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• Note On Graunt's “observations.”
• To the Right Honourable John Lord Roberts 1 , Baron of Truro , Lord Privy Seal , and One of His Majesties Most Honourable Privy Council.
• To the Honourable S R Robert Moray 1 , Knight, One of His Majestie's Privy Council For His Kingdom of Scotland , and President of the Royal Society of Philosophers Meeting At Gresham- Colledg , and to the Rest of That Honourable Society.
• The Preface.
• Natural and Political Observations, &c.
• Chap. I.: Of the Bills of Mortality, Their Beginning, and Progress. 1
• [chap. II.] 1: General Observations Upon the Casualties.
• Chap. III.: Of Particular Casualties.
• Chap. IV. of the Plague.
• Chap. V.: Other Observations Upon the Plague, and Casualties.
• Chap. VI.: Of the Sickliness, Healthfulness, and Fruitfulness of Seasons.
• Chap. VII.: Of the Difference Between Burials and Christenings.
• Chap. VIII.: Of the Difference Between the Numbers of Males and Females.
• Chap. IX.: Of the Growth of the City.
• Chap. X.: Of the Inequality of Parishes.
• Chap. XI.: Of the Number of Inhabitants.
• Chap. XII.: Of the Country-bills.
• The Conclusion.: an Appendix 1 .
• Appendices to Graunt's Observations.
• Quantulumcunque Concerning Money. 1682
• Note On the Essays In “political Arithmetick.”
• Another Essay In Political Arithmetick, Concerning the Growth of the City of London: With the Measures, Periods, Causes, and Consequences Thereof.1682. By Sir William Petty , Fellow of the Royal Society. London: Printed By H. H. For Mar
• Observations Upon the Dublin-bills of Mortality, M D C L X X X I. State of That City.
• Further Observation Upon the Dublin-bills: Or, Accompts of the Houses, Hearths, Baptisms, and Burials In That City.
• Two Essays In Political Arithmetick, Concerning the People, Housing, Hospitals, &c. London and Paris.
• Observations Upon the Cities of London and Rome.
• Five Essays In Political Arithmetick, Viz.
• Note On the “five Essays.”
• To the King's Most Excellent Majesty.
• The First Essay.
• The Second Essay.
• The Third Essay.
• The Fourth Essay 1 Concerning the Proportions of People In the 8 Eminent Cities of Christendom Undernamed , Viz.
• The Fifth Essay. Concerning Holland and the Rest of the United Provinces.
• A Treatise of Ireland, 1687. the Elements of Ireland; and of Its Religion, Trade & Policy. By Sir William Petty , Fellow of the Royal Society.
• Note On the “treatise of Ireland.
• An Essay In Political Arithmetick Concerning Ireland 1 .
• Preface.
• Chap. I.: By This Title We Mean the Several Points Following. (vizt)
• Chap. II.: The State of the Case Represented In Terms of Number, Weight, and Measure; and Thereby Made Capable of Demonstrations. ( Vizt )
• Chap. III.: The 6 First Mention'd Points Are Proved Out of the 20 Suppositions Or Assertions Next Before-going. ( Vizt )
• Chap. IV.: How to Enable the People of England and Ireland to Spend 5 Millions Worth of Commodities More Than Now: and How to Raise the Present Value of the Lands and Goods of Ireland From 2 to 3.
• Chap. V.: That the King's Revenue In England and In Ireland, Supposed to Be 2070 Thousand Pounds, Will Be Increased to Above ⅕ Part More (vizt) to 1 Above 414 Thousand Pounds; and Even to 450 Thousand Pounds: So As to Be In All 2520 Thousand Pounds.
• Chap. VI.
• Chap. VII.: How to Take Away All the Evils Arising From Differences of Births, Extractions, Languages, Manners, Customs, Religion, and Laws, and Pretence Whatsoever.
• Chap. VIII.: How the Names, Bounds, Titles, and Values, of Lands May Be Settled and Ascertained; With Remedy of the Miscarriages, Which Have Happened In the 35 Years Last Past In the Disposures of Them.
• Chap. IX.: A Repetition and Enlargement of What Has Been Here Said.
• An Appendix of Objections to This Essay, With Answers to the Same.
• Appendix.
• Bibliography of the Printed Writings of Sir William Petty 1 .
• Supplement to the Bibliography of Petty's Works.
• Bibliography of the Natural and Political Observations.

The THIRD ESSAY.

PRoofs that the number of People in the 134 Parishes of the London Bills of Mortality, without reference to other Cities, is about 696 thousand, viz.

I know but three ways of finding the same.

1. By the Houses, and Families, and Heads living in each.

2. By the number of Burials in healthfull times, and by the proportion of those that live, to those that die. ‖

3. By the number of those who die of the Plague in Pestilential years, in proportion to those that scape.

The First way.

To know the number of Houses I used three methods, viz.

1. The number of Houses which were burnt Anno 1666, which by authentick Report was 13200; next what proportion the People who dyed out of those Houses, bore to the whole; which I find Anno 1686, to be but part, but Anno 1666 to be almost ⅕, from whence I infer the whole Housing of London ‖ Anno 1666 to have been 66 thousand, then finding the Burials Anno 1666 to be to those of 1686 as 3 to 4, I pitch upon 88 thousand to be the number of Housing Anno 1686.

