Political Arithmetick (1899)

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Political Arithmetick
by William Petty, edited by Charles Henry Hull
Title, Notes, Dedication, Preface and Contents
2388475Political Arithmetick — Title, Notes, Dedication, Preface and ContentsWilliam Petty

LET this Book called Political Arithmetick, which was long since Writ by Sir William Petty deceased, be Printed.

Given at the Court at Whitehall the 7th Day of Novemb. 1690.


Political Arithmetick,




The Extent and Value of Lands, People, Buildings; Husbandry, Manufacture, Commerce, Fishery, Artizans, Seamen, Soldiers; Publick Revenues, Interest, Taxes, Superlucration, Registries, Banks; Valuation of Men, Increasing of Seamen, of Militia's, Harbours, Situation, Shipping, Power at Sea, &c. As the same relates to every Country in general, but more particularly to the Territories of His Majesty of Great Britain, and his Neighbours of Holland, Zealand, and France[1].


Late Fellow of the Royal Society.

London, Printed for Robert Clavel at the Peacock, and Hen. Mortlock at the Phœnix in St. Paul's Church-yard. 1690.


The Political Arithmetick, like the Political Anatomy, belongs to the third period of Petty's literary activity and was written during his second prolonged residence in Ireland. The precise date of its composition cannot now be determined. The Rawlinson MS. is dated 1671, and in Petty's "Collection of [his] several Works" it is likewise entered under 1671[2]. Lord Edmond Fitzmaurice accordingly says that it was written in that year[3], and his opinion is confirmed by Sir Peter Pett, who calls the Political Arithmetick a "manuscript discourse in the year 1671— 2"[4]. But Petty's list is not infallible. It enters under 1654 the Discourse against the Transplantation into Connaught published in 1655, and under 1671 the Anatomia Politica Hiberniae, which was not finished before the close of 1672[5]. The date 1671 is, perhaps, that at which Petty began the Political Arithmetick. He was still working upon it at the end of 1672[6], and internal evidence points to its completion not earlier than 1676. This internal evidence is drawn from three passages whose indications pretty closely coincide:   1st, the expenditure of the King of France "in any of these last seven years" is compared with his revenue "as the same appears by the book entitled The State of France... printed anno 1669[7]";   2nd, "since the year 1636, the taxes and public levies... have been prodigiously greater,... yet the kingdoms have increased in their wealth and strength for these last forty years[8]";   3rd, "his Majesty's navy is now triple or quadruple what it was forty years since, and before the Sovereign was Built[9]." The "Sovereign of the Seas" was launched 14 October, 1637[10]. These three passages, which all point to 1676 or 1677, occur in the Rawlinson MS. as well as in the undated Southwell MS., and the 1690 edition. The opinion that the Political Arithmetick was completed at a date later than the Political Anatomy is also confirmed by the larger estimate of the population of Ireland which the Arithmetick[11] makes.

Of the numerous MSS. of the Political Arithmetick, by far the most important is that bound in the same volume with the MS. Treatise of Ireland, and called by Lord Edmond Fitzmaurice the Neligan MS.[12] The history of this MS. is similar to that of the Southwell MS. of the Political Anatomy already traced[13]. It was given to Sir Robert Southwell by Petty and remained in Southwell's family until purchased by Thorpe[14] at the De Clifford sale in 1834. It passed into Dr Neligan's possession, and after his death it was bought for the British Museum[15] becoming Additional MS. 21,128. In view of its history, I call it the Southwell MS., and refer to it in the footnotes as S. This MS. is not so neatly written as the Southwell Political Anatomy; the ink is similar but the paper is of a different size, and it has one similar and one different watermark[16]. The corrections are far more numerous, and are unmistakably in Petty's hand[17]. It may be the very same MS. which Petty corrected for Southwell in March, 1681 and wished to have compared with "what goeth abroad[18]." If it be the same, Petty 's wish is at length fulfilled: the readings of the Southwell MS. are now compared with the text that went forth in 1690 wherever the differences between them are significant. But mere variations in spelling and minor grammatical differences (like "hath" for "has") are disregarded, and the punctuation of the MS. is noted only where it gives the passage a meaning different from that of the printed version. All Petty's corrections are noted.

