supplement to the Annals of the American Academy of Political and Social Science, march, 1 89 1. HISTORY, THEORY, AND TECHNIQUE OF STATISTICS BY U*JU AUGUST MEITZEN, Ph.D., PROFESSOR AT THK UNIVERSITY OF BERLIN. TRANSLATED, WITH AN INTRODUCTION, BY ROLAND P. FALKNER, Ph.D., m INSTRUCTOR OF STATISTICS, UNIVERSITY OF PENNSYLVANIA. PART FIRST: HISTORY OF STATISTICS. PHILADELPHIA: AMERICAN ACADEMY OF POLITICAL AND SOCIAL SCIENCE. 189I. *$ INTRODUCTION BY THE TRANSLATOR. In presenting to the English public a work like the present a word of explanation seems in order. Professor Meitzen's work, "Geschichte, Theorie, und Technik der Statistik," represents the most complete statement of theoretical statistics, in the smallest compass, in the German language. Its translation therefore has appeared desirable as well on account of its form as its matter. In regard to form, the work covers systematically the whole field of statistical theory, and thus furnishes the student an insight into the relation of the parts not to be gained by the consideration of special problems. In this respect the work represents a familiar habit of the German mind which has some signal advantages. We are apt in Eng- land and America to devote our study to special problems, and whole fields of research, long since systematized in Continental Europe, and there known, inaptly perhaps, as sciences, must be studied by the English student from treatises on special subjects, and he must in his own thought establish the connecting-links which bring about the harmony of the whole. If it be necessary to adduce instances of this fact let us consider for a moment the whole subject of public finance. An exhaustive treatment of the subject in English cannot be named, whereas the student of the subject at once recalls the names of Ger- man, French, and Italian writers who have devoted systematic treat- ises to it. The same is true of other topics, but notably so of that which we are now considering, statistics. It may be*A*mbted whether the conception of statistics as a connected organic science is familiar even to those whose achievements in this field have been most hon- orable. Certainly no exhaustive treatise on the subject exists in our language despite the valued contributions made by English science to the subject. Hence the translation of the present work has been pre- pared partly with a view to the opportunity which it afforded for the comparison of German methods of thought with our own. No attempt will be made here to weigh the relative merits of each. Only in passing it may be observed that if the German plan tends to a super- ficial treatment of certain subjects in the endeavor to preserve the symmetry of the system, our own more special investigation tends to (3) iOO 4 Annals of the American Academy. deprive us of that insight into the general relations of things which illuminates and corrects our conception of special problems. Now as respects the contents of the work, it may be remarked that the general interest in statistical results, and the increasing use of statistical figures in all kinds of scientific and popular discussion, are in marked contrast to the paucity of our scientific literature on the subject of statistics itself, which furnishes an additional motive for the present translation. In England we have the valuable works of Farr and Newsholme, and the Journal of the Statistical Society, in the United States the suggestive monograph of Prof. R. M. Smith on " Statistics and Economics," and the publications of the American Statistical Association, besides certain highly-prized official docu- ments, and special studies from which the student of statistics may gather invaluable suggestions as to the statistical method and a keen insight which prevents his erring in the use of it. Nevertheless a complete formulation of the method and its processes, reinforcing that statistical instinct which is essential to all true work, is lacking in our literature. It is in part with the view of supplying this deficiency that the translation has been undertaken. Prof. Meitzen's clear and logical discussion of the processes of statistical argument must, we believe, be helpful to all who are confronted by such arguments and who feel the necessity of testing their reliability. If not the purpose, it is at least the result of the work that it furnishes the tests whereby we can readily ascertain whether a statistical argument can hold water. The Translator takes pleasure in acknowledging that in his own work he owes more to the inspiration of the present work than to any other treatment of the subject of statistics. To make the same opportuni- ties accessible to the English public as far as may be possible is the aim of the translation. It is our sincere conviction that the study of statistical methods is not a merely theoretical but an eminently prac- tical one, a necessary corrective of that false use of statistical results which is everywhere so abundant, and which, as we glean from the author's preface, is as much an evil in Germany as it is among us. It is hoped that the present work may accomplish something toward spreading more accurate conceptions of the possibilities and the limits of statistical argument. . Statistics, according to Prof. Meitzen, is a method of scientific inves- tigation by means of enumeration of objects and the numerical com- parison of the results of such enumeration. Hence they may be applied to any field whatever of human knowledge if the necessary conditions of the investigation are present. In other words, they are in no wise limited in their field of research. If scientific in character, however, they must possess distinct features in common wherever applied. It is the discussion of these common features, in short, of the method which forms the subject of the work. As a result, the treat- History and Theory of Statistics. 5 ment is not only broader, but different from the usual treatment of statistics to be found in the foreign treatises on the subject, or in the monograph of Prof. Smith above mentioned. As a rule, these treat- ises deal in statistics as our knowledge numerically expressed of a group of phenomena variously designated as the state, society, human communities, etc. They contain therefore many statistical tables and the consideration of the conclusions to be drawn from the figures presented. The discussion of methods occupies a minor place. To Prof. Meitzen all this is explanatory matter, the method itself~Tne~ jsence of the subject. This view of the matter enables him to treat tTTe~subJect in a. smaller compass than is customary, and further to invest it with a general interest, not confining it to the needs of econ- omists and sociologists simply, but furnishing precepts to all who may be engaged in the collection or use of figures for the purposes of argu- ment or demonstration. In conformity with this conception of statistics the first part of the work traces historically the growth of our knowledge, and processes of thought in using figures, up to the point where it has become possi- ble for us to formulate connectedly the underlying principles, in short, to present a science of statistics which should be a science of method. To this end, it was highly desirable that the presentation of the subject should proceed in the historical form. The reader is able to follow in the light of this underlying conception with interest and intelligence what might otherwise appear a recital of insignificant details. The reader is forced to the conviction that the unity of statistical effort is to be found nowhere else than in the methods pursued by statisticians the world over. The unfolding of this conviction is purposed by the historical part of the work, and thus the reader is prepared for the better appreciation of the theoretical discussions which form the second part of the work. The theory of statistics to Prof. Meitzen consists of the logical re- quirements of statistical proof. It is the discussion of these elements which forms the contents of the theory of statistics. The mental pro- cesses involved in the statistical statement and the statistical argument are carefully analyzed. This analysis proceeds to the very minute details, giving everywhere a complete statement of the nature which logical necessity demands that they should have in order to fulfil the conditions of correct statement or proof. Thus the model statistical argument is constructed. Its parts are analyzed, their true nature explained, the necessary connection between the parts displayed. Those who are familiar with this model argument are thus supplied with tests which, applied to the arguments presented to them, will enable them at once to discover their truth or falsity. Practical statistics, the work of official bureaus, is not a matter of drawing inferences but of collecting material. Their work is largely 6 Annals of the American Academy. preparatory to statistical argument. Theirs is the technique of statis- tics. What demands does theory make upon them ? The answer to this question forms the topic of the third part of the work. How should the bureaus conduct their work that the logical requirements of the model statistical argument be fulfilled ? What light does the analysis of the statistical argument throw upon the workings of these bureaus ? These are some of the questions discussed in this portion of the work. The unity of the work rests, as is seen from the above, in the funda- mental conception of statistics. The various parts of the work must be read in the light of this conception. The result is a harmonious grouping of the subject which well justifies for it the claim to the name of science. Whether or not this name is accorded to it is a question after all of small moment, provided that the continuity and organic union of the various parts be fully recognized. If the translation of the work as a whole shall be useful in the formulation for science of the canons of statistical thought its purpose will have been accomplished. It is published in parts, I. History, II. Theory and Technique. Part II. is to be issued shortly. Part I., the history of statistics, forms the contents of the present volume. It is, as above noted, preparatory to the theory which follows. The thread of development is carefully traced, and the reader is conscious of the real and important connection of events which follows from the author's fundamental conception of the essence of statistical science. In addition to this organic bond of union with the theoretical portion of the work, attention should also be called to the fact that the present volume contains one of the most complete surveys of statistical literature which is to be found anywhere. This feature must give it a special value for those seeking to inform themselves in this line, and render the book a useful work of reference. With the kind encouragement of the author, and with the cour- teous permission of the publisher of the German edition, 1 the work is given to the English public. The Translator. Philadelphia, October, 1890. 1 The original of the work has the following title-page : Geschichte, Theorie, und Technik der Statistik, von August Meitzen, Dr. ph., Geheimer Regierungs-Rath a. D., Professor an der Universitat zu Berlin. Mit Tafeln. Berlin. Verlag von Wilhelm Hertz (Bessersche Buchhandlung), 1886. PREFACE OF THE AUTHOR. In the following outline I have endeavored to give concise and sys- tematic expression to a complete theory of statistics together with many ideas drawn from experience in practical work. I am con- scious that it might have been desirable to devote to the subject a larger treatise and to include the discussion of the more important problems of social and political statistics. Extensive literary obliga- tions and the pressing need of a basis for my lectures have led me to prefer an outline. Its brief, rather sketchy form seemed to me to pos- sess certain advantages. No more of the customary apparatus of illustration has been introduced than was deemed necessary to dispel the slightest doubt as to the propositions stated. It is however my opinion that no text-book can ever fully replace for the student dem- onstrations with the use of the actual statistical material itself, and the consideration of questions arising from it. The treatment is based throughout on the conception of statistics as a science of method. I hold this view to be correct, though I lay no greater stress upon it than is expressed in § 59. So far as the question of the position of statistics in the sphere of sciences does not concern the method nor the conception of statistics based upon it, it becomes merely a discussion of the definition of the word " science " and no essen- tial condition of the theory is affected by the answer. No teacher of statistics can neglect to consider the requisites and some of the results of the statistics of population, of political organization and finance, of the soil and agriculture, of industry and trade, nor finally of national prosperity and morality. Whether these subjects taken together are to be called the " science," or whether they are to be regarded as the field of systematic statistics, is, as shown in g 90, of merely formal con- sequence. These subjects undoubtedly form appropriate material for connected treatment, and they are dependent on the same methods of investigation. In a clearly-formulated conception of statistics as a science of method, I see the possibility of realizing an object which I consider essential, and which I desire above all. I hold it to be of the highest importance to demonstrate the logical character and logical rigor of statistics, and, if possible, to make these ideas common property. The (7) io Annals of the American Academy. § 19. Further Development of the Statistics of Population. \ 20. Extension of the Range of Statistical Problems. \ 21. Beginnings of Tabular and Graphic Presentation. II. Institutions for National Statistics on a Scientific Basis. $ 22. Necessity for Statistics during the French Revolution. \ 23. Bureaus for Statistics in France. § 24. Statistical Bureaus in Italy, Spain, Westphalia, and Bavaria. § 25. Foundation of the Prussian Statistical Bureau. § 26. Reestablishment of the Prussian Statistical Bureau. HI. Limitation of the Field of Statistical Science. Vg 27. Limitation of Achenwall's Statistics. \ 28. Elimination of Political Economy, of Public and Administration Law. § 29. Elimination of the Geographical Element. § 30. Separation of Practical Life Insurance from Statistics. # 31. Decline of Statistics as a System. \ 32. State of Official Statistics. IV. Rise of National Statistics in the Various Civilized Nations. § 33. France. \ 34. Prussia and the other German States. § 35. The German Customs Union (Zollverein). § 36. Holland, Luxembourg, and Belgium. §37. Austria- Hungary. § 38. Great Britain. \ 39. United States of America. § 40. Denmark, Norway, and Sweden. § 41. Russia. § 42. Switzerland, Italy, Spain, Portugal, and Greece. V. Conceptions of the Method and Purpose of Statistics. $ 43. Influence of Official Statistics. § 44. Perfecting of Sussmilch's Statistics. § 45. Pauperism and Quetelet's Work on Man. § 46. Conceptions of Statistical Theory. D. The Development and Predominance of the Statistical Method. I. The International Statistical Congress. § 47. Occasion, Organization, and Duration of the Congress. # 48. Work and Influence of the Congress. II. Modern Statistical Practice. § 49. Increasing Need of Statistics and Statistical Offices. \ 50. Character of Statistical Work. III. Statisticians of Morals. \ 51. Idea of Constraining Regularity. \ 52. Incompatibility with Ethics and Psychology. \ 53. Solution of the Problem by the Statistical Method. History and Theory of Statistics. ii IV. Conceptions of Statistical Theory. \ 54. Opposing Positions. \ 55. Conception of Statistics as Science of the State. § 56. Conception of Statistics as Science of Human Communities. \ 57. Conception of Statistics as Science of Method. \ 58. Conception of Statistics as Applied Logic. PART SECOND. THEORY AND TECHNIQUE OF STATISTICS. Introduction. § 59. Position of Statistics as a Science. \ 60. Points of View for the Theory of Statistics. # 61. Relation of the Statistical Method to Logic. § 62. Leading Thoughts of the Statistical Method. A. Principles of Enumeration. /. Fundamental Conceptions. § 63. Empirical Conditions of the Enumeration, g 64. Enumeration and Calculation. \ 65. Enumeration of Things and Measurement of Qualities. # 66. The Unit of Enumeration. \ 67. The Field of the Enumeration ; The Limits of Time and Space. II. The Process of Enumeration. § 68. Observation and Summation. \ 69. Substitutes for Enumeration, Calculations, Estimates, and the Enquetc. # 70. Possibility of Error in Enumeration. $ 71. Peculiarities of the Returns. § 72. Enumeration of Units in Combination. § 73. Results of the Enumeration. B. Principles of Statistical Judgments. /. Quantitative Relations. $ 74. The Measure of Quantity from Analogous Aggregates. # 75. The Choice of Analogous Aggregates, g 76. Reduction to Common Terms. § 77. Series, Maxima, Minima, and Averages. \ 78. Results from Quantitative Judgments. II. Causal Connections. I 79. Requirements and Limitations in Judgments of Causality. § 80. Discovery of Causality through Functional Series, g 81. Symptoms and their Application in Determining Causality. 12 Annals of the American Academy. III. Probability and Regularity, $ 82. The Conception of Probability. # 83. Suppositions Based on Similar Causality. § 84. The So-called Law of Large Numbers. # 85. The Regularity of Seemingly Voluntary Actions. \ 86. Statistical Regularity. C. The Form of the Process. § 87. Steps of the Statistical Investigation. g 88. Predominance of Statistical Materials. § 89. The Elaboration of Systematic Statistics. § 90. Tendencies of Systematic Statistics. $ 91. Problems of Systematic Statistics. § 92. The Form of Questions in Systematic Statistics. $ 93. Form of Judgments of Causality and Probability. D. The Requirements of the Technique. 7". The Problem and the Plan. £ 94. The Separate Phases in the Technical Process. \ 95. The Development of the Plan, g 96. Estimates of the Time and Cost. I 97. The First Draft of the Plan. § 98. Instructions to Enumerators. II. Enumeration. $ 99. Organization of the Process. § 100. The Observation in Enumeration. § 101. The Observation in Estimates. $ 102. Summarizing. III. Examination of Returns. § 103. Examination. Correction, and Criticism of the Result. § 104. The Comparison with Analogies. § 105. Reductions to Ratios for Comparison. IV. Presentation of the Results* § 106. Requirements of the Presentation. § 107. Tabulation. § 108. Graphical Presentation. g 109. The Demonstration of Quantitative Judgments. £ no. The Demonstration of Judgments of Causality and Probability. § ill. The Character of the Solution. V. PrpsMtatwtL and Application of the Results. $ 112. Collection of the Richest Possible Materials. § 113. Archives of Official Bureaus. \ 114. Applied Statistics, Political Arithmetic. Conclusion. § 115. The Character of Statistical Theory. § 116. The Work of the Professional Statistician. § 117. The Position of Statistics in General Culture. PART I. THE HISTORY OF STATISTICS. INTRODUCTION. § I. THE SUBJECT AND DEVELOPMENT OF STATISTICS. We understand as statistics somewhat superficially con- sidered an extensive range of practical rather than theo- retical problems. They are characterized by the effort to penetrate into the multitudinous phenomena of political and social life, of nature and civilization, by the enumera- tion of characteristic facts, by classification and explana- tion. Among these characteristic facts are those relating to topography ; to the population, and its classes in regard to social rank, age, religion, and occupation ; to births, mar- riages, and deaths ; to the state and its administration, its martial force, its property, its expenditures and receipts; to the territory in its physical aspects, its elevation, water- supply, climate, and fertility ; to the agricultural, industrial, and commercial pursuits of the people, also to their resources and capital ; and finally to their strength, their riches, their morality, their public-spiritedness, their social and religious culture, and to their enjoyment of life in its outward manifestations. All of these facts are to be ascer- tained in reference to actual status and to changes in the course of time. The scientific interest in the solution of these problems is double in its character. It attaches in the first place to 1 13) 14 Annals of the American Academy. the subject, and secondly to the process of investigation, to the method. The results of such investigations are embodied in various branches of human knowledge. They consist of data concerning the quantitative and causal relations in which the objects observed have been found, and in which their reappearance may be expected. These results are sources of information for various sciences when other modes of investigation are inapplicable. Scientific criticism, and therefore the theory of statis- tical science, concerns itself with the correctness of this mode of investigation and its development. Objects and their relations are the material with which the theory has to operate. The material appears to be indefinite and unlimited, and to embrace all phases of actual existence. We must therefore know something about it in order to measure the scientific accuracy and reliability of the means adopted to investigate it. In the work of investigation, the methods are gradually more clearly understood, and thus we arrive at well-defined prin- ciples of research which have the value of scientific propo- sitions. The development of statistical science began, like that of all others, with a period of unconscious empiricism. Later the awakening scientific conception of the systematic investigation was so dominated by the mass of facts that methods secured for themselves only gradually a place in the system. The question is indeed still unde- cided whether the true contents of statistical science are certain groups of phenomena, particularly those of human communities (Lebensgemeinschaften), and the method simply the mode of securing knowledge in this field; or whether, on the contrary, the method with its logical and technical basis forms the true contents of the science, the objects serving simply as explanatory of the principles of method, or as examples of possible new problems. From these preliminary considerations it is however History of Statistics. 15 evident that the history of statistics cannot be an account of the results of enumerations obtained in the course of time for the solution of statistical problems. Its aim must be to point out the ideas which have arisen in the develop- ment of the science, and the range of ideas and experi- ences from which the demands made upon it by criticism have been finally answered. It must show systematically the character of the problems to which statisticians have devoted their efforts and the ideas underlying their solu- tion. It must show the progress of the critical compre- hension of the value of the results and demonstrate the growing clearness and definiteness of the theoretical and Jechnical requirements. Undoubtedly the history of sta- tistical science must be a history of statistical theory and technique. A. EMPIRICAL STATISTICS IN THE CLASSIC AND MEDIEVAL WORLD. § 2. THE OLDEST CIVILIZED NATIONS. Problems, such as we to-day call statistical, were sug- gested and solved in the earliest periods of history. Prac- tical necessity forced them upon the rulers of peoples on various occasions. Concerning numerous statistical under- takings definite testimony has been preserved. Egypt : c. 3050, Arrangements for the construction of the pyramids; 2200, Maps of the country; 1400, Division of the land by Rameses II. ; 600, Registration by the police of all heads of families (Herodotus II., 109, 125, 177). Judea: Census of the population, estimated 1500 B. C. at c. 100,000 souls (Numbers III., 49-43) ; in 2030 B. C, at c. 3,800,000 (II. Samuel xxiv. 9; I. Chron. xxi. 5 ; xxvii. 24; xxiii. 3-5). China : c. 2300, Description of the provinces by Yuking ; 1200 B. C, Topographical officials (Ferd. Frhr. v. Richt- hofen, China. Berlin, 1877, Vol. I. p. 177). y 16 Annals of the American Academy. Persia : Messenger mail, survey of roads, assessment of real estate tax in Ionia (Herodotus III., B; V., 49, 52 ; VI., 42; VII., 21). (Moreau de Jonnes, Statistique des peuples de l'antiquite, Paris, 185 1. M. Duncker, Geschichte des Alterthums.) § 3. GREECE AND ROME. The distribution of real property, of classes of citizen- ship, of military and naval service, of taxes and public burdens, and privileges, was arranged in many Greek states in a manner which presupposed many inquiries of a statistical nature. 850. Lykurgus divided the territory of Laconia into 39,000 portions, assigning to the Spartans 9000 portions and to the Lacedaemonians 30,000 portions. 594. Solon's tax census divided the people into four classes according to the supposed returns from their property measured in wheat, and imposed a poll tax on the alien residents. 309. A census in Athens showed a population of 21,000 citizens, 10,000 alien residents, and 400,000 slaves. (Boeckh, Staatshaushalt der Athener. 2d Ed. 185 1. Buchsenschutz, Besitz und Erwerb im griechischen Alter- thum. Halle, 1864. Hermann, Griechische, Staatsalter- thiimer, 1875,98, 7. Clinton, De Graeciae magnitudine et frequentia, in the Fasci Hellenici, Kriiger's edition, p. 391. M. Duncker, Die Hufen der Spartiaten. Monatsbericht der Berliner Academie 7, 2, 1881.) In Rome periodical enumerations of the population as well as investigations of property of an exactness not attainable in recent times existed from the time of Servius Tullius. There were also after Augustus surveys of roads and districts, assessment of real estate taxes in Italy and the provinces, and later detailed official state handbooks. 550. The constitution of Servius Tullius distinguishing six property classes. History of Statistics. 17 435. The first census in the presence of the Censors, which in the following 470 years was repeated 69 times. Births were reported in the temple of Juno Lucina, puberty in that of Juventus, and deaths in that of Libitina. c. 90 A. D. Hygin's treatise on surveys for real estate taxes (in Auctores gromatici of Lachmann and Rudorff I., P. 113)- c. 296. Tabula Peutingerana (Philippi d. t. P. Bonn, 1876). c. 330. Itinerarium Antonini (Tobler's edition, 1863). 404. Notitia omnium dignitatum administrationumque (Boeking's edition, Bonn, 1839). (Niebuhr, Romische Geschichte I. 619, II. 78. De la Malle, Economie politique des Romains 1840. Theod, Mommsen, Staatsrecht der Romer 1876, I. 207, II. 304. Die amtliche Bevolkerungsstatistik im alten Rom, Hilde- brand's Jahrbuch fur Nationalokonomie und Statistik, 1866, Vol. I. p. 82.) § 4. THE MIDDLE AGES. Taxes, military service, tithes, and customs duties alone gave rise to inquiries and records of some degree of a statistical character. Of those which have been preserved, the most important are the land registers of different coun- tries showing the number and obligations of the holdings, something in the same way as a cataster. 807. Caroli magni memoratorium and 808. Brevis capitulorum, concerning military service (Monum. Germ. leg. Set. II., Tom I., Berolini, 1880, pp. 134, 137)- c. 830. Al-Mamum, Description of the provinces of the Khalifate (Fallati, Einleitung, in die Wissenschaft der Statistik. Tubingen, 1844, p. 125). 950. List of judicial districts and provinces of the Emperor Constantin Porphyrogeneta (Ibid.). 1088. Domesday book of William I. (Gneist, Englisches Verwaltungs Recht, 1876, I. p. 1 16). 1 8 Annals of the American Academy. 1 23 1. Land Register of Waldemar II. (Lappenberg, Script, rer. Danic. 1792). 1 241. Inventory of Emperor Frederick II. of the crown estates in Sicily (v. Raumer, Hohenstaufen 1841, II. 409). 1327. Katasto of Duke Charles of Calabria (Quadri, Storia della Statistica, Venice, 1824). 1337. Landbuch der Neumarkt (Gollmert's edition, 1862). 1358-67. Landbuch fur das Furstenthum Breslau-Neu- markt (Stenzel, 1842, in the Bericht des historischen Sektions der schlesischen vaterlandischen Gesellschaft). 1375. Landbuch der Mark Brandenburg (Fidicin's edi- tion, 1856). 1377. Poll tax in England under Edward III. and Rich- ard II. (Pelgrave, the Parliamentary Writs Collection, London, 1827). 1442. Salt tax in Sicily under Alphonse I (Galanti, Descr. geogr. et statistica delle Sicilie, 1787). 1460. De ritu, situ, et moribus Germanise of Pope iEneas Sylvius Piccolomini. 15 15. Machiavelli, Ritratti della Francia et della Alle- magna. B. FROM THE BEGINNING OF SCIENTIFIC STATISTICS TO THE YEAR 1750. y ->, I. Comparative Political Statistics (Achenwall's Statistics). § 5. statistical needs of the modern state. All science is based on a practical art, but it soon over- steps these limits in the~search for the general connection of things. Thus it becomes a system, and promotes in turn practical purposes by means of systematic principles which extend the limits of our general knowledge. It is History of Statistics. 19 at first simply a search for a system, for a logical concep- tion, and is developed and completed gradually. In the beginning, statistics considered as its material the (most urgent need of the period, namely the knowledge of the state, and as its method comparison, without, however, possessing an exact sense of proportion nor a distinct consciousness of the necessity of measurements. The stimulus came from the remarkably rapid transfor- / t mation of mediaeval society into the form of the modern I state. At the end of the 15 th century the general longing "* for order and security gave monarchy a rapidly-increasing power. An experienced bureaucracy took the reins of government, a standing army crushed out every resistance to the measures of the courts and the administration. The nobility came to prefer court life, official position, or the management of their large estates to the ruinous feuds of earlier periods. Fiscal necessities gave rise to the ideas of " Kameralistik " and " Wohlfahrtspolizei " (productive administration of public property, and police regulations for the promotion of general prosperity). Without a knowledge of the state of the country, its resources could not be developed. The totally changed character of foreign relations was another factor. In the circle which surrounded the mon- s arch there was a possibility of rapid resolution and a dan- gerous secrecy hitherto unknown. Noiseless preparations and agreements could turn the whole power of the state suddenly on some unforeseen aim. The intriguing state policy of Italy, there a hundred years old, became the common property and the common danger of Europe. ^ ^""'Modern diplomacy arose and with it a fabric of distrustful mutual observation. The key to success was cau tious, considerate judgment, based on the best attainable infor- mation as to one's own military, financial, and political resources, and those of other powers. • No wonder therefore that writers of this period con- ceived the idea of investigating scientifically the elements 20 Annals of the American Academy. of strength and power of existing states, and making this the subject of instruction, though the ways and means of such investigation might be new and difficult. § 6. FUNDAMENTAL WORKS. Tl^ejfirstJ^pical work in this field was the Cosmographia of Sebastian Muenster (born 1489 at Ingelheim, died 1552 at Basle, a Franciscan, but after 1529 Protestant professor at Heidelberg and Basle). A portion of the work appeared in 1536, the whole in 1544. The 1st book describes the world according to Ptolemy; the 2d, Ireland, England, Spain, France, and Italy; the 3d, Germany; the 4th, the rest of Europe; the 5th, Asia; the 6th, Africa. Maps are given for all known countries and they are treated system- atically under the following heads : boundaries, divisions, principal towns ; history ; state organization, rulers, nobles, estates, army, military capacity, church relations, laws, customs and manners ; and in detail the chief cities with their wealth and trade. , ■ In 1562, Francesco Sansovino (born 1521 at Rome, died 1586 at Venice, lawyer and author) followed with his work: Del governo ed amministratione di diversi regni ed republiche libri XXII. It treats of France, Germany, England, Spain, Turkey, Persia, Tunis, Fez, Poland, Por- tugal, ancient Rome, modern Rome, Switzerland, Ragusa, Sparta, Genoa, Athens, Lucca, Venice, Nuremberg, and Utopia, i. e. } Plato's republic, and gives in a small compass a concise and elegant description of their public law and their customs. In 1589 appeared from the pen of Giovanni Botero (born at Bene, died 1608, secretary of Cardinal Charles Borromeo, tutor of the children of Duke Charles Emanuel of Savoy, and an experienced diplomatist), Le relationi universali divisi in quatro parti, or in the Latin edition, Relationes universales de viribus, opibus et regimine prin- cipum Europae, Asiae et Africae. The modest volume History of Statistics. 21 with rich contents gives estimates in figures of the areas, revenues, taxes, military strength, and the importance of the commerce of the various countries. In 1614 Pierre d'Avity, Seigneur de Montmarin (born 1572, died 1635, serious and learned author in usum del- phini), wrote under the initials D. V. T. Y. : Les etats, empires et principautees du monde, representes par la description des pays, moeurs, des habitans richesses des provinces, les forces, les gouvernements, la religion et les princes, qui ont gouverne chacun Etat Volume I. con- tains the account of a circumnavigation of the globe with the description of Asia, Africa, and America; volumes II.