multiplyed by 30, (one dying Yearly out of 30, as appears in the 94 pag. of the afore-mentioned Observations[16] maketh the said Number; and because there are 84 Thousand Tenanted Houses (as we are Credibly Informed[17]) which, at 8 in each, makes 672 Thousand 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,) The People of London are about the Eleventh part of all England and Wales. that the City of London hath doubled, and the present Number of Inhabitants to be about 670 Thousand. We must now also endeavour the same for the whole Territory of England and Wales. In Order whereunto, we |11|

First say, That the Assessment of London is about an Eleventh part of the whole Territory[18], and therefore, that the People of the whole may well be Eleven times that of London, viz. about 7 Millions, 369 Thousand Souls; with which Account that of the Poll-money, Hearth-money[19], and the Bishops late Numbring of the Communicants[20], do pretty well agree; The people of England about 7 Millions and 400 thousand. wherefore, although the said Number of 7 Millions, 369 Thousand, 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 94 pag. of the afore-mentioned Observations) That |12| in the Countrey, but one of fifty dye 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 1200 Years. As for Example: Suppose there be 600 people, of which let a fiftieth part dye per Annum, then there shall dye 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 1126 Years, which to reckon in round Numbers, and for that the afore-mentioned Fractions were not exact, we had rather call 1200.

There are also other good Observations, That even in the Countrey, one in about 30, or 32 per Annum |13| hath dyed, and that there have been five Births for four Burials[21]. Now, according to this Doctrine, 20 will dye per Annum out of the above 600, and 25 will be Born, so as the Increase will be 5, 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 |14| 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 shewn 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 10 Years, which differs yet more from 1200 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 pitch'd upon 40; and I also took the Medium between 24 Births and 23 Burials, and 5 Births for 4 Bu-|15|rials, viz. allowing about 10 Births for 9 Burials; upon which Supposition, there must dye 15 per Annum out of the above-mentioned 600, and the Births must That the time of doubling is here and now 360 Years. be 16 and two Thirds, and the Increase 1, and two Thirds, or five Thirds of a Man, which Number compared with 1800 Thirds, or 600 Men, gives 360 Years for the time of doubling (including some Allowance for Wars, Plagues, and Famine, 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 20 Years hath carried away scarce an Eightieth part of the People of the whole Nation; and the late 10 Years Civil Wars, (the like whereof hath not been in several Ages before) did not take away |16| 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 Millions 400 Thousand People, there were about 5 Millions 526 Thousand in the beginning of Queen Elizabeths Reign, Anno 1560. and about two Millions at the Norman Conquest, of which Consult the Dooms-day Book, and my Lord Hale's Origination of Mankind[22].

320 Millions now in the World.Memorandum, That if the People double in 360 Years, that the present 320 Millions 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[23], will within the next 2000 Years so increase as to give one |17| 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 1200 Years, we do for the present, and in this Countrey 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 Thousand, and if the whole Territory be 7 Millions 400 Thousand, and double in 360 Years, as aforesaid; then by the underwritten Table it appears, that Anno 1840, the People of the City will be 10718880, and those of the whole Country but 10917389, which is but inconsiderably more. Where-|18|fore 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, Anno 1800, when the Number of the City will be Eight times its present Number, viz. 5 Millions 359 Thousand. And when (besides the said Number) there will be 4 Millions 466 Thousand to perform the Tillage, Pasturage, and other Rural Works Necessary to be done without the said City, as by the following Table, viz .

Annis. Burials People in
People in
1565 2568 77040 5526929
As in the
1605 5135
1642 11883
1682 22331 669930 7369230
1722 44662
1762 89324
1802 178648 5359440 9825650
1842 357296 10718880 10917389 |19|

That London will be at its highest growth, and eight times as great as now, Anno 1800.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 Anno 1800, when it will be eight times more than now, with above four Millions for the Service of the Countrey and Ports, as aforesaid.

