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Essays on Mankind and Political Arithmetic
by Sir William Petty
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Transcribed from the Cassell & Co. edition by David Price, email ccx074@coventry.ac.uk



ESSAYS ON MANKIND AND POLITICAL ARITHMETIC



Contents:

Introduction (by Henry Morley) Another Essays The stationer to the reader The principal points of this discourse Of the growth of the city of London Further observation upon the Dublin bills The stationer to the reader A postscript to the stationer Two essays in political arithmetic To the king's most excellent majesty An essay in political arithmetic Five essays in political arithmetic The first essay The second essay The third essay. The fourth essay The fifth essay Of the people of England (by Gregory King)



INTRODUCTION.



William Petty, born on the 26th of May, 1623, was the son of a clothier at Romsey in Hampshire. After education at the Romsey Grammar School, he continued his studies at Caen in Normandy. There he supported himself by a little trade while learning French, and advancing his knowledge of Greek, Latin, Mathematics, and much else that belonged to his idea of a liberal education. His idea was large. He came back to England, and had for a short time a place in the Navy; but at the age of twenty he went abroad again, and was away three years, studying actively at Utrecht, Leyden, and Amsterdam, and also in Paris. In Paris he assisted Thomas Hobbes in drawing diagrams for his treatise on optics. At the age of twenty- four Petty took out a patent for the invention of a copying machine. It was described in a folio pamphlet "On Double Writing." That was in 1647, in Civil War time, and although Petty followed Hobbes in his studies, he did not share the philosopher's political opinions, but held with the Parliament. In 1648 he added to his former pamphlet a "Declaration concerning the newly invented Art of Double Writing."

Samuel Hartlib, the large-hearted Pole, who in those days spent his worldly means in England for the advancement of agriculture and of education, and other aids to the well-being of a nation, had caused Milton to write his letter on education, as has been shown in the Introduction to the hundred and twenty-first volume of this Library, which contains that Letter together with Milton's Areopagitica. Young Petty's first published writing was a Letter to Hartlib on Education, entitled "The Advice of W. P. to Mr. Samuel Hartlib for the Advancement of some Particular Parts of Learning." This appeared in 1648, when Petty's age was twenty-five, and its aim was to suggest a wider view of the whole field of education than had been possible in the Middle Ages, of which schools and colleges were then preserving the traditions, as they do still here and there to some extent. This pamphlet has been reprinted in the sixth volume of the "Harleian Miscellany." William Petty wished the training of the young to be in several respects more practical.

His own activity of mind caused him to settle at Oxford, where he taught anatomy and chemistry, which he had been studying abroad. He had read with Hobbes the writings of Vesalius, the great founder of modern practical anatomy. In 1649 William Petty graduated at Oxford as Doctor of Medicine, obtained a fellowship at Brasenose, and practised. In 1650 he surprised the public by restoring the action of the lungs in a woman who had been hanged for infanticide, and so restoring her to life.

Dr. Petty now took his place at Oxford among the energetic men of science who had been inspired by the teaching of Francis Bacon to seek knowledge by direct experiment, and to value knowledge above all things for its power of advancing the welfare of man. The headquarters of these workers were at Oxford, and in London at Gresham College.

In 1650 Petty was made Professor of Anatomy at Oxford, and it is a characteristic illustration of his great activity of mind that he was at the same time Professor of Music at Gresham College. Music had then a high place in the Seven Sciences, as that use of regulated numbers which expressed the harmonies of the created world. The Seven Sciences were divided into three of the Trivium, and four of the Quadrivium. The three of the Trivium concerned the use of speech; they were Grammar, Rhetoric, and Logic. The four of the Quadrivium concerned number and measure; they were Arithmetic, Geometry, Music; and Astronomy, which led up straight to God. Advance to Music might be represented in the student's mind by his reaching to a sense of the harmonious relation of all his studies, which, so to speak, lived in his mind as a single well-proportioned thought.

In 1652 Dr. Petty was sent to Ireland as physician to the army of the Commonwealth. While there his active mind observed that the Survey on which the Government had based its distribution of fortified lands to the soldiers had been "most inefficiently and absurdly managed." He obtained the commission to make a fresh Survey, which he completed accurately in thirteen months, and by which he obtained in payments from the Government and from other persons interested ten thousand pounds. By investing this in the purchase of soldiers' claims, he secured for himself an Irish estate of fifty thousand acres in the county of Kerry, opened upon it mines and quarries, developed trade in timber, and set up a fishery. John Evelyn said of him "that he had never known such another genius, and that if Evelyn were a prince he would make Petty his second councillor at least." Henry Cromwell as Lord Deputy in Ireland made Petty his secretary.

Petty's Maps were printed in 1685, two years before his death, as "Hiberniae Delineatio quoad hactenus licuit perfectissima;" a collection of thirty-six maps, with a portrait of Sir William Petty, a work answering to its description as the most perfect delineation of Ireland that had up to that time been obtained. There is a coloured copy of Petty's maps in the British Museum, and also an uncoloured copy, with the first five maps varying from those in the coloured copy, and giving a General Map of Ireland, followed by Maps of Leinster, Munster, Ulster, and Connaught. There was afterwards published in duodecimo, without date, "A Geographical Description of ye Kingdom of Ireland, collected from ye actual Survey made by Sir William Petty, corrected and amended, engraven and published by Fra. Lamb." This volume gives as its contents, "one general mapp, four provincial mapps, and thirty-two county mapps; to which is added a mapp of Great Brittaine and Ireland, together with an Index of the whole."

At the Restoration William Petty accepted the inevitable change, and continued his service to the country. He was knighted by Charles the Second, and appointed in 1661 Inspector-General of Ireland. He entered Parliament. He was one of the first founders of the Royal Society, established at the beginning of the reign of Charles the Second; and the outcome of these scientific studies along the line marked out by Francis Bacon, which had been actively pursued in Oxford and at Gresham College. In 1663 he applied his ingenuity to the invention of a swift double-bottomed ship, that made one or two passages between England and Ireland, but was then lost in a storm.