Among the remaining MSS. perhaps the most interesting is one endorsed "Pettys Pl. Arithmetic I take to be Corrected by Sr Wm himself having formerly seen a good deal of his Hand Writing," now among the Rawlinson MSS. in the Bodleian Library[19]. The MS. is in two hands, that of the second copyist beginning with chapter five. Petty's corrections are few compared with those in the Southwell MS., and most of them are merely formal, such as changing "300,000" to "300 Thousand." The more important variations marked R, are given in the foot notes. A transcript of the Political Arithmetick, presented by Willoughby, is in the Library of Trinity College, Dublin[20]. It contains no corrections by Petty. A transcript in quarto, made for Essex, is, or was, at Ashburnham Place[21], and the British Museum has, in addition to the Southwell MS., a comparatively worthless copy, unintelligently abridged[22]. Besides these, a MS. of the Political Arithmetick was presented by Petty to the King[23] and both Sir Joseph Williamson[24] and Sir Peter Pett[25] had MSS. of it.

Manuscript copies of the Political Arithmetick being thus circulated among Petty's friends, soon after its composition, they seem to have urged him to publish it at once. A letter to Southwell[26] in reply to some such request was once in the possession of Thomas Thorpe, who described it as discussing the printing [reprinting] of the Treatise of Taxes, the Polltical Arithmetick, and the translation of the 104th psalm, "which Petty here expresses his reluctance to be printed[27]." The unauthorized reprinting of the Treatise of Taxes in 1679[28] apparently convinced Petty that it was safer to have his books printed under supervision, for he subsequently wrote to Aubrey, 12 July, 1681, that he was not forward to print the Political Arithmetick but did wish that what went abroad might be compared with the copy in Southwell's possession, which he had corrected in March[29]. In this letter there is no hint of the reason for nonpublication which Lord Shelbume advances[30], and Petty's care to secure a good text indicates that he expected the book to be published soon. Nearly a year after the letter to Aubrey, Petty came to London, where he remained until the summer of 1683, being occupied about the reform of the Irish revenues[31]. It was probably about this time that he wrote the dedication of the Political Arithmetick to the King[32], and presented his Majesty with a copy of the book in MS. He appears, however, presently to have abandoned the project of publication, and there can be little doubt that the ill-printed edition of the Political Arithmetick which was soon anonymously issued under the title of England's Guide to Industry[33], appeared without his consent.

After Petty's death the demand for an authentic edition of the Political Arithmetick was renewed, and Lady Petty, who was executrix of her husband's will, asked Southwell's advice in the matter. Sir William himself, so she wrote[34], would not suffer the book to be printed, wherefore she was very loath to do it upon any account whatsoever, unless it were to prevent a greater evil. She was told, however, that five hundred false copies were in circulation and that the book would be published to disadvantage unless she authorized the printing of it. Southwell's reply is not preserved, but inasmuch as the Political Arithmetick was issued in 1690 with a dedication written by Lady Petty's son, it may be inferred that her scruples were at length overcome.



Most Excellent



WHilest every one meditates some fit Offering for Your Majesty, such as may best agree with your happy || Exaltation to this Throne; I presume to offer, what my Father long since writ, to shew the weight and importance of the English Crown.

It was by him stiled Political Arithmetick[36], in as much as things of Government, and of no less concern and extent, than the Glory of the Prince, and the happiness and greatness of the People, are by the Ordinary Rules of Arithmetick, brought into a sort of Demonstration, He was allowed[37] by all, to be the Inventor of this Method of Instruction; where || the perplexed and intricate ways of the World, are explain'd by a very mean peice of Science; and had not the Doctrins of this Essay offended France, they had long since seen the light, and had found Followers, as well as improvements before this time, to the advantage perhaps of Mankind.