-IV. treat of Europe with exact and useful data. All these books appeared in numerous editions and in several languages. In 1626 the book-dealers Elzevir in Leyden, celebrated for their editions of the classics, began the publication of the so-called Respublicae Elzeviranae, consisting of 34, and later 60 descriptions of single states by distinguished statesmen such as Jean de Laet (director of the Dutch West India Company, died 1649), Contarini, Josias Simler, Janotti, and others. § 7. STATISTICAL LECTURES AND COMPILATIONS. Statistical studies were first introduced into the Uni- versity curriculum in 1660 at Helmstedt, by Hermann Conring (born 1606 at Norden, died 168 1, well-known medical and physiological authority, physician in ordinary to several princes, professor of the law of nature, and distinguished polyhistor). His lectures were published, in 1668 by Poepping, 1675 by Ph. Andr. Oldenburger, and 1730 according to corrections left by Conring himself, by Goebel. His data are drawn chiefly from Botero, the Respublicae Elzeviranae, and J. A. de Thou, Historiae sui temporis (1606-1614). Conring requires not only a de- scription of the bn, as he says, but also of the causal 22 Annals of the American Academy. connection, 6c6rc, of Aristotle distinguished in time and space. He groups the causes according to the four Aris- totelian principles; the caus a- fflatedalis, t he^ people and its energy, the land and its production ; the causa finalis, prosperity and its means ; the causa formalis, the form of the state and the mode of government; and the causa efficiens, the actual ruler, the officials, and the estates with their auxiliaries and resources (V. John, Geschichte der Statistik, 1884, Part I. p. 52). Lectures on the model of Conring's were read in the 17th century by Oldenburger (Geneva), Herz (Giessen), Bose, Sagittarius, Schubart (Jena), and Beckmann (Frank- fort-on-the-Oder). In 1673 the last-named wrote his His- toria orbis terrarum geographica et civilis. Thomasius in Halle begins in 1694 the list of the so- called " Kameralisten," most of whom besides teaching the science of administration and finance delivered the customary statistical lectures. Among their publications that of Everard Otto (in Utrecht), Primae lineae notitiae Europae rerum publicarum, 1726, is most widely known. By far the best work of this period is that of Thomas Salmon, The present state of all nations, 1724. § 8. GOTTFRIED ACHENWALL. The range of ideas represented in these works received from Gottfried Achenwall a generally acknowledged sci- \ entific form. He is therefore called the father of statistical j \science. Achenwall (born 17 19 at Elbingen, died 1772), a pupil -of Schmeitzel in Jena, began in 1746 statistical lectures at Marburg, and wrote in 1748 the essay " Vorbereitung zur Staatswissenschaft der europaischen Reiche " upon being called to Gottingen. This work became later the intro- duction to his " Abriss der neusten Staatswissenschaft der heutigen vornehmsten europaischen Reiche und Repub- liken " (later Reiche und Volker), published in 1 749. History of Statistics. 23 In this introduction he uses for the first time the word "Statistik " (statistics, statistical science). 1 Up to this time the word had been merely suggested by Philander von Sittenwald's statista, one versed in the knowledge of the state, or by the adjective use, rationes statistics, by Olden- burger, 1668, bibliotheca statistica, by Thurmann in 1701, and the collegium statisticum of Schmeitzel. Achenwall derives the word from the Italian, ragione di stato, practi- cal politics, and statista, statesman. Concerning the definition of statistics, and its scientific method of investigation, Achenwall says : *' When I con- sider a single state, I discern a vast number of things actually to be found therein. Among them are some which concern obviously its jDrosjp^ritv^either in obstruct- ing it or contributing to it. Such things we might call ' Staatsmerkwiirdigkeiten ' (the remarkable things of the state). The totality of these ' Staatsmerkwiirdigkeiten ! of a kingdom or a republic, makes up its constitution iiK£he broadest sense, and the account of such consti- tutions of one or more states , is ' statistik.' Its final object is to gain political wisdom by means of knowledge of the various states* The internal interests of the state, the means of increasing its wealth, of stimulating popula- tion and riches, of promoting science, industry, and com- merce, and of improving the defects of the constitution, may be treated separately for each particular state. The external interests of the state, whether it can dispense with foreign allies or must seek them, whether it has much or little to fear from foreign powers, require comparisons of the state with all other states, and cannot therefore be understood without a knowledge of these foreign powers."/ 1 M. Block (Traite de la statistique, p. 9, note) tells us : " It seems to have been Brion de la Tour who employed for the first time the word ' statistique ' in France. At least he published in 1789 Tableau de la population de la France, avec citation des auteurs, au nombre de soixante douze qui ont ecrit sur cette partie de la statistique. According to Bachaumont, ' M6moires secrets,' the econo- mists employed the word earlier. It was Sinclair who introduced the word into England." (Translator's note.) 24 Annals of the American Academy. Achenwall, however, treats only Spain, Portugal, France, » Great Britain, the Netherlands, Russia, Denmark, and j Sweden. He gives a careful picture of each, of land and people, in seven distinct groups of questions : i. The lit- erature and sources of information. 2. The state, its ter- ritory and the changes of the same. 3. The land, its climate, rivers, topography, divisions, abundance or scarcity of products. 4. The inhabitants, numbers and character. 5. The rights of the rulers, the estates, the nobility, and the classes of the inhabitants. 6. The constitution of the court and the government, laws, and administration of churches, schools, and justice, industry, home and foreign commerce, currency, finances, debt, army and navy. 7. The interests of national life and politics, as well as the outlook for the future. This conception of the matter which statistics treats coincides, it is obvious, with that of Conring and Muen- ster. ([ Achenwall limits his researches to the collection of materia! from the existing literature, does not criticise either the sources of the information or the proofs of the causal connections, but is satisfied with very general polit- ical, economic, and ethical reflections. y - Nevertheless the short narrative is a model of conciseness, diligence, and : lucidity. The work found such general recognition that it was translated into all languages. As a consequence, all nations received the word statistics, and with it at the : outset that conception of statistics which was supported by Achenwall. II. Official Statistics (Busching's Statistics). §9. scientific demands leading to official statistics. The literary treatment of the data relating to the state which has just been considered was far from excluding the idea that an insight into the state of social and political affairs might be obtained by the cooperation of the official History of Statistics. 25 organs in the collection of information on sound scientific principles. The idea appeared as early as the period of the Reformation. Jean Bodin (born 1530 at Angers, died 1596, lawyer and professor of public law at Paris) expresses it in his " Six livres de la republique." He pleads for the reinstatement of the Roman census as an adjunct of the police power, as a safeguard against the arbitrary and usurious demands of the tax farmers, and finally as a means of information as to the number and position in life of the population. Similar inquiries are desired by Jac. Franc. Lottini (ambassador of Venice at the court of the Emperor) in his essays on. the Tesoro publico, 1600. ' A remarkable theoretical and technical insight into "the statistics of population is shown by Georg Obrecht (born 1547, died 1612, professor at Strassburg) in " Fiinf unter- scheidliche secreta politica " published in 1617. In the essay " Eine sondere Polezei-Ordnung und Constitution, etc., wie die gemeine Wohlfahrt zu vermehren " he pro- poses continuous statistics of population based, to be sure, on very extended inquisitorial privileges of the govern- ment organs. Lists of legitimate and illegitimate births, marriages, deaths, and guardianship, as well as the ages of the people in groups of three years, could be obtained by a permanent combination with the collection of taxes. Data concerning moral deportment and for convicts con- cerning reformation and repetition of offences could be obtained also. His propositions are accompanied with explanations as to their application which approach a legal ordinance in clearness and exactness, and contain schedules and estimates of probable cost. These all reveal a wonderfully-clear conception of the decisive factors in practical statistics. A second essay gives the project of a law to authorize the fiscus to establish a life insurance and pension institution (W. Roscher, Geschichte der National- okonomie in Deutschland, 1874, p. 152). 26 Annals of the American Academy. Various statistical inquiries were demanded also by : 1623. Christoph Besold (born 1577, died 1638, professor in Tubingen) in Synopsis politicae doctrinae. i656./Veit Ludw. von Seckendorf (born 1626, died 1692) in " Deutscher Furstenstaat." 1674. Joh. Heinr. Boeder (born 1614, died 1672, pro- fessor at Strassburg and Upsala) in Institutiones political II. 10. c. 1700. Gottfr. Wilh. Frhr. von Leibniz (born 1646, died 17 16) in a project for the Saxon Society of Science. (Ed. Bodemann in Preussischen Jahrbucher, 1884, Vol. 53, p. 378.) § 10. completed official investigations. , Among the first official undertakings in which material was collected and treated statistically were the following : 1575. Seventy-five questions of Philip II. directed to the prelates and corregidors of Spain, concerning the state of their districts. The answers were classified for the king's use (L. von Ranke, Fiirsten und Volker, I. p. 120). 1 58 1. Nicol Froumenteau, Secret des finances, and 1586. Et. Pasquier, Recherches de la France, both from the books of the state chamber of accounts. 1 597-1610. Sully (born 1560, died 1 641) presented to Henry IV. official statements as to the state of the finances and the army, and proposed in 1609 a plan for a compre- hensive cabinet d'etat et de guerre (Memoires des sages et royales oeconomies d'estat de Henry le Grand, 1634. Petitot, Collection des memoires relatifs a l'histoire de France; Series II., Vols. I.-IX., Paris, 1820). 1622, 1639, etc. Registration of local citizenship every twelve years in Wiirtemberg. 1637. Status regiminis Ferdinandi in Austria. 1645 in Brandenburg, 1647 in Hesse, registration of the tax collection bureaus, the peasant proprietors, and men of other occupations. History of Statistics. 27 1665. Colbert's statistics of trade. 1 67 5- 1 725. The so-called Etats, numerous semi-official public documents. 1679. Almanach royal de la France. 1684. Annual accounts of births, deaths, and marriages in all sections of Brandenburg. 1688. Louvois, Depot de la guerre. 1696 the English Parliamentary Papers first appear. 1697 the first enumeration of cattle in Saxony. 1699 Louis XIV. required reports from the general in- tendants. The dissimilar and deficient returns are used by Count Boulainvilliers, 1727, in his Etat de la France. In 1719 Frederick William I. of Prussia began the semi- annual tables of population, occupations, artisans, domes- tics, houses, real estate holdings in the city and country, taxes, city finances, etc., which were arranged at a central bureau. Later these tables were made every three years (R. Boeckh, Geschichtliche Entwickelung der amtlichen Statistik des preussischen Staates, 1863). §11. FREDERICK THE GREAT. King Frederick II. of Prussia regarded statistics from a high scientific standpoint as a necessary methodical obser- vation and a continuous test of the efficacy of administra- tive measures. He extended the scope of the tables, by including data relating to social state, nationality, age, deaths by months, and causes of deaths in 56 classes, speci- fications of the agricultural population and property ac- cording to numerous classes, improved and settled terri- tory, industrial pursuits with 460 classes, linen and woollen industry, mining and smelting. Beginning with 1747, de- tailed reports of trade distinguishing 70-100 different wares were prepared; beginning with 1748 annual enumerations, population, 175 1, of cattle were undertaken and continued regularly after 1770. In 1772 a general table of factories was introduced, 1778 seed and harvest were reported, and 28 Annals of the American Academy. 1782 the number of ships. Besides these there are numerous reports drawn from the operations of the tax, justice, mili- tary, and school departments. In 1750 were commenced the triangulation of the state and the preparation of the chart of the general staff, by the Field Marshal and Col- onel von Schmettau. The statistical details were collected in general outline tables which the king carried with him on his journeys. His personal examination, his interest in the collection and his use of the results, his severity, his acuteness, and his remarkable topographical knowledge secured for these reports greater exactness than might have been expected considering the difficulties to be over- come. The universal obedience to the royal wish was' naturally an important factor in obtaining correct returns. (Boeckh, see § 10 — Meitzen, Der Boden und die landwirt- schaftliche Verhaltnisse des preussischen Staates, 1868. Part I. p. 10.) § 12. ANTON FRIEDERICH BUSCHING. The systematic publication of the details of official statistics jowes its origin to Anton Friederich Biisching. By ffi!s~publication the use of the facts in scientific study be- came general, and a mass of matter preserved which might be of much value in later investigations. Biisching (born 1724 at Stadthagen, teacher in Copen- hagen and St. Petersburg, 1754 professor at Gottingen, 1766 director of a Gymnasium at Berlin, died 1793) wrote 1754-1792 the first ten parts of his "Neue Erdbeschrei- bung," which however was not completed until 1807 by Sprengel and others. In 1758 he wrote a " Vorbereitung zur gnindlichen und niitzlichen Kenntniss der geograph- ischen Beschaffenheit und Staatsverfassung der europa- ischen Reiche," in which he does not, like Achenwall, describe single states, b ut seek s rather to comp are the different^ states in the main phenome na of politi cal life. History of Statistics. 29 In 1767 he founded "das Magazin far Historiographie und Geographie," which appeared in 23 parts down to 1793. Here were collected statistical figures from numerous Ger- man and other lands, so that it may be considered as the first periodical work on statistics. The importanc e of Btisching as compared w ith Achen- wall, is c hiefl y that the former instead of indulging in general reflections and observations, and being content with the totals, directed his attention to the details . This led to a careful examination as to the completeness and correctness of the data, and promoted, by the scrutiny of their origin and arrangement, the progress of critical methods. III. Statistics of Population (Sussmilch's Statistics). hz> § 13. CONNECTION WITH THE CHURCH REGISTERS. In a limited field the statistical details had attracted at an early date the attention of investigators. These studies had for their subject the typical relations of human lj fe and death , and extracted the materials almost exclusively from the church registers. Regular and continuous registration of births, marriages, and deaths was first introduced, as far as is known, in Augsburg in 1501, and then in several German cities. It was prescribed generally but ineffectually in 1524 by the Synod of Seez in Alencon, where the Huguenots were • numerous. In 1533 the Brandenburg-Nurnberg evan- gelical Church Ordinance required baptismal and marriage registers, and that of Liegnitz in 1534 baptismal records. Henry VIII. in 1537 and Francis Lin 1539 ordered church registers to be kept. In Breslau registers were ordered in 1542 for marriages, 1570 for baptism, and 1599 for deaths, the same in Brandenburg in 1573, and in the Electorate of Saxony in 1580 (A. L. Richter, Die evangelischen Kirchen- Ordnungen des 16. Jahrhunderts, 1846. E. Rehnisch, 30 Annals of the American Academy. Graetzer, Halley, und Neumann, in Gottinger Gelehrten Anzeigen, 1883, p. 1576). ^In London baptismal records were introduced in 1550, and in consequence of the plague, death registers in 1592. From 1629 women were employed to inspect the dead. They were required to estimate the probable age, and to register this with a statement of the illness or accident ca using deat h. The results were published weekly. V John Gr aunt fborn 1620, died 1674, shopkeeper, musician, member of the Academy) compared and criticised these figures for the years 1629 to 166 1 in his work "Natural and political observations upon the bills of mortality, chiefly with reference to the government, religion, trade, growth, air, diseases, etc., of the city of London, by Cap- tain J. G." It was presented in 1662 to the newly-founded Royal Society. Graunt comes to the surprising result that the sexes are nearly equal in numbers, that herein war and pestilence exercise no appreciable effect, that 14 boys are born for every 13 girls, and that the ratio of births to deaths is quite uniform. He calculates that of 100 persons born, 36 die in the next 6 years, 24 in the next decade, 15 in that following, and then successively 9, 6, 5, 4, 2, and 1, and demonstrates finally that from this ratio of deaths the number of living persons could be calculated (G. F. Knapp, Theorie des Bevolkerungswechsels, 1874, pp. 57 and 121. John, see §7). Graunt's discoveries excited the greatest interest, and particularly the large population which he ascribed to London aroused the jealousy of Paris and led 'to further discussions and investigations. William Petty (born 1623, died 1687, physicist, physi- cian, the friend of Hobbes) in particular espoused the cause. His chief work of 1679 is "Political Arithmetick, j\ or a Discourse concerning the Extent and Value of Lands, ^yV People, Buildings; Husbandry, Manufacture, Commerce, Fishery, Artizans, Seamen, Soldiers; Public Revenues, Interest, Taxes, Superlucration, Registries, Banks; Valua- tion of Men, Increasing of Seamen, of Militia's, Harbors, History of Statistics. 31 Situation, Shipping, Power at Sea, etc. As the same relates to every country in general, but more particularly to the Territories of His Majesty of Great Britain, and his Neigh- bors of Holland, Zealand, and France." He complains in it of the lack of figures based on actual enumeration and says of his met hod. " I have taken the course to express myself in Termsj^Number, Weig ht, or Measure , to use only Arguments of Sense and to consider only such Causes as have visible Foundations in Nature." His posthumous works were published in 1690 and 1699 by John Williamson. In 1696 Gregory King calculated from the hearth tax, assessed in 1690 on 1,319,215 houses, the population of England at five and a half million souls. Numerous simi- lar calculations are to be found in the Philosophical Trans- actions of this period. § 14. EDMUND HALLEY'S MORTALITY TABLES. In order to prove that it was superstitious to ascribe any special importance to the seventh and ninth year for the expectation of life, the % prebendary Caspar Neumann of Breslau collected from the parish registers of the city, in the years 1687-91, notes of 5869 deaths, from which he counted those falling in the fateful years and those lying between . These figures and the notes on which they were based came into the possession of the Royal Society in 1692, as it appears through the intervention of Leibnitz. The Society asked Halley for an expression of opinion on them. Edmund Halley (born 1656, died 1742), who made at St. Helena in 1676 a catal ogue of the stars of the_southern heavens, and calculated in 1681 the comet bearing his name, made in 1693 a report which was printed in the Philosophical Transactions of the Royal Society for that year (Vol. XVII., Nos. 196 and 198) under the title "An Estimate of the Degrees of Mortality of Mankind, drawn from curious Tables of the Births and Funerals at the 32 Annals of the American Academy. City of Breslaw ; with an Attempt to ascertain the Price of Annuities on Lives." In this he gives in the form shown in Appendix L, Halley's mortality tables, which were the earliest apart from the figures given by Graunt. Though his methods of calculation even with the light thrown on them by the papers preserved by the Royal Society are obscure, his figures are gained essentially by eliminating from Neumann's figures apparent accidental variations, and developing from the deaths at the various ages a general scale. On the basis of the ages of those^ who die he shows how many of a certain number, born in a given year, will die or survive in each succeeding year. From this he calculates for vlifejiisjirance the average ex- pectation of life at each age, and for the statistics of popu- / lation the probable number of the population of a given \ district from the number of births in a year. ^ However, Halley erred in the hope s whj ch he expressed of the reliability of , such calculations from h is figures. He himself .. li mits their applicability , in pointing out that they would not be exact for cities such as London and Dublin, on account of the continual changes of trade. Though he speaks of an excess of births over deaths he does not notice that his figures apply only to a stationary popula- tion, which neith er increas es, nor d ecreases in th e course hoLa Jluman life . If the yearly increase of population in » Europe be assumed to be on an average one per cent., it is evident that those who die at the age of 100 would come from a smaller population, in fact about 2.7 times less, than that of the children of one year. \\ The percent- ages, therefore, which are calculated from the various ages, from the deaths of one year or of several, without consid- eration of the increase of population, must undoubtedly be ' incorrect somewhere in the table, either at the beginning or at the end. According to Halley, the average length of life is only about 31 years, whereas counting I percent, annual increase it would be 37.5 years. In how far the mode of calculation which Halley em- History of Statistics. 33 ployed is original with himself we do not know. His conte mporar ies recognized^ him as the founder of this method of calculating mortality tables, which however is only applicable to a statio njuxj^pulat ion (Knapp, p. 61, see § 13). C ^2 f . § 15. ANNUITY AND LIFE INSURANCE INSTITUTIONS. Life insur ance was known in the Middle Ages for per- sons going on sea v oyages_or^pi lgrim ages. Out of it grew a species of wager on one's own or another's life, which as being questionable was forbidden in 1570 in Holland, in 1598 in Genoa, in 168 1 in France, though permitted in England up to 1773. During the 17th century the games of hazard grew into prominence. In 1660 lotto was invented; 1634-37 was the period of the tulip swindle in Holland; and in 1653 France accepted the project of the physician Lorenzo Tonti, to contract State debts by selling annuities in the tontine form, whereby the income of the dying accrued to the surviving. The probable duration of the annuities having been calculated too short, the state drew little profit from them, and supplied their place with lotteries (Bender, Die offentliche Gliickspiele, 1862). In 1657 Ch. Huygens, and in 1660 Format and Pascal calculated the probabilities in games of chance. In 1670 Jean de Witt (executed 1672) formulated the_j? rinciples _for annuity life insurance from the death registers of Dutch cities. In_ 1698 the first life insurance insti tution was founded in London on Ascheton's plan, and in 1699 the Society of Assurancy for Widows and_Orphans. Both existed up to 1730. In 1706 the Amicable or Perpetual Assurance was founded in London, which in 1866 ceded its business to the Norwich Union; 1721 saw the foundation of the Royal Exchange and the London Assurance Company, both of which exist at present. In 17 1 3 there appeared by Jac. Bernoulli (born 1654,, 3 34 Annals of the American Academy. died 1705, professor in Basel) " Ars conjectandi," a scien- tific demonstration of the theory of probabilities. More exact calculationslJfTrfortality were furnished in 1724 by de Moivre (born 1667, died 1754, Huguenot, Lon- don) Annuities of lives; 1737 to 1748 by W. Kerseboom (born c. 1 691, died 177 1, Hague, treasury official) in vari- ous essays in which as he says he follows Halley's method, but whose defects he points out (Knapp, p. 60, see § 13); also in 1740 by Nicol Struyk, who for the first time calls attention to the different mortality of men and women. § 16. johann peter sussmilch. The investigations of the course of human life, which had hitherto been carried on in England, Holland and t France from mathematical, political and industrial points ( of view, were taken up first in Germany by S ussmilch, who placed them under the more comprehensive and more ideal standpoint of scientific statistics. Joh. Peter Sussmilch (born 1707 at Berlin, died 1767, military chaplain, Qberkonsistorialrath, member of the Academy) wrote " Betrachtungen iiber die gottliche Ord- nung in den Veranderungen des menschlichen Geschlechts aus der Geburt, dem Tode, und der Fortpflanzung desselben erwiesen," dated 1741, on the march to Schweidnitz, and provided with a preface by Chr. Wolff. (The same in 1742.) He rests his work on the auth ority of Gr aunt^Petty, King, Arbuthnot, Derham. Niuwentyt, and upon the new and rich material for th e Prussia n provinces. For the regularity of the movement of the population of middle Europe he calculates averages which are substantially c orrect t othe presen t. In these results he perceives a providential ordinance (Genesis i. 28), contrary to which mankind cannot act with impunity. He proves the birth of 21 sons for 20 daughters, and the /equality of the sexes at the age of marriage, from which he derives the History of Statistics. 35 I ■co mmand of monoga my. The higher order of things\ reveals itself further in the fact that in each year about the same number die as in every other, and this applies alike to children, youths, men, and old men and to the two sexes alike, that sickness and epidemics do not essentially alter these relations, and also that multiple births, still- births, and accidents have certain numerical relations. For the order of decease he takes Riciotti's estimate of 1000 millions as the population of the globe, and describes it under the metaphor of a body of passing troops. The first detachment of children from birth up to 5 years of age consists of something over 108 millions, those of 5 to 10 years 65, those from 10 to 15 years 62, those from 15 to 20 years 60 millions, etc. Alwa^s^Jhowjever, when 10 die 13 newly-born begin... their. course, and each age furnishes a fixed contingent of deaths. He does not doubt that the order thus created by the will of God can be disturbed by outward circumstances and wilful acts. He finds a proof of this in the fact thatK in c7ties~one person dies out of every 25 to 32 ; in the coun-j try, however, one out of every 40 to 45. He censures/ therefore, with earnestness all unnaturalness, immorality, and luxury of life. In want, waste, wars, and worthless \ constitutions, he perceives a source of unnatural and un- \ sound conditions whose prevention by all legitimate means j is the duty of the state. Here he stands upon the stand- < ^"' point of the most enlightened p^Hticians_of his time. The second edition of 176 1 recommends expressly the emanci- pation of the person and the real property of the peasant, the abolition of feudal burdens, the cultivation of wild lands, protection against filling up with sand or other >*^y^ waste, proper distribution of the field holdings, renting of the public domains, the use of oxen instead of horses, fruit and bee culture, encouragement of manufactures and trades, especially such as require much labor, encourage- ment of commerce by reliable wares, reasonable prices and freedom from burdensome taxes. To work in law 36 Annals of the American Academy. and ordinance from the points of view shown to be bene- ficial for the welfare of the population, is the occupation of the ruler and his God-appointed duty. Sussmilch does not discuss the mathematical basis of the order of mortality, although he is familiar with the standpoint. He emphasizes the necessity of proper calcu- lations for annuities and life insurance. C. DEVELOPMENT OF UNIFORM SCIENTIFIC STATISTICS. I. Broader Views and Problems. § 17. THE SCHOOL OF ACHENWALL. N About the middle of the eighteenth century the various lines of statistical activity which had appeared found almost contemporaneously distinguished representatives — men who systematized and broadened the field. These men belonged exclusively to Germany and lived in Got- tingen and Berlin, not without personal relations to each other, yet without scientific connection or cooperation. Each had a circle of pupils and successors, and these in turn remained for a long time in the traditional ways. ^^ Acliejiwall was able to bring his fifth edition of 1772 in accord with the latest data. The sixth was edited by A. L. v. Schlozer in 1781, the seventh in 1790 by Sprengel. Among the works of the school may be named — 1757. Reinhard, Einleitung der vornehmsten Reiche und Republiken in Europa and Africa. 1 76 1. Baumann, Kurzer Abriss der Statistik. 1772. Meusel, Lehrbuch der Statistik. 1773. Gatterer, Ideal einer allgemeinen Weltstatistik (with a history of the literature). 1782. v. Hertzberg, Reflexions sur la force des etats, and History of Statistics. 37 1785. Sur la population des etats en general et sur celle des etats Prussiens en particulier. 1787. Antonio Mont Palau, Description politica de las soberanies de Europa. 1787. Ed. Zimmermann, Political Success of the present state of Europa. 1792. M. de Beaufort, Grande portefeuille politique. Grundrisse der Staatskunde, were written in 1792 by Liiders, in 1793 by Sprengel, in 1796 by Luca, in 1797 by Fabri, and in 1805 by Mannert. - The most influential pupil of Achenwall, August Ludwig v. Schlozer (born 1735, died 1809, official at St. Petersburg, professor at Gottingen), wrote in 1804 "Theorie der Sta- tistik nebst Ideen iiber das Studium der Politik iiberhaupt." The plan of his theory is arranged as follows ; vires (re- sources, soil, money), unites (form of the state and the administration), agunt (influences and effects). History is for him continuous statistics, statistics stationary history. (Th. Zermelo, Aug.. Ludw. v. Schlozer, ein Publizist im alten Reich, 1875.) ' § l8. CONTINUATION OF OFFICIAL STATISTICS. In the bureaucracy and finance administration of all states, statistical matter coveri ng a la rge field was collected and considered necessar y, but sel dom p ublished. But little, therefore, of it is known. """ Enumerations of the population took place : in Hesse- Darmstadt, 1742, 70, 88, 91 et seq.; Hesse-Cassel, 1747, 7$,%\,et seq.; Gotha, 1754 et seq. annually ; Saxony, 1755, 72, 83, 90; Hannover, 1755 ; Brunswick, 1756, 60, 88, 90; Denmark, 1769, 87; Bavaria, 1777; Mecklenburg-Strelitz, 1784; German Austria, 1785; Spain, 1787; the two Sici- lies, 1788 ; Savoy and Nice, 1789. In. North America the decennial census provided for in the constitution was car- ried out for the first time in 1790. In France a census of hearths was taken by the Due d'Argenson in 1753. \ 38 Annals of the American Academy. Finance Statistics were published for Prussia, 1780, by v. Hertzberg, " Huit dissertations," for France by Necker, 178 1, " Compte rendu au roi." General statistics of countries were published for the two Sicilies by Galanti, Descriptione geographica et sta- tistica delle Sicilie, 1 787-1 791; and for Tuscany Governo della Toscana sotto il regno de Leopoldo II. 1790; for Spain by Larruga, Memoires, 1790-1797. Collections of materials were published as follows : Aug. Ludw. v. Schlozer, " Briefwechsel," 60 pamphlets, 1775— 1782, continued till 1794 as " Staatsanzeiger," with the co- operation of Count Carmer v. Hertzberg, Count Firmian, Duke of Saxe-Meiningen, and other prominent statesmen ; Dohm, Materialien zur Statistik der neuesten Staatenge- schichte, 1777-85; Le Bret, Magazin zum Gebrauch der Staaten und Kirchengeschichte, 10 parts, 1781-88. State Almanacs appeared from 1700 on for the Nether- lands, from 1704 for Prussia, from 1720 at Ratisbon, from 1728 for the Electorate of Saxony, from 1730 the royal calendar in England, from 1736 at Frankfort-on-the-Main, from 1740 the Almanach de Gotha, from 1775 for Meck- lenburg. Von Schlozer praises, in 1806, the new era of things in regard to publications, " How fortunate we statisticians of the new century, the disgraceful distinction between uni- versity and cabinet statistics has ceased to exist." § 19. FURTHER DEVELOPMENT OF THE STATISTICS OF POPULATION. , Sussmilch had not gathered like the rest a circle of pupils (the third edition of his work was published by Ch. J. Baumann, 1790), yet the movement of population re- mained the subject of muc h attention. Upon the proposal of Menajider, Sweden commenced in 1 74 1 the registration in all parishes of births, marriages, and deaths. The results were arranged by the Academy History of Statistics. 