Adolphe Quetelet as statistician

Prefatory Note

It is not presumed that the dissertation here presented will add much to the knowledge of Quetelet possessed by those who have read rather extensively in statistical literature. But it is hoped that the increasing number of those who are becoming interested in Quetelet and his work may find these pages useful. The first two chapters give brief sketches of the man, his work and his place in the history of statistics. The last three chapters present what are believed to be the most important of Ouetelet's statistical principles. These include the conception of the Average Man as a type, the significance for social science of the regularities found in the moral actions of man, and the theoretical basis of the distribution of group phenomena about their type.

Grateful acknowledgment should here be made to Professor Henry L. Moore for directing me to this stimulating subject, and for continued helpfulness in its pursuit.

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CHAPTER I Biographical Sketch PAGE

Parentage — Youthful literary activity — At the University of Ghent; the influence of Gamier — Called to the Athenaeum at Brussels — Contributions to mathematics — Educational activity at Brussels ; his elementary treatises and characteristics as a teacher — Founding of the Brussels Observatory; sojourn in Paris — Travels in Germany, Italy and Sicily — Research work at the Observatory — Studies in meteorology and terrestrial physics — His activity in connection with V Acaditnie royale de Belgique — Activity as an official statistician — Founding of the Commission centrale de statistique, of the Statistical Society of London and of the International Statistical Congress — Stroke of apoplexy in 1855 — Member of many learned societies — His personality — Home life — The Brussels statue 9

CHAPTER II QUETELET IN THE HlSTORY OF STATISTICS

Two lines of development in statistical literature — One of these, the German University ' '' Statistic ,'' " traced through the writings of Muenster, Conring, Achenwall, Von Schlozer and Busching — The growth of official statistics and the gradual modification of the university discipline — Quetelet's contribution to this change -—A second line of statistical development traced through the works of Graunt, Petty and others of the School of Political Arithmetic, Derham, Siissmilch, and the first formulators of mortality tables — The influence of Malthus, Laplace, and especially of J. B. Fourier — Quetelet's contribution to this line of development, treated under (I) population statistics, (II) moral statistics; (III) technique and (IV) application of the normal law of error to the physical measurements of men — Summary .... 36

Chapter III

Importance of this concept in Quetelet's writings — Survey of its development— Its generalization in Du Systeme social — Studies to determine the qualities of the average man — Role of the average man in various sciences — Objections: the average man cannot be constructed as a composite being — The average as the type of 449] 7

CONTENTS [450

PAGE

perfection — Distinction of results obtained in some of Quetelet's studies — The average man as a biological type — The permanence of the type — Quetelet's approach to the doctrine of selection by environment 62

Chapter IV

Moral Statistics Introductory— Definition — Quetelet's principal works on moral statistics and his emphasis upon statistical regularities — His explanation of these regularities — The viewpoint of science and its bearing upon the doctrine of free will and upon the explanation of statistical regularities — Explanation of the fluctuations in the numbers from year to year — And of the variations about an average — Because of the way in which they are formed, the regularities exert no compulsion over the individual — Significance of the regularities for the doctrine of free will — Bearing of statistical inquiry on this doctrine — The statistical regularities and social laws — The difficulty of establishing quantitative relations between social events and their conditions — The effect of the dynamic character of social life upon statistical regularities and their laws — Two basic principles of method in moral statistics — And their importance for the quantitative study of social phenomena 83

CHAPTER V Statistical Method

The basis of statistical method found in the variability of organic and social phenomena about type forms — The probability of an event when all its chances are known — Inductions from experience when the number of chances is unknown — The distribution of chances when their number is small— Agreement between theory and experience tested — The distribution of chances when their number is very large — Quetelet's scale of possibility and precision — The derivation of this scale explained — The curve representing the distribution of chances when their number reaches the conceptual limit — Theory provides for extremely improbable combinations, but such are not met with in experience — Quetelet's distinction of "means properly so called" from "arithmetic means " — The theory of the distribution of chances related to the theory of the distribution of errors of measurement and to the distribution of biological measurements— Description of the application of Quetelet's scale to a statistical problem — The probable error — The normal curve only one of many possible forms — The significance of narrowing limits of deviation — Quetelet's classification of causes — Constant causes not revealed by statistical inquiry — Variable causes — Kinds of accidental causes — Causes classified as general and minute — Causes studied by correlation . . . 106

