Front Page Titles (by Subject) APPENDIX. - The Economic Writings of Sir William Petty, vol. 2
The Online Library of Liberty
A project of Liberty Fund, Inc.
Search this Title:
Also in the Library:
APPENDIX. - Sir William Petty, The Economic Writings of Sir William Petty, vol. 2 
The Economic Writings of Sir William Petty, together with The Observations upon Bills of Mortality, more probably by Captain John Graunt, ed. Charles Henry Hull (Cambridge University Press, 1899), 2 vols.
About Liberty Fund:
Liberty Fund, Inc. is a private, educational foundation established to encourage the study of the ideal of a society of free and responsible individuals.
The text is in the public domain.
Fair use statement:
This material is put online to further the educational goals of Liberty Fund, Inc. Unless otherwise stated in the Copyright Information section above, this material may be used freely for educational and academic purposes. It may not be used in any way for profit.
[Extract from The Discourse Concerning the Use of Duplicate Proportion1 , 1674.]
The Eleventh Instance.
In the Life of Man, and its Duration.
It is found by Experience, that there are more persons living of between 16 and 26 years old2 , than of any other Age or Decade of years in the whole life of Man (which David and Experience say to be between 70 and 80 years:) The reasons whereof are not abstruse, viz. because those of 16 have passed the danger of Teeth, Convulsions, Worms, Ricketts, Measles, and Smallpox for the most part: And for that those of 26. are scarce come to the Gout, Stone, Dropsie, Palsies, Lethargies, Apoplexies, and other Infirmities of Old Age. Now whether these be sufficient reasons, is not the present Enquiry; but taking the afore-mentioned Assertion to be true: I say, that the Roots of every number of Mens Ages under 16 (whose Root is 4) compared with the said number 4, doth shew the proportion of the likelyhood of such mens reaching 70 years of Age. As for example; ‘Tis 4 times more likely, that one of 16 years old should live to 70, then a new-born Babe. ‘Tis three times more likely, that one of 9 years old should attain the age of 70, than the said Infant. Moreover, 'tis twice as likely, that one of 16 should reach that Age, as that one of 4 years old should do it; and one third more likely, than for one of nine. On the other hand, 'tis 5 to 4, that one of 26 years old will die before one of 16; and 6 to 5 that one of 36 will die before one of 26; and 3 to 2, that the same person of 36 shall die before him of 16: And so forward according to the Roots of any other year of the declining Age compared with a number between 4 and 5, which is the root of 21, the most hopeful year for Longævity, as the mean between 16 and 26; and is the year of perfection, according to Our Law, and the Age for whose life a Lease is most valuable. To prove all which I can produce the accompts of every Man, Woman, and Child, within a certain Parish of above 330 Souls; all which particular Ages being cast up, and added together, and the Sum divided by the whole number of Souls, made the Quotient between 15 and 16; which I call (if it be Constant or Uniform) the Age of that Parish, or Numerus Index of Longævity there. Many of which Indexes for several times and places, would make a useful Scale of Salubrity for those places, and a better Judg of Ayers than the conjectural Notions we commonly read and talk of. And such a Scale the King might as easily make for all his Dominions, as I did for this one Parish.
The Sixteenth Instance.
In the Price of several Commodities.
Suppose a Mast for a small Ship be of 10 inches Diameter, and as is usual, of 70 foot in heighth, and be worth 40s; then a Mast of 20 inches through, and double length also, shall not onely cost eight times as much, according to the Octuple quantity of Timber it contains, but shall cost 16 times 32l. And by the same Rule, a Mast of 40 inches through shall cost 16 times 32l. or 516l. Of which last Case there have been some instances. But whereas it may be objected, That there are no Masts of four times 70, or 280 feet long, I will say, that the Rule holds in common practice and Dealing. For, if a Mast of 10 inches thick, and 60 foot long, be worth 30s; a Mast of 20 inches throughout, and 80 foot long, shall be worth 15l. And a Mast of 40 inches through, and 100 foot long (not 280 foot) shall be worth near 100l.