39 in a work of Tables, beginning 1749, which were made the subject of scientific treatment in 1765-82 by War- gentin. (Knapp, p.74. See § 13. Memoires de 1' academie des sciences de Suede, trans, by Kastner, 1767.) Simpson in 1742, Deparcieux 1746, Deslandes 1750, fur- nished calculations of mortality. Euler (born 1 707, died 1783) wrote Calcul de la proba- bility dans le jeu de rencontre, and demonstrated in 1753 the means of correcting Halley's tables on the basis of the average growth of population. n 1765 the Equitable Life Insurance Institution on the mutual principle was founded at London. Methods of calculation were made more exact by Price, 1771 ; Morgan, 1779; Tetens, 1786, and finally through the method of smallest squares by Friederich Gauss (born 1777, died 1855). Condorcet (born 1743, died 1794) maintains in his " Es- quisse d'un tableau historique des progres de l'esprit humain,"(tiiat human actions can only b e con ceived as happening accordingjto the materialistic laws of nature. \ Y*^§ 20. EXTENSION OF THE RANGE OF STATISTICAL PROBLEMS. The mere continuation of the chief lines of statistical thought hitherto considered does not, however, exhaust the development of the science in this period. Numerous methods of observation and ideas were suggested, which seemed to show, on the contrary, that the range of subjects and ideas was capable of a very considerable extension. In a certain sense this may be termed a period of dis- covery in this field. Among characteristic works may be mentioned — (a) On Population : Messance, Recherches sur la popu- lation de quelques provinces et villes du royaume avec des reflexions sur la valeur du bled tant en France qu'en An- gleterre *depuis 1674, j usque, 1764, 1766, and Nouvelles recherches sur la population en France avec des remarques 40 Annals of the American Academy. sur divers objects de V administration, 1788, concerning Athe effect of the price of grains and other contemporary \!bonditions and measures upon the population. *v Moheau, Recherches et considerations sur la population pVla France, 1778 (assisted by Montyon). De la Pommelles, 1789, Re- cherches statistiques sur la population de la France, concern- ing the results of the levy of troops. Th. Rob. Malthns (born 1766, died 1834, clergyman, professor of political economy), Essay on the principles of population, 1798; population, according to his view, increasing in a geo- metrical, the means of subsistence, on the other hand, in an arithmetical, progression, the danger of over-population is produced. (b) On Agriculture: Arthur Young(bom I74i,died 1820, merchant ancPagriculturalist), Political Arithmetic, 1774; Economic voyages in England, France, Spain, Italy, 15 vols., 1768-1795 ; Annals of Agriculture, 45 vols., 1784 et seq. (c) On Commerce: Raynal, Histoire philosophique et politique des etablissements et du commerce des Euro- peens dans les deux Indes, 177 1. Seitwein, Anfrage an das deutsche Publikum, die Handelsbilanz zwischen England und Deutschland betreffend, 1773. K. v. Sttuensee and J. C. Sinaphis, Kurz gefasste Beschreibung der Handlung der vornehmsten europaischen Staaten, 1 778-1 782. A. R. W. Crome, Europas Produkte, 1782. De Tolosan, Memoires sur la commerce de la France et ses colonies, 1798. J. A. Noack, Statistischer Versuch iiber die Handelsbilanz zwischen Deutschland und Frankreich, 1794. (d) On Taxe s : Mauvillon (Mirabeau), Monarchic Prus- sienne, 1788. (e) On Churches : Schonemann, Grundriss einer Statistik des deutscnen Religions- und Kirchenwesens, 1797. (/) On Civilization in general: Due oV Argenson, Con- siderations~sur la gouvernement ancien et present de la France, 1765. UNtVEKSrnr History of Statistics. 41 §21. beginnings of tabular and graphic presentation. With the endeavor to establish causal connections the statistical argument turned more and more toward the proof by numbers and away from descriptions and opin- ions of a gen eral character. The excess and diminution, M\e rise and falFoT the rows of figures became the means /of measurement and proof. This means had a value of its own of the utmost importance for the investigations. Here, therefore, are the first steps toward a further progress in the method. As early as 174 1 Acherson, a Dane, had attempted in his Description statuum cultiorum in tabulis, to portray the most important features of the European states in tables of figures only. His data embrace area, population, re- ligion, finances, armies, the political constitution, money, weights and measures! As long, however, as only highly unreliable and defective figures could be obtained, such efforts could not be crowned with success. Even in 1782 little attention was paid to the idea of Crome in Giessen, who proposed to present the results graphically with geometrical figures. In 1785, however, he renewed his chart of the sizes of the European states, and in the year 1786 Plaifair in England came forward simultaneously with Randel and Remer in Germany with a very extended tabular treatment of statistical data. Beau- fort in Paris and Gaspari and Boetticher in Germany in 1789, v. Hoeck in 1794, Ehrmann in 1796, Ockhart in 1804, and others followed in the same line, in part with charts and graphic presentations. These efforts did not meet with the general approval of the statisticians. They remain, nevertheless, an important symptom of the developments which were to revolutionize the whole structure of statistical science. 42 Annals of the American Academy. II. Institutions for National Statistics on a Scien- tific Basis. §22. necessity for statistics during the french , - revolution. The necessity of resorting to statistics makes itself felt at every essential change in the form of the state, just as in the transformation from the mediaeval to the modern state. It proved to be so much the more indispensable in the unheard-of overturning of all existing conditions in the French revolution. According to the remarkable resolutions of the night of August 4, 1789, with irre- pressible enthusiasm, the policy was accepted of creating new forms based on ideas along entirely new lines. A new administration, new courts, general elections, and general military service were the principles to be built up, on a new and geographical division of the state, designed to wipe out every remembrance of the historic ties which bound the districts together. In addition, there were new means of transportation, a new plan of custom duties, new weights and measures, new money, but above all the project of a new tax system, to be founded chiefly on the general income tax. "All these projects were obliged to seek the aid of sta- tistics, and it was found with surprise how little material was in existence which could be used for their perfection. The National Assembly therefore commissioned Lavoi- sier (born 1743, executed 1794) to collect as quickly as possible the data necessary for the preparation of the reforms in administration and finance. He fulfilled his task in an " Aperc,u de la richesse territoriale et des reve- nues de la France," which he presented in 1790. He com- plains therein of the lack of sufficient material upon which to build. He estimates the population according to the ratio of one birth to 25.75 inhabitants, which had been History of Statistics. 43 ascertained for other countries, though the ratio for France at least in the present century is 1 to 36.8. His calcula- tions on the amount of land under cultivation proved sur- prisingly correct, though estimated simply from the num- ber and capacity of the ploughs. (Statistique generale de la France, Agriculture, Tome III., 1840, Rapport.) These considerations tended to spread the conviction of the necessity of systematically regulated returns. § 2^. BUREAUS FOR STATISTICS IN FRANCE. With considerable enthusiasm quite a comprehensive statistical activity was developed, and the organization of statistical bureaus took place. The whole movement ■ proved, however, to be merely temporary. Necker had established for the statistics of finance and - commerce a Bureau des renseignements, which was con- tinued for the publication of the balance of trade. For the general statistics of the country it was proposed to have expert agents in every borough, and in 1792 they were required to report certain facts to their supervisors, the Agents nationaux. In 1795 the minister Frangois de Neufchateau established a bureau under Duquesnoy for the departmental statistics to be collected by the Pre- fects. The newly-established Kataster Bureau began some publications in 1798. In 1801 Chaptal commissioned Jac- ques Peuchet to give a description of a department to serve as a model, and organized a Bureau de statistique under Coquebert de Montbret for the purpose of securing statis- tics of the departments on this plan. The descriptions were completed for only 53 departments and were discon- tinued in 18 1 5. Nevertheless, with the assistance of the cooperators in these works, there appeared, in 1 803, Her- bin's ° Statistique generale et particuliaire de la France et de ses colonies avec une description topographique, agri- cole, politique, industrielle et commerciale de cet etat." In 1804 appeared the " Dictionnaire universel geograph- 44 Annals of the American Academy. ique, statistique, historique et politique de la France," which had been ordered in 1790 by the National Assem- bly, and meritoriously completed by Prudhomme. In 1804 the official work, Statistique generate de la France publiee par ordre de M. l'Empereur et Roi et redigee sur les memoires, adresses au Ministere de l'lnte- rieur par MM. les prefets, was successfully brought to completion. Very few data of these works rest upon actual enumera- tion. Even the census of the population, which had been attempted in 1801 and again in 1805 had each time been successful only in the departments and the results varied greatly. An actual enumeration in Paris was accomplished for the first time in 18 17, according to the plans of J. B. de Fourier. The estimates of experts furnished the largest portion of the material. Great errors were therefore pos- sible. It required, however, by this method very little effort to broaden the sphere of the questions, and even secure estimates concerning things about which the per- sons interested would be disinclined to furnish information. The predominance of this form of official inquiry, which we call the enquete, is characteristic for French statistics down to the present day. That under the circumstances statistics attracted general interest and became the fashion, is easily comprehended. In 1803, under the protection of Cambaceres, a Societe de Statistique was founded at Paris. Donnant and Peuchet published in 1805 text-books, in Achenwall's style, of Statistique elementaire; in 1802-1804 Ballois edited An- nates de Statistique ; Deferriere, the chief of the statistical bureau, published in 1 803-1 804 Archives statistiques de la France. The " Moniteur universel," founded in 1789, as well as the "Journal des Mines," appearing since 1792, contained numerous statistical essays. The empire, however, brought an end to all these efforts. Although Napoleon had said " La statistique est le budget 'des choses et sans budget point de salut public," he dis- History of Statistics. 45 solved in 1806 the Commissions and the Societe de Statis- tique, and prohibited all publications with the exception of four Exposees de la situation de l'Empire, which were pre- pared by the Minister of the Interior, Count Montalivet, in 1809, 181 1, 1 8 13, and again in 18 15 during the hundred days. § 24. STATISTICAL BUREAUS IN ITALY, SPAIN, WESTPHALIA, AND BAVARIA. As a result of the increased interest in statistics in j France, and in part at the orders of the French adminis- j tration, some of the neighboring countries created statisti- ' cal bureaus. They were, as a rule, short-lived. The Italian I Republic received one in 1803, which, placed under the .- direction of Gioja, continued in existence until 1809. In Spain, during the French rule, a Departamento del fomento general del Reino was established. For Westphalia there was a statistical bureau under Hassel, in 1809, which did not survive the fall of the kingdom. In Bavaria, General Raglowich attempted, in 180 1, to found a military statistical bureau, which, however, did not last long. Later, an ordinance of December 12, 1806, provided for a regular report of lists of all births, mar- riages, and deaths in the new kingdom, and further ordi- nances of July 17, 1808, and September 27, 1809, directed the provincial authorities to send in annual reports of ad- ministration, and to combine with them the material for as complete statistics of the kingdom as possible. Returns were required especially concerning dwellings, number and movement of the population, immigration and emi- « gration, mining, agriculture, trades, laborers and products, commerce, prices, institutions of credit, care of the poor, sanitary conditions, medical arrangements, and schools. As it was soon perceived that returns upon so various sub- jects could not be compared and were of little value unless • made according to uniform schedules, ordinances of 18 10 46 Annals of the American Academy. and 1812 provided special tables for the arrangement of the data. The returns for 1809-10 and 1811-12 embraced, nevertheless, 438 volumes in folio, and the bureau for topography and statistics, established in 18 1 3, held the continuation and preparation of this material to be im- practicable. § 25. FOUNDATION OF THE PRUSSIAN STATISTICAL BUREAU. Much greater was the influence of the reorganization of \ the official statistics of Prussia. It was brought about in 1805 by Minister v. Stein on the proposal of Leopold Krug. Krug (born 1770, died 1843) nac * written several statis- tical and economic works while still in subordinate official position in Halle. At his request, in 1799, he was admitted into the Prussian service as registrar in the " Lehn " depart- ment, with permission to make use of the secret registers of the departments in which, as in the time of Frederick the Great, statistical material was collected. Upon these foundations he prepared, in 1805, his Betrachtungen iiber den National- Reichtum des preussischen Staates. The two moderate-sized volumes contain his calculations on the Physiocratic basis of the gross national income from the returns of agriculture and the excess in foreign trade. From these he attempts to ascertain the net income of the nation after exclusion of the income which simply passes from hand to hand, by subtracting the entire consumption of home raw products and imported foreign products and manufactures. The method is obviously open to objection, but as a most careful turning to account of statistical data the book has great merits. A Cabinet order of May 28, 1805, gave Minister v. Stein directions to establish a bureau for the continuation and correction of these data annually. In it the statistical material collected in the various departments could be united and formed into a systematized whole. History of Statistics. 47 The bureau was established immediately with the Min- ister as chief. Krug was the only official, though Beguelin and others rendered assistance. Soon after, on May 22, 1806, the first annual report was ready. It comprehended 24 tables of varied contents on population, topography, agriculture, manufactures and commerce, transportation, excise, consumption, morality, and culture. Returns of churches and municipalities, of postal and tax administra- tion, were lacking. Upon the remonstrance of various bureaus and their demand that their communications should be kept secret, a Cabinet order of October 16, 1806, the second day after the battle of Jena, ordered that the publication of returns on population, production, manufactures, culture, com- merce, shipping, and civil status should be permitted, but that the returns of private property, of moneyed institutions, credit systems, state debts, and public revenues (Boeckh, p. 28. See § 1 1) should not be published. § 26. REESTABLISH MENT OF THE PRUSSIAN STATISTICAL BUREAU. As soon as the peace of Tilsit permitted the regulation of the state affairs, an administrative order of the govern- ment of December 26, 1808, confirmed the previous regu- lations as to the statistical returns. Yet the necessary economy in the official service and the examination of Krug's plan by the " Oberprasidien " led to some restric- tion of its scope. * Joh. Gottfr. Hoffmann (born 1765, died 1847. At this time " Bauass^ssor," later Ministerialrath fur Gewerbe * Polizei, and professor) contended that only those questions should be asked to which it seemed reasonable to expect correct answers. He reduced Krug's questions to less than one-third, but drew within their scope all suitable material which could be gathered together from the affairs of the public offices. On account of these reasonable pro- 48 Annals of the American Academy. posals a Cabinet order of October 4, 18 10, appointed him. Director of the statistical bureau, with Krug and the topographer Engelhardt as associates. His own principles, as well as the state of the finances, led Hoffmann to exercise the greatest caution, so as to burden as little as possible the officials who made the returns. What he brought together, however, was the result of an actual ascertainment of the facts. He preferred to abandon altogether the attempt to secure returns on agri- culture, causes of death, churches, schools, and sanitary conditions than to content himself with unreliable data. % His principle was a direct enumeration in everything. In this conception of the method he stood in an essentially contradictory position to that of the French statistics, and though enumeration and enquete are certainly to be justi- fied or rejected according to the specific objects and pur- poses for which they are to be used, the enquete has never won for itself a prominent place in Prussian or in German statistics generally. The German statistics have not en- couraged multiplicity in the returns, where it could not be obtained by additional enumerations, or by distinctions introduced into the enumeration, or by a combination of results obtained by direct enumeration. Hoffmann's work rests, therefore, on an uncommonly limited basis of materials, but he understood how to use them with surprising versatility and productive power, and to supply the deficiencies from the rich treasure of his scientific acquirements and experience. (Boeckh, § 44. See § 11.) HI. Limitation of the Field of Statistical Science. §27. limitation of achenwall's statistics. The appearance of the official statistics in such vigor in France and Prussia was combined with a decisive revolu- tion in the whole field of scientific statistics. History of Statistics. 49 Although statistical bureaus were organized only grad- ually in other states, yet the necessity was generally felt of I studying the state of the nation from the current affairs of J its administrative offices, ,as well as from special returns at stated intervals. This attention to the internal affairs of the nation con- tained in itself a certain antithesis to Achenwall's general descriptive comparisons of all nations. It soon appeared from the interdependence of the results that the statistics of Achenwall, of Busching, and of Siissmilch, were merely parts of the same sphere of ideas. This was first recog- nized theoretically by Niemann in his " Abriss der Sta- tistik oder Staatenkunde " (1804) 1807. (John, p. 119. See § 7.) Even before the death of v. Schlozer it was felt that the fundamental ideas of Achenwall's statistics were shaken* by the ever-increasing stream of official statistics and by the numerical treatment which was based on them. Tabu- lar and graphic presentations and comparisons came more and more in vogue through the efforts of v. Brunn, Don- nant, Lichtenstern, v. Schmidtberg, and especially Hassel (Grundriss der Statistik, 1805, 1809, 1825). But v. Schlozer with Luder, Rehberg, Brandis, Heeren, considered this as an aberration (Luder, Geschichte der Statistik, p. 214; Kritik der Statistik, § 14). In 1806 and 1807 a passionate controversy arose against the brainless bungling of the number statisticians, the slaves of the tables, the skeleton- makers of statistics. Undoubtedly the pupils of Achen- I wall were right that statistics cannot evade the considera- ; tion of the highest problems of political life. But they i deceived themselves as to the manner in which this ideal, purpose of statistics was to be attained. They underesti- mated the significance of the material prepared for com- parison according to number and measure, the indispensa- ble premise of every critically correct conclusion from statistics. The opponents in the sharp attack were them- 4 50 Annals of the American Academy. selves, however, not sufficiently clear how new and precise limits for their science should be determined. § 28. ELIMINATION OF POLITICAL ECONOMY, OF PUBLIC AND ADMINISTRATIVE LAW. In this state of affairs the decisive factor in the develop- ment of statistical theory was the specialization of the various fields of knowledge which at the beginning of the century accompanied the increased intellectual activity and the unusual extension of the field of investigation and research. Adam Smith, in his " Inquiry into the Nature and Causes of the Wealth of Nations," 1776, furnished a firm footing for the science of political economy by his clear definition, system, and method. With the beginning of the century political economy began to appear as an independent sub- ject with special professors in the lectures and studies of the German universities, as well as in England and France. Thus the connection with other political sciences, and hence with statistics was dissolved. In England, Stewart (1799), Malthus (1804), Ricardo (18 1 2), McCulloch (1825), and others represented the new science; in France, Say (1803), Sismondi (18 19), and Droz (1828). In Germany there were besides Garve, who trans- lated Smith, Sartorious (1796), Jacob (1805), Kraus (died 1807), Hufeland (1807), Liider (1820), Rau (182 1), Politz (1823), and v. Rotteck (1829), all of whom lectured on 1 political economy in Smith's manner as a discipline, which included all that related to economic policy, which the i. '■older school of Achenwall and indeed v. Schlozer held to be a field of statistics. Similarly the closely connected subjects of public and administrative law severed their connection with statistics. There had been before this time separate chairs for these subjects in the universities, but at this time the separation became general and permanent. History of Statistics. 51 The philosophical consideration of state and law by- Kant (1796), Fichte (1796), and Hegel (1821), as well as the historical conception for which Justus Moser (1765) had given the stimulus, and which Schlosser (1777), Putter (1786), and Eichhorn (1808) had moulded, gave new points of departure, and none of the works of Welker (18 13), Haller (1816), Kluber (1818), Sal. Zachariae (1820), P61itz (1823), and Heffter (1829), hold fast to the traditional con- nection with Achenwall's statistics. § 29. ELIMINATION OF THE GEOGRAPHICAL ELEMENT. The geographical notions which Seb. Miinster and Pierre d'Avity and even Busching had incorporated with statis- tics, showed themselves more and more to be a special branch of science. Gatterer had endeavored in 1775 to lead geography away from the political and statistical basis, by giving prominence rather to the natural differences of the surface of the earth and the conditions which they impose on civ- ilization. Zeune's " Gaea," 1808, had the same tendency. Decisive in the matter, however, was the distinguished example of C. Ritter (born 1779, died 1859) in n ^ s volumi- nous " Erdkunde im Verhaltniss zur Natur und Geschichte des Menschen oder allgemeine vergleichende Geographic" He places the reader in the position of the traveller, he ap- peals to the eye and heart, and gives exact information of events and experiences. The gaps in the material he does not attempt to conceal, but endeavors to place the reader in a position to supply them, as well as may be, by the analogies which his own judgment suggests. The result, therefore, is a difference in the principles of geographical and statistical observation. From the totality of the phenomena, geography judges from its standpoint as to what is unseen, and assumes by induction that what is typical may be found there. Statistics searches its entire field for distinct units, none of which may escape observa- 52 Annals of the American Academy. tion, but cannot draw into consideration any other phe- nomena. The results are for both mutually useful, but the methods by which they are obtained so totally different that the geographer is not as such a statistician, nor is the statistician as such a geographer. § 30. separation of practical life insurance from STATISTICS. * In the field of life insurance a complete separation from the statistics of population occurred, which continues up to the present day. Life insurance assumed such dimensions that at the end of the century there were more than ten large institutions in England. Others were established in 1806 at Hamburg, 1 8 19 at Paris, 1824 in Belgium, 1826 in Italy, 1828 at Lubeck, 1829 at Gotha, 1830 at New York, 1835 in Russia. Of a similar nature were the widows' treasuries, which, in part at least, had been founded on earlier institutions, among them the Prussian treasury for the widows of offi- cials, founded in 1776. The failure of several inadequately equipped institutions in England, the investigation of the Caisse Lafarge in 1809 at Paris, and the discovery in 1836 of the swindle of the bubble companies did not interrupt this develop- ment. Laplace, Baily, Lacroix, and Littrow advanced the neces- sary mathematical calculations. The more critically the basis of life insurance was examined the more evident it became that the order of mortality did not furnish a suffi- cient basis of calculation for the expectation of life among the persons of various ages and occupations who were seeking insurance. The attempt was, therefore, made to gain a scale for the tariffs from the growing material of the companies themselves. Milne prepared, about 18 15, the Carlisle table on the basis of observations in Carlisle History of Statistics. 53 from 1779-87; Finlaison, in 1829, the Government Tables from the tontines and annuities; Morgan, 1834, the Equi- table experience table, from the experiences of that com- pany between 1762 and 1829; and, finally, Brune prepared from the records of the Preussischen Allgemeinen Witt- wenverpflegungs-Anstalt, from 1776 to 1834, a death table of great value for the widows' treasuries. While the gen- eral calculations of mortality did not lose their value as a measure of the welfare of the population, the close con- nection between life insurance and Sussmilch's statistics ceased to exist. §31. DECLINE OF STATISTICS AS A SYSTEM. The development of the new scientific studies, with their much more profound treatment, deprived Achenwall's Sta- tistics of essential parts of its subject-matter. The data of the traditional system of " Staatsmerkwiirdigkeiten" assumed unavoidably a superficial character, and statistics as a university study sank into insignificance. It is true Luder (died 18 19) in Jena, Meusel (died 1820) in Erlangen, Niemann (died 1832) in Kiel, Mannert (died 1834) in Munich, and Heeren (died 1842) in Gottingen, still taught statistics with success according to v. Schlozer's ideas. In Austria v. Holzgethan, Schnabel, v. Schlieben, Franzl, and others were able to keep the traditions of the school alive, as statistics so understood still formed a part of the re- quirements in the examinations for position in the official service. But the old teaching died out with the teachers. Tabu- lar statistics in their then condition could not be taught j from the professorial chair. Luder, although he recog- nized the merits of Sussmilch's statistics, felt the change so strongly that he doubted the possibility of scientific statistics (Luder, Kritik der Statistik und Politik, 1 8 12, § 57). 52 Annals of the American Academy. tion, but cannot draw into consideration any other phe- nomena. The results are for both mutually useful, but the methods by which they are obtained so totally different that the geographer is not as such a statistician, nor is the statistician as such a geographer. § 30. separation of practical life insurance from statistics. -, In the field of life insurance a complete separation from / the statistics of population occurred, which continues up to the present day. Life insurance assumed such dimensions that at the end of the century there were more than ten large institutions in England. Others were established in 1806 at Hamburg, 1 8 19 at Paris, 1824 in Belgium, 1826 in Italy, 1828 at Liibeck, 1829 at Gotha, 18 30 at New York, 1835 in Russia. Of a similar nature were the widows' treasuries, which, in part at least, had been founded on earlier institutions, among them the Prussian treasury for the widows of offi- cials, founded in 1776. The failure of several inadequately equipped institutions in England, the investigation of the Caisse Lafarge in 1809 at Paris, and the discovery in 1836 of the swindle of the bubble companies did not interrupt this develop- ment. Laplace, Baily, Lacroix, and Littrow advanced the neces- sary mathematical calculations. The more critically the basis of life insurance was examined the more evident it became that the order of mortality did not furnish a suffi- cient basis of calculation for the expectation of life among the persons of various ages and occupations who were seeking insurance. The attempt was, therefore, made to gain a scale for the tariffs from the growing material of the companies themselves. Milne prepared, about 18 15, the Carlisle table on the basis of observations in Carlisle History of Statistics. 53 from 1779-87; Finlaison, in 1829, the Government Tables from the tontines and annuities ; Morgan, 1834, the Equi- table experience table, from the experiences of that com- pany between 1762 and 1829; and, finally, Brune prepared from the records of the Preussischen Allgemeinen Witt- wenverpflegungs-Anstalt, from 1776 to 1834, a death table of great value for the widows' treasuries. While the gen- eral calculations of mortality did not lose their value as a measure of the welfare of the population, the close con- nection between life insurance and Sussmilch's statistics ceased to exist. §31. DECLINE OF STATISTICS AS A SYSTEM. The development of the new scientific studies, with their much more profound treatment, deprived Achenwall's Sta- tistics of essential parts of its subject-matter. The data of the traditional system of " Staatsmerkwiirdigkeiten" assumed unavoidably a superficial character, and statistics as a university study sank into insignificance. It is true Liider (died 18 19) in Jena, Meusel (died 1820) in Erlangen, Niemann (died 1832) in Kiel, Mannert (died 1834) in Munich, and Heeren (died 1842) in Gottingen, still taught statistics with success according to v. Schlozer's ideas. In Austria v. Holzgethan, Schnabel, v. Schlieben, Franzl, and others were able to keep the traditions of the school alive, as statistics so understood still formed a part of the re- quirements in the examinations for position in the official service. \ But the old teaching died out with the teachers. Tabu- i lar statistics in their then condition could not be taught I from the professorial chair. Liider, although he recog- nized the merits of Sussmilch's statistics, felt the change so strongly that he doubted the possibility of scientific statistics (Liider, Kritik der Statistik und Politik, 1 8 12, §57)- / 54 Annals of the American Academy. § 32. state of official statistics. To supply this deficiency seems to have been in a cer- tain sense part of the idea which led to the foundation of the statistical bureaus. Originally topographical — statisti- cal descriptions of the land, the character of its soil, its national and political relations, and economic conditions were required from them. It soon became evident that the answers even to the sim- plest questions of population and industrial statistics, which, were indispensable to the government, gave rise to a mass of material which could hardly be handled. It was found that often the most desirable information could by no means always be obtained from the current affairs of the offices, but required special investigations and returns. The officers were bound by the bureaucratic rules of the service. Problems with distinct objects in view, and in- volving responsibility in their decision, were sent to them, cases where the solution could have the necessary cer- tainty only by a wholly impartial, well-considered, and unerring investigation. The demands extended generally to all the details, to the differences between various dis- tricts, industrial classes, or local institutions, so that the greatest specialization was necessary. For this imperative labor neither the officials nor the assistants, generally only temporarily employed, nor least of all the appropriations for these subordinate functions, were sufficient. The activity of the bureaus became, therefore, on the one hand, more intense ; on the other, more restricted. The concentration of all statistics in one bureau could not yet be thought of, and neither the same principles nor treat- ment governed the "ressort" arrangements in the different states. Though uniformity appeared later, yet until the middle of the century the organization and the enterprises History of Statistics. 55 of official statistics retained an individual character, which makes them interesting on account of their many specific peculiarities. IV. Rise of National Statistics in the Various Civilized Nations. § 33. FRANCE. The Restoration was by no means more favorably in- clined toward statistics than the Empire (§ 23). The pub- lications were very meagre. From 18 1 5 appeared a yearly "Tableau general du commerce de la France," with returns on the coasting trade, published by the administration of customs. In addition there appeared from 18 13 reports on recrutement (1830 by Petigny), and from 1820 by the Marine Ministry "Notices sur les colonies franchises," and also " Comptes rendus des travaux des ingenieurs des mines." In 1821,-1829 Count Chabral, Prefect of the Seine, pub- lished comprehensive statistics of Paris, prepared by Vil- lot, and 1825 and 1833 Guerry de Champneuf prepared reports on the administration of criminal justice. In 1827 a Societe de statistique was founded with official permission at Marseilles. At Paris the Societe francaise de statistique universelle was permitted to organize in 1829. It was not till after the July revolution of 1832 that the Institut de France was allowed to reestablish the Academie des sciences morales et politiques, which had been suppressed during the Consulate. It contained a section for Economie politique et statistique. In 1833 Thiers announced his intention to the Chambers of repeating the Statistique generale de la France on a new plan. He founded under Moreau de Jonnes a Bureau de la statistique. This bureau published, 1835, Tom. I. Finances; 1837, Tom. II. Territoire et population; 1838, Tom. X. Com- 56 Annals of the American Academy. merce exterieur; 1840 and 1841, Tom. III.