Chapter I

It might be set down as a rule of mental conduct that, when we become interested in the achievements of a great man, we desire a more intimate acquaintance with his personality and with the routine of his daily life. The deeds of statesmen and warriors are readily appreciated by the generality of men. This is due, not only to their conspicuousness and to the glamour and fascination attending those who achieve notable success in the world of affairs, but to the immediate responsiveness of human emotions to the heroic. But not infrequently does it happen that many years are required for the most important contributions to knowledge to become the possession of an extended and appreciative group of initiated disciples. Herein is found the reason for this brief sketch of Adolphe Quetelet. 1 Not that his scientific achievements have been passed by with little or no comment, but that there is to-day a rapidly widening group

x Quetelet's name is sometimes accented — Quetelet. There is, however, abundant reason for omitting the accent. In the Nouveau Mimoires, the Bulletins and the Annuaire of the Brussels Academy, in the Annales and the Annuaire of the Brussels Observatory, and in a number of his works brought out at Brussels, the name is uniformly unaccented. When it is recalled that Quetelet was Secretary of the Academy for forty years and Director of the Observatory for even a longer term, it seems certain that he himself did not accent his name. Moreover in places where he has signed his name it is not accented. The accented spellings seem to be due to Paris publishers.

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of scholars who appreciate the distinctive merit of his development of statistical methods of research. It is believed that such will be interested in a brief account of the man himself. J

Born on the twenty- second of February, 1796, in the ancient and historic town of Ghent, Quetelet grew up there amid the stirring scenes which marked the fall of the old regime and the rise of the empire of the brilliant and ambitious Napoleon. Little is known of his parents. No mention is anywhere made of his mother except that her maiden name was Anne-Frangoise Vandevelde. His father, Frangois-Augustin-Jacques-Henri Quetelet, is known to have been born at Ham, in Picardy, in 1756. Being of a somewhat adventurous spirit, Frangois crossed the English Channel at an early age and is said to have become an English citizen. He soon became secretary to a Scotch nobleman, with whom he spent several years traveling on the Continent and sojourning in Italy. He then settled permanently at Ghent, about 1787. Here he was at length elevated to the position of a municipal officer, in which capacity he rendered valuable and well-

1 The chief source for this sketch is the ' ' Essai sur la vie et les ouvrages de Quetelet," by Edward Mailly, one of Quetelet's students and his assistant for thirty-seven years, in the Annuaire de V acadimie royale des sciences, des lettres et des beaux-arts de Belgique (Brussels, 1875), vol. xli, pp. 109-297. In addition should be mentioned the following: (1) Naum Reichesberg, " Der beriihmte Statistiker, Adolphe Quetelet, sein Leben und sein Wirken," Zeitschrift fur schweizerische Statistik (Berne, 1893), Jahrg. xxxii, pp. 418-460; (2) the " Discours " pronounced at Quetelet's funeral, Bulletins de V acadhnie royale des sciences, des lettres et des beaux-arts de Belgique (Brussels, 1874), Second Series, vol. xxxvii, pp. 244-206; (3) Mailly, "Notice sur Adolphe Quetelet," ibid., vol. xxxviii, pp. 816-844; (4) Wolowski, " Eloge de Quetelet," Journal de la sociiti de statistique de Paris (1874), vol. xv, pp. 118-126. Other less important references will be found in the notes.

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esteemed services. He died in 1803, when Adolphe was but a boy of seven.

It was thus that, upon his graduation from the Lyceum at Ghent, young Quetelet was compelled, at the age of seventeen, to turn his talents to good account. He spent the next year as teacher of mathematics in a private school at Audenaerde. x On his nineteenth birthday he was chosen instructor in mathematics at the newly organized college in his native city.

The time between his election and the opening of the University in October, 181 7, seems to have been spent largely in literary composition. In collaboration with G. Dandelin, a former student at the Lyceum, he prepared the libretto for an opera "en un acte, en prose et a grand spectacle," entitled Jean Second ou Charles Quint dans les murs de Gand. This was successfully presented at Ghent, and led to the partial construction of two more dramas by the same authors. Quetelet published quite a number of poems, 2 and until the age of thirty he continued to exercise his poetical talents as pastime and relief from his scientific studies. His poems were of a serious tone, but were well received by both public and critics. We may mention here an Essai sur la romance, which Quetelet brought out in 1823. In this, from a survey of romance among different peoples, he found the origin of romance in the days of chivalry. This essay, together with translations, in prose and in verse, of German, English, Italian and Spanish romances, shows Quetelet's wide acquaintance at that early age with the

x One of his students here was M. Liedts, who afterwards, as minister of the interior, authorized the Commission centrale de la statistique.