In 1670 Sir William Petty established on his lands at Kerry the English settlement at the head of the bay of Kenmare. The building of forty-two houses for the English settlers first laid the foundations of the present town of Kenmare. "The population," writes Lord Macaulay, "amounted to a hundred and eighty. The land round the town was well cultivated. The cattle were numerous. Two small barks were employed in fishing and trading along the coast. The supply of herrings, pilchards, mackerel, and salmon, was plentiful, and would have been still more plentiful had not the beach been, in the finest part of the year, covered by multitudes of seals, which preyed on the fish of the bay. Yet the seal was not an unwelcome visitor: his fur was valuable; and his oil supplied light through the long nights of winter. An attempt was made with great success to set up ironworks. It was not yet the practice to employ coal for the purpose of smelting; and the manufacturers of Kent and Sussex had much difficulty in procuring timber at a reasonable price. The neighbourhood of Kenmare was then richly wooded; and Petty found it a gainful speculation to send ore thither." He looked also for profit from the variegated marbles of adjacent islands. Distant two days' journey over the mountains from the nearest English, Petty's English settlement of Kenmare withstood all surrounding dangers, and in 1688, a year after its founder's death, defended itself successfully against a fierce and general attack.

Sir William Petty died at London, on the 16th of December, 1687, and was buried in his native town of Romsey. He had added to his great wealth by marriage, and was the founder of the family in which another Sir William Petty became Earl of Shelburne and first Marquis of Lansdowne. The son of that first Marquis was Henry third Marquis of Lansdowne, who took a conspicuous part in our political history during the present century.

Sir William Petty's survey of the land in Ireland, called the Down Survey, because its details were set down in maps, remains the legal record of the title on which half the land in Ireland is held. The original maps are preserved in the Public Record Office at Dublin, and many of Petty's MSS. are in the Bodleian Library at Oxford.

He published in 1662 and 1685 a "Treatise of Taxes and Contributions, the same being frequently to the present state and affairs of Ireland," of which his view started from the general opinion that men should contribute to the public charge according to their interest in the public peace—that is, according to their riches. "Now, he said, "there are two sorts of riches—one actual, and the other potential. A man is actually and truly rich according to what he eateth, drinketh, weareth, or in any other way really and actually enjoyeth. Others are but potentially and imaginatively rich, who though they have power over much, make little use of it, these being rather stewards and exchangers for the other sort than owners for themselves." He then showed how he considered that "every man ought to contribute according to what he taketh to himself, and actually enjoyeth."

In 1674 Sir William Petty published a paper on "Duplicate Proportion," and in 1679 he published in Latin a "Colloquy of David with his Own Soul." In 1682 he published a tract called "Quantulumcunque, concerning Money;" and "England's Guide to Industry," in 1686. From 1682 to 1687, the year of his death, Sir William Petty was drawing great attention to the "Essays on Political Arithmetic," which are here reprinted. There was the little "Essay in Political Arithmetic, concerning the People, Housings, Hospitals of London and Paris;" published in 1682, again in French in 1686, and again in English in 1687. There was the little "Essay concerning the Multiplication of Mankind, together with an Essay on the Growth of London," published in 1682, and again in 1683 and 1686. There was in 1683, "Another Essay in Political Arithmetic concerning the growth of the City of London." There were "Farther Considerations on the Dublin Bills of Mortality," in 1686; and "Five Essays on Political Arithmetic" (in French and English), "Observations upon the Cities of London and Rome," in 1687, the last year of Sir William Petty's life. Other writings of his were published in his lifetime, or have been published since his death. He was in the study of political economy one of the most ingenious and practical thinkers before the days of Adam Smith.

But the interest of those "Essays in Political Arithmetic" lies chiefly in the facts presented by so trustworthy an authority. London had become in the time of the Stuarts the most populous city in Europe, if not in the world. This Sir William Petty sought to prove against the doubts of foreign and other critics, and his "Political Arithmetic" was an endeavour to determine the relative strength in population of the chief cities of England, France, and Holland. His application of arithmetic in the first of these essays to a census of the population at the Day of Judgment he himself spoke of slightingly. It is a curious example of a bygone form of theological discussion. But his tables and his reasonings upon them grow in interest as he attempts his numbering of the people in the reign of James II. by collecting facts upon which his deductions might be founded. The references to the deaths by Plague in London before the cleansing of the town by the great fire of 1666 are very suggestive; and in one passage there is incidental note of delay in the coming of the Plague then due, without reckoning the change made in conditions of health by the rebuilding. Nobody knew, and no one even now can calculate, how many lives the Fire of London saved.

There was in Petty's time no direct numbering of the people. The first census in this country was not until more than a hundred years after Sir William Petty's death, although he points out in these essays how easily it could be established, and what useful information it would give. There was a census taken at Rome 566 years before Christ. But the first census in Great Britain was taken in 1801, under provision of an Act passed on the last day of the year 1800, to secure a numbering of the population every ten years. Ireland was not included in the return; the first census in Ireland was not until the year 1813.

Sir William Petty had to base his calculations partly upon the Bills of Mortality, which had been imperfectly begun under Elizabeth, but fell into disuse, and were revived, as a weekly record of the number of deaths, beginning on the 29th of October, 1603; notices of diseases first appeared in them in 1629. The weekly bills were published every Thursday, and any householder could have them supplied to him for four shillings a year. These essays will show how inferences as to the number of the living were drawn from the number of the dead. And even now our Political Arithmetic depends too much upon rough calculations made from the death register. It is seven years since the last census; we have lost count of the changes in our population to a very great extent, and have to wait three years before our reckoning can be made sure. The interval should be reduced to five years.

Another of Sir William Petty's helps in the arithmetic of population was the Chimney Tax, a revival of the old fumage or hearth-money— smoke farthings, as the people called them—once paid, according to Domesday Book, for every chimney in a house. Charles the Second had set up a chimney tax in the year 1662; the statistics of the collection were at the service of Sir William Petty. The tax outlived him but two years. It was promptly abolished in the first year of William and Mary.