Of the afore-mentioned vast difference between 10 Years and 1200 Years for doubling the People, we make this use, viz. To justifie the Scriptures and all other good Histories concerning the Number of the People in Ancient Time. A digression of the use of the vast difference between 10 and 1200 Years of doubling.For supposing the eight Persons who came out of the Ark, Increased by a Progressive doubling in every 10 Years, might grow in the |20| first 100 Years after the Flood from 8 to 8000, and that in 350 Years after the Flood (when abouts Noah dyed) to one Million, and by this time 1682, to 320 Millions (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 10 Years at first, and within 1200 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 extreams whereof we have demonstra-|21|ted to be real and true) it is impossible to solve what is written in the Holy Scriptures and other Authentick 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's time (being 800 Years after the Flood) when 603 Thousand Israelites of above 20 Years Old (besides those of other Ages, Tribes, and Nations) were found upon an exact Survey appointed by God[24], Whereas our Table makes 12 Millions. And there would have been but 8000 in David's Time, when were found 1100 Thousand of above 20 Years Old (besides others, as aforesaid) in Israel, upon the Survey instigated by Satan[25], whereas our Table makes 32 Millions. And there would have been but a quarter of a |22| Million about the Birth of Christ, or Augustus his Time, when Rome and the Roman Empire were so great, whereas our Table makes 100 Millions. Where Note, That the Israelites in about 500 Years between their coming out of Egypt to David's Reign, increased from 603 Thousand to 1100 Thousand.

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 Phænomena, 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 Countrey of the World.

We did (not long since) assist a worthy Divine[26], writing against some |23| Scepticks, 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 dyed since the beginning of the World, and did withal shew, that half the Island of Ireland would afford them all, not only Footing to stand upon, but Graves to lye down in, for that whole Number; and that two Mountains in that Countrey 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 |24| 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.

Anno 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 1024
80 2048
90 4096
100 8000 and more.
  120 Years after
In 20 Years the Flood. 16 Thousand.
  140 32
  170 64
  200 128
40   240 256
50 290 512
60 350 1 Million and more.
70 420 2 Millions.
100 520 4 Millions.
190 710 8 Millions.
290 1000 16 In Moses Time.
400 1400 32 About Davids Time.
550 1950 64
750 2700 128 About the Birth of Christ.
1000 3700 256
In 4000 320 |25|

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 Worlds 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. |26|

The Causes of its Growth from 1642 to 1682, may be said to have been as followeth, viz. From 1642 to 1650, That Men came out of the Countrey 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 Kings Friends and Party came to receive his Favours after his Happy Restauration; 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 Mans Sickness to be |27| 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 Arithmetick, 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 four |28| Millions 690 Thousand People, and that in all the other Cities, Ports, Towns, and Villages, there are but two Millions 710 Thousand 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 Thousand, and that the rest of the Inhabitants (being 7 Millions 304 Thousand) do Co-habit thus, 104 Thousand of them in small Cities and Towns, and that the rest, being seven Millions 200 Thousand, do Inhabit in Houses not contiguous to one another, viz. in 1200 Thousand Houses, having about 24 Acres of Ground belonging to each of them, accounting about 28 Millions 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. |29|

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 it self into the several Questions, relating to the following Particulars, viz.

1. For the Defence of the Kingdom against Foraign 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 easie Levying the same.