But this has been reserved to the felicity of Your Majesty's Reign, and to the expectation which the Learned have therein; and if while in this, I do some honor to the Memory of a good Father, I || can also pay Service, and some Testimony of my Zeal and Reverence to so great a King, it will be the utmost Ambition of

Your Majesty's Most Dutiful
and Most Obedient Subject,


Forasmuch as Men, who are in a decaying condition, or who have but an ill opinion of their own Concernments, instead of being (as some think) the more industrious to resist the Evils they apprehend, do contrariwise become the more languid and ineffectual in all their Endeavours, neither caring to attempt or prosecute even the probable means of their relief. Upon this Consideration, as a Member of the Common- Wealth, next to knowing the precise Truth in what condition the common Interest stands, I would in all doubtful Cases think || the best, and consequently not despair, without strong and manifest Reasons, carefully examining whatever tends to lessen my hopes of the publick Welfare.

I have therefore thought fit to examin the following Perswasions, which I find too currant in the World[40], and too much to have affected the Minds of some, to the prejudice of all, viz. The fears of many concerning the Welfare of England.

That the Rents of Lands are generally fall'n; that therefore, and for many other Reasons, the whole Kingdom grows every day poorer and poorer[41]; that formerly it abounded with Gold, but now[42] there is a great scarcity both of Gold and Silver; that there is no Trade nor Employment for the People, and yet that the Land is under-peopled; that Taxes have been many and || great; that Ireland and the Plantations in America and other Additions to the Crown, are a Burthen to England; that Scotland is of no Advantage; that Trade in general doth lamentably decay; that the Hollanders are at our heels, in the race of Naval Power; the French[43] grow too fast upon both, and appear so rich and potent, that it is but their Clemency that they do not devour their Neighbors; and finally, that the Church and State of England, are in the same danger with the Trade of England; with many other dismal Suggestions, which I had rather stifle than repeat[44].

'Tis true, the Expence of foreign Commodities hath of The real Prejudices of England. late been too great; much of our Plate, had it remain'd Money, would have bet-||ter served Trade; too many Matters have been regulated by Laws, which Nature, long Custom, and general Consent, ought only to have governed; the Slaughter and Destruction of Men by the late Civil Wars and Plague have been great; the Fire at London, and Disaster at Chatham[45], have begotten Opinions in the Vulgus of the World to our Prejudice; the Nonconformists increase[46]; the People of Ireland think long of their Settlement; the English there apprehend themselves to be Aliens, and are forced to seek a Trade with Foreigners, which they might as well maintain with their own Relations in England. But notwithstanding all this (the like whereof was always in all Places), the Buildings of London grow great and glorious; The Improvements of England. the American Planta-||tions employ four Hundred Sail of Ships; Actions in the East-India Company are near double the principal Money; those who can give good Security, may have Money under the Statute- Interest; Materials for building (even Oaken-Timber) are little the dearer, some cheaper for[47] the rebuilding of London[48]; the Exchange seems as full of Merchants as formerly; no more Beggars in the Streets, nor executed for Thieves, than heretofore; the Number of Coaches, and Splendor of Equipage exceeding former Times; the publique Theatres very magnificent; the King has a greater Navy, and stronger Guards than before our Calamities; the Clergy rich, and the Cathedrals in repair; much Land has been improved, and the Price of Food so reasonable, as that Men refuse || to have it cheaper, by admitting of Irish Cattle[49]; And in brief, no Man needs to want that will take moderate pains. That some are poorer than others, ever was and ever will be: And that many are naturally querulous and envious, is an Evil as old as the World.

These general Observations, and that Men eat, and drink, and laugh as they use to do, have encouraged me to try if I could also comfort others, being satisfied my self, that the Interest and Affairs of England are in no deplorable Condition.