The interest taken at home and abroad in these calculations of Political Arithmetic set other men calculating, and reasoning upon their calculations. The next worker in that direction was Gregory King, Lancaster Herald, whose calculations immediately followed those of Sir William Petty. Sir William Petty's essays extended from 1682 until his death in 1687. Gregory King's estimates were made in 1689. They were a study of the number population and distribution of wealth among us at the time of the English Revolution, and the unpublished results were first printed in a chapter on "The People of England," which formed part a volume published in 1699 as "An Essay upon the Probable Methods of making a People Gainers in the Balance of Trade, by the Author of the Essay on Ways and Means." The volume was written by a member of Parliament in the days of William and Mary, who desired to apply principles of political economy to the maintenance of English wealth and liberty. It has been wrongly scribed to Defoe; and its suggestion of the plan a trading Corporation for solution of the whole problem of relief to the poor who cannot work, and relief from the poor who can, might indeed make another chapter in Defoe's "Essay on Projects." The chapter, which gives the Political Arithmetic of Gregory King, with such comment and suggestions as might be expected from a liberal supporter of the Revolution, and with this suggestion of a Corporation, is in itself a complete essay. It follows naturally upon the Political Arithmetic of Sir William Petty in close sequence of time, and in carrying a like method of inquiry forward until it reaches a few more conclusions. I have, therefore, added it to this volume. It seems, at any rate, to show how Sir William Petty's books, of which the very small size grieved the stationer, had a large influence on other minds; his figures bearing fruit in a new search for facts and careful reasoning on the condition of the country at one of the most critical times in English history.

H. M.



THE STATIONER TO THE READER



The ensuing essay concerning the growth of the city of London was entitled "Another Essay," intimating that some other essay had preceded it, which was not to be found. I having been much importuned for that precedent essay, have found that the same was about the growth, increase, 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, only I have obtained from a gentleman, 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 Arithmetic, concerning the value and increase 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 commerce, and how many upon art, and labour; how many upon alms, how many upon offices and public 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.

4. How many men and women are prolific, and how many of each are married or unmarried.

5. What the value of people 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 10,000 people in a colony may be 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 earth's globe were fittest for a general and universal emporium, whereby all the people thereof may best enjoy one another's 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 solve 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 earth's men.



THE PRINCIPAL POINTS OF THIS DISCOURSE



1. That London doubles in forty years, and all England in three hundred and sixty years.

2. That there be, A.D. 1682, about 670,000 souls in London, and about 7,400,000 in all England and Wales, and about 28,000,000 of acres of profitable land.

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 itself 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 ways whereby to try any proposal pretended for the public good.

8. How the city of London may be made (morally speaking) invincible.

9. A help to uniformity in religion.

10. That it is 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 thereof, Westminster, the Borough of Southwark, and so much of the built ground in Middlesex and Surrey, whose houses are contiguous unto, or within call of those aforementioned. 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 six parishes of Westminster, and the fourteen out-parishes in Middlesex and Surrey, contiguous to the former, all which, 133 parishes, are comprehended within the weekly bills of mortality.

The growth of this city is measured. (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 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 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 page of the book of the observations upon the London bills of mortality, printed in the year 1676. The other showeth what number of people died at a medium of two years, indifferently taken, at about twenty years' distance from each other.

The first of the said two tables.

A.D. 97 16 Out Buried Besides of Christened Parishes Parishes Parishes in all the Plague 1665 5,320 12,463 10,925 28,708 68,596 9,967 1666 1,689 3,969 5,082 10,740 1,998 8,997 1667 761 6,405 8,641 15,807 35 10,938 1668 796 6,865 9,603 17,267 14 11,633 1669 1,323 7,500 10,440 19,263 3 12,335 1670 1,890 7,808 10,500 20,198 11,997 1671 1,723 5,938 8,063 15,724 5 12,510 1672 2,237 6,788 9,200 18,225 5 12,593 1673 2,307 6,302 8,890 17,499 5 11,895 1674 2,801 7,522 10,875 21,198 3 11,851 1675 2,555 5,986 8,702 17,243 1 11,775 1676 2,756 6,508 9,466 18,730 2 12,399 1677 2,817 6,632 9,616 19,065 2 12,626 1678 3,060 6,705 10,908 20,673 5 12,601 1679 3,074 7,481 11,173 21,728 2 12,288 1680 3,076 7,066 10,911 21,053 12,747 1681 3,669 8,136 12,166 23,971 13,355 1682 2,975 7,009 10,707 20,691 12,653

According to which latter table there died as follows:-

THE LATTER OF THE SAID TWO TABLES

There died in London at the medium between the years -

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.

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 aught I know) to be maintained 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 landlord till that can be done; for there need 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 livelihood, whereas moderate labour will produce a better. But of this see Sir Thomas More, in the first part of his "Utopia."

10. As to the propagation and improvement of useful learning.

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 hindered or promoted in either from the same causes.

12. As to the plague.

It is to be remembered that one time with another a plague happeneth in London once in twenty years, or thereabouts; for in the last hundred years, between the years 1582 and 1682, there have been five great plagues—viz., A.D. 1592, 1603, 1625, 1636, and 1665. And it is also to be remembered 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 20,000, and in twenty years 400,000. But if in the city of London there should be 2,000,000 of people (as there will be about sixty years hence), then the plague (killing one-fifth of them, namely, 400,000 once in twenty years) will destroy as many in one year as the whole nation can re-furnish in twenty; and consequently the people of the nation shall never increase. But if the people of London shall be above 4,000,000 (as in the first of our two extravagant suppositions is premised), then the people of the whole nation shall lessen above 20,000 per annum. So as if people be worth 70 pounds per head (as hath elsewhere been shown), then the said greatness of the city will be a damage to itself and the whole nation of 1,400,000 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.

POSTSCRIPT.

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 justify 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 impertinences (perhaps as sauce to a dry discourse) have desired that the same might be explained and made out, I, therefore, say as followeth:-

1. If the number of acres in the habitable part of the earth be under 50,000,000,000; if 20,000,000,000 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 2,000 years) the present 320,000,000 will exceed the said 20,000,000,000.

2. That the number of all those who have died 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 12,570,000,000; whereunto may be added, for those that died before the Flood, enough to make the last-mentioned number 20,000,000,000, as the full number of all that died from the beginning of the world to the year 1682, unto which, if 320,000,000, 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 28,000 square English miles, each whereof will afford about 4,000,000 of graves, and consequently above 114,000,000,000 of graves, viz., about five 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 are sufficient for all that ever died, and if the earth of one grave weigh five times as much as the body interred 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 aforementioned in the body of this discourse. From all which it is plain how madly they were mistaken who did so petulantly vilify what the Holy Scriptures have delivered.