-VI. Agricul- ture (the results of the agricultural enquete of 1839-42); 1843 and 1844, Tom. XL, XII. notices from the general administration (Bienfaisance, Etablissements de repres- sion); finally, 1847-52, Tom. VII. and VIII., Industrie manufacturiere et arts et metiers, the results of an in- dustrial enquete begun in 1839 and taken up again in 1845. Besides the above there were the publications of the administration of customs, of the Ministries of finance, of agriculture, and of commerce. The events of the year 1848 led to a new enquete on rural and industrial labor. It was completed only in Paris by the Chamber of Commerce, and the results published in the valuable work, Statistique de l'industrie a Paris. On January 1, 185 1, 2941 statistical cantonal and district commissions were organized for carrying through the agricultural enquete of 1852. The commissions super- vised the returns to 500 questions in every canton. In i860, on the occasion of the treaty of commerce with England, a new and comprehensive enquete was under- taken by the Conseil superieur de l'agriculture, du com- merce et de l'industrie, of which "Agriculture" appeared in 1 86 1. The enquete of Parisian industry was repeated in i860 (Statistique de l'industrie a Paris, 1864). In 1866 it was deemed important to demonstrate the influence of the treaty of commerce of i860 on French agriculture. An enquete, concluded in May, 1870, was, therefore, undertaken under a special commission, whose labors, Enquete agricole, ministere de l'agriculture, 1869- 70, fill 36 volumes. In 1879 a new agricultural enquete was assigned offi- cially to the Societe nationale d'agriculture de France, the results appearing in 2 volumes, 1880, "Enquete sur la situation de l'agriculture en 1879," by Barral. History of Statistics. 57 § 34. prussia and the other german states. The official statistics of all German states assumed in contents and character great uniformity from the example of Prussia, and in consequence of the gradual development of common custom and tax systems. The organization of the bureaus and the mode of publication remained very divergent. In Prussia the statistical bureau continued without changes to be the centre of the system (§ 25). Under Hoffmann, who surrendered the place in 1844 to Dieterici, and died in 1847, no regular publications were made. Hoffmann wrote essays in the " Staats-Anzeiger " and in the reports of the Academy. His first more extensive work was " Die Bevolkerung des preussischen Staates nach den Ergebnis- sen der 1837 aufgenommenen Nachrichten " ; in 1838 ap- peared " Die Lehre vom Gelde"; 1840, "Die Lehre von den Steuern"; 1843, *' Bevolkerungs- Geburts- Ehe- und Sterblichkeits-verhaltnisse im Preussischen Staate." In the same period Ferber published, beginning in 1829, regularly his " Beitrage zur Kenntniss des gewerblichen und kom- merziellen Zustandes des Preussischen Staates " from the papers of the ministry of finance. These were continued by Dieterici as " Uebersichten von Verkehr und Verbrauch im Preussischen Staate und Zollverein " in 1838, and from the following year by the " Centralblatt der Abgaben, Gewerbe- und Handels-Gesetzgebung und Verwaltung." Dieterici (born 1790, died 1859) published, 1846, the work " Der Volkswohlstand des Preussischen Staates," which compares the state of things in 1806, 1830, and 1845 '■> anc * began after the census of 1845 with the " Statistische Ta- bellen des Preussischen Staates" the periodical publica- tions of the bureau, for whose extension into all the details of the materials the new legislature of the country in 1850 had provided the means. From i860 to 1882 the bureau was in charge of Ernst Engel (born 1821). In 1861 a central statistical commission was appointed. 58 Annals of the American Academy. In Bavaria (§ 24) the statistical-topographical bureau, established in 1813, transferred the preparation of special topographical charts to the Ministry of War. In the year 1 8 18 the yearly reports were limited to a few returns, and after 1825 the reports were issued triennially. In 1833 and 1839 new ordinances wrought a change. With the last v. Hermann (born 1795, died 1868) began his work as Director. In 1850 he founded the " Beitrage zur Statistik des Konigreiches Bayern." Hannover made plans in 183 1 for the regular preparation of the statistical material of the various branches of the administration. However, it was not till 1848 that the plan was carried into execution, with the organization of a statistical bureau. It published from 1850 "Zur Statistik des Konigreiches Hannover." In Saxony the first impulse was given by the Statistische Vereine fur das Konigreich Sachsen, which were founded in 1837 by v. Schlieben. The cooperation of the govern- ment enabled them to publish, up to 1849, 18 parts of their " Mittheilungen." This very honorable private work was transferred in 1850 to the Ministry of the Interior, which founded a statistical bureau on the Prussian model. A statistical-topographical bureau was established in Wurtemberg, in 1820, under Memminger, but it was de- voted almost exclusively to topographical labors. Statis- tics were furthered by the Verein fur Vaterlandskunde, founded in 1822. It had almost an official character, and published its transactions in Memminger's Jahrbiicher, founded in 1818. In 1856 the society was united with the bureau into a real statistical organ. Baden endeavored, in 1836, to secure, by a commission of higher officials of the various departments, a preparation of its administrative statistical material. In 1852 a statis- tical bureau was founded. The Electorate of Hesse collected in 1842 and 1850 the materials for a comprehensive statistical description of the country. But they were never published officially, though History of Statistics. 59 used in the private works of Pfister, Landau, and Hilde- brand. Comprehensive materials were collected also in Hesse- Darmstadt, but they were not prepared till after the estab- lishment, in 1861, of a central bureau for statistics. Similarly the older returns in Oldenburg were prepared by the " Statistische Nachrichten," appearing after 1855. Nassau published in its State almanacs, beginning in 18 19, the results of its official statistics. Hamburg created in 1844 a Bureau for Indirect Taxes ancf Shipping, which published from 1849 " Hamburgs Handel und SchirTfahrt." In 1866 another bureau for population and tax statistics was established. In 1846 Bremen organized a bureau for the returns of • the movement of trade, which gradually enlarged its func- tions into a general statistical office. § 35. THE GERMAN CUSTOMS UNION (ZOLLVEREIN). The German Customs Union was of the greatest impor- tance in the growth of German statistics. The customs treaty, of October 25, 18 19, between Prussia and Schwarzburg-Sondershausen contains all essential I ideas of this preliminary step in the political regeneration of Germany, and among them certain important statistical requirements. The uniform custom duties collected at the boundary of the State which, by law of May 28, 18 18, superseded the former provincial customs system in Prussia, included in the customs limits parts of other German states. Prussia, therefore, proposed to divide the net income of customs with them upon the basis of population. The fulfilment of the plan required a triennial census of population, and a uniform system of internal taxes on production and con- sumption. Sondershausen accepted, and between 1823 and 1826 most of the Thuringian and Saxon states fol- lowed. In 1828 the Customs Union treaty with Hesse- 60 Annals of the American Academy. Darmstadt gave rise to the idea of a common administra- tion by the states of the Union, to which were added in 1832 the Electorate of Hesse and Homburg, in 1833 Bavaria and Wurtemberg, and in 1836 Nassau and Frankfort-on-the-Main. The foundation of a uniform census of population, of exact returns concerning revenue and expenditures, and the movement of merchandise and the uniformity in various matters relating to customs and taxes constituted the sub- jects for settlement by the General Conferences in affairs of Customs and the Union, of which fifteen took place between 1836 and 1863, and of which the discussions were published. The statistical returns appeared from 1 84 1 in 20-30 pamphlets yearly, the so-called " Commer- zialnachweisungen," which were carried back to 1834. As far as possible, it was sought to ascertain for each state the actual consuming population in each year. The resolutions of the general conferences of 1834, 1843, anc * 1845, which abandoned the simple distinctions of actual population and legal population, and required the return of the resident population, led to great difficulties and to the utmost complication in the form of the questions to be answered. In 1845 tne ordinance required that the enu- meration be made on a single day, the 3d of December, by house to house visitation, and with the return of each person by name. Tariff politics came more and more to the front, particu- larly when the union with the Tax Union of Hannover, Brunswick, and Oldenburg was consummated in 1852, and during its discussion. The returns concerning trade were therefore extended, and industrial statistics resolved upon. They were collected in 1846, and on a larger scale in 186 1. From i860 yearly statistics of mines were published. After the treaty of July 8, 1867, the Customs Parliament replaced the Customs Union. The defects and faults of the existing statistics were so strongly felt that the Bundesrath agreed to the appointment of a commission for the further History of Statistics. 6i development of the statistics of the Union. Before they could complete their labors the constitution of the German Empire, of April 16, 1 871, united all the German states. But from their investigations were determined the founda- tion and sphere of action of the Statistical Office of the German Empire, established July 21, 1872. (Statistik des deutschen Reiches, Bd. I., 1873, Einleitung.— Meitzen in (Holtzendorff) Schmoller, Jahrbuch fur Gesetzgebung und Verwaltung, I., 1872 II., III.) § 36. HOLLAND, LUXEMBOURG, AND BELGIUM. In Holland the published reports of the administrations of finances and colonies reach back to an early date. In 1 80 1, 1806, 1829, and every ten years since a census of pop- ulation has taken place, and in 18 16 and 1825 enumerations of cattle. A statistical bureau under Smits and a statistical commission were established in 1826; but both of these institutions fell to pieces when Smits, in 1830, joined the Belgian uprising. By the treaty of February 8, 1842, with Prussia (Preus- sische Gesetzsammlung, p. 92), which has been continued to the present day, the Grand Duchy of Luxembourg was included in the German Customs Union. All custom laws and ordinances had the same force there as in the Rhine province. Luxembourg took part, therefore, in the statis- tics of the Customs Union. Holland established in 1848 a statistical bureau in the Ministry of the Interior, which flourished under Baum- hauer (died 1876), but was replaced in 1878 by a statistical commission, as the greater part of the statistics had re- mained the concern of the various departments. Belgium in 1830 established, under Smits, the Direction de la statistique generate au ministere de l'lnterieur. The entirely new organization of the state, the census and elec- tions of 1832, and, above all, the law of May 1, 1843, whereby the state undertook the construction of the rail- 62 Annals of the American Academy. roads, with the consequent struggles and decisions on the plan to be pursued, made great demands on the official statistics. This led to the development of an intense activity in various fields. In 1 84 1 Quetelet, who had the supervision of statistics in the ministry, created the Central Commission for Statis- tics. It was composed of officials and scholars, and its valuable deliberations were published, after 1843, in the Bulletin de la commission de la statistique beige. Pro- vincial commissions supervised the collection of the data. The preparation for the general census of October 15, 1846, is to be noted as the turning-point in the ideas as to stricter methods for all kinds of statistical returns. This census of 1846 (population, agriculture, industry) was the first of the series of enquetes of 1856, 1866, 1876, and 1880. Besides this, the work " Statistique generate de la Belgique, expose de la situation du royaume," in 1852, gave a de- scription of the development of the country in the ten years from 1840 to 1850. Since then it has been con- tinued in decennial periods. § 37. AUSTRIA-HUNGARY. The establishment of a topographical-statistical- bureau for the Empire was proposed in 18 10 and 18 19, but not carried out until 1829, by the General Auditing Depart- ment, under v. Metzburg (died 1839). At that time 104 tables and charts were prepared from the material of the previous year, and 100 copies of them in writing were distributed among the various governmental offices. The repetition ordered in 1830 covered the period subsequent to 1 8 19. A hand-book on the state of the realm was pre- pared in 1830. Freiherr v. Kubeck secured an imperial order of March 31, 1840, creating the Direction of Administrative Statistics as an independent body. Lucam was the first director, his History of Statistics. 63 successors 1841-66, v. Czornig (born 1804), Fricker, and v. Inama-Sternegg. It was not until 1845 that publication of the returns was permitted, and then only for selected portions. In 1846 the "Tafeln zur Statistik der oesterreichischen Monarchie fur 1842 " appeared. Up to 1853 four other works, contain- ing the data for the years 1843-48, followed. After the trans- fer in 1848 of the statistical work to the Ministry of Trade, a new series of tables on Territory, Population, Adminis- tration of the state, and civilization, began with 1849. The customs administration published from 1840, reports of the movement of trade. After 1859 there appeared from the Ministry of Finance reports on the finances. Nevertheless centralization of the official statistics remained the rule, and this was continued under the Statistical Central Com- mission, created in 1863, except in so far as after 1867 it was limited to the kingdoms and countries represented in the Reichsrath. In 1872, however, a statistical department was formed in the Ministry of Trade, and in 1873 in the Ministry of Agriculture. The Hungarian statistics have been prepared since 1867 by a statistical bureau in Buda-Pesth. Centralization is here the rule, according to a law of 1874. In 1868 a statistical central commission was formed here also. § 38. GREAT BRITAIN. No other country gave such early and extensive pub- licity to its statistics as Great Britain. The Parliamentary papers mentioned in § 10 are in addition to the reports of revenue and expenditures, very rich in reports from offi- cials, and Parliamentary Commissions, on the various questions which engage the attention of Parliament. These often led to annual repetitions, and had as a con- sequence the establishment of statistical departments, such as that in the Board of Trade 1832, and in the Home Office 1834. s/ 64 Annals of the American Academy. The proposal of a general census of population was first made in 1753, but was not acted upon. When renewed in 1800, it was agreed to. It was decided that the census should take place every ten years. The first, under the charge of Rickmann, took place in 1 80 1. With it was required an abstract from the parish registers, giving the number of baptisms and funerals for every decade from 1700 to 1750, and for every year after the last named. From them Finlaison calculated backward the population of England in 1700 at 5,131,516 souls. The returns of 1801 distinguished simply sex, pos- session of a house, and chief occupation in agriculture, commerce, manufacture, or as an artisan. Gradually the questions were increased. The return of age was in 182 1 voluntary, and in 1841 the attempt was made to obtain the ages in certain classes — twenty-year periods for the rural and five-year periods for the urban population. The census of 185 1, however, attained a high degree of completeness. Returns of the movement of population were first re- | quired from the parishes in England in 1800, in Scotland 1807, and in Ireland 18 10. The numerous sects necessitated the registration by the state. The law of August 17, 1836 (6 & 7 Will. IV. Ch. 36), for England and Wales required the commissioners of the poor to establish registration districts, with registrars responsible to a superintendent. From every registry a copy is sent to the Registrar-General in London, in whose office they are carried into the Gen- eral book accessible to the public. Similar institutions were created in Scotland 1854 (17 & 18 Vict. Ch. 80), and in Ireland 1863 (26 Vict. Ch. 11). The Registrar-General's office has since received charge of the census, formerly the work of special commissions, and in Ireland also of the statistics of agriculture. In England and Scotland statistical societies undertake I the collection and preparation of agricultural and other \ statistics. The Manchester Soceity was founded in 1833. The London Society, which includes almost all statistical History of Statistics. 6$ A j authorities of the country, and has published since 1838 a J valuable journal, was founded in 1834. The great agricul- * tural Enquete for the United Kingdom, in 1879-82, was the work of a Parliamentary Commission on Agricultural In- terests. § 39. UNITED STATES OF AMERICA. The English colonies in North America had an obvious x interest in ascertaining, even earlier than the mother coun- try, the number of their population. Data on the subject reach as far back as 1607 for Virginia, 1700 for South Car- olina, and 1 7 10 for North Carolina. In all the British pos- sessions in North America 1,083,000 souls were enumer- ated in 1753, The Constitution of September 17, 1787, prescribed as a legal basis of the elections an actual enumeration of the population within three years, and a repetition every'"" successive decade. Poll taxes and other direct taxes cart be laid only in accordance with the population thus ascer- tained. The first census took place in 1790, and has since been continued regularly. It is the concern of the National Government, and was carried out before 1880 by the United States Marshals. Besides the enumeration of the popula-v tion, the census contains statistics on the movement of population, on agricultural, industrial, commercial, and other economic relations. The Constitution further provides that Congress shall legislate on finance, currency, national defence, and gene- ral welfare, and that all duties and taxes shall be uniform.. The care of the postal service and the regulation of patents, are in the hands of the Union. From these functions, and from the right of supervision vested in Congress, there has arisen a mass of public documents, as in England, full of reports and statements. The necessity of a permanent statistical office has not been felt until recently. The work of the census is carried on in bureaus organized for the purpose. A law of 1866 created a statistical bureau for 5 66 Annals of the American Academy. ( commerce and shipping in the Department of the Treasury. The United States Bureau of Labor has issued valuable statistical reports since 1886, and in the publications of other government offices, to which reference has been made, much material is to be found. Many of the states have established bureaus for labor statistics, which have furnished some excellent studies. j A prosperous statistical society, the American Statistical Association, founded in 1839 in Boston, is doing good work for statistics. § 40. DENMARK, NORWAY, AND SWEDEN. Before 1833 all statistical data in Denmark were govern- ment secrets. Among the general public, neither the value of imports and exports, nor the results of the financial administration were known. Nevertheless, a census of population occurred in 1769, and in 1801 for the kingdom and the Faroe Islands, and in 1803 and 18 10 for Schleswig and Holstein. In 1 83 1 representation of the estates had been intro- duced, and in 1833 tne king appointed a commission of higher officials, who, without a special bureau, published 18 volumes of tables on all branches of statistics between 1833 and 1849. I n x ^49 with the constitution a statis- tical central office was established, whose chief was to have a voice in all statistical questions which might arise in the various departments. The bureau continued, aside from the separation of Schleswig-Holstein, the former tables, and united the statistics of the country, so that now only medical statistics are in other hands, a com- mittee of the Royal Medical Society. Sweden and Norway built up their official statistics of population chiefly on a thorough and exact preparation of the parish registers, which had existed (§ 19) in Sweden since 1749. In Norway a general census of the population occurred in 1801 and in 1845. F° r tne greater part of the v History of Statistics. 67 administrative statistics, and particularly for the agricul- tural returns, reports of the chief branches were published every five years after 1830 in both kingdoms. A suitable preparation of these reports in connected form was pro- posed as early as 1839. For this purpose, in 1846, a statistical bureau was at- tached to the Ministry of the Interior in Norway. It publishes statistical tables of the kingdom. In addition, medical statistics have been published since 1827, and finance reports since 1838. In Sweden statistical bureaus were established in 1830 in the Ministries of Trade and Justice. Since 185 1 have appeared the " Contributions to the Official Statistics of Sweden," which contain the publications of the various departments. A statistical central office was established in 1857 and united with the Tables Commission. §41. RUSSIA. An ordinance of 1802 prescribed in Russia for the eight newly established ministries the collection and publication of statistical data and periodical reports. At that time were begun the publications of certain departments, par- ticularly the tables of foreign trade and shipping, which have not been interrupted. Further facts may be found in the annual report of Minister Kotschubey in 1804, pub- lished in Storch's journal. In 1 83 1 Pogodin investigated historically the reports which had been required as early as the time of Peter the Great. In 1833 it was ordered that proper subjects from his work, at least in outline, should be published. In 1834 statistical committees were formed in the gouv- ernements, consisting of the chiefs of departments and members chosen by the committee, with the Civil Gov- ernor as president. The results were sent for further preparation to the statistical department of the Ministry V' 68 Annals of the American Academy. of the Interior, which beginning in 1843 published*" Ma- terials for the Statistics of the Russian Empire." In 1852 a central statistical commission was created in the same Ministry. At the same time there existed sta- tistical sections in the Ministries of Finance and Agricul- ture, and since 1853 a statistical committee in the admin- istration of roads, transportation, and public buildings. The central commission published, in i860, "Tables of the Russian Empire," and since 1866 regularly the statistics of the empire. Besides these there are the publications of the various departments. However, actual returns even of population are so difficult to obtain that the data for the greater number of the gouvernements rest not upon actual enumeration, but merely on the reports of officials and committees. §42. SWITZERLAND, ITALY, SPAIN, PORTUGAL, AND GREECE. In Switzerland some of the cantons had enumerations of population very early, at least at the beginning of the present century. In 1836 a table of the results for all cantons was published. Before 1848 common statistics for all Switzerland could only be obtained on trade and cus- toms. The Federal law concerning the organization of the Federal Council of May 16, 1849, designates the col- lection of statistics as one of the functions of the latter. In 1850 a general census of population took place, and was prepared by Franscini for publication in Vol. I. of the " Beitrage zur Statistik der schweizerischen Eidgenossen- schaft." But without money and executive power over the cantons the federal statistics of the movement of the population proved, in 1852, to be impracticable. The Federal law of January 21, i860, improved this state of affairs, though it limited the obligation of the cantons to enumerations of population and cattle. Since then a Fed- eral Statistical Bureau is in operation. In Italy (§ 24) there was always the greatest interest for History of Statistics. 69 statistics, but Zuccagni-Orlandini shows in his " Corografica Italica" (1835-1845) how nearly impossible it was to com- bine the data of the numerous states. (Caesare Correnti in Annuario Statistico Italiano for 1857-58.) Sardinia had a Commissione superiore di statistica which published the census in 18 19 and 1838 with comparisons. In 1842 ap- peared Avet's " Statistica giudiciaria," which was continued in 1852 and 1857 by a special commission for civil and criminal justice. Tuscany collected annually by means of a central bureau the movement of the population, and founded under Zuccagni, 1849, a Direzione di statistica generale. Sicily received as early as 1832 a statistical bureau, the continental part of the kingdom in 185 1. Parma was described from official sources by Molossi, and Modena by Roncaglia, in 1829. For Rome the census of the population of 1853 was prepared by Grisi. The data then extant were collected in 1862 in the official work, Censimento degli antichi stati Sardi e censimenti di Lombardia, di Parma, et di Modena. Since the foundation of the kingdom of Italy statistics have gained in uniformity and in extent and importance. In 1 86 1 a statistical bureau, and in 1868 a statistical cen- tral commission were established. The Statistica del Regno d'ltalia appears since 1864 in numerous volumes, and besides these there are the extensive publications of the various departments. The Direzione della Statistica had been attached to various Ministries, but as a rule, and permanently since 1878, to the Ministero di agricultura industria et commercio. The director was until 1872 Maestro, since then Bodio (born 1840). In Spain (§ 24) periodical statements of trade with for-^ eign countries and with the colonies exist since 1849. In 1856 a Direcion general de estadistica was established, and reorganized by law of June 5, 1859. I* began in 1859 the publication of an Annuario estadistico. Before this we have only a few private works, such as the Diccionarii yo Annals of the American Academy. estadistici of Minano, 1826, Madoz, 1846, and de Plaza, 1852, which were based on official sources. For Portugal there appeared in 18 17 a Diccionario, and in 1822 a statistical description by Balbi. The different Ministries among which the statistics are divided, published only a few details. The Ministry of the Interior under- took a census of population in the years 1838, 1843, 1849, and 1850. In 1857 a statistical central commission was established, and in the year 1859 a statistical bureau in the Ministry of Trade and in i860 in the Ministry of War. In Brazil a census of population was attempted in 18 17, and repeated in 1872. Greece incorporated, at the organization of the state in 1834, a statistical bureau in the economic section of the Ministry of the Interior. It has published since 1861 the ics of Greece. onceptions of the Method and Purpose of Statistics. §43. influence of official statistics. The development of official statistics in the most impor- tant countries, the participation of numerous statistical and other offices, the occupation of trained statisticians in the service of the state, have all combined to make this par- ticular branch of statistical activity the predominant one. In the nature of things there was a certain limitation, a one-sided specialization in these labors of the official insti- tutions. Their functions must be exercised rather as an art than as a science. Their work is divided up for immediate practical purposes into a host of changing single problems, and the more successfully the special effort attains its goal the weaker becomes the incentive to seek for underlying reasons and general interdependence. Special branches of-St»tistical practice csu!d therefore undergo quite an History of Statistics. 71 independent and individual development. They could indeed receive a more or less complete theoretical foun- dation, and yet the science as a whole lack entirely the necessary uniformity and simplicity of a theoretical basis and the needed rounding off of its sphere of ideas. \\ The development of the technique, its adaption to the end in / view, and its application under given circumstances were the results of the work of the official institutions in this periods The acute criticism of a man like Hoffmann had, therefore, no pronounced tendencies for any line of theory. Almost averse to all theoretical exposition, he drew his conclusions with remarkable simplicity and directness. His critical demands scarcely appear to us to-day as particularly remarkable, but at the time they were new and led to great innovations. Their tone seems to us modest and reserved, but the reason is to be found in the limited means and the undeveloped processes of secur- ing returns of that day. Every conclusion of empirical science is based on I something which must be assumed as fixed and known. ■ This, however, may be open to question, and we may, of course, go on indefinitely calling into question the basis of the reasoning. Nevertheless somewhere in this course these critical doubts must be considered as removed ; but this point is determined only gradually, but as time goes on more and more thoroughly by theory and practice. The progress of criticism is hesitating because more exact demands are conditioned upon more exact means for their realization. Preoccupation with the specific problem to be solved, criticism of the results rather than the origin of the data, 1 and a certain empiricism in the conception of the method are the predominating characteristics of the official statis- ticians of the period. The same is also true of the private persons who devoted themselves to the statistical descrip- tion of countries or comparisons of them, as Padovani 72 Annals of the American Academy. (1817), Balbi (1822), v. Malchus (1826), Schubert (1835-48), Frhr. v. Reden (1846), and others. 1 44. perfecting of sussmilch's statistics. Sussmilch's statistics, by their special field of investiga- . tion, were obviously limited to the numerical conception/ and treatment of their data, and were theoretically, there- fore, the most developed. This was not because they had successfully surmounted greater difficulties, but rather because the limited field permitted more facile demon- strations, and therefore a certain completeness in their conclusions. The details of the investigations concerned only a small sphere of phenomena. It naturally suggested itself therefore to note the coincidences or divergences of the results, to observe their continuity, and to draw con- clusions as to the causes and effects of these facts. ! It followed as a matter of course that the clear numerical relations should become the subject of consideration and lead to the attempt to ascertain further regularities. Among the works may be mentioned : 18 14. Laplace (born 1749, died 1827), Essai philoso- phique sur les probabilites, quite in the line of the views expressed by Condorcet (§ 19). 1821-29. Fourier (born 1768, died 1829, physicist), No- tions generates sur la population, and two Memoires sur les resultats moyens, etc., appendices to Recherches sta- tistiques sur la ville de Paris and to the census of Paris of 18 17 (§ 23). In these he states the first algebraic formula for calculating mortality tables in a stationary population, and calls attention to the differences in the calculation re- sulting from taking whole years or dividing the years into sections. (Knapp, p. 78; see § 11.) 1825-37. J. C. Casper (born 1796, died 1864, Medizinal- rath in Berlin), Beitrage zur medizinischen Statistik. 1826. L. R. Villerme published an investigation of the monthly distribution of conceptions and births in their relations to climate, labor, nutriment, customs, etc. History of Statistics. 73 1839. Ludw. Moser (professor in Konigsberg), Gesetze der Lebensdauer. This criticises keenly the results of preceding work, and establishes precise propositions as to various methods of calculation and interpolation, mor- tality in various classes and positions in life in a non- sfationary population, and in the relations of marriages, conceptions, births, stillbirths, widowhood, as well as life and annuity insurance, tontines, etc. In 1842 Hermann (§ 34) began in Bavaria his attempt to ascertain the mortality by direct observation of the deaths of persons born in a given calendar year. §45. PAUPERISM AND QUETELET'S WORK ON MAN. The study of population was broadened by certain con- temporaneous conditions and circumstances into a philo- sophical and sociological treatment of moral statistics. About the end of the third decade of the present century the fear of over-population, which, based on the ideas of Malthus, had its origin in England, became general. In 1828 de Gerando wrote " La visitateur des pauvres." The preparatory labors for the English poor law of 1834 be- came well known. Between 1834-36 numerous works on • pauperism appeared by Jiirgen-Hanssen, v. Liittwitz, Gode- froy, Villeneuve-Bargemont, Heiberg, Senior, Schmidt, Duchatel-Neuville. In 1832 Fourier published the peri- odical " Phalangstere." The general tendency of thought is reflected in the successes of the novels of Alexander Dumas and Eugene Sue. In 1839 " Les crimes celebres " appeared, and in 1842 " Les mysteres de Paris." With the increasing consciousness of human community awoke also the feeling of the contrasts of society, which, however, degenerated into a specious apologetic of moral offences. Crime was treated as an unavoidable conse- quence of untenable social conditions, and in this way an approach was made to those conceptions of population V. 74 Annals of the American Academy. statistics which regard the numbers as evidence of natural laws. The* first representatives of moral statistics, Francis d'lvernois, in his investigations of the comparative mo- rality of nations, 1833, and Guerry, in his essay on the moral statistics of France, 1834, perceive in the constancy of the numbers nothing more than the influence of con- stant factors and conditions. A confirmation of these views, and at the same time a more profound, more humane, and more interesting expo- sition of them was given in Quetelet's work, "Sur l'homme et le developpement de ses facultes ou essai de physique social," which appeared in this agitated period, in 1835. Lambert Adolphe Jacques Quetelet (born 1796 at Ghent, died 1874, 1 8 14 professor of mathematics, 1828 director of the observatory at Brussels) published in 1829 Recherches statistiques sur le Royaume de Pays Bas, and was appointed chief of the Belgian statistics (§ 36). His work, Sur l'homme, declares expressly the constant averages in moral statistics to be a proof that the actions of mankind are regulated by laws. Among individuals the natural forces which tend toward the preservation of these laws are indeed influenced by disturbing forces resulting in accidental and individual phenomena. In the totality of mankind, however, the laws clearly appear. They are not however inalterable, but dependent on existing societary conditions. Natural influences are more or less counter- acted by others, the products of civilization. The general and periodic influences are more effective than the indi- vidual ones. In all cases an average standard is the best,^, and is obtainable statistically. The average man would, it is true, be different at every period, but would neverthe- less represent a state of equilibrium, the true type of the totality of operating influences. Man advances, however, by his intelligence to a condition no longer that of nature. Virtue, like nature, is unchangeable, but the intelligence of mankind develops just as does that of individuals. All History of Statistics. 