b'* w .... \xc2\xabk # *-\\v* > \n\n\n\n% *\xe2\x80\xa2" \n\n\n\nV \n\n\n\n\n\n\n\n0* .LVL% *> \n\n\n\n^ "\xe2\x80\xa2-\xe2\x80\xa2\xe2\x80\xa2 ^ \n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\'*.<& \n\n\n\n\n\\ ^ .\' \n\n\n\nv \n\n\n\n\n\n*\xc2\xb0^ \n\n\n\n*> \n\n\n\n\n\n\n\n\n\n\n\n\n\n\nX/\' -** 4 *\xc2\xb0* \n\n\n\n\nV f \n\n\n\n\nV \'V* \n\n\n\n\n%/ .\'^K^v \\>/ :\xc2\xbb\\ V** \n\n\n\n\n\n\n\n\n\n\n\n\n\nI \n\n\n\n/ \n\n\n\nADOLPHE QUETELET 9?/ \n\nSTATISTICIAN \n\n\n\nBY \n\nFRANK H. HANKINS, A. B. \n\nSometime University Fellow in Statistics \n\n\n\nSUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS \n\nFOR THE DEGREE OF DOCTOR OF PHILOSOPHY \n\nIN THE \n\nFaculty of Political Science \nColumbia University \n\n\n\n1908 \n\n\n\nPREFATORY NOTE \n\n\n\nIt is not presumed that the dissertation here presented \nwill add much to the knowledge of Quetelet possessed \nby those who have read rather extensively in statistical \nliterature. But it is hoped that the increasing number \nof those who are becoming interested in Quetelet and \nhis work may find these pages useful. The first two \nchapters give brief sketches of the man, his work and \nhis place in the history of statistics. The last three \nchapters present what are believed to be the most im- \nportant of Ouetelet\'s statistical principles. These in- \nclude the conception of the Average Man as a type, the \nsignificance for social science of the regularities found in \nthe moral actions of man, and the theoretical basis of the \ndistribution of group phenomena about their type. \n\nGrateful acknowledgment should here be made to \nProfessor Henry L. Moore for directing me to this \nstimulating subject, and for continued helpfulness in its \npursuit. \n\n447] 5 \n\n\n\nCONTENTS \n\nCHAPTER I \nBiographical Sketch \n\nPAGE \n\nParentage \xe2\x80\x94 Youthful literary activity \xe2\x80\x94 At the University of Ghent; \nthe influence of Gamier \xe2\x80\x94 Called to the Athenaeum at Brussels \xe2\x80\x94 \nContributions to mathematics \xe2\x80\x94 Educational activity at Brussels ; \nhis elementary treatises and characteristics as a teacher \xe2\x80\x94 Found- \ning of the Brussels Observatory; sojourn in Paris \xe2\x80\x94 Travels in \nGermany, Italy and Sicily \xe2\x80\x94 Research work at the Observatory \xe2\x80\x94 \nStudies in meteorology and terrestrial physics \xe2\x80\x94 His activity in \nconnection with V Acaditnie royale de Belgique \xe2\x80\x94 Activity as an \nofficial statistician \xe2\x80\x94 Founding of the Commission centrale de \nstatistique, of the Statistical Society of London and of the Inter- \nnational Statistical Congress \xe2\x80\x94 Stroke of apoplexy in 1855 \xe2\x80\x94 Mem- \nber of many learned societies \xe2\x80\x94 His personality \xe2\x80\x94 Home life \xe2\x80\x94 The \nBrussels statue 9 \n\nCHAPTER II \n\nQUETELET IN THE HlSTORY OF STATISTICS \n\nTwo lines of development in statistical literature \xe2\x80\x94 One of these, \nthe German University \' \'\' Statistic ,\'\' " traced through the writings \nof Muenster, Conring, Achenwall, Von Schlozer and Busching \xe2\x80\x94 \nThe growth of official statistics and the gradual modification of \nthe university discipline \xe2\x80\x94 Quetelet\'s contribution to this change \n-\xe2\x80\x94A second line of statistical development traced through the \nworks of Graunt, Petty and others of the School of Political \nArithmetic, Derham, Siissmilch, and the first formulators of \nmortality tables \xe2\x80\x94 The influence of Malthus, Laplace, and espe- \ncially of J. B. Fourier \xe2\x80\x94 Quetelet\'s contribution to this line of \ndevelopment, treated under (I) population statistics, (II) moral \nstatistics; (III) technique and (IV) application of the normal law of \nerror to the physical measurements of men \xe2\x80\x94 Summary .... 36 \n\nCHAPTER III \n\nThe Average Man \n\nImportance of this concept in Quetelet\'s writings \xe2\x80\x94 Survey of its \ndevelopment\xe2\x80\x94 Its generalization in Du Systeme social \xe2\x80\x94 Studies \nto determine the qualities of the average man \xe2\x80\x94 Role of the aver- \nage man in various sciences \xe2\x80\x94 Objections: the average man cannot \nbe constructed as a composite being \xe2\x80\x94 The average as the type of \n449] 7 \n\n\n\nCONTENTS [450 \n\n\n\nPAGE \n\nperfection \xe2\x80\x94 Distinction of results obtained in some of Quetelet\'s \nstudies \xe2\x80\x94 The average man as a biological type \xe2\x80\x94 The permanence \nof the type \xe2\x80\x94 Quetelet\'s approach to the doctrine of selection by \nenvironment 62 \n\nCHAPTER IV \n\nMoral Statistics \nIntroductory\xe2\x80\x94 Definition \xe2\x80\x94 Quetelet\'s principal works on moral sta- \ntistics and his emphasis upon statistical regularities \xe2\x80\x94 His explana- \ntion of these regularities \xe2\x80\x94 The viewpoint of science and its bearing \nupon the doctrine of free will and upon the explanation of statis- \ntical regularities \xe2\x80\x94 Explanation of the fluctuations in the numbers \nfrom year to year \xe2\x80\x94 And of the variations about an average \xe2\x80\x94 \nBecause of the way in which they are formed, the regularities \nexert no compulsion over the individual \xe2\x80\x94 Significance of the reg- \nularities for the doctrine of free will \xe2\x80\x94 Bearing of statistical inquiry \non this doctrine \xe2\x80\x94 The statistical regularities and social laws \xe2\x80\x94 The \ndifficulty of establishing quantitative relations between social \nevents and their conditions \xe2\x80\x94 The effect of the dynamic character \nof social life upon statistical regularities and their laws \xe2\x80\x94 Two basic \nprinciples of method in moral statistics \xe2\x80\x94 And their importance \nfor the quantitative study of social phenomena 83 \n\nCHAPTER V \n\nStatistical Method \n\nThe basis of statistical method found in the variability of organic \nand social phenomena about type forms \xe2\x80\x94 The probability of an \nevent when all its chances are known \xe2\x80\x94 Inductions from exper- \nience when the number of chances is unknown \xe2\x80\x94 The distribution \nof chances when their number is small\xe2\x80\x94 Agreement between \ntheory and experience tested \xe2\x80\x94 The distribution of chances when \ntheir number is very large \xe2\x80\x94 Quetelet\'s scale of possibility and \nprecision \xe2\x80\x94 The derivation of this scale explained \xe2\x80\x94 The curve rep- \nresenting the distribution of chances when their number reaches \nthe conceptual limit \xe2\x80\x94 Theory provides for extremely improbable \ncombinations, but such are not met with in experience \xe2\x80\x94 Quetelet\'s \ndistinction of "means properly so called" from "arithmetic \nmeans " \xe2\x80\x94 The theory of the distribution of chances related to the \ntheory of the distribution of errors of measurement and to the \ndistribution of biological measurements\xe2\x80\x94 Description of the ap- \nplication of Quetelet\'s scale to a statistical problem \xe2\x80\x94 The probable \nerror \xe2\x80\x94 The normal curve only one of many possible forms \xe2\x80\x94 The \nsignificance of narrowing limits of deviation \xe2\x80\x94 Quetelet\'s classifi- \ncation of causes \xe2\x80\x94 Constant causes not revealed by statistical in- \nquiry \xe2\x80\x94 Variable causes \xe2\x80\x94 Kinds of accidental causes \xe2\x80\x94 Causes clas- \nsified as general and minute \xe2\x80\x94 Causes studied by correlation . . . 106 \n\n\n\nCHAPTER I \n\nBIOGRAPHICAL SKETCH \n\nIt might be set down as a rule of mental conduct that, \nwhen we become interested in the achievements of a \ngreat man, we desire a more intimate acquaintance with \nhis personality and with the routine of his daily life. \nThe deeds of statesmen and warriors are readily appre- \nciated by the generality of men. This is due, not only \nto their conspicuousness and to the glamour and fascina- \ntion attending those who achieve notable success in the \nworld of affairs, but to the immediate responsiveness of \nhuman emotions to the heroic. But not infrequently \ndoes it happen that many years are required for the most \nimportant contributions to knowledge to become the \npossession of an extended and appreciative group of \ninitiated disciples. Herein is found the reason for this \nbrief sketch of Adolphe Quetelet. 1 Not that his scientific \nachievements have been passed by with little or no com- \nment, but that there is to-day a rapidly widening group \n\nx Quetelet\'s name is sometimes accented \xe2\x80\x94 Quetelet. There is, how- \never, abundant reason for omitting the accent. In the Nouveau Mim- \noires, the Bulletins and the Annuaire of the Brussels Academy, in the \nAnnales and the Annuaire of the Brussels Observatory, and in a num- \nber of his works brought out at Brussels, the name is uniformly unac- \ncented. When it is recalled that Quetelet was Secretary of the Academy \nfor forty years and Director of the Observatory for even a longer term, \nit seems certain that he himself did not accent his name. Moreover in \nplaces where he has signed his name it is not accented. The accented \nspellings seem to be due to Paris publishers. \n\n45i] 9 \n\n\n\nIO ADOLPHE QUETELET AS STATISTICIAN [452 \n\nof scholars who appreciate the distinctive merit of his \ndevelopment of statistical methods of research. It is \nbelieved that such will be interested in a brief account of \nthe man himself. J \n\nBorn on the twenty- second of February, 1796, in the \nancient and historic town of Ghent, Quetelet grew up \nthere amid the stirring scenes which marked the fall of \nthe old regime and the rise of the empire of the brilliant \nand ambitious Napoleon. Little is known of his parents. \nNo mention is anywhere made of his mother except that \nher maiden name was Anne-Frangoise Vandevelde. His \nfather, Frangois-Augustin-Jacques-Henri Quetelet, is \nknown to have been born at Ham, in Picardy, in 1756. \nBeing of a somewhat adventurous spirit, Frangois crossed \nthe English Channel at an early age and is said to have \nbecome an English citizen. He soon became secretary \nto a Scotch nobleman, with whom he spent several years \ntraveling on the Continent and sojourning in Italy. He \nthen settled permanently at Ghent, about 1787. Here \nhe was at length elevated to the position of a municipal \nofficer, in which capacity he rendered valuable and well- \n\n1 The chief source for this sketch is the \' \' Essai sur la vie et les ouv- \nrages de Quetelet," by Edward Mailly, one of Quetelet\'s students and \nhis assistant for thirty-seven years, in the Annuaire de V acadimie \nroyale des sciences, des lettres et des beaux-arts de Belgique (Brussels, \n1875), vol. xli, pp. 109-297. In addition should be mentioned the fol- \nlowing: (1) Naum Reichesberg, " Der beriihmte Statistiker, Adolphe \nQuetelet, sein Leben und sein Wirken," Zeitschrift fur schweizerische \nStatistik (Berne, 1893), Jahrg. xxxii, pp. 418-460; (2) the " Discours " \npronounced at Quetelet\'s funeral, Bulletins de V acadhnie royale des \nsciences, des lettres et des beaux-arts de Belgique (Brussels, 1874), \nSecond Series, vol. xxxvii, pp. 244-206; (3) Mailly, "Notice sur \nAdolphe Quetelet," ibid., vol. xxxviii, pp. 816-844; (4) Wolowski, \n" Eloge de Quetelet," Journal de la sociiti de statistique de Paris \n(1874), vol. xv, pp. 118-126. Other less important references will be \nfound in the notes. \n\n\n\n4 ^3] BIOGRAPHICAL SKETCH IX \n\nesteemed services. He died in 1803, when Adolphe was \nbut a boy of seven. \n\nIt was thus that, upon his graduation from the Lyceum \nat Ghent, young Quetelet was compelled, at the age of \nseventeen, to turn his talents to good account. He \nspent the next year as teacher of mathematics in a \nprivate school at Audenaerde. x On his nineteenth birth- \nday he was chosen instructor in mathematics at the \nnewly organized college in his native city. \n\nThe time between his election and the opening of the \nUniversity in October, 181 7, seems to have been spent \nlargely in literary composition. In collaboration with \nG. Dandelin, a former student at the Lyceum, he prepared \nthe libretto for an opera "en un acte, en prose et a grand \nspectacle," entitled Jean Second ou Charles Quint dans \nles murs de Gand. This was successfully presented at \nGhent, and led to the partial construction of two more \ndramas by the same authors. Quetelet published quite \na number of poems, 2 and until the age of thirty he con- \ntinued to exercise his poetical talents as pastime and \nrelief from his scientific studies. His poems were of a \nserious tone, but were well received by both public and \ncritics. We may mention here an Essai sur la romance, \nwhich Quetelet brought out in 1823. In this, from a \nsurvey of romance among different peoples, he found the \norigin of romance in the days of chivalry. This essay, \ntogether with translations, in prose and in verse, of Ger- \nman, English, Italian and Spanish romances, shows \nQuetelet\'s wide acquaintance at that early age with the \n\nx One of his students here was M. Liedts, who afterwards, as minister \nof the interior, authorized the Commission centrale de la statistique. \n\n2 Chiefly in the Annates belgiques and Etudes et tecons francaises de \nlittirature et de morale. Mailly, Essai, pp. 114-131, quotes at length \nfrom these poems. \n\n\n\n12 ADOLPHE QUETELET AS STATISTICIAN [454 \n\nvarious European literatures. Mailly, who must be \nviewed as a friendly critic, believes the Essai sur la \nromance and many of the poems deserving of republi- \ncation. \n\nDuring the three years of his service at the College of \nGhent the most important influence brought to bear \nupon him was that of Jean Guillaume Gamier, 1 professor \nof astronomy and higher mathematics. This expert \nmathematician and refined scholar was called from Paris \nto the University of Ghent by the King of the Low \nCountries in 181 7. His influence over Quetelet\'s eager, \nyouthful spirit was quite decisive. Quetelet says of him, \n\nLittle by little his conversation, always instructive and ani- \nmated, gave a special direction to my tastes, which would \nhave led me by preference towards letters. I resolved to \ncomplete my scientific studies and followed the courses in \nadvanced mathematics given by M. Gamier. It was at the \nsame time agreed by us that, in order to relieve him in his \nwork, I should give some of the other courses with which he \nwas charged. I thus found myself his pupil and his colleague. 2 \n\nThe aspiring dramatist soon found a favorite occupation \nin the reading of Pascal. \n\nQuetelet was the first to receive the degree of doctor \nof science from the new university. His dissertation was \nan original contribution of much importance to the \n\n1 1 766- 1 840. He was examiner at l\'Ecole polytechnique, 1795-1800; \nadjunct professor with Lagrange at the same place, 1800-1802; one of \nPoisson\'s instructors and an intimate of J. B. Fourier. See Nouvelle bio- \ngraphie ge\'ne\'rale (Paris, 1858), vol. xix, also " Notice sur J. G. Gamier," \nby Quetelet, in the Annuaire de Vacadimie royale de Bruxelles (1841), \nvol. 7; and sketch by Quetelet in Sciences mathimatiques et physiques \nau commencement du xixe Steele (Brussels, 1867). \n\n2 " Notice sur J. G. Gamier," Annuaire de Vacad. roy. de Brux. \n(1841), vol. vii, pp. 200-201. \n\n\n\n45 5] BIOGRAPHICAL SKETCH l ^ \n\ntheory of conic sections : it demonstrated two new prop- \nositions, one of which developed the properties of a new \ncurve, the "focale." 1 In October of this same year \n(1819) he was called to the chair of elementary mathe- \nmatics in the Athenaeum at Brussels. Repairing thither \nat once, he was soon in the midst of a learned circle of \nBelgian and French scholars. Among the former may \nbe mentioned the old Commandeur de Nieuport, the only \nBelgian scientist then known abroad, and the Baron de \nReiffenberg. The French savants were refugees enjoying \nthe hospitality of the tolerant Pays-Bas. Quetelet\'s inti- \nmacy with them, no doubt, helped to fix his political \nviews and, in particular, to accentuate his leanings toward \nliberalism. They were a distinguished company, includ- \ning such men as the poet Arnault, the artist David, the \nnaturalist and traveler Bory de Saint-Vincent and the \nstatesman and jurist Merlin de Douai. \n\nIn February, 1820, Quetelet was elected to member- \nship in the Acadkmie royale des sciences et belles-lettres de \nBruxelles. The meetings of the Academy, at this time, \nwere attended by scarce half a dozen Belgian scholars; 2 \ninterest in it had almost ceased. Quetelet was soon to be- \ncome its moving spirit, to arouse it to renewed activity \nand to make it the inspiration of a new intellectual \nawakening throughout Belgium. His first year in the \n\n1 The discovery of this curve was hailed as a brilliant achievement by \nhis contemporaries. From Reichesberg\'s essay " Der beriihmte Statis- \ntiker, etc." p. 422, we learn that Raoul, a colleague of Garnier\'s and \nlike him a Parisian and a mathematician, compared this discovery to \nthat of Pascal\'s cycloid, saying that this alone sufficed to place Quete- \nlet\'s name alongside that of the great geometrician. See also Mailly, \nEssai, pp. 115 and 150. \n\n"Among these were the pharmacist Kickx, the chemist Van Mons, \nand Quetelet\'s teacher and friend, Gamier, "who strongly urged the \nelection of his favorite pupil." Mailly, Essai, p. 135. \n\n\n\nI4 ADOLPHE QUETELET AS STATISTICIAN [456 \n\nAcademy was marked by the presentation of two mathe- \nmatical memoirs, the second of which, Nouvelle theorie \ndes sections coniques considZrees dans le solide, brought \nhim much honor. \n\nDuring the next nine years, or until 1829, Quetelet \ndevoted much attention to mathematics. Physics also \ninterested him at this time. 1 His memoirs on these sub- \njects, published in the Nouveau mkmoires of the Brussels \nAcademy, and the Correspondance were both numerous \nand meritorious. 2 " The mere enumeration of his con- \ntributions to pure and mixed mathematics would occupy \na very large space, and from their intrinsic merit, patient \nand conscientious research and earnest regard for truth, \nwould alone have secured him a foremost place among \nthe distinguished and scientific men of the present \ncentury." 3 \n\nDuring this period appeared the first volumes of the \nCorrespondance mathfonatique et physique, 4 with Quet- \nelet and Gamier as joint editors. Beginning with the \nthird volume Quetelet alone was editor. Leading mathe- \nmaticians and scientists of all Europe, and particularly of \nEngland, France, Germany and Holland, were con- \ntributors. 5 In this manner Quetelet came into touch \n\n1 For the flattering reception given one of his memoirs on caustics, \nsee Revue encyclopidique, Sept., 1825, vol. xxvii, pp. 794-795. \n\n2 A general survey of them is given by Mailly, Essai, pp. 131-154. \n3 F. J. Mouat, "Monsieur Quetelet," Journal of the Statistical \n\nSociety of London (1875), vol. xxxvii, p. 114. \n\n4 Eleven vols.: vols, i and ii at Ghent, the others at Brussels. Vols. \ni-vi, 1825-1830; vols, vii-viii (not located); vols, ix-x-xi, 1837, 1838, \n1839- \n\n6 Among these were Herschel, Babbage, Wheatstone, Whewell, \nChasles, Villerme, Ampere, Bouvard, Hachette, Gautier, Gauss, Hans- \nteen, Olbers, De la Rive, Wartmann, Encke, Brandes and Hansen. \nQuetelet has given an account of the Correspondance in his Premier \nsiecle de I\'acadimie royale de Bruxelles (Brussels, 1872), pp. 36, et seq. \n\n\n\n4 57] BIOGRAPHICAL SKETCH 1 c ) \n\nwith the foremost scholars of his time. The Correspond- \nance covered every branch of mathematics, as well as \nmechanics, astronomy, physics, meteorology and statis- \ntics. 1 The character of the contributions made this \njournal, for a time, the foremost of its kind in Europe. 2 \nIts place was gradually taken by numerous publications \nat home and abroad covering the special fields more in- \ntensively. \n\nBut the chief work of Quetelet during these first years \nat Brussels was educational. We have seen that he came \nto the city in 1820 as professor of elementary mathe- \nmatics at the Athenaeum. Four years later he succeeded \nM. Thiry in the chair of higher mathematics in this insti- \ntution, 3 and at the same time began giving popular \ncourses in geometry, probabilities, 4 physics and astronomy \nat the Museum, Brussels. The success of these popular \nlectures was so marked that, after two years, the Musee \ndes sciences et des lettres was organized, by royal decree, \non the basis of a plan drawn up by Quetelet. In this \ninstitution he began giving a course on the history of \n\nNumerous references in these volumes show Quetelet\'s early famil- \niarity with past and current statistical development. As an instance of \nthe influence of Jean-Baptiste Fourier, we find in a note, vol. ii, p. 177, \none of Quetelet\'s frequent references to Fourier\'s statement that, " Sta- \ntistics will make progress only as it is retained in the hands of those \nversed in higher mathematics." The first six volumes only (I have \nnot seen volumes vii and viii) have statistical articles from Quetelet. \n\n2 Von John, Geschichte der Statistik (Stuttgart, 1884), p. 334. \n\n3 Meanwhile he had spent three momentous months in Paris, where \nhe met Laplace and others, who profoundly influenced his thought. \nSee p. 20, infra. \n\n4 His first course of instruction in probabilities was given in the \nscholastic year 1824-5 at the Athenaeum; this was the year immediately \nfollowing his sojourn in Paris; the next year (1825-6) he gave an intro- \nductory course at the Museum. \n\n\n\nl6 ADOLPHE QUETELET AS STATISTICIAN [458 \n\nthe sciences. x The following very characteristic state- \nment, which he often referred to afterwards, was made \nat the opening 1 of this course : \n\nThe more advanced the sciences have become, the more they \nhave tended to enter the domain of mathematics, which is a \nsort of center towards which they converge. We can judge \nof the perfection to which a science has come by the facility, \nmore or less great, with which it may be approached by calcu- \nlation. 2 \n\nHe continued his courses on physics and astronomy at \nthe Athenaeum until 1828, when he resigned on account \nof his appointment as astronomer at the observatory. \nBut his lectures at the Musee des sciences et des lettres* \nwere maintained until the absorption of the Musee by the \nUniversity libi\'e in 1834. But he was not allowed to re- \nmain long free from professional duties. Two years \nlater (1836) he was made professor of astronomy and \ngeodesy at the newly erected Ecole militaire at Brussels. \n\nFor his courses at the Mnske he prepared a number of \nelementary treatises which, on account of their clearness \nand exactness, obtained well-merited popularity. The \nfirst of these, Astro7iomie elhnentaire* was soon followed \n\n1 This course bore fruit in the publication by him of " Apergude l\'etat \nactuel des sciences mathematiques, chez les Beiges," prepared at the \nrequest of the British Association and published in Report of the British \nAssociation for the Advancement of Science, vol. v (1835), PP- 35~o6 \nand in Correspondance , vol. ix, pp. 1-47; Histoire des sciences mathe- \nmatiques et physiques chez les Beiges (Brussels, 1864), and Sciences \nmathematiques et physiques chez les Beiges, au commencement du xix* \nsiecle (Brussels, 1866). \n\n2 Mailly, Essai, p. 159; found also in "Conclusions" of Instruc- \ntions populaires sur le calcul des probabilitis, p. 230. \n\n"These lectures after 1828 were in astronomy and physics. \n\n4 Paris, 1826. \n\n\n\n4 ^ 9 ] BIOGRAPHICAL SKETCH jy \n\nby the TraitS populaire d\' astronomies a work of unusual \nmerit. It was often reprinted in France and Belgium \nand was translated into several languages. Houzeau 2 \nsays it was of almost epoch-making importance for the \nspread of the knowledge of astronomy; for, in addition \nto the wide circle of general readers whom it reached, it \nopened the way for popular instruction in the science of \nastronomy. It attained the distinction of being placed \non the Index librorum prohibitorum by the Catholic \nChurch, a fact which hastened and augmented its wide \ninfluence. About the same time he published his Posi- \ntions de physique ou rksumk d?un cours de physique gkne- \nrale, 3 which was translated into English by Robert Wal- \nlace. 4 The translator says in his preface, "No other \nwork in the English language contains such an extensive \nand succinct account of the different branches of physics \nor exhibits such a general knowledge of the whole field \nin so small a compass." \n\nAmong these treatises, besides the De la chaleur, 5 \nwas the Instructions populaires sur le calcul des proba- \nbility? which, Quetelet says, is "a resume of lectures \ngiven at the Musee as an introduction to my courses in \nphysics and astronomy." 7 It bears on the title-page the \nsignificant aphorism Mundum numeri regunt. We meet \nin the preface several distinctly typical thoughts. Thus, \n\n1 Paris, 1827. 2 Reichesberg, " Der beriihmte Statistiker," p. 433. \n3 Three volumes, Paris, 1826. \n\n4 Facts, Laws and Phenomena of Natural Philosophy, or a Summary \nof a Course in General Physics (Glasgow, 1835). \n\n5 Brussels (?), 1832. \n\n6 Brussels, 1828, 236pp. English translation by R. Beamish, London, \n1839. \n\n7 Preface, p. 1. These courses and this book are of later date than his \ntrip to Paris from Dec, 1823, to Feb., 1824. See p. 19, et seq. infra. \n\n\n\n1$ ADOLPHE QUETELET AS STATISTICIAN [ 4 6o \n\nhe says, " It has seemed to me that the theory {calcul) \nof probabilities ought to serve as the basis for the study \nof all the sciences, and particularly of the sciences of \nobservation." " Since absolute certainty is impossible, \nand we can speak only of the probability of the fulfill- \nment of a scientific expectation, a study of this theory \nshould be a part of every man\'s education." The book \nis intended for the general reader, and the only prere- \nquisite is a knowledge of the rules of arithmetic. In a \nmost perspicuous manner he expounds the fundamental \npropositions of probabilities, Bernoulli\'s principle of \nagreement between experience and calculation, precision, \nthe principle of least squares, the construction of a mor- \ntality table for a stationary population, and the calcula- \ntion of probable and of average life. We cannot forbear \nanother quotation : \n\nChance, that mysterious, much abused word, should be con- \nsidered only a veil for our ignorance ; it is a phantom which \nexercises the most absolute empire over the common mind, \naccustomed to consider events only as isolated, but which is \nreduced to naught before the philosopher, whose eye embraces \na long series of events and whose penetration is not led astray \nby variations, which disappear when he gives himself suffi- \ncient perspective to seize the laws of nature. 1 \n\nAs a teacher and lecturer Quetelet was very successful. \nHe was considerate and amiable, free from pedantry and \nconceit, and " endowed with a true talent for exposi- \ntion." 2 His courses at the Museum attracted a great \nnumber of auditors from all ranks of society. Several \nof his pupils at the Athenaeum afterwards became distin- \n\n1 " Conclusion," p. 230; see also p. 8. \n\'Mailly, Essai, p. 156. \n\n\n\n4 6i] BIOGRAPHICAL SKETCH T g \n\nguished. Joseph Plateau, probably the most eminent \nof these, in dedicating to Quetelet his greatest work, \nStatique experimentale, etc., says : ] \n\nVous, qui avez ete 1\' un des actifs promoteurs de la regeneration \nintellectuelle de la Belgique, et dont les travaux ont tant \ncontribue a l\'illustration de ce pays ; vous, qui avez guide mes \npremiers pas dans la carriere des sciences, et qui m\' avez \nappris, par votre example, a exciter chez les jeunes gens \nl\'amour des recherches ; vous, enfm, qui n\'avez cesse d\'etre \npour moi un ami devoue, etc. \n\nQuetelet is said to have taken an almost paternal \ninterest in those of his students who showed special ap- \ntitude. He entertained them and opened to them freely \nthe rich treasures of his own learning. 2 \n\nDuring these years of educational activity, an import- \nant series of events had taken place. Soon after his \nelection to the Academy (1820) Quetelet began arousing \ninterest in favor of an astronomical observatory. He \nmade friends for the project on every hand, secured \nresolutions from the learned societies of Belgium and \npersonally won the support of the minister of public in- \nstruction, M. Falck. Quetelet himself, having no ex- \nperience with the methods and instruments of practical \nastronomy, was sent to Paris in December, 1823, at the \nexpense of the state. He was kindly received at the \nParis observatory by Arago and Bouvard, the latter of \nwhom took special interest in instructing him in the \nknowledge of practical astronomy. 3 \n\n1 Bulletins de I\'acad., 2nd series, vol. xxxvii, pp. 253-254, note. \n\n2 Wolowski, " Eloge de Quetelet," Journal de la sociUi de statistique \nde Paris, vol. xv, p. 122. \n\n3 For Quetelet\'s very interesting account of his introduction at the \nobservatory at Paris, see " Notice biographique de M. Bouvard," An- \nnuaire of the Brussels Academy (1844), vol. x, pp. 112-113. \n\n\n\n20 ADOLPHE QUETELET AS STATISTICIAN [462 \n\nBouvard also introduced him to an inner circle of \nfriends. Among these were Laplace, Poisson, Alexander \nvon Humboldt and Fresnel. It is probable that Quetelet \nat this time formed the acquaintance of Fourier, from \nwhom he received some instruction. 1 During his three \nmonths\' 2 study in Paris, doubtless the most significant \ninfluence on the direction and character of his thought \nwas that exerted by the immortal Laplace. Under this \ngreat mathematician, Quetelet received instruction in \nthe theory of probabilities. 3 This course must have ex- \nerted a profound influence on Quetelet\'s scientific and \nphilosophical views. The emphasis which Quetelet laid \nupon the principles of probabilities in his courses at the \nMuseum during the years immediately following this \nsojourn in Paris has already been noted. 