FURTHER OBSERVATION UPON THE DUBLIN BILLS; Or, Accounts of the Houses, Hearths, Baptisms, and Burials in that City.



THE STATIONER TO THE READER.



I have not thought fit to make any alteration of the first edition, but have only added a new table, with observation upon it, placing the same in the front of what was before, which, perhaps, might have been as well placed after the like table at the eighth page of the first edition.

DUBLIN, 1682.

Parishes Houses Fireplaces Baptised Buried St. James's 272 836 } St. Katherine's 540 2,198 } 122 306 St. Nicholas } Without and } 1,064 4,082 145 414 St. Patrick's } St. Bridget's 395 1,903 68 149 St. Audone's 276 1,510 56 164 St. Michael's 174 884 34 50 St. John's 302 1,636 74 101 St. Nicholas } Within and } 153 902 26 52 Christ Church Lib. } St. Warburgh's 240 1,638 45 105 St. Michan's 938 3,516 124 389 St. Andrew's 864 3,638 131 300 St. Kevin's 554 2,120 } 87 233 Donnybrook 253 506 } 6,025 25,369 912 2,263

The table hath been made for the year 1682, wherein is to be noted -

1. That the houses which A.D. 1671 were but 3,850 are, A.D. 1682, 6,025; but whether this difference is caused by the real increase of housing, or by fraud and defect in the former accounts, is left to consideration. For the burials of people have increased but from 1,696 to 2,263, according to which proportion the 3,850 houses A.D. 1671 should A.D. 1682 have been but 5,143, wherefore some fault may be suspected as aforesaid, when farming the hearth-money was in agitation.

2. The hearths have increased according to the burials, and one- third of the said increase more, viz., the burials A.D. 1671 were 1,696, the one-third whereof is 563, which put together makes 2,259, which is near the number of burials A.D. 1682. But the hearths A.D. 1671 were 17,500, whereof the one-third is 5,833, making in all but 23,333; whereas the whole hearths A.D. 1682 were 25,369, viz., one- third and better of the said 5,833 more.

3. The housing were A.D. 1671 but 3,850, which if they had increased A.D. 1682 but according to the burials, they had been but 5,143, or, according to the hearths, had been but 5,488, whereas they appear 6,025, increasing double to the hearths. So as it is likely there hath been some error in the said account of the housing, unless the new housing be very small, and have but one chimney apiece, and that one-fourth part of them are untenanted. On the other hand, it is more likely that when 1,696 died per annum there were near 6,000; for 6,000 houses at 8 inhabitants per house, would make the number of the people to be 48,000, and the number of 1,696 that died according to the rule of one out of 30, would have made the number of inhabitants about 50,000: for which reason I continue to believe there was some error in the account of 3,850 houses as aforesaid, and the rather because there is no ground from experience to think that in eleven years the houses in Dublin have increased from 3,850 to 6,025.

Moreover, I rather think that the number of 6,025 is yet short, because that number at 8 heads per house makes the inhabitants to be but 48,200; whereas the 2,263 who died in the year 1682, according to the aforementioned rule of one dying out of 30 makes the number of people to be 67,890, the medium betwixt which number and 48,200 is 58,045, which is the best estimate I can make of that matter, which I hope authority will ere long rectify, by direct and exact inquiries.

4. As to the births, we say that A.D. 1640, 1641, and 1642, at London, just before the troubles in religion began, the births were five-sixths of the burials, by reason I suppose of the greaterness of families in London above the country, and the fewer breeders, and not for want of registering. Wherefore, deducting one-sixth of 2,263, which is 377, there remains 1,886 for the probable number of births in Dublin for the year 1682; whereas but 912 are represented to have been christened in that year, though 1,023 were christened A.D. 1671, when there died but 1,696, which decreasing of the christening, and increasing of the burials, shows the increase of non-registering in the legal books, which must be the increase of Roman Catholics at Dublin.

The scope of this whole paper therefore is, that the people of Dublin are rather 58,000 than 32,000, and that the dissenters, who do not register their baptisms, have increased from 391 to 974: but of dissenters, none have increased but the Roman Catholics, whose numbers have increased from about two to five in the said years. The exacter knowledge whereof may also be better had from direct inquiries.



OBSERVATIONS UPON THE DUBLIN BILLS OF MORTALITY, 1681: AND THE STATE OF THAT CITY.



The observations upon the London bills of mortality have been a new light to the world, and the like observation upon those of Dublin may serve as snuffers to make the same candle burn clearer.

The London observations flowed from bills regularly kept for near one hundred years, but these are squeezed out of six straggling London bills, out of fifteen Dublin bills, and from a note of the families and hearths in each parish of Dublin, which are all digested into the one table or sheet annexed, consisting of three parts, marked A, B, C; being indeed the A, B, C of public economy, and even of that policy which tends to peace and plenty.

Observations upon the Table A.

1. The total of the burials in London (for the said six straggling years mentioned in the Table A) is 120,170, whereof the medium or sixth part is 20,028, and exceeds the burials of Paris, as may appear by the late bills of that city.

2. The births, for the same time, are 73,683, the medium or sixth part whereof is 12,280, which is about five-eighth parts of the burials, and shows that London would in time decrease quite away, were it not supplied out of the country, where are about five births for four burials, the proportion of breeders in the country being greater than in the city.

3. The burials in Dublin for the said six years were 9,865, the sixth part or medium whereof is 1,644, which is about the twelfth part of the London burials, and about a fifth part over. So as the people of London do hereby seem to be above twelve times as many as those of Dublin.

4. The births in the same time at Dublin are 6,157, the sixth part or medium whereof is 1,026, which is also about five-eighth parts of the 1,644 burials, which shows that the proportion between burials and births are alike at London and Dublin, and that the accounts are kept alike, and consequently are likely to be true, there being no confederacy for that purpose; which, if they be true, we then say -

5. That the births are the best way (till the accounts of the people shall be purposely taken) whereby to judge of the increase and decrease of people, that of burials being subject to more contingencies and variety of causes.

