Two essays in Political Arithmetick (Petty 1899)


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Aug. 26th 1686.

Let this Paper be printed.

Sunderland P.


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Political Arithmetick,

Concerning the

People, Housing, Hospitals, &c.


London and Paris.



Fellow of the Royal Society.



——————Qui sciret Regibus uti
Fastidiret olus



Printed for J. Lloyd in the Middle Exchange
next Salisbury-House in the Strand. 1687.




Petty's Two Essays concerning London and Paris, though first published in French, were originally written in English.[2] They were probably finished between the 17 July, 1686, the day on which was licensed no. 180 of the Philosophical Transactions containing the account of Verbiest's journeys referred to in the first essay[3], and the 26 August of the same year, when the Two Essays were themselves approved.[4]




Most Excellent MAJESTY.


IDo presume, in a very small Paper, to shew Your Majesty that Your City of London seems more considerable than the Two best Cities of the French Monarchy, and for ought I can find, greater than any other of the Universe, which because I can say || without flattery, and by such Demonstration as Your Majesty can examine, I humbly pray Your Majesty to accept from

Your Majesty's

Most Humble, Loyal

and Obedient Subject,

William Petty.





Political Arithmetick,



Tending to prove that London hath more People and Housing than the Cities of Paris and Rouen put together, and is also more considerable in several other respects[5].

1.  THE Medium of the Burials at London in the three last years, viz. 1683, 1684 and 1685, (wherein there was no extraordinary Sick-|2|ness, and wherein the Christenings do correspond in their ordinary proportions with the Burials and Christenings of each year one with another) was 22337, and the like Medium of Burials for the three last Paris Bills we could procure, viz. for the years 1682, 1683 and 1684 (whereof the last as appears by the Christenings to have been very sickly) is 19887[6].

2. The City of Bristol[7] in England appears to be by good estimate of its Trade and Customes as great as Rouen in France, and the City of Dublin in Ireland appears to have more Chimnies than Bristol, and consequently more People, and the Burials in |3| Dublin were Anno 1682 (being a sickly year) but 2263.

3. Now the Burials of Paris (being 19887) being added to the Burials of Dublin (supposed more than at Rouen) being 2263, makes but 22150, whereas the Burials of London were 187 more, or 22337, or as about 6 to 7[8].

4. If those who die unnecessarily, and by miscarriage in L'hostel Dieu in Paris (being above 3000) as hath been elsewhere shewn[9], or any part thereof, should be subtracted out of the Paris Burials aforementioned, then our assertion will be stronger, and more proportionable to what fol-|4|lows concerning the Housing of those Cities, viz.

5. There were burnt at London, Anno 1666, above 13000 houses, which being but a fifth part of the whole, the whole number of houses in the said year, were above 65000; and whereas the ordinary Burials of London have increased between the years 1666 and 1686, above one third the total of the houses at London Anno 1686, must be about 87000, which Anno 1682, appeared by accompt to have been 84000[10].

6. Monsieur Morery, the great French Author of the late Geographical Dictionaries[11], who makes Paris the greatest City in the World, |5| doth reckon but 50000 houses in the same, and other Authors and knowing Men much less; nor are there full 7000 houses in the City of Dublin, so as if the 50000 houses of Paris, and the 7000 houses in the City of Dublin were added together, the total is but 57000 Houses, whereas those of London are 87000 as aforesaid, or as 6 to 9.

7. As for the Shipping and foreign Commerce of London, the common sense of all Men doth judge it to be far greater than that of Paris and Rouen put together.

8. As to the Wealth and Gain accruing to the Inhabitants of London and Paris by Law-suits (or La chicane)[12] I onely say that the Courts |6| of London extend to all England and Wales, and affect seven Millions of People, whereas those of Paris do not extend near so far: Moreover there is no palpable conspicuous argument at Paris for the Number and Wealth of Lawyers like the Buildings and Chambers in the Two Temples, Lincoln's Inn, Gray's Inn, Doctors Commons, and the seven other Inns in which are [13] Chimnies, which are to be seen at London, besides many Lodgings, Halls, and Offices relating to the same.

9. As to the plentifull and easie living of the People we say,

1. That the People of Paris to those of London, being as a-|7|bout 6 to 7, and the Housing of the same as about 6 to 9, we infer that the People do not live at London so close and crouded as at Paris, but can afford themselves more room and liberty.

2. That at London the Hospitals are better and more desirable than those of Paris, for that in the best at Paris there die 2 out of 15[14], whereas at London there die out of the worst scarce 2 of 16, and yet but a fiftieth part of the whole die out of the Hospitals at London, and 25 or 20 times that proportion die out of the Paris Hospitals which are of the same kind; that is to say, the number of those at London, who chuse to lie sick in Hospitals rather than |8| in their own Houses, are to the like People of Paris as one to twenty; which shews the greater Poverty or want of Means in the People of Paris than those of London.