2 Chiefly in the Annates belgiques and Etudes et tecons francaises de littirature et de morale. Mailly, Essai, pp. 114-131, quotes at length from these poems.

various European literatures. Mailly, who must be viewed as a friendly critic, believes the Essai sur la romance and many of the poems deserving of republication.

During the three years of his service at the College of Ghent the most important influence brought to bear upon him was that of Jean Guillaume Gamier, 1 professor of astronomy and higher mathematics. This expert mathematician and refined scholar was called from Paris to the University of Ghent by the King of the Low Countries in 181 7. His influence over Quetelet's eager, youthful spirit was quite decisive. Quetelet says of him,

Little by little his conversation, always instructive and animated, gave a special direction to my tastes, which would have led me by preference towards letters. I resolved to complete my scientific studies and followed the courses in advanced mathematics given by M. Gamier. It was at the same time agreed by us that, in order to relieve him in his work, I should give some of the other courses with which he was charged. I thus found myself his pupil and his colleague. 2

The aspiring dramatist soon found a favorite occupation in the reading of Pascal.

Quetelet was the first to receive the degree of doctor of science from the new university. His dissertation was an original contribution of much importance to the

1 1 766- 1 840. He was examiner at l'Ecole polytechnique, 1795-1800; adjunct professor with Lagrange at the same place, 1800-1802; one of Poisson's instructors and an intimate of J. B. Fourier. See Nouvelle biographie ge'ne'rale (Paris, 1858), vol. xix, also " Notice sur J. G. Gamier," by Quetelet, in the Annuaire de Vacadimie royale de Bruxelles (1841), vol. 7; and sketch by Quetelet in Sciences mathimatiques et physiques au commencement du xixe Steele (Brussels, 1867).

2 " Notice sur J. G. Gamier," Annuaire de Vacad. roy. de Brux. (1841), vol. vii, pp. 200-201.

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theory of conic sections : it demonstrated two new propositions, one of which developed the properties of a new curve, the "focale." 1 In October of this same year (1819) he was called to the chair of elementary mathematics in the Athenaeum at Brussels. Repairing thither at once, he was soon in the midst of a learned circle of Belgian and French scholars. Among the former may be mentioned the old Commandeur de Nieuport, the only Belgian scientist then known abroad, and the Baron de Reiffenberg. The French savants were refugees enjoying the hospitality of the tolerant Pays-Bas. Quetelet's intimacy with them, no doubt, helped to fix his political views and, in particular, to accentuate his leanings toward liberalism. They were a distinguished company, including such men as the poet Arnault, the artist David, the naturalist and traveler Bory de Saint-Vincent and the statesman and jurist Merlin de Douai.

In February, 1820, Quetelet was elected to membership in the Acadkmie royale des sciences et belles-lettres de Bruxelles. The meetings of the Academy, at this time, were attended by scarce half a dozen Belgian scholars; 2 interest in it had almost ceased. Quetelet was soon to become its moving spirit, to arouse it to renewed activity and to make it the inspiration of a new intellectual awakening throughout Belgium. His first year in the

1 The discovery of this curve was hailed as a brilliant achievement by his contemporaries. From Reichesberg's essay " Der beriihmte Statistiker, etc." p. 422, we learn that Raoul, a colleague of Garnier's and like him a Parisian and a mathematician, compared this discovery to that of Pascal's cycloid, saying that this alone sufficed to place Quetelet's name alongside that of the great geometrician. See also Mailly, Essai, pp. 115 and 150.

"Among these were the pharmacist Kickx, the chemist Van Mons, and Quetelet's teacher and friend, Gamier, "who strongly urged the election of his favorite pupil." Mailly, Essai, p. 135.

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Academy was marked by the presentation of two mathematical memoirs, the second of which, Nouvelle theorie des sections coniques considZrees dans le solide, brought him much honor.

