# Petty's Place in the History of Economic Theory/2

published in The Quarterly Journal of Economics, May 1900, pp. 307-340
II.
The claim of Petty's writings to economic recognition rests upon a twofold basis: first, upon their method; second, upon their content. The method is named first, not because it is more important than the content, but because, being a statistical method, and as such inapplicable to many subjects, it restricts to some extent the ​content of the writings. This restriction, it should be borne in mind, was much more considerable in Petty's day than it would be in our own, because the masses of raw material for statistical treatment which now lie open upon every hand were at that time almost altogether wanting. Petty's predilection for a statistical method is due, I fancy, to the influence of Bacon, which was predominant among his scientific associates in the inchoate Royal Society. Like all Baconians, he believed in the usefulness of observations, and, by implication, in the uniformity of nature, and looked forward with confidence to the time when a precise knowledge of the external world should lay firm foundations for invention, and thus introduce the rule of man. Accordingly, he was unwearying in suggesting accurate physical and chemical experiments, many of which he himself assayed to perform. When, in a session of the Royal Society, some one chanced to use the words "considerably bigger," he characteristically requested that thenceforward "no word might be used but what marks either number, weight, or measure."
In the field of his particular interests he sought the same quantitative precision which, as a true Baconian, he demanded of his scientific colleagues. He had a clear notion both of the end at which he aimed and of the means by which it must be achieved. "The Method I take," he says, "is not 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 Arithmetick I have long aimed at) to express myself 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 myself 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 practice,) by virtue of the most elaborate Conceptions that ever have been written De Projectilibus & Missilibus, or of the Angles of Incidence and Reflection."
At many other points he returns to the idea that quantitative precision is necessary in economics as in other sciences. For example, the first chapter of the Treatise of Ireland contains "six points" which the author proposes to establish. In the second chapter we encounter, in twenty postulates, "the state of the case represented in terms of number, weight, and measure, and thereby made capable of demonstrations." And in the third chapter "the 6 first mention'd points are proved out of the 20 suppositions or assertions next before going." It must not be supposed that the pseudo-geometrical form of Petty's argument is either important or novel. On the contrary Roger Coke's Treatise wherein is Demonstrated that the Church and State of England are in Equal Danger with the Trade of it (London, 1671)—the very book against which Petty's Political Arithmetick was specifically directed—is more strictly Euclidian in form than anything that Petty wrote. But Coke's demonstrations rest, in every case, upon "comparative and superlative words," not upon quantitative determinations.
Judging from Petty's professions, we might expect his works to show the strictest of statistical methods. But, as has already been said, trustworthy numerical data of social interest were far more scanty at the time when Graunt and Petty began statistical investigation than they now are. No census of England had been taken. Since Domesday no complete survey or valuation of the lands had been made. Even the amounts of imports and exports were inaccurately known. Petty was unceasing in his demands for more precise information. With that end ​in view he drew up a schedule for the improved registration of births, marriages, and deaths in Dublin, and tried in vain to secure royal approbation for an Irish statistical office. He saw clearly that government alone could ascertain the desired facts, and that governors would profit greatly thereby. "Until this be done," he adds, "trade will be too conjectural a work for any man to employ his thoughts about." Meanwhile he made the best practicable use of such materials as were at hand, anatomizing Ireland with "only a commin Knife and a Clout, instead of the many more helps which such a Work requires." In one field alone was it possible to find a body of statistical data sufficiently extended and complete to warrant confidence in deductions properly made from it. For more than half a century the Company of Parish Clerks had kept weekly and annual records, in considerable detail, of births and deaths occurring in and about the city of London. Upon these so-called "bills of mortality" Graunt had based the London Observations already mentioned. The most fertile field being thus pre-empted, Petty was obliged to cultivate ground whose arable spots were few and far separated. It is, indeed, surprising how slight his materials were. A few scattering bills from Dublin and Paris, hap-hazard returns of customs,—collections and the hearth tax, here and there a guess as to the area of a city, that is substantially all. Under these circumstances Petty had recourse, whenever he could not determine directly the number, weight, or measure of some fact under discussion, to that substitute for direct enumeration which distinguishes his Political Arithmetick from modern statistics. Statisticians enumerate: he multiplied. The value of his results varies according to the nature of the terms employed.