3. We infer from the premisses, viz. the dying scarce 2 of 16 out of the London Hospitals, and about 2 of 15 in the best of Paris, (to say nothing of L'hostel Dieu). That either the Physicians and Chirurgeons of London are better than those of Paris, or that the Air of London is more wholesome.

10. As for the other great Cities of the World, if Paris were the greatest we need say no more |9| in behalf of London. As for Pequin in China, we have no account fit to reason upon; nor is there anything in the Description of the two late Voyages of the Chines's Emperour from that City into East and West Tartary[15], in the years 1682 and 1683, which can make us recant what we have said concerning London. As for Dely and Agra belonging to the Mogull we find nothing against our position, but much to shew the vast numbers which attend that Emperour in his business and pleasures.

11. We shall conclude with Constantinople and Gran Cairo; as for Constantinople it hath been said by one who endeavour'd to shew |10| the greatness of that City, and the greatness of the Plague which reigned in it, that there died 1500 per diem, without other circumstances: To which we answer, that in the year 1665 there died in London 1200 per diem, and it hath been well proved that the Plague of London never carried away above 15 of the People, whereas it is commonly believed that in Constantinople, and other Eastern Cities, and even in Italy and Spain, that the Plague takes away 25 one half or more; wherefore where 1200 is but 15 of the People it is probable that the number was greater, than where 1500 was 25 or one half, &c. |11|

12. As for Gran Cairo it is reported, that 73000 died in 10 weeks or 1000 per diem[16], where note, that at Gran Cairo the Plague comes and goes away suddenly, and that the Plague takes away 2 or 35 parts of the People as aforesaid; so as 73000 was probably the number of those that died of the Plague in one whole year at Gran Cairo, whereas at London Anno 1665, 97000 were brought to account to have died in that year. Wherefore it is certain, that that City wherein 97000 was but 15 of the People, the number was greater than where 73000 was 25 or the half. |12|

We therefore conclude, that London hath more People, Housing, Shipping and Wealth, than Paris and Rouen put together; and for ought yet appears, is more considerable than any other City in the Universe, which was propounded to be proved. |13|





Political Arithmetick,



Tending to prove that in the Hospital called L'hostel Dieu at Paris, there die above 3000 per Annum by reason of ill accommodation.

1.  IT appears that Anno 1678 there entred into the Hospital of La Charité 2647 Souls, of which there died there within the said year 338, which |14| is above an eighth part of the said 2647, and that in the same year there entred into L'hostel Dieu 21491, and that there died out of that number 5630, which is above one quarter, so as about half the said 5630, being 2815, seem to have died for want of as good usage and accommodation as might have been had at La Charité[17].

2. Moreover in the year 1679 there entred into La Charité 3118, of which there died 452, which is above a seventh part, and in the same year there entred into L'hostel Dieu 28635, of which there died 8397; and in both the said years 1678 and 1679 (being very different in their degrees of |15| Mortality) there entred into L'hostel Dieu 28635 and 21491, in all 50126, the Medium whereof is 25063, and there died out of the same in the said Two years 5630 & 8397, in all 14027, the Medium whereof is 7013.

3. There entred in the said years into La Charité 2647 and 3118, in all 5765, the Medium whereof is 2882, whereof there died 338 and 452, in all 790, the Medium whereof is 395.

4 Now if there died out of L'hostel Dieu 7013 per annum, and that the proportion of those that died out of L'hostel Dieu is double to those that died out of La Charité (as by the above |16| Numbers it appears to be near there abouts) then it follows that half the said Numbers of 7013 being 3506, did not die by natural necessity, but by the evil administration of that Hospital.

5. This Conclusion seem'd at the first sight very strange, and rather to be some mistake or chance than a solid and real truth, but considering the same matter as it appeared at London, we were more reconciled to the belief of it, viz.

1. In the Hospital of St. Bartholomew in London there was sent out and cured in the year 1685, 1764 Persons, and there died out of the said Hospital 252. |17| Moreover there were sent out and cured out of St Thomas's Hospital 1523, and buried 209, that is to say, there were cur'd in both Hospitals 3287, and buried out of both Hospitals 461, and consequently cured and buried 3748, of which number the 461 buried is less than an eighth part; whereas at La Charité the part that died was more than an eighth part; which shews that out of the most poor and wretched Hospitals of London there died fewer in proportion than out of the best in Paris.