6. If births be as yet the measure of the people, and that the births (as has been shown) are as five to eight, then eight-fifths of the births is the number of the burials, where the year was not considerable for extraordinary sickness or salubrity, and is the rule whereby to measure the same. As for example, the medium of births in Dublin was 1,026, the eight-fifths whereof is 1,641, but the real burials were 1,644; so as in the said years they differed little from the 1,641, which was the standard of health, and consequently the years 1680, 1674, and 1668 were sickly years, more or less, as they exceeded the said number, 1,641; and the rest were healthful years, more or less, as they fell short of the same number. But the city was more or less populous, as the births differed from the number 1,026, viz., populous in the years 1680, 1679, 1678, and 1668, for other causes of this difference in births are very occult and uncertain.

7. What hath been said of Dublin, serves also for London.

8. It hath already been observed by the London bills that there are more males than females. It is to be further noted, that in these six London bills, also, there is not one instance either in the births or burials to the contrary.

9. It hath been formerly observed that in the years wherein most die fewest are born, and vice versa. The same may be further observed in males and females, viz., when fewest males are born then most die: for here the males died as twelve to eleven, which is above the mean proportion of fourteen to thirteen, but were born but as nineteen to eighteen, which is below the same.

Observations upon the Table B.

1. From the Table B it appears that the medium of the fifteen years' burials (being 24,199) is 1,613, whereas the medium of the other six years in the Table A was 1,644, and that the medium of the fifteen years' births (being in all 14,765) is 984, whereas the medium of the said other six years was 1,026. That is to say, there were both fewer births and burials in these fifteen years than in the other six years, which is a probable sign that at a medium there were fewer people also.

2. The medium of births for the fifteen years being 984, whereof eight-fifths (being 1,576) is the standard of health for the said fifteen years; and the triple of the said 1,576 being 4,728, is the standard for each of the ternaries of the fifteen years within the said table.

3. That 2,952, the triple of 984 births, is for each ternary the standard of people's increase and decrease from the year 1666 to 1680 inclusive, viz., the people increased in the second ternary, and decreased from the same in the third and fourth ternaries, but re-increased in the fifth ternary beyond any other.

4. That the last ternary was withal very healthful, the burials being but 4,624, viz., below 4,728, the standard.

5. That according to this proportion of increase, the housing of Dublin have probably increased also.

Observations upon the Table C.

1. First, from the Table C it appears, 1. That the housing of Dublin is such, as that there are not five hearths in each house one with another, but nearer five than four.

2. That in St. Warburgh's parish are near six hearths to a house. In St. John's five. In St. Michael's above five. In St. Nicholas Within above six. In Christ Church above seven. In St. James's and St. Katherine's, and in St. Michan's, not four. In St. Kevin's about four.

3. That in St. James's, St. Michan's, St. Bride's, St. Warburgh's, St. Andrew's, St. Michael's, and St. Patrick's, all the christenings were but 550, and the burials 1,055, viz., near double; and that in the rest of the parishes the christenings were five, and the burials seven, viz., as 457 to 634. Now whether the cause of this difference was negligence in accounts, or the greaterness of the families, &c., is worth inquiring.

4. It is hard to say in what order (as to greatness) these parishes ought to stand, some having most families, some most hearths, some most births, and others most burials. Some parishes exceeding the rest in two, others in three of the said four particulars, but none in all four. Wherefore this table ranketh them according to the plurality of the said four particulars wherein each excelleth the other.

5. The London observations reckon eight heads in each family, according to which estimation, there are 32,000 souls in the 4,000 families of Dublin, which is but half of what most men imagine, of which but about one sixth part are able to bear arms, besides the royal regiment.

6. Without the knowledge of the true number of people, as a principle, the whole scope and use of the keeping bills of births and burials is impaired; wherefore by laborious conjectures and calculations to deduce the number of people from the births and burials, may be ingenious, but very preposterous.

7. If the number of families in Dublin be about 4,000, then ten men in one week (at the charge of about 5 pounds surveying eight families in an hour) may directly, and without algebra, make an account of the whole people, expressing their several ages, sex, marriages, title, trade, religion, &c., and those who survey the hearths, or the constables or the parish clerks (may, if required) do the same ex officio, and without other charge, by the command of the chief governor, the diocesan, or the mayor.

8. The bills of London have since their beginning admitted several alterations and improvements, and 8 or 10 pounds per annum surcharge, would make the bills of Dublin to exceed all others, and become an excellent instrument of Government. To which purpose the forms for weekly, quarterly, and yearly bills are humbly recommended, viz.

TABLE A— YEARLY BILLS OF MORTALITY FOR A.D. LONDON and DUBLIN. Burials Births Burials Births 1680 21,053 12,747 1,826 1,096 1679 21,730 12,288 1,397 1,061 1678 20,678 12,601 1,401 1,045 1674 21,201 11,851 2,106 942 1672 18,230 12,563 1,436 987 1668 17,278 11,633 1,699 1,026 120,170 73,683 9,865 6,157 The medium or 6th part whereof is part whereof is 20,028 12,280 1,644 1,026

TABLE A—CONTINUED

A.D. LONDON. BURIALS. BIRTHS. Male Female Male Female 1680 11,039 10,044 6,543 6,041 1679 11,154 10,576 6,247 6,041 1678 10,681 9,977 6,568 6,033 1674 11,000 10,196 6,113 5,738 1672 9,560 8,070 6,443 6,120 1668 9,111 8,167 6,073 5,566 62,545 57,030 37,992 35,697 The medium or 6th part whereof is part whereof is 10,424 9,505 6,332 5,949

TABLE B.—DUBLIN.

A.D. Burials Births In Ternaries of Years 1666 1,480 952 } 1667 1,642 1,001 } 4,821 2,979 1668 1,699 1,026 } 1669 1,666 1,000 } 1670 1,713 1,067 } 5,353 3,070 1671 1,974 1,003 } 1672 1,436 967 } 1673 1,531 933 } 5,073 2,842 1674 2,106 942 } 1675 1,578 823 } 1676 1,391 952 } 4,328 2,672 1677 1,359 897 } 1678 1,401 1,045 } 1679 1,397 1,061 } 4,624 3,202 1680 1,826 1,096 } 24,199 14,765 24,199 14,765 The medium } or 15th }1,613 984 1,613 984 part whereof } is }

TABLE C.