The Author's Method and Manner of Arguing.The Method I take to do this, is not yet very usual; for instead of using only comparative and superlative Words, and intellectual Arguments, I have taken the course (as a Specimen of the Political A-||rithmetick I have long aimed at) to express my self in Terms of Number, Weight, or Measure; to use only Arguments of Sense, and to consider only such Causes, as have visible Foundations in Nature; leaving those that depend upon the mutable Minds, Opinions, Appetites, and Passions of particular Men, to the Consideration of others: Really professing my self as unable to speak satisfactorily upon those Grounds (if they may be call'd Grounds), as to foretel the cast of a Dye; to play well at Tennis, Billiards, or Bowles, (without long praflice,) by virtue of the most elaborate Conceptions that ever have been written De Projectilibus & Missilibus, or of the Angles of Incidence and Reflection.||

The Nature of his Positions and Suppositions.Now the Observations or Positions expressed by Number, Weight, and Measure, upon which I bottom the ensuing Discourses, are either true, or not apparently false, and which if they are not already true, certain, and evident, yet may be made so by the Sovereign Power, Nam id certum est quod certum reddi potest[50], and if they are false, not so false as to destroy the Argument they are brought for; but at worst are sufficient as Suppositions to shew the way to that[51] Knowledge I aim at. And I have withal for the present confined my self to the Ten principal Conclusions hereafter particularly handled, which if they shall be judged material, and worthy of a better Discussion, I hope all ingenious and candid Persons will rectifie the Errors, Defects, and || Imperfections, which probably may be found in any of the Positions, upon which these Ratiocinations were grounded. Nor would it misbecome Authority it self, to clear the Truth of those Matters which private Endeavours cannot reach to.||


Principal Conclusions[52]




CHAP. 1.That a small Country, and few People, may by their Situation, Trade, and Policy, be equivalent in Wealth and Strength, to a far greater People, and Territory. And particularly, How conveniences for Shipping, and Water Carriage, do most Eminently, and Fundamentally, conduce thereunto.Pag. 1 [249]

Chap. II.That some kind of Taxes, and Publick Levies, may rather increase than diminish the Common-Wealth. pag. 35 [268]||

Chap. III.That France cannot, by reason of Natural and Perpetual Impediments, be more powerful at Sea, than the English, or Hollanders. 51 [278]

Chap. IV.That the People, and Territories of the King of England, are Naturally near[53] as considerable, for Wealth, and Strength, as those of France. pag. 64 [284]

Chap. V.That the Impediments of Englands Greatness, are but contingent and removeable. pag. 87 [298]

Chap. VI.That the Power and Wealth of England, hath increased above this forty years. pag. 96 [302]

Chap. VII.That one tenth part, of the whole Expence, of the King of England's Subjects; is sufficient to maintain one hundred thousand Foot, thirty thousand Horse, and forty thousand Men at Sea, and to defray all other Charges, of the Government: both Ordinary and Extraordinary, if the same were regularly Taxed, and Raised. pag. 101 [305]

Chap. VIII.That there are spare Hands enough among the King of England's Subjects, to earn two Millions per annum, more than they now do, and there are Employments, ready, || proper, and sufficient, for that purpose. pag. 104 [307]

Chap. IX.That there is Mony sufficient to drive the Trade of the Nation. pag. 110 [310]

Chap. X.That the King of England's Subjects, have Stock, competent, and convenient to drive the Trade of the whole Commercial World. pag. 112 [311]||


PAge 7. line 25. read the Rent.p. 8. l. 21. r. a part.p. 20. l. 3. r. for cheap.p. 21. l. 14. r. cold, moist.p. 26. l. 7. r. that Church.p. 32. l. 7. r. yearly profit.l. 18. r. to be the value.p. 47. l. 4. r. fifty thousand.l. 28. r. sixteen thousand.p. 49. l. 13. r. the said half together.p. 52. l. 6. r. should bring.p. 59. l. 24. r. they coast.p. 72. l. 8. r. or above.p. 91. l. 9. r. Exotics.p. 95. l. 13. r. paying for.