2. Farthermore, it hath been above shewn that there died out of La Charité at a Medium 395 per annum, and 141 out of Les |18| Incurables making in all 536; and that out of St. Bartholomew's and St. Thomas's Hospital, London, there died at a Medium but 461, of which Les Incurables are part; which shews that although there be more People in London than in Paris, yet there went at London not so many People to Hospitals as there did at Paris, although the poorest Hospitals at London, were better than the best at Paris; which shews that the poorest People at London have better accommodation in their own houses, than the best Hospital of Paris affordeth.

6. Having proved that there die about 3506. Persons at Paris unnecessarily to the damage of France, || we come next to compute the value of the said damage and of the Remedy thereof, as follows, viz. the value of the said 3506 at 60 li. Sterl. per head, being about the value of Argier Slaves, (which is less than the intrinsick value of People at Paris) the whole loss of the Subjects of France in that Hospital seems to be 60 times 3506 li. Sterl. per Annum, viz. 210 thousand 360 li. Sterl. equivalent to about two Millions 524 Thous. 320 French Livers.

7. It hath appeared that there came into L'hostel Dieu at a Medium 25063 per Annum, or 2089 per Mensem, and that the whole stock of what remain'd in the |20| precedent Months is at a Medium about 2108 (as may appear by the third Line of the Table N° 5, which shall be shortly published)[18] viz. the Medium of Months is 2410 for the sickly year 1679, whereunto 1806, being added as the Medium of Months for the year 1678, makes 4216, the Medium whereof is the 2108 above mentioned; which number being added to the 2089 which entred each Month, makes 4197 for the Number of Sick which are supposed to be always in L'hostel Dieu one time with another.

8. Now if 60 French Livers per Annum for each of the said 4197 sick Persons were added to |21| the present ordinary Expence of that Hospital (amounting to an addition of 251 Thousand 820 Livers) it seems that so many lives might be saved as are worth above ten times that sum, and this by doing a manifest deed of Charity to Mankind. || Memorandum, That Anno 1685, the Burials of London were 23222, and those of Amsterdam 6245; from whence, and the difference of Air, 'tis probable that the People of London are quadruple to those of Amsterdam[19].

  1. 'Si pranderet olus patienter, regibus uti
    Nollet Aristippus.' 'Si sciret regibus uti,
    Fastidiret olus, qui me notat.' Utrius horum
    Verba probes et facta doce vel junior audi,
    Cur sit Aristippi potior sententia.
    Horace, Epistles, I. 17, 13—17.