6. For Gain by Foraign Commerce.

7. For Husbandry, Manufacture, and for Arts of Delight and Ornament. |30|

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 Contagions. And withal, which of the said two states is most Practicable and Natural, for in these and the like particulars, do lye the Tests and Touch-stones of all Proposals, that can be made for the Publick 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 Elizabeths Reign, should be seven times bigger than now it is, |31| and 49 times bigger than Anno 1560. To which I say,1. That the present City of London stands upon less than 1500[27] Acres of Ground, wherefore a City, seven times as large may stand upon 10500 Acres, which is about equivalent to a Circle of four Miles and a half in Diameter, and less than 15 Miles in Circumference.2. That a Circle of Ground of 35 Miles Semidiameter will bear Corn, Garden-stuff, Fruits, Hay, and Timber, for the four Millions 690 Thousand Inhabitants of the said City and Circle, so as nothing of that kind need be brought from above 35 Miles distance from the said City; for the Number of Acres within the said Circle, reckoning one[28] Acre 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 Hedge-rows of the |32| Fields within the said Circle, may furnish Timber for 600 Thousand Houses.3. That all live Cattel and great Animals can bring themselves to the said City; and that Fish can be brought from the Lands-end and Berwick as easily as now.4. Of Coals there is no doubt: And for Water, 20s. per Family (or 600 Thousand 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 enquire (as to the first Question) which |33| state is most Defensible against Forraign Powers, saying, that if the above-mentioned Housing, and a border of Ground, of 3 quarters of a Mile broad, were encompassed with a Wall and Ditch of 20 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 Foraign Prince could bring an Army from beyond Seas, able to beat,1. Our Sea-Forces, and next with Horse harrass'd at Sea, to resist all the fresh Horse that England could make, and then Conquer above a Million of Men, well United, Disciplin'd, and Guarded within such a Wall, distant everywhere 3 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 Millions 690 Thousand People United within this great |34| 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 manner as the Soveraign shall think fit.3. As to Uniformity in Religion, I conceive, That if St. Martins Parish may (as it doth) consist of about 40 Thousand Souls, That this great City also may as well be made but as one Parish, with 7 times 130 Chappels, 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 Chappels without any subsequent Repetition of the same, as in the Case of Homilies. Whereas in England (wherein are near 10 Thousand Parishes, in each of which upon Sundays, Holy-days, |35| and other Extraordinary Occasions, there should be about 100 Sermons per 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 Millions 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, & 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 easie 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 |36| thrice as much for the Hearths in London as those in the Countrey, in proportion to the People of each, and that the Charge of Collecting these Duties, have been about a sixth part of the Duty it self. 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 gain'd by Foraign Commerce[29].

The Gain which England makes by Lead, Coals, the Freight of Shipping, &c. may be the same, for ought I see, in both Cases. But the Gain which is made by Manufactures, will be greater, as the Manufacture it self is greater and better. For in so vast |37| 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 easie; 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 |38| 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 Inhance the Price of such Manufacture, and lessen the Gain upon Foraign Commerce. And lastly, when the Imported Goods are spent in the Port it self, where they are Landed, the Carriage of the same into other places, will create no surcharge upon such Commodity; all which particulars tends to the greater Gain by Foraign 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 Millions than 400 Persons. But as for Husbandry, viz. Tillage and Pasturage, I see no Reason, but the second state (when |39| each Family is charged with the Culture of about 24 Acres) will best promote the same.

8. As for lessening the Fatigue of Carriage and Travelling,

The thing speaks it self, 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, when the charge of Carriage and Travelling could be little.

9. As to the preventing of Beggars and Thieves,

I do not find how the differences of the said two states should make much difference in this particular; for Impotents (which are but one in about 600) ought to be maintained by the rest.2. Those who are unable to work, through the evil Education of their Parents, ought (for ought I know) to be main-|40|tained by their nearest Kindred, as a just Punishment upon them.3. And those who cannot find Work (though able and willing to perform it) by reason of the unequal application of Hands to Lands, ought to be provided for by the Magistrate and Land-Lord till that can be done; for there needs be no Beggars in Countries, where there are many Acres of unimproved improvable Land to every Head, as there are in England, As for Thieves, they are for the most part begotten from the same Cause; For it is against Nature, that any Man should venture his Life, Limb, or Liberty, for a wretched Livelyhood, whereas moderate Labour will produce a better. But of this see Sir Thomas Moor, in the first part of his Utopia[30].

10. As to the Propagation and Improvement of Useful Learning, |41|

The same may be said concerning it as was above-said concerning Manufactures, and the Arts of Delight and Ornaments; for in the great vast City, there can be no so odd a Conceit or Design, whereunto some Assistance may not be found, which in the thin, scattered way of Habitation may not be.