75 individual development is determined by the conditions of society, by the course of great events. Society is respon- sible for the criminal as well as for the great man. The criminal is merely the instrument of society. He is the propitiatory sacrifice of society ; his crime the fruit of the * conditions under which he lives. Quetelet nevertheless excludes any thought of fatalism (Letters a S. A. le due de Saxe-Coburg, 1846). He sees the workings of law merely in the phenomena of the great ' masses, and denies expressly any constraining force on the individual. But it cannot be denied that he does not solve the contradiction, and that he does not speak clearly as to the responsibility of the individual for his actions. The masterly book found a warm reception, more among the general public, it is true, than among the statisticians. The latter could not fail to perceive the weak points in the deductions and in the idea of the average man. But the depth and moderation of his views and the noble humanity of his spirit won for the author great personal influence and regard among them, which he preserved till his death. §46. CONCEPTIONS OF STATISTICAL THEORY. If we mean by theory the fundamental idea from which the varied contents of a sphere of knowledge recognized as homogeneous can be uniformly understood and sys- tematically grouped in the circle of general knowledge, then we may see already the beginnings of such penetra- tion into the material and processes of statistical investi- gation. The train of thought in Achenwall's school was directed merely toward the description, comparison, and examina- tion of a certain mass of essential conditions in various single states. The contents of the numerous theories of statistics which emanated from the school, and which ap- peared to them to exhaust the subject, consisted simply in the systematic arrangement of these particular data. j6 Annals of the American Academy. When, however, the table statisticians brought forward the idea that the examination of the "Staatsmerkwurdig- keiten " cannot be fruitful without distinct numerical meas- urements, the consequence was obvious that the essence of statistics must be sought in this measurement of phe- nomena. Thus the idea of a distinct methodical procedure, , which had thus far been limited to the calculation of probabilities, was greatly extended in its scope. F. J. Mone (Theorie der Statistik, 1824) says in this view of things, " The method of statistics is the art or science of uniting as a whole all statistical material. For this pur- pose the materials must be sought, collected, classified, ordered, arranged, and combined, in order to make a single or, so to speak, an organized entirety." Melchior Gioja (§ 24) presented in 1826 in his Filosofia della statistica, a well-developed system on the nature and the evidential value of the indications, which permit con- , elusions as to certain conditions and influences, and as to the causes and intensity of these influences. His friend Romagnosi demonstrated in 1827 and 1828 in Questioni sull' Ordinamento delle statistiche (Annali universali di statistica, Vol. XIV.), that every statistical problem requires for its solution a well-considered plan, "~ exact execution of the necessary observations, examination and scrutiny of the results obtained, and, finally, conclu- sions capable of demonstration. The London Statistical Society in its programme of 1838 (Journal, Vol. I., 1838), declares that the discussion of cause and effect is not within the province of statistics. " It is not, however, true that the statist rejects all deduc- tions, or that statistics consist merely of tables of figures ; it is simply required that all conclusions should be drawn from well-attested data, and shall admit of mathematical demonstration." •About the same time Potlock (an address explanatory of the objects and advantages of statistical inquiries, 1838) History of Statistics. jy declared that all actual things, or facts, qualities, and the like which could be collected in numbers were statistics. Cournot (Exposition de la theorie des chances et des probabilitees, 1843) understands as statistics the science which has for its subject the collection and comparison of numerous facts of every kind, with the purpose of ascer- taining the numerical relations which appear independent of accidental exceptions, and thus denote the presence of regular causes whose effects are combined with those of accidental causes. Moreau de Jonnes (§ 33) says (1847) briefly statistics is the science of social facts expressed in numerical terms. Yet all these obvious advances in the conception of the theory were isolated. In addition to the traditional ideas of the State statistics, we now have Quetelet's almost mystical hopes of finding in the statistical figures, laws of the cosmological order, and of the world's history, and of making this aim the fundamental principle of statistics. At that time J. Fallati (born 1809, died 1855) attempted in his " Einleitung in die Wissenschaft der Statistik " (1843) to determine the real conception of statistics. It seems, however, that although he makes some important distinctions, and shows some insight into important prob- lems, his explanation of the essence of statistics remains obscure. There was so much confusion among these contradictory * views that in 1847, at the instance of Fallati, Schubert and v. Reden, a special commission to investigate them was appointed by the Germanisten-Versammlung, founded in 1846. This state of affairs led A. A. Knies (born 1 821) to write " Die Statistik als selbststandige Wissenschaft, zur Losung des Wirrsals in Theorie und Praxis dieser Wissenschaft.' , u He proposes to exclude from statistics proper the statistics \ of Achenwall as merely historical, and to hold fast to the \ political arithmetic, which should be developed by exact mathematical methods. 7$ Annals of the American Academy. D. THE DEVELOPMENT AND PREDOMINANCE OF THE STATISTICAL METHOD. I. The International Statistical Congress. §47. OCCASION, ORGANIZATION, AND DURATION OF THE CONGRESS. The prevailing confusion in regard to the scientific de- velopment of statistics was removed to such an extent by the International Congress, that this forms a decisive turning-point for theory and practice. The plan of the Congress was formed in 185 1, at the London Industrial Exposition, by Quetelet, Vischer, Dupin, Farr, Porter, Fletcher, Kennedy, and others. On account of the interesting features in the Belgian statistics (§ 36) Brussels was fixed upon as the place of meeting. The Belgian government was highly favorable to the plan. It presented to the representatives of all nations the plan of a gathering for free discussion, requested the appointment of delegates, and invited numerous statisticians and other scholars. The Statistical Central Commission formed the plans for the meeting, and entrusted their execution to a committee on organization, with Quetelet as chairman. For the purposes of the meeting a programme containing the questions to be discussed and the answers of the ref- erees was prepared, and a division into sections adopted. Rules of order, containing provisions for resolutions, min- utes, the language to be used, publication of proceedings and papers, etc., were also prepared. The first assembly took place September 19, 1853. The success was unexpected. Repetitions of the Congress at intervals were generally desired, and meetings occurred in 1855 at Paris, in 1857 at Vienna, in i860 at London, in 1863 at Berlin, in 1866 at Florence, in 1869 at the Hague, in 1872 at St. Petersburg, and in 1876 at Budapesth. The History of Statistics. 79 preparations for the first meeting had been so well made that the permanent organization of the Congress was effected on the same basis. The encouragement of the governments, the numerous attendance, and the dignified and earnest character of the deliberations were features of all the assemblies. In 1869 and 1872 it was decided to organize a Perma- nent Commission. Its duties were to publish the resolu- tions of the Congress, to secure information as to their effect, to promote the possibility of comparison in the publications of the various states, to prepare subjects for discussion, and request from the various states the statis- tical material necessary for their investigation, and, finally, to promote comprehensive international statistical investi- gations. Further assemblies were frustrated by the en- deavor to make this commission a permanent organ in the official statistics of the various states, and the failure to see that the practical statistics of any country could not be determined by such a Congress. §48. WORK AND INFLUENCE OF THE CONGRESS. At the inauguration of the Congress Quetelet defined its purpose as follows : The deliberations should endeavor to influence the statistical work of the various states, in order to increase as much as possible the facility of com- parison, and, further, to bring about uniformity in the investigations and terminology. The subsequent attempt to establish international statis- tics met with little success. Even the simplest problems proposed (Population by Quetelet and Heuschling, 1865, and Etat de la Population by Berg, 1867) showed that the obstacles to the desired completeness and comparability could not be overcome without recourse to a complicated system of hazardous hypotheses. The investigations which were proposed by the Congress were adopted nowhere without essential changes and limitations. It would have 8o Annals of the American Academy. been impossible for the Congress to determine what in each particular country might be practicable. Neverthe- less its discussions were of very great utility. As shown in Appendix II., the discussions of the Congress touched nearly every single problem of official statistics. As a rule, I the referee for each problem was a statistician, from the country in which the most satisfactory solution of the problem had been given. The general features of the problem were familiar at the outset. The proposals did not touch upon them, but had reference to the details of the execution, organization, the form of the interrogatories, the explanations and schedules. The proposals might per- haps go too far, but all was well thought out and carefully formulated for each step in the investigation. This was a , great gain for the comprehension of the method. The I Congress did not concern itself with theory. It is an I exception to the rule when a resolution of 1869 says: The Congress is of the opinion (1) that in all statistical researches it is important to know the number of the observations as well as also the quality or nature of the facts observed ; (2) that in a series of large numbers, the qualitative value is to be measured by the divergences of the numbers among themselves as well as from the average of the series; (3) that it is desirable to calculate not only the averages, but also the oscillations, in order to know the average deviation of the numbers of a series from the average of the series. The Congress brought to the mem- bers a clear conception of the statistical method, and com- plete agreement in regard to it. The entire contents of the Compte-rendu general (the last St. Petersburg, 1872) bear testimony to this point. Although the proposals were but partially applicable beyond the land which gave them birth, they furnished, nevertheless, instructive models, and served to spread similar views as to what was possible and useful for cer- tain purposes. Certain ideas on the systematization and improvement of the investigations were accepted as a mat- History of Statistics. 8i ter of course by the large number of statisticians, and were incorporated in the statistics of all countries, even in those but little developed. The proceedings and dignified repre- sentative character of the Congress increased the interest for statistics and the understanding of them in the general public. It became easier for the governments to obtain the means, and to demand from the officials and the public things which could not have been thought of earlier. In 1 a brief period the recognition of the scientific character of statistics and the necessary extent and uniformity of its contents has been greatly extended. Everything which has occurred for statistics since the beginning of the Con- gress has been essentially a consequence of its stimulating and invigorating influence. II. Modern Statistical Practice. § 49. increased need of statistics and statistical OFFICES. The effects of the Congress were however based also on ■the needs of the age. Since the movements of the year 1848, the constitution and administration of most states had undergone a reor- ganization on a new basis. The budgets, and the business I affairs of the various departments, the " motifs " of the laws, and the discussions of the legislative bodies required and furnished a rich statistical material, usually with an- nual repetitions. This increased the investigations which had been the subject of general statistics since the intro- duction of the statistical bureaus. Numerous private institutions began to feel the need of statistics, and they were soon indispensable. Besides life insurance institutions the railway companies required com- prehensive investigations (Deutsche Eisenbahn Statistik,. yearly since 1849; Statistische Nachrichten iiber die preussischen Eisenbahnen, since 1852, etc.). The same 82 Annals of the American Academy. is true of the credit institutions and the various stock companies required by law to publish statements and reports. Reports from institutions of all kinds, founda- tions, and societies became general with the increased availability of printing and the newspapers. Thus there accumulated from year to year an enormous mass of ma- terial. As soon as printed it could be referred to, often in public life, and hence it could not be ignored by the official statistics. States which up to this time had possessed no statistical (bureaus found it urgent to establish them on the model of the other states. Besides those named in §§ 34-42, statis- tical bureaus were founded in 1853 in Brunswick, 1858 in Gotha, 1859 in Roumania, 1861 in the Argentine Republic, and in 1862 in Servia. In 1864 a common bureau for some of the Thuringian States (Weimar, Altenburg, Meiningen, the two principalities of Schwarzburg, and the two of Reuss) was established at Jena, and in 1865 bureaus were estab- lished in Finland and Anhalt. In 1869 Egypt, 1871 Lubeck and Venezuela, 1872 Alsace and Lorraine, 1874 Turkey, and 1875 Japan founded statistical bureaus. The last named has had for some time highly-developed official statistics. A number of Central Commissions are also to be men- tioned. Beside those already noticed, they had been organized by 1 861 in the Electorate of Hesse, Mecklen- burg-Schwerin, Wurtemberg, Hesse-Darmstadt, and Old- enburg. If Since 1865 municipal bureaus have been created in increasing number. Before 1870 they had been founded pat Berlin, Leipzig, Frankfort-on-the-Main, Breslau, Altona, Dresden, and outside of Germany in Vienna, Buda-Pesth, Riga, Venice, Genoa, Florence, Rome, and Naples. In 1876 municipal bureaus existed further in Chemnitz, Stet- tin, Munster, Prague, Triest, Brussels, Copenhagen, Milan, Messina, and Palermo. History of Statistics. 83 § 50. character of statistical work. The statistical offices assumed at this time in their, administration, still more however in their work and the 1 scope of their labors, a uniformity of character which, \i considering the differences of the nations, was truly sur- J prising. In their administration the offices had as director a state official directly or indirectly dependent on the Ministry, and according to the extent of the work specialist asso- ciates, as well as subordinate officials and assistants for the clerical operations. Requests and directions to be transmitted to government offices were required, as a rule, to pass through the Ministry, except where for special purposes direct intercourse was permitted. The Provin- cial and municipal bureaus are subject to central authority for such statistics as concern the whole country, but inde- pendent for their own particular investigations. The labors of the bureaus are directed chiefly to the compilation of the numerical material. Although formerly the idea prevailed of obtaining in the statistical bureaus organs for the supervision or col- lection of all the statistics of the country, the field of the investigations to which they have devoted themselves has become, on the contrary, comparatively restricted. It includes generally the statistics of population and terri- tory ; also agricultural statistics, and in some cases also the statistics of trade and commerce. Apart from this they were generally over-burdened by the collection of archives, the partial publication of the material coming from various quarters, and by the replies required for the numerous questions put to them by the governments. For all their publications the details of the numbers , occupied unconditionally the foreground. To determine with the differences of time and locality the exact results of the investigations, and to preserve them for future comparisons and problems of all kinds by means of the 84 Annals of the American Academy. printing press, must be admitted to be a much more useful and necessary application of time and money than the preparation of essays, criticisms, and calculations, in which one is apt to lose sight of the basis of the work,, as the form of presentation will not admit of exhaustive explanations. Besides this, it is to be considered that the criticism of the correctness of this basis, of the method of making returns, of the avoidance and removal of errors by- means of more stringent requirements, had become much more strict, and that in consequence the labors of the bu- reaus had increased accordingly. This was the reason that in the course of time the publications of the statistical institutions were limited almost exclusively to critically sifted and systematically arranged numerical materials, as complete as possible, i. e., essentially to the comprehensive volumes of tables which pour out in such numbers every year from all civilized nations. The publications consist primarily of materials (Quel- lenwerke) which give the material detailed in tables, and generally only the most necessary combinations, with the directions and the explanations of the method of investi- gation; further of Annuals (Jahrbucher), which give short tabular abstracts of the main results ; and finally of Peri- odicals (Zeitschriften), which are open to the essays of private investigators. (The long list of such publications from the various states can be best found, though even here not quite complete, in the " Katalog der Bibliothek des Koniglichen Statistischen Bureaus zu Berlin," Vol. I., 1874, II., 1879, and the more recent ones in the " Katalog^ der Bibliothek des Deutschen Reichstags," 1882.) If under these conditions the drawing of conclusions as far as it was not required by the actual needs of the gov- ernment, was mainly left to private persons, scholars, legislators, and others, it could not but follow that the stringency of the method should become an object of the highest interest to the official statistician. The need and the essence of stringent critical requirements revealed them- History of Statistics. 85 selves to all who had to educate a number of subordinates in making uniform observations. It was felt most urgently, it is true, by the central orifices, which, like the Statistical Office of the German Empire, were obliged to formulate regulations which should be uniformly understood in numerous and greatly differing states, and which, despite the fact that the freedom in the execution could be limited as little as possible, should nevertheless lead to homoge- neous results. On the basis of this continuous progress and stimulus to the methodical procedure, the official statisticians came into close contact with the statisticians of morals, whose learned researches had led them also to the development of the critical method. III. The Statisticians of Morals. §51. IDEA OF CONSTRAINING REGULARITY. The more official statistics were limited to the numeri- cal presentation of the ascertained facts, and the more, therefore, a certain dryness in the treatment and the points of view became apparent, the more the statisti- cians who sought more profound contents, and results which appealed more to the imagination, turned their attention to the subject of social physics, as Querelet had named it. Quetelet left no doubt that he was convinced of the presence of laws, capable of proof by calculation, which govern the life and actions of man and society. He drew no further conclusions. Sir F. W. Herschel, the astronomer (born 1792, died 187 1), drew in 1850 the more definite conclusion that the freedom of mankind was hardly perceptible. H. Thomas Buckle (born 1822, died 1862) declared in his " History of Civilization in England," 1857, quite can- 86 Annals of the American Academy. didly that a necessity based upon natural law must be pre- supposed in all human actions, and that the dogma of free will must be totally rejected. With this consequential fatalism he hoped to place all historical science on the basis of statistics. This opinion found at the same time support and oppo- sition in Adolf Wagner's " Gesetzmassigkeit in den schein- bar willkiirlichen Handlungen," 1864; support in the strict deductions, reaching beyond Quetelet's material, and in the manner of treating large numbers ; opposition, however, in the emphatic rejection of every deterministic consequence, not better founded but more distinctly pronounced than by Quetelet. Other and particularly Italian statisticians adhere with preference to Quetelet's idea of a constraining force of natural law for the masses and freedom for the individual. We cite Messedaglia, Studii sulla populatione, 1866; Cor- radi, Hygiene of Italy; Bodio, Statistica nei rapporti coll' economia politica, 1869; E. Morpurgo, Statistica et le sci- enze sociale, 1876 (German, 1877). The last named ex- presses the general opinion in holding that the individual can choose freely between virtue and vice, but is helpless in face of the laws which govern the masses, and that the knowledge of these laws will enable statisticians to por- tray the development of the intellectual and moral forces of mankind, and the ethical order of the universe with the same precision as physics explains the mechanism of existence. § 52. INCOMPATIBILITY WITH ETHICS AND PSYCHOLOGY. These ideas conflict with the accepted foundations of ethics and psychology, and would therefore, should they prove correct, lead to a revolution in the essential princi- ples of both sciences. The representatives of the latter have very generally rejected the claims of these ideas. History of Statistics. 87 Some works attack this conception of the statistics of morals from an ethical or psychological standpoint. M. W. Drobisch, " Die moralische Statistik und die menschliche Willensfreiheit," 1867, accuses Wagner of abandoning the doctrine of free will, and allowing it to appear that the idea of moral responsibility could not be supported. A. v. Oettingen, " Die Moralstatistik und die christ- liche Sittenlehre, Versuch einer Sozialethik auf empir- ischer Grundlage," 1868, pronounces Wagner free from fatalism, but does not approve his deductions. In oppo- sition to Quetelet's social physics, resting on a naturalistic conception of the universe, and also to the common theo- logical personal ethics resting on an atomistic spiritualism, he endeavors to construct a theological system of social ethics. It has for its point of departure that unless man- kind can will, state and church would be senseless and purposeless, that man cannot be separated entirely from his connection with the human community, and that this constitutes a collective body, which renders it improper for the individual man to be prompted in all his actions solely by egoism. / A. Heuermann, " Die Bedeutung der Statistik fur die Ethik," 1876, has maintained that it is ethically valueless to leave merely the small oscillations in the great num- bers to the freedom of the will, but to consider the law of the large number as unconditionally operative. The law of causal connection requires that all human actions should be entirely accounted for. It does not exclude freedom, but rather comprehends it, for it demands that every action shall be the comprehensible product of a being, weighing the motives and deciding one way or the other without compulsion. 88 Annals of the American Academy. §53- SOLUTION OF THE PROBLExM by the statistical METHOD. The solution of the problem propounded by the statis- ticians of morals has been most effectively given by statis- 1 tics themselves. The reasons and the statistical necessity •for the uniform series of numbers have been convincingly proved to be totally without connection with any com- pulsion of the free moral decision, or, indeed, with any limitation whatsoever of the will, by natural law. G Rumelin, "Ueberden Begriffeines sozialen Gesetzes," 1867 (Reden und Aufsatze, Vol. I.), had already denied that a constraining necessity, either for the individual or for the mass, which could be considered a law, as under- stood by Buckle, resulted from the numerical relations which the statisticians of morals quote. G. Schmoller, " Ueber die Resultate der Bevolkerungs- und'l^foralstaTistik,'' 1871, and G. F. Knapp, " Die neuen ) Ansichten iiber Moralstatistik," 1871, have demonstrated ! more in detail, and quite convincingly, that the regular i repetition of equally large effects proves nothing more ■ than the continuous existence of equally strong causes, \ whether they be internal or external. And further, they show that this regularity which is explained so easily and radically by the assumption of natural laws, is by no means so constant as the effect of physical law. The regularity ' is different for every group of phenomena, so that we must have for each group a particular law, and for the whole so intricate a complex of laws that the result has a remark- able similarity with that which follows when we consider mankind as acting according to inner motives. It is in fact a most remarkable predetermined harmony, that ex- ternal law should lead men' to steal wood when cold prevails, and bread when times are hard. Therefore, a constancy of certain phenomena of moral statistics must be considered better than variations, for it signifies a tri- History of Statistics. 89 umph of the moral decision of the will over tempting sensual desires, a triumph of mind over matter. Chr. Sigwart in " Logik" (1878, Vol. II. p. 528) declares further: the regularly recurring figures express nothing more than that the effects which show that the causes present in individual cases, for a portion of the community, are equally distributed in time. This result of an equal distribution in time would be most expected when a great number of causes operating independently, variably, and according to the most diverse laws, are brought to bear upon a mass of objects, uniform in number and composi- tion. It is just the accidental nature which causes us to expect the equal distribution, and we should seek rather a special cause in perceiving an accumulation of such events. The regularity of the numbers permits a conclusion that the conditions are constant. All these considerations as to the nature of the regular phenomena of the statistics of morals, which place the question in the proper scientific light, presuppose a cor- respondingly profound penetration into the comprehension of the statistical method. IV Conceptions of Statistical Theory. § 54. OPPOSING POSITIONS. The question of statistical theory, is closely allied to that of the essence of statistics as a science, that of its sphere as a portion of human knowledge, and that of its specific contents whereby the limits of this knowledge are extended. These fundamental ideas, which either help- fully or misleadingly influence the theory, have been sel- dom, however, discussed in connection. But few specifically theoretical treatises of a comprehensive character can be mentioned. The conception of each statistician appears most clearly in his definition of the subject. Most of them, however, simply pronounce such a definition as an go Annals of the American Academy. introduction to the subject, with scarcely an endeavor to make the definition the fundamental idea and crowning point of a detailed system. In these definitions we find essentially the old opposing views of the statistics of the state and those of population. The idea of a distinct method of investigation is a new feature which begins to make itself felt in the discussion. Every scientific treatment must either place in the fore- ground the object or else attach itself to the method of the investigation. In the first instance no mode of investiga- tion maybe neglected in order to gain a systematic knowl- edge of the object. If the state is to be the subject of the science, it would obviously be a one-sided, arbitrary limita- tion, to consider it only from the results of enumerations. In the second case the more a particular process is matured, and the more critical its applications the more numerous and diverse are the objects which are accessible to it. There may result such a general connection of the prin- ciples that a systematic knowledge of the method will be possible. The opposing opinions of statistical theorists oscillate between these two possibilities. §55. conception in the sense of statistics of the state. In their adherence to the object simply, without consid- eration of the method used to obtain their knowledge of it, Achenwall's school weremostpersistent. To obtain "Staats- kunde, Staatsbesonderheiten, and Staatenvergleichungen " (political descriptions, phenomena, and comparisons of states) in such a form as should exhaust as far as possible everything worth knowing was Achenwall's aim. The method by which this information should be gained was of little consequence. The so-called theoretical essays of 1 the school treat rarely of anything beyond the manner of grouping facts and a few principles for comparisons. One can no longer speak of a school of Achenwall, yet History of Statistics. 9r there are quite a number of statisticians who in theory \ remain true to its traditions. J. E. Wappaus (born 18 1 2, died 1879) in " Bevolkerungs- statistik," 1859, and Robert v. Mohl (born 1799, died 1875), in " Geschichte und Literatur der Staatswissenchaften " (1858, Vol. III. p. 647), express the same opinion that if statistics is not to lose its character as a science, it must adhere in essence to the definition of Achenwall, that it is by no means limited to such facts and conditions as can be expressed in numbers, but must rather reflect in an exhaustive manner all actual and social conditions of the population. Lorenz v. Stein, "System der Staatswissenschaften" (1852, Vol. I. p. 83), finds Schlozer's definition appro- priate: "Statistics is stationary history." Also A. Gaillard, " Elements de statistique humaine ou demographie comparee " (1855); Jonak, "Theorie der Sta- tistik " (1856); and, similarly, Zuccagni-Orlandini, Iginio, Zambetti, and Nardi consider the physical, economic, political, and moral conditions of the state as the subject of the data and research of statistics. The underlying ideas of the Austrian " Prufungs regle- ment" of July 29, 1850, and the rescript appointing the Prussian Central Commission of July 9, i860, correspond also to this point of view. Further, it cannot be overlooked that though the Inter- national Statistical Congress was thoroughly convinced that statistical information is entirely dependent on me- I thodical, exact, numerical investigations, yet, nevertheless, that its whole system coincided very closely with Achen- wall's statistics, and that it gave support to the idea that an examination of the life of states and peoples, and a comparative description of states, were to be understood as statistics. Indeed, the Congress says expressly in the Report of 1853, "without doubt statistics operates with numbers, numbers are its chief element, but they are not v4 92 Annals of the American Academy. the only one, statistics is also * la science raisonnee des felts.' " Finally, this conception finds support in a great number of literary works, which, as W. Roscher, in " Geschichte der Nationalokonomie in Deutschland " (1874, p. ion), expressly says, cannot properly be classed elsewhere than under statistics. He mentions : Wappaus, Amerika (1855) ; v. Viebahn, Zollvereintes Deutschland (1858); Bavaria (i860); Meitzen, Der Boden des Preussischen Staates (1868). He could have added "Das Konigreich Wurt- temberg" (1863); Wirth, Schweiz (1871); Ratzel, Ver- einigte Staaten (1878); "Das Grossherzogthum Baden" (1885), and others. His reference to W. Riehl's " Natur- geschichte des Volkes" shows, on the other hand, the obvious necessity of separating from statistics the descrip- tion of countries as an independent scientific department. § 56. conception as science of human communities. Though the metaphysical flights of the statisticians of morals must be considered as too ambitious, and their explanation of facts as a deviation from true principles of science, yet a large number of professional statisticians adhere to the same field of research as the essential one of their science. That is to say, the penetration into the condition and changes of the social life of mankind, the observation of the so-called human communities (Gemein- schaften) appears to them as the scientific object of sta- tistics. What Quetelet and his followers looked upon as constraining laws, this more realistic school in statistics regards as a sphere of regularities which lead to the dis- covery and explanation of similar conditions and causes. Two decades after Moreau de Jonnes (§ 46) this idea be- came very general. F. B. W. v. Hermann (§ 34) (Die Bewegung der Bevolk- erung in Bayern, 1863) says : Everything in the activity of the state and the life of the people which can be reduced History of Statistics. 