Moreover, suppose Diamonds or Pearls be equal and like in their Figures, Waters, Colours, and Evenness, and differ onely in their Weights and Magnitudes; I say the Weights are but the Roots of their Prices, as in the Case aforgoing. So a Diamond of Decuple weight, is of Centuple value. The same may be said of Looking-glass-Plates. I might add, that the Loadstone A, if it take up 10 times more than the Loadstone B, may be also of Centuple value.
Lastly, A Tun of extreme large Timber may be worth two Tuns of ordinary dimensions; which is the cause of the dearness of great shipping above small; for the Hull of a Vessel of 40 Tuns may be worth but 3l., per Tun, whereas the Hull of a Vessel of 1000 Tuns may be worth near 15l., per Tun. From whence arises a Rule, how by any Ships Burthen to know her worth by the Tun, with the Number and Size of her Ordinance, &c.
[The Dialogue of Diamonds1 .]
A. You have a fine ring there on your finger, what did it cost you?
B. I am ashamed to tell you for I am afrayd I gave too much for it, & the truth is I wonder how any man [can] tell what to give, there be so many nice considerations in that matter in all which one has nothing but meere guesse to guide himself by.
A. Why, did you buy it set?
B. What should I doe with it unset?
A. If you bought it set you lost two of the best guides & measures whereby to have known its price, namely the weight and the extent, both which are computable otherwise then by meer guesse; beside the water and colour of the stone as also the clouds icecles & points are somewhat better discerned when you can look round about it, then when you look upon it but as through a window.
B. Well, I was not so wise; but I must needs buy some more diamonds shortly, wherefore pray instruct me if you can.
A. I will & first take notice that the deerness or cheapness of diamonds depends upon two causes, one intrinsec which lyes within the stone it self & the other extrinsec & contingent, such as are [1.] prohibitions to seek for them in the countrys from whence they come. 2. When merchants can lay out their money in India to more profit upon other commoditys & therefore doe not bring them. 3. When they are bought up on feare of warr to be a subsistence for exiled and obnoxious persons. 4. They are deer neer the marriage of some great prince, where great numbers of persons are to put themselves into splendid appearances, for any of theise causes if they be very strong upon any part of the world they operate upon the whole, for if the price of diamonds should considerably rise in Persia, it shal also rise perceivably in England, for the great merchants of Jewels all the world over doe know one another, doe correspond & are partners in most of the considerable pieces & doe use great confederacys & intrigues in the buying & selling them.
B. I like this discourse very well but have no occasion for so deep an inspection into the matter. I have but 2 or 300l., to lay out and I heare that the market at this time is at a midling pitch & therfore I had rather heare from you upon the intrinsec causes & such as lye within the stone it self.
A. I am content. You must therfore know that these intrinseck causes are principaly foure, vizt. weight, extent, colour or water, cleaness from faults, & to theise you may adde the mode and workmanship of the cutting.
B. When I bought my ring I did not divide my consideration into so many branches: methought it made a fine shew in general & I bid 85, 86 & 87l., for it, & the merchant swore he could not afford it so & seemed to goe away once or twice and thereupon I gave him 90l., & he told me that he would give me 85l., for it at any time within a twelvemoneth & defys me to match it anywhere for the money I gave him. Besides I had shewed it to 2 or 3 friends, who all, to shew their skill, made some special animadversions upon the business & told me I could not be much out if I gave between 80 & 90l., for it; and this is all the art I had. I expect now to be wiser from you.
A. I told you there must be four intrinsick causes of dearnesse & cheapness, vizt. Weight, Extent, Colour & Clearness. As for the weight you must get you a pair of Scales that will weigh with certainty to less then a quarter of a grain. As for extent you must get a piece of Muscovia glasse or very fine horne, wherein must be a square drawn of an inch in the side & the said Square divided into 400 Squares, dividing each side into 20 parts by the finest lines that can be drawn, making every fourth division in a line somthing bigger then the rest for distinction sake. Thirdly you must have 5 or 6 diamonds to lye constantly by you, each of a several water, & you must have in the opinion of the best jewellers the proportion of value which the said waters do beare one to another, as for Ex.: Suppose a stone weigh a graine & being of the best water is worth 253, of the black water 203, of the red 163, of the yellow 143, of the blewish 133, of the brownish 123 &c. Fourthly you must have as many foule diamonds as doe contein Samples of every sort of fault & a note of such abatements as an experienced Jeweller would make for every such fault, the same to be expressed in aliquot parts of the whole value, & you must also have a pair of excellent Spectacles for the older sight with a good microscope, & then I conceive you are furnisht with the means of knowing more than most jewelers doe know.