During the next nine years, or until 1829, Quetelet devoted much attention to mathematics. Physics also interested him at this time. 1 His memoirs on these subjects, published in the Nouveau mkmoires of the Brussels Academy, and the Correspondance were both numerous and meritorious. 2 " The mere enumeration of his contributions to pure and mixed mathematics would occupy a very large space, and from their intrinsic merit, patient and conscientious research and earnest regard for truth, would alone have secured him a foremost place among the distinguished and scientific men of the present century." 3

During this period appeared the first volumes of the Correspondance mathfonatique et physique, 4 with Quetelet and Gamier as joint editors. Beginning with the third volume Quetelet alone was editor. Leading mathematicians and scientists of all Europe, and particularly of England, France, Germany and Holland, were contributors. 5 In this manner Quetelet came into touch

1 For the flattering reception given one of his memoirs on caustics, see Revue encyclopidique, Sept., 1825, vol. xxvii, pp. 794-795.

2 A general survey of them is given by Mailly, Essai, pp. 131-154. 3 F. J. Mouat, "Monsieur Quetelet," Journal of the Statistical

Society of London (1875), vol. xxxvii, p. 114.

4 Eleven vols.: vols, i and ii at Ghent, the others at Brussels. Vols. i-vi, 1825-1830; vols, vii-viii (not located); vols, ix-x-xi, 1837, 1838, 1839-

6 Among these were Herschel, Babbage, Wheatstone, Whewell, Chasles, Villerme, Ampere, Bouvard, Hachette, Gautier, Gauss, Hansteen, Olbers, De la Rive, Wartmann, Encke, Brandes and Hansen. Quetelet has given an account of the Correspondance in his Premier siecle de I'acadimie royale de Bruxelles (Brussels, 1872), pp. 36, et seq.

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with the foremost scholars of his time. The Correspondance covered every branch of mathematics, as well as mechanics, astronomy, physics, meteorology and statistics. 1 The character of the contributions made this journal, for a time, the foremost of its kind in Europe. 2 Its place was gradually taken by numerous publications at home and abroad covering the special fields more intensively.

But the chief work of Quetelet during these first years at Brussels was educational. We have seen that he came to the city in 1820 as professor of elementary mathematics at the Athenaeum. Four years later he succeeded M. Thiry in the chair of higher mathematics in this institution, 3 and at the same time began giving popular courses in geometry, probabilities, 4 physics and astronomy at the Museum, Brussels. The success of these popular lectures was so marked that, after two years, the Musee des sciences et des lettres was organized, by royal decree, on the basis of a plan drawn up by Quetelet. In this institution he began giving a course on the history of

Numerous references in these volumes show Quetelet's early familiarity with past and current statistical development. As an instance of the influence of Jean-Baptiste Fourier, we find in a note, vol. ii, p. 177, one of Quetelet's frequent references to Fourier's statement that, " Statistics will make progress only as it is retained in the hands of those versed in higher mathematics." The first six volumes only (I have not seen volumes vii and viii) have statistical articles from Quetelet.

2 Von John, Geschichte der Statistik (Stuttgart, 1884), p. 334.

3 Meanwhile he had spent three momentous months in Paris, where he met Laplace and others, who profoundly influenced his thought. See p. 20, infra.

4 His first course of instruction in probabilities was given in the scholastic year 1824-5 at the Athenaeum; this was the year immediately following his sojourn in Paris; the next year (1825-6) he gave an introductory course at the Museum.

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the sciences. x The following very characteristic statement, which he often referred to afterwards, was made at the opening 1 of this course :

The more advanced the sciences have become, the more they have tended to enter the domain of mathematics, which is a sort of center towards which they converge. We can judge of the perfection to which a science has come by the facility, more or less great, with which it may be approached by calculation. 2

He continued his courses on physics and astronomy at the Athenaeum until 1828, when he resigned on account of his appointment as astronomer at the observatory. But his lectures at the Musee des sciences et des lettres* were maintained until the absorption of the Musee by the University libi'e in 1834. But he was not allowed to remain long free from professional duties. Two years later (1836) he was made professor of astronomy and geodesy at the newly erected Ecole militaire at Brussels.