11. As for the Increase of People by Generation,

I see no great difference from either of the two states, for the same may be hindred or promoted in either, from the same Causes.

12. As to the Plague,

It is to be remembred that one time with another, a Plague happeneth in London once in 20 Years, or thereabouts; for in the last hundred Years, between the Years 1582 and 1682, there have been five great Plagues, viz. Anno 1592, 1603, 1625, 1636, and 1665. And it is also to |42| be remembred that the Plagues of London do commonly kill one fifth part of the Inhabitants. Now, if the whole People of England do double but in 360 Years, then the Annual Increase of the same is but 20000, and in 20 Years 400000. But if in the City of London there should be two Millions of People, (as there will be about 60 Years hence) then the Plague (killing one fifth of them, namely, 400000 once in 20 Years) will destroy as many in one Year, as the whole Nation can re-furnish in 20: And consequently the People of the Nation shall never Increase. But if the People of London shall be above 4 Millions (as in the first of our two Extravagant Suppositions is premised) then the People of the whole Nation shall lessen above 20000 per Annum. So as if People be worth 70l. per Head (as hath elsewhere been shown[31]) |43| then the said greatness of the City will be a damage to it self and the whole Nation of 14 hundred Thousand pounds per Annum, and so pro rata, for a greater or lesser Number; wherefore to determine, which of the two states is best, (that is to say, towards which of the said two states Authority should bend the present state) a just Balance ought to be made between the disadvantages from the Plague, with the Advantages accruing from the other Particulars above-mentioned; unto which Balance a more exact Account of the People, and a better Rule for the Measure of its Growth is Necessary, than what we have here given, or are yet able to lay down. |44|


IT was not very pertinent to a Discourse concerning the Growth of the City of London, to thrust in Considerations of the Time when the whole World will be fully Peopled; and how to justifie the Scriptures concerning the Number of People mentioned in them; and concerning the Number of the Quick and the Dead, that may Rise at the last Day, &c. Nevertheless, since some Friends liking the said Digressions and Impertinencies (perhaps as sauce to a dry Discourse) have desired that the same might be explain'd and made out. I therefore say as followeth.

i. If the Number of Acres in the Habitable part of the Earth, be under |45| 50 Thousand Millions; if Twenty Thousand Millions of People, are more than the said Number of Acres will feed; (few or no Countries being so fully Peopled;) and for that in six doublings (which will be in 2000 Years) the present 320 Millions will exceed the said 20 Thousand Millions.

2. That the Number of all those who have dyed since the Flood, is the sum of all the Products made by Multiplying the Number of the doubling Periods mentioned in the first Column of the last Table, by the Number of People respectively affixed to them, in the third Column of the same Table; the said sum being Divided by 40 (one dying out of 40 per Annum, out of the whole Mass of Mankind) which Quotient is 12570 Millions; Whereunto may be added, for those that dyed before the Flood, enough to make the last-|46|mentioned Number 20 Thousand Millions, as the full Number of all that dyed, from the beginning of the World, to the Year 1682; unto which, if 320 Millions, the Number of those who are now alive, be added, the Total of the Quick and the Dead, will amount but unto one fifth part of the Graves, which the surface of Ireland will afford, without ever putting two Bodies into any one Grave; for there be in Ireland 28 Thousand square English Miles, each whereof will afford about 4 Millions of Graves, and consequently above 114 Thousand Millions of Graves, viz. about 5 times the Number of the Quick and the Dead,' which should arise at the last Day, in case the same had been in the Year 1682.

3. Now, if there may be place for five times as many Graves in Ireland, as sufficient for all that ever |47| dyed; And if the Earth of one Grave weigh five times as much as the Body Interrd therein, then a Turf, less than a Foot thick, pared off from a fifth part of the surface of Ireland, will be equivalent in bulk and weight to all the Bodies that ever were Buried; And may serve as well for that purpose, as the two Mountains afore-mentioned in the body of this Discourse. From all which it is plain, how madly they were mistaken, who did so petulantly vilifie what the Holy Scriptures have delivered.