B. I cannot remember all you have said: therfore repeat the same over again in parts, & first concerning the weight.
A. I shal. The general rule concerning weight is this that the price rises in duplicate proportion of the weight, that is to say as the Squares of the weight are one to another or the weight multiplyd by it self. As for Ex.: Suppose a diamond weighing one grain to be worth 20 then diamond of 2 grains is worth 4l., because the square of two is 4, that is, 2 multiplyd by 2 makes 4; & the diamond of 2 greins is to be paid for as if it weighed 4 & by the same rule a diamond of 3 grains must be reckoned as if [it] weighed 9, because 3 times 3 makes 9, & a diamond of 4 grains is to be reckond as 16, & according to this rule the great Moguls diamond of 1000 grains is reckoned worth a million of pounds Sterling and the Duke of Florences 200000l. Now judge you whether it be safe buying a diamond of 20 grains by the eye without weighing, in which a graine difference in the weight makes about 43l., difference in the price, reckoning the single grain but for 20s.
B. I have one notable & obvious objection against your rule, which is that Lapidarys do use to divide a stone into 2 parts, making according to your rule each half to be but a quarter of the value of the whole & the two halfs after the charge and hazard of dividing to be worth but half what the whole was worth before dividing—answer me that.
A. I doe acknowledge that the rule of weight alone is insufficient, as you have judiciously observed. Wherfore you must come to the next measure which is extent; and extent is chiefly measured by the magnitude of the superficies which the great section of the stone doth make, and by cutting the stone into two parts, if the stone were valued only by the said superficies, the value of the stone cut is doubled, whereas according to the weight it was halfed. But this would better appear in an example. Suppose a stone intire to be worth 8l. Now if the same be cut in two halfs, each half reckoned by the weight alone would be reduced to 40s. and the two halfs to 4l. But if the stone be reckoned according to the extent and superficies only, then the two halfs would be worth two eight pounds or 16l. But forasmuch as the rule of weight alone and the rule of extent alone are each of them insufficient, you must joyne them both together and take the medium. For joining 4l.: the value by weight, to 16l., the value by measure, the total is 20l., the half whereof is 10l.; and thus you see the stone which intire is worth but 8l., being divided is worth 10l., yielding an advantage of 40s. which is more than the charge of dividing it doth commonly amount to.
B. Your answer is very satisfactory & ingenious & from whence I now understand the use of your glass or horne table. For I suppose that by applying the flat section to the squared table you may with diligence measure the difference of any superficies almost exactly.
A. you apprehend it right & when I have measured so the extent of two several stones, I cast up their values by the aforementioned rule of duplicate, & having cast them up both by weight & by measure, I take the medium.
B. Lord bless me, what a fool was I wholy to omit those two guides neither of which could I make use of whilest the stone was set, & how easy is it for the best jeweler in the world to mistaken one grain or one square in 20, nay, to mistake one in 100 where the value of one grain is above 200l., and how doe the workmen who doe set diamonds indeavor so to set them as to make them look 5 grains or 5 squares in 100 bigger then they are. I am very well pleased with this discourse by which in a quarter of an houre one may learn to get or save 2 or 300l., & to learn an art which is so little the worse for the wearing.
A. I am glad you accept my advice. Some men would have made a frivolous objection against it, or have received it with a scornfull smile as a prety useless fancy and no more. But because you are so candid, I will proceed to the other points.
B. I heartily thanke you.
A. You must make such a measure upon your glass table as may correspond to the value of your grain, and when you have by the weight found how many grains you are to pay for, and by your note of colours at how much per grain, & when you have again by your table of magnitudes found how many squares you are to pay for at the same rate at which you reckoned the graine, then adding the value by weight to the value by extent, the half of that summ is the value of that stone according to its weight, extent & colour.