  1. The long descriptive title was probably supplied by Lord Shelburne; neither the Southwell, the Rawlinson, nor the Sloane MS. has it. In line six 'Manufacture' should be 'Manufactures,' an 's' has dropped out.
  2. Fitzmaurice, 318.
  3. P. 185.
  4. Happy future State (written 1680), p. 106.
  5. Polit. Anat., note, pp. 122—123, cf. p. 197.
  6. Letter to Anglesea, 17 Dec, Fitzmaurice, 158.
  7. Pp. 252—253.
  8. P. 271.
  9. P. 304.
  10. Archæologia, xii. 281—282.
  11. P. 272, note, cf. Anatomy, p. 142, note.
  12. Life of Petty, p. 273, also preface, 6—7. Lord E. Fitzmaurice slips in saying that the volume contains the Political Anatomy. The Neligan, or Southwell, MS. of the Political Anatomy is a separate volume, B. M. Addl. MS., 21,127.
  13. P. 123.
  14. Thorpe's Cat. lib. MSS. bibl. Southwellianæ, no. 712, p. 410.
  15. Cat. of books sold by Sotheby, 17 Aug., 1855, no. 306.
  16. The characteristic water mark of the Pol. Arith. occurs also in an Order in Council dated 21 May, 1680. State Papers, Dom., Charles II. 413.
  17. See Facsimile.
  18. Fitzmaurice, 262.
  19. Rawlinson MS. D 25.
  20. MSS. E. 2: 20. Fourth Rept. Hist. MSS. Com., 596 b.
  21. Eighth Rept. Hist. MSS. Com., iii. 39a.
  22. Sloane MS. 2572.
  23. Wood, Athenæ Oxon., ii. 810.
  24. Ib.
  25. Pett, Happy future State, 106, 193.
  26. Dated 5 Oct., 1678.
  27. Thorpe, Cat. lib. MSS. bibl. Southwellianæ, p. 403.
  28. P. 4.
  29. Fitzmaurice, 262.
  30. "Had not the Doctrins of this Essay offended France, they had long since seen the light.—Dedication of 1690 edition, p. 240.
  31. Ibid, 250—253; Birch, iv. 168, 173, 196.
  32. Note on p. 239.
  33. Bibliography, 11. Several readings from England's Guide (G) are given in the footnotes to the Political Arithmetick in order to show how corrupt the text of the Guide was.
  34. Lady Petty to Sir R. Southwell, 18 Feb., 1688, quoted in Thorpe's Cat. lib. MSS. bibl. Southwellianæ, p. 409.
  35. R and S have the following original dedication to Charles II. (from S):
    To the Kings most Excellent Majestie
    May it please your majte.
    As few dare venture their Discretions wholly to Disparage Arithmetick, So few doe think much practice of it very necessary in matters of State, otherwise then in what concerns the Revenue. I have therefore for the Sake of severall Young Noblemen who are now fitting themselves for your Majtes Service adventured to shew the vse of comon and easie computations in the ten Political conclusions mentioned in this Treatise, And doe now humbly beg your Majtes Pardon, for having presumed to practice a Vulgar Art upon Matters of so high a nature, and so much beyond my owne calling and Capacity. But since whatever is firm and high must have low and euen foundations, I hope I have done no incongruous thing, nor what your Majte will blame, being the Candid Endeavours of
  36. Petty appears to have been the inventor of this famous phrase. It occurs in the following passage, quoted because it throws light on Petty's conception of his new science, "My Lord Ogle being now about to carve a significant figure upon my Lord his Son, by his careful Education of him, I thought it a service to his Lordship, as well as an Expression of my Thanks for his former Endeavours, to call upon him, not only to instruct my Lord his Son in some Mathematicks, but also to store and stock him with variety of Matter, Data and Phænomena, whereupon to exercise the same; since Lines & Numbers without those, are but like Lute-strings without a Lute or Hand. For, my Lord, there is a Political Arithmetick and a Geometrical Justice to be yet further cultivated in the World; the Errors and Defects whereof, neither Wit, Rhetoric, nor Interest can more than palliate, never cure. For, Falsity, Disproportion, and Inconsistence cannot be rectified by any sermocinations, though made all of figurate and measured periods, pronounced in Time and Cadence, through the most advantageous organs; much less by Grandisonous or Euphonical Nonsense, farded with formality; no more than vicious Wines can be remedied with Brandy and Honey, or ill Cookery with enormous proportions of Spice and Sugar: 'Nam Res nolunt male administrari.'" Epistle to the Duke of Newcastle prefixed to Petty's Discourse of Duplicate Proportion (1674). This has been considered the earliest use of the term "Political Arithmetick." S. Bauer, History of Political Arithmetic, in Palgrave's Dict. of Polit. Economy, i. 56. Petty, however, had devised the phrase at an earlier date. He employed it in a letter to Lord Anglesea, 17 December, 1672 (Life, 158), and in his preface (p. 244) he describes the book as "a Specimen of the Political Arithmetick I have long aimed at."