For example, in the absence of a census he was forced ​to reckon the population of London, of England, and of Ireland. So far as London is concerned, he had as a basis certain facts—the number of burials and the number of houses—which bear some relation to the number of people. He then multiplied the number of burials by thirty, satisfying himself by quoting Graunt's authority for that number. The result thus obtained he sought to confirm by multiplying the number of houses by a factor assumed to represent the average number of inhabitants to a house. This factor is sometimes six and sometimes eight, as chanced to suit his purpose. He next assumes that the population of England is eleven times that of London, or 7,369,000, because London pays one-eleventh of the assessment, and asserts that the results thus obtained "do pretty well agreee" with the returns of the hearth and poll money and with "the bishops late numbering of the communicants." He does not himself give any of these figures; but it has been discovered that, according to the accepted rules of political arithmetic, the bishops' enumeration accounted for only 82 per cent. of the number that Petty calculated. In all these cases, however, there is some real basis for his calculations; and Petty was himself under no delusions as to the accuracy of his result. Thus he says, "Although the said number of 7 millions, 369 thousand, 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." Both the strength and the weakness of his method are abundantly exemplified in his writings. Such of his terms of number, weight, and measure as result from actual enumeration are often the basis for conclusions of value; for he had large capacity for distinguishing the essential from the incidental in any economic problem. But the obstacles in the way of enumeration were, in almost all quarters, ​insuperable even to so energetic and resourceful a man as Petty; and, while he repeatedly demanded governmental assistance in his quests, his eagerness for results too often led him to resort, in the absence of specific facts, to calculations that were nothing more than guesses. Whenever he took time to consider them, he recognized keenly enough their conjectural character. "I hope," he writes to Aubrey, "that no man takes what I say about the living and dying of men for a mathematical demonstration." But, when the afflatus was on him, he was prone to take what he said for a mathematical demonstration himself. He did not hesitate to advance, in all seriousness, the most astounding proposals for increasing the national wealth of the three kingdoms by a wholesale deportation of the Irish and Scotch into England,—proposals based solely upon the results of a complicated series of guesses and multiplications. Still, we may not condemn him without mitigation. He was a beginner; and his mistakes in method, if not in advocacy, are not without their modern analogies. The neatness with which industrial facts can be represented by the use of mathematical terms, integral, symbolic, or graphic, carries undeniable advantages for purposes of analysis. It helps to keep ideas distinct and uniform. It throws light upon their possible permutations and combinations. But this very neatness has its dangers. The mistakes of political arithmetic may be repeated by sociological geometry and economic calculus. An investigator may fancy his problem solved when it is merely restated in a new form. The new and neater form may be a step toward eventual solution. Achieved solution it generally is not.
The influence of the statistical method, as exemplified in Graunt's Observations and in Petty's writings, can be traced ​in two directions. One springs primarily from Graunt, flows through Petty's Essays, and leads, as has already been said, to modern vital statistics: the other proceeds from Petty's Political Arithmetick through Davenant and Gregory King to Arthur Young and Chalmers. It has perhaps affected even Sir Robert Giffen. Parallel with it goes the development of the German Universitäts-statistik from Conring to Achenwall and Schlözer, whose relations to English political arithmetic have not been fully worked out. So far as I can see, the German discipline was at no time superior to the English in any respect save in the possession of the name "statistics." And Knies has forced it to yield up that.