2. Those who have been employed in making the general Map1 of London, set forth in the year 1682, told me that in that year, they had found above 84 thousand Houses to be in London, wherefore Anno 1686, or in 4 years more, there might be or 8400 Houses more (London doubling in 40 years) so as the whole, Anno 1686 might be 92400. ‖

3. I found that Anno 1685, there were 29325 Harths in Dublin, and 6400 Houses, and in London 388 thousand Harths, whereby there must have been at that rate 87000 Houses in London. Moreover I found that in Bristol there were in the same year 16752 Harths, and 5307 Houses, and in London 388 thousand Harths as aforesaid; at which rate there must have been 123 thousand Houses in London, and at a Medium between Dublin and Bristol proportions 105 thousand Houses.

Lastly, By Certificate from the Harth-Office, I find the Houses within the Bills of Mortality to be 105,315. ‖

Having thus found the Houses, I proceed next to the number of Families in them, and first I thought that if there were 3 or 4 Families or Kitchins in every House of Paris, there might be 2 Families in of the Housing of London; unto which supposition, the common opinion of several Friends, doth concur with my own conjectures.

As to the number of Heads in each Family, I stick to Grant's observation in page1 of his fifth Edition, That in Tradesmen of London's Families, there be 8 Heads one with another, in Families of higher Ranks, above 10, ‖ and in the poorest near 5, according to which proportions, I had upon another occasion2 pitch'd the medium of Heads in all the Families of England to be 6兓, but quitting the Fraction in this Case, I agree with Monsieur Auzout for 6.

To conclude, the Houses of London being 105315, and the addition of double Families 10531 more, in all 115846; I multiplied the same by 6, which produced 695076 for the number of the People.

The Second way.

I found that the years 1684 and 1685, being next each other, and ‖ both healthfull, did wonderfully agree in their Burials, viz. 1684 they were 23202, and Anno 1685 23222, the Medium whereof is 23212; Moreover that the Christnings 1684 were 14,702, and those Anno 1685 were 14730, wherefore I multiplied the Medium of Burials 23212 by 30, supposing that one dies out of 30 at London, which made the number of People 696,360 Souls1 .

Now to prove that one dies out of 30 at London, or thereabouts, I say,

1. That Grant in the2 page of his fifth Edition, affirmeth from observation, that 3 died of 88 per ‖ an. which is near the same proportion.

2. I found that out of healthfull places, and out of adult persons, there dies much fewer, as but 1 out of 50 among our Parliament men, and that the Kings of England having reigned 24 years one with another, probably lived above 30 years each.

3. Grant, page hath shewn3 that but about 1 of 20 die per an. out of young Children under 10 years old, and Monsr. Auzout thinks that but 1 of 40 die at Rome, out of the greater proportion of adult persons there, wherefore we still stick at a Medium to the number 30. ‖

4. In 9 Countrey Parishes lying in several parts of England, I find that but one of 37 hath died per an. or 311 out of 11507, wherefore till I see another round number, grounded upon many observations, nearer than 30, I hope to have done pretty well in multiplying our Burials by 30, to find the number of the People, the product being 696,360, and what we find by the Families they are 695,076, as aforesaid.

The Third way.

It was prov'd by Grant1 , that ⅕ of the People died of the Plague, but Anno 1665 there died of the ‖ Plague near 98 thousand persons2 , the Quintuple whereof is 490 thousand, as the number of People in the year 1665, whereunto adding above ⅓, as the increase between 1665 and 1686, the total is 653 thousand, agreeing well enough with the other two Computations above mentioned.

Wherefore let the proportion of 1 to 30 continue till a better be put in its place.

Memorandum, That 2 or 3 hundred new Houses would make a Contiguity of 2 or 3 other great Parishes, with the 134 already mentioned in the Bills of Mortality; and that an oval Wall of about 20 Miles in compass would enclose the ‖ same, and all the Shipping at Deptford and Black-wall, and would also fence in 20 thousand Acres of Land, and lay the foundation or designation of several vast advantages to the Owners, and Inhabitants of that Ground, as also to the whole Nation and Government. ‖

[1]Petty twice refers to a map of London “set forth in the year 1682” (see also p. 542), but no such map can be found at the British Museum. Mr C. H. Coote, of the Department of Maps, thinks it probable that the map which Petty used was Ogilby and Morgan's. This map was published with the title: A large and accurate map of the city of London Ichnographically Describing all the Streets, Lanes, Alleys, Courts, Yards, Churches, Halls and Houses, &c. Actually Surveyed and Delineated By John Ogilby Esq.… dedicated and presented by… William Morgan, and was accompanied by a descriptive text entitled London Survey'd: or, an explanation of the large map of London. Giving a Particular Account Of the Streets and Lanes, in the City and Liberties. By John Ogilby & William Morgan, His Majesty's Cosmographers. London, Printed and Sold at the Authors House In White Fryers, 1677. So far as I can discover, neither the map nor the text makes any calculation of the population or of the houses of London.

[1]Page 82 of the fifth ed., p. 385 of this reprint.

[2]In some calculation now probably lost.

[1]Cf. p. 506, where, by averaging more years, Petty gets a smaller population.

[2]Page 82 of the fifth ed., p. 385 of this reprint. Graunt says that 3 died out of 11 families and guesses that the families have, one with another, 8 members.

[3]Graunt makes no such assertion. Petty's proposition appears to be a guess which may find some slight support on pp. 386–387 of Graunt.

[1]Graunt does not say this.

[2]In 1665 there died in all 97,306, whereof 68,596 of the plague. On this basis, Petty's method would give a population of about 460,000 in 1686, agreeing ill enough with the other two computations above mentioned.