4 Quetelet\'s \n\n*In the Physique sociale (Paris, 1869), vol. ii, notes, p. 446, Quetelet \nsays, " During a temporary sojourn at Paris, about a half century ago, \nI had the honor of the kindly friendship of M. Bouvard, who was \npleased to present me to the illustrious author of the MScanique cileste, \nof which he was the collaborator for a part of the calculations and ob- \nservations. I had the good fortune then of being able to profit by the \ncounsel of this great geometrician and to win the friendship of several \nof the most distinguished scholars of France, who ordinarily grouped \nthemselves about him. Later Jean-Bapt. Fourier, . . . was pleased \nalso to express to me sentiments of kindness ... I had the good fortune \nof enjoying the lessons of these two great masters and I still remember \nwith gratitude the encouragement which they were pleased to give me." \n\n2 Von John, Geschichte der Statistik, p. 233, says two years, but this is \nundoubtedly wrong. Quetelet himself says, " I arrived at Paris towards \nthe end of 1823" and "I returned to Belgium in 1824," in sketch of \nBouvard, Sciences mathimatiques et physiques au commencement du \nxix e siicle, pp. 611-614; Mailly, Essai, p. 172, says that Quetelet re- \nturned to Brussels at the beginning of 1824, and that on the first of \nMarch he addressed the Academy on the establishment of an obser- \nvatory. \n\n\'See Reichesberg, " Der beruhmte Statistiker," p. 450. \n\n4 Pp. 15 and 17, supra. \n\n\n\n4 6 3 ] BIOGRAPHICAL SKETCH 2 I \n\nwritings previous to this time, show none of that em- \nphasis on the importance of probabilities in scientific \nresearches, which from this time on becomes more and \nmore prominent. It would seem, therefore, that this \ncontact with Laplace, and with others holding like views, \nimplanted in Quetelet\'s mind the germs of those thoughts \nwhich afterwards developed into his conception of the \nsocial system and his methods of investigating its laws. \n\nAfter his return to Brussels, the project of an observa- \ntory was advanced, but with discouraging slowness. In \n1827 Quetelet was charged by the King with making the \nfirst purchase of instruments. In company with his long- \ntime friend, Dandelin, he repaired to London. After \nattending to business matters, he spent a couple of \nmonths in visiting the universities, observatories and \nlearned societies of England, Scotland and Ireland. 1 The \nfollowing January he was named astronomer of the Royal \nObservatory at Brussels. However, delays in construc- \ntion, due to differences between the city and national \ngovernments as to financial support and to the revolution \nof 1830, prevented his occupying the Observatory until \n1832. \n\nMeanwhile he traveled. From July to October, 1829, \naccompanied by his accomplished wife, 2 he made a tour \nthrough Holland and Germany. He visited numerous \nastronomers and men of science, inspected the chief \nobservatories and made himself familiar with the state of \nastronomical science in Germany. One of the most \nmemorable incidents of this eventful journey was Quet- \nelet\'s visit with the great Goethe at Weimar. Here he \n\n1 " Description des plusieurs observatoires d\'Angleterre," Corres- \npondance, vols, iv and v. \n\n2 He had been married in 1825 to the daughter of the French physician \nand refugee, M. Curtet, who was also a niece of the chemist Van Mons. \n\n\n\n22 ADOLPHE QUETELET AS STATISTICIAN [464 \n\nspent eight days, at the time of Goethe\'s eightieth birth- \nday, discussing, among many things, the latter\'s optical \ntheories. This afforded the greatest pleasure to Goethe, \nas well as to Quetelet and his wife, and led to an un- \nusually felicitous correspondence. 1 \n\nThe following summer he made a four months\' tour \nthrough Italy and Sicily, making the acquaintance of \nscholars and learned societies. On this trip, as also on \nthe preceding, he made numerous observations on the \nstrength of terrestrial magnetic currents. 2 \n\nAfter his installation at the Observatory, in 1832, his \nlife for the next forty-two years was devoted almost en- \ntirely to three major interests : the various lines of re- \nsearch carried on at the Observatory, the work of the \nAcademy and his statistical inquiries. These three \nspheres of activity will be treated separately. \n\nAt the Observatory a vast amount of research work \nwas organized, dealing with astronomy, meteorology \nand physics of the globe. 3 Quetelet had always been \ninterested in falling stars. In his doctor\'s dissertation \nhe had defended Olbers\'s theory of the lunar origin of \naeroliths. As early as 1826 he developed a method for \n\n: Quetelet has given two accounts of the sojourn at Weimar: " Notes \nextraites d\'un voyage scientifique, fait en Allemagne pendant l\'ete de \n1829," in the Correspo?idance , vol. vii, pp. 126-148, 161-178 and 225-239, \nand " Johann Wolfgang Goethe," in Sciences math, et phys. chez les \nBeiges au commencement du xixe Steele, pp. 656-669. There is another \naccount, "Quetelet bei Goethe," in Festgabe fur Johannes Conrad \n(Jena, 1898), pp. 31 1-334- \n\n" Results published in Nouveaux mimoires, vol. vi, and Correspond- \nance, vol. vi. He made a three months\' trip through Italy and Tyrol \nbeginning in August, 1839, at which time he gathered another series of \nmagnetic observations. \n\n3 At the Observatory Quetelet had almost from the beginning two as- \nsistants, one of whom was Edward Mailly, the author of the Essai \nwhich has been the chief source for this sketch. \n\n\n\n465] BIOGRAPHICAL SKETCH 2 $ \n\ncalculating the height of a meteor from two observa- \ntions. 1 This plan, being well received, enabled Quetelet \nto organize simultaneous observations in four Belgian \ncities. At this time we find him emphasizing what must \nbe considered one of his most important contributions \nto the various fields of science in which he labored, \nnamely, the necessity of simultaneous observations at \ndifferent points. His introduction of it here into astro- \nnomical research was followed, as we shall see, by his \ndevelopment of it on a large scale in meteorological and \nphysical research and by his efforts to secure uniform \ninternational statistics. At the same time he emphasized \nthe necessity of correcting astronomical observations for \nthe personal equation in order to render them com- \nparable. In 1836 his observations of falling stars led to \nthe discovery that the nights of August ten and eleven, \nlike those of November thirteen and fourteen, were con- \nspicuous for meteoric showers. \n\nAmong other facts connected with his astronomical \nactivity, we may note a series of observations of sunspots, \nbegun in 1832; observations on tides on the coast of \nBelgium, undertaken at the request of Whewell in 1835 J \nthe commencement, the same year, upon the initiative of \nSir John Herschel, of hourly meteorological observa- \ntions at the time of the solstices and equinoxes, but, \nafter 1841, made every two hours throughout the year; \nmagnetic observations, begun in 1840 at the request of \nthe Royal Astronomical Society of London, and made at \nfive-minute intervals during one twenty-four hours each \nmonth; the erection from 1838 to 1839, at government \nrequest, of small telescopes in the five largest cities out- \n\n1 See Correspondance, vol. i, also Report of the British Association \nfor the Advancement of Science, 1833, p. 489; 1835, p. xxxviii. \n\n\n\n24 ADOLPHE QUETELET AS STATISTICIAN [^ \n\nside of Brussels, and of sundials in forty-one towns, in \norder to guarantee uniformity of time throughout the \nkingdom; and the determination of the difference in \nlongitude between Greenwich and Brussels. The publi- \ncation of the Annuaire and of the Ann ales of the Ob- \nservatory began in 1834. In 1854 a volume entitled \nAlmanack skculaire was issued from the Observatory. \nAfter 1857 the. work of the Observatory was carried on \nlargely by Quetelet\'s only son, Ernest, who became an \naccomplished astronomer and his father\'s successor as \ndirector. \n\nBut Quetelet\'s dominant scientific interest seems to \nhave been other than strictly astronomical. The study \nof meteorological and physical phenomena, especially \ntheir periodicity, absorbed much of his attention. These \nobservations began with the temperature of the earth, 1 \nand the intensity of atmospheric electricity and were ex- \ntended to include the variations of barometric pressure \nand periodic phenomena of the life of plants and animals. 2 \nHis study of atmospheric electricity and its annual and \ndiurnal variations, established the law of the variation of \nintensity with height. This study was looked upon as \nof considerable importance by French, German and \nEnglish scientists. 3 Wheatstone and Faraday made it \nthe subject of special reports to the British Association \nand the Royal Society respectively. 4 \n\n1 Suggested by Fourier\'s MSmoire sur les temperatures du globe ter- \nrestre et des espaces planHaires (Paris, 1827). \n\n2 Many of these studies, first published in the Annates of the Obser- \nvatory and in the MSmoires of the Academy were brought together in \nSur le climat de la Belgique (2 vols., 1849-1857). \n\n3 See Archives des sciences physiques et naturelles (Geneva, July, \n1849). \n\n4 See Report of the British Association (1849), vol. 19, "Transactions \nof the Sections," pp. 11-15. \n\n\n\n467] BIOGRAPHICAL SKETCH 2 $ \n\nMore important by far were the observations of \nbarometric pressures leading to the discovery of atmos- \npheric waves. l He had conceived the advantage of \nsimultaneous observations in various places in dealing \nwith matters of climatology. Securing the assistance \nof scientists throughout Belgium, and later throughout \nEurope, he secured a mass of observations of hourly \nbarometric pressures. When these were chartered they \nrevealed the succession of variations in pressure due \nto atmospheric waves. This study 2 of the form, size \nand velocity of atmospheric waves was pioneer. When \ncarried out on the basis of simultaneous international \nobservations, this discovery led to most important \nconsequences for our knowledge of storms and prob- \nable weather conditions. 3 A long stride was made \ntoward international cooperation and uniformity by the \nSea Conference, held at Brussels in 1853. 4 Ten states \nwere represented and Quetelet was chosen president. \nFurther advance was made in 1873 at the first Interna- \ntional Meteorological Congress, 5 an assemblage Quetelet \nhad long desired to call. He was represented by his \nson, and his plan for the observation of natural phe- \nnomena was made the central theme of discussion. \n\n1 He was probably led to such research by the suggestion of Sir John \nHerschel. But Quetelet organized independently five stations in Bel- \ngium and later seventy scattered over central and western Europe, \nwhose observations were forwarded and tabulated at the Brussels Obser- \nvatory. See Bulletins de V acad., 2nd Series, vol. xxxviii, p. 838. \n\n2 Published in the Annales of the Observatory, vol. viii, part I. \n\n3 See quotation, Mailly\'s Essai, p. 253, from the Annuaire de la \nsociety mHeorologique de France, 1867. \n\n* The suggestion for this conference came from Matthew Maury, of \nWashington. At his suggestion Quetelet induced the Belgian govern- \nment to call the conference, "to establish a uniform system of meteoro- \nlogical observations for the sea." Mailly, Essai, p. 224. \n\ns At the World\'s Exposition at Vienna. \n\n\n\n26 ADOLPHE QUETELET AS STATISTICIAN [ 4 68 \n\nIn close connection with these observations were those \nmade on the periodic, annual and diurnal, phenomena of \nplants and animals. These had been begun in 1839 by a \nstudy of the time of blooming of flowers, and were ex- \ntended in 1 841 to include the time of foliation and of \nfalling leaves. In this work, leading to many interesting \nand significant correlations, he enlisted the cooperation \nof scientists in every country of western Europe. For \nthis purpose, Quetelet prepared in 1842 an extensive \nscheme of investigation 1 embracing meteorology, physics \nof the globe, and the annual and diurnal habits of plants \nand animals. 2 \n\nDe la Rive, in reviewing Sur la physique du globe? at- \ntributed the highest importance to these studies in mete- \norological and terrestrial physics, placing Quetelet in the \n"first rank among meteorologists." 4 Reichesberg re- \nmarks that there are few physicists who have advanced the \ndevelopment of meteorology and physics of the globe to \nsuch an extent as Quetelet. 5 The great merit of these \nstudies is found in the admirable plan for the study of \nperiodic phenomena, particularly in the continued insist- \nence on the simultaneous observation of the same phe- \nnomena from many scattered points. He was the first to \ncollect material in such manner and quantity as made \npossible the discovery of regularity where the human \n\n*For this plan see Bulletins de I\'acad., 1st Series, vol. ix, part I, pp. \n65-95. \n\n\' Results published annually in Nouveaux mimoires of the Academy \nbeginning with vol. xv. \n\n3 Published in the Annales of the Observatory (1861), vol. xiii; also \nseparately Brussels, 1861. \n\n* Archives des sciences physiques et naturelles (Geneva, 1862, vol. xv, \nJuly). \n\n5 " Der beruhmte Statistiker," p. 442. \n\n\n\n469] BIOGRAPHICAL SKETCH 2 J \n\nmind had previously found only chance. The wonderful \nscientific imagination of the man is strikingly shown in \nhis conception of a world physics as presented in his \nSur la physique du globe and his Mktkorologie de la \nBelgique compare" e a celle du globe. ] Here was a vast \nconception, embracing in its realization the most com- \nplete observations of the magnetic, meteorological, \nanimal and vegetable phenomena of the entire earth on a \nsystematic and uniform basis with a view to discovering \nthe order in a vast mass of apparently disordered events. \nWe take up now Quetelet\'s connection with the Acad- \nemy. Chosen to membership in 1820, he soon came to \nplay a leading role in its activities. He was named \ndirector for the years 1832 and 1833, and was chosen \nperpetual secretary in 1834. This office he held for forty \nyears, during which he was the "guiding spirit\'\' 2 of the \nAcademy. " He so ruled his little republic as to secure \nthe regard, esteem and veneration of all within its walls, \n. . . " 3 At his suggestion, the Academy began the publi- \ncation of its Bulletin in 1832, and three years later, as \nsecretary, he brought out the first volume of the A11- \nnuaire. When the Academy was reorganized in 1845, 4 \nQuetelet secured the addition of the class of Beaux- \nArts. 5 This he had attempted in 1832. Having failed \n\nBrussels, 1867. \n\n2 Mouat, "Monsieur Quetelet," Jour. Stat. Soc. of London, vol. \nxxxvii, p. 114; see also "Discours," pronounced at Quetelet\'s funeral, \nBulletins de V acad., 2nd Series, vol. xxxvii, p. 249. \n\n3 Mouat, loc. cit. \n\n4 It was known as "l\'Academie royale des sciences et belles-lettres \nde Bruxelles " until 1845, and since then as "l\'Academie royale des \nsciences, des lettres, et des beaux-arts de Belgique." \n\n5 He seems to have had a natural and decided taste for art. He first \ncame into public notice as a youth through the exhibition of the prize \ndrawing at the Lyceum at Ghent in 1812. \n\n\n\n2 g ADOLPHE QUETELET AS STATISTICIAN [470 \n\nhe contented himself with assisting in the organization \nof the Cercle artistique et littkraire, of which he was for \nsome time the president. As secretary of the Academy \nhe was always prompt and painstaking in fulfilling his \nduties. Fifteen days before his death, though already \nsuffering from his death malady, he attended the session. \n" In his appreciations of the works of his fellows, he was \nusually fair-minded, but superficial." ! Many of his own \narticles were first published by the Academy, and it was \nlargely through the medium of the Academy that Quete- \nlet became the stimulator of a new intellectual life in \nBelgium. There are many testimonials to his stimulating \ninfluence. He was declared, at his death, to be virtually \nthe creator of the Academy, as also of the Observatory \nand other scientific and educational institutions, all potent \nin the intellectual regeneration of Belgium. 2 \n\nBut, though Quetelet\'s influence in and through the \nAcademy and his researches in meteorology and terres- \ntrial physics are of importance, he became known to the \nworld through, and will be remembered chiefly for, his \nstatistical studies. After 1825 his articles dealing with \nevery phase of statistics became more and more promi- \nnent among his various publications. Since these writ- \nings are to be studied in some detail in later chapters, \nwe will give here a sketch only of his practical activity \nwith reference to official statistics. \n\nUpon the formation of the statistical bureau of Hol- \nland under Smits, in 1826, Quetelet became correspond- \nent for Brabant. He at once urged that a census be \ntaken and assisted in formulating plans for the census of \n1829. The results of this census were published \n\n1 Mailly, Essai, p. 261. \n\n2 See "Discours," pronounced at his funeral, Bulletins of the Acad- \nemy, 2nd series, vol. xxxvii, pp. 244-266. \n\n\n\n4 7 1 ] BIOGRAPHICAL SKETCH 29 \n\nseparately in each country after the revolution of 1830. \' \nHe later became supervisor of statistics in the adminis- \ntration, and in 1841 he was instrumental in the organiza- \ntion of the Commission centrale de statistique. This \nCommission, of which he was president until his death, \nsupervised the subsequent censuses, organized the work \nof the provincial commissions, and brought the Belgian \nstatistics to a standard of completeness and reliability \nthat was pre-eminent. Wolowski said, in 1874, that \n"the success of the Commission, thanks to Quetelet, \nwas so great that many nations . . . hastened to found \na central commission of statistics patterned after that \nwhich he had founded. " 2 \n\nMeanwhile, as official Belgian delegate to the meeting \nof the British Association at Cambridge, in 1833, he had \nbeen the immediate cause of the formation of a statistical \nsection. 3 This section was put in charge of a permanent \ncommittee, having Babbage as chairman and Quetelet as \none of its members. Quetelet considered the scope of \nthis section too narrowly limited by the rules of the \nAssociation. " He accordingly suggested to M. Bab- \nbage, from whom we have the statement, the formation \nof a statistical society in London." 4 This society was \n\n1 Recherches sur la reproduction et la mortalitS de Vhomme aux differ- \nent s ages, et sur la population Belgique {premier recueil officiel) par \nMM. Quetelet et Smits (Brussels, 1832). \n\ns "\xc2\xa3loge de Quetelet," Jour, de la soc. de sta. de Paris, vol. xv, \np. 120. \n\n3 See Report of the British Association, 1833, p. 484; also Quetelet, \n" Notes extraites d\'un voyage en Angleterre en 1833," Correspondance, \nvol. viii. \n\n*F. J. Mouat, " History of the Statistical Society of London," Jour. \nSta. Soc. of London, Jubilee vol., pp. 14-15. See also in the same Journal, \nvol. i, p. 4; vol. xxxiv, p. 412, and vol. xxxvii, pp. 309 and 415; and \nF. X. Neumann-Spallart, " Apergu historique," in the Bulletin de V In- \nstitut international de statistique , vol. i, pp. 1-2. \n\n\n\n3 o ADOLPHE QUETELET AS STATISTICIAN [ 4 ^ 2 \n\nfounded March 15, 1834, and the same year Quetelet \nwas elected a corresponding member of the British Asso- \nciation. \n\nThe need of international uniformity and comparability \nof statistical data impressed itself deeply upon Quetelet, \nas had the similar need with respect to astronomical and \nmeteorological data at an earlier date. 1 With character- \nistic zeal he sought to bring about the practical realiza- \ntion of this highly important end. The idea of inter- \nnational cooperation, bearing the approval of the Com- \nmission centrale, was presented to a group of scientists \nat the Universal Exposition at London in 185 1. The \nproject met with heartiest approval. Brussels was desig- \nnated as the place of meeting for the first session because \nof the excellence of the Belgian statistics. Further pro- \nceedings devolved on the Commission centrale. A com- \nmittee was chosen to draw a plan of organization, pre- \npare rules of order and propose questions. As chairman \nof this committee, Quetelet became the moving and di- \nrecting force in what followed. The government was \ninduced to issue invitations to an International Statistical \nCongress, plans of organization were drawn providing \nfor three sections, and a set of eleven questions was pro- \nposed for discussion. At the first session of the Con- \ngress, Brussels, 1853, Quetelet was chosen president, and \nin his opening address he dwelt upon the advantages of \ninternational uniformity in plans, purposes and termini- \nology of the official statistical publications. \n\nThe Congress was a decided success and other sessions \nfollowed. The influence of this Congress on both the \ntheory and practice of statistics was immense. Meitzen 2 \n\nipp. 23 and 25, supra. \n\n5 August Meitzen, History, Theory and Technique of Statistics, tr. by- \nRoland P. Falkner, Supplement to Annals of the American Academy \nof Political and Social Science (March, 1891), p. 81. \n\n\n\n4 7 3 ] BIOGRAPHICAL SKETCH 3! \n\nsays, "Everything which has occurred for statistics 1 \nsince the beginning of the Congress has been essentially \na consequence of its stimulating and invigorating influ- \nence." Ficher, in opening the Statistische Monatschrift* \nwith a sketch of Quetelet, says " International Statistics \nwill ever remain Quetelet\'s most splendid creation." \nQuetelet was a prominent figure at all but two sessions \nof the Congress; 3 Wolowski tells us that "it was always \nthe spirit of Quetelet that animated them." 4 We see \nhim at the age of seventy-six, upon urgent request, re- \npairing to St. Petersburg to the last but one of these \nsessions. And we see him returning, refreshed and re- \njuvenated by the splendid ovation he had received. 5 This \nwas one of his greatest triumphs and was to him a \nsource of deepest gratification. \n\nBefore closing this sketch, mention should be made of \nan attack of apoplexy from which Quetelet suffered in \nthe summer of 1855. He was stricken suddenly while \nstudying on the veranda of his home at the Observatory. \nHe recovered strength in a few weeks to resume his \nlabors, but his intellect had lost its acuteness, his memory \nits certainty and his literary style much of its beauty and \neloquence. His writings, for a long time, needed the \nmost thorough revision. Mailly, who was one of his \nassistants at this time, tells us that he would use the \nsame word over and over again, and would express the \nsame thoughts with monotonous repetition. He even \n\n1 Meitzen must mean official statistics. \n\n3 Vienna, 1875, vol. i, p. 13. \n\n\'Paris, 1855, and the session after his death, Budapest, 1876. \n\n*"\xc2\xa3loge de Quetelet," Jour, de la soc. de sta. de Paris, vol. xv, \np. 120. \n\n5 See " Obituary Notice," Jour. Stat. Soc. of London, vol. xxxvii, p. \nUS- \n\n\n\n32 ADOLPHE QUETELET AS STATISTICIAN [474 \n\nconstructed sentences whose ends bore no relation to \ntheir beginnings, and, when such were corrected, Quetelet \nwould be unconscious of change. 1 His books published \nafter 1855, in so far as new in composition, are full of \nambiguous or unintelligible phrases, ill-arranged and \nvefy repetitious. This is notably true of his histories of \n1864 and 1866, 2 and his works on meteorology, 3 as well \nas of some of his statistical writings. His affliction was in- \ntensified by the death of his wife and of his only daughter. \nYet, in time, he very largely regained his former eager- \nness of spirit and worked on to the end with unabated \nintensity and care. In his latest years, further saddened \nby the loss of some of the younger spirits about him, he \nbecame more and more absorbed in his daily labors. He \nhad for so many years guided the work of the Academy \nand the Observatory, that it is little to wonder at, that \nthey were the burden of his incoherent mumblings in the \nbrief spell of deliriousness preceding his death. \n\nHis life was crowned with honors. He was a member \nof more than one hundred learned societies, and had been \ndecorated with the badges of many royal and honorable \norders of all lands. Among the learned societies were \nacademies of science, institutes, royal societies, and medi- \ncal, statistical, geograplical, meteorological, anthropo- \nlogical, philosophical, physical and astronomical societies \nthe world over. 4 The Acadkrnie des sciences morales et \n\n1 Mailly, Essai, p. 266, and Reichesberg, " Der beriihmte Statis- \ntiker," p. 460. \n\n2 To those mentioned in note p. 16, supra, should be added Premier \nsiecle de I \'acadimie (Brussels, 1872). \n\n3 Among these were: Sur le climat de la Belgique (Brussels, 2 vols., \n1849-1857); Physique du globe {ibid., 1861); MttZorologie de la Belgique \ncompare" e a celle du globe {ibid., 1867). \n\n4 Ficher, Statistische Monatschrift, vol. i, p. 13, says that, aside from \n\n\n\n475 ] BIOGRAPHICAL SKETCH 33 \n\npolitiques of Paris bestowed upon him its highest honor \nby electing him an associate in 1872. At the same time \nthe Academy of Sciences of Berlin hailed him as " the \ncreator of a new science." 1 Reichesberg observes that \nas the founder of a new statistics he developed the scien- \ntific method by which the laws of social life may be dis- \ncovered, and thus established the foundation of a new \nscience, Social Physics, as he himself called it, or Soci- \nology, as it is customarily called today. 2 Doubtless one \nof Quetelet\'s greatest merits lies in his development of \nmoral statistics. Of this development two features are \nof lasting significance. One of these is the deA^elopment \nof a method of investigation having a mathematical basis \nin the theory of probabilities. The other is found in the \nemphasis on the word moral. Others had studied birth, \ndeath and marriage statistics, but Quetelet was the first \nto perceive in such studies a field that could be expanded \nto include the whole nature of man and the characteristics \nof human society. The simple proposition that the \nmoral nature of men and the qualities of a group of men \ncan be best determined by a statistical study of their \nactions was exalted by him into the foundation of exact \nsocial science. \n\nQuetelet\'s personality is represented as most winning. \nModest and generous, convinced but respectful of others\' \nopinions, always calm and considerate, a man of broad \nlearning and an attractive conversationalist, he won and \nkept friends wherever he went. A man of excellent tact, \n\nlearned societies of Belgium, he was a member of ninety-six in Europe, \none in Asia, one in Africa, and nine in North and South America. For \na list of these societies see Bulletins de Vacad. roy. de Belg., 2nd series, \nvol. xxxvii, pp. 246 and 265. \n\n1 Bull, de Vacad., 2nd series, vol. xxxvii, p. 257. \n\na "Der beriihmte Statistiker," pp. 443-444. \n\n\n\n34 ADOLPHE QUETELET AS STATISTICIAN [476 \n\nas well as of tremendous enthusiasm, he readily enlisted \nsupport for many schemes of cooperative scientific \nendeavor. A man of wide intellectual interests, and at \nthe same time, endowed with a prodigious capacity for \nlabor, he contributed to the advancement of several \nsciences, aroused anew the entire intellectual life of his \ncountry and stimulated the activity of artists and scien- \ntists throughout the world. Until the attack of 1855, he \nis represented as always animated and genial, fond of wit \nand laughter. " Rabelais was almost as dear to him as \nPascal." r \n\nHis home life was of marked beauty and serenity. He \nfound great pleasure in his two children, and the astro- \nnomical ability of his son was a source of great pride to \nhim. Quetelet was himself a modest musician, and his \nwife an accomplished one. Friends were regularly en- \ntertained at dinner on Sundays, and Sunday evenings \nwere usually given over to music and charades. Per- \nsonally acquainted with the leading scientists of his time, \nhe exercised the most generous hospitality in the home \nat the Observatory. Distinguished men, coming to \nBelgium from any of the European capitals or centers of \nlearning, brought letters of introduction to Quetelet and \nwere always assured a gracious reception by him. One \nof the speakers at his funeral said of him, "as a man of \nscience he was admired ; in political affairs he was re- \nspected ; in private life he was beloved." 3 \n\nHe died on the seventeenth of February, 1874, and was \nburied with honors fitting one of earth\'s nobility. His \nfuneral was the occasion of a most numerous and dis- \ntinguished gathering of members of royal families, \n\n1 Mailly, Essai, p. 262. \n\n\' x Bulletins of the Belgian Academy, 2nd series, vol. xxxvii, p. 261. \n\n\n\n4 77] BIOGRAPHICAL SKETCH ?,$ \n\nscientists, men of letters and representatives of learned \nsocieties. Funds for a statue of him were soon raised \nby popular subscription, the monument being unveiled \nat Brussels in 1880. He is represented seated in an arm- \nchair, the fingers of his left hand spread out on a nearby \nglobe; his right arm rests on the arm of the chair and \nhis head is raised as he peers into the secrets of space. 1 \n\nThe extent of Quetelet\'s scientific activity was so great, \ncovering as it did the various fields of mathematics, \nastronomy, physics and statistics, that his rank among \nmen of science is difficult to estimate. It may be said \nwithout fear of contradiction that few men have so \nlargely contributed to the spread of scientific knowledge \nor stimulated such wide and persistent discussion and \ninquiry as did he. One historian says of him, " In the \nhistory of natural science, Quetelet will, with good right, \nbe placed in the rank of Pascal, Leibnitz, Bernoulli, La- \nplace, Poisson and such scientists. " 2 \n\n1 Reichesberg, " Der beriihmte Statistiker," p. 460. \n\n2 Von John, Geschichte der Statistik, p. 335. \n\n\n\nCHAPTER II \n\nQUETELET IN THE HISTORY OF STATISTICS \n\nIt is proposed in this chapter to relate Quetelet to \nthe historical development of statistics previous to 1825, \nwhen he began to show some statistical activity. This \ndevelopment can be traced through two series of writ- \nings, showing different conceptions and methods. One \nseries includes the works by Muenster, Conring and \nAchenwall and his disciples ; the other, works by Graunt, \nthe School of Political Arithmetic, Derham and Suss- \nmilch. Those of the first series embrace the whole life \nand organization of the state as their object, and rely on \nverbal analysis and description. Those of the second are \nrelatively limited in scope and use enumeration and calcu- \nlation as distinctive methods. The conception, scope and \nmethod of each of these two classes of statistical writings \nwill be briefly traced, and Quetelet\'s contribution to their \nfurther development and transformation stated. 1 \n\nSince nations began there have been records of a sta- \ntistical character. The rise of modern nations, with the \ngrowing sense of national unity and of international \njealousy, gave rise to comprehensive descriptions of \n\n1 For general guidance the following works have been used: Von John, \nGeschichte der Statistik, erster Teil, von dem Ur sprung der Statistik \nbis auf Quetelet (1835), (Stuttgart, 1884); August Meitzen\'s History- \nTheory and Technique of Statistics, tr. by Roland P. Falkner, Supple, \nment to Annals of the American Academy of Political and Social Sci- \nence, March, 1891. \n\n36 [478 \n\n\n\n479] Q UETELET IN THE HISTORY OF STATISTICS 37 \n\nnations and estimates of their relative resources in men \nand materials of war. Meitzen l finds the first of these \nin the Cosmographia (1536 and 1544) of Sebastian \nMuenster. This work treated systematically Europe, \nAsia and Africa, covering the geography, history, man- \nners and customs, industries, commerce, political and \necclesiastical organization, and military power of all \nknown countries. This was followed by others of the \nsame nature, 2 which furnished the basis for the develop- \nment of statistics as a discipline in the German universi- \nties. The first university lectures of such character were \nthose of Herman Conring 3 (1606-1681). These lectures \nwere begun at the University of Helmstadt in 1660 and \nwere published first in 1668, but in best form, post- \nhumously in 1730. 