In the field of vital statistics the connection from Graunt to Süssmilch can be traced without a break. The extent to which Petty's Essays depend upon Graunt has been noted already. The next link in the chain is Edmund Halley's Estimate of the Degrees of Mortality of Mankind, which was published in 1693 in the Philosophical Transactions of the Royal Society. From this paper springs modern life insurance. It cannot be doubted that Caspar Neumann materially assisted Halley by furnishing him figures for a stationary population from the Breslau bills, and it seems clear that Halley's suggestions were less esteemed in England than in Germany in the years immediately succeeding their publication. It is nevertheless true that Halley published the first real life table, and that he mentions at the outset of his paper the prior work done upon the bills of mortality by Petty and Graunt. After Halley the next writer who acknowledges his indebtedness to them is the Rev. William Derham (1657-1735), who was also a member of the Royal Society. Derham was appointed to lecture upon the famous Boyle foundation for proving the Christian religion against atheists, deists, pagans, Jews, and Mohammedans; and, as became a ​scientific clergyman of the pre-Darwinian era, he decided to demonstrate the being and attributes of God from his works of creation. While in the midst of that great argument, a chance reading of Graunt's book drew his attention to the constant relation subsisting between marriages, births, and burials. He recognized at once that this was but an admirable plan and management to keep the balance of mankind even; for, says he, "what can the maintaining throughout all ages and places of the proportions of mankind and all other creatures, this harmony in the generations of mankind, be but the work of One that ruleth the world?" Derham's lectures in no sense constitute a statistical work; and his incidental comments on Graunt and Petty would be unimportant in the history of statistics, had not their theological setting brought them to the hands of a Prussian military chaplain named Johann Peter Süssmilch. Süssmilch himself says that die göttliche Ordnung in den Veränderungen des menschlichen Geschlechtes first became clear to him while he was reading Derham's book; and he thereupon sent to England for the writings of Graunt and Petty, which were mentioned by Derham, and was in large part guided by them in producing his famous work. In view of these facts it is clear that the German historians of statistics are mistaken in making Süssmilch the father of vital statistics. The true beginnings of the science are to be found in the Observations on the Bills of Mortality of London. The author of that book thoroughly appreciated the importance of his work. He is the creator of statistics quite as truly as Boyle among his contemporaries is the father of chemistry, or Ray of botany, or as Newton was the originator of calculus. And it is not too much to say that no subsequent statistician has as yet modified Graunt's work so fundamentally as ​Lavoisier did Boyle's, or Linnaeus Ray's, or as the application of the method of limits modified the Newtonian fluxions.
If we turn to the history of political arithmetic in England, we find the influence of Petty alone as clear and decisive as was the joint influence of Petty and Graunt upon vital statistics. Davenant declared that Petty first began the application of this art to the particular objects of revenue and trade, in which he had as yet been followed by very few. If there had been open to the industrious doctor such opportunities to examine the correspondence of Southwell, Williamson, Sir Peter Pett, Halley, and Justel as the student now enjoys, he might have been led to modify his belief that nobody but Gregory King and himself appreciated this side of Petty's activities. Yet it must be admitted that King and Davenant, working as they did under the direct influence of Petty upon the fuller data afforded by a new financial policy, brought the art to the highest pitch which it ever reached. Their followers, with the possible exception of Arthur Young, exaggerated its methodological fault of multiplying conjectural averages to secure aggregates instead of deducing the averages from aggregates directly enumerated; and when the income tax and the census of 1801 afforded more accurate estimates of national wealth and of population, political arithmetic was driven forever from its two chosen fields. It is probable, however, that the interest which it had excited and the suggestions which it had evolved contributed not a little towards making a census possible both in England and elsewhere.
* ↑ Preface to Political Arithmetick, Writings, i. 244.
* ↑ Writings, i.53, cf. 49, 51, 104, 115, 127, 120, 180, 245; ii. 476, 485.
* ↑ The London bills of mortality are discussed historically and critically in the introduction to Petty's Writings, i. lxxx-xci.
* ↑ Writings, ii. 332, 393.
* ↑ Vol. ii. 527, 534.
* ↑ Vol. ii. 459.
* ↑ Vol. ii. 461, cf. i. p. xxxi.
* ↑ Italics in the original.
* ↑ "By laborious Conjectures and Calculations to deduce the number of People from the Births and Burials, may be ingenious, but very preposterous." Observations on the Dublin Bills, 7; Writings, i. 485.
* ↑ Cf. J. Gratzer, E. Halley und Caspar Neumann, 1883.
* ↑ Physico-theology. By W. Derham. London, 1713. I use the 1798 edition, vol. i. p. 267.
* ↑ John is far more appreciative of Graunt than the others.
* ↑ Discourses on the Public Revenues, 1698, in Davenant's Works, i. 128.