THE PARISHES OF DUBLIN A.D. A.D., 1670-71-72 1671. at a medium Families Hearths Births Burials St. Katherine's 661 2,399 161 290 and St. James's St. Nicholas Without 490 2,348 207 262 St. Michan's 656 2,301 127 221 St. Andrew's with Donnybrook 483 2,123 108 178 St. Bridget's 416 1,989 70 100 St. John's 244 1,337 70 138 St. Warburgh's 267 1,650 54 103 St. Audaen's 216 1,081 53 121 St. Michael's 140 793 44 59 St. Kevin's 106 433 64 133 St. Nicholas Within 93 614 28 34 St. Patrick's Liberties 52 255 21 44 Christ Church and Trinity College, per estimate 26 197 - 1 3,850 17,500 1,013 1,696

Houses built between 1671 and 1681, per estimate 150 550 4,000 18,150

A WEEKLY BILL OF MORTALITY FOR THE CITY OF DUBLIN, Ending the XXX day of XXX 1681.

PARISHES' NAMES. St. Katharine's and St. James's St. Nicholas Without St. Michan's St. Andrew's with Donnybrook St. Bridget's St. John's St. Warburgh's St. Audaen's St. Michael's St. Kevin's St. Nicholas Within St. Patrick's Liberties Christ Church and Trinity College Totals

[The columns for the table are: Births, Males, Females, Burials, Under 16 years old, Plague, Small Pox, Measles, Spotted Fever. In the book there are no figures in the table at all.—DP.]

A QUARTERLY BILL OF MORTALITY, Beginning XXX and ending XXX for the City of DUBLIN PARISHES' NAMES. St. Katharine's and St. James's St. Nicholas Without St. Michan's St. Andrew's with Donnybrook St. Bridget's St. John's St. Warburgh's St. Audaen's St. Michael's St. Kevin's St. Nicholas Within St. Patrick's Liberties Christ Church and Trinity College Totals

[The columns for the table are: Births 1.; Marriages 2.; Buried under 16 years olds; Buried above 60 years old; Measles, Spotted Fever, Small Pox, Plague; Consumption, Dropsy, Gout, Stone; Fever, Pleurisy, Quinsy, Sudden Death; Aged above 70 years old; Infants under 2 years old; All other Casualties. In the book there are no figures in the table at all.—DP.]

AN ACCOUNT OF THE PEOPLE OF DUBLIN FOR ONE YEAR, Ending the 24th of March, 1681. PARISHES' NAMES. St. Katharine's and St. James's St. Nicholas Without St. Michan's St. Andrew's with Donnybrook St. Bridget's St. John's St. Warburgh's St. Audaen's St. Michael's St. Kevin's St. Nicholas Within St. Patrick's Liberties Christ Church and Trinity College Totals

[The columns for the table are: Number of person; Males; Females; Remarried Persons; Persons under 16 years old; Persons above 60 years old; Protestants of above 16 years old; Papists of above 16 years old; Of all other religions above 16 years old; Births; Burials; Marriages. In the book there are no figures in the table at all.—DP.]

CASUALTIES AND DISEASES. Aged above 70 years Epilepsy and planet Abortive and still-born Fever and ague Childbed women Pleurisy Convulsion Quinsy Teeth Executed, murdered, Worms drowned Gout and sciatica Plague and spotted fever Stone Griping of the guts Palsy Scouring, vomiting Consumption and French bleeding pox Small pox Dropsy and tympany Measles Rickets and livergrown Neither of all the other Headache and megrim sorts



A POSTSCRIPT TO THE STATIONER.



Whereas you complain that these observations make no sufficient bulk, I could answer you that I wish the bulk of all books were less; but do nevertheless comply with you in adding what follows, viz.:

1. That the parishes of Dublin are very unequal; some having in them above 600 families, and others under thirty.

2. That thirteen parishes are too few for 4,000 families; the middling parishes of London containing 120 families; according to which rate there should be about thirty-three parishes in Dublin.

3. It is said that there are 84,000 houses or families in London, which is twenty-one times more than are in Dublin, and yet the births and burials of London are but twelve times those of Dublin, which shows that the inhabitants of Dublin are more crowded and straitened in their housing than those of London; and consequently that to increase the buildings of Dublin will make that city more conformable to London.

4. I shall also add some reasons for altering the present forms of the Dublin bills of mortality, according to what hath been here recommended—viz.:

1. We give the distinctions of males and females in the births only; for that the burials must, at one time or another, be in the same proportion with the births.

2. We do in the weekly and quarterly bills propose that notice be taken in the burials of what numbers die above sixty and seventy, and what under sixteen, six, and two years old, foreseeing good uses to be made of that distinction.

3. We do in the yearly bill reduce the casualties to about twenty- four, being such as may be discerned by common sense, and without art, conceiving that more will but perplex and imbroil the account. And in the quarterly bills we reduce the diseases to three heads— viz., contagious, acute, and chronical, applying this distinction to parishes, in order to know how the different situation, soil, and way of living in each parish doth dispose men to each of the said three species; and in the weekly bills we take notice not only of the plague, but of the other contagious diseases in each parish, that strangers and fearful persons may thereby know how to dispose of themselves.

4. We mention the number of the people, as the fundamental term in all our proportions; and without which all the rest will be almost fruitless.

5. We mention the number of marriages made in every quarter, and in every year, as also the proportion which married persons bear to the whole, expecting in such observations to read the improvement of the nation.

6. As for religions, we reduce them to three—viz.: (1) those who have the Pope of Rome for their head; (2) who are governed by the laws of their country; (3) those who rely respectively upon their own private judgments. Now, whether these distinctions should be taken notice of or not, we do but faintly recommend, seeing many reasons pro and con for the same; and, therefore, although we have mentioned it as a matter fit to be considered, yet we humbly leave it to authority.



TWO ESSAYS IN POLITICAL ARITHMETIC, Concerning the People, Housing, Hospitals, &c., of London and Paris.