    The story of the conversation between Aristippus and Diogenes is told by Diogenes Laertius.
    (Translation: 'If Aristippus knew how to dine on vegetables, he wouldn't be so often at the king's table.' 'If he (Diogenes) knew how to entertain the king, he would soon disdain his herbs.' Which of these two was right? Tell me, or learn from me, who am older than yourself, that Aristippus is wiser. - Wikisource ed.)
  2. Bibliography, 18. The French Version declares itself to be "Traduit de l'Original Anglois."
  3. P. 508.
  4. P. 500.
  5. The common notion at the time when Petty wrote appears to have been that Paris must be larger than London because the court of Louis XIV. was more splendid than that of Charles II. Petty was not the first who held London the larger, but he appears to have been the first who gave an adequate reason for his belief. Gregorio de Leti says that he himself had once believed Paris the more populous city, but 'all the more general and infallible rules' had shewn him the superiority of London. De Leti had unusual opportunities for observation, but his estimate of the actual population of the two cities is absurdly high. He appears to credit, somewhat grudgingly, the assertion of an (unidentified) French ambassador, who had told him that Paris contained a million and a half of people. And he is 'forced to believe' that in London there are not less than two million souls! Del teatro britannico (1683), p. 75. A more trustworthy account is given by Le Maire, the author of Paris ancien et nouveau, 1685. After quoting Giovanni Botero (1540-1617) on "Parigi città che di popolo & di abbondanza d'ogni cosa avanza de gran lunga tutte l'altre di Christianità," Le Maire gives the number of people and of houses in each of the sixteen quarters of La Ville de Paris—as in the case of London, an area smaller than that included in the bills of mortality—according to an enumeration made in 1684. The totals are 91,252 persons and 20,641 houses. Le Maire, pp. 5—15. The enumeration of 1684 is reprinted in Boislisle's Mémoire de la Généralité de Paris (in the Documents inédits), p. 422. A modern estimate gives 543,270 inhabitants to the Paris of 1684. Husson, Les Consommations de Paris (1856), p. 20.
  6. In Paris there died 17,493 in 1682 and 17,764 in 1683, which, according to Petty's average of 19,887, would leave 24,404 deaths in the "very sickly" year 1684. In the first nine months of 1684, for which alone the official compilers of the Recherches statistiques could recover the figures, there died 18,737. The average mortality 1670—1675, 1678—1683 was 19,684. Recherches, ii., tableau 53. The figures for 1676, 1677 and 1685—1687 are probably lost. They may perhaps be preserved in Grimperel's MS. in the Bibliotheque de l'lnstitut National de France (n° x. 214, 2 vols. in f°), which I have not seen.
  7. Petty's informant concerning Bristol may have been Sir Robert Southwell, whose seat, King's Weston, was near that town, cf. p. 480, note on the Dublin Observations.
  8. Six to seven is approximately the ratio between the burials of Paris alone and the burials of London.
  9. See p. 511.
  10. See p. 459, note 5.
  11. "Les Modernes assurent qu'elle [la ville de Paris] a aujourd'huy environ cinquant mille Maisons." Le grand dictionnaire historique ou le mélange curieux de l'histoire sacrée et profane. Seconde édition, revue par M. Louys Moreri. A. Lyon, M.D.C.LXXXI., vol. ii. p. 823 b.
  12. On Petty's attitude towards the law and lawyers see Fitzmaurice, 169—172.
  13. A blank in both French and English editions.
  14. The Paris bills entered the hospitals separately from the parishes in which they were situated. See p. 510.
  15. Ferdinand Verbiest, S. J. (1625—1688) wrote Voyage de l'Empereur de la Chine dans la Tartarie; aux quelles on a joint une novelle découverte aux Mexique. Paris: chez E. Michellet; 1685, 12°. Verbiest's accounts were received with great interest in Europe. An English translation of them was included in A Relation of the Invasion and Conquest of Florida by the Spaniards, under the Command of Fernando de Soto. Written in Portuguese by a Gentleman of the Town of Elvas. Now Englished. To which is subjoyned Two Journeys of the present Emperour of China into Tartary in the Years 1682 and 1683. London: printed for John Lawrence, 1686 (licensed 7 June), 12°, and a translation was also published in the Philosophical Transactions, vol. xvi. no. 180, pp. 39—62. On Verbiest see R. H. Major's introduction to the Earl of Ellesmere's translation of P. J. d'Orleans's History of the two Tartar Conquerors of China, Hakluyt Soc., 1834. p. vii., also pp. 69—96, 103—131.
  16. In Hale's Primitive Origination of Mankind, 213, citing Leo's History of Africa, Such figures were frequently printed in the 17th century, e.g. Purchas, Pilgrimes (1625), p. 833.
  17. The source of this information is doubtless the Paris bills, which reported the deaths in each of the seventeen hospitals in the city and gave after 1671, a monthly État de l'hotel dieu, cf. Morand in Histoire de l'Académie Royale des Sciences, année 1771, pp. 832—842.
  18. The table was not published.
  19. In the Philosophical Transactions for July—September, 1686 (vol. xvi. no. 183, p. 152) appeared the following, unsigned:
    "An Extract of two Essays in Political Arithmetick concerning the comparative Magnitudes, &c. of London and Paris by Sr. William Petty Knight, R.S.S.
    The excellent Author of these two Essays, has in several former of the same Nature made it appear that Mathematical Reasoning, is not only applicable to Lines and Numbers, but affords the best means of Judging in all the concerns of humane Life. In the present he endeavours to prove London, as it now is, the most considerable City now in being, by shewing it much to exceed Paris, (which not only the French but foreigners have asserted to be the chief City of Europe), both in People, Housing, and Wealth. The first by comparing the Bills of Mortality, whereby he finds that the People of London are as many as those of Paris and Rouen put together. The second by comparing the number of Houses, which by the Chimney-Books are found above 80000 in London, whereas a great Author among the French, (who seldome faile to magnifie their own things), reckons but 50000 Houses in Paris. As to the third, to wit the Wealth, he conceives that there is yet a much greater disposition, there being no comparison between them for Trade, and besides a good argument drawn from the Law-Suites of both places, he concludes from the Paris bills of Mortality, that two 5ths of the People of Paris are so poor that they chuse rather to die in Hospitals, than lie sick at their own Charges; and that a third of the whole People of that City, die out of the most wretched Hospitall of L'Hostel Dieu; wheras at London there dies scarce one in fiftie in our Hospitals. Hereupon in the second Essay, our Author extends his Charity to those poor wretches, shewing how by a reasonable expence, 3000 persons might be there saved per Annum, who die for want of good accomodation. The whole is so close writt, that it will not bear Epitomizing, wherefore I rather recommend it to the Curious who cannot but be satisfied therewith.


This work was published before January 1, 1925, and is in the public domain worldwide because the author died at least 100 years ago.