  1. See p. 466 and note, also p. 468.
  2. Cf. pp. 438, 480.
  3. See Bibliography 13, 17.
  4. In the first edition.
  5. "Only a sort of syllabus of it [pp 454, 455] remains." Fitzmaurice, 216.
  6. Probably Sir Robert Southwell, through whom Petty had other dealings with Mark Pardoe, the stationer.
  7. See Treatise of Taxes, p. 62, note.
  8. Petty reckons the "value of people" variously at more than £60, Two Essays, post, at £69, Verbum Sap., p. 108, at £70, Polit. Anatomy, p. 152, Treatise of Ireland, post, and this Essay, p. 476, and at £80, Polit. Arith., p. 267.
  9. 2d ed., 'Acres of Profitable Land.'
  10. 2d ed., 'Twelve ways.'
  11. 2d ed., 'The six parishes of Westminster, and the fourteen out parishes in Middlesex and Surrey, contiguous to the former; all which one hundred and thirty-three parishes.'
  12. Petty's arrangement of ninety-seven parishes within the walls, sixteen next without, ten in Westminster, and seven without them all, is a division unknown to the bills. It probably arose from a transposition of the figures for Westminster (seven parishes) and for the parishes without them all (ten) given by Graunt. In the first edition Petty cites bills for 1665—1682, during which years the division was in fact 97, 16, 12, and 5 parishes in 1665—1670 and 97, 16, 14, and 5 parishes in 1674—1682. In the second edition, published m 1686, Petty corrected the division of the parishes (see preceding note) to correspond not to his table, which still stopped with 1682, but to the last yearly bill published when he wrote, (the bill for 1685), which included 97, 16, 14 and 6 parishes. On these changes see the Introduction.
  13. The numbers A, B, C, and D are calculated from Graunt's table, pp. 407—409. The number A, 5135, is miscalculated or misprinted; it should be 5185. The error makes, on the whole rather for than against Petty's contention.
  14. In figuring that one number "is double to" another within a certain sum, Petty uses, in every case but the first, a process indicated by the formula x = 2y ± n. But in order to get the result that "C is double to A and 806 over" one must use the formula x/2 = y ± n. Had Petty calculated the relation of C to A as he does the relation of D to B, etc., the surplus would have been 1613, his erroneous valuation of A being accepted.
  15. '1736' should be '1738.'
  16. On the page cited (p. 393 of this edition) Graunt says that "about one in 33 dies." But in the Index (p. 333) is the statement, with reference to page 93, that "at London one of thirty" dies yearly.
  17. Probably by the makers of Ogilby and Morgan's map; cf. a note to Five Essays below.
  18. By 31 Charles II., c. 1. (1679), the last assessment before Petty wrote, London paid £2145 15s. 8d., Middlesex, including Westminster, £1520 5s., Surrey, including Southwark £798 10s. 1d., in all £4464 10s. 9d. or little more than one eighth the monthly assessment of £34410 9s. 6d. But the proportion of London proper, which was the basis of Petty's earlier calculation (Verbum Sap., p. 107, note) now fell to less than one sixteenth. On the proportion of London in different assessments see Thorold Rogers, Economic Interpretation of History, 145—156.
  19. The hearth money was imposed by 14 Charles II. c. 10. By 15 Charles II. c. 13 it was enacted that whereas the revenue from hearth money had "beene much obstructed for want of true and just Accompts under the hands of the respective Occupiers of Houses Edifices Lodgings and Chambers as by the said Act is required," therefore the account should be verified upon visitation by the constable. He should make out "a Booke or Roll fairely written wherein shall be Two Columnes, The one containing the Names of the persons and the number of Hearthes and Stoves in their respective Possessions that are chargeable by the said Act, and the otner the Names of the persons... not chargeable." This roll was to be transmitted to the high constable, then to the Justices of the peace, then to the Clerk of the peace, who should " within Two Moneths engrosse in Parchment a true Duplicate of the said Booke or Roll, which being signed by him, and by two Justices of the Peace at least of the respective County and places aforesaid shall be transmitted within one Moneth after such Engrossment into his Majestie's Courts of Exchequer."
  20. In Stowe MS. 322 at the British Museum, ff. 89—90, is contained the following memorandum: The Telling of Noses; Or The Number of Freeholders in England according to Sr W. P.
      Conformists   Nonconf.   Papists
    In the Province of Cant. 2123362 93151 11878
    York 353892 15525 1978