4 Volume four of the latter edition \ntreats of " Statskunde" or " notitia rerum publicanim." \nAccording to Conring the notitia rerum publicarum \ntreat of the condition of individual states in whole or in \npart, and properly should be confined in time to the \npresent. The chief aim is to gain a knowledge of the \nstate for the guidance of practical statesmen. For this \nreason they treat not only facts, but causes. Conring, \nbeing scholastic in his treatment, gives as causes the \nAristotelian classification. The material causes are land \nand people; the formal and final are the kinds of union, \nsuch as government and administration, with reference \nto special objects of state; and the efficient causes are the \nrevenues and land and sea power. Coming\'s work is \n\nx Op. cit., p. 20. \n\n"See especially Von John, op. cit., p. 34, ei seq. \n\n3 Meitzen, p. 21; John, p. 52; Block, Traite" th&oretique et pratique de \nstatistique (2nd ed., Paris, 1886), pp. 4-5. \n\n* This work was entitled Exercitatio historico-politica de notitia singu- \nlaris alicujus reipublicae. \n\n\n\n38 ADOLPIIE QUETELET AS STATISTICIAN [ 4 go \n\nworthy of much emphasis. It was the first notable \nattempt at the systematic presentation of both the theory \nand the material of political statistics. The form he gave \nto such presentation was lasting. John observes that "a \ncomparison of the theories set forth a century later by \nAchenwall, Von Schlozer and followers always discloses \nagain this scholastic system formulated by Conring." \nFor this reason " the great German poly-histor of the \nseventeenth century can alone be called the \' father \' of \nthis 2 form of statistics." 3 \n\nMeitzen, however, falls in with the custom by desig- \nnating Achenwall (1719-1772) "the father of statistical \nscience." 4 Achenwall tells us 5 that his first statistical \nwork was his Vorbereitung zur Statswissenschaft der \neuropaischen Reiche, published in 1748. This appeared \nas the introduction of a work of the year following, enti- \ntled Abriss der Statswissenschaft der europaischen \nReiche. 6 \n\nThe advance of Achenwall over his predecessors was \nin more systematic treatment and more exact definition. \nThis is evidenced by the manner in which he takes up \nthe theoretical problems. " Before we begin to observe \nthe constitution of the most important European states \nof to-day, it will be fitting to make some general remarks \n\nl Op. cit., p. 61. \n\n*The word " this " evidently refers to the German university statistics. \n\n3 Ibid., p. 70. \n\ni Op. cit., p. 22. See Block, op. cit., p. 7. \n\n5 Statsverfassung der heutigen vornehmsien europaischen Reiche und \nVolker im Grundriss, edited by M. C. Sprengel (Gottingen, 1st pt., \n1790, 2nd pt., 1798), Vorrede zur ersten Ausgabe. \n\n8 This ran through five editions in the author\'s lifetime; a sixth was \nbrought out by Von Schlozer in 1781. References here are to the sev- \nenth edition by Sprengel, the St atsver fas sting mentioned in the pre- \nceding note. \n\n\n\n481] QUETELET IN THE HISTORY OF STATISTICS 39 \n\non \' Statistik,\' 1 as that discipline which is concerned with \nthis object; to set forth its meaning, limit and divisions \nand its natural connections ; as also to indicate briefly \nthe uses, the history and the sources of the same." 2 In \nobserving a state, Achenwall says that he finds many \nthings which notably advance or hinder its prosperity. \n"Such things can be called Statsmerkwurdigkeiten " 3 \n(the noteworthy things of a state). " The totality of the \nactual \' Statsmerkwurdigkeiten \' of a kingdom or repub- \nlic makes up its constitution in the broadest sense; and \nthe account of the constitutions of one or more states, \ntreated individually, is \'Statistik, (Statskunde), oder \nStatsbeschreibung.\'" 4 \'Statistik\' studies the life of a \nstate with a view of ascertaining its sources of weakness \nand strength. 5 It will not include all facts of interest \nregarding a state, but only such as are important for \n" politische Kenntniss," 6 that is, \'Statistik\' seeks to ob- \ntain, through a description of the state, a guide for the \nstatesman. 7 Though thus limited, \' Statistik \' still in- \ncluded much that later became differentiated, as geogra- \nphy, ethnography, public and administrative law and \npolitical economy. Achenwall\'s work was translated into \nmany languages and his definition of statistics thus came \ninto general use. \n\n\' Statistik \' thus owed the fixity of its definition to \nAchenwall, but there was little change in the real char- \nacter of the discipline from the very early time of Muen- \nster to the beginning of the last century. Von Schlozer \nepitomized the definition, 8 and he and other representa- \n\n1 He first uses this word in the " Vorrede " of the first edition. \n\n2 Vorbereitung, p. 2. * Ibid., p. 4. * Ibid., p. 5. \n\xc2\xb0Ibid.,p.6. * Ibid.,?. 6. \' Ibid., p. 46. \n\n8 \' \' Statskunde ist eine stillstehende Statsgeschichte ; so wie diese eine \nfortlaufende Statskunde," ibid., p. 5, in brackets. \n\n\n\n4 ADOLPHE QUETELET AS STATISTICIAN [ 4 g 2 \n\ntives of the school made such improvement in the analy- \nsis and arrangement of results as the continued enrich- \nment of material suggested. Both the theory and the \nmethod were simple. This school of statisticians be- \nlieved the possibilities of their science were exhausted by \na verbal description of a contemporary social condition, \nso arranged as to be useful to statesmen, and accompan- \nied by general observations on the results. But an \nalmost revolutionary change was impending. A symp- \ntom of this change is found in the works of Ancherson * \n(1741) and Biisching 2 (1758). Though Achenwall had \nstated that knowledge of the strength of a nation would \nrequire a comparison of its resources with those of other \nnations, 3 these men were the first to make such compari- \nsons directly. Moreover, they used, so far as possible, \nnumerical tables drawn from official sources. Besides, \nBiisching gave slight space to the geography, constitu- \ntion and administration of the countries described and \nemphasized the economic and material factors of social life. \nBut the real change followed the establishment of \nstatistical bureaus and the publication by them of the \nresults of censuses and inquiries. " Die Tabellen-Statis- \ntik\' 5 quickly came into vogue. A tragic, but bloodless, \nwarfare ensued between the orthodox statisticians and \nthe worshipers of rows of figures. 4 The latter had the \nassistance of continuous new recruits in the form of large \nquotas of official numerical data, which could not fail of \n\n1 Von John, op. cit., p. 88. \n\n2 Meitzen, op. cit., p. 24, et seg., and p, 41. \n\na Vorbereihcng, pp. 47-48. \n\n*The followers of Achenwall claimed that their statistics were "the \nright eye of political science," and accused the table statisticians of re- \nducing statistics to a "veritable cadaver, on which one could not look \nwithout abhorrence," Von John, op. cit., p. 129. \n\n\n\n4 83] QUETELET IN THE HISTORY OF STATISTICS 4I \n\neffect. When the atmosphere cleared it was found that \na considerable change had been wrought in the character \nof descriptive statistics. \' Statistik \' disappeared as a \nuniversity discipline and was replaced by two rather dis- \ntinct kinds of descriptive material in which numerical \ntables and verbal explanation divided honors. These \ntwo were the official statistical publications, and the \nstatistical compendiums prepared mostly by private en- \nterprise. \n\nMuch of Quetelet\'s activity was connected with per- \nfecting these two kinds of statistical works. His own \ndefinition of statistics * evidently restated that given by \nAchenwall and Von Schlozer, and the objects of statisti- \ncal inquiry, as given by him 2 were those treated by this \nschool. But we shall see that it was primarily his own \nactivity that led to the conception of statistics as a \nmethod of observation based on enumeration and ap- \nplicable to any field of scientific inquiry. It is impossible \nto state just what elements in the betterment of descrip- \ntive statistics were due uniquely to Quetelet, but he con- \ntributed to the development in the following ways: (i) \nperfection of plans for census taking; (2) criticism of \nsources; (3) arrangement of materials; and (4) pro- \ngress toward uniformity and comparability of data. \n\nQuetelet\'s direct interest in public statistics dates from \nhis appointment in 1826 as correspondent for Brabant to \n\n1 Letters on the Theory of Probabilities , as Applied to the Moral and \nPolitical Sciences, translated from the French by O. G. Doivnes (Lon- \ndon, 1849), pp. 176, 179, 180, 182. \n\n*Ibid,, p. 183. Note also headings treated in " Recherches statis- \ntiques sur le royaume des Pays-Bas," Nouveaux mimoires de V acad- \nimie royale des sciences et belles-lettres de Bruxelles, vol. v (1829), and \nthe elaborate Statistique Internationale \', Bulletin de la commission cen- \ntrale de staiistique (Bruxelles), vol. x (1866). \n\n\n\n4 2 ADOLPHE QUETELET AS STATISTICIAN [484 \n\nthe statistical bureau of Holland. His connection with \nthe early censuses of Holland (1829) and of Belgium \n(1832), his position as supervisor of the statistics of the \nadministration and later as president of the Com?nissio?i \nce?itrale, made it possible for him to impress a high \ncharacter of excellence on the statistical publications of \nhis own country. He gave careful consideration to the \ncollection of data, both as to the blank forms to be used \nand as to the nature of the questions to be asked, to the \ntabulation and forms of presentation of the material, to \nmethods of averaging and summarizing data, and to the \ncriticism, both of the sources and of the results of the in- \nvestigation. \n\nThe practical rules developed by him still form the \nessential guides in census taking. 1 His predecessors had \ngiven some attention to the criticism of results, but \nQuetelet assisted materially in the advance of criticism \nof sources. " Statistics are of value only according to \ntheir exactness. Without this essential quality they \nbecome useless, and even dangerous, since they conduce \nto error." 2 He insisted that every statistical work \nshould give both the sources of the data and the manner \nof their collection. The checking of statistical documents, \nhe held, should be both moral and material. 3 By moral \nexamination he meant an inquiry into the influences \nunder which the data are collected and the nature of \ntheir sources. The material examination consists in \nobserving whether the numbers are sufficiently large to \nassure the predominance of constant causes, and suffi- \nciently continuous or uniform to make certain that acci- \ndental causes have not unduly influenced some of them, \n\n1 See Letters, p. 195, et seq. \n\n-Ibid., p. 198. \'\'\'Ibid., " Letter xxxix." \n\n\n\n485] QUETELET IN THE HISTORY OF STATISTICS 43 \n\nand whether they have been combined with mathematical \naccuracy. As to the arrangement and presentation of \nresults, Quetelet made progress both in official docu- \nments, so as to secure clearness and ready comprehensi- \nbility, and in scientific studies, so as to show the greatest \npossible number of correlations. To group the data so \nthat permanent factors would be thrust into prominent \nview, and so as to make comparisons on the basis of \ntime, place, sex, age, etc., easily possible, were essential \nprinciples with him. The study of correlations, the \nattempt to find the causal relations of phenomena, marks \na very great advance over the works in this particular \nline of statistical development. Such studies required \nthe development of a more precise technique, which, in \nturn, reacted on the criticism of sources and gave to \ndescriptive statistics a deeper significance. It is pre- \ncisely at this point that descriptive statistics felt most \ndecisively the influence of the statistics begun by the \nSchool of Political Arithmetic. And it is in and through \nthe work of Quetelet that this influence was first clearly \nexerted. That is, the development of official statistics \nfurnished more abundant numerical data, and the elabo- \nration by Quetelet of a method for treating such data \nmade possible the correlation of statistical results with \neconomic and social conditions and the consideration of \nquestions involving the public weal. The disciples of \nAchenwall had upbraided the table statisticians with \nneglecting the consideration of the deeper questions of \nsocial life. They failed to recognize the necessity of \nprecise data, of number and measure, in order to draw \nreasonably correct and at the same time significant con- \nclusions on such questions. \n\nFinally Quetelet contributed to the progress toward \nuniformity and comparability in official statistics. By \n\n\n\n44. ADOLPHE QUETELET AS STATISTICIAN [486 \n\ncomparability he meant two things, namely, (1) uni- \nformity of all data collected under a given schedule for \none time and place, and (2) uniformity of all data under \na given schedule for different times and places. 1 Uni- \nformity of the first sort is absolutely essential to the \nvalidity of any conclusions whatever. Uniformity for \ndifferent times makes possible the measurement of the \nchange in a social condition within a nation through a \nperiod of time, while uniformity for different countries \nmakes possible the direct comparison of social conditions \nin these countries. Quetelet would not only test the \nprogress of his own country but he dreamed of present- \ning in comparable data the status and the progress of \nall nations. Hence his leadership in the organization of \nthe International Statistical Congress. In his opening \naddress, as well as in the formulation of the plans for the \nfirst session, Quetelet sounded the keynote of this move- \nment in his emphasis on international uniformity. He \nfelt keenly the need of comparability among the official \nstatistics of western nations. This end was to be realized \nthrough the collection of material on the basis of a com- \nmon plan, following similar instructions, classifications \nand schemes of presentation and using the same termin- \nology. This end is still far from realization, but there \ncan be little doubt that through this Congress Quetelet \ninfluenced, directly or indirectly, the statistics of many \nnations. The value to science of the realization of inter- \nnational uniformity would be immense, inasmuch as it \nwould make possible a multitude of correlations and \ncomparisons that are now either dangerous or altogether \nimpossible. \n\nAnother line of statistical development gave rise to \n\n1 Letters, p. 177. \n\n\n\n4 8^] QUETELET IN THE HISTORY OF STATISTICS 45 \n\nvery different conceptions and methods. In 1662 Cap- \ntain John Graunt, F. R. S. (1620-1674) presented to the \nRoyal Society his Natural and Political Observations \nupon the Bills of Mortality with reference to the Govern- \nment, Religion, Trade, Growth, Air, Diseases, and the \nseveral cha?tges of the City of London. l This work has \nnot been sufficiently emphasized by the historians of \nstatistics. As a scientific study of population it was not \nsurpassed until the appearance of Siissmilch\'s work, \neighty years later. It contains the first presentation of \na number of the inductions from population statistics, \nwhich Quetelet presented much more convincingly and \nimpressively in Sur Vhomme, published in 1835. Graunt \nfound that the deaths due to various diseases and even \nto certain kinds of accidents " bear a constant proportion \nunto the whole number of burials." 2 He pointed out the \nconstancy in the number of abortions and still-births; 3 \nthe variation of the death rate by seasons ; 4 the ratio of \nbirths to deaths in city and in country ; 5 and the ratio of \nmale to female births ; 6 he also presented the rough out- \nline of a table of mortality. 7 \n\nThe interesting feature of Graunt\'s work is not the ap- \nproximate accuracy of his conclusions, but the method \nhe followed. He was permeated with the Baconian \nphilosophy and sought truth through observation rather \nthan speculation. His conclusions were faulty both be- \ncause of the incompleteness of his data and his utter lack \nof comprehension of the law of large numbers. His \nmortality table is, in fact, only a piece of rational guess- \nwork. But his book stimulated the widest interest, and, \n\nReferences here are to the 5th edition, London, 1676. \n\n% Ibid., p. 26. z Ibid., p. 41. *Ibid., p. 56. \n\n3 Ibid., p. 57, et seq. (i Ibid., pp. 87, 103-104. 7 Ibid., pp. 83-84. \n\n\n\n4 6 ADOLPHE QUETELET AS STATISTICIAN [ 4 gg \n\nabove all, opened the way for a new method of studying \nsocial life, namely, observation, enumeration and calcula- \ntion. It is with Graunt, in fact, that we find the begin- \nning of statistics as a method of observation in the service \nof inductive social science. 1 \n\nPetty\'s first researches were stimulated by Graunt\'s \nObservations, which he designated as "a new light to \nthe world." 3 Petty was dominated by the same empir- \ncal philosophy; he would "use only arguments of \nsense," and would express himself in terms of "number, \nweight and measure." 3 Owing to the dearth of accurate \nenumerations he resorted to calculation, as, for example, \nthe estimation of the number of inhabitants from the \nnumber of houses, or from the number of deaths. He \nappreciates the value of an average of several such com- \nputations, and "pitched the medium" 4 between extreme \nestimates. \n\nThe cultivation of Political Arithmetic, " the art of \nreasoning by figures upon things relating to govern- \nment," 5 was continued, notably, by Davenant, Arbuthnot \nand King. The essays of these writers were used by Sir \nWm. Derham, F. R. S., in his Physico-Theology; or a \nDemonstration of the Being and Attributes of God from \nhis Works of Creation. 6 This work is an elaborate argu- \n\n1 For an excellent estimate of Graunt\'s influence see The Economic \nWritings of Sir Wm. Petty (Cambridge, 1899), by Chas. H. Hull, vol. i, \npp. lxxv-lxxix. He traces this influence through Derham, Siissmilch \nand Malthus to Darwin. \n\n- Observations upon the Dublin Bills of Mortality (1681), to be found \nin Several Essays in Political Arithmetick (London, 1659), p. 55. \n\ns Ibid. , \' \' Preface . \' \' * Ibid. , p . 1 23 . \n\n6 Davenant, Discourses on the Public Revenues, and on the Trade of \nEngland (London, 1698), pt. I, "Discourse I," p. 2. \n6 London, 1699. \n\n\n\n489] QUETELET IN THE HISTORY OF STATISTICS 4 y \n\nment from design. He finds in the admirable propor- \ntions of marriages to births, of births to deaths, of males \nto females, the surest evidence of "the work of One that \nruleth the World." 3 The perusal of Derham\'s Physico- \nTheology by Siissmilch, led him to undertake researches \non the number of births, deaths and marriages according \nto the lists of the city of Breslau. 2 Meanwhile, he sent \nto England for the writings of Graunt and Petty. 3 His \nwritings, especially the second edition, 4 proved to be a \ngreat advance upon the preceding, not only in the variety \nand exactness of conclusions, but also in the clearer con- \nnection between the concrete phenomena of social life \nand economic conditions. \n\nMoreover, he made distinct advances in method. \nUpon those wishing to controvert his conclusions he \nimposes the following conditions : \n\n(1) The lists must be correct, else contradiction is of no \nvalue. To this end it is necessary to consider well the condi- \ntions and changes of a place, to see whether war, plague or \nother disease has wrought any variation. (2) The numbers \nmust not be small ; the greater they are and the more years \nincluded thereunder the better. ... If I have a hundred \ncases in support of my conclusion, then can nothing to the \ncontrary be drawn from one case. 5 \n\nIt was, in fact, only by observing large numbers that he \n\nx Eighth edition (London, 1727), bk. iv, chap. 10, "Of the Balance \nof Animals or the Due Proportion in which the World is stocked with \nthem." \n\n2 Die gottliche Ordnung in den Veranderungen des menschlichen \nGeschlechts (Berlin, 1st ed., 1742), " Vorrede," p. 13. \n\n3 /did., p. 16. \n\n4 2 vols., Berlin, 1761 and 1762. \n\n5 First edition, "Vorrede," pp. 38-39. \n\n\n\n48 ADOLPHE QUETELET AS STATISTICIAN [ 4 g \n\ncould ascertain the great regularities in mathematical \nratios which represented to him " the rules of order \nwhich God\'s wisdom and goodness have established." \n\nThese quotations show Siissmilch\'s recognition in a \ngeneral way, of three principles highly important for the \ndevelopment of statistical method, namely, (i) Social \nphenomena have causes; (2) the regularities found in \nstatistical results reveal the rules of the existing social \norder; and (3) constancy in results can be obtained only \nby viewing large numbers. 2 All of these principles are \nfound in the work of Quetelet. It required only a \nchange from a theological to a scientific viewpoint to \nexpand the first of these principles into a complete denial \nof chance and the assertation of an absolute solidarity in \nthe sequence and the co-existence of social phenomena. \nSuch a view became a philosophical tenet, and was a \nfavorite doctrine of Quetelet\'s great friend and teacher, \nLaplace. It appears in Quetelet\'s writings in the form, \n"effects have causes and are proportioned to them," a \nform which suggests the theory of probabilities. The \nsecond of the above principles remained without emphasis \nuntil Quetelet sought to find in the statistical regulari- \nties the laws of a social mechanics. The third was defin- \nitely recognized in the construction of mortality tables \nby Halley, Deparcieux, Wargentin and Kersseboom, and \nwas well established as the "law of large numbers" by \nthe development of the mathematical theory of prob- \nabilities. \n\nComing down to the early years of Quetelet\'s life we \nfind the most significant influences on the course of de- \nvelopment of the statistics of population and of statistical \n\n1 Second edition, vol. i, title page. \n\n3 On this see ibid., vol. ii, pp. 262 and 408. \n\n\n\n491 ] QUETELET IN THE HISTORY OF STATISTICS 49 \n\nmethod in the works of Malthus, Laplace and Fourier, \nall of whom Quetelet knew personally. Malthus\'s Essay \non Population, though apparently not influenced by \nSussmilch\'s Gbttliche Ordnung, gave a world-wide stim- \nulus to the study of population in its economic and social \naspects. Laplace continued the development of the the- \nory of probabilities and instructed Quetelet therein. \nFourier\'s influence was exerted through the Recherches \nstatistigties sur la ville de Paris et le department de la \nSeine} The first four volumes of this series have intro- \nductory essays by Fourier of very great value. In the \nfirst of these, Notions gfatkrales sur la population? he \ndevelops both algebraic and geometrical expressions for \ntables of population and of mortality, average duration \nof life and expectation of life, assuming the population to \nbe stationary. He points out the greater accuracy of \nresults when age groups of one-half year or one month, \ninstead of one year, are taken. Several principles of \nprobabilities are stated and applied to the study of popu- \nlation. He inquires into the causes affecting the growth \nof population and classes these as general and fortuitous. \nHe shows clearly the advantages of large numbers, and \nespecially of averages deduced from a series of such \nnumbers extending over several years. Finally he states \nrepeatedly that average values depend on general causes, \nand change only very slowly " by the secular progress of \ninstitutions and customs." \n\nIn the memoir of the second volume of the Recherches \nstatistiques should be noted the fourth section, Remarque \ngknkrale sur le degrk de precision des rSstiltats moyens. \n\n1 Paris, 6 vols.; Fourier\'s essays are in the volumes for 1821 (2nd ed., \n1833), 1823 (2nd ed., 1834), 1826 and 1829. \n\n2 Vol. i (1821), pp. ix-lxxiii. \n\n\n\n50 ADOLPHE QUETELET AS STATISTICIAN [ 4 g 2 \n\nThe third introductory essay, Memoire sur les resultats \nmoye?i$ cfun grand nombre cC observations? presents for- \nmulas for finding the degree of precision 2 and the prob- \nable error of the average. 3 He presents a method of \nfinding the quantity which when multiplied by three \ngives the positive and negative limits of error in a group \nof measurements, 4 and when multiplied by .47708 gives \nthe probable error, which he calls the average error. \nThese results are then generalized in the Second mkmoire \nsur les rhultats moyens et sur les erreurs des mesures, 5 \ntreating by the use of the calculus the probable error of \na result derived from any number of values each having \nits own probable error. Quetelet undoubtedly had early \naccess to these volumes and was much stimulated by \nthem. 6 \n\nThus the School of Political Arithmetic in contradis- \ntinction from the descriptive school, began by laying \nemphasis on the method of inquiry. Their central ob- \nject of statistical investigation was the population, and, as \nmore abundant data accumulated, they perfected both \ntheir conclusions and their technique. This is especially \ntrue of the development of mortality tables, which by \nthe close of the eighteenth century had led to consider- \n\n1 Ibid., vol. iii (1826), pp. ix-xxxi. \n\n\'\'\xe2\x80\xa2Ibid., pp. xv, et seq. and p. xxv. \n\n3 Ibid., pp. xviii, et seq. \n\n4 The probability is \\\\%%% that the true result lies within A (average) \n-f 3g and A \xe2\x80\x94 3g. \n\nh Ibid., vol. iv (1829), pp. ix-xlviii. \n\n\'Thus Quetelet says in the preface to Instructions populaires sur le \ncalcul des probability (Brussels. 1828), that he has made large borrow- \nings from Laplace and that "lessons 12 and 13 are extracted in great \npart from the excellent introduction to Recherches statistiques sur la \nville de Paris." He should have included also lesson 14, for it is clearly \nfrom the same source. \n\n\n\n493] QUETELET IN THE HISTORY OF STATISTICS 5I \n\nable insight into the nature of statistical data and the \ntrue method of treating them. Finally in the works of \nLaplace and Fourier we note decided indications of a \ntendency to give direct attention to the problem of tech- \nnique and to extend the application of such technique to \nobservations of natural and social phenomena. It was the \nfunction of Quetelet to gather up these various tenden- \ncies, to perfect the method, to extend the scope of its \napplication and to give the whole a new and profound \nsignificance. His activity may be treated under the \nheadings, (I) population statistics, (II) moral statistics, \n(III) development of technique and (IV) application of \nthe normal law of error to the physical measurements of \nmen. \n\n(I) The studies in the statistics of population com- \nprised in Quetelet\'s works 1 may be classed under three \n\n*The chief studies of population statistics are: \n\ni . " Memoire sur les lois des naissances et de la mortalite a Bruxelles, \' \' \npresented to the Brussels Academy, April 25, 1825, Nouveaux mimoires \nde V acad. roy. des sci. et bell. -lei. de Bruxelles, vol. iii (1826), pp. 493- \n512. \n\n2. " Recherches sur la population, les naissances, les deces, les \nprisons, les depots de mendicite, etc., dans les Pays-Bas," presented to \nthe Academy, February, 1827, ibid., vol. iv (1827), pp. 115-165. \n\n3. " Recherches statistiques sur le royaume des Pays-Bas," presented \nto the Academy, December, 1829, ibid., vol. v (1829), pp. vi, 57 and \ntables. \n\n4. Recherches sur le reproduction et la mortalite* et sur la population \nde la Belgique. Publie avec M. Smits. Premier recueil officiel (Brus- \nsels, 1832). \n\n5. Sur V homme et le diveloppemeni de ses faculty\'s, ou essai de phy- \nsique sociale (2 vols., Paris, 1835), book 1. \n\n6. " De l\'infiuence des saisons sur la mortalite aux difrerens ages dans \nla Belgique," Nouv. mim., vol. xi (1838), 30 pp. \n\n7. " Sur le recensement de la population de Bruxelles," Bulletin de \nla commission centrale de statistique, vol. i (1843), PP- 27-164. \n\n8. " Nouvelles tables de mortalite pour la Belgique," ibid., vol. iv \n(1851), pp. 1-22. \n\n\n\n5 2 ADOLPHE QUETELET AS STATISTICIAN [ 494 \n\nheading\'s, (a) studies of births, deaths and marriages, \n(b) treatment of the law of population, and (c) develop- \nment of tables of mortality and of population. \n\nThe study of births, deaths and marriages had been \ntreated in a most thorough-going and extensive manner \nby Sussmilch in his second edition of the Gbttliche \nOrdnung (1,761 and 1762), but, since his time, there had \naccumulated a large quantity of material and there had \nbeen numerous more or less intensive researches on these \nsubjects. 1 Among the most important of these were \nthose by Quetelet\'s Parisian friends De Chateuneuf 2 \nVillerme and Fourier. The chief merit of Quetelet is in \nthe comprehensiveness of his treatment of various phases \nof births and deaths. The best results of his memoirs \npreceding 1835, together with material gathered from \nmany sources are found in the Sur V komme? \n\n(a) Thus in the study of births he inquires into the \neffect of numerous natural and perturbative causes on \nboth sex and fecundity ; he inquires into the ratio of \nmale to female births (1) throughout Europe, (2) in free \nand slave populations, (3) in town and country, (4) \namong legitimate and illegitimate births ; he investigates \nthe influence of age of parents and of conjugal condition \n\n9. " Nouvelles tables de population pour la Belgique," ibid., pp. 71-92. \n\n10. " Sur les tables de mortalite et de population," ibid., vol. v (1853), \npp. 1-24. \n\n11. " Statistique Internationale (population) par A. Quetelet et X. \nHeuschling," ibid., vol. x (1866), CXV pp. of text and 406 pp. of \ntables. \n\nOf these, numbers 3 and 10 might be classed as descriptive of official \nstatistics. \n\n1 For list see references, Sur Vhomme, bk. 1. \n\n\'Von John, op. cit., p. 333 note, says that De Chateuneuf, at the insti- \ngation of his friend Poisson, devoted himself most zealously to statistics. \n\nr \'Sur Vhomme, bk. 1, chaps, i, ii and iii. \n\n\n\n495] QUETELET IN THE HISTORY OF STATISTICS 53 \n\non the sex of offspring ; he studies the influence of age \nof parents, of place, of years of abundance and scarcity, \nof years of peace and war, of seasons and of hours of the \nday, on the number of births. All the foregoing being \nclassed as natural causes, he studies profession, economic \ncondition, morality and political and religious institutions \nas perturbative causes. Similar correlations were made \nfor still-births \xe2\x96\xa0 and for deaths. 