For his courses at the Mnske he prepared a number of elementary treatises which, on account of their clearness and exactness, obtained well-merited popularity. The first of these, Astro7iomie elhnentaire* was soon followed

1 This course bore fruit in the publication by him of " Apergude l'etat actuel des sciences mathematiques, chez les Beiges," prepared at the request of the British Association and published in Report of the British Association for the Advancement of Science, vol. v (1835), PP- 35~o6 and in Correspondance , vol. ix, pp. 1-47; Histoire des sciences mathematiques et physiques chez les Beiges (Brussels, 1864), and Sciences mathematiques et physiques chez les Beiges, au commencement du xix* siecle (Brussels, 1866).

2 Mailly, Essai, p. 159; found also in "Conclusions" of Instructions populaires sur le calcul des probabilitis, p. 230.

"These lectures after 1828 were in astronomy and physics.

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by the TraitS populaire d' astronomies a work of unusual merit. It was often reprinted in France and Belgium and was translated into several languages. Houzeau 2 says it was of almost epoch-making importance for the spread of the knowledge of astronomy; for, in addition to the wide circle of general readers whom it reached, it opened the way for popular instruction in the science of astronomy. It attained the distinction of being placed on the Index librorum prohibitorum by the Catholic Church, a fact which hastened and augmented its wide influence. About the same time he published his Positions de physique ou rksumk d?un cours de physique gknerale, 3 which was translated into English by Robert Wallace. 4 The translator says in his preface, "No other work in the English language contains such an extensive and succinct account of the different branches of physics or exhibits such a general knowledge of the whole field in so small a compass."

Among these treatises, besides the De la chaleur, 5 was the Instructions populaires sur le calcul des probability? which, Quetelet says, is "a resume of lectures given at the Musee as an introduction to my courses in physics and astronomy." 7 It bears on the title-page the significant aphorism Mundum numeri regunt. We meet in the preface several distinctly typical thoughts. Thus,

1 Paris, 1827. 2 Reichesberg, " Der beriihmte Statistiker," p. 433. 3 Three volumes, Paris, 1826.

4 Facts, Laws and Phenomena of Natural Philosophy, or a Summary of a Course in General Physics (Glasgow, 1835).

6 Brussels, 1828, 236pp. English translation by R. Beamish, London, 1839.

7 Preface, p. 1. These courses and this book are of later date than his trip to Paris from Dec, 1823, to Feb., 1824. See p. 19, et seq. infra.

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he says, " It has seemed to me that the theory {calcul) of probabilities ought to serve as the basis for the study of all the sciences, and particularly of the sciences of observation." " Since absolute certainty is impossible, and we can speak only of the probability of the fulfillment of a scientific expectation, a study of this theory should be a part of every man's education." The book is intended for the general reader, and the only prerequisite is a knowledge of the rules of arithmetic. In a most perspicuous manner he expounds the fundamental propositions of probabilities, Bernoulli's principle of agreement between experience and calculation, precision, the principle of least squares, the construction of a mortality table for a stationary population, and the calculation of probable and of average life. We cannot forbear another quotation :

Chance, that mysterious, much abused word, should be considered only a veil for our ignorance ; it is a phantom which exercises the most absolute empire over the common mind, accustomed to consider events only as isolated, but which is reduced to naught before the philosopher, whose eye embraces a long series of events and whose penetration is not led astray by variations, which disappear when he gives himself sufficient perspective to seize the laws of nature. 1

As a teacher and lecturer Quetelet was very successful. He was considerate and amiable, free from pedantry and conceit, and " endowed with a true talent for exposition." 2 His courses at the Museum attracted a great number of auditors from all ranks of society. Several of his pupils at the Athenaeum afterwards became distin-

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guished. Joseph Plateau, probably the most eminent of these, in dedicating to Quetelet his greatest work, Statique experimentale, etc., says : ]

Vous, qui avez ete 1' un des actifs promoteurs de la regeneration intellectuelle de la Belgique, et dont les travaux ont tant contribue a l'illustration de ce pays ; vous, qui avez guide mes premiers pas dans la carriere des sciences, et qui m' avez appris, par votre example, a exciter chez les jeunes gens l'amour des recherches ; vous, enfm, qui n'avez cesse d'etre pour moi un ami devoue, etc.