93 to size and number, and be quantitatively compared, be- comes the object of statistics. Bruno Hildebrand, in the essay " Die wissenschaftliche Aufgaben der Statistik " (Jahrbuch fur Nationalokonomie und Statistik, Vol. I., 1866) writes: Statistics notes all similar actions and experiences of men in a given space, and calculates the relation of the total of these phe- nomena to the total number of men, or of actions and experiences, in the same time and locality, and thus finds relative numbers which express as unimpeachable gen- eral facts the rules which govern the occurrence of the individual actions and experiences. A. Frantz (Handbuch der Statistik, 1864), Rameri (1869), de Luca, and Racioppi agree with this conception. W. Lexis (Theorie der Massenerscheinungen, 1877) expresses the same thought as follows : Statistics have the inde- pendent problem of considering and investigating accord- ing to exact methods the characteristic collective phe- nomena of human life which are accessible to scientific observation. The enumeration of all individual cases of the phenomenon forms the basis of its method. G. Mayr (Gesetzmassigkeit im Gesellschaftsleben, 1877, p. 13) distinguishes between the statistical method and the narrower sphere of statistics as an independent science. The application of the statistical method is not confined to the life of society, but is used also in the observation and study of purely natural facts. But the observation of the purely natural facts which have no connection what- ever with the social life of mankind, must be excluded from the sphere of the independent science of statistics. He defines statistical science as the systematic presenta- tion and exposition of the actual occurrences of social life and the laws resulting therefrom, upon the basis of the quantitative observation of aggregates. Quite in accord with these views are M. Block (Traite theorique et pratique de statistique, 1878, 1886) and Th. v. Inama-Sternegg (Statistische Monatshefte, Wien, 1882). 94 Annals of the American Academy. E. Engel (§ 34), to whom particular merit in the forma- tion of the theory and practice of statistics is justly- accorded, declares statistics to be a science, to which he gives the name of demology or the science of human \Zcommunities. Its aim is to observe in its phenomena the physical, intellectual, and moral life of the peoples of organized states, to formulate its observations arithmeti- cally, and to demonstrate, as it were, by analysis the con- nection of cause and effect in these phenomena. Its field of observation is not individuals but aggregates united and grouped into communities, on the one hand, of families, clans, tribes, nations, and peoples, and, on the other, in classes of rank, wealth, occupation, faith, and so forth. It becomes the physics and physiology of society, and forms, as it were, a link between the social and natural sciences. Besides the physiological, positive, comparative, and prag- matic demology, which he further divides according to particular modes of treatment, he considers also practical demology or the method of statistics, which includes its methods and resources, its applications, its workshops, its aims, and its achievements. Upon this conception of the scientific sphere of statis- tics a great number of acute, penetrating works on method have appeared, which though they treat only of special phases of the statistics of population, are capable, never- theless, of casting a bright light on every kind of statis- tical investigation. E. Engel, Methode der Volkszahlungen, 1861; Fabri- cius, Zur Theorie und Praxis der Volkszahlungen, 1868; M. M. v. Baumhauer, Bevolking in 1863 (Statistisch Jaar- boekv. h.koningrijk der Nederlanden,Vol.i4, Part I., 1867). Wittstein, Mathematische Statistik in ihrer Anwendung, 1867; Zeuner, Abhandlungen aus der mathematischen Statistik, 1869; G. F. Knapp, Ueber die Ermittelung der Sterblichkeit, 1868, and Theorie des Bevolkerungswech- sels, 1874; K.Becker, Zur Berechung von Sterbetafeln, 1874, and Bericht von July 10, 1874 (Statistik des Jf History of Statistics. 95 Deutschen Reiches, Vol. XX., I., p. 145); R. Boeckh, Ster- ol ichkeitstafel fur den preussischen Staat, im Umfange vor 1865, 1875 ; W. Lexis, Einleitung in die Theorie der Bevol- kerungsstatistik, 1875, and Theorie der Massenerscheinun- gen in der menschlichen Gesellschaft, 1877. § 57. CONCEPTION OF STATISTICS AS A SCIENCE OF , METHOD. b Opposed to this numerous list of statisticians who regard k the distinctively numerical method proper for statistical practice, but find the theoretical essence of statistics in the idea that it has for its subjects the life of states and peo- ples, or of human communities, there is another group of ^statisticians who consider this object, the life of mankind, to be, though prominent, merely accidental, the result of circumstances, or not exclusive of other things, and who on the contrary find the scientific character of statistics in the method itself. This view was pronounced by Potlock and Cournot (§ 46). "" Riimelin (Zur Theorie der Statistik, Tiibinger Zeitschrift, 1863) treats it with great penetration. He sees in statis- tics proper a methodical auxiliary science, which he com- pares to other auxiliary sciences, which, like philosophical critique and hermeneutics, consist merely in the exercise of formal and methodical processes. His conception is based on the nature of the phenomena capable of enumera- tion, in their relation to those numerically fixed or typical. In nature, as he says, the individual is typical, hence a single accurately ascertained fact justifies an induction. Logic puts together only the constant qualities as making up the idea, but cannot turn to account scientifically that, which in one case occurs so, in another differently, in a word, the variable factors. The statistical method enters in the empirical sciences just at the point where induction, the conclusion from the single typical case to other cases, is not available. Briefly, the statistical procedure may be ^ g6 Annals of the American Academy. called the methodical observation of aggregates. It con- sists in spreading, as it were, a network of observations over entire groups of individuals, in order to observe and register by a single method all phenomena of the same class. This method of observation dissolves the collec- tive ideas of race, church, district, rank, and others into the individuals which compose them, in order to observe for each individual whether in his case a certain phe- nomena occurs or not. It is, therefore, clear that it is always concerned with an enumeration, and that the num- ber is typical of this method of observation. The more numerous the objects of such observation, the more ex- tended the single groups, and the more numerous the groups subjected to the same observation the more com- plete and thorough does the characterization of the col- lective idea become, and the richer becomes the material for inductive reasoning and for the knowledge of the in- terdependence of human phenomena. Thus a way is obtained to characterize correctly collective ideas. 4dolf Wagner (§ 5 1. Article Statistik in Bluntschli und Brater, Staatsworterbuch, 1867) characterizes the general idea of statistics as the methodical inductive procedure for the solution and explanation of the mechanism of human- ity and nature, of the real world generally, i. e., for the derivation and explanation of the laws according to which the mechanism acts, and for the discovery and explanation of the causal connection between the individual human and natural phenomena, by means of a system of methodical observations of the aggregates of these phenomena, lead- ing to a determination of their quantitative relations. M. Haushofer (Lehr- und Handbuch der Statistik, 1872) designates statistics as an essentially methodical science. He says statistics is a method and a science. Conceived as systematic investigation of aggregates it is a method. To be a science there must be beyond the unity of the method a certain unity of the object. This object is the aggregate of phenomena as such. Statistics is, therefore, History of Statistics. 97 the science of aggregate, and in particular of the aggre- gate of human and political phenomena, of their move- ment, and its laws. Statistics is for him, nevertheless, merely an auxiliary science. It seeks and finds truth, but only such truth as is utilized by other sciences. Its char- acter as method is therefore predominant. The idea that the scientific essence of statistics was not to be sought in a specific object, but in the manner according to which any object in its multiplicity is investigated, is found accordingly in certain works which treat of special problems as examples of methodical procedure: G. Mayr, Ueber die Grenzen der Vergleichbarkeit statisticher Daten, 1866 ; and Ueber die Anwendung der graphischen Methode, 1877 ; Die Aerzte und das medizinische Hulfspersonal (Sta- tistik des Deutschen Reiches, Vol. XXV., 1877); G. Tam- meo, Le medie et loro limiti, 1878; Marey, La methode graphique dans les sciences experimentales, 1879; Perozzo, on the graphical representation of successive entireties with three coordinates (Annali di statistica, Ser. II., Vol. XIV., 1880). The application of the statistical method to phenomena which are totally distinct from, or else only remotely con- ected with, political and social life, or, as it has been'? / called, "demography," has done much to confirm the view of the scientific character of statistics which we are con- sidering. Meteorology, particularly from the standpoint of telluric and cosmic physics, exceeds in the precision of the statis- tical observations and conclusions every other field of sta- tistics. Botany and zoology have besides the history also statistics of their living and fossil genera and species. I Astronomy has based upon the consequences of Herschel's f system exact statistics of the stars in their order of mag- I nitude. Medicine applies the statistical method in the broadest sense for the comparative judgment of the phe- nomena of sickness and health. Even philology has profited ■ 1 u 98 Annals of the American Academy. from the statistical treatment of the recurrence of words and sounds. M. Block (§ 56) declared as early as i860 (Statistique de la France) all such applications of the method to be sta- tistics. Rumelin wrote, 1874: "The statistical method takes hold everywhere, where it finds variable factors in the phenomena brought under its observation. And these exist everywhere and in all the realms of nature. Some interest may attach itself in every case to these variable elements. It could possibly be deemed worth while to sort grains of sand according to size and count them." (This actually takes place with great accuracy in recent investigations of soils.) " It is at present not to be fore- seen what significance the method may attain in the vari- ous fields of natural science. Up to the present moment it finds extensive and steadily increasing employment in a number of them, in meteorology, in physiology, and in medicine." § 58. conception of statistics as applied logic. From the recognition of the idea that the scientific char- acter of statistics was its peculiar method, irrespective of the object to which it might be applied, it was an easy step to the conception of the method as a branch of logic, as an extension of the logical mental processes, and with a cer- tain scientific independence. A similar general character has been ascribed to statis- tics by John Stuart Mill in his ".System of deductive and inductive logic," 1843. He treats of the methods of proba- bilities and of comparison in the same spirit. Caporale also said in his Lezioni, 1863, "statistics is logic, numerical analysis, and synthesis of facts, presented in tables for definite useful purposes," Christoph Sigwart in "Logik" (Vol. I., 1873, II., 1878) gives the subject the first exhaustive treatment. He begins with the proposition that the general purposes of thought History of Statistics. 99 demand of human perception that it should describe ob- jectively, exhaustively, and accurately the single things and occurrences which present themselves, and class them according to time and species. This completeness of human perception in time and space could, as he says, be repre- sented only by a description of the world, comprising all perceptible things in their order of time and space, a spe- cies of universal catalogue of all single objects and their changes. Uranography and geography are already far advanced in the discovery of things and their designation with proper names. As far as such completeness of de- scription is not possible it is supplemented by the statistical enumeration of similar things and occurrences under the assumption of an existing classification of the objects. As far as the classification of form and matter proceeds accord- ing to perceptible qualities, every description of a single object serves to include it among the classes already formed, or else to extend the sphere of the latter. Thus it is discovered what single objects belong to one and the same class, and this leads to ascertaining how many similar objects exist, in short, to their enu- meration. In this enumeration the individual thing is lost — it becomes one of a group of similar units. The common designation of this species of cataloguing by rubrics the number of single objects included under a general idea, is statistical returns or tables. The main characteristic of statistical returns consists in the fact that 1 the single objects are not enumerated and catalogued as uch, but that they furnish totals of similar objects and phenomena, thus summarizing the individual perceptions in distinct rubrics. Enumeration has special importance as a means of describing aggregates whose constituent elements are either all similar or else included under a limited number of general ideas. This description or characterization of aggregates is the primary aim of ^statistics. The next step in the use of the results obtained by enumeration is the presentation of the relations existing ioo Annals of the American Academy. between the numbers in the most easily observed form. It replaces the various totals, which as such afford little insight into the subject, by average values, in order to have a measure of their size, a means of comparison with others. Its purpose is to establish a permanent measure, a rule. The averages show empirical regularities, descrip- tive in their nature and incapable of expressing a necessity without the aid of the assumption that the occurrences which produce the individual varying instances in a certain field are constant in their totality. A rule can only be assumed when the average of a large field repeats itself uniformly in the smaller fields which go to make up the whole. The statistical conclusion on causality can be based | only on the variations and not on the constancy of the s numbers. The deviation from the average is an indication that the features distinguishing a part from the whole cause the differences in the number of the phenomena of that part. Statistics show that causes known from other sources have had their effects, that they have not been neutralized by others, and give thus a measure of the intensity of each force in relation to all the others. But it is impossible for statistics to be an expression of a ruling necessity in the single cases enumerated. In as far as we are able to reduce the individual occurrence to actual laws, enumerations of the objects is the only way of obtaining satisfactory information concerning certain phenomena presented to our intelligence. As soon as laws are found, which can only be hoped for by means of analysis and the application of inductive methods, the statistical enu- meration ceases to be of interest. supplement to the Annals of the American Academy of Political and Social Science, May, 1891. HISTORY, THEORY, AND TECHNIQUE OF STATISTICS. BY AUGUST MEITZEN, Ph.D., PROFESSOR AT THE UNIVERSITY OF BERLIN. TRANSLATED, WITH AN INTRODUCTION, BY ROLAND P. FALKNER, Ph.D., INSTRUCTOR OF STATISTICS, UNIVERSITY OF PENNSYLVANIA. PART SECOND: THEORY AND TECHNIQUE OF STATISTICS. PHILADELPHIA: AMERICAN ACADEMY OF POLITICAL AND SOCIAL SCIENCE. 189I. PART II. THEORY AND TECHNIQUE OF STATISTICS. INTRODUCTION. §59. POSITION OF STATISTICS AS A SCIENCE. That statistics has long since attained the importance and general recognition of a science is shown by the his- tory of its development. This history also demonstrates the complete unanimity which exists in regard to the pur- pose and processes of the statistical method. None the less the scientific character of statistics, and its position in the general system of sciences, have remained a matter of controversy. A conflict of opinion still exists on the question, whether statistics is to be considered as a science of things or a science of method. One group of statisticians considers statistics as a sci- ence to be wholly independent of any distinct method, but as attached to certain objects, constituting our scientific knowledge of them. These investigators either hold fast to the opinion that the knowledge of the State, con- ceived somewhat as Achenwall formulated it, is the only true and valuable object of statistics as a science, or, with Sussmilch, they consider the reign of law in the phe- nomena of human existence, in the physiological and moral occurrences of the life of nations, as the peculiar content of statistical inquiry. Another group recognizes the importance of the statis- (103) 104 Annals of the American Academy. tical method as such, and finds in its application to the conditions of nations and peoples or human communities the field of scientific statistical knowledge. A third party finally declares statistics to be exclusively a science of method, applicable to every object — to be applied logic, and to be classed with other independent methodological sciences, such as logic, mathematics, cri- tique, and hermeneutics. It must be clear that the questions, whether statistics is a science, and if so, what is its place in the general system of sciences, cannot be decided upon the basis of statistics itself. To bring into clear relief the many related ideas and manifold actual connections of thought, and assign to every field of investigation its proper place, would require a comprehensive analysis of all human knowledge, a general theory of science. The lack of such a standard for the sciences, which on account of the necessity of metaphysical premises, must, in any case, receive a coloring from the individual tem- perament, makes itself very keenly felt in the development of the system of statistics. A clear definition of the sphere of ideas to be considered is demanded not only for the elegance of the treatment, but as an almost indispensable proof of a clear and precise system of ideas. Statistics is therefore called upon all the more urgently to form its own ideas into a sound theoretical system, taking into account all particulars and details. § 60. POINTS OF VIEW FOR THE THEORY OF STATISTICS. Obviously the theory of statistics cannot treat of the \ J actual situation of innumerable phenomena, which have so long been ascertained in civilized countries, and which vary as they do from year to year. How many inhabitants there may have been in Rome at a certain period, how great the public debt of Spain, how extensive the railroad traffic in Russia, etc., are facts of interest merely for the Theory and Technique of Statistics. 105 description or history of Rome, Spain, and Russia. And if on the average 21 boys are born for every 20 girls, it is not for statistics but for anthropology to examine whether this statistical probability can or must be ac- cepted as final. Even in the most exclusive circle of Achen- wall's school, the theory of statistics treats of the system and not of the contents of the " Staatsmerkwiirdigkeiten." The problems which practical and theoretical statisticians are called upon to solve are part of the theory of statistics, not with reference to their anthropological, geographical, political, or economic importance, but as the subjects of dif-h ferent varieties of investigation. Each case is for {he »\ theory an illustration or a problem. The theoretical point of view must necessarily be con- cerned with the propriety and practicability of the plan of observation, the manner of execution, the reliability and utility of the results, the combination of the facts, and the correctness of the conclusions. These are all questions of method. For all these phases the theory needs authorita- tive principles, an understanding of the relations, and the means for facilitating an examination and judgment of them. \ The theory of statistics must therefore be based on the statistical method. While it penetrates to the foundation of this peculiar procedure, tested by long experience, the logical contents of the method must on the one side de- velop into a system the theory of statistics, and upon the other it must appear what form the technique of statistics should assume in order to satisfy the requirements made by the statistical method, theoretically and critically de- veloped. What in general should be regarded as statistical method, which is the subject of our investigation, can be gathered from its relation to logic, and from a survey of its specific leading thoughts. io6 Annals of the American Academy. §61. relation of the statistical method to logic. From the history of statistics, the method appears to us empirically as a procedure of obtaining judgments and conclusions as to the relations of a mass of changeable and variable things, by an enumeration of characteristic qualities. More briefly the same thought may be expressed as the method of judging collective phenomena from the results of enumerations. Scientific logic might, as §§ 57 and 58 show, express the i contents of this sentence more precisely, thus : the statisti- ** ical method is a process, based on an enumeration of char- acteristic phenomena, of forming empirical judgments and I conclusions relating to the varied and complicated aggre- gates of existence. It is used where the experimental investigation of an individual or collective object is pos- sible neither by induction, the conclusion from the special to the general, or by deduction, the conclusion from the general to the special. The meaning of the definition must be explained. All actual existence appears to man as inexhaustible multipli- city. It appears to his thinking powers as made up of certain things with constant qualities despite the changing appearances. From the constancy of these qualities we form ideas. Of the things thus divided by ideas we know actually but few exactly, by closer view, or strict experiment; to the rest, on finding single qualities, we apply, inductively or deductively, the presumption of similar qualities, and, as experience shows, the nature of things permits this in a degree sufficient for ordinary purposes. No one thing is however actually identical with another, no one can occupy the space of another, and all things which follow each other in time are different. Each is an individual, and has, as such, certain qualities which dis- Theory and Technique of Statistics. 107 tinguish it from every other. All things can be considered, according to the point of view, as single, or as in com- bination, forming larger things. Here we derive the ideas of individuals and collectives or aggregates. Each one of them can be dissolved finally into a multiplicity of things simply inexhaustible for human observation, and as diffi- cult of complete comprehension in its constitution as in its variations. Each thing forms, therefore, according to the conception of the moment, a unit or an aggregate. Con- sidered as an aggregate, it is divisible even to the atoms, into the most various constituent objects. The investi- gation of all these parts, which appear, according to the point of view, as individuals or collectives, exceeds the power and resources of any observer. According to its nature, such an accumulation of dissimilar objects permits no satisfactory knowledge of its full content, of the inner relations, and of the possible expectation of permanency or change, by induction or deduction, which could only deal with the single objects. Much less is the possibility conceivable of acquiring by experiment any knowledge of the continually changing multiplicity in each single thing, and in mutual relations and conditions of them all. The method of statistics, immaterial whether it be con- sidered as a general one of alljs mpiric al ^cien^ce, or as specifically statistical in every case of its application, appears therefore as the means of obtaining knowledge as to aggregates, i. e. y things conceived in the confused and variable multiplicity of their components. § 62. THE LEADING THOUGHTS OF THE STATISTICAL METHOD. The method of statistics must unconditionally abandon the effort to investigate completely the inexhaustible dif- ferent combinations of the aggregates. But its fundamental idea is to penetrate in a limited, yet systematic way, into the aggregate in order to ascertain whether and how often certain things are to be found there, or how often they y 108 Annals of the American Academy. pass in and out of it. This search and enumeration is the simplest observation possible, not influencing in any way the condition of the aggregate. The result can, in the first instance, be only a more or less defective description. The statistical method aspires, however, to draw conclusions from such enumerations, as to the relative measure of the phenomena, the causal connection, and the expectation of regular reappearance of the things counted. The idea is, thus, to approach the investigation of the multiplicity, with a certain purpose in view, and to observe merely such things whose number in the particular aggre- gate it is necessary to ascertain for this purpose. Things which are to be sought must be known before- hand. When it is purposed to find their number the idea chosen in advance must designate something capable of enumeration which can serve as the unit of the count. This presupposes that it can be distinguished in the con- fused and changing real multiplicity of the aggregate as a certain object, with definite perceptible qualities. All objects whose characteristics correspond with those of the unit selected are to be counted. With the sum which results from this counting the first step demanded by the statistical method, the methodical enumeration, has been taken. As far as the purpose of the problem requires the enumeration of a group of different things instead of that of a definite thing, it must take place in the same way for each distinct thing. The description, by means of the number of any kind of things, can form the basis of a methodical judgment only when the number can be measured. The meaning is not at once apparent, but depends upon the relation to a certain scale. This scale can only be derived by seeing low large or small is the number of units in the aggregate investigated in comparison with the average number of the same units found in analogous aggregates. Such ag- gregates are analogous which, considered either as indi- viduals or collectives, come in the same category. The Theory and Technique of Statistics. 109 comparison may be as different, according to the special purpose, as the conception of the aggregate as a unit. Upon this quantitative relation further judgments may be based. Certain points for the determination of causal connec- k tions can be obtained, if the selection of the things counted had this end in view, or suffices for the purpose. The greater measure of cause must bring about the greater measure of effect. In the aggregate investigated only that measure of things can be recognized as an essential or prominent cause which, by comparison with analogous a gg re g ates , appears to be in a functional relation to the effect. When units which express the effect or cause directly are not suited to enumeration, others must be selected which furnish an indirect or symptomatic evidence. If no «- functional relation exists between the units which have been chosen each time with reference to probable causal relations, we have simply discovered that of the possible causes considered all are inapplicable. From the judgment as to causality the last step leads toL ; that of probability. The same causes bring about the same effects under the same conditions. Under like circum- stances the average measure of things in analogous aggre- gates would also be the most probable in that to be inves- tigated. The average relation of cause and effect which appears among them could also be considered as the regu- lar one. When regularities are observed they are to be considered as based upon like circumstances. .With this judgment as to the expectation of phenomena the last aim of the problem of penetrating into the multiplicity of the aggregate is attained. On account of the necessity of observing and counting considerable numbers of distinct units in a series of anal- ogous aggregates this process requires generally very con- siderable expenditure of effort. Nevertheless, it leads only to a partial description, and at the most to an approximate, an hypothetical judgment as to the inner structure of the no Annals of the American Academy. investigated aggregate. But the impossibility of investi- gating each single thing with experimental precision is common to all empirical sciences. Inductive and deduc- tive judgments are also hypothetical. The results of the ^statistical researches do not refer so much to the typical phenomena, which are the premises for inductive and deductive reasoning, but consist rather in a classification of the non-typical, which is unattainable in any other manner. Formally, the procedure consists of two stages, one pre- paratory, which counts the units in the aggregate selected for the specific purpose, and describes the same by means of totals; the other, or completing stage, which, obtaining for comparison the sums from enumerations of similar units in different analogous aggregates, forms judgments on the relations of quantity, of the causality and the prob- ability or regularity of the phenomena. The technique of the method follows closely these logical steps. The theory of statistics has for its object to establish the proper foundation for each stage of the process, and thus determine the principles according to which in a given case we may test the accuracy of statistical results and the mode of obtaining them. A. THE PRINCIPLES OF ENUMERATION. I. Fundamental Conceptions. § 63. EMPIRICAL CONDITIONS OF THE ENUMERATION. The first step of the statistical method indicated by the general outline of the procedure is that of the enumeration. Characteristic things in the multiplicity to be investigated are to be ascertained with respect to their number as they exist in it, or as they enter and leave it. Theory and Technique of Statistics. hi To define in sharp and concise terms the conditions of this first step as well as of the further processes is not without difficulty. In particular it may be observed that in regard to necessary requirements of the method com- plicated problems are often more comprehensible than the most simple ones. It might readily appear that the enumeration of any- thing, whether for statistical purposes or for the purposes of daily life, a mere counting-off according to the numeri- cal series, was a complete operation, whose aim was attained absolutely without any reference to the consid- erations mentioned in the preceding paragraph. That this view is erroneous appears readily by carefully observing any empirical attempt to count. Suppose someone were asked to count paper or fruit lying before him. He would see at once that before begin- ning he must settle which of the objects should be con- sidered as fruit or paper, for the purpose in view. The explanation given must be perfectly clear and perceptible to the person counting. Further, it must be settled what is a piece of paper, or fruit, and whether, perhaps, fruit is to be counted by piece or weight, or the paper by the size of the sheets. A change in these particulars could not take place during the count. Besides, it must be clearly defined what the words " before him " express ; that is, there must be evidently a limit of space. There must be . a limit of time during which pieces should not be removed nor added. If objects change their positions during the count, they must be considered as changing objects, and measures must be framed for their treatment. Simple as these conditions may appear, no one can remain unfulfilled if the result of the enumeration is to be correct or in accordance with the intentions of the questioner. They need not, it is true, always be expressed, but the most complete understanding must exist between the questioner and the counter as to the smallest de- tail. It is not to be doubted that these requirements are V H2 Annals of the American Academy. alike indispensable for the greatest and smallest problems in enumeration. What, however, is their theoretical significance ? § 64. enumeration and calculation. The complex conditions of the empirical process of counting indicate that these peculiarities have a basis in the fundamental relations of logical knowledge. Enumera- tion presupposes the idea of number. Number is one of the earliest abstractions that arose in the formation of ideas. As soon as thought grasps objects and distinguishes be- tween them in classification, it is impossible to escape the notion of plurality. Things agreeing in their conceptions appear no longer as isolated things, but as several of the same species. The necessity of dealing in thought with indefinite pluralities, and of expressing them in communi- cation to others, makes itself felt very early in the forma- tion of language. There is hardly a language, however crude, which lacks the plural denominations. But the plural, and evidently also the dual, are not numerical expressions. The dual seems to be the expression for the frequent symmetrical double phenomena of nature, as the eyes, hands, etc. (W. v. Humboldt, Ueber den Dualismus, 1828.) Number is developed first in the progress of conscious observation from one thing to another similar one. It presupposes that the idea of the thing is conceived of as a unit. Number is not formed by observing 1 and 1 and and 1, or placing them in succession. It is formed when in a continuous observation each occurrence of the unit is grouped with those which have already taken place, and an expression given to each successive group. Each expression indicates the total of all occurrences of the unit up to a given point of time. Numerical terms belong to the oldest traditions in all languages, and yet the difficulty of counting and retaining numerical ideas is shown by the Theory and Technique of Statistics. 