2 These studies contain \nfew conclusions that were new at the time, but because \nof their clearness and comprehensiveness in both material \nand number of correlations, they afforded a striking and \nstimulating indication of the advancement of vital statis- \ntics and were an excellent medium for the spread of such \nknowledge. \n\n(b) Quetelet\'s treatment of the law of population 3 \ndoes not deserve lengthy treatment. The distinguishing \nfeature about it is the statement that the resistance to \nthe growth of population increases, all other things being \nequal, as the square of the rate at which population tends \nto increase. He presents neither data nor course of \nreasoning to support this conclusion nor does he explain \nany of the possibilities lurking in the phrase " all other \nthings being equal." The theorem therefore is certainly \nnot demonstrated. \n\n(c) Quetelet\'s first statistical memoir, 4 giving a table \nof mortality with a distinction of sex, sought to provide \na reliable basis for life insurance in Brussels. A second \nmemoir 5 extended the tables of mortality and of popula- \n\nl Nouv. mini., vol. iv (1827); SurVhomme, bk. 1, chap. iv. \n2 I6id., bk. 1, chap. iv. 3 Ibid., bk. 2, chap. vii. \n\n4 Nouv. mhn., vol. iii (1826), pp. 493-512. \nh Nouv. mint., vol. iv (1827). \n\n\n\n54 ADOLPHE QUETELET AS STATISTICIAN [ 49 6 \n\ntion to the southern provinces, while studies of 1832 E \nand 1833 2 gave tables for all Belgium. Quetelet early \nmade the distinction of sex and of residence in city or \ncountry; he also brought out the varying rates of mor- \ntality at different ages, as in the early months cf child- \nhood, at the ages preceding puberty, and at the ages \ntwenty-four and thirty, in men. Fie perfected these \ntables on the basis of the registers of death for the five \nyears 1841-5. 3 The chief importance of these tables lies \nin their great practical value in his own country. His \nfirst serious attempt at the treatment of the mathemati- \ncal theory of tables of mortality and of population was in \nthe memoirs of 185 1 and 1853. 4 This last memoir is in \nthree sections, the first two of which treat these tables \nfor a stationary population following very closely Fourier\'s \nmethod. He however makes the evident error of confus- \ning the population at the end of a calendar year with \nthat at the end of a year of life. The third section treats \nthe subject for any population whatever. He however \nassumes that the births of a calendar year occur simul- \ntaneously and that all the generations represented in a \npopulation at a given time have the same rate of mortal- \nity whether the population be increasing or decreasing. \nNeither of these assumptions being true he fails to reach \na general formula. Nevertheless his studies were not \nwithout value to the general progress of the theory. 5 \n\n1 Recherches stir la reproduction et la morialiti de Vhomme aux diffir- \nens dges (Brussels, 1832). \n\n2 Sur V influence des saisons et des dges sur la mortaliii, presented to \nthe Academy of Moral and Political Sciences of the Institute of France \nin 1833, reproduced in Sur Vhomme, bk. 1, chap. 5, sec. 5, and elabor- \nated in Nouv. mhn., vol. xi (1838). \n\n3 Bull, de la cent. com. de sta., vol. iv (1851), pp. 1-22. \ni Idid., pp. 72-92, and vol. v (1853), pp. 1-24. \n\n5 See Knapp, Theorie des Bevolkerungs-wechsels . pt. 2, p. 93, et seq.\\ \nBlock, Traitf de statistique, p. 206, et seq. \n\n\n\n497] Q UETELET IN THE HISTORY OF STATISTICS 55 \n\n(II) In 1826 appeared the first of the Comptes gknkr- \naux de V administration de la justice criminelle e7i France. \nIn these annual reports were enumerated the number \nand kind of crimes and misdemeanors, as well as the sex, \nage, occupation and education of the accused. Quetelet \nuses these reports in his " Recherches statistiques sur le \nroyaume des Pays-Bas." l In this he compares the sexes \nas to the kind of crimes, presents the relative number of \ncrimes committed against persons and against property \nat each age, and tentatively sets forth the relative degree \nof tendency to crime at each age. 2 Comparing the \nfigures for the three years, 1825-1827, he emphasizes the \n" astounding exactitude with which crimes are repro- \nduced." 3 He adds, \n\nThus we pass from one year to another with the sad perspec- \ntive of seeing* the same crimes reproduced in the same order \nand calling down the same punishments in the same propor- \ntions. Sad condition of humanity ! The part of prisons, of \nirons and of the scaffold seems fixed for it as much as the \nrevenue of the state. We might enumerate in advance how \nmany individuals will stain their hands in the blood of their \nfellows, how many will be forgers, how many will be poison- \ners, almost as we can enumerate in advance the births and \ndeaths that should occur.* \n\nThe same year, 1829, A. M. Guerry brought out his \nStatistique compare* de V ktat de V instruction et du \n\n1 Nouv. mint., vol. v (1829), pp. 25-38; read to the Brussels Academy- \nDecember 6, 1828. \n\n2 /did., p. 33. % Ibid., p. 35. \n\n*Nouv. mim., vol. v, pp. 35 and 36. This quotation shows that Quet- \nelet had reached, in 1828, practically the same position as in the " Re- \ncherches sur le penchant au crime aux differens ages" of 1831, which \nis usually tieated as his first work in moral statistics. There is thus \ngood ground for giving to Quetelet priority in this field, instead of to \nGuerry as is usually done. \n\n\n\n5 6 ADOLPHE QUETELET AS STATISTICIAN [ 49 g \n\nnombre des crimes\' 1 in which was sought an estimate \nof the moral level of France by the use of statistical data. \nSo also, he and D\'lvernois endeavored to compare the \nmoral level of different countries by comparing their \ncriminal records. Quetelet had made such a comparison \nbetween France and the Low Countries in his " Re- \ncherches " of 1829, 2 but Guerry and D\'lvernois saw no \nespecial significance in the constancy of the numbers \nfrom year to year, while it was precisely this that Quetelet \nemphasized. 3 This constancy of the budget of crimes \nwas strikingly brought out in his " Sur le penchant au \ncrime aux differens ages.\'\' 4 Regularity in the number \nof suicides was noted in the Sur Vhomme y and the \nconstancy in the number of marriages for each age and \nsex, first shown in this same work, became the principal \nobject of his later studies in moral statistics. \n\nThus it was that, though Guerry coined the term \n" moral statistics," Quetelet gave it significance. He did \nthis in the following ways : \n\n(a) He emphasized the relation of the statistical regu- \nlarities to man\'s moral freedom. The regularities \nwhich Arbuthnot, 5 Derham and Sussmilch had found \nto be the surest evidence of a divine order main- \ntained for the good of man, Quetelet elevated to the \n\n1 Paris, 1829. \n\n2 Nouv. mem., vol. v, p. 27, et seq. \n\ns Jealousy seems to have existed between Quetelet and Guerry. The \nformer, however, relented and in 1847 used Guerry\'s term "statistique \nmorale," but the latter remained unfriendly to the last. See especially \n"Note" following " Recherches sur le penchant au crime" and note \nin Sur Vhomme, English translation, p. 96, near the end of book third. \n\ni Nouv. mim., vol. vii (1831), 81 pp. \n\n5 "An argument for Divine Providence, taken from the constant \nRegularity observed in the Births of both sexes," Phil. Tr., vol. xxvii. \n\n\n\n499] Q UETELET IN THE HISTORY OF STATISTICS 57 \n\nrank of social laws, comparable to the laws of physics. \nHe gave a scientific, rather than a theological interpreta- \ntion of the facts and thus threw doubt on man\'s free will. \n" It seems to me that what relates to the human species, \nconsidered en masse, is of the order of physical facts." 1 \nThe possibility of predicting in advance the number and \nkind of crimes weighed heavily, at times, upon Quetelet\'s \nhumanitarian spirit. " This possibility .... must give \nrise to serious reflections, since it concerns the fate of \nseveral thousand men who are driven, as it were, in an \nirresistible manner toward the tribunals and toward the \ncondemnations that await them." 2 The picturesqueness \nof his language and the clearness with which he joined \nthe issue, compelled attention and led to wide discussion \nof the true nature of statistical regularities and their \nethical implications. \n\n{b) At the same time that Quetelet held his averages \nto be " of the order of physical facts," he held them to \nbe dependent on social conditions and therefore to vary \nwith time and place. This made possible the study of \ncausal relations in social phenomena, for a change in \nsocial conditions would be followed by a change in the \naverages. Thus, social conditions were made responsible \nfor the criminal budget and moral statistics was directly \nconnected with social science. The problem then be- \ncame that of expressly connecting social evils with \ncertain social conditions, and by changing the latter also \nchange the former. \n\n(c) But this study of casual relations requires much \nmore critical methods of treatment than a purely descrip- \ntive problem. The basic principles of the method pre- \nsented by Quetelet for this study were derived from the \n\n1 Nouv. mem., vol. vii, p. 80. \' 2 Ibid., p. 23. \n\n\n\n58 ADOLPHE QUETELET AS STATISTICIAN [500 \n\ntheory of probabilities. They were: (a) effects have causes \nand are proportioned to them, and (\xc2\xa3) reliable conclusions \ncan be deduced from large numbers only. These prin- \nciples are strikingly like those recognized by Sussmilch, 1 \nbut no doubt they reached Quetelet by way of French \nmathematicians and astronomers, rather than directly or \nindirectly from the German theologian and statistician. \nFrom the first of these he derived the principle that \nman\'s moral and intellectual nature would be shown in \nhis actions, and that the true nature of a social state \nwould be shown in its products. But the effects of for- \ntuitous circumstances can be avoided, and the results of \ngeneral conditions can be seized, only by considering \nlarge groups of homogeneous data. \n\n(III) These principles formed a part of his general de- \nvelopment of the methods of statistical inquiry. The \nessential features of this are to be noted later, 2 hence it \nwill suffice here to say that, although most of the prin- \nciples utilized by Quetelet in the development of the \nnormal law of error and its use in statistical inquiry had \nbeen already developed by the students of probabilities \nand in the essays of Fourier, yet it was doubtless the \nwritings of Quetelet that led to their general appreciation \nand adoption. This was due to the clearness with which \nhe stated the results of mathematical analysis and to the \nwide public which his writings reached. It may be em- \nphasized here, moreover, that it was largely through \nQuetelet\'s application of the same statistical method to \nanthropology, meteorology, astronomy, medicine and \nsocial science that arose the conception of statistics as a \nwidely applicable method of observation. \n\n(IV) But there is one feature of the application of this \n\n1 See pp. 47-48, supra. 2 Chapters iv and v. \n\n\n\n501] QUETELET IN THE HISTORY OF STATISTICS 59 \n\nnormal law of error which is distinctly his own, and \nwhich has been of especial significance both for the \nfurther perfection of statistical method and for the de- \nvelopment of biological science. He likened society to \na body having as its center of gravity the average man.\' \nThe determination of the properties of this average man \nwould, he thought, give a true picture of the general \nfeatures of the social body. These ideas were first pre- \nsented in " Recherches sur la loi de croissance aux dif- \nferens ages," 2 in which was presented the average height \nof groups of individuals of each age from birth to \nmaturity. It was not, however, until much later that \nthe idea of the average man as a type about which all \nmen of the same class were grouped in accordance with \na definite law was expressly developed. 3 The average \nman as a type varies with time and place. 4 Similar con- \ncepts were readily applicable to any plant or animal. \nWhat was true of the distribution of the heights of men \nmight prove to be true of any characteristic of a plant \nor animal; and what was true of the average man might \nprove to be true of the type of a species. Hence the \npossibility of studying the subject of biological variation \nby means of exact numerical measurements. \n\nThe preceding survey of Quetelet\'s statistical activity \nshows both its broadly inclusive character and its epochal \nimportance in the history of the science. It is with good \nreason that Von John declares that " Quetelet\'s master- \npiece of 1835 . . . is in fact a landmark in the historical. \n\n1 See chap, iii, infra. \n\n^Nouv. mitn., vol. vii (1831), 31 pp. \n\nr \' See chap, iii, infra. \n\n4 Quetelet was not consistent on this point of the variability of the \naverage man. \n\n\n\n60 ADOLPHE QUETELET AS STATISTICIAN [502 \n\ndevelopment, not only of political arithmetic, but also of \nthe German university statistics." 1 Among the causes \nof this eminent position must be included (1) the abun- \ndance of new data ; (2) Quetelet\'s close contact with the \nFrench scholars interested in the theory of probabilities \nand in statistics; and (3) the wide publication of his \nresults. \n\nThe abundance of new data was of primary impor- \ntance. It made possible the comprehensive treatment 2 \nof vital statistics, including a practical table of mortality \nfor Belgium, and it raised questions of criticism of \nsources and of method of treatment. Official documents \nbeing a chief source, Quetelet exerted upon them a far- \nreaching influence both through his own writings and the \nmovement for international comparability represented by \nthe Statistical Congresses. He was, in this way, largely \ninstrumental in bringing such documents to a character \nmid-way between the purely verbal Achenwall-statistics \nand the purely numerical table statistics, by including with \nthe tabular results descriptive and explanatory material. \nHe extended the scope of statistical inquiry by adding the \nnew field of moral statistics. It was mainly by this addi- \ntion and the results following thereupon that the term \nfirst used to designate a new discipline in the German \nuniversities came to have that scientific character sought \nby the school of political arithmetic. Emphasizing the \nconnection between social conditions and statistical \nresults, he made the fundamental aim of the science of \nstatistics the study of the co-existence and sequence of \nsocial phenomena in correlation with the environing con- \nditions of social life. \n\nBut he not only gave meaning to statistics as a descrip- \n\n1 Geschichte, p. 370. - Sur Vho-mme, bk. i. \n\n\n\n503] QUETELET IN THE HISTORY OF STATISTICS 6l \n\ntive science, he also developed the conception of statistics \nas a method of scientific investigation serving all the sci- \nences of observation. The law of error, developed by \nastronomers, and the theory of probability, cultivated \nzealously by that group of bright men centering around \nthe great Laplace, found in the writings of Quetelet both \nsimplification and elaboration and a channel of communi- \ncation to an extensive group of readers. Moreover, this \nmethod found a new, and, to-day, highly significant ex- \ntension in his studies of physical anthropology. \n\nFinally should be emphasized the fact that practically \neverything of importance that Quetelet hit upon, he pub- \nlished time and again. The Correspondance math&mat- \nique et physique, the Nouveaux mkmoires \xe2\x96\xa0, the Bulletins, \nand the Annuaire of the Brussels Academy, the Annu- \naire of the Observatory, and the Bulletin de la commis- \nsion centrale de statistique, as well as his numerous \nworks, furnished a varied means of communication with \nan extensive public. If further means were needed they \nwould be found in his voluminous correspondence and in \nhis connection with learned societies throughout the \nworld. \n\nQuetelet thus gathered up the chief statistical tenden- \ncies of his time, and contributed, in more or less notable \ndegree, to the advancement of each. His genius con- \nsisted not so much in original conceptions as in a keen \nappreciation of the importance of various ideas and the \ngreat practical sense with which he applied them. \n\n\n\nCHAPTER III \n\nTHE AVERAGE MAN \n\nQuetelet\'s name is customarily associated with the \nterm average man {homme moyen) and with considera- \ntions on the importance of this homme moyen for a \nstatistical study of society. The ideas involved in the \nconcept, average man, are central in all of Quetelet\'s re- \nsearches and are critical for an understanding of his writ- \nings. Apart from the unity derived from the more or \nless general presence of the notion of the average man, \nhis writings on population and moral statistics, physical \nanthropology, statistical methods and the social system \nare completely lacking in a unifying principle. G. F. \nKnapp holds that there was no continuous unfolding of \nQuetelet\'s chief ideas. 1 \n\nNo doubt the germ of all he has to say is found in the \nwritings preceding the Sur f homme of 1835, ^ ut Quete- \nlet himself has indicated the natural development of his \ncentral thoughts. He says in the preface of Du Systeme \nsocial that in his first work, Sur V homme, he pre- \nsented the idea of the average man as the mean between \ntwo limits ; that in the Letters he showed that the aver- \nage man as to height is a type about which the heights \nof other men are grouped according to the law of acci- \n\n^\'Bericht iiber die Schriften Quetelets zur Socialstatistik tmd An- \nthropologic." Hildebrand\'s Jahrbucher fur Nationalokonomie und \nStatistik, vol. xvii, p. 358. \n\n62 [504 \n\n\n\n\n\n\n5 05] THE AVERAGE MAN 63 \n\ndental causes. " In this new work I show that the law \nof accidental causes is a general law which is applied to \nindividuals as well as to peoples and which dominates \nour moral and intellectual qualities as well as our physi- \ncal qualities." There was thus, after 1835, development \nin the concept of the average man and an extension of \nits application as a means of interpreting social pheno- \nmena. \n\nA brief survey of this development and extension will \nserve to bring out the nature of this concept in its final \nform. The first researches on the qualities of the average \nman dealt with the physical qualities of height and \nweight, which are susceptible of direct measurement. In \nthe memoir " Recherches sur la loi de croissance de \n1\'homme" 2 he says, \n\nThe man that I consider here is analogous to the center of \ngravity in bodies ; he is the mean about which oscillate the \nsocial elements ; he is, so to speak, a fictitious being for whom \nall things proceed conformably to the average results obtained \nfor society. If we wish to establish the basis of a social me- \nchanics (mScanique sociale) , it is he whom we should consider, \nwithout stopping to examine particular or anomalous cases. \n\nThus the normal law of growth expressed in tabular \nform for each sex gives the average heights of male \nand female Belgians, at each age, from five months pre- \nceding birth to maturity, at about the ages of twenty- \nfive and twenty years, respectively. These tables do not \nshow the heights any particular individuals will attain at \ngiven ages, any more than a mortality table would give \nthe time of death of particular persons, but they give \n\n1 Du Systeme social el des lots qui le rigissenl (Paris, 1848), p. ix. \n2 Nouv. mim., vol. vii. \n\n\n\n64 ADOLPHE QUETELET AS STATISTICIAN [- Q 6 \n\nrather the height of the average man at each age. The \nnormal law of growth thus shown applies to the whole \ngroup of Belgians of either sex, viewed as an aggregate. \nIt is the law of growth for the average man, the heights \ngiven being those about which the heights of all persons \nof given age and sex "oscillate." Just how this oscilla- \ntion takes , place Quetelet does not at this time state. \n\xe2\x96\xa0He did state however that studies similar to this on the \nlaw of growth in height should be made for man\'s various \nphysical, intellectual and moral qualities. \n\nIn the memoir " Recherches sur le penchant au crime \naux differens ages," 1 he uses the term average man \n(homme moyen) for the first time. " If the average man \nwere determined for a nation he would present the type \nof that nation; if he could be determined from the \nensemble of men, he would present the type of the \nentire human species." He here studies the possi- \nbility and the means of determining the average man \nand hints at the average man as the type of the beautiful. \n\nThe next memoir 2 studies the relation of height to \nweight at each age, but it adds nothing to the general \nnotion of the average man. The Sur V homme gives, be- \nsides a reproduction of the preceding studies, much gen- \neral discussion of the average man 3 but adds little to the \nprecision of the concept. But in the article " Sur l\'ap- \npreciation des documents statistiques et en particulier \nsur 1\'appreciation des moyennes" 4 is developed carefully \nthe view of the average man as a type. Here, for the \n\nx Nouv. mint., vol. vii, p. i of the memoir. \n\n2 Recherches sur le poids de l\'homme aux differens ages, Nouv. rnirn., \nvol. vii. \n\n3 Especially bk. iv. \n\n* Bulletin de la com. cent, de stat., vol. ii (1845), pp. 205-287. \n\n\n\n507] THE AVERAGE MAN 65 \n\nfirst time, he gives exact connotation to the word type \nand shows just how the members of a group oscillate \nabout the average. Even in the first memoir x certain of \nthe tables showed symmetrical distribution about the \naverage, but Quetelet did not comment on the symmetry. \nBut in this later article this distribution is his theme. \n\nHaving established his scale of possibility, he begins \nan examination of the manner in which the numbers from \nwhich an average are deduced are grouped about it. 2 \nHe first distributes 8192 measurements of the height of \nthe same person about the average, seven groups above \nand seven below, according to his scale. This leads to \nthe question \n\nwhether there exists in a people a type-man, a man who \nrepresents this people as to height and in relation to whom all \nthe other men of the same nation might be considered as pre- \nsenting variations more or less great. The numbers we would \nobtain in measuring these latter would be grouped about the \naverage in the same manner as those which we would obtain \nif the same type-man were measured a great many times with \nmeans more or less clumsy. 3 \n\nA study then of the distribution of the chest measure- \nments of 5738 Scotch soldiers and of the heights of \n100,000 French conscripts shows a close agreement \nbetween the actual distribution and that calculated ac- \ncording to his scale. In fact he believes that in the \nlatter case he is able to prove fraud by the lack of con- \ntinuity in the actual distribution : a congestion below the \nrequired height and a scarcity just above it indicate that \nsome 2000 have escaped service by reducing their height \n\n1 " Recherches sur la loi de croissance de l\'homme." \n* " Sur 1\' appreciation, etc" p. 250. \n3 Ibid., p. 258. \n\n\n\n66 ADOLPHE QUETELET AS STATISTICIAN [508 \n\ntwo or three centimeters. Thus he finds not only con- \nfirmation but a practical use of the conception that there \nis a type-man from which all men are but variations. \n\nIn the Letters 1 - the matter is further elucidated \nwith much of the same data. If one should make 1000 \nmeasurements of the chest of the Gladiator, or of a liv- \ning person, or if 1000 sculptors, working without pre- \nconceived notions, should copy the Gladiator and their \ncopies should be measured, each set of measurements \nwould be grouped in accordance with the law of possi- \nbility. If we assume\' that one would likely as not make \nan error of one inch in measuring the chest of a living \nperson, then the chest measurements of the 5738 Scotch \nsoldiers are grouped with as much regularity as would \nbe the same number of measurements made on one in- \ndividual. " The measurements occur as though the \nchests measured had been modelled from the same type. \nIf such were not the case the measurements would not, \nin spite of their imperfections, group themselves with \nthe astonishing symmetry which the law of possibility \nassigns them." 2 To the objection that the Scotch \nsoldiers represent a selected group, Quetelet replied that \nthe accurate verification of the principle is more easy \nwhen all the men of a nation are taken ; the only effect \nof embracing a larger number is to widen the limits of \nvariation. 3 \n\nIn similar manner Quetelet then treats the heights of \n100,000 French conscripts. The probable error in this \ncase, however, is two inches, and his argument for the \nexistence of a type rests on the condition that a very \n\n^Letters on the Theory of Probabilities, trans, by Downes (London, \n1849), pp. 90-105. \n2 Ibid., p. 93. 3 Ibid., p. 94. \n\n\n\n5 9 ] THE AVERAGE MAN 67 \n\nunskillful person with crude instruments would be liable \nto an error of two inches in measuring a conscript of the \naverage height. \n\nEverything- occurs then as though there existed a type of man \nfrom whom all other men differ more or less. . . . Every peo- \nple presents its mean and the different variations from this \nmean in numbers which may be calculated d priori. This \nmean varies among different peoples and sometimes even \nwithin the limits of the same country, where two peoples of \ndifferent origins may be mixed together. 1 \n\nThus was presented the definite concept of the average \nman as a biological type, about which the actual men of a \ngiven group were distributed according to the normal law \nof error, or the law of accidental causes as Quetelet \ncalled it. This type was always spoken of as due to con- \nstant causes and the variations from it as due to acci- \ndental causes. The next step was to generalize this con- \ncept by extending it to all of man\'s physical properties \nand to his intellectual and moral qualities, whether with \nreference to the normal state of an individual, or to the \naverage man of a nation or of humanity considered at a \ndefinite period of time, or through all the vicissitudes of \nnational and human history. \n\nThis generalization is the theme of the Systeme social. \nThis work is divided into three books devoted respec- \ntively to man, societies and humanity. The first two \nbooks are divided into three sections each, treating re- \nspectively the physical, moral and intellectual qualities, \nwhile the third considers in a general way the effect of \nprogress in knowledge on these various qualities, their \nrelations to each other and the limits through which they \n\n1 Letters, p. 96. \n\n\n\n68 ADOLPHE QUETELET AS STATISTICIAN [$ la \n\nvary. Probably most of the points made in this work \nhad been previously noted by Quetelet, but here they are \ngrouped systematically. The aim is to show the universal \nvalidity of the law of accidental causes. " There is a \ngeneral law which dominates our universe . . . ; it \ngives to everything that breathes an infinite variety." 1 \n" Among organized beings all elements vary about an \naverage state, and these variations, due to accidental \ncauses, occur with such harmony and precision that we \ncan, in advance, classify them by number and extent." 2 \n\nThus the average man, at first somewhat vaguely con- \nceived as a mean between limits more or less extended, \nwas at length definitely conceived as a type. His delinea- \ntion was based on a law derived from the mathematical \ntheory of chances but believed to have the widest possible \nrealization in the phenomena of organic nature. The \naverage man, according to Quetelet, will show the effects \nof the operation of "constant" causes, while the varia- \ntions about him will show the effects of " perturbative " \nor "accidental" causes. Thus we have here not only a \nmanner of viewing living things, but a criterion for dis- \ntinguishing that which is typical and general, from that \nwhich is only individual. \n\nIn the determination of the properties of the average \nman, Quetelet carried on many extensive researches. \nThis was in fact the particular aim of most all of his \nstatistical studies. From the data of population statis- \ntics he sought to discover the conditions attending the \nbirth of the average man, and the time and conditions of \nhis death. The law of growth showed the height of the \naverage man at each age. 3 This was followed by a mul- \n\n1 Du Systeme social, p. 16. i Ibid., p. 17. \n\n* " Recherches sur la loi <ie croissance de l\'homme." \n\n\n\n5 1 1 ] THE A VERA GE MAN 69 \n\ntitude of studies of men\'s physical proportions at each \nage culminating in the Anthropomktrie of 1871. Simi- \nlar studies in the development of mental and moral traits \nwere those dealing with the products of dramatic talent 1 \nand with the propensity to crime. 2 Still other moral \nqualities of the average man were sought in the study of \nforesight, of suicides 3 and of marriages. 