    In both 2477254 108676 13858
    Conf. 2477254
    Nonconf. 108676

    Together 2585930
    Papists 13856

    In all Engld 2599786
    According to wch Account the proportion of
    Conformists to Nonconformists, is 22 4/5
    Conformists to Papists, is 178 10/10
    Conf. & Nonconf. together, to Papists, is 186 2/3
    to One.
    [Endorsed]. Calculation of the People of England. 1687.

    The MS. in the hand of a copyist, who has unquestionably misdated it, was formerly at Ashburnham Place. Eighth Report Hist. MSS. Com., App. iii. p. 12. The same calculation, but at much greater length, is assigned by Sir John Dalrymple's Memoirs of Great Britain and Ireland, 2d ed., appendix, pt. 11. pp. 11 —15, to the reign of William III. The origin of the figures is revealed by Petty's friend, Sir Peter Pett. Pett discusses "the Result of the Bishops Survey, which was made of the Province for Canterbury and wherein none under the age of Communicants or 16 were return'd, and but very few Servants, or Sons, and Daughters, or Lodgers, or Inmates of the people of several perswasions of Religion: and the thing endeavour'd was that the heads of Families or House-Keepers, i.e. Man and Wife might be truly return'd: and at that rate, the Total at the foot of the account for the Province of Canterbury is 2,228,386, the which according to the forementioned currant Rule of Calculation to be necessarily about doubled on account of the people under 16, makes the Total of the Souls in that Province to be 4 Millions 4 Hundred 56 thousand, 7 hundred seventy two; and the Province of York bearing a sixth part of the Taxes, and having therefore the 6th. part of the people, that the Province of Canterbury hath, which is 742,795, that being added to those of Canterbury, makes 5 Millions, a hundred ninety nine thousand, five hundred sixty seven." Happy future State of England, 117—118. Writing in 1680, although his book was not published until 1688, Pett goes on to say that this enumeration was taken in 1676, that it was defective, and that the total population of England was, at the time when he wrote, more than five million two hundred thousand.