TO THE KING'S MOST EXCELLENT MAJESTY.



I do presume, in a very small paper, to show your Majesty that your City of London seems more considerable than the two best cities of the French monarchy, and for aught 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.



AN ESSAY IN POLITICAL ARITHMETIC



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.

1. The medium of the burials at London in the three last years— viz., 1683, 1684, and 1685, wherein there was no extraordinary sickness, and wherein the christenings do correspond in their ordinary proportions with the burials and christenings of each year one with another, was 22,337, 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 19,887.

2. The city of Bristol in England appears to be by good estimate of its trade and customs as great as Rouen in France, and the city of Dublin in Ireland appears to have more chimneys than Bristol, and consequently more people, and the burials in Dublin were, A.D. 1682 (being a sickly year) but 2,263.

3. Now the burials of Paris (being 19,887) being added to the burials of Dublin (supposed more than at Rouen) being 2,263, makes but 22,150, whereas the burials of London were 187 more, or 22,337, or as about 6 to 7.

4. If those who die unnecessarily, and by miscarriage in L'Hotel Dieu in Paris (being above 3,000), as hath been elsewhere shown, or any part thereof, should be subtracted out of the Paris burials aforementioned, then our assertion will be stronger, and more proportionable to what follows concerning the housing of those cities, viz.:

5. There were burnt at London, A.D. 1666, above 13,000 houses, which being but a fifth part of the whole, the whole number of houses in the said year were above 65,000; 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, A.D. 1686, must be about 87,000, which A.D. 1682, appeared by account to have been 84,000.

6. Monsieur Moreri, the great French author of the late geographical dictionaries, who makes Paris the greatest city in the world, doth reckon but 50,000 houses in the same, and other authors and knowing men much less; nor are there full 7,000 houses in the city of Dublin, so as if the 50,000 houses of Paris, and the 7,000 houses in the city of Dublin were added together, the total is but 57,000 houses, whereas those of London are 87,000 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) I only say that the courts 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 chimneys, which are to be seen at London, besides many lodgings, halls, and offices, relating to the same.

9. As to the plentiful and easy living of the people we say,

(a.) That the people of Paris to those of London, being as about 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 crowded as at Paris, but can afford themselves more room and liberty.

(b.) That at London the hospitals are better and more desirable than those of Paris, for that in the best at Paris there die two out of fifteen, whereas at London there die out of the worst scarce 2 out of 16, and yet but a fiftieth part of the whole die out of the hospitals at London, and two-fifths, or twenty 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 choose to lie sick in hospitals rather than in their own houses, are to the like people of Paris as one to twenty; which shows the greater poverty or want of means in the people of Paris than those of London.

(c.) We infer from the premises, viz., the dying scarce two of sixteen out of the London hospitals, and about two of fifteen in the best of Paris, to say nothing of L'Hotel 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 in behalf of London. As for Pekin in China, we have no account fit to reason upon; nor is there anything in the description of the two late voyages of the Chinese emperor from that city into East and West Tartary, in the years 1682 and 1683, which can make us recant what we have said concerning London. As for Delhi and Agra, belonging to the Mogul, we find nothing against our position, but much to show the vast numbers which attend that emperor in his business and pleasures.

11. We shall conclude with Constantinople and Grand Cairo; as for Constantinople it hath been said by one who endeavoured to show the greatness of that city, and the greatness of the plague which raged in it, that there died 1,500 per diem, without other circumstances; to which we answer, that in the year 1665 there died in London 1,200 per diem, and it hath been well proved that the Plague of London never carried away above one-fifth 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 two-fifths, one half, or more; wherefore where 1,200 is but one-fifth of the people it is probable that the number was greater, than where 1,500 was two-fifths or one half, &c.

12. As for Grand Cairo it is reported, that 73,000 died in ten weeks, or 1,000 per diem, where note, that at Grand Cairo the plague comes and goes away suddenly, and that the plague takes away two or three-fifths parts of the people as aforesaid; so as 73,000 was probably the number of those that died of the plague in one whole year at Grand Cairo, whereas at London, A.D. 1665, 97,000 were brought to account to have died in that year. Wherefore it is certain, that that city wherein 97,000 was but one-fifth of the people, the number was greater than where 73,000 was two-fifths or the half.

We therefore conclude, that London hath more people, housing, shipping, and wealth, than Paris and Rouen put together; and for aught yet appears, is more considerable than any other city in the universe, which was propounded to be proved.



AN ESSAY IN POLITICAL ARITHMETIC



Tending to prove that in the hospital called L'Hotel Dieu at Paris, there die above 3,000 per annum by reason of ill accommodation.

1. It appears that A.D. 1678 there entered into the Hospital of La Charite 2,647 souls, of which there died there within the said year 338, which is above an eighth part of the said 2,647; and that in the same year there entered into L'Hotel Dieu 21,491, and that there died out of that number 5,630, which is above one quarter, so as about half the said 5,630, being 2,815, seem to have died for want of as good usage and accommodation as might have been had at La Charite.

2. Moreover, in the year 1679 there entered into La Charite 3,118, of which there died 452, which is above a seventh part, and in the same year there entered into L'Hotel Dieu 28,635, of which there died 8,397; and in both the said years 1678 and 1679 (being very different in their degrees of mortality) there entered into L'Hotel Dieu 28,635 and 2l,491—in all 50,126, the medium whereof is 25,063; and there died out of the same in the said two years, 5,630 and 8,397—in all 14,027, the medium whereof is 7,013.

3. There entered in the said years into La Charite 2,647 and 3,118, in all 5,765, the medium whereof is 2,882, whereof there died 338 and 452, in all 790, the medium whereof is 395.

4. Now, if there died out of L'Hotel Dieu 7,013 per annum, and that the proportion of those that died out of L'Hotel Dieu is double to those that died out of La Charite (as by the above numbers it appears to be near thereabouts), then it follows that half the said numbers of 7,013, being 3,506, did not die by natural necessity, but by the evil administration of that hospital.