Quetelet is said to have taken an almost paternal interest in those of his students who showed special aptitude. He entertained them and opened to them freely the rich treasures of his own learning. 2

During these years of educational activity, an important series of events had taken place. Soon after his election to the Academy (1820) Quetelet began arousing interest in favor of an astronomical observatory. He made friends for the project on every hand, secured resolutions from the learned societies of Belgium and personally won the support of the minister of public instruction, M. Falck. Quetelet himself, having no experience with the methods and instruments of practical astronomy, was sent to Paris in December, 1823, at the expense of the state. He was kindly received at the Paris observatory by Arago and Bouvard, the latter of whom took special interest in instructing him in the knowledge of practical astronomy. 3

1 Bulletins de I'acad., 2nd series, vol. xxxvii, pp. 253-254, note.

2 Wolowski, " Eloge de Quetelet," Journal de la sociUi de statistique de Paris, vol. xv, p. 122.

3 For Quetelet's very interesting account of his introduction at the observatory at Paris, see " Notice biographique de M. Bouvard," Annuaire of the Brussels Academy (1844), vol. x, pp. 112-113.

Bouvard also introduced him to an inner circle of friends. Among these were Laplace, Poisson, Alexander von Humboldt and Fresnel. It is probable that Quetelet at this time formed the acquaintance of Fourier, from whom he received some instruction. 1 During his three months' 2 study in Paris, doubtless the most significant influence on the direction and character of his thought was that exerted by the immortal Laplace. Under this great mathematician, Quetelet received instruction in the theory of probabilities. 3 This course must have exerted a profound influence on Quetelet's scientific and philosophical views. The emphasis which Quetelet laid upon the principles of probabilities in his courses at the Museum during the years immediately following this sojourn in Paris has already been noted. 4 Quetelet's

*In the Physique sociale (Paris, 1869), vol. ii, notes, p. 446, Quetelet says, " During a temporary sojourn at Paris, about a half century ago, I had the honor of the kindly friendship of M. Bouvard, who was pleased to present me to the illustrious author of the MScanique cileste, of which he was the collaborator for a part of the calculations and observations. I had the good fortune then of being able to profit by the counsel of this great geometrician and to win the friendship of several of the most distinguished scholars of France, who ordinarily grouped themselves about him. Later Jean-Bapt. Fourier, . . . was pleased also to express to me sentiments of kindness ... I had the good fortune of enjoying the lessons of these two great masters and I still remember with gratitude the encouragement which they were pleased to give me."

2 Von John, Geschichte der Statistik, p. 233, says two years, but this is undoubtedly wrong. Quetelet himself says, " I arrived at Paris towards the end of 1823" and "I returned to Belgium in 1824," in sketch of Bouvard, Sciences mathimatiques et physiques au commencement du xix e siicle, pp. 611-614; Mailly, Essai, p. 172, says that Quetelet returned to Brussels at the beginning of 1824, and that on the first of March he addressed the Academy on the establishment of an observatory.

'See Reichesberg, " Der beruhmte Statistiker," p. 450.

4 Pp. 15 and 17, supra.

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writings previous to this time, show none of that emphasis on the importance of probabilities in scientific researches, which from this time on becomes more and more prominent. It would seem, therefore, that this contact with Laplace, and with others holding like views, implanted in Quetelet's mind the germs of those thoughts which afterwards developed into his conception of the social system and his methods of investigating its laws.

After his return to Brussels, the project of an observatory was advanced, but with discouraging slowness. In 1827 Quetelet was charged by the King with making the first purchase of instruments. In company with his longtime friend, Dandelin, he repaired to London. After attending to business matters, he spent a couple of months in visiting the universities, observatories and learned societies of England, Scotland and Ireland. 1 The following January he was named astronomer of the Royal Observatory at Brussels. However, delays in construction, due to differences between the city and national governments as to financial support and to the revolution of 1830, prevented his occupying the Observatory until 1832.

Meanwhile he traveled. From July to October, 1829, accompanied by his accomplished wife, 2 he made a tour through Holland and Germany. He visited numerous astronomers and men of science, inspected the chief observatories and made himself familiar with the state of astronomical science in Germany. One of the most memorable incidents of this eventful journey was Quetelet's visit with the great Goethe at Weimar. Here he

1 " Description des plusieurs observatoires d'Angleterre," Correspondance, vols, iv and v.

2 He had been married in 1825 to the daughter of the French physician and refugee, M. Curtet, who was also a niece of the chemist Van Mons.