  37. Cf. Davenant, Works, i. 128.
  38. Charles, Sir William Petty's eldest surviving son, born 1673, was created Baron of Shelburne in the peerage of Ireland in 1688 and died in 1696.
  39. S, R, 'The Preface.'
  40. On the idea that England's industries were declining during the reign of Charles II. see Roscher, Engl. Volkswirthschaftslehre, 74. The formidable list of 'trades lost' in the preface of Child's New Discourse of Trade, though not printed until 1693 was written before 1669 and doubtless reflected current opinion.
  41. On rent as a criterion of prosperity see Cunningham, English Industry, II. 191; Patten, Interpretation of Ricardo in Qu. Jour. of Economics, vii. 324.
  42. S, 'but that now.'
  43. S, 'Power, That the French.'
  44. Petty's whole paragraph is almost a summary, as its closing sentence indicates, of A Treatise Wherein is demonstrated. That the church and state Of England, are in equal danger With the trade Of it. Treatise I. By Roger Coke. London, 1671, 4°. The book comprises two treatises, with continuous pagination and signatures, but with a second title, at p. 91, Reasons of the increase of the Dutch Trade. Wherein is demonstrated from what Causes the Dutch Govern and Manage Trade better than the English; whereby they have so far improved their Trade above the English. Treatise II. Coke declares that the peopling of the American plantations has diminished the valuable trades of England. Before the accession of the plantations England lost £480,000 yearly in woollen manufactures for want of men to do them, and above £1,372,000 in the fishing trade, and "now we have opened a wide gapp, and by all encouragement excited all the growing youth and industry of England, which might preserve the trades we had herein, to betake them to those of the Plantations"—p. 16. Ireland also is a disadvantage to England for similar reasons—pp. 19—20. The Dutch sell more commodities in trade cheaper and with much more gain than the English, so as now they are swelled to be of such a prodigious greatness by sea that it is a question whether they can be controlled by any power in the world—pp. 128—129. Coke has, curiously, little to say of the rivalry of France under Colbert. Sir Roger L'Estrange's Discourse of the Fishery (1674) says that the cod, herring and ling taken in his Majesty's seas by the Dutch and other nations are valued communibus annis at no less than ten millions of pounds sterling, "which computation has been often published and constantly received for current without contradiction." (In A small Collection of valuable Tracts relating to the Herring Fishery (1751), p. 45.) Cf. p. 257, note.
  45. Refers to the presence of the Dutch fleet in the Thames, the attack on Chatham, and the burning of the English ships there 10 June, 1667. Mahan, Influence of the Sea Power, 132.
  46. Among the 'nonconformists' Petty may have included Roman Catholics. In the Further Observations he numbers them among the 'dissenters.'
  47. Edward Arber, in his ed. of the Polit. Arith. inserts an 'all' in brackets.
  48. Coke admitted that the superior durability of English timber had theretofore offset the advantage which the Dutch enjoyed in being able to build ships for half what the English could. But he held that all the best English timber was at length wasted and destroyed and still more must be in rebuilding the City of London. He could not therefore, understand how, for the future, the English could possibly build as good ships as either Dutch, Dane or French for three times the price. Treatise II, p. 115.
  49. S, R omit 'so' and 'as that Men refuse to have it cheaper, by admitting of Irish Cattle.' Cf. p. 160, 161, note.
  50. "Albeit there appears no certainty of years in the lease, yet if by reference to a certainty it may be made certain it sufficeth, Quia id certum est quod certum reddi potest." Coke upon Littleton, 45 b.
  51. S, 'the,' altered to 'that' by Petty, R, 'yt.'
  52. S has not the list of 'principal conclusions,' R has it.
  53. R omits 'near.'