5. This conclusion seemed 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.:-

(a.) In the Hospital of St. Bartholomew in London, there was sent out and cured in the year 1685, 1,764 persons, and there died out of the said hospital 252. Moreover, there were sent out and cured out of St. Thomas's Hospital 1,523, and buried, 209—that is to say, there were cured in both hospitals 3,287, and buried out of both hospitals 461, and consequently cured and buried 3,748, of which number the 461 buried is less than an eighth part; whereas at La Charite the part that died was more than an eighth part; which shows that out of the most poor and wretched hospitals of London there died fewer in proportion than out of the best in Paris.

(b.) Furthermore, it hath been above shown that there died out of La Charite at a medium 395 per annum, and 141 out of Les Incurables, making in all 536; and that out of St. Bartholomew's and St. Thomas's Hospitals, London, there died at a medium but 461, of which Les Incurables are part; which shows 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 shows 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 3,506 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 3,506 at 60 livres sterling per head, being about the value of Argier slaves (which is less than the intrinsic value of people at Paris), the whole loss of the subjects of France in that hospital seems to be 60 times 3,506 livres sterling per annum, viz., 210,360 livres sterling, equivalent to about 2,524,320 French livres.

7. It hath appeared that there came into L'Hotel Dieu at a medium 25,063 per annum, or 2,089 per mensem, and that the whole stock of what remained in the precedent months is at a medium about 2,108 (as may appear by the third line of the Table No. 5, which shall be shortly published), viz., the medium of months is 2,410 for the sickly year 1679, whereunto 1,806 being added as the medium of months for the year 1678, makes 4,216, the medium whereof is the 2,108 above mentioned; which number being added to the 2,089 which entered each month, makes 4,197 for the number of sick which are supposed to be always in L'Hotel Dieu one time with another.

8. Now, if 60 French livres per annum for each of the said 4,197 sick persons were added to the present ordinary expense of that hospital (amounting to an addition of 251,820 livres), 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 A.D. 1685, the burials of London were 23,222, and those of Amsterdam 6,245; from whence, and the difference of air, it is probable that the people of London are quadruple to those of Amsterdam.



OBSERVATIONS UPON THE CITIES OF LONDON AND ROME



1. That before the year 1630 the christenings at London exceeded the burials of the same, but about the year 1655 they were scarce half; and now about two-thirds.

2. Before the restoration of monarchy in England, A.D. 1660, the people of Paris were more than those of London and Dublin put together, whereas now, the people of London are more than those of Paris and Rome, or of Paris and Rouen.

3. A.D. 1665 one fifth part of the then people of London, or 97,000, died of the plague, and in the next year, 1666, 13,000 houses, or one fifth part of all the housing of London, were burnt also.

4. At the birth of Christ old Rome was the greatest city of the world, and London the greatest at the coronation of King James II., and near six times as great as the present Rome, wherein are 119,000 souls besides Jews.

5. In the years of King Charles II.'s death, and King James II.'s coronation (which were neither of them remarkable for extraordinary sickliness or healthfulness) the burials did wonderfully agree, viz., A.D. 1684, they were 23,202, and A.D. 1685, they were 23,222, the medium whereof is 23,212. And the christenings did very wonderfully agree also, having been A.D. 1684, 14,702, and A.D. 1685, 14,732, the medium whereof is 14,716, which consistence was never seen before, the said number of 23,212 burials making the people of London to be 696,360, at the rate of one dying per annum out of 30.

6. Since the great Fire of London, A.D. 1666, about 7 parts of 15 of the present vast city hath been new built, and is with its people increased near one half, and become equal to Paris and Rome put together, the one being the seat of the great French Monarchy, and the other of the Papacy.



FIVE ESSAYS IN POLITICAL ARITHMETIC



I. Objections from the city of Ray in Persia, and from Monsier Auzout, against two former essays, answered, and that London hath as many people as Paris, Rome, and Rouen put together.

II. A comparison between London and Paris in 14 particulars.

III. Proofs that at London, within its 134 parishes named in the bills of mortality, there live about 696,000 people.

IV. An estimate of the people in London, Paris, Amsterdam, Venice, Rome, Dublin, Bristol, and Rouen, with several observations upon the same.

V. Concerning Holland and the rest of the Seven United Provinces.



TO THE KING'S MOST EXCELLENT MAJESTY

Sir,

Your Majesty having graciously accepted my two late essays, about the cities and hospitals of London and Paris, as also my observations on Rome and Rouen; I do (after six months' waiting for what may be said against my several doctrines by the able men of Europe) humbly present your Majesty with a few other papers upon the same subject, to strengthen, explain, and enlarge the former; hoping by such real arguments, better to praise and magnify your Majesty, than by any other the most specious words and eulogies that can be imagined by

Your Majesty's Most humble, loyal And obedient subject, WILLIAM PETTY.



THE FIRST ESSAY.



It could not be expected that an assertion of London's being bigger than Paris and Rouen, or than Paris and Rome put together, and bigger than any city of the world, should escape uncontradicted; and 'tis also expected that I (if continuing in the same persuasion), should make some reply to those contradictions. In order whereunto,

I begin with the ingenious author of the "Republique des Lettres," who saith that Rey in Persia is far bigger than London, for that in the sixth century of Christianity (I suppose, A.D. 550 the middle of that century), it had 15,000, or rather 44,000 mosques or Mahometan temples; to which I reply, that I hope this objector is but in jest, for that Mahomet was not born till about the year 570, and had no mosques till about 50 years after.

In the next place I reply to the excellent Monsieur Auzout's "Letters from Rome," who is content that London, Westminster, and Southwark may have as many people as Paris and its suburbs; and but faintly denieth, that all the housing within the bills may have almost as many people as Paris and Rouen, but saith that several parishes inserted into these bills are distant from, and not contiguous with London, and that Grant so understood it.

To which (as his main if not his only objection) we answer: —(l) That the London bills appear in Grant's book to have been always, since the year 1636; as they now are; (2) That about fifty years since, three or four parishes, formerly somewhat distant, were joined by interposed buildings to the bulk of the city, and therefore then inserted into the bills; (3) That since fifty years the whole buildings being more than double have perfected that union, so as there is no house within the said bills from which one may not call to some other house; (4) All this is confirmed by authority of the king and city, and the custom of fifty years; (5) That there are but three parishes under any colour of this exception which are scarce one-fifty-second part of the whole.

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