B. I apprehend. And I thinke there remains nothing more then to teach me how to make my abatements of the value so found as aforesaid according to the several natures & numbers of the defects.
A. Well this I will doe. You must remember you were to keep by you such and so many stones as doe contain all the usual faults of diamonds with the quota parts of the value which for each defect is to be abated. As for example, suppose there be a black speck in a stone which without it were worth 10l. according to our former rules, but with it is worth 4s. lesse. Now you must remember that this 4s. must be looked upon as the 50th part of the value, and therfore you must abate 10l. in a stone of 500l. tho you abated but 4s. in a stone of 10l. Moreever suppose there be not only the black speak abovementioned but an icecle also in your stone of 10l. for which you are not abate 10l. and consequently the icecle & the speck 14s. Now I conceive that, becasue there are two faults, you must not only abate 10s. & 4s. but the double of the same, namely 28s. Again suppose that beside the speck and the icecle there be also a cloud, for which alone you might abate 6s. more, that is 4s., 10s. & 6s., in all 20s. I say that in this case you must not only abate barely 20s', nor the double thereof as when there were but two faults, but because there are three faults, you must abate the treble of all three, which is 3l., leaving your stone of 10l. reduced to 7l. Now this triple abatement in a stone of 500l. would be 150l., because that 150l. is of 500l. as the 3l. was of 10l.
B. I thinke I understand this doctrine, but there comes a conceit in my head which makes me laugh, for how if all the faults thus cast up together should amount to more then the value, will you say that the stone in such a case is so much worse then nothing? Certainly its worth something to make diamond powder of, were it never so foul or mishapen.
A. Your objection is good. Tis a pleasure to teach you, and to what you have said I can only answer theise two things: that I have heard able jewelers say that the difference of stones of equal weight is seldome more then between 15 & 5 or 3 & 9, namely that the best with all its perfections is but triple to the worst with all its faults. The other thing I say is that in case your defects cast up as aforesaid should bring your stone below of its full value resulting from the weight, extent & colour, I say in such a case that the estimate of your defects must be reviewed, tempered & better proportioned & adjusted.
1. The King has a Prerogative which Lawyers must expound.
2. The King makes Peers in Parliament who are perpetuall Legislators, as also the Last and highest Judicature of England and Ireland, and have great Priviledges and Immunitys for themselves and Servants.
3. The King is the fountain of Honour Titles & Precedencys and of all the Powers which the Lrd Marshall & Heralds exercise.
4. The King makes Bishops; and They Priests & Deacons, & Clerks of the Convocation, and has also all the Power which the Pope had formerly. Bpps make Chancellors and other officers of the Spirituall Courts have power to Excommunicate &c.
5. The King makes the Chancellors of the Universitys, makes Heads and Fellows in Severall Colledges, and is also Visitor in some Cases.
6. The King has the Power of Coynage, & can give the Name, Matter, fineness, Character and Shape to all Species of Money and can cry Money up and downe by his Proclamation; which some extend to this vizt That if A. Lend B. 100l. weighing 29 pounds of Sterling Silver, If the King by his Proclamation declare that one Ounce of Silver shall be afterward calld One hundred pounds, that then B. paying to A. the said Ounce of Silver, the Debt is answer'd.
7. The King makes Sheriffs and they Juries upon Life and Estate, Limb and Liberty, as also Jaylors Baylifs & Executioners of All Sorts.
8. The King makes a Chancellor or Chief Judge in Equity who Stopps proceedings in other Courts of Law &c. The Chancellor makes Justices of Peace, & they High & petty Constable, & Sessions of Peace, &c.
9. The King makes Judges durante bene placito. They sett fines and punish at their own Discretion in Severall Cases. They Govern Proceedings at Law, Declare and Interpret the Law, Repreive, &c. & the King can suspend the Law, pardon, or prosecute.
10. The King can give Charters for Boroughs to Parliament, appoint Electors and Judges of Elections, prorogue adjourn and disolve Parliaments from time to time, and from Place to Place, disprove the Speaker &c.