113 fact that many races have no numerals beyond three or five. The expressions corresponding to the successive groups «/ of units form the numerical series. In counting concrete things memory applies the numerical order to the obser- vations of experience to determine how often the thing which forms the unit has been found. This finding things by observation is a real operation, and where the enumera- tion takes place in the recollection, it is an image of the real world. The succession of expressions in the numerical series is a succession of totals. The numerical series can be com- pletely separated from concrete things and be continued without aid from them. It forms in that case a succession of ideas, each of which exceeds the sum preceding by one unit. This order permits a progress by sums more than unity, as well as a division into series of pluralities. This facilitates the use of numerical signs, mere figurative images of the numerical expressions. The consideration of the abstract numbers and the re- lations of numerical series awakened much interest at an early date, and led to deductive conclusions from the ideas of the totals. Thus were founded calculation and mathe- ' matics, which appear to be the oldest human sciences. It would, however, be a mistake to see in the early and astounding development of mathematical calculation also a development of enumeration. On the contrary, this art remained all the more neglected. Closer consideration shows that calculation has nothing in common with enu-V> meration except the number. It can proceed apparently from actual existing pluralities, but only apparently, for it depends entirely upon the idea of the identity of the units. It can apply this idea to any object, but in reality the objects are not identical, and this cannot influence the idea of the units. Calculation necessarily deprives the unit with which it operates of every specific content, and perceives in each number only a certain quantity of wholly empty and abstract H4 Annals of the American Academy. units, which permit only repetitions and divisions just as empty and abstract. All judgments and conclusions of , calculation are therefore analytical. Every logical thinker obtains by correct conclusions from the first premises the final results of all arithmetic without actual experience. Upon this analysis is founded the science of mathematics. With empty numerical conceptions it can combine only similar ideas of corporeal dimensions, point, line, surface, and volume. All these ideas are so empty and abstract, that they can be represented by no phenomena of actual existence, nor do they correspond to any. All construc- tions are entirely ideal. None of their propositions con- tains a synthesis. All these propositions and formulas simply relieve the investigator by the aid of memory from undertaking the almost insurmountable labor of repeating in his own thought the abstractions of centuries. Here we see the difference between enumeration and y calculation. Calculation elaborates by analysis the neces- sary consequences from given ideas of magnitude, with- out asking whether or not these ideas correspond to any reality. Enumeration endeavors to ascertain how often a designated unit is present in a limited reality and is a thoroughly real and synthetic operation. As reality is concrete, so must the unit be also, and must be found by concrete methods. From calculation, which can never undertake a large or small task in practical enumeration, the latter can obtain assistance only when the actual unit is found in typical division or multiples, so that the divisors a|nd multiples can be calculated from the sums counted; i. e. } can be ..derived by analysis. §65. ENUMERATION OF THINGS AND MEASUREMENT OF QUALITIES. I The distinctive theoretical peculiarities of enumeration J require that the collective phenomena which statistics are f to investigate must have the character of real independent \ Theory and Technique of Statistics. 115 things in order to be counted. They may indeed exist merely in thought or be counted in memory, having their limits fixed in our imagination, but in one way or the other they must be fixed and accessible to observation. This requirement is perfectly comprehensible for well- rounded concrete objects, as men, houses, ships. It be- comes a question, however, how the numerous distinctions are to be treated, which result from the qualities of such objects, and again how a phenomena may be utilized for the. investigation when it does not appear to be so de- finitely limited. A necessary premise of enumeration is that all the qual- ities of an object which characterize it as the unit of the < count must be fixed and invariable for the period of the I observation upon which the count is to be based. As the statistical observation is always instantaneous, or at least must be regarded so, and as the quality always attaches to ( an object and never exists without it, the quality cannot be variable for the statistical observation ; for when the quality changes so does the object also. The change in the quality would necessitate two enumerations. In the two the object is different, as explained. Qualities are never counted, but simply the objects pos-/({ sessing one quality or another. On the contrary, air // qualities of things can be measured, and this is always/ / necessary if it is desired to observe the exact differences in the same quality. Every quality of a thing is perceptible to us through impressions of the senses, and upon the greater or less force of these impressions depends their measure, or their proportion. To observe the difference in which a quality appears, we seek certain easily- found limiting points, and divide the space between them into equal parts to form a scale. One division forms the unit of measure, which in an observation will be found either in multiples or frac- tions. The qualities of things which are most frequently the 116 Annals of the American Academy. subject of measurement, are magnitude (measures of length, surface, volume), gravity (measures of weight), duration (measures of time), value (money, the measures of cur- rency). Measures can also be obtained for the intensity of other qualities. For color, heat, sound, hardness, such measures are quite familiar. Every regular progressive gradation contains the ele- ments of a measure in the succession of its parts. But it can be utilized only when an invariable known scale is taken as a basis. The ordinances of weights and measures of the governments rest upon such bases. They should always be founded upon a normal measure, certified, as far as possible, by physics. As in every measurement the number of the units of measure must be ascertained, it is evident that, strictly speaking, no measurement can be obtained without enu- meration. Yet, counting off the degrees of a quality is different in its nature from the statististical enumeration. Statistics use it only exceptionally, partly as a supplement to the observations, partly as a means of making them objective. The first case occurs when things of the same general class are to be distinguished in the enumeration according M n to certain degrees of a quality — e. g. t horses according to ages, houses according to the number of stories. The enumeration of the degree of quality is only preparatory to the enumeration of the things differentiated. If persons are to be numbered in the census according to ages, this preparation of the classes, etc., like many other measure- ments not to be carried out at the instant, cannot be under- taken by the enumerating official. Distinctions easily recognized or estimated, can naturally be made in con- nection with his observations. The other case occurs when the things have in them- selves no sufficient limitation as independent objects, such as air, rain, area, arable land — time and space generally; or, indeed, actual things, such as products, grain, iron, h Theory and Technique of Statistics. 117 wood, where the number of pieces furnishes no practical nor sufficiently distinct idea. In this case the quality, measure, or weight must replace the limitation lacking in the thing itself. But the enumeration cannot, nevertheless, be performed according to the quality, but only according to the units of quality, thus established in the thing to be counted. The quality alone can never replace the thing. One cannot count ages without the persons, or weights without the goods to which they belonged ; and it is impossible to count prices, market prices, and similar data of measure or value without the articles for which they are counted or calculated. Every such general datum requires, if it is to be correct and not merely an inexact estimate, classification of the objects according to the prices paid, noting the num- ber or the weight of the things of each class, and calcula- tion of the price, as the average of the number of units reduced to a uniform measure. The fundamental premise \ *g of statistical enumeration, whether measurements of quality \ lV come in question or not, is, first of all, the real objective / nature of the unit of enumeration. §66. THE UNIT OF ENUMERATION. Intimately connected with the requirement of the method that only concrete things can be objects of the enumeration, is the further one that these objects can only be enumerated according to a previously well-defined idea. The things to be included in the enumeration must correspond entirely with the preconceived notion of the unit of enumeration. Nothing contained in the aggregate which corresponds to this idea can be passed by unnoticed. This is the indispens- able condition of the correct enumeration, and, therefore, of paramount importance as the basis of the entire process.. All essential characteristics of the unit of enumeration must be definitely fixed before the process begins. They cannot be changed by any modification or seeming expla- II u8 Annals of the American Academy. nation during the process. The unit should be so defined as to leave no room for doubt. This is essential to the uniformity of the enumeration, and indispensable for the subsequent use of the results. But it is seldom possible to determine expressly for the enumerator the whole group of characteristics essential to the idea of the unit of enu- meration. The common usage of the language must, with the greatest possible simplification, serve as the basis of the idea. Often it is sufficient in itself, as " man," "animal," "tree." Certain ideas have a legal meaning or one equally capable of proof, such as "letter," "merchant," "criminal." But it must always be considered whether the word in com- mon usage is applicable to the enumeration of independent things, or requires some more precise definition, as "house," "dress," "book." As a rule, it is necessary, besides the designation of common usage, to determine expressly certain particular characteristic qualities. This is especially true where things of the same general class are to be counted differ- ently, according to certain features. Here the process of measuring qualities, described in §65, comes into play. At the same time it may be observed that the ideas of quality, which seem to have great, even mathematical, exactness, do not apply strictly in reality, as, for instance, the term " spherical." Further, it must be remarked that, especially in the designation of qualities, the use of language is exceedingly variable, and can seldom dispense with an exact scale. A systematic selection of essential characteristics facili- tates the proper comprehension of them. The value of the determination of the idea agreed upon depends on the capacity of the observer. For a group of a few experi- enced enumerators, the units of enumeration can be de- fined very differently than when numerous different and inexperienced persons are drawn into the service. Theory and Technique of Statistics. 119 §67. THE FIELD OF THE ENUMERATION — THE LIMITS OF TIME AND SPACE. The consideration of a mere off-hand counting of things (§ 63), shows that, besides a definite unit, the enumeration requires a limit of the time and space in which it was to be made. The objects which are to be counted may form either a^ stationary number, i. e., be found in the same space at the same moment; or a succession or movement, i. e. t pass through the same space in a certain period of time, or they can appear variously in the given limits of time and space. If the same object be found more than once in the given time, it becomes necessary to determine whether it is to be counted but once or oftener. For all these cases, it is to be remarked that while the objects to be enumerated may completely fill out the given limits of time and space, this is only accidental, and, ac- cording to the nature of the enumeration, rather improbable. For the problem is, to find these units in a given time and space. They may or may not be found. The needs of the enumeration have been complied with, even when the result is zero. Thus it is evident that the limitation of time and space does not take place in the unit, but upon some connected fundament, considered as a whole, which is the field of the investigation. Such a field, limited in time and space, in which real objects are to be enumerated, must consist necessarily of a more or less extended portion of actual space, either at a given instant or for a longer period. Actual space is not a vacuum, but filled with an immense multiplicity of real things, and in the course of any longer or shorter period these can change in incon- ceivably numerous ways. Each field thus limited must of necessity be conceived as a whole, as individual or collective. But every unit can, as we have seen, be considered in regard to its inter- V' 120 Annals of the American Academy. nal complexity, as an aggregate, and thus become the field of an enumeration. Thus it appears that the idea of the aggregate, the in- vestigation of which by enumeration forms the purpose of statistics, is included in the idea of an enumeration strictly considered. II. The Process of Enumeration. § 68. OBSERVATION AND SUMMATION. The enumeration investigates how often the unit chosen is to be found in the given aggregate. It consists, there- fore, of an observation of the units, and a summation of the observed cases of its existence. The observation must distinguish the components of the aggregate into such things as possess the characteristics of the unit and such as do not. It must be so planned that everything which might possibly correspond to the unit shall be noticed and examined with reference to the decisive characteristics. No unit should be omitted or counted more than once. When there are several ob- servers this must be avoided by a careful division of the field among them. The observation is direct, when the observer searches the entire aggregate himself for them ; indirect when he has his resort to records and registrations and announce- ments and lists of various kinds. If the fact of record is conditioned on the same qualities which make the thing a unit of enumeration, the observation is properly in the hands of those who make the records. For records which serve statistical purposes exclusively, specific schedules are in use. They seek to obtain the notes of the single observations, systematically arranged according to the required points, with as little writing as possible, yet definite in form and convenient for summar- izing. If they form a system of coordinates, in the lines Theory and Technique of Statistics. 121 of which the distinctions of the unit of enumeration are to be arranged according to like ideas, they are called lists. If they are limited to a single unit, whose characteristics are so reported that afterward distinctions can be made in the summation, they are called cards. (Statistik d. Deutschen Reiches, Bd. I., pp. 77, 103.) The summation is direct when the totals are given in the course of observation ; indirect, when, as is usual, the single observations are noted and afterward added together. A tabular scheme, which presents the summations of the re- sults systematically and in conformity with the purpose of a statistical problem, is called a combination formula. (Cf. pp. 99, 395 of work above quoted.) -^ § 69. SUBSTITUTES FOR ENUMERATION, CALCULATIONS, ESTI- MATES, AND THE ENQUETE. Enumeration by observation and summation of the units is, as a rule, a very extensive, tedious, and expensive operation, as most statistical inquiries are concerned with the affairs of peoples and nations. In every case the en- deavor must be to make the solution as simple as possi- ble. But it is often altogether impossible to attain the practical end in view, unless it can be done with small means, or in a limited period of time. Hence operations have been devised which can be used in a measure as substitutes for enumeration. Such sub- stitutes are, however, always imperfect. They are based on the effort to use results already known, in order to dispense with the necessity of new investigations. The simplest is the so-called " estimate." It is, when based upon a cursory observation, simply a very inexact enumeration ; when it is formed without an observation it necessarily supposes previous observations on the basis of which a species of inexact enumeration is carried out men- tally. To do this, however, one must be permitted to « (1 ■\ 122 Annals of the American Academy. suppose a certain degree of constancy of the units and the aggregates. Another means to this end is sought in calculation. Enumeration seeks to determine the unknown frequency of the unit in the aggregate, but a calculation must be based upon known elements. If a unit of enumeration is a distinct function of another, the number of the latter can be calculated from that of the former ; and conversely, when one such unit has been obtained by an enumera- tion, there is obviously no need of one for the other. But calculation cannot replace enumeration, for calculation is always analytical, never synthetical. The use of probabilities, so frequently applied in place of enumeration, can only replace it up to a certain point. This is not because it is hypothetical. On the contrary, such a hypothetical conclusion as to a number must, where it is critically permissible, be regarded as the highest aim of statistical inquiry. It is based on the most difficult com- bination of the results of the various enumerations. The method known as expert estimate or enquete is generally a combination of these various modes of ob- viating a direct enumeration. In the stead of actual results of enumeration, it deals with the data furnished by persons whose knowledge and capacity for judging ex- isting observations, estimates, enumerations, elements of calculation and probability, renders them worthy of con- fidence. The enquete is usually applied as a simplification and acceleration of statistical inquiries. It is for many things the only form of investigation which can be used. It can- not be dispensed with, where the organization of competent enumerators to go over the entire aggregate is not feasible ; or where merely such enumerators can be obtained whose self-interest, opposition to the matter, or false notions stand in the way of correct enumeration. But if the results of an enquete are to be statistically useful, they must be capable of replacing completely the Theory and Technique of Statistics. 123 results of actual enumeration ; they must retain the com- plete precision of the idea of the unit of enumeration ; they must comprehend the entire aggregate; and they must express numerically and distinctly the totals estimated as if they had been counted, or at least must make it possible to calculate them. Enquetes which are carried on with an indefinite idea as / to the aggregate and the unit, or express their opinions \ without any definite gradations in number and measure, are nothing more than general descriptions. They are of no use for the investigation of aggregates, and can be utilized only for such purposes as are served by a subjec- tive description, without an exact comparison of relations. Allied to the enquete is the so-called "political arith- metic," where it endeavors to give information of certain definite conditions. The statistician here appears as an expert. But political arithmetic concerns itself, on the one hand, with general problems in the most varied fields of statistical research, and, upon the other hand, with questions of methods and arithmetical conclusions from the results. Hence the term is a broad one. §70. POSSIBILITY OF ERROR IN ENUMERATION. Enumeration is a practical process upon actual founda- tions, and must therefore struggle with mistakes and im- perfections. Errors in observation or in summing up are always to be apprehended. The easier it is to mistake the characteristics of the unit of enumeration, or the limits of time and space, or to judge them falsely, the more must omissions and duplications be expected. The more figures are written, and the less the calculations are proved, the greater is the probability of errors in transcribing. The improvement of the technique must seek to limit as much as possible the sources of error, but they are no reproach to the method as such. Errors in the observation may be subsequently corrected, when the existence or non- 124 Annals of the American Academy. existence of the units falsely counted can be ascertained for the time of the original enumeration. A certain possibility of error must always remain, and the attempt must be made to estimate its extent. For certain purposes the presumption of even small errors can render the result useless, whereas in other cases even very considerable errors may be of no consequence. The latter is particularly the case when the problem is sufficiently solved by a certain maximum or minimum number of units. The more restricted the purpose the greater may be the possibility of error, generally speak- ing, but the more general the purpose, the more the results must serve for indefinite, not yet known problems, the more must the limits of possibility of error be contracted. An unlimited possibility of error would render the result worthless for all purposes. A judgment with reference to this matter is indispensable to anyone proposing to use the numerical results obtained. Properly prepared statistical enumerations must there- fore include in their presentation sufficient explanation of their basis and processes to permit a conclusion as to the possibility of error, and in general to furnish the guaranty, that for the usual sphere of statistical problems, the relia- bility of the figures is sufficient. §71. PECULIARITIES OF THE RETURNS. The number of units present in the aggregate can be obtained directly by observation and summation, or by complicated calculations. In every case it represents a total — that is, a definite number which tells how many times the unit has been found in the mass. This total, because a total, gives no picture of the ar- rangement of the units in the aggregate. It would be an egregious error to suppose that anything was known as to the position of the units, as, for instance, a map shows the positions of the cities of a country. This is by no Theory and Technique of Statistics means the case. Every single unit is observed at the time of the enumeration, but it is not located. It disap- pears completely in the final result, which is the total sum of the enumerated units. The results of the observation are not susceptible, after the enumeration is complete, of any further subdivision of either time or space. If it is possible to say, as is often done, how many of the enumerated units were found in this or that portion of the space or time in question, it must be clear that separate enumerations have been made for these portions. The same unit of enumeration has been employed, but it has been applied to an aggregate corresponding to these por- tions, and necessarily limited in time and space in the same manner. The aggregate to be investigated has been sep- arated into independent minor aggregates. The results of these enumerations for the smaller aggregates may be' combined to form the total for the general aggregate. But in so far as the enumeration has been divided into particular enumerations for particular aggregates, the re- sult for each aggregate is a single total, incapable of further subdivision. Again, the results furnish information only as to the constitution of the aggregate and not of the units of enu- meration ; for the unit is known and its limits prescribed before the enumeration. To fill the conditions of problems the things counted must correspond to this idea. They agree because they fall within the limits of this character- istic idea, but only so far as this is the case. As to other peculiarities their constitution may be very different. Everything counted as a unit must necessarily have other characteristics besides those in question. These other characteristics remain unknown quantities. The addition made to our knowledge is simply that things which correspond to the given idea are found in a certain total, or possibly not at all in the aggregate. As to this aggregate, the field of the investigation, there is some new knowledge. But as to the things enumerated 126 Annals of the American Academy. there is a new insight, only in so far as they may be char- acterized by their presence in definite numerical relations in the aggregates investigated. § 72. ENUMERATION OF UNITS IN COMBINATION. The problem of investigating the manifold character- istics of an aggregate from the number of fixed known and definite things which go to make it up, is rendered easier and more profitable the greater the number of things which may be counted and the more they may be brought into combination. This combination of the units of enu- meration may be of several kinds. The different units may be related simply in their juxta- position. The enumeration finds the unit A (persons) x times, the unit B (houses) y times, and the unit C (horses) z times. The judgment is that x A, y B, and z C are in the aggregate. The units can be chosen from their relations to certain qualifying ideas. The unit A can be counted as qualified by several characteristics ; a (male) b (single). Then the result is that y (A + a), z (A + b) are found among x units of A. These qualifications may or may not exhaust the idea A. They may describe it from the different points of view : D (arable land) enumeration according to c (area), or d (value), hence w (D + c) = v (D + d). The choice of units may be made according to some supposed causal connection ; e. g. y E (children), F (teach- ers). The result is, for u E there were t F. Whether cause and effect are here at work, and if so, how, is not determined. The greater the number of possible relations among the units, as suggested by induction, and the more sys- tematically the effort is made to bring out such relations, so much the more must the numerical data obtained add to our knowledge of the conditions existing in the aggre- gate. Theory and Technique of Statistics. 127 § 73. results of the enumeration. The results of the enumeration form, it is obvious, a de- scription of the subject investigated. This description is more comprehensive when large and systematically con- nected groups of different units are counted. It is attained, however, when the enumeration is carried through with a single unit. It must be recognized that such a description would be attained, either positively or negatively, if the observer, having before him a real field of view, and without any knowledge of it, should conceive a certain thing as a unit, count it without any definite purpose. This would be true whether he found it within the definite limits of the field or not. The fact that it is a conscious problem lends a meaning of the description which is the result of method- ical enumeration. Essential premises are drawn from this conscious purpose, which cannot be separated from the process. This purpose follows necessarily from the fact > that the methods of statistics are applied to fill out, if pos- sible, some gap which inductive and deductive methods have consciously left open in the investigation of the mul- tiplicity of actual existences. The aggregate investigated is known as a whole, as an individual or collective idea ; and it is examined in its composition and internal connec- tions, which are unknown. This examination is not without plan. It is not directed toward any chance object, but the enumeration bears upon a unit chosen expressly with reference to its significance for our knowledge of the whole. So simple and apparently superficial a process as the mere counting of certain things is only chosen because it is believed that some gain in knowledge will result from the determination of the number. I Statistics presupposes for its method a wealth of expe- riences and abstractions. The methodical description ob- tained by enumeration rests upon a basis of well-connected 128 Annals of the American Academy. ideas, which is to be further built up by the results attained, or to be better adapted by them for certain definite pur- poses. Nevertheless, the peculiar barrenness and inflexibility of this summation is not to be mistaken. The question is not of this mere description, but of the real importance of the gain which these figures promise. While the units observed correspond to real facts, these facts are determined beforehand by fixing certain well- defined characteristics, not by exhausting all. The only additional determination of the idea of the phenomenon which is obtained, is whether it is contained once, twice, more frequently, or not at all, in the aggregate. Here the size of this number is of decisive value. Numbers and numerical successions have a certain gradation in themselves ; i. e., i is half as much as 2, and 40 ten times as much as 4, and so forth. But when in a certain aggregate A is found 10 times, B 40 times, and C 1000 times, or 20 a and 30 b among 100 c, these figures give obviously no measure of each other, nor in fact any comprehensible measure. Whether it is much or little is impossible to tell. Empirically it may indeed appear otherwise, because in our general thought, and by recollection of numerous sta- tistical enumerations, we have a number of hazy ideas as to the number of units (men, houses, goods) which were in a certain locality, and such ideas are used instinctively as measures, however deficient they may be. The strict methodical process cannot rely upon such uncertain support. It must require that the true impor- tance of figures be measured on an exact standard. Such a standard might be obtained, one would think, by such an investigation of the aggregate as would show how many of the things counted it ought to contain, and must contain, conformably to its essential character, and in what degree it had the capacity or possibility of containing fewer or less. But this method is obviously that of the experi- Theory and Technique of Statistics. 129 mental investigation of the aggregate with all its confused and changing complexities, with all the possible combina- tions of its elements, and their wealth of mutual inter- relations. Such an investigation may be said to be im- practicable in principle. But if by any possibility it might appear actually possible, it could not be avoided, and in that case the statistical method would be rendered super- fluous. Under the conditions of statistical inquiry it is not pos- sible to obtain a measure of the results of the enumeration of an aggregate, simply from the nature of the aggregate as apparent from the enumeration. With the demand for such a measurement the whole process reaches a point where it can no longer confine itself to the observation of the aggregate to be investigated, and where the total work of enumeration, however complicated, difficult, and exten- sive it may have been, is clearly recognized as only of a preparatory character. B. PRINCIPLES OF STATISTICAL JUDGMENTS. & I. Quantitative Relations. § 74. THE MEASURE OF QUANTITY FROM ANALOGOUS AGGREGATES. The description of any investigated aggregate by a statement of totals obtained by counting its component parts, does not furnish any new information, unless we can form a judgment of the meaning of these sums. Whether a single unit or a number of units has been counted, is wholly immaterial A judgment on the number of observed phenomena must necessarily be one of proportion ; that is, of a quan- titative nature. Are the figures obtained to be considered large or small, and if so, in what degree ? This is the y 130 Annals of the American Academy. question which arises, and the necessity of some measure, some scale by which to judge the results, becomes obvious. Statistics finds this measure in the comparison of the results obtained for similar units in analogous aggregates. These may be the fruit of previous or of simultaneous investigations. The proportion which the different units of enumeration bear on the average to equal portions of the analogous aggregates is calculated, and the limits of the deviation from the average in both an ascending and a descending scale are observed. Thus, a measure is furnished with which to judge of the numerical relations of the units in any par- ticular aggregate. What is meant by analogous aggre- gates scarcely needs explanation. It appears clearly that they are aggregates which considered as a whole come in the same category. It is from this point of view possible to conceive of the number of analogous aggregates, changing, as they do, according to the problem in hand, as almost inexhaustible. The number may, however, be very small. In every case it is limited by the fact that we can actually use only such aggregates for purposes of comparison in which units similar to those of the aggregate investigated are or have been counted. Hence the measure of comparison must be drawn from a comparatively restricted group of analogous aggregates, and everyone using it must bear in mind upon what group of analogies the judgment is based. The analogous aggregates are sufficiently known. They are not chosen from those manifold and confused charac- teristics, which are the subjects of statistical inquiry, but I from those definite qualities which as a whole place them in some general class. Conceived as a whole, they must be judged by inductive methods, and it can be seen which have more importance than others for the compari- son, and which, therefore, would constitute more valuable elements of the scale. This building up on information Theory and Technique of Statistics. 