  21. Graunt, p. 390.
  22. Petty's allusion to Domesday Book rests, probably, upon such knowledge only as he drew from reading Sir Matthew Hale's The primitive Origination of Mankind considered and examined, (1672). Hale, however, does not estimate the population of England at the time of the Conquest at all. That, he thinks, would be "a labourious piece of work, but it is not difficult to be done in any one County; I have tryed the comparison in the County of Gloucester., and I do find… that the number of inhabitants now are above twenty times more than they were at that time," p. 235. The laborious piece of work has since been performed by Sir Henry Ellis, but the "recorded population" (287,045) must be multiplied "by four, five or six, according to knowledge or taste, before the population of England will be attained."-Maitland, Domesday Book and beyond, 408; cf. pp. 17—22, 400, 437, also Pell in Domesday Studies, 1. 561.
  23. Petty's learned men have not been identified. In 1685 Isaac Vossius estimated the population of the world at 500 millions, a number which Bayle ridiculed as too large: Vossii variorum observationum liber, 68; Bayle, Nouvelles de la République des Lettres, Janvier, 1685, Oeuvres, i. 212—214. See the chapter on the "Historische Entwickelung der Versuche, die Gesammt-bevölkerung der Erde zu schätzen," in Behm and Wagner, Die Bevolkerung der Erde, ii. 3—8, Petermann's Geogr. Mittheilungen, Ergänzungsband, viii. nr. 35.
  24. Numbers i. 1—46. The precise number is 603,550. Petty has overlooked the later enumeration of 601,730, Numbers xxvi. 1—51.
  25. 1 Chronicles xxi. 1-8, 'and all Israel were a thousand thousand and a hundred thousand men that drew the sword; and Judah four hundred three score and ten thousand men that drew the sword.' The account in 2 Samuel xxiv. 1—9 gives 800000 fighting men in Israel and 500000 in Judah.
  26. Concerning his assistance to the worthy divine, Petty writes thus to Sir Robert Southwell:
    Dublin, 20th Augt. 1681.
    Dear Cosen,
    Once more pay the Postage of 4 Sheets. By ye last you saw ye Quantum of my Damage; by this you shall ye Quomodo, & consequently ye Injury. Oh! that I could get some body to read my Papers.
    There is a good man about this Town writing agst Atheisme, and in particular at this time answering their Cavills against ye Resurrection; Which are, That ye whole Globe of ye Earth will not afford sufficient Matter to the Bodies that must Rise, much less will the surface thereof (say they) afford footing to all those Bodies. Now ye assistances which I have given this good man are viz.
    Supposing ye People in England, Scotland & Ireland to be abt nine Millions, Those in Holland and Zealand abt one Million, and in France 16, I say that by comparing ye rest of ye World therewth there are but between 300 & 400 Millions of Souls now living.
    Upon this and Grant's Measures I ascertain ye Number that ever have died since ye Creation, & find that Munster would afford them all Graves, and ye Mangerton Bodies, or ye Equivalent in weight of Earth.
    Having thus help'd my Friend, I took occasion to proceed, viz.
    1stI find yt ye World being 5630 years old [Scaliger's Chronology, cf. p. 388, note 1], and Adam & Eve doubling but every 200 years (as Grant also saies) there must be now 316 Millions of People upon ye Earth; wch answers admirably, and is a brave Argument agst Scripture-Scoffers and Prœ-Adamites.
    Nevertheless upon Examination of our Friend Grant's Positions,
    2dlyI find People do double very differently in every Century of ye World, and have (as I think) rectitified his Doctrine, by making many Numbers in continuall Proportion.
    3dlyI further find, that ye World at a Medium is at this day not much better peopled then our wretched Baronies in Keery, nor above 110 part so well as our poor Ireland is; nor above 1100 part so well as Holland, wch is over-peopled.
    4thlyI find yt in ye next 1400 years ye World doubling it's People in my corrected proportion, must be over-peopl'd, and then that there must be great Wars and Slaughters, and yt ye Strong must then destroy ye Weak, or ye World must (of necessity) come to an end.
    5thlyI find by looking far back upon ye paucity of People in ye Asyrian, Persian, and other first Monarchies, how easy a thing 'twas for a few resolute Fellows to conquer ye World, as then it was. And that (whatever ye King of France may think) ye Universall or Great Monarchy does and will grow every Century more & more difficult by ye Course of Nature.
    6thlyI conclude, that as People double faster now then they did in former Ages, so ye Rents of Lands must also rise proportionably, and ye number of years Purchase also: Wherefore let us get possession of what ye Affidavit saies is kept from us.
    Thus, Dear Cosen (having ended where I began) I am still Yours.
    [Endorsement] Dublin, Augt. 20th. 1681. A Copy of Sr. Wm. Petty's Letter to Sr. Robt. Southwell. Abt. ye Number of Mortals, &c.
    Rawlinson MS. A. 178, ff. 71—72, Bodleian Library, among the Pepys papers. The letter has been printed in Rev. John Smith's Life, Journals, and Correspondence of Pepys (1844), ii. 317.
  27. 2d ed.; '2500 Acres.'
  28. 2d ed.; 'reckoning two Acres.'
  29. 2d ed.; 'by commerce?'
  30. Lupton's ed., p. 58.
  31. See note 2, p. 454.

This work was published before January 1, 1929, and is in the public domain worldwide because the author died at least 100 years ago.

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