[11.] The King appoints his Lieutenants to command the Grand Standing Militia, can press any Man to serve his Allys beyond Seas, as Soldiers, can equip & appoint what number of Shipps and Seamen he pleases & their Wages & pari Ratione a Mercenary Army to serve at Land, as also Guards for his Person of Severall Sorts.
12. The King has some Revenue by Common Law and Prerogative & can by his Judges interpret Statutes concerning the Branches and the Collection thereof.
13. The King has great power over Forests and Mines, Colonys Monopolys.
14. The King can doe noe Wrong, & his coming to the Crown clears him from all punishments &c. due before, and obedience to him after Coronation excuses from1
15. The King by ceasing or forebearing to administer the Severall Powers above nam'd can doe what harm he pleases to his Subjects.
The fundamental idea of Petty's “Discourse of Duplicate Proportion” is that certain phenomena, capable of expression in terms of number, weight and measure, stand related to one another as the squares or cubes, or as the square or cube roots of their respective quantities. Petty illustrates his theory by a number of “instances,” drawn for the larger part from the physical sciences. Some of his instances are correct, some are fantastic. Only two of them, the eleventh and the sixteenth, are at all closely connected with the subject of his economic writings, and these instances are reprinted as apposite illustrations of an idea which was not without influence upon his work in political arithmetick. The eleventh instance is found at pages 82–88, the sixteenth at pages 106–109 of the “Discourse,” as printed in 1674. See Bibliography. Cf. also Birch, iii. 156, Fitzmaurice, 268. Bishop Barlow's Remains contain a sharp criticism of the “Discourse.”
Cf. Graunt's “Observations,” p. 387.
The “Dialogue of Diamonds” is found among the Philosophical Papers collected by Abraham Hill. Brit. Mus. Sloane MS. 2903, f. 44 seq. Dr Hill (1635–1721) was resident in Gresham College in 1660 and was one of the twenty-one persons, Petty being another, who were named members of the Council in the second charter of the Royal Society, 1663. Birch, 1. 223. The “Dialogue,” apparently in Hill's hand, is without title or caption, but it is ascribed by him to Petty and both its method of reasoning and its style of expression confirm the correctness of his ascription. I have followed the suggestion of Dr Bevan in calling the paper “The Dialogue of Diamonds” Bevan, Petty, p. 63.
The “Powers of the King of England” are printed from a MS volume bearing the title “Adversaria Literaria I. P,” Brit. Mus. Addl MSS. 27,989, f. 17–18. The volume contains a book-plate of Sir John Perceval, of county Cork, Ireland, dated 1702. Cf. Hamilton, Dated Book-plates, 28. Perceval was born in 1683. The death of his father, Sir John Perceval, a friend of Petty's (Fitzmaurice, 270), in 1686, left him an orphan and ward of Sir Robert Southwell. He was created Baron Perceval in 1715, and Earl of Egmont in the peerage of Ireland in 1733, and died in 1748. Perceval, who was in a position to procure copies of Petty's writings, was a diligent collector of MSS. Other volumes of “Adversaria” apparently compiled by him, are in existence, one of them containing a “character” of Petty. 7thRept. Hist. MSS. Com. pp. xiii. 232–249. The “Powers of the King” are in the same hand, probably Perceval's, as the remaining, very miscellaneous, contents of the British Museum's volume of the “Adversaria.” Another MS. of the “Powers of the King” is the property of the Marquis of Bath, at Longleat. 3rd Rept. Hist. MSS. Com. 199.
The 17th November, James had replied to the address of the Commons on the test. On the 19th there ensued the notable debate in the House of Lords in which not only Halifax, but Compton, Mordaunt, and Devonshire criticised the King's policy with vigour. The following day Parliament was prorogued. Under such circumstances it is not surprising that so active-minded a man as Petty should have set down his ideas as to the extent of the prerogative. His expectations of reform, based upon the exercise of the royal power, though mistaken, seem to have been sincere, and it is to them that we owe, in part at least, several of his later writings.
Unfinished in the MS.