131 gained by induction, is a very general and necessary ele- ment of statistics. The ideas of empirical thought are earlier than the questions of statistics. Inductive knowl- edge is only supplemented by statistics where gaps remain and further progress is barred. The difficulty of the process does not lie in the often very limited sphere of- analogies which can be used in forming the scale, but rather in the proper conception of the aggregates which in concrete cases may be looked upon as analogous. § 75. THE CHOICE OF ANALOGOUS AGGREGATES. The choice of analogous aggregates necessarily depends upon their character as units. This depends in the first place on that particular conception of the aggregate as an entirety, required by the problem. In this connection it is of course requisite that every field of statistical investigation may be generally conceived in its entirety as a single thing, whether as an individual or as a collective. Evidently, statistical enumeration and the kind of de- scription which follows from it are utterly incapable of characterizing the aggregate as individual or collective. All essential qualities of the individual, as well as of the collective, which are conceived as fixed, or changeable, relate to its organization as an entirety. But the statistical enumeration concerns only certain things among the vari- ous elements which compose this entirety and determine their number. If this number belongs to the notion of the entirety, then it is typical. But in that case it would be known already by means of general or experimental observations, and have found a place in inductive and de- ductive generalizations. There could no longer be any question of an element still to be found in an unexplored and changing complex. Nevertheless, each of these complexes, with confused 132 Annals of the American Academy. and unknown elements, would have certain definite char- acteristics as an entirety. A State, a country, a harbor, a town, a section of the heavens, the monthly weather of a station, and so forth, have all general qualities that char- acterize them as entireties, so that other entireties falling in the same categories may be recognized. According to his notion a human being is known as an individual, but he is capable of conception as collective, at any rate as an aggregate. Numerous more or less changeable elements are to be observed upon him, as teeth, eye-brows, and freckles, which, for a medical or anthropological purpose, might be subjected to a statistical enumeration and com- parison. The idea, therefore, which is to be held of the inves- tigated aggregate as an entirety determines the analogy with other aggregates. Particular attention must be given to the elasticity of the terms used, and the application of very different notions to one and the same actual entirety. For each statistical problem the aggregate to be investi- gated can be conceived only in a single way. If that be changed the notion of the aggregate changes, and with it the problem. What are apparently two identical problems become two different ones. The reverse holds, and the change of the problem involves a change in the notion of the whole. If it be asked whether Prussia had a large growth of population during the last census period, the notion of the aggregate Prussia, and hence of all analo- gous aggregates, is very different, according as the ques- tion means, was the growth large as growth or large for Prussia. In the first place, Prussia is conceived as a civil- ized country, and the analogy attaches to that notion ; but, in the second case, Prussia is conceived with all its peculi- arities, and it has no analogy but itself. Here the task is simply to compare the aggregates of Prussia at different census periods among themselves. Now, it is obvious that according to the nature of the Theory and Technique of Statistics. 133 problem a limited group of aggregates, instead of many, may be sufficient to furnish a standard of comparison. It would certainly be sufficient in the first case to compare Prussia with the most important States with trustworthy statistics, and in the second case the Prussian figures for the last three or four decades. The notion under which an aggregate to be investigated may be conceived for comparison may vary from a definite individual to a part of concrete existence, limited in time and space, but otherwise wholly unknown. Hence the choice of analogies requires acute distinctions, but is always possible. It is questionable how far comparison must be abandoned because an enumeration of like units in analogous aggregates has not taken place, or cannot be effected. The problems of practical statistics are usually those for which provision for comparison can be readily made at the time of enumeration, or already exist in previous results. If these problems are to be solved within the limits of a single country, there are, as a rule, a great number of com- parable aggregates for which exactly the same enumeration has been made. We have, on the one hand, the minor subdivisions of the country, as provinces, counties, even to townships, which are distinguished in the enumeration, so that each division is a separate aggregate, the sum of whose units may be compared with that of others. On the other hand, from year to year, or at definite periods, certain enumerations are made where like units are counted in the various subdivisions of the country, and thus a new series of analogous and comparable aggregates is obtained. For such questions which extend beyond the limits of one's own country, there are means of solution to be found. Most civilized States undertake, from similar necessities, similar statistical enumerations. But it cannot be denied that international statistics show some very bad gaps and other imperfections. They are not caused by a lack of analogies, but by a 134 Annals of the American Academy. lack of sufficient agreement in units of enumeration. Like names for things counted may lead one to overlook that different States apply the same designation to units which are different for purposes of comparisons, because unlike in composition and origin. (O. Haussner, Vergleichende Statistik von Europa, 1864.) Statistical problems are always incapable of solution / / when it is impossible to find a basis of comparison in analogous aggregates examined with reference to exactly the same units. § 76. REDUCTION TO COMMON TERMS. A comparison of the analogous masses is not attainable directly. Some basis of comparison must be found by reducing the results to common terms. This reduction depends, like the choice of the units, upon the nature of the problem. If the purpose of the problem is to determine the relative frequency of the occurrence of the phenomena, the com- mon terms must be in measures of time and space for the various analogous aggregates. Hence there must always // be an equal measure of time and space — thus, for 1 square mile in 1 year x wheat. No limitation of space is neces- sary when the aggregate has changed in time only and not in space (Province A, 1 year y taxes), or, when in an observation of movement, the place is a point from which the number is counted (Canal B, 1 week z vessels). In like manner the time needs no limitation, when the condi- ) ) tion in all parts is recorded at one moment (State C, 1 sq. m., x inhabitants, y houses, z arable land). In all these cases time and space are bases of the comparison. The measurement of time has naturally few difficulties. On the contrary, the measurement of space requires often very extensive operations of survey and triangulation, which statistics are not in a position to carry out. It has to presuppose the existence of this, and expects to find it completed, just as much as the measuring of the qualities i Theory and Technique of Statistics. 135 of the units. The survey and triangulation of territories, or calculations which are not always exact from the geographical boundaries, furnish the necessary data in this matter. The number of things enumerated for each common term is found by calculating what part of the entire aggre- gate it forms. The same proportion of the total number of units must fall upon this term. Therefore, for these common terms the most various units can be shown side by side with all their distinctive differences. This division of the total is simply one of calculating proportions, and would never justify the conclusion that a similar distribu- tion in the density of units occurs in the real parts of the field. As the aggregate is to be measured by mutual relations of the units, the reduction to common terms takes the form of the reduction of various units to an equal quantity of one unit, and, as a rule, percentually (for 100 units A there are x units B). Any unit. can be used for this purpose. Specifications of the main unit are hereby rendered much clearer in their relations to the central idea. Sometimes for such combinations an equal period of time must also be drawn into the problem (as for 100 inhabitants y births in 1 year). In like manner a restriction of place may be necessary. But here the percentual number expresses simply an average, not at all that in the aggregate or its parts, or anywhere in particular, for 100 units A there are x units B in nearer or more definite relations. The reduc- tion to common terms which always has the same purpose, becomes a very extended calculation when it deals with many distinctions and differently graded qualities. (Ernte- statistik, Bd. I. d. Stat. d. Deutsch. Reiches, p. 1 10.) § 77. SERIES, MAXIMA, MINIMA, AND AVERAGES. The results obtained by reducing the results of enumer- ation to common terms always furnishes a series admitting 136 Annals of the American Academy. of comparison. The figures for the same unit show in which aggregate relatively the largest and in which the smallest number of units is to be found. Arranged from minimum to maximum, they show the order in which the degrees of intensity progress. Arranged according to the geographical position of the masses, they show the intensity in its distribution, and arranged by their succes- sion in time, the fluctuation of their historical development. The fluctuation appears either as regular growth or de- crease, or as an oscillation which, though changing, returns to similar maxima and minima. Two or more such series placed beside each other, and thus showing a comparison of different units, may be ex- amined as to the similarity or dissimilarity of their courses, whether they oscillate in the same or opposite directions, and whether the maxima occur positively or negatively at the same point of the series or not. (Compare Appendix mo For the fluctuations of a single series we find the measure \ J in the average. The average expresses the mean figure, ^the mean importance of all the fluctuations of the series, so that the individual figures extend beyond it, some nega- tively, some positively, in equal proportions. The average cannot be gained immediately from the series itself. It must give the mean value of the totals of all the aggregates, and cannot, therefore, be calculated from the ratios, but only from the absolute figures, the sum of all the units of enumeration of all the aggregates compared, divided by the sum of all the quantities used for the reduction to common terms. For the comparison of several series, there must be an average for each to serve as a basis of comparison. (Lexis, quoted § 16, and Marey, quoted § 57.) § 78. results from quantitative judgments. From such series of relative numbers we can form a quantitative judgment, that is to say, a conclusion as to Theory and Technique of Statistics. 137 the greater or lesser measure in which the things deter- mined upon as units of enumeration are present in the aggregate investigated. The more numerous the series the clearer is our insight into the subject, since we know the relations of a larger number of component things. And the more varied the relations among the things are, their grouping as genera and species, as well as other relations, the greater is the definiteness which the aggregate assumes. We also know in what relations these things occur in other aggregates, which, however variable, may be regarded when considered as units as belonging to the same class as the aggregate which has been investigated. The things themselves are not examined. We find \\ simply the frequency of their occurrence, their quantita- tive distribution in certain limits of time and space, among other things which remain unknown, but which fill out the space. Thus a certain general measure of their mutual relations is determined, in a somewhat sum- mary manner, it is true, but in one not to be reached by other methods. Thus the aggregates themselves are better known and are more capable of comparison. As they agree in those essential items which characterize them as individuals or as collectives, it is very important to find that other ele- ments, which appear fluctuating and unstable, can be measured, at least as to their intensity and probable mutual relations, by definite measures, and in relation to similar aggregates. Thus the first step of statistical judgment, i. e. } the judg- ment of quantitative relations, is complete. It is the indis- » pensable basis of any further progress. By far the greater part of the statistical activity whose results reach the public and become common property, does not go further than this first step in the knowledge to be gained from statistical enumerations. Ponderous statistical publications of official bureaus deal in the main with this class of description. It 138 Annals of the American Academy. is rarely that an investigation steps beyond the limits of this quantitative judgment. This is all the more explain- able, as this is the field in which, as much as possible for empirical knowledge, exact results and conclusions may be reached. All further conclusions based upon these results, as- sume unavoidably a more or less hypothetical character. Nevertheless, it would be quite impossible to confine sta- tistical investigations to quantitative judgments, even if we should follow the most restricted conception of the limits of statistical science. The final and conclusive utility of this primary requisite of methodical statistical investigation is certainly not to be found in the rich mate- rials that it presents, but in the conclusions to be drawn from them. II. Causal Connections. § 79. REQUIREMENTS AND LIMITATIONS OF JUDGMENTS OF CAUSALITY. The next step in statistical investigation after the details of the quantitative relations must be an effort to explain the reasons for the numerical relations which have been discovered ; in short, their relations of cause and effect. It is in the nature of our reasoning to suppose a cause for every effect, and to seek to find it. All phenomena are subject to the rule. For every phenomenon we think at once of a cause and try to find it ; or, in other words, we seek a satisfactory explanation of the phenomenon. While our perceptions have the form of descriptions, the interest we take in them is the effort to determine causality. To demonstrate the causes empirically is very difficult. We are conscious of causes only in our own actions. In the external world they appear only as succession in time, and whether A is the cause of B, which follows it in point of time, cannot be maintained without danger of error. Theory and Technique of Statistics. 139 For individual cases, therefore, the proof is carried out by experiment. The object is placed successively under one influence to the exclusion of all others, and the conse- quences observed, until it appears which influence brings about the effect. Statistics can make no such experiment with the phe- nomena of aggregates with v/hich it deals. In the com- plex aggregate the most varied and opposite causes must always be at work. Statistical methods cannot expect a knowledge of all the things in the aggregate, and cannot, therefore, attempt an investigation of all the causes in operation. In the judgment of causal connection, it is limited to certain phenomena, the frequency of whose occurrence has been numerically measured. It can only ask what causes have produced these relations, or what effect may be traced to them. The process by which the answer is made resembles somewhat that of experiment. We take up in succession the possible causes. We may suppose, at first, the most probable to be actually operative, and look for indications whether or not this is the case. If not, each probable cause must be examined successively, until one appears to be sufficiently well founded. If the supposed causes are exhausted without success, then there remains simply the same result as in a fruitless experiment, that, of all conceivable causes, none seem to be at work. § 80. DISCOVERY OF CAUSALITY THROUGH FUNCTIONAL SERIES. Statistical methods can only look for indications of the causal connections of two phenomena, in the mutual rela- tions of the quantities in which they are found. Their frequency in the aggregate investigated is not alone suffi- cient for a demonstration. This is expressed by two figures which are otherwise unrelated. For any judgment as to the meaning of these 140 Annals of the American Academy. figures it is indispensable to compare the figures which have been observed within a group of analogous aggre- gates for the same units. 1/ Since the cause produces the effect, the cause and effect must be weaker or stronger together. Whether an increase in the intensity of the cause shows itself positively or negatively is indifferent. Our idea of a sufficient cause is based upon its functional relation to the effect. The proof of causality can only be given in the course of two series of relative numbers : one which shows the measure of the cause, the other the measure of the effect, in the aggregates compared. If the effect A is really the result of the cause B, the relative number of the units A must in all these aggregates vary in the same or opposite ratio as that of the units B. But if such a relation, with the exception of such devia- tions as may be explained, does not appear, the supposition of causality is to be rejected. On the other hand, the agreement of two series is not to be considered an abso- lute demonstration of the causal connection of the phe- nomena. It is only a presumption of such a connection. Both may be the effects of the same cause, or, indeed, numerous combinations of the most divergent causes might lead to a similar final resultant in each series. Hence, to decide as to the nature of connection between agreeing series we require still further evidence. Such evidence can be found, as in the choice of analo- gous masses, only by the use of knowledge which has //been gained by the inductive processes of experiment and ' observation. Numerous causal connections between single things, individual as well as collective, are sufficiently well grounded to be generally known. From such knowledge one may by induction or deduction presume the effect of a given cause which is the most immediate and prob- able. In order to know the cause whose effect is expressed in the series A we must fix our attention upon the cause Z, Appendix III. (to § 80). aire U3AV f98/ 998/ 9987 OPS/ S187 048/ £887 in > fcl * •J >> £ 4 db o^ns 11 1 i \ 1 ft ^ s / /' / /^ \ \ ,''/ n .. Jj * "* -•''„-• A J V /] 7 '•• Hi \V >■ / / s i \ \j J# 1 > iC "i ,»*•»" i^ii — ■ ■ \S -.\ s ... / .--^ '' V > \ "\ y "^ < : N> -- ■ I ■*» ^^ L, v ;V *; i V \ / .N s -^-^ B»«", "" |— ss ^ >- j \ \ *-- & j l^ ^* ^^ / ' \ k '^ $S. \ •. / ■;'/ y / f. ^ [/ \X \ / 1 I rV^ o* . v \ 00 \ \ \ ^^v 5~ y \ \ [ f / ' rt .o u '■a ,x>we cd 8 1 O £ — «j «•> * *i \ •«» •» q S 5 « 5f § «8 i ** "»" ^) U «J ^ o >N I 1 M J - S5> *Q» 1 c OS © 1 3 OF THE UNIVERSITY Theory and Technique of Statistics. 141 which inductive knowledge tells us is the most immediate cause of which A is the effect. We then note the series of the phenomenon Z in all the analogous aggregates to be compared. If the series Z is present among the enu- merated units, it is easy to decide whether the functional relation of the two series permits us to suppose a causal connection in the case. If the series Z has not been counted, this must take place, or a sufficient substitute, which can take the place of the series Z, be gathered from the enumeration. If it appears that no functional relation exists between the two series we cannot assume this cause to be of influ- ence, even though under ordinary circumstances it may be the most probable. We must rather look for the cause Y, next in order of probability, and apply to it the same process, and so the successive probable causes, X, W, V, T, etc. Thus we continue until we find a correspondence between the series with one of the causes, or else we must abandon the hope of establishing the real cause from among the probable ones which we know. In this case the negative result is undoubtedly of great value. All presumptions are cut off which seemed most reasonable, and this negation may serve for the solution of exceedingly important problems. The result may be that another series, B, which no one supposed to be connected with the causes, is now found to be important through excluding the seemingly more imme- diate causes. It may be apparently improbable and diffi- cult of comprehension, but must, when all other connec- tions fail, be recognized as the fact in which the forces at work find a clear expression. An example is given in Appendix III.: marriages and the prices of rye. // 142 Annals of the American Academy. §8l. symptoms and their application in determining causality. In finding an explanation of cause and effect we do not have all the elements of the solution in the problem itself, as in the case of the quantitative relations of the phe- nomena. The necessity of introducing certain phenomena for comparison appears in the course of the proof. The in- vestigation of causality does not look for the scattered and characteristic features of a picture, but the confirmation of a chain of more or less obvious or obscure conjectures, none of which can be disregarded without fear of error. It is purely a happy accident if all the figures necessary for the comparison are in existence or can be obtained. In case no enumerations have been made for analogous aggregates of units essential to the proof, or are wholly impracticable, something else must, as pointed out in §62, take their place. We thus arrive at the question of so- called symptoms. These symptoms are indications, but they cannot, as demonstrated by §65, be found in qualities or abstrac- tions from conditions. Statistical methods cannot say that things (money, capital) are symptoms of qualities (rich), or of abstractions from this quality (riches). Only per- sons can be rich ; whether they are rich and in what degree can only be determined in considering persons, and to say what capital constitutes riches, makes sense only in connection with persons. Capital expressed in money can be counted, but it shows riches only in the relative possessions of persons. A symptom means in statistics something capable of enumeration, which shows by its number that something may be inferred in a corresponding number, or one to be estimated or calculated. For different degrees of rich per- sons, whom it would be very difficult to count, we find a symptom in the returns of persons liable for income or Theory and Technique of Statistics. 143 property taxes. In the statistical inquiry as to causality one of the most important problems is the choice of these symptoms. Gioja (see § 46) called attention to this in an instructive way. On the other hand, there are no general rules for the proper choice and use of symptoms. One thing can never be replaced exactly by another. The acuteness of the judg- ment must suffer in some degree. At the same time the application of the theoretically best symptom is oftentimes quite as impossible as the use of direct results of enumera- tion. A suitable choice must remain a matter of a clear and keen conception of the special problem, and of all the resources which may be drawn upon for its solution. Some misgiving may arise from the need of symptoms, but it cannot be overlooked that they bring an important element of flexibility and variety into the methods of sta- tistics. By means of one unit replacing another the results of enumeration may be utilized for conclusions, which would have required in the original problem or in others an enumeration under totally different circumstances. III. Probability and Regularity. § 82. the conception of probability. The hypothetical demonstration of causal connections in statistical aggregates furnishes the basis for the solution of a vast number of practical and scientific problems. It is, moreover, indirectly of peculiar significance for statist tical methods. (The insight into causal connections ren~ ders possible a judgment of probabilities and the expecta- tion of regularities. This further step in statistical knowledge opens up a wide possibility of solving many problems, even quite complicated ones. By its means conclusions may be formed as to the quantities in which qualities, which have not been enumerated, are to be found in the aggregate to 144 Annals of the American Academy. be investigated, and which may, therefore, be expected with adequate regularity in similar aggregates. What we know as probability is based upon the idea that what occurs regularly in our experience under certain circum- stances is very likely to occur again in the same way if the circumstances do not change. Phenomena which have been demonstrated to be the result of a certain com- bination of circumstances, even though some are not . wholly known, may be expected with greater probability than any other phenomena from the same combination. This line of thought is distinctively causal. The cir- cumstances are the causes, which being uniform must produce uniform effects. If the circumstances cannot by any possibility change, and permit only a limited series of possible results, a calculation may be made of the degree of probability of each of these results. This is the idea of the calculation of games of chance, and of Bernouilli's principle of Probability (§ 15). This principle is expressed as follows : " If a large num- ber of cases have been observed of several events which have a certain probability, the number of cases in which each event has occurred will approach very closely to its probability, and this more and more precisely the more extended the number of observations." Bernouilli, how- ever, limits this rule, inasmuch as when the number of possible events is infinitely great, that is, when the num- ber of events is not limited, but may expand indefinitely, the principle does not hold. In many statistical problems, as in the calculation of death tables, the series of possible cases may be regarded as complete, on account of the in- finitesimal number of those dying at very advanced ages, and Bernouilli's principle may be considered applicable. As a rule, however, the form of the calculation of prob- abilities, as applied by statistical methods, undergoes a two-fold modification. On the one hand, it results from the nature of the aggregates to be investigated, that they include an infinitely great number of different possible Theory and Technique of Statistics. 145 phenomena. On the other hand, it is only exceptionally that statistical problems require the degree of probability of a certain phenomena, but rather in what quantity or what relation a certain phenomena may be expected. This is a reversal of the problem which simplifies it, and ren- ders less important the lack of a definite limitation of the phenomena. In all cases it is clear that a large series of aggregates is much more likely to comprehend all the possibilities of the occurrence of a phenomena than a small series. It is, nevertheless, just as little to be doubted that without limi- tation even the largest series does not give any absolute security that all possibilities are actually contained in it. In order, therefore, to obtain a definite numerical ex- pression by a calculation of probability instead of by . enumeration, statistics must make use of a fiction. This fiction expressed in logical terms is that in the series of enumerated aggregates which are compared, the possi- * bilities in question are to be regarded as exhausted. Actually this supposition has a concrete justification in the fact shown in § 75, that the analogous aggregates are chosen with knowledge of and reference to their peculi- arities. Statistical problems employ this fiction so exten- sively that the sphere of comparison becomes frequently very narrow. In case of necessity the probability is often . judged from the results of a single enumeration; i. e., the possible variation is estimated. But, as a matter of fact, the difficulties and the interest of these problems do not hinge so much on the questions, which cases are possible, and hence may interfere with the action supposed, but they rest on the doubt whether known possibilities have been correctly judged in their I causal connections. 146 Annals of the American Academy. § 83. suppositions based on similar causality. The process of assuming by probabilities the number of things which have not been counted is based wholly upon the idea explained in the foregoing section, that in the ag- gregate to be investigated the same causes operate as in . the analogous aggregates. Like numerical relations under dissimilar conditions would be highly improbable. These conditions of the conclusion as to probability cannot but exert an influence upon the choice of analogous aggre- gates. The analogy of the aggregates is determined by the same conception, be it broad or narrow, of them as entireties, either individual or collective, presupposing always that the distinctions have been drawn with care and attention. Whether or not the analogous aggregates have actually been subject to such similar circumstances, that the causes at work from which the probable figure is deduced have been actually identical, is one of those ques- tions for whose answer statistics must draw upon general empirical knowledge. Here it is necessary to consider, according to the nature of the problem, the different influences which may be at work in contemporary his- tory, in political or economic life, and in the processes of nature. » Such influences may often be determined statistically, and be observed in the search for cause and effect. Whether this takes place depends largely on the time and cost involved, and on the importance attached to the question. Influences which are generally operative are to be regarded as causes, since they affect the relations of the parts to the whole in the same way in all cases. When it is known that influences are at work whose effects are partial only, the aggregates in which they occur must be withdrawn from the examination. For it is preferable to know positively that like conditions exist among the aggregates compared than to extend the comparison to a great number of them. Theory and Technique of Statistics. 147 In all events no effort should be spared to ascertain whether special influences have been at work in some of the aggregates considered as analogous, or indeed whether the aggregate to be investigated has not been subjected to some unknown influence, which would render unreliable any conclusion upon the basis of probabilities. Nevertheless it would not answer to indicate these pos- sibilities of error by expressing the probability in hypo- thetical or indefinite numbers. The probability would be useless for any scientific purpose by such uncertainty. On the contrary, any doubts as to the certainty of the result must find expression with sufficient explanation in a critical examination of the margin of error. Employing the fiction already named, that the aggre- gates compared exhaust all the possibilities to be con- sidered, it is an easy matter to obtain the most probable number. In one case the desired phenomena has not been counted in the aggregate to be investigated, but in the analogous aggregates, whereas the series of causes or effects corresponding to this phenomena have been enu- merated in all. Here the phenomena in question will bear the same relation in this series in the aggregates to be investigated as it does on an average in the analogous ones. In another case the series of causes and effects have not been determined for the aggregate under investigation, but it is supposed that like circumstances affect this and the analogous aggregates. Here the desired result would be the average of the analogous aggregates reduced to an equal size with that investigated. When a series