4 All of these \nstudies have great historical significance. Those in the \nplr sical proportions of men were the precursors of the \nphysical measurements of criminals as a means of identi- \nfication, and of the measurement of head forms and other \nbodily parts by physical anthropologists as a means of \nracial discrimination. Especially were they the antece- \ndents of the studies in biological variation which bid fair \nto make of biology a relatively exact science. Quetelet\'s \nstudies of mental trials were the forerunners of studies \nin experimental psychology, which seem destined to lay \nthe foundation for a science of education. Finally the \nstudies in moral statistics opened the way for the induc- \ntive study of social life. \n\nQuetelet presented a most important and extensive \nrole for the average man. 5 Many scientists, so Quetelet \nthought, would find his properties of the highest useful- \nness. The physician could thus determine the most use- \nful remedies and the action to be taken, both in the \nusual case and in the unusual, by comparing his patient \nwith the fictitious average. The artist and man of letters \n\n1 Sur V homme , bk. iii, chap. i. \n\n2 Especially " Recherches sur le penchant au crime aux differens ages." \nNotiv. mhn., vol. vii. \n\n3 Sur V homme, bk. iii, chap. ii. \n\n4 Especially " Statistique morale," Bulletin de la com. cent, de stat., \nvol. iii, and " Sur la statistique morale," Nouv. mSm., vol. xxi. \n5 Sur V homme, bk. iv. \n\n\n\njo ADOLPHE QUETELET AS STATISTICIAN [ 5I2 \n\ncould thus present a most truly representative art and \nliterature. The politician could thus more accurately \nplay upon the general sentiments and beliefs in the form- \nation of public opinion. The naturalist by the use of \nthe average man could fix racial characteristics and \ndemarcations, and determine the extent of any changes \nin racial types from time to time. Finally the social \nscientist, by determining the average man for various \nnations, from year to year, throughout the course of \nnational history, would be able to ascertain for nations \nas well as individuals, their laws of birth, growth and \ndecay, of equilibrium and motion, \xe2\x80\x94 the course followed, \nso to speak, by their centers of gravity. \n\nThere is something fascinating in this conception of \nthe average man, while the task of its complete realiza- \ntion is stupendous. It is a statistical conception of the \nuniverse possessing qualities of poetic and artistic beauty. \nEverything is to be viewed as varying about a normal \nstate in a manner to be accurately described by beautiful \nbell-shaped curves of perfect symmetry but of varying \namplitude. Thus it is that the individual varies about \nhis normal self; thus members of a group vary about \ntheir average ; thus the men of a nation, viewed as indi- \nviduals, vary about the average man of the nation ; thus \na nation varies about its normal state ; and finally, inas- \nmuch as the qualities of the average man change from \ntime to time and place to place in obedience to general \ncauses, to follow the course of the average man in the \nwhole series of nations would give us, in Quetelet\'s view, \nthe principles of a social physics, the true mechanics of \nhuman history. \n\nOne of the early objections made to the conception of \nthe average man was that he could not be constructed as \na composite being; that the attempt to put together \n\n\n\n5 !3] THE AVERAGE MAN y T \n\nnumerous average qualities would result in a monstros- \nity. Cournot argued that the averages of the bodily pro- \nportions of a group of men would not be consistent with \none another or with the conditions of viability. 1 \n\nSuch objections have often been repeated. But such \ncontroversy comes to naught. Quetelet himself called \nthe average man a " fictitious being" in his first use of \nthe term. 3 It would seem then pertinent to remark that \nthe conditions of viability for a fictitious being, or the \ngeneral harmony of his parts, can have only a speculative \ninterest and value. The result obtained by dividing the \nsum of a series of measurements by their number is \nmerely a numerical average and becomes the quality of \nan average man only by a flight of constructive imagina- \ntion. The average height of a group is readily trans- \nposed into the height of the average man of that group, \nbut no practical utility is gained by such transposition. \nIt may also be stated that the essential thing is adequately \nto represent the group, and, for this purpose, the average \nalone is not sufficient. Significant changes may occur in \n\n1 Cournot reasoned by analogy. He stated that the averages of the \nsides of a series of right triangles do not give a right triangle; nor are \nthe sides, angles and areas of a series of any kind of triangles so con- \nsistent with each other as to form a triangle. In like manner average \nbodily proportions will not fit together so as to make life possible. See \nExposition de la thiorie des chances et des probabilitis (Paris, 1843), \npp. 213-214. Quetelet replied to this in Du Systeme social, p. 35, et seq. \nHe divided a group of thirty men into three sections in such a way that \nthe average heights of all three were the same. He then found that \nother average measurements for the three sections were nearly the same. \nHe believed this experiment proved Cournot\'s criticism invalid. Now \nwhile Cournot\'s reasoning by analogy is not convincing, Quetelet\'s ex- \nperiment does not meet the issue. It proves only that the averages of \nthe same trait of several homogeneous groups are nearly equal, not that \nthe averages of several different traits are mutually harmonious. \n\n2 See p. 63, supra. \n\n\n\n72 ADOLPHE QUETELET AS STATISTICIAN [-74 \n\nthe limits of distribution, or in the standard deviation of \nthe group measurements, without affecting the average. \nMoreover, in problems of correlation very great impor- \ntance attaches to the association of group characteristics \nthroughout the whole scale of distribution. \n\nIt was one of Quetelet\'s repeated assertions that the \naverage man was the type of perfection in beauty and \ngoodness. Believing the race to be intellectually pro- \ngressive, he held the average man to be the most perfect \nintellectually, only for the time being. But believing the \nrace to be morally unprogressive, he held the average \nman to represent the type of the absolutely good. The \nsystematic presentation of Quetelet\'s argument on this \npoint should begin doubtless with the assumption of \nperfectly normal distribution of every characteristic. \nThis he fairly well established in connection with physical \nmeasurements, and he assumed it with reference to \nmental and moral traits. With respect to physical man \nhe then represented nature as an artist making a multi- \ntude of copies of the type-man, a type which, he thought, \nremained ever the same z though actual men might vary \nfrom it more or less. The type was in his mind directly \ncomparable to the true ratio of white and black balls in \nthe urn from which chance draws are made, a ratio to be \nindefinitely approached by more numerous draws. Thus \nnature is apparently "striving to produce the type," 2 \nbut fails only because of the interference of a multitude \nof accidental causes. The type may therefore be con- \nsidered the perfect model. Now the only means of dis- \ncovering nature\'s type is by finding an average from the \n\n1 See p. 78, et seq., infra. \n\n"Pearson, Grammar of Science (London, 1900), p. 484, uses a similar \nphrase, " Nature aims at a type, i. e., selects round it. etc.\'* \n\n\n\n5 j 5 ] 7\'tf\xc2\xa3 A VERA GE MAN -3 \n\nmeasurement of many products of nature\'s art. Hence \nthe average found fairly represents the perfect in phy- \nsical proportions for the time being. \n\nJust how Quetelet reached the conclusion that the \naverage man represents perfection in mental and moral \ntraits is not equally clear. It seems however to have \nbeen reached through manipulation of the phrase "free \nfrom excess and defect." This phrase he frequently ap- \nplied to the average, the excesses and defects being the \neffects of accidental causes. An excess or defect prop- \nerly denotes quantitatively more or less cf a trait than \nthe average. But the average, as shown in the preced- \ning paragraph, having become in many studies the type \nof the perfect, an excess or defect readily came to desig- \nnate too much or too little of a trait, and thus acquired \nqualitative significance. What he meant by an excess of \nmental ability or morality or health Quetelet nowhere \nclearly states. Nevertheless it seems reasonably clear \nthat, in his use of the terms, an " excess " was no better \nqualitatively than a "defect." Thus he could use the \nphrase in the most general manner, and, disregarding \nstatistical possibilities, speak of a fictitious average man, \nhaving a group of perfectly harmonious qualities, "free \nfrom every excess or defect" and hence the type cf per- \nfection of his time. 1 \n\nIt is useless here to discuss what may or may not con- \nstitute a standard of perfection. Such standards are \nprone to vary with individual ideals and with the uses to \nwhich the qualities considered are to be put. But the \nfollowing considerations may be brought to bear upon \n\nl Sur Vhornme, bk. iv. chap, i, \xc2\xa73; English translation of same, spe- \ncial preface, p. x; Du Systeme social, p. 28, et seq.; Physique sociale, \np. 391, et seq. \n\n\n\n74 ADOLPHE QUETELET AS STATISTICIAN [ 5I 6 \n\nQuetelet\'s position as presented in the two preceding \nparagraphs, (i) With reference to physical proportions \nthe average may be made a standard of beauty by pre- \nliminary definition. (2) If, however, we take Quetelet\'s \nobjective standard, namely, the type which nature is \nstriving to produce, the average is not the standard of \nperfection. For, contrary to Quetelet\'s supposition, the \nbiological type is changing, with the result that nature \nmust be represented as striving to produce not the aver- \nage height, for example, but a height somewhat above \nor below the average \xe2\x80\x94 a height more favorable to sur- \nvival and, in this respect also, more perfect. With re- \nspect to the average of mental and moral traits as the \ntype of perfection it may be stated, (1) that here, as well \nas in physical traits, the average gives a tolerably perfect \ntype of the group but by no means the most perfect in \nthe group; (2) that Quetelet seems to have juggled with \nthe phrase "free from excess and defect," using it in \ntwo senses; and (3) that average ability or average \npower in any mental trait is in no danger of being con- \nfused with superior grades of ability or power. If it be \ncontended that the perfection of Quetelet\'s average man \nconsisted largely in the harmony and balance of mental \nand moral qualities it could be replied not only that the \nconcept of the average man as a composite being having \nbeen abandoned as of doubtful utility this contention be- \ncomes futile, but also that a man combining only average \nqualities would be a mediocre person, without intellectual \nvigor or moral flavor. It might be stated also that \ntheoretically the combination of causes provides that a \nlarge group may include one or more individuals pos- \nsessed of superior grades of abilities, whether physical or \nmental, all as well-proportioned as in the average of the \ngroup. \n\n\n\n517] THE AVERAGE MAN 75 \n\nIt is usual, in criticisms of Quetelet\'s average man, to \npoint out the inconsistency of viewing - him as a type of \nperfection and nevertheless as somehow endowed with a \npropensity to crime. But while such a criticism may \npossibly be apropos, it is an extremely obvious one, and \none that neither throws any light on the true nature of \nthe so-called " propensities " nor advances our compre- \nhension of the nature of Quetelet\'s efforts. \n\nThe nature of his studies and the true criticism on the \npoint raised in the preceding paragraph may be brought \nout by distinguishing the results obtained by different \nstatistical inquiries made by Quetelet. In the first place \nhe distributed the individuals of certain groups on the \nbasis of the normal law for the purpose of finding the \naverage height or average weight of the groups. Such \na group might be the entire population of a country, a \nlarge group of soldiers, or a large number of persons of \na given age. The result obtained was the average height \nor weight of the groups studied. Quetelet called such a \nresult a quality of the average man, and certainly, if the \nqualities of the average man are to be determined at all, it \nmust be by such a process. Quetelet always thought of \na population group as distributed with reference to every \ntrait, physical, mental and moral, in such a way that the \ndepartures from the average "become rarer as they be- \ncome greater, whether above or below, and so that these \nvariations, both in number and size, are subject to a law \nwhich is that of accidental causes." z He did not how- \never make such a distribution with reference to any \nmental or moral trait. 2 A second sort of statistical \n\n1 "\' Sur la statistique morale et les principes qui doivent en former la \nbase," Nouv. m\xc2\xa3m., vol. xxi, p. 10. \n\n- On the page cited in the preceding reference he suggests such a dis- \n\n\n\ny6 ADOLPHE QUETELET AS STATISTICIAN [ 5I g \n\nstudies was that in which certain kinds of social events, \nas suicides or marriages, occuring in a group viewed col- \nlectively, were counted and the average number for a \nseries of years was found. The result was a so-called \nstatistical regularity, indicating the probable number of \nsimilar events that would occur in the same group dur- \ning the succeeding year. Very similar to these were the \nstudies in which Quetelet distributed the number of cer- \ntain moral acts, as crimes, according to the ages of the \npersons committing them. He then divided the number \nof acts by the total number of persons in the respective \nage groups. The results showed the respective prob- \nabilities of committing crime at various ages. These \nprobabilities Quetelet called the \'\'propensity to crime" \n{penchaiit au crime). x If these distinctions be sound, \nit should be evident that the so-called "propensities" to \ncrime, to marry, to commit suicide, as Quetelet found \nthem, are not characteristics of the average man of the \ngroup. The average man may have a certain inclination \nto commit crime, but it is not ascertainable from a study \nof the criminal registers. The persons committing \ncrime are, with respect to the group average, all on one \n\ntribution with reference to the tendency to marry, and, on page 14 of \nthe same essay, he presents a curve to illustrate the distribution of a \npopulation with reference to the propensity to crime, or the probability \nof committing crime. The actual distribution, however, is not made. \nMoreover the accompanying discussion shows that his curve actually \nrepresents the comparative probability of committing crime at each age. \nIt does not represent the distribution about the average propensity or \nprobability. \n\nJ In the " Recherches sur le penchant au crime aux differens ages," \nNouv. mim. t vol. vii, p. 17, Quetelet defines the penchant au crime as \nthe greater or less probability of committing crime. Moreover in Du \nSysteme social he suggests as a substitute for the word penchant the \nword possibility . \n\n\n\n519] THE AVERAGE MAN yy \n\nend of the curve of distribution, the other end of the \ncurve representing those persons who have an abhorrence \nof crime, or a propensity to conformity to law. Owing \ntherefore to the prominence given by Quetelet to the con- \ncept average man, even in the " Recherches sur le pench- \nant au crime aux differens ages," he may be criticised \nfor not indicating just when he did and when he did not \nascertain a quality of this fictitious being. \n\nBut far more important than the foregoing was Quete- \nlet\'s conception of the average man as a biological type. \nHis argument here was very similar to that already pre- \nsented with regard to the average man as the type of \nphysical beauty.\' It rested on the analogy between the \ndistribution about the average and the distribution of \nthe accidental errors. As already shown, 2 Quetelet found \nin the symmetrical distribution about the average evi- \ndence that the average was a type which nature was seek- \ning to produce. Chest measurements of Scotch soldiers \nand heights of French conscripts were distributed in the \nsame way that the same number of measurements on one \nperson would be distributed, on the assumption that one \nwould in the latter case likely as not make errors equal \nto the probable errors of the measurements of chests or \nheights. Thus, the men of a nation were grouped about \ntheir average "as if they were the results of measure- \nments made on one and the same person, but with instru- \nments clumsy enough to justify the size of the varia- \ntions." 3 \n\nQuetelet\'s analogy between the efforts of nature in \nproducing a type and of man in measuring a height of a \nperson was in appearance considerably weakened by the \n\n1 Pp. 72-73 supra. 2 Pp. 65-67 supra. \n\n8 Du Systhme social, p. 18. \n\n\n\nyg ADOLPHE QUETELET AS STATISTICIAN [520 \n\nfact that an error of three feet eleven inches in measuring \na height of five feet four inches is extremely improbable. 1 \nBut Quetelet\'s comparison may be viewed as an illustration \nof how the distribution of biological measurements in na- \nture may be expected to occur, not as a proof of nature\'s \nintentions. Moreover, as Professor Venn has pointed \nout 2 the "ideal" series of chance must be distinguished \nboth from the series obtained by measuring a group of \nhomogeneous things and from that secured by many \nmeasurements of the same thing. The first of these is \narrived at deductively, expressed by the binomial law and \nremains ever the same; the others are arrived at induc- \ntively and vary with conditions. In the case of the third \nalone does the limit represent a real thing which may be \napproached indefinitely by multiplying the number of \nmeasurements. The type in this case is real and fixed. \nBut in the second case the type is fictitious, and in living \nthings is changing, with the result that measurements \ncontinued through a long period of time do not give an \nindefinite approach to the type. \n\nQuetelet was by no means clear and consistent as to \nthe permanence of the type. He usually spoke of the \naverage man as varying from country to country, as not \nbeing the same for urban and for rural populations, as, \nin fact, being different in different environmental and \nsocial conditions. 3 In other words, "the average man \nis always such as is comformable to and necessitated by \ntime and place." 4 In direct contradiction to these ideas \n\n1 He found the average height of Frenchmen to be five feet four \ninches, and the extremes, seventeen inches and nine feet three inches. \n2 Logic of Chance (3rd ed., London, 1888), p. 26, et seq. \n3 Letters, p. 96; Du Systhne social, p. 14, et seq. \n* Sur I\'homme, bk. iv, chap, i, \xc2\xa7 3; or, Physique sociale, vol. ii, p. 391. \n\n\n\n^2l] THE AVERAGE MAN yg \n\nhe stated as his belief that the average physical proper- \nties of man have not varied from the earliest times. 1 He \nheld that plants and animals, subject to the immutable \nlaws of nature, have ever "an unalterable type." " The \ntree type has remained the same" for the olive since the \ndays of Codrus ; even to the size and number of leaves it \nhas not changed. 2 Among plants and animals not only \nhas the average, according to Quetelet, remained the \nsame, but the limits through which variations occur have \nlikewise remained unchanged. 3 He then introduces still \ngreater confusion by the apparently contradictory state- \nment that man has been able not only to raise his aver- \nages but also to restrict the limits of variation, through \nthe acquisitions of science. 4 \n\nIt seems impossible to reconcile these various proposi- \ntions. It is clear from the examples he gives that the \nlast statement does not imply in any way a conscious \napplication of laws of inheritance and biological selection, \nbut merely the effect of the advance of such sciences as \noptics and surgery in reducing physical defects, and the \neffect of the spread of knowledge in reducing illiteracy \nand in raising the average intelligence. As regards \nchanges in the human type, therefore, either in the \ntype itself or the limits of variation about it, the ac- \nquisitions of science which Quetelet had in mind, are \nin all probability ineffective, their effectiveness being de- \npendent upon the extremely doubtful tenet that acquired \ncharacteristics are inherited. A partial reconciliation of \nthe other statements of Quetelet regarding the perma- \n\n1 Du Systhne social, pp. 252 and 257; Physique sociale, vol. ii, p. 392. \n2 JDu Systeme social, pp. 252 and 257, et seq. 3 Ibid. \n\n4 Ibid., p. 259; see also Sur Vhomme, bk. iv, chap, i, \xc2\xa7 3, or Physique \nsociale, vol. ii, p. 396. \n\n\n\ngo ADOLPHE QUETELET AS STATISTICIAN [- 22 \n\nnence of the type may be found in his division of causes \ninto natural and perturbative. He says, \n\nThe average height of man is an element which has nothing- \naccidental about it ; it is the product of fixed causes which \nassign to it a determined value. 1 . . . Professions, wealth, \nclimate may cause the development of height among different \npeoples to vary. Nature and man work together to produce \nthese modifications. I have distinguished these two kinds of \naction by the names of 7iahiral and perturbative forces. The \nfirst have a character of fixity and permanence vhich does not \npertain to the second. The latter work as do accidental \ncauses. 2 \n\nThus, assuming unchanging physical conditions, an un- \nchanging average height would result, while different \ngroups within the same physical environment, selected \non the basis of occupations, for example, might have dif- \nferent average heights. So much may be said by way of \nreconciliation, keeping in mind the analogy of drawing \nballs from a bowl which served Quetelet as an epitome \nof nature. \n\nBut even this falls short of being satisfactory. If \n"perturbative" cause act as do accidental causes, then \nthey should not be linked with " natural " causes to ex- \nplain the difference in the average height of two peoples. \nIf man\'s action is only " perturbative," and therefore \naccidental, it could not change the average. But it is \ninteresting to note how very close Quetelet came to the \ndiscovery of the selective action of environment. He \nwas only one step from it in his proposition that the \naverage conforms to the necessities of time and place. \nThis statement strongly suggests modification through \n\n1 Du Systems social, p. 17. 3 Ibid., p. 21, et seq. \n\n\n\n523] THE AVERAGE MAN 8l \n\nchange of environment and adjustment to environment. \nBut Quetelet posits unchanged physical conditions \nthroughout recent geologic time 1 and apparently over- \nlooks the possibility of the migration of a species from \none environment to another. \n\nThere are other passages in Quetelet which likewise \nsuggest a selective process in nature. These are the \npassages dealing with asymmetrical distribution, or \ncases "when the chances are unequal." He found an \nexception to the general rule of symmetry in the distri- \nbution of weights. His limits here were 19 livres and \n649 livres, with an average of 140 livres. These limits \ndiffer from the average in the ratio of one to four. 2 But \nQuetelet passes over this exception to his general rule \nby insisting that the distribution is continuous and that \nthe numbers of individuals above and below the average \nare the same. In the Letters 3 he finds similar sets of \nobservations in the daily fluctuations of temperature in \nwinter, changes in the prices of grain, variation in the \nmortality rate, and the ratio of the sexes at birth, while \nbarometric pressures extend farther below than above the \naverage. He concludes that " Nature is like man in this \n\xe2\x80\x94 when it differs from its type, it is more often in exag- \ngeration than in diminution." 4 This is evidence, he \nsays, that the causes tending to produce variation in one \ndirection are stronger or more numerous than those \noperating in the opposite direction. His illustrative \nexplanation of the condition in nature which the unsym- \nmetrical curve represents is based on the distribution of \nchances in drawing balls from a bowl in which the white \nand black balls are not equal but in the ratio of three to \n\n1 \xc2\xa3>u Systeme social, p. 257. 2 Ibid., pp. 44-45. \n\n\xe2\x96\xa0" Letters xxv and xxvi." 4 Du Systtme social, p. 113. \n\n\n\n8 2 ADOLPHE QUETELET AS STATISTICIAN [524 \n\ntwo. 1 But Quetelet undoubtedly thought of the ratio \nin nature as "determined and immutable." 2 Thus, \nthough he used many expressions suggestive of evolu- \ntionary change of the type, he did not grasp the notion \nof such change. 3 Though he developed and used the \nmethod which has come to serve in the work of Galton, \nPearson and others as the basis for the mathematical \ndemonstration of evolutionary development, he did not \nhimself make any such use of it. \n\n1 Du Systeme social, p. 118, et sea. 2 Ibid., p. 118. \n\n3 This does not overlook those passages in which he speaks of the \nprogressive development of man\'s intellectual faculties. In these he \nrefers not to any biological change, but only to the increase in man\'s \ncommand over nature through the growth of scientific knowledge. \n\n\n\nCHAPTER IV \n\nMORAL STATISTICS \n\nIt has already been stated that Quetelet\'s studies in \nmoral statistics opened a new field to statistical research, \nthe sphere of human actions, where all is apparently in- \ndeterminate and individual. His venture into this field \ncreated very wide discussion, especially in Germany, fur- \nnished a statistical basis for some of the generalizations \nin the early pages of Buckle\'s History of Civilization in \nEngland, and was significant in the development of the \nmethods, concepts and scope of statistics. The purpose \nof this chapter is to survey the principles and methods \nof moral statistics as Quetelet presented them. \n\nBy moral statistics is meant that portion of the general \nscience dealing with such individual actions as are com- \nmonly classed as moral or immoral. The phenomena \nusually dealt with are crimes, suicides and marriages. \nThese actions have the characteristics of occurring more \nor less frequently in a social group, of giving opportu- \nnity for the exercise of individual discretion, judgment, \nwill, and of being correlated quite directly with social \nconditions. Any similar acts would supply data for \nmoral statistics. The first aim is to establish the norms \nfor various kinds of moral actions, that is, the average \nnumber that occur under given conditions during a \nperiod of time. These norms form the statistical regu- \nlarities, for it is found that in a series of years the \nnumbers of crimes, suicides or marriages vary about \n525] 83 \n\n\n\n84 ADOLPHE QUETELET AS STATISTICIAN [526 \n\ntheir average, showing a tendency for the average num- \nber to be repeated from year to year. These regularities \nare often called statistical or sociological laws. Moral \nstatistics then attempts to correlate the phenomena under \ninvestigation with certain physical and social conditions, \nby showing variations in the numbers as the conditions \nare changed. To do these things it follows certain well- \ndefined canons and methods. The following pages will \npresent briefly Quetelet\'s work and conclusions in this \nfield, and will consider the nature and value of statistical \nregularities and the principles of the method followed. \n\nIn the " Recherches staiistiques surle Royaume de Pays- \nBas," 1 Quetelet makes his first study in moral statistics. \nAside from the comparisons of France and the Low \nCountries he studies the ratio of condemned to accused, \nthe distribution of crimes by the age and sex of the per- \npetrators, and the number of crimes against persons and \nagainst property committed by the persons of each age \ngroup. This last matter is presented in a table, there \nbeing twelve age groups between those under sixteen and \nthose over eighty. In this he gives for the first time a scale \nof the penchant au crime for the various age groups, \nthat is, the ratio between the number of persons and the \nnumber of crimes for each group. He then compares the \nnumbers for three years under various aspects, emphasiz- \ning the remarkable uniformity of the numbers from one \nyear to another. 2 \n\nThe " Recherches sur le penchant au crime aux diffkr- \nens dges" 3 is easily Quetelet\'s most comprehensive study \nof crimes. It contains sections on the penchant au crime \n\nl Notiv. mim., vol. v, pp. 25-38. \n\n2 See quotation, chap. II, p. 55, supra. \n\n3 Nouv. mim., vol. vii. 88 pages. \n\n\n\n^ 2 J\'\\ MORAL STATISTICS 85 \n\nin general, and on the influence of education, climate, \nseasons, sex and age on this propensity. The distinction \nof crimes against persons and against property is preserved \nthroughout. At this point we wish to note only his \nemphasis on the constancy of the numbers from year to \nyear. He places as much confidence in his scale of pro- \npensity to crime as in his scale of stature or of mortal- \nity. 1 After pointing out that murders often follow quar- \nrels and other apparently fortuitous encounters, he says, \n"Nevertheless experience has proven, that not only mur- \nders are annually almost in the same number, but even \nthe instruments which are used to commit them are em- \nployed in the same proportions. . . Thus . . . we pass, \netc., 2 as quoted in chapter II, p. 55. And he closes with \nthe famous sentence, "There is a budget which we pay \nwith a frightful regularity ; it is that of prisons, chains and \nthe scaffold. " 3 \n\nThe Sur V homme of 1835 added to the preceding essay \na chapter on suicides and duels in the characteristic man- \nner, and several brief articles of 1835 and 1836 in the \nBulletins de V acadkmie royale de Bruxelles* were de- \nvoted partly to general considerations on the freedom of \nthe will and the regularity of certain social phenomena. \nSo great does he find the constancy in the number of \nmarriages by age groups that in the essay of 184.7 ne * s \nable to present a scale of the propensity to marry, 5 and \nsimilarly in the essay of 1848 he calculates a scale for \n\n1 Op. cit., p. 71; also English trans, of Sur V homme, p. viii. \n\n2 Ibid., p. 79. z Ibid., p. 81. \n\n* " Sur Ies maladies des conscrits en France," vol. ii (1835), pp. 277- \n279; "Sur la justice criminelle en Belgique," ibid., pp. 360-372: and \n" De 1\'influence de l\'age sur l\'alienation mentale et sur le penchant au \ncrime," vol. iii (1836), pp. 180 and 210. \n\n5 " Statistique morale," Bulletin de la com. cent, de slat., vol. iii \n(1847), especially note pp. 140 and 141. \n\n\n\nS6 ADOLPHE QUETELET AS STATISTICIAN [ 52 g \n\nsuicides. 1 In these later studies he repeatedly emphasizes \nthe impressive regularity in the figures from year to year. 2 \n\nIt was this emphasis upon the constancy of the social \n" budgets" which brought upon Quetelet the charge of \nbeing a fatalist and a materialist. It was this also which \ncalled forth the widest discussion and an abundant liter- \nature on the meaning and implications of the regularities \nrevealed by moral statistics. 3 Quetelet\'s explanation of \nthis constancy is therefore not without interest. He has \nnowhere given a formal and thorough discussion of this \nquestion, hence it will be necessary to bring together \nsome of his most pertinent ideas. \n\nQuetelet held quite consistently to the proposition that \nthere is no such thing as a real chance occurrence, that \nis, there is no such thing as an uncaused or unrelated \nevent. 4 If events have causes, and the same causes per- \nsist from one period of time to another, then the same \nevents may be expected to reoccur. This principle \nreceived its first expression in the Recherches statistiqties \nof 1829 in the form, "The same causes persisting we \nought to expect the same effects to be reproduced." 5 \n"The laws presiding over the development of man, and \nmodifying his actions are in general the result of his or- \nganization, of his education or knowledge, means or \nwealth, institutions, local influences and an endless variety \n\nl " Sur la statistique morale." Nouv. mim., vol. xxi, p. 36. \n\n2 See particularly " Statistique morale," p. 143, et seq., where he speaks \nof the number of marriages as another "budget controlled by the cus- \ntoms and the needs of our social organization." \n\n8 See Von John, Geschichte der Statistik (Stuttgart, 1884), pp. 362, \net seq.; for a summary of views of many writers on this subject see \nBlock, TraitS statistique, pp. 137, et seq. \n\n*See chap, i, p. 18, supra. \n\n5 Page v, and repeated many times, especially English trans, of Sur \nVhomme, p. vii and p. 6. \n\n\n\n5 2o] MORAL STATISTICS 87 \n\nof causes . . ." * Quetelet lays much stress on the in- \nfluence of physical environment 2 and of social conditions \nand institutions. Man not only possesses individuality, \nhe is also a member of society. " From this point of \nview, the regularity which we note in the formation of \nmarriages ought to be attributed not to the volition of \nindividuals, but to the habits of this concrete being which \nwe call a people, and which we regard as endowed with \na volition of its own and with habits from which it frees \nitself with difficulty." 3 "Moral causes which leave their \ntraces in social phenomena are then inherent in the nation \nand not in the individual." 4 Variations in the marriage \nstatistics of different provinces are due " to moral causes \nwhich exist outside of the individual and which are pecu- \nliar to each people. These moral causes have not essen- \ntially a character of fixity, as have causes in nature, but \nthey fluctuate and vary with time." 5 \n\nIt seems to me that that which relates to the human species, \nco7isidered en masse, is of the order of physical facts ; the greater \nthe number of individuals the more the individual will is \neffaced and leaves predominating the series of general facts \nwhich depend on the general causes, in accordance with which \n\nl Ibid., p. 7; first stated in " Recherches sur la loi de croissance de \nl\'homme," Nonv. mfrn., vol. vii, p. 1 of the essay. \n\n2 Du Systeme social, p. 8. \n\n3 " Statistique morale," p. 142. \n\n4 " Sur la statistique morale/\' Nouv. mim., vol. xxi, p. 6. In " Statis- \ntique morale," p. 138, he says, "All occurs as if a people had intended \nto contract annually almost the same number of marriages and to divide \nthem in the same proportions among the different provinces, between \ncity and country, and between bachelors, maidens, widowers and \nwidows." \n\n5 " Statistique morale," p. 142; in Sur l\'homme, \xc2\xa7 2, he says, "The \nlaws which relate to the social body are not essentially invariable; they \nchange with the nature of the causes producing them." \n\n\n\n88 ADOLPHE QUETELET AS STATISTICIAN [530 \n\nsociety exists and maintar\'ns itself. These are the causes we \nseek to ascertain, and, when we shall know them, we shall de- \ntermine effects for society as we determine effects by causes \nin the physical sciences. l \n\nThis last quotation contains the gist of Quetelet\'s ex- \nplanation. General social conditions influencing the \ngreater part of the social group, result in tolerably con- \nstant social phenomena, because, according to the law of \nlarge numbers, the effects of general causes gradually \nprevail amidst the multitude of variations due to minute \ncauses. \n\nSeveral consequences followed, in Quetelet\'s view, from \nthese principles. In the first place, if the general social \nconditions act upon man in such an apparently irresisti- \nble manner when a social group is observed, then society \nas a whole must be made responsible for the moral \n" budgets " due to social conditions. \n\nThe crimes which are annually committed seem to be a nec- \nessary result of our social organization. . . . Society prepares \nthe crime and the guilty is only the instrument by which it is \naccomplished. Hence, it happens that the unfortunate person \nwho loses his head upon the scaffold, or who ends his life in \nprison, is in some manner an expiatory victim for society. His \ncrime is the result of the circumstances in which he finds him- \nself, and the severity of his punishment is perhaps another \nresult of it. 2 \n\nA second consequence is that the sphere of individual \nfreedom is very narrowly limited. Ouetelet seems some- \n\n1 " Recherches sur le penchant au crime," pp. 80-81 of the essay; see \nalso " Recherches sur le poids de l\'homme," p. 10. \n\n2 Sur Vlwmme, last section; English trans., p. 108; see also p. 6 of the \ntranslation. \n\n\n\n-3 1 ] MORAL STATISTICS 89 \n\ntimes wholly to deny the existence of free will, but, as a \nrule, he speaks of it as a capricious element acting within \na narrow circle of possibilities. 1 In this view man\'s will \nis capable of producing the infinite variety found in indi- \nvidual action, but cannot upset the rules of the social \norganization. The individual becomes an accidental \ncause, and its effects mere accidentalities ; hence, when a \nsocial group is viewed, these effects are neutralized in \nthe same manner that accidental errors are eliminated in \nmaking a series of measurements. \n\nCharged with being a fatalist Quetelet answered by \nasserting a positive conviction that man can ameliorate \nhis own condition by his own efforts. 2 We have seen \nthat he believed the "moral causes which leave their \ntraces in social phenomena " to be capable of change. 3 \nSuch changes are, in his view, to be brought about \nthrough the action of " moral forces " exercised by man \nin modifying the conditions in which he lives. 4 But these \n" moral forces" are perturbative in their manner of action \nand the changes they bring about are very slow, like the \nsecular changes in the solar system : for this reason the \n"moral causes" which predominate in the social system \ncannot undergo any sudden change. 5 This perturbative \naction of man, according to Quetelet, depends upon the \nexercise of his reason and increases with the growth of \n\nl Sur Vhomme, Eng. trans., p. vii; ibid., " Introductory," \xc2\xa7 2, p. 6; \nDu Systeme social, pp. ix, 8, 9, 65, passim; " Statistique morale," p. \n136; " Sur la statistique morale," pp. 6, 22 and 35, et seq. \n\n2 " Recherches statistiques " (1829), note, p. 25; English trans, of Sur \nVhomme, p. vii. \n\n3 Supra, p. 87. \n\n*" Recherches sur la loi de croissance," pp. 1 and 2, and " Recher- \nches sur le penchant au crime," pp. 2 and 80. \nb " Recherches sur le penchant, etc." p. 80. \n\n\n\ngo ADOLPHE QUETELET AS STATISTICIAN [532 \n\nknowledge. 1 The causes over which man has some con- \ntrol are the social institutions; and since the modifica- \ntion of effects must begin with the modification of causes, \nthe betterment of results must begin with a reform of \nsocial institutions. 2 In order that this reform may be \ncarried out with wisdom and intelligence, it should be \nthe part of the statistician, thought Quetelet, to make \nknown, so far as possible, the social effects traceable to \nspecial institutions, and the part of the legislator, in the \nlight of this knowledge, to ameliorate social conditions. 3 \n\nThe preceding paragraphs make more or less clear \nQuetelet\'s explanation of statistical regularities, his de- \nliverances on the question of social responsibility for \ncrime, and his hope for a positive progress as man grows \nin scientific knowledge. Is his position satisfactory? \n\nAttempted explanation of the regularities of moral \nstatistics has been the cause of much fruitless discussion, \nbecause attention has been centered upon the implica- \ntions that may or may not be drawn with reference to \nthe freedom of the human will. We may avoid this \nbarren philosophical discussion by starting from a prin- \nciple which makes it impossible and by limiting ourselves \nstrictly to the field of scientific inquiry. It does not \nseem possible for any science to take any other attitude \ntoward the phenomena with which it deals, than that \nthey are related in direct and complete continuity with \n\n1 " Recherches sur la loi de croissance," p. 2. \n\n2 " De Finfluence de Fage sur Falienation mentale et sur le penchant \nau crime," Bull, de I\'acad., 1st Series, vol. iii, p. 185. \n\n* Sur Vhomme, bk. iv, final section; Eng. trans., p. 108; " Statistique \nmorale," p. 146; " Sur la statistique morale," pp. 18-19 an( ^ 3^; "Sur \nla statistique criminelle du Royaume-Uni. de la Grande-Bretagne. \nLettre a M. Porter, a Londres, par M. A. Quetelet," Bull. cent, com^ \nde sta., vol. iv, p. 121. \n\n\n\n5 33] MORAL STATISTICS gj \n\npreceding or contemporaneous phenomena. That is, the \ncausal explanation of a phenomenon must be found in \nantecedent and coexisting conditions where it arises, \nwithout resort to some extraneous, unrelated or capri- \ncious element. In so far as a phenomenon is a pure acci- \ndentally it is not material for scientific inquiry. If any \nseries or group of phenomena of a pure-chance sort were \nsubjected to investigation, no order or relation would be \ndiscernible among them. Human reason would be use- \nless and powerless in their presence, and inference would \nbe impossible. If man\'s choices were of this sort, psy- \nchology would be forever a futile pursuit and education \nuseless and purposeless. To illustrate such a condition \nby the usual figure of drawing balls from a bowl, one \nmust conceive a bowl to contain a multitude of balls of \nan equal number of shades of color. 1 The problem to \nbe solved would be to ascertain from a finite number of \ndraws the probable order of future draws, or the ratio of \nballs of one shade to those of other shades. Even the \nlargest conceivable number of draws would give no \ngrounds for inference. Under such circumstances we \nmust forever remain in the dark with no guide for our \nconduct other than unreasoning fear and superstition. \nThe reasoned and ordered knowledge which science \nseeks is possible only under the assumption that the \nefficient causes of events are found in antecedent con- \nditions. \n\nThis principle of efficient causation must then be ex- \ntended to the sphere of human conduct. This is where \nthe rub usually comes. The older view of a self with a \nwill extraneous to the motives to action and with a power \n\n^evons, Principles of Science (London, IQ05), p. 2. refers to Con- \ndorcet\'s expression, "an infinite lottery." \n\n\n\ng 2 ADOLPHE QUETELET AS STATISTICIAN [-34 \n\nof fiat regardless of the conditions of life has generally \nbeen discarded. But many, like Quetelet, who give \ngreat emphasis to the necessities which the conditions of \nlife force upon us, still reserve a little circle within which \nthis old-time self may disport at pleasure, and exercise \nits will without let or hindrance. According to the view \nwhich we present as the only basis for scientific inquiry, \neven this little circle and the self, independent of char- \nacter, motives and conditions, must be given up. This \nis a completely and frankly deterministic basis. It still \npreserves that conception of free will which means ability \nto act in accordance with our own character and motives \n\xe2\x80\x94the sort of freedom of which all are conscious. More- \nover, when it is once seen that scientific knowledge is de- \npendent on their being an order in man\'s world, and \nthat true freedom for man is dependent upon the acquisi- \ntion of a knowledge of that order, it may be added that \nthe deterministic basis makes possible the only freedom \nthat is worth while or even possible for rational creatures. \nIt seems perfectly sound then to find the explanation \nof statistical regularities in the persistence of causes. \nWere we in imagination to reduce society to a state akin \nto the static state of the economist, in which the in- \nternal and external conditions obtaining throughout the \npopulation were exactly duplicated from one year to the \nnext, we should not be astonished at the repetition with \na dull monotony of the whole gamut of social budgets. \nBut in actual dynamic society, conditions change slowly. \nCertainly the physical environment does not greatly vary \nfrom one year to the next ; the physical qualities and the \nmental traits of the population, and its distribution by \nage groups, change little in two succeeding years; the \nsocial institutions, the customs and beliefs, and knowledge \nlikewise change little. Hence the approximate repetition \n\n\n\n53 5] MORAL STATISTICS 93 \n\nof the numbers of social events from year to year. There \nwill be, for example, about the same number of persons \nin the population, who by hereditary qualities and experi- \nence, are capable of committing murder under certain in- \ncentives. From one year to another about the same \nnumber of persons thus prepared meet the needed incen- \ntives, and the deeds are done. Similarly with the number \nof suicides, or births or marriages. The explanation is \nat bottom not different from that of the recurrence of \napproximately the same number of deaths from year to \nyear. \n\nHow then shall the fluctuations in the numbers from \nyear to year be explained? Quetelet seemed to think \nthat these fluctuations were the effects of man\'s free \nwill. 1 For this reason the average of the numbers for \nseveral years shows the effect of general causes, to the \nexclusion of free will, even, as the true ratio of the balls \nin the bowl is approached as the number of draws is in- \ncreased. This however must be viewed as an erroneous \nexplanation of the fluctuations. It seems to assume that \nthe causes are perfectly constant, but that the number of \npersons who capriciously willed to yield or not to yield \nto their influence varied. But if the tolerable constancy \nof results is explained by a tolerable persistence of causes, \nthen the fluctuations must similarly be explained by \nvariations in the causes. The number of causes is ex- \ntremely large, and the fluctuations in the results are due \nto differences either in the intensities or in the combi- \n\n1 This seems to have been the view also of Prof. Richmond Mayo- \nSmith. He says, " With all the regularities there are numerous irregu- \nlarities which leave room for the freedom of the individual. And it is \nscarcely possible that statistics will ever be so perfect an instrument of \ninvestigation as to destroy these variations." Statistics and Sociology \n(New York, 1895). p. 27. \n\n\n\n94 ADOLPHE QUETELET AS STATISTICIAN [536 \n\nnations of the causes. Moreover these variations in the \ncauses, instead of being an evidence of man\'s free will, are \nfor the most part entirely, as yet, beyond his control. \nBiological variations in the structure of brain and ner- \nvous system, some unknown element in ancestral hered- \nity, may be partially responsible for fluctuations in the \nrate of suicide; or a crop failure may account for an \nincrease in crimes against property. The point is simply \nthat we cannot assume a causal explanation with respect \nto the regularities and a fantastic free-will explanation \nwith respect to the fluctuations. \n\nThis holds true also of the variations about the mean \nwere the population distributed with respect to some \nmoral trait, as tendency to crime. 1 Such a distribution \nwould be more or less well represented by the normal \nlaw of error, the variations running through all degrees \nfrom abhorrence of crime to a keen delight in it. Such a \ndistribution would thus approximate the distribution of \nchances. Does this not indicate that there is some \npurely chance or free-will element which makes it neces- \nsary to provide for more or less extensive deviations \nfrom the type form? The deviations undoubtedly exist \nbut they are not due to some capricious element assumed \nto exist in each person. The deviations indicate a free- \ndom on the part of each person in the group to act in \n\n1 We may recall here a distinction made in the preceding chapter \nbetween those statistical studies which ascertain the so-called social bud- \ngets, and those which distribute the members of a social group with \nrespect to some trait, the distribution being assumed usually to be nor- \nmal. In the preceding paragraph the fluctuations from year to year, \nfound by the former kind of studies, were considered. In this para- \ngraph the variations represented by the law of error are considered. \nQuetelet suggested such a distribution as this for mental and moral \ntraits, but did not actually make any such distribution. See chap, iii, \nPP. 75-76, st/pra. \n\n\n\n5 37] MORAL STATISTICS 95 \n\nagreement with his character and motives, but even as \nthe location of each chance in a scale of chances is de- \ntermined by a possible combination of causes, so the \nlocation of each person in the scale of distribution is de- \ntermined by that combination of causes which has de- \ntermined his character and motives. What that combi- \nnation is in any particular case may be inscrutable, with \nthe result that particular actions are as unpredictable as \nthe result of a chance draw. But the word chance in \nthis case differs from what we have called pure or abso- \nlute chance, in that it is merely a blanket term for our \nignorance of and inability to weigh the many minute \ncauses which determine the result. So the variations of \nthe members of a group about their mean, and the loca- \ntion of every member in the scale of distribution are de- \ntermined by the inscrutable and almost infinitely variable \ndifferences in heredity and environment. The differences \nin natural abilities, in experience, training, education, \nbeliefs, are sufficient to explain, in the scientific sense, \nthe variations about the mode or the mean. \n\nTt has often been stated by writers on this subject that \nthe statistical regularities have no compelling power \nover the individual. 1 Recall at this point the manner in \nwhich the regularity is formed. It is formed by count- \ning the repetitions of a particular moral act during equal \nperiods of time in a population group. The number of \nsuicides in the United States in a series of years would \nconstitute such a regularity. Now what can be meant \nby the statement that the regularity exerts no com- \npulsion over the individual, that the individual is free but \nthe mass is not, that the rule exists, but the individual \nmay or may not follow it? From the point of view \n\n*See, for example, Majro-Smith, op. cit., p. 27. \n\n\n\n9 6 adolphe quetelet AS STATISTICIAN [-33 \n\nadopted in this essay the only possible interpretation is \nthat, whereas there is a high degree of probability that \nthe group as a whole will show about the same number \nof suicides during the year following, it is impossible to \nsay what particular individuals will do the deeds. But \nthis is due merely to our ignorance of the causes 1 oper- \nating in particular cases. The regularity of moral sta- \ntistics is in this respect similar to the figures of a \nmortality table, as has often been pointed out. The in- \nability to predict the death of a given person from the \ndata of a mortality table is no evidence that this person \nwilled not to die at any particular time we might set. \nThe conditions of life and character determine whether \nthis or that individual shall be numbered among the \nsuicides. Moreover, from the manner in which the \nstatistical regularity is formed it is evident that the per- \nsons contributing to the so-called budget in any year \nare a small, and, in many cases, a selected group. They \nare found at one extreme of the curve representing the \nwhole social group. They show the results of particular \ncombinations of causes. The persons represented by the \nother slope of the curve are in no danger of becoming \nsuicides ; their conditions of nature and nurture prevent \nsuch a result. It would seem then that the statement that \nthe regularity of the mass exerts no compelling power \nover the individual is at least unenlightening. It is only a \ntruism or corollary from the method of rinding the regu- \nlarity. A more accurate description is given by the \nstatement that the same causes which produce the regu- \nlarities do, through differences in their intensity or their \n\n1 By causes as used throughout this essay is meant simply the ante- \ncedent conditions of an act, that is, inherited structure and the im- \npresses of past experience. \n\n\n\n5 39] MORAL STATISTICS gy \n\ncombination, determine the course of the individual ; but \nthat only a very small part of the group is subject to \nthose particular combinations of causes, whose effects \nappear in the regularities. If the statement in question \nshould be interpreted to mean that the individual is not \nsubject to the general conditions of the life of the group \nin which he lives, then we may invoke the whole body \nof social science to show that it is distinctly not true. \n\nIt is usually assumed as a corollary of the statement \nconsidered in the preceding paragraph that the demon- \nstration of the regularities does not disprove the doctrine \nof free will. This is true if by free will is meant action in \nagreement with our character and motives, but not true \nif a capricious element is meant. As already stated, if \nwe explain the regularities by constancy of causes, it is at \nleast inconsistent not to explain the variations by changes \nin the causes. Furthermore, when it is shown that the \nregularity changes with a change in the conditions, what \nother interpretation is possible, than that human action \nis determined by the conditions of human life? \n\nSimilar to the foregoing is the statement that the doc- \ntrine of free will cannot be disproven by statistics. With \nequal facility it might be said, the doctrine can be proved \nor disproved only by statistics. 1 If by this doctrine is \nmeant an uncaused cause, a self-originating something \nwithout an antecedent but with a consequent, though \nhaving only a small circle of activity, then it is certainly \ntrue that statistics cannot demonstrate its non-existence. \nFor statistics deals only with groups, and it will never be \nable to eliminate one cause of group variation after an- \n\n1 Quetelet, English translation of Sur Vhomme, \xc2\xa7 2, says, in answer \nto his question " Are human actions regulated by fixed laws," " Exper- \nience alone can with certainty solve a problem which no d priori rea- \nsoning could determine;" also Du SysQme social, p. 65. \n\n\n\n9 8 ADOLPHE QUETELET AS STATISTICIAN [ 54 q \n\nother, and correspondingly reduce the group, until the in- \ndividual is reached. The causes of variation are practically \ninnumerable, and to attempt to eliminate them one after \nanother to see whether a final capricious and unac- \ncounted-for element remains is not only impossible but \nwould be unending were it possible. If however the \ndoctrine means only that we are able to do this or that \nif we wish to do it, then it is not at all in conflict with \nthe explanation of statistical regularities here set forth. \nFor this would simply mean that our character and mo- \ntives determine our actions \xe2\x80\x94 character and motives being \nthemselves products of the past brought into contact \nwith present stimuli. \n\nAre the statistical regularities of such a nature as pro- \nperly to be called social laws ? Quetelet seems to have \nthought that his regularities were social laws comparable \nto the laws of physics. He speaks frequently of the \nsocial system in such terms as suggest the Systeme du \nmonde of the astronomer. After defining the average \nman as analogous to the center of gravity in bodies, he \nsays, " If we wish in some way to establish the bases of a \nsocial mechanics, it is he whom we ought to consider, \nwithout stopping to examine particular or anomalous \ncases." 1 In the Recherches sur le penchant au crime" 1 he \nstates that the average man will undergo modification \nin time. It should then be determined \n\nwhether these modifications are due to nature or ... to cer- \ntain forces, of which man disposes according" to his free \nwill. . . The science which would have for its object such a \nstudy would be a true social mechanics, which, no doubt, would \n\nRecherches sur la loi de croissance de l\'homme," p. 4. \n2 Page 2. See also " Recherches sur le poids de rhomme," pp. 10, \n11 and 12. \n\n\n\n541] MORAL STATISTICS gg \n\npresent laws quite as admirable as the mechanics of physical \nbodies, and would bring- to light principles of conservation \nwhich might be perhaps only analogous to those which we \nalready know. r \n\nHe often repeated the statement that the results ob- \ntained by viewing a large group of men were of the order \nof physical facts. 2 In the Letters 1 \' he says : \n\nThis great body (the social body) subsists by virtue of con- \nservative principles, as does everything which has proceeded \n\nfrom the hands of the Almighty When we think \n\nwe have reached the highest point of the scale we find \nlaws as fixed as those which govern the heavenly bodies : we \nturn to the phenomena of physics, where the free will of man \nis entirely effaced, so that the work of the Creator may pre- \ndominate without hindrance. The collection of these laws, \nwhich exist independently of time and of the caprices of man, \nform a separate science, which I have considered myself en- \ntitled to name social physics. \n\nIn the first place it is doubtless an exaggeration, or an \ninaccuracy to speak of the regularity itself as a statistical \nor social law. The average number of suicides in Bel- \ngium, for example, merely acquaints us with a social fact. \nSuch a fact is itself variable and has only a greater or \nless degree of probability of being repeated in the suc- \nceeding year. Such a fact however becomes the basis of \nmore or less inclusive social laws when relations of co- \nexistence and sequence are established between it and \nthe conditions in which it arises. The establishment of \nsuch relations will of course pass through all the stages \n\n*Page 2. See also " Recherches sur le poids de l\'homme," pp. 10, \nii and 12. \n\n2 See supra, p. 87. s Page 178. \n\n\n\nIO o ADOLPHE QUETELET AS STATISTICIAN [ 542 \n\nfrom hypothetical generalization to more or less exact \nquantitative statement. Changes in the fact thus be- \ncome clearly and even quantitatively correlated with \nchanges in its conditions. But while both the statistical \nfact and the social laws found through its correlations \nhave considerable scientific value, when tested by their \nusefulness in prevision, such value is not so great as that \nof many of the laws of astronomy and physics. In the \ncase of these latter, inferences have a degree of assurance \nonly slightly removed from certainty, owing to the com- \npleteness of the induction, the permanency and simplicity \nof conditions and the facility with which effects attribu- \ntable to a certain condition or to certain conditions may \nbe isolated. But in the statistical study of social phe- \nnomena the complexity and variability of conditions and \nthe very great difficulty of isolating the effects of par- \nticular causes give to inferences from established causal \nrelations to future events more or less uncertainty. Not \nonly do we not know with exactness the influence to be \nattached to each one of the conditions essential to the \nproduction of a social event but we do not know the \nproportions which will persist among the conditions \nthemselves. Thus it may be shown that the marriage \nrate in England tends to vary directly with the amount \nof foreign trade per capita of the population, T but a \nquantitative statement of the degree of change in the \nformer following a specified change in the latter can be \nmade only with a considerable margin of error. This is \nbecause the influence of the amount of imports and ex- \nports (or any other index of industrial activity) on the \nmarriage rate cannot be sufficiently isolated from other \n\n1 A. L. Bowley, Elements of Statistics (2d ed., London, 1902), pp. \n174, et seq. \n\n\n\n543] MORAL STATISTICS ioi \n\ninfluences, such as age grouping of the population, \nstandards of living and social customs. It is also due to \nthe fact that all the conditions determining the marriage \nrate, and consequently the marriage rate itself, change \nmore or less rapidly from decade to decade. \n\nIt does not seem probable therefore that social laws \nderived from the study of the regularities of moral sta- \ntistics will ever become sufficiently general to be " inde- \npendent of time and the caprices of man," as Quetelet \nexpected. Even the law of mortality changes slowly \nwith succeeding generations. But concrete social phe- \nnomena change from place to place and time to time \nand may come quickly into vogue and as quickly disap- \npear. Not only are there variations about the average \nresult for a series of years but the type itself changes \nwith its conditions. Quetelet\'s hope of arriving at \nstatistical laws independent of time and place was based \napparently on his assumption of constant causes. He \nalways spoke of the average as resulting from such \ncauses and hence free from the effects of variable and \naccidental causes. But yet he believed man capable of \nbringing about secular changes in the social budgets. 1 \nQuetelet however did not reconcile these conflicting \nnotions, 2 nor did he anywhere demonstrate the existence \nof a constant cause. Were the types of social phe- \nnomena the results of really constant causes, then their \ntrue values could be indefinitely approached by more and \nmore observations. But the average keeps shifting in \nobedience to the changing conditions of dynamic social \nlife. The illustration of drawing balls from a bowl in \n\n1 See pp. 87 and 89, supra. \n\n\'For the same conflict with reference to the Average Man, see chap, \niii, p. 78, et seq., supra. \n\n\n\n102 ADOLPHE QUETELET AS STATISTICIAN [ 544 \n\nwhich are an infinite number of white and black balls in \na fixed or determined ratio, which may be forever ap- \nproached, is not true to the conditions in society. The \nratio must be represented as changing slowly. While \ntherefore holding to the mechanical nature of social \ncausation, which was fundamental in Quetelet\'s view, the \nproblem of discovering or verifying social laws by a \nstatistical process must be made immensely more difficult \nthan he ordinarily represented it to be. For the want \nof the concept of evolutionary change Quetelet\'s social \nphysics did in fact provide only for a "social statics." \nTo this must be added the more difficult sphere of \n"social dynamics." Not only must the statistical regu- \nlarity be correlated with certain dominant social condi- \ntions, but the order of changes in the regularities them- \nselves as correlated with developing social life must be \ndiscovered and epitomized in the form of scientific law. \n\nThe preceding paragraph makes it unnecessary to em- \nphasize a point made much of in Venn\'s Logic of Chance* \nthat, inasmuch as the type in moral statistics is con- \nstantly changing, not only can it not be indefinitely ap- \nproached by long-continued observation, but it may be \neven missed altogether if statistics are collected through \nso long a time that the results arise under different sets \nof circumstances. \n\nIt remains in this chapter to state certain basic prin- \nciples of procedure followed by Quetelet in the study of \nthe moral actions of men. In estimating the physical \nqualities of men; some, as height and weight, may be \nmeasured directly, while others, as strength, can be ap- \npreciated only by their effects. It is not absurd to say \nthat one man is twice as strong as another with respect \n\n1 Second edition (London, 1876), pp. 15, 16 and 83 to 89. \n\n\n\n545 ] MORAL STATISTICS 10 $ \n\nto pressure of the hands, if this pressure applied to an \nobstacle produces effects in the ratio of two to one, con- \nditions being the same for the two men. 1 Similarly in \nthe appreciation of man\'s moral and intellectual traits it \nis necessary to admit as fundamental that " causes are \nproportional to the effects produced by them"* Thus, \nfrom a study of actions, literary products, or other effects \nwhich may be attributed to the presence of a particular \nmental or moral trait, there is sought a knowledge of the \ntrait itself. This principle was probably derived by \nQuetelet from the principle of probabilities that the ratio \nof white to black balls in an urn is that shown by \nmany drawings. Quetelet applied it in the measure- \nment of certain mental and moral traits at different ages, \nin the same way in which it would be used by the psy- \nchologist in the study of mental traits and abilities. \nThis principle is however precisely the same as that which \nmust be used by the sociologist in the inductive study \nof "types of mind" and "types of character" of a pop- \nulation. 3 \n\nThe second principle posited by Quetelet is one that \nis essential to all statistical inquiry, namely, that reliable \nresults can be obtained only by the study of many rather \nthan few individuals. It is the group rather than the in- \ndividual upon which attention must be centered. It is \nonly thus that any order or generality can be ascertained \namidst the apparently chaotic diversity that is so be- \nwildering when the members of a social group are viewed \nsingly. Here again we meet with a principle derived \nfrom the study of probabilities, namely, " that many in- \n\nlil Recherches sur le penchant au crime/\' p. 6. \n3 Ibid., p. 7. " Sur la statistique morale," p. 7. \n\'Giddings, Inductive Sociology (New York, 1901), chap. ii. \n\n\n\nIQ 4 ADOLPHE QUETELET AS STATISTICIAN [546 \n\ndependent disturbing causes of small individual effect \nneutralize one another in the mass." 1 To these two \ngeneral principles might be added many particular ones \nderived from Quetelet\'s discussion of the necessity of \ncomparability of data, of the extent to which small diver- \nsities in the data may be neglected when the numbers \nare large, and of the incompleteness of the records of \nmoral actions." 2 \n\nIt is possible to make a number of criticisms of Quet- \nelet\'s results, both in the study of the development of \ndramatic talent and in the study of the penchant au \ncrime by ages. Suffice it to say that he was inclined to \nmake an exaggerated use of the second principle noted \nabove. He relied too much on mere multiplication of \ninstances to overcome divergences in the instances \nthemselves. 3 But such criticisms by no means affect the \nvalidity of the general principles of his procedure. A \nscale of penchant au crime derived from the mere num- \nber of crimes by age groups, without regard either to the \ndifferences in the gravity of the crimes or to the varying \nproportions in which different kinds of crime are de- \ntected, 4 would not be thoroughly accurate. But this \nmeans only that attention must be given to these causes \nof error. To study man\'s nature from the manifestations \n\nRowley, op. cit., p. 263. \n\n2 See " Recherches sur la Roy. dePays-Bas," pp. 29-30; " Recherches \nsur le penchant au crime," pp. 10 and 17, et seq.; Bull, de Vacad., \nvol. ii, note p. 370; Letters, p. 219, et seq., and especially the first \npages of " Sur la statistique morale." \n\n3 That he was not unaware of the error here involved is shown by his \nstatements in Sur Vhomme, bk. iii, chap, i, \xc2\xa7 3, fourth paragraph. \n\n4 A larger proportion of crimes of violence are detected and brought \nto justice than of petty thefts. Since therefore crimes of violence, by \nQuetelet\'s tables, are more numerous at ages 21-25 and 26-30 than at \nothers, the scale based on numbers only is unduly large for these groups. \n\n\n\n54 7] MORAL STATISTICS IC >5 \n\nof that nature, to study social conditions by means of \ntheir products, and to study groups rather than indi- \nviduals in order to neutralize individual peculiarities are \nnot only valid but absolutely indispensable in statistical \nresearch. \n\nIt is thus in Quetelet\'s studies of the moral actions of \nmen that is to be found the basis of the quantitative \nstudy of social life. The Berlin Academy of Science and \nNaum Reichesberg doubtless exceeded strict accuracy in \nhailing Quetelet as " the founder of a new science,\'\' \n"social physics," or " sociology." x Sciences pass through \nvarious stages before they become quantitative. As the \ntrue pioneer in the field of moral statistics, however, he \nformulated and applied with impressive effectiveness the \nmethod of research which is especially appropriate in \nsociology and economics. It does not seem at all impos- \nsible that the social sciences may one day approximate \nthe exactness of the physical sciences. Quetelet would \nthen appear as the most conspicuous among the early \nworkers in the field of exact social science, and as the \nfirst formulator of the quantitative method in the study \nof social phenomena. The demonstration of those regu- \nlarities in human actions which evidence the presence of \nlaw, and the formulation of the method for their dis- \ncovery were immense contributions to man\'s knowledge \nof and power over his world. Though Comte used both \nthe words social physics and sociology, he did not suc- \nceed in formulating a method of investigation. This \nwas done by his scorned 2 contemporary, Quetelet. \n\n1 See chap, i, p. 33, supra. \n\na Auguste Comte, Cours de philosophie positive, (4th ed., Paris, 1877), \nvol. iv, p. 15, note. \n\n\n\nCHAPTER V \n\nSTATISTICAL METHOD \n\nIn the preceding chapter it was stated that Quetelet\'s \nmain contributions to social science were his demonstra- \ntions of and insistence upon the regularity and order in \nsocial phenomena and his formulation of a method for \ndiscovering this order. The exaltation of statistics into \nan exact instrument of observation was more uniquely \nhis service than his contention that there are laws of \nhuman action and social life. The latter was by no \nmeans a new doctrine \xe2\x80\x94 even the inductive study of sta- \ntistical regularities had been more or less steadily carried \non since the days of Graunt\'s Observations. But no one \nbefore Quetelet saw so clearly as he that the basis of the \nmethod of observation in the biological and social sciences \nmust be founded on a general characteristic of social \nphenomena themselves, namely, their variability about \ntype forms. This variability is in fact a very general \ncharacteristic of all observations in which counting or \nmeasuring is resorted to. Whether in estimating the \nheight of an animate or inanimate object from many \nmeasurements, or the average height of a group of like \nthings, as a group of men, whether we seek the reaction \ntime of a single individual or of a group of individuals \nthere is found a variation of the results about the average \nor type. Quetelet\'s conception of the average man was \nbased on the doctrine that in all that relates to social \ngroups there will be found this variability about the \n106 [548 \n\n\n\n549 ] STATISTICAL METHOD 1Q y \n\ngroup average. His statistical method therefore became \na search for averages, for the limits of variation and for \nthe manner in which this variation, under ordinary con- \nditions, would occur. It was his general supposition \nthat the distribution about the mean would agree with \nthe distribution of probabilities shown by the probability \ncurve. The first step in the presentation of his method \nwill therefore be an exposition of the derivation of his \nprobability scale, and its use in the study of averages \nand deviations. Then we shall pass to Quetelet\'s classi- \nfication of causes and his methods of locating them. \n\nOn its theoretical side Quetelet\'s statistical method \nwas the outgrowth of an application of certain principles \nof the theory of probabilities to his researches. Such \napplication is shown in a general way throughout his \nearlier works in his insistence upon the study of groups, \nor the employment of large numbers of observations, in \norder to allow the effects of accidental causes to neutralize \nthemselves; in his statement that "the precision of results \nincreases as the square root of the number of observa- \ntions ; " x and in his suggestion of the use of the probable \nerror in determining the value of data. 2 But his ideas \nwere not given systematic treatment previous to the \nessay Sur V appreciation des documents statistioues, et en \nparticulier sur \xc2\xa3 appreciation des moyennes? \n\nIn the first part 4 of this essay he classifies causes as \nconstant, variable and accidental, and shows by examples \nhow to detect their presence and how to eliminate the \n\n1 Sur I\'homme, bk. iv, chap, ii; English translation, p. 105. \n\n2 Ibid., p. 103. \n\n5 Bulletin de la commission centrale de statistigue, vol. ii (1845), pp. \n205-286. \n\n* " Premiere partie. Appreciation generate des causes etde leurs ten- \ndances." \n\n\n\nI0 8 ADOLPHE QUETELET AS STATISTICIAN [550 \n\neffects of periodically variable and of accidental causes. 1 \nIn the second part 2 he sets for himself the problem of \ndetermining "the degree of energy and the mode of \naction" of these causes. As introductory to this he in- \nquires into the probability of results under various sup- \npositions. In the first place, 3 he supposes the number \nof chances to be known, and to be rigorously equal to \neach other. The probability of the desired result is then \nexpressed by a fraction having as its numerator the num- \nber of chances favorable to the event, and as its denom- \ninator the total number of chances. Thus, in drawing a \nball from an urn containing three white and one black \nballs, the probability of drawing a white ball is f. The \nprobability of drawing a black ball is i, and the sum of \nthese two probabilities is unity, the symbol of certainty. \nIf the urn contain an infinite number of white and black \nballs in equal numbers, the probability of drawing a \nwhite ball is i. In a few draws the ratio of the white to \nthe black balls drawn may vary considerably from their \nratio in the urn, that is, may be now too large and now \ntoo small, owing to the action of many accidental causes ; \nbut in a large number of trials there will be drawn \nalmost as many white as black balls. This is due to the \nfact that the true ratio of the balls in the urn acts as a \nconstant cause, giving to balls of each color the definite \nprobability of one-half. \n\nQuetelet supposes, secondly, that the number of \nchances is unknown. 4 In this case one knows neither \nthe colors of the balls in the urn nor the ratio of balls \n\n1 See infra, p. 129, et seg. \n\n3 " Deuxieme partie. Appreciation mathematique des causes et de \nleurs tendances." \nz Ibid., \xc2\xa7ii; Letters, p. 7, et seg. i I6id., \xc2\xa7 iii. \n\n\n\n55 1 ] ST A TISTICAL METHOD 10 g \n\nof one color to those of another. But by repeated draw- \nings one can determine both of these unknown facts. \nThe precision of the ratios thus found, or their approxi- \nmation to the true ratios, " increases proportionally to \nthe square root of the number of trials." 1 "But the \nurn we interrogate is nature." 3 Thus, if one asks what \nis the ratio of male to female births, it is necessary to \nbring together the results for a series of years. The \nnumber of male births for every one thousand female \nbirths is found to vary in Belgium, 1834 to 1842 in- \nclusive, from 1055 to 1076, with an average of 1065 to \n1000. This ratio in nature is comparable to the fixed \nratio of white to black balls in the urn ; and in either \ncase the true ratio is approached more and more closely \nas the data increase. \n\nIn the third place Quetelet inquires into the law of \npossibility when the number of chances is limited ; that \nis, when the number of chances is small, how are they \ndistributed? If the balls are drawn one at a time from \nan urn containing an equal number of white and black \nballs, it is clear that there are two equal chances, either \na white or a black ball may be drawn. The two chances \nare divided equally between the two possible results or \nin the ratio of 1:1. If we wish to speak in terms of \nprobabilities, instead of chances, we may say that either \nresult has a probability of h The sum of the probabilities \nof drawing a white and of drawing a black ball is there- \nfore i + i, or unity. \n\nSuppose next that from a long record of draws made \none at a time, we unite the first and second, the third \nand fourth, the fifth and sixth, and so on, and that we \nrepresent white by a and black by b. The first one of \n\n1 Ibid., p. 230. 2 See also Letters, p. 10. \n\n\n\nHO ADOLPHE QUETELET AS STATISTICIAN [552 \n\nthe two balls drawn may be equally either a or b, and \nlikewise the second may be equally a or b. If the first \nbe a, the result of adding the second may be either aa \nor ab, and if the first be b, the result of adding the \nsecond may be either ba or bb. All four of these results, \naa, ab< ba and bb are equally probable. Since however \nab and ba are alike in composition, each being composed \nof one white and one black ball, there are in reality only \nthree possible combinations, namely two white, one \nwhite and one black and two black, or aa, ab or ba, and \nbb. Among these three combinations the four chances \nare distributed in the order 1, 2, 1, or in the order of \nthe coefficients in the expansion of (a + b) 2 or a 2 -f \n2ab J cb 2 . If now we inquire as to the probability of \neach of the combinations, we note that aa has one out \nof the four equal chances, ab (or ba) two out of the four \nand bb, one out of the four; therefore their respective \nprobabilities are i 3 f, I, 1 the sum of which again gives \nunity. The probabilities may be obtained directly by \nexpanding (i + |) 2 . \n\nAt the risk of tediousness the demonstration may be \ncarried one step further, by supposing the draws to be \ntaken in groups of three at a time. To each of the four \nequally likely results obtained by taking them two at a \ntime will thus be added a or b. There is thus obtained \neight equally probable combinations, namely aaa, aab, \naba, abb, baa, bab, bba and bbb. 2 Out of these eight, \n\nx In the article "Sur l\'appreciation, etc.,\'" Quetelet does not touch \nupon the probability of a compound event. But in the Letters (" Let- \nter vi ") he shows that the probability of a compound event is equal to \nthe product of the probabilities of the simple events composing it. Thus \nin the case just noted, the probability of drawing a or b is y 2 \\ hence \nthe probability of drawing aa, ab, ba or bb is % X x /i or %. \n\n2 From the preceding note it is clear that the probability of any one \nof these eight combinations is (/^) 3 . \n\n\n\n553 ] STATISTICAL METHOD IIT \n\nonly one contains all white or all black, while three con- \ntain two white and one black, and three contain two \nblack and one white. There are thus four different com- \nbinations, acta, aab, abb and bbb, and the eight chances \nare distributed among them in the order i, 3, 3, 1, or in \nthe order of the coefficients in the expansion of the \nbinomial (a -f- b) s . The probabilities of the four com- \nbinations are evidently 1, f , f and 1, or the results ob- \ntained by expanding (i + i) 3 , the sum of the probabili- \nties being here, as always, equal to unity. If taken four \nat a time, there are five different combinations, among \nwhich are distributed sixteen equal chances in the order \n1, 4, 6, 4, 1 or the coefficients of (a + b) i . Moreover \nthe probabilities of the five combinations are -ft, t\\, t \\, \ntV and tV respectively, or the results given by (i+ i) 4 . \nFrom these examples it appears that the distribution \nof the chances of the various combinations follows the \norder of the coefficients in the successive powers of the \nbinomial expansion, or the series given by the successive \nlines of the arithmetic triangle. 1 There is in every case \na perfectly symmetrical distribution of chances on either \nside of the most probable combinations. It must not \nhowever be supposed that the various combinations will, \nin actual experiment, be drawn in the proportions indi- \ncated by theory. Many accidental causes lead to fluctu- \nations of the experienced distributions about the theo- \nretical distribution ; but in the long run these fluctuations \nare neutralized so that by a sufficient number of draws \nthe actual distribution of the frequencies of the combina- \ntions can be made to approach indefinitely the theoretical \ndistribution. 2 \n\nx Quetelet presents this triangle {ibid., p. 235, and Letters, p. 60) up \nto the 13th line. See Jevons, Principles of Science (London, 1905), \np. 182, et seq. \n\n2 Letters, pp. 35-36. \n\n\n\nII2 ADOLPHE QUETELET AS STATISTICIAN [554 \n\nQuetelet next tests this agreement between theory and \nexperience by making 4096 draws, one ball at a time, \nfrom an urn containing forty white and forty black balls. 1 \nEach draw is registered and the ball returned to the urn. \nThe results are then studied to determine the proportion \nof black balls in all the possible combinations, when the \ndraws are grouped two at a time, three at a time and so \non up to twelve at a time. He also tests with satis- \nfactory results the validity of the principle that the pre- \ncision of results increases as the square root of the num- \nber of draws. \n\nIn the fourth place Quetelet inquires into the laws of \npossibility (or the scale of the distribution of chances) \nwhen the number of chances is u?ili?nited. t He states that \n\nwhen we interrogate nature, the number of chances is gen- \nerally presented to us as unlimited, that is to say, one must \nconceive that each group which is drawn from the urn may be \ncomposed of an infinite number of balls, and that, conse- \nquently, the number of groups may be likewise unlimited, and \nmay present white and black balls in every imaginable com- \nbination. \n\nBut since the number of trials with which one deals in \nexperience is always relatively limited, and since one can \nneither actually conceive nor calculate an infinite series, \nQuetelet believes all practical purposes will be served by \nthe probabilities of the 1000 combinations that are pos- \nsible when 999 balls are drawn at once from a bowl con- \ntaining a multitude of white and black balls in equal \nnumbers. The total number of chances in this case is \nrepresented by a number composed of more than three \n\n1 " Sur r appreciation, etc.," 2nd part, \xc2\xa7\xc2\xa7 vi and vii. \nIbid., \xc2\xa7 viii. \n\n\n\n555] STA TISTICAL METHOD 1 T 3 \n\nhundred figures. Since in all these chances there is only \none of drawing all 999 balls of one color, such a result \nmay be viewed as impossible. All the combinations \nhaving more than 549 balls or fewer than 450 balls of \none color, whether white or black, have all together \nlittle more than one chance in one thousand, while all \nthose combinations having more than 579 balls or fewer \nthan 420 balls of one kind, have scarcely one chance in \nten million. Hence it is useless to consider the proba- \nbilities of combinations beyond these latter limits. \n\nQuetelet then presents a table (see Table A on the next \npage) showing the probabilities of drawing each of the \ncombinations from the most probable one of 499 white \nand 500 black to the scarcely probable one of 420 white \nand 579 black. 1 Each of these eighty groups is paralleled \nby an equally probable one in which the colors are inter- \nchanged. Alongside of the scale showing the probability \nof each combination is a table (Table B) which gives the \n"scale of precision," or the sum of the probabilities be- \nginning with the most probable group, and a table (Table \nC) giving the relative probability of drawing each group. \nEach combination is ranked, the most probable com- \nbination being rank one. The first twenty-two ranks of \nthis scale are presented herewith. 2 \n\n1 " Sur l\'appreciation, etc.," pp. 244-245. \n\n2 For the complete table see Letters pp. 256-258; Bowley, op. cit., p. \n273 gives Table B and Table C for the eighty ranks. \n\n\n\nII4 ADOLPHE QUETELET AS STATISTICIAN \n\nScale of Possibility and Precision \n\n\n\n[556 \n\n\n\n\n\n\n\n\n\nScale of \n\n\nScale of \n\n\nScale of \n\n\n\n\nOUPS OF \n\n\n3 \n\nO \n\n\nPossibility. \n\n\nPrecision. \n\n\nPossibility. \n\n\nGr \n\n\n\n\nSum of the \n\n\n\n\n\n\n\n\na \n\n\nProbability \n\n\nprobabilities, \n\n\nRelative \n\n\n\n\n\n\n\n\nof drawing \n\n\ncommencing \n\n\nprobability \n\n\n\n\n\n\n\n\neach group \xe2\x80\x94 \n\n\nwith most \n\n\nof drawing \n\n\n\n\n\n\n\n\nTable A. \n\n\nprobable group \n\n\neach group \n\n\n\n\n\n\n1 \n\n\n\n\n\xe2\x80\x94Table B. \n\n\n\xe2\x80\x94 Table C. \n\n\n499 white and 500 black. \n\n\n.025225 \n\n\n.025225 \n\n\n1. 000000 \n\n\n498 \n\n\n501 " \n\n\n2 \n\n\n.025124 \n\n\n\xe2\x80\xa2G 50349 \n\n\n.996008 \n\n\n497 \n\n\n502 " \n\n\n3 \n\n\n.024924 \n\n\n.075273 \n\n\n.988072 \n\n\n496 \n\n\n503 " \n\n\n4 \n\n\n.024627 \n\n\n.O999OO \n\n\n.976285 \n\n\n495 \n\n\n504 " \n\n\n5 \n\n\n.024236 \n\n\n.124136 \n\n\n.9607\' 9 \n\n\n494 \n\n\n505 " \n\n\n6 \n\n\n.023756 \n\n\n.I47892 \n\n\n.941764 \n\n\n493 \n\n\n506 " \n\n\n7 \n\n\n.023193 \n\n\n.171085 \n\n\n.919429 \n\n\n492 \n\n\n507 " \n\n\n8 \n\n\n.022552 \n\n\n.193637 \n\n\n.894040 \n\n\n491 \n\n\n508 " \n\n\n9 \n\n\n.021842 \n\n\n\xe2\x80\xa2215479 \n\n\n.865882 \n\n\n490 \n\n\n509 " \n\n\n10 \n\n\n.021069 \n\n\n.236548 \n\n\n.835261 \n\n\n489 \n\n\n510 " \n\n\n11 \n\n\n.020243 \n\n\n.256791 \n\n\n.802506 \n\n\n488 \n\n\n511 " \n\n\n12 \n\n\n.019372 \n\n\n.276163 \n\n\n.767956 \n\n\n487 \n\n\n512 " \n\n\n13 \n\n\n.018464 \n\n\n.294627 \n\n\n.731058 \n\n\n486 \n\n\n513 " \n\n\n14 \n\n\n.027528 \n\n\n.312155 \n\n\n,604860 \n\n\n485 \n\n\n514 " \n\n\n15 \n\n\n.016573 \n\n\n.338728 \n\n\n,657008 \n\n\n484 \n\n\n515 " \n\n\n16 \n\n\n.015608 \n\n\n.344355 \n\n\nX 18736 \n\n\n483 \n\n\n\' 516 " \n\n\n17 \n\n\n.014640 \n\n\n.358975 \n\n\n.580364 \n\n\n482 \n\n\n517 " \n\n\n18 \n\n\n.013677 \n\n\n.372652 \n\n\n.542197 \n\n\n481 \n\n\n\' 518 " \n\n\n19 \n\n\n.012726 \n\n\n.385378 \n\n\n.504516 \n\n\n480 \n\n\n519 " \n\n\n20 \n\n\n.011794 \n\n\n.397172 \n\n\n.467576 \n\n\n479 \n\n\n520 " \n\n\n21 \n\n\n.010887 \n\n\n.408060 \n\n\n.431609 \n\n\n478 \n\n\n521 " \n\n\n22 \n\n\n.010008 \n\n\n.41807O \n\n\n.396815 \n\n\n\nIn deducing this scale Quetelet first found Table C. 1 \nAs already shown the number of chances of any com- \nbination is given by its coefficient in the binomial expan- \nsion. If one represents the probability of the most fre- \nquent combinations by unity, the relative probabilities of \nother combinations with respect to unity may be readily \n\n\n\nIbid., " Addition," p. 274, et seq.; Letters, "Notes," p. 259, et seq. \n\n\n\n557] STATISTICAL METHOD n ^ \n\nfound. Now the coefficient of the general term in the \ndevelopment of the binomial is \n\nm (m\xe2\x80\x94i) (m \xe2\x80\x94 2) . . . (m \xe2\x80\x94 n-\\-i) \n1. 2. 3 ... ft \n\nand the term immediately following is \n\ntn (jn \xe2\x80\x94 1) (m\xe2\x80\x94 2) . . . (m \xe2\x80\x94 n-\\-i) (m \xe2\x80\x94 n) \n1. 2. 3. . . n (\xc2\xbb + i) \n\nThese coefficients show the respective chances of two \n\nTn \xe2\x80\x94 n \n\nsucceeding- combinations. Their ratio is as 1 : \xe2\x80\x94 , \n\nfe n-\\-i. \n\nIf therefore the probability of the most frequent com- \nbination is represented by unity, the probability of the \n\n,. \' .. 1 \xe2\x80\xa2 \xe2\x80\xa2 \xe2\x96\xa0, m \xe2\x80\x94 n \n\nimmediately succeeding combination becomes \xe2\x80\x94 j_ \xe2\x80\x94 \n\nMoreover the coefficient of any term being known, the \n\ncoefficient of the succeeding term may be found by \n\nm \xe2\x80\x94 n \nmultiplying the known value by \xe2\x80\x94 ^r \xe2\x80\x94 It must be \n\nnoted that n is always one less than the number of the \nknown term. In drawing 999 balls at a time the most \nprobable combination is 499 of one color and 500 of the \nother. This term in the series would be either the 500th \nor the 501st; as however Quetelet works with the second \nhalf of the symmetrical series, he begins with the 501st \nterm. Representing its probability by unity, the prob- \nability of the succeeding combination, that is, 498 white \n\n999 \xe2\x80\x94 500 499 \nand 501 black, becomes , i or ~~ This reduces \n\nto .996008. This is also the relative probability of draw- \ning 498 black and 501 white. The probability of draw- \ning 497 of one color and 502 of the other becomes \n\n\n\nH6 ADOLPHE QUETELET AS STATISTICIAN [558 \n\n, m \xe2\x80\x94 n 499 498 \n\nmultiplied by -^q~f or \xe2\x80\x94-- X - Q \xe2\x80\x94 By this process \n\nwere found the successive values of Table C. \n\nTable A is next deduced. Designating by a, a \', a\'\\ \netc., the successive values of Table C, and their sum by \nza, Quetelet states that the absolute probabilities of \n\nTable A result from the divisions indicated by \xe2\x80\x94 , \xe2\x80\x94 , \n,, ia la \n\na \n\xe2\x80\x94 , etc. 1 Quetelet\'s description of his procedure is not \n\nz*a \n\nquite accurate at this point. The values of Table A are \n\nin fact found by the following divisions: , , , \n\n21a 22a 22a \n\netc. The result of dividing each of the relative proba- \nbilities given in Table C by their sum is that the sum of \nthe quotients thus obtained is equal to unity. This \nwould mean that the sum of the absolute probabilities \nof one-half of the combinations should be considered \nequal to unity. But since the symbol of certainty is \nunity, the sum of the probabilities of one-half of the \ncombinations must equal .50, as Table B indicates. \nHence the individual relative probabilities must be \ndivided by twice their sum in order to get the absolute \nprobabilities. \n\nFrom Table A is found Table B by adding the suc- \ncessive values. The sum of the probabilities as given \nfor eighty ranks in Table B, amounts to .4999992. \nDoubling this, so as to include the probabilities of the \nparallel groups, gives .9999984. As unity represents \ncertainty, the difference between one and .9999984 or \n.0000016 represents the total probability of all combina- \ntions beyond 579 of one color and 420 of the other. \n\n^\'Sur 1\' appreciation, etc.,\' 1 p. 275; Letters, pp. 260-261. \n\n\n\n559] STATISTICAL METHOD ny \n\nThe distribution of the chances or probabilities for \nfifty combinations on each side of the most probable \ncombinations is then presented graphically. 1 The re- \nspective probabilities are represented by rectangles, \nwhich by their relative sizes show the rapidity with \nwhich the probabilities diminish. Assuming that in \nnature the accidental causes of variation are infinite in \nnumber, and that consequently " events vary through \ninfinite and imperceptible degrees," 2 it is necessary, in \norder accurately to represent nature, to conceive the \nnumber of rectangles to be indefinitely increased and \ntheir width indefinitely diminished, until the lines joining \ntheir tops merge into a continuous curve. This curve \nis the curve of possibilities (courbe des possibility). It \nshows the distribution of chances when their number is \nunlimited. Quetelet deduces the value of the mean term, \nor coefficient of the most probable combination when \nthe number of terms is infinitely great, the probability of \nthis term, and the formula for the curve of possibility \nitself. 3 He also makes a comparison between his scale, \n"calculated on the basis of a thousand different events," \nand that given by Cournot, " in which the probability of \nthe expected event may pass through every possible \ngradation." He finds that one rank of his table corre- \nsponds closely to four and one-half ranks of Cournot\'s \ntable. 4 \n\nThroughout the foregoing development Quetelet con- \ntinually assumed that the chances were equally favorable \n\nx<< Sur l\'appreciation, etc." \xc2\xa7 ix, and chart at end of that essay; \nLetters, p. 68. \n2 Ibid., p. 249. \n\n3 Ibid., p. 276, et seq.\\ Letters, p. 263, et seq. \n"Ibid., p. 280, et seq.; Letters, p. 255, et seq. \n\n\n\nIl8 ADOLPHE QUETELET AS STATISTICIAN [560 \n\nto white and black balls. On this assumption he gets, \nin theory, the perfectly symmetrical distribution of \nchances shown by the coefficients of the binominal ex- \npansion. Moreover, this hypothesis provides for the \noccurrence of combinations farthest removed from the \nmost probable one. Theoretically there is an infinites- \nimal probability for the combination having an infinite \nnumber of balls of one color. But, as Quetelet points \nout, 1 these extremely small probabilities may be ne- \nglected. When he comes to test the agreement between \ntheory and practice 2 he finds that even in drawing as \nfew as ten, eleven or twelve balls at a time, he does not \nget, in several hundred draws, a single combination of \nballs all of one color. Thus in experience the extreme \ncombinations do not occur if the number of possible \ncombinations is very great. \n\nQuetelet passes next to the application of his law of \npossibility to scientific observations. This application \ninvolves Quetelet\'s theory of means. He says, " the \ntheory of Means serves as a basis to all sciences of obser- \nvation." 3 "In all things to which plus or minus may \nbe applied, there are necessarily three things to consider, \n\xe2\x80\x94 one mean and two extremes." 4 "Means properly so \ncalled " are to be distinguished from " arithmetic means." 5 \nTheir difference was not in the process by which they are \nfound, for both are found by the method of finding an \narithmetic average, but rather in the nature of the obser- \nvations from which they are derived. The average of \nmany measurements of the height of a certain house \nwould give a true mean, while that of the heights of the \n\nl " Sur 1\'appreciation, etc.," p. 243; Letters, pp. 66-67. \n\n*Ibid., \xc2\xa7\xc2\xa7 vi and vii; Letters, pp. 62, 254-255. \n\n% Letters, p. 38. K Ibid., p. 39. h Ibid., " Letter xi." \n\n\n\ng6l] STATISTICAL METHOD Iir) \n\nhouses on a given street would be only an arithmetic \nmean. Many measurements of the same thing are bound \ntogether by a "law of continuity," I they are grouped \nabout their average " in a determinate order, which is \nthat assigned by the scale of possibility." 3 It was one \nof Quetelet\'s most important discoveries that the meas- \nurements of the height or other physical trait of a group \nof men were likewise grouped about their average. \nThus the average height, as represented by the average \nman, is a true mean. \n\nQuetelet\'s law of the distribution of chances must first \nbe related to the distribution of a set of measurements \nof the same thing about their mean and then to the dis- \ntribution of biological measurements. 3 We deal then \nfirst with the errors of the measurements. Quetelet did \nnot define the term error. It may be defined (i) as the \ndifference between the true value sought and any meas- \nurement or (2) as the difference between the average and \nany measurement. 4 As the average approaches the true \nvalue through more and more measurements, the two \ndefinitions finally coincide. Quetelet made no systematic \nstatement of the hypotheses underlying the theory of the \ndistribution of errors, but they may be found, expressly \nor impliedly, in his work. They may be stated as follows : \n\n(1) The average of a series of measurements repre- \n\n1 Letters, p. 42. \n\n2 Ibid., p. Jj; " Sur 1\'appreciation, etc.," p. 250. \n\n8 Quetelet speaks indifferently of the distribution of errors and the \ndistribution of measurements; and while of course the former distribu- \ntion determines the latter, it is to the distribution of errors that the dis- \ntribution of chances by the binominal law is assimilated. \n\n*See Mansfield Merriman, A Text-book on the Method of Least \nSquares (3rd ed., New York, 1888), p. 5. \n\n\n\n120 ADOLPHE QUETELET AS STATISTICIAN [$6 2 \n\nsents an approximation to the true value sought. 1 \nTheory indicates that the precision of this approxima- \ntion increases as the- square root of the number of obser- \nvations. 2 \n\n(2) The causes of the errors are called accidental \ncauses. They are very numerous, even infinite in num- \nber; they act independently of each other; each is of \nsmall effect. 3 \n\n(3) These causes are equally favorable to excess and \nto defect. " Each of the accidental causes . . . has the \nsame probability of acting in one direction as (in) the \nother. This probability is then i-" 4 This is the same \nas the probability of drawing a white or a black ball from \na bowl containing an equal number of balls of each color. \nFor this reason the errors resulting from the various \ncombinations of many accidental causes of error will be \ndistributed according to the binomial law. From this it \nfollows both that the errors are symmetrically distri- \nbuted about the mean and that "small errors are more \nnumerous than large ones," 5 or as Quetelet phrases it, \nthe greater number of observations " occur in the im- \nmediate neighborhood" of the mean, and "the further \nwe depart from the mean, the fewer observations will \neach group include." 6 \n\n(4) Though the theory provides for errors of any \namount, there are always more or less narrow limits \nbeyond which errors do not occur. \n\n1 Letters, pp. 72, 76, 90. \n\n2 Ibid., p. 36, and " Letters" xvi and xvii. \n\n3 Ibid., pp. 22, 107, 108, et seq., passim. \n\n^Ibid., p. 280; see also pp. 77-78, 84. \n\n5 Merriman, op. cit., p. 15. \n\n6 Letters, pp. 77, go; "Sur l\'appreciation, etc.," p. 250. \n\n\n\n563] STATISTICAL METHOD I2 i \n\nBy very similar principles to the foregoing the law of \nthe distribution of chances may be related to the distri- \nbution of biological measurements. In this case the \naverage is an approximation to the group type. There \nare assumed to be a vast number of minute independent \ncauses of deviation from the type or average, equally \nfavorable to excess or deficiency of development. \nFinally small deviations are most numerous, the devia- \ntions become less numerous as they become larger, and \nthere are limits beyond which deviations from the type \ndo not occur in nature. Thus the Average Man becomes \nthe type, about which all other men of a homogeneous \ngroup are distributed according to a definite law. \n\nIt was in the foregoing manner that Quetelet trans- \nformed the law of the combinations of two independent \nevents when the number of chances is very large, that is \nthe binominal law, into a law of error, and then made \nthis latter serve as the law of distribution of variations \namong living things. \n\nIn testing the fit of a series of measurements to his \nscale of precision Quetelet usually made use of a table \nconsisting of nine columns. 1 \n\nThe following example, showing the distribution of \nthe chest measurements of 5738 Scotch soldiers, serves \nbetter than any other from Quetelet\'s writings to illus- \ntrate the process involved : \n\n1 Sqq " Sur 1\' appreciation, etc.," pp. 251, 252, 255, 259, 260; Letters, \npp. 85, 88, 276, 277; and Bowley, Elements of Statistics (2d ed., Lon- \ndon, 1902), pp. 278-279. \n\n\n\n122 \n\n\n\nADOLPHE QUETELET AS STATISTICIAN \n\n\n\n[564 \n\n\n\n\n\n1. \n\n\n2. \n\n\n1 \n\n3- \n\n\n4. \n\n\nI \n5- \n\n\n6. \n\n\nI \n\n7- \n\n\n8. \n\n\n9- \n\n\n\n\nO \n\n\n\xc2\xa3 \n\n\n!? \n\n\ns \n\n\n# \n\n\n*J \n\n\nhd \n\n\nO \n\n\nO \n\n\n\n\na ^ \n\n\n3 \n\ncr \n\xe2\x96\xba1 \n\n\n3 !=t \n\ncrff. \n\n\nV O \n\nET. 3 aj \n\n\n^3- \n\n\n\n\n\n\n\na ST \n\n\n\xc2\xab s \xc2\xab $ \n\n<-* 3 a \n\n\n\n\n2, \n\n\nCD O \n\n2 \xc2\xbb \n\n\noCfq a.- \na r+v; \n\n\nb3 \n\n\n\n\n\n\n*^ o*cr. \n\n\n^gmS \n\n\n\n\n\n\nn> \n\na \n\n\n\xe2\x80\xa2 \xc2\xa3L \n\n\n1 \n\n\n\n\nO 3 \n\n? cr \n\n\n1 \n0.5000 \n\n\n\n\nft. ? \n\n\xe2\x80\xa2-t \n\nT \' \n\n\n33 \n\n\ninches. \n\n\n3 \n\n\n0.0005 \n\n\n0.5000 \n\n\n\n\n0.0007 \n\n\n\xe2\x80\x940.0002 \n\n\n34 \n\n\n\n\n18 \n\n\n0.0031 \n\n\n0-4995 \n\n\n52.0 \n\n\n50 \n\n\nO.4993 \n\n\n0.0029 \n\n\nH- 0.0002 \n\n\n35 \n\n\n\n\n81 \n\n\n0.0141 \n\n\nO.4964 \n\n\n42.5 \n\n\n42.5 \n\n\nO.4964 \n\n\n0.0110 \n\n\nH- 0.0031 \n\n\n36 \n\n\n\n\n185 \n\n\n0.0322 \n\n\nO.4823 \n\n\n33-5 \n\n\n34-5 \n\n\nO.4854 \n\n\n0.0323 \n\n\n\xe2\x80\x940.000 1 \n\n\n37 \n\n\n\n\n420 \n\n\n0.0732 \n\n\n0.4501 \n\n\n26.0 \n\n\n26.5 \n\n\n0.4531 \n\n\n0.0732 \n\n\n0.0000 \n\n\n38 \n\n\n\n\n749 \n\n\n0.1305 \n\n\nO.3769 \n\n\n18.0 \n\n\n18.5 \n\n\n0.3799 \n\n\n0.1333 \n\n\n\xe2\x80\x940.0028 \n\n\n39 \n\n\n\n\n1073 \n\n\n0.1867 \n\n\nO.2464 \n0.0597 \n\n\n10.5 \n\n2-5 \n\n\n10.5 \n\n2.5 \n\n\nO.2466 \nO.0628 \n\n\n0.1838 \n\n\n-f 0.0029 \n\n\n40 \n\n\n\n\n1079 \n\n\n0.1882 \n\n\nO.1285 \n\n\n5-5 \n\n\n5-5 \n\n\n0.1359 \n\n\n0.1987 \n\n\n\xe2\x80\x94 0.0105 \n\n\n41 \n\n\n\n\n934 \n\n\n0.1628 \n\n\nO.29T3 \n\n\n13.0 \n\n\n13.5 \n\n\n0.3034 \n\n\n0.1&75 \n\n\n\xe2\x80\x94 0.0047 \n\n\n42 \n\n\n\n\n658 \n\n\n0.1148 \n\n\nO.4061 \n\n\n21.0 \n\n\n21.5 \n\n\nO.413O \n\n\n0.1096 \n\n\n+0.0052 \n\n\n43 \n\n\n\n\n370 \n\n\n0.0645 \n\n\nO.4706 \n\n\n30.0 \n\n\n29.5 \n\n\nO.469O \n\n\n0.0560 \n\n\n-fo.0085 \n\n\n44 \n\n\n\n\n92 \n\n\n0.0160 \n\n\nO.4866 \n\n\n35-0 \n\n\n37-5 \n\n\nO.49H \n\n\n0.0221 \n\n\n\xe2\x80\x94 0.0061 \n\n\n45 \n\n\n\n\n50 \n\n\n0.0087 \n\n\n0-4953 \n\n\n41.0 \n\n\n45.5 \n\n\nO.4980 \n\n\n0.0069 \n\n\n+0.0018 \n\n\n46 \n\n\n\n\n21 \n\n\n0.0038 \n\n\n0.4991 \n\n\n49-5 \n\n\n53-5 \n\n\nO.4996 \n\n\n0.0016 \n\n\n-f 0.0022 \n\n\n47 \n\n\n\n\n4 \n\n\n0.0007 \n\n\n94998 \n\n\n56.0 \n\n\n61.8 \n\n\nO.4999 \n\n\n0.0003 \n\n\n-j- 0.0004 \n\n\n48 \n\n\n\n\n1 \n5738 \n\n\n0.0002 \n\n\nO.5000 \n\n\n\n\n.... \n\n\n0.5000 \n\n\no.ooor \n\n\n4- 0.0001 \n\n\n\n\n1. 0000 \n\n\n1. 0000 \n\n\n\n\n\nThe first column of this table gives the distribu- \ntion of the units of measurement, in this case inches. \nThe second column gives the frequencies of each \ngroup. The third column presents a series of propor- \ntional numbers, or the proportion represented by each \ngroup frequency when their sum is made equal to unity, \nthe symbol of certainty. The process followed is to \ndivide the total number of observations into unity, and \nthen to multiply this quotient by each frequency in turn. \nThis column gives in fact the probabilities that a meas- \nurement will fall under the corresponding groups noted \nin column one. The distribution being assumed to be \nnormal or symmetrical, one-half of the total number of \n\n\n\n565 J STATISTICAL METHOD I2 $ \n\nmeasurements, or .5000 of the total probabilities should \nbe on either side of the mean. The fourth column \nshows the probability of not exceeding a given measure- \nment, that is, the total probabilities of all measurements \nfrom and including the given measurement to the mean. \nIt thus corresponds to Table B of the probability scale. \nIt is found by working inward toward the mean from \neither extreme, subtracting from .5000 the successive \nprobabilities given by column three. In the fifth column \nare given the ranks corresponding to the probabilities \ngiven in column four, Table B being used for this pur- \npose. Column five thus gives the actual distribution of \nthe observations in ranks of Quetelet\'s scale. \n\nIn order to find the correspondence between experi- \nence and theory the foregoing process is now reversed. \nFrom the actual distribution of column five a theoretical \ndistribution is found, column six showing the ranks with \na uniform difference between them. By this process the \ndistribution is so " smoothed" that each group covers \nthe same number of ranks. Quetelet does not show how \nhe selected the common difference in smoothing the \ndistribution, though it can be approximated by averag- \ning the differences between the ranks as given in column \nfive. There is doubtless an element of arbitrariness in \nthe choice of this difference. The object being to find \nthe difference which gives the closest fit of the curve to \nthe measurements, the true value can be indefinitely ap- \nproached by repeated trials. From this sixth column is \ncalculated, by the use of Table B, column seven corre- \nsponding to column four. The successive differences of \ncolumn seven, working from the mean outward, give \ncolumn eight, corresponding to column three. Column \neight thus gives the probabilities that a measurement \nwould fall under the respective groups, were they actu- \n\n\n\n124 ADOLPHE QUETELET AS STATISTICIAN [566 \n\nally to occur according to the assumptions of the prob- \nability curve. In column nine appear the differences \nbetween the numbers of columns three and eight, show- \ning the amount of the misfit for each group. \n\nBut " each series of observations has its particular scale \nof possibility. . . . The nature of this scale is determined \nby the number of observations, as also by the more or \nless precise means employed in making such observa- \ntions." 1 If the observations are represented graphically \nby the curve of possibility, this curve contracts towards \nits axis in the ratio of the increase in the square root of \nthe number of observations. 2 But assuming the observa- \ntions to be equally numerous, " the contraction towards \nthe axis is proportional to the degree of precision of the \nobservers, and gives a measure of that precision. Our \naim then should be to seek means of appreciating the \ncontraction of the curve." 3 Such a means is found in \nthe probable error. As its name implies this is that \nerror or deviation from the mean which is as often ex- \nceeded as not exceeded. It thus designates the limits \nbetween which one-half of all the observations fall, or the \ndivergence either side of the mean between which and \nthe mean one-fourth of the observations are found. 4 \nSince Table B of Quetelet\'s scale gives the sum of the \nprobabilities on either side of the mean, it is only neces- \nsary to locate the value .2500 in this Table in order to \ndetermine the rank of the probable error. The precision \nfor rank 10 is .236548, and for rank 11 it is . 256791. 5 \nInterpolating, one gets 10.6645 as the rank of the prob- \nable error. 6 The number of ranks included between the \n\n1 Letters, p. 77. % Ibid., "Letter xvi." % Ibid., p. 80. \n\n4 " Sur l\'appreciation, etc.," p. 257. 5 See p. 114, supra. \n\n6 Quetelet commonly speaks of this rank as "about 10.5;" "Sur \nl\'appreciation, etc.," p. 257. In the Letters he gives the rank as 10.67 \non p. 271, and as "nearly 10.66" on p. 274. \n\n\n\n567] STATISTICAL METHOD I2 $ \n\npositive and negative limits of the probable error would \ntherefore be twice 10.6645 or 2I -339\xc2\xb0J Quetelet usually \nconsidered 21 ranks as sufficiently near the true value. \n\nAssuming that the distribution should be normal, \nQuetelet calculated the probable error from the smoothed \ndata. Having determined the best uniform difference \nbetween the ranks as given in column six, 1 he divides \nthis number into 21 and multiplies the quotient by the \ndimension of a group as given in column one. This \ngives him in concrete units the distance between the two \nlimits of probable error. One-half of this distance gives \nthe probable error. A comparison of the probable errors \nof two sets of measurements of the same thing he con- \nsidered a measure of their relative precision. 2 \n\nIn the notes of the Letters Quetelet calculates the odds \nof not exceeding \'various sizes of the probable error. \nThis is done easily from Table B. Thus twice the prob- \nable error is 21.34 ranks. The precision for this rank is \n.411463, that is, .411463 out of .5000 of the probabilities \nlie between twice the probable error and the mean, while \n.500000 \xe2\x80\x94 .411463 or .088537 of them lie beyond this \nlimit. The ratio of .411463 to .088537 is 4.64: 1. Simi- \nlarly the odds in favor of three or more times the prob- \nable error may be calculated. 3 Quetelet also gives 4 the \nrelation of the probable error to the standard deviation. \nHe, however, does not seem to have made any use of \nthe standard deviation, though he says it is a quantity \n"of great importance." \n\nIt has been stated that Quetelet assumed the distribu- \n\n1 See p. 122, supra, 2 Letters, p. 82. \n\n5 Quetelet\'s method is somewhat more cumbrous though it gives sim- \nilar results; Letters, p. 270, et seg. \nK Ibid., p. 272, et seg. \n\n\n\nI2 6 ADOLPHE QUETELET AS STATISTICIAN [568 \n\ntion of the errors of a set of measurements to be sym- \nmetrical. This same assumption, extended to the varia- \ntions in nature, gave a type about which the variations \nwere evenly distributed. . Thus his mean in theory be- \ncame not only an arithmetic average but also the median \nand the mode. 1 It was on this basis that Quetelet viewed \nthe degree of misfit of the measurements to the scale of \npossibility as a test of the degree of accuracy with which \nthe measurements were made. 2 It would seem to be \nquite as plausible to consider the degree of misfit as a \ntest of the accuracy with which the assumptions under- \nlying the theoretical law of normal distribution can be \napplied to a particular set of observations. While we \ncannot, as the basis for a theory of the distribution, find \nany less arbitrary assumptions than that the causes of \nvariation are infinite, minute and equal and that they are \nequally favorable to excess and deficiency, 3 yet it strains \nour credulity to believe that these assumptions must \nalways be true to experience, especially in measurements \nof mass phenomena. In fact a perfect realization of \nthese assumptions in experience would seem to be \nfortuitous, and deviations from the perfectly symmetrical \ndistribution may vary through many degrees of asym- \nmetry. The normal curve is thus to be viewed as a form \nof the distribution of variable objects in nature, approx- \nimately realized in some classes of phenomena, but as \nonly one of the many possible forms. \n\nOf this Quetelet seems to have been quite aware. For \nwhile in his illustrations he always assumed the normal \n\n1 Bowley, op. tit., p. 119, apparently does not consider Quetelet\' s \naverage as the median and the mode. It is impossible to see how this \nconclusion can be reached. \n\n2 " Sur 1\' appreciation, etc.," p. 272. \n\n3 See Jevons, op. tit., pp. 255 and 380. \n\n\n\n569] STATISTICAL METHOD 12 j \n\ndistribution, he was fully aware of asymmetrical distri- \nbution and gave a satisfactory explanation of it. l He \neven contemplated part authorship of a treatment of \nsuch cases. 2 Quetelet explained the variations in nature \nnot only by the various combinations of an infinite num- \nber of independent and minute causes, but also by the \ndifferent " degrees of intensity of which these causes are \nsusceptible." 3 When therefore variations in one direc- \ntion are found to exceed those in the other, it is due to \nthe causes operating in one direction having " much \nmore probability than the contrary causes, either because \nthey are more numerous or because they are more ener- \ngetic." 4 When the observations are numerous, the \nskewness of their distribution becomes an indication of \none or more causes more or less powerful, peculiarly \nfavorable to variation in one direction. The normal dis- \ntribution being viewed as natural, skewness requires \nspecial explanation. 5 \n\nIt should be noted that while Quetelet gave very great \nimportance to the determination of the average, and the \nprobable deviation from the average, he also frequently \nemphasized the importance of changes in the limits of \nvariation. His reason for this emphasis was his belief \nthat " one of the principal effects of civilization is that it \nmore and more contracts the limits within which the dif- \nferent elements relating to man oscillate." 6 Believing \nthe averages of human qualities to be for the most part \nstationary, he believed the perfectibility of man would be \n\n1 Some discussion of the unsymmetrical distribution as related to the \ntheory of the Average Man was given on p. 81, et seg., supra. \n\n2 See Letters, p. 113. d Z6id., p. 106. \n\ni I5id., p. 124. 5 Bowley, op. cit., p. 267. \n\n*Sur Vhomme, closing section; English translation, pp. x and 108; \nPhysique sociale, vol. ii, p. 428; Du Systeme social, p. 252, et seg. \n\n\n\n128 ADOLPHE QUETELET AS STATISTICIAN [570 \n\nshown in an ever-increasing equality among men, physi- \ncally, intellectually and morally, until all approached the \nstate of the Average Man. * His interpretation of the \nnarrowing of the limits of variation was thus very differ- \nent from the more recent view which finds in such nar- \nrowing an evidence of a more intense struggle for exist- \nence, of more severe economic competition, 2 or of \nincreased social pressure. 3 \n\nQuetelet used the word " civilization " in the most gen- \neral sense; its effects were shown in such phenomena as \nincreased political equality, the prevention of famines and \nthe general diffusion of a sufficiency of food, and the \nspread of knowledge through all classes. We may then \nnote (1) that he centered attention upon the limits of \nvariation from the type rather than upon the standard \ndeviation of the group; it is the latter which shows best \nthe massing of the group about the type, or the con- \nformity to the type; (2) that he did not give an inter- \npretation of restricted variation in terms of biological or \nsociological causation, nor does his statement in any way \nsuggest the process of natural selection or increased en- \nvironmental or social pressure as the explanation of the \nnarrowed limits; and (3) from the sociological viewpoint \nsocial evolution (in order to avoid the term "civiliza- \ntion") seems to have resulted not only in an increased \nconformity of men to a type of individual capable of co- \noperation, but also in an increase of liberty, which im- \nplies greater freedom of variation. 4 The interpretation \n\nx For a discussion of Quetelet\'s confusion on this point see chap, iii, \np. 72, et seq., supra. \n\n2 H. L. Moore, "The Variability of Wages," Political Science Quar- \nterly, March, 1907. \n\n3 F. H. Giddings, "The Measurement of Social Pressure," Quarterly \nPublications of the American Statistical Association, March, 1908. \n\n* Giddings, Sociology, a lecture delivered at Columbia University in \n\n\n\n571 ] STATISTICAL METHOD I2 g \n\nof a statistical fact which Quetelet readily found in " one \nof the effects of civilization," is thus seen to be, sociolog- \nically, a difficult problem in balancing the effects of op- \nposing and complex processes and conditions. \n\nIt remains to note Quetelet\'s classification of causes \nand his method of studying them. For besides making \npossible a more accurate description of social facts, \nQuetelet\'s principle of studying groups rather than in- \ndividuals opened the way for the study of the causal re- \nlation among mass phenomena. Having described a \ngroup by means of the average and an index of varia- \nbility, changes in these constants may be related to \nchanges in the group conditions, that is, to causes suf- \nficiently general to affect the whole or a large part of the \ngroup. The method itself thus suggests a classification \nof causes. \n\nAs to their manner of action, Quetelet classified causes \nas constant, variable or accidental. I He says : \n\nConstant causes are those which act in a continuous man- \nner, with the same intensity and in the same direction. Var- \niable causes act in a continuous manner, with energies and \ntendencies which change. . . . Among variable causes it is \nabove all important to distinguish such as are of a periodic \ncharacter, as for instance the seasons. Accidental causes only \nmanifest themselves fortuitously 2 and act indifferently in any \ndirection/ \n\nthe Series on Science, Philosophy and Art, February 26, 1908, p. 34, ei \nseg., especially pp. 39-40- \n\n1 Stir Vhomme, bk. iv, chap, ii; English translation, p. 103; " Sur \nl\'appreciation, etc.," p. 207; Letters, p. 107. \n\n2 In Du Systeme social, pp. 305-306, he explains that he does not mean \nthat any cause is really accidental. In using the term he merely follows \nestablished usage. The accidental causes are themselves necessary re- \nsults of their antecedents, but are called accidental because we cannot \ntrace these antecedents. s Letters, p. 107. \n\n\n\nX^o ADOLPHE QUETELET AS STATISTICIAN [^ 2 \n\nAmong constant causes Quetelet named sex, age, pro- \nfession, season, latitude and economic and religious insti- \ntutions. In the first place it may be noted that Quetelet \ninterpreted social phenomena in terms of external and \npurely formal conditions. To-day we are interested in \nsex, age,, profession as explanatory of social phenomena, \nonly because of their implications with regard to human \ninterests and mental traits. But it should not be over- \nlooked that it is not possible to interpret social pheno- \nmena in terms of mental types until these types have \nbeen correlated with the external and formal conditions \nwhich Quetelet proposed. In the second place it may \nbe doubted whether the above or any other causes are \nconstant according to Quetelet\'s definition. He himself \nseems not to have been quite certain that really constant \ncauses could be found. 1 Finally it should be recalled \nthat Quetelet looked upon the average as the result of \nconstant causes. It seems nearer the truth however to \nview the average as the final resultant of all causes, \nremembering that the more numerous the observations \nthe more prominent become the effects of those causes \nwhich are most general in their influence. Since causes \nare appreciated through changes in the averages, per- \nfectly constant causes must remain inscrutable. Our \nnearest approach to such causes in statistical inquiry will \nbe general causes which are relatively constant. \n\nVariable causes would seem to occupy a larger place \nin a satisfactory classification of causes than Quetelet \ngave them. Seasons appear in his discussion among \nboth constant and variable causes. But if phenomena \nvary as we pass from one season to another, so do they \nas we pass from one age, sex, profession, or latitude to \n\n1 Letters, pp. 133, 144. \n\n\n\n273] STATISTICAL METHOD L ^ L \n\nanother. It would seem in fact that all causes of social \nand organic phenomena, considered as mass phenomena, \nare more or less variable. Accepting the term then as a \ngeneral characteristic of all such causes, we may find \nQuetelet\'s distinction of periodically variable causes \nhighly useful. The seasons of the year and the hours of \nthe day, or the revolution of the earth about the sun and \nits rotation on its axis, are of immense influence on \norganic life and in human affairs. \n\nThe theoretical characterization of accidental causes \nhas already been given. In measurements of social and \norganic phenomena they include two quite different sets \nof influences. These are first the causes of accidental \nerrors in counting or measuring, as carelessness, lack of \nskill or variations in the precision of instruments, and \nsecondly the many minute causes of variations in the \nphenomena themselves resulting in a more or less sym- \nmetrical grouping about their average. Thus in ascer- \ntaining the average height of a group of men, there \nwould be mingled both the causes of errors of measure- \nment and the causes of differences in the heights them- \nselves. That in both cases the causes are equal and act \nindifferently in favor of or in opposition to the average \nresult is only a convenient hypothesis to be fulty justified \nin every case only by experience. But the point to be \nnoted here is that the causes of variability though rela- \ntively "feeble" and "indirect," 1 are of varying degrees \nof feebleness and indirectness, depending upon the scope \nof the investigation. Thus in studying the heights of \nthe men of a nation, the differences in race, age, place of \nhabitation, nourishment, occupation would be merged \ntogether in the average. The group studied may how- \n\n1 Letters, p. 130. \n\n\n\n! 3 2 ADOLPHE QUETELET AS STATISTICIAN [574 \n\never be steadily narrowed and each one of these condi- \ntions, which in the general study were deemed of minor \nimportance, can be made most prominent. What is a \nminor cause for a wide group, becomes a general cause \nfor a narrower group. There is of course a limit to this \nprocess of narrowing the group, for causes do not act \nsingly, and with a very small group one condition can- \nnot be sufficiently isolated \xe2\x80\x94 the number and variability of \nmany small causes make the results too irregular. \n\nIt would seem then that in any given group the causes \ninfluencing the observations range in extent from the \nvery minute causes affecting individual cases only, \nthrough relatively minute causes to those general causes \nwhich affect most or all members of the group. It is \nonly the latter which can produce a change in the \naverage. These are the causes whose effects become \nmore pronounced as the observations increase, the effects \nof all others being at the same time neutralized. We \nmay thus classify all social causes as variable, and as \neither minute or general in their influence. \n\nQuetelet states that the art in the study of causes is to \ngroup the observations " in such a manner that all the \ncauses, except those whose influence we wish to appreci- \nate, may be considered as having acted equally on the \nmembers of each group." 1 If then differences in the \nresults are found, they may be attributed to the influence \nstudied. Thus he studied the relation of age, sex, \nseason to the committing of crime by comparing the \nobservations for one age, sex or season with those of \nanother. This is in reality a study of causation through \ncorrelation or concomitant variation. With many meas- \nurements Quetelet held that accidental (or minor) causes \n\n1 Letters, p. 131. \n\n\n\n575] STATISTICAL METHOD ^3 \n\nmay be neglected, and the effects of constant (or gen- \neral) causes will become prominent. The effects of peri- \nodic causes maybe studied by comparing parts of a period, \nas one season with another, and may be avoided by \nembracing an entire period, as a year. 1 From this \nsimple and general basis given by Quetelet, the diffi- \ncult problem of studying causal relationships has been \nadvanced to a method of quantitatively measuring the \ncorrelation of two variable elements throughout their \ndistribution. \n\n"Letters, p. 141. \n\n\n\nBIBLIOGRAPHICAL NOTE. \n\nIt does not seem necessary to give here a list of \nQuetelet\'s statistical publications, owing to the very \nthorough studies made by Georg Friedrich Knapp and \npublished in Hildebrand\'s Jahrbilcher fur Nationalbkono- \nmie und Statistik, vol. xvii. Under the general title, \n" Bericht uber die Schriften Quetelets zur Socialstatistik \nund Anthropologic," Knapp gives first a classification of \nthese writings both by form and by subject matter \n(p. 167, et seq.), secondly a statement of their contents, \nthe writings being divided into three chronological \nperiods (p. 342, et seq.) and thirdly a selection of the \nmore important passages for the presentation of Quete- \nlet\'s views on many topics (p. 427, et seq.). It is only \nnecessary to refer the interested reader to these studies \nfor bibliographical material. \n\n134 [576 \n\n\n\nVITA \n\n\n\nThe author of this dissertation was born in Willshire, \nVan Wert County, Ohio, September 27, 1877. After \nreceiving the degree of A. B. from Baker University in \n1 90 1, he was principal of the public schools at Waverly, \nKansas, for two years. He was enrolled as a graduate \nstudent under the Faculty of Political Science of \nColumbia University during the three years 1903-6 and \nduring 1907-8. He was Scholar in Sociology 1904-5, \nand Fellow in Statistics 1905-6. During 1906-7 he was \ninstructor in Economics and Sociology at Clark College, \nWorcester, Mass. While at Columbia he attended \ncourses given by Professors Giddings, Clark, Seligman, \nMoore, Seager and Dunning. \n\n135 \n\n\n\nLEMr\'09 \n\n\n\n\n\n\n^ \n\n\n\nk, \n\nADOLPHE QUETELET \n\n\n\n* tf \n\n\n\nAS \n\n\n\nSTATISTICIAN \n\n\n\nBY \n\nFRANK H. HANKINS, A. B. \n\nSometime University Fellow in Statistics \n\n\n\nSUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS \n\nFOR THE DEGREE OF DOCTOR OF PHILOSOPHY \n\nIN THE \n\nFaculty of Political Science \nColumbia University \n\n\n\n1908 \n\n489\xc2\xa7ii \n\n\n\nV \n\n\n\n\n\n\n\nv \xe2\x96\xa0 \xc2\xab \n\n\n\n\n\n\n\n\nr** <& \\> \xc2\xb0? \n\n,0 \n\n\n\n\n\n\n\n\n\n\nt-\xc2\xb0V \n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\nDeacidified using the Bookkeeper process. \nNeutralizing agent: Magnesium Oxide \nTreatment Date: August 2010 \n\n\n\nW \n\n\n\n<?% \n\n\n\nPreservationTechnologies \n\nA WORLD LEADER IN COLLECTIONS PRESERVATION \n\n111 Thomson Park Drive \nCranberry Township, PA 16066 \n(724)779-2111 \n\n\n\n\n\n\n^ \n\n\n\n,*- \n\n\n\n\n\nX \n\n\n\n% \xe2\x96\xa0 /.-5Sfe- x \xc2\xab* \n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\xe2\x80\xa2^ i* \n**<* \n\n\n\n\n\n\n\n\n\n\n\n\n\n\nj. \'*. \n\n\n\n\n\n\n\n\n\n\n\n\noK \n\n\n\n\nV*0> \n\n\n\n\n\n\n^ MAR 81 \n\nN. MANCHESTER, \nINDIANA 46962 \n\n\n\n\n\n\n\n\n% a* \xe2\x80\xa2jfife\'- *<fc \n\n.4/ ^, \n\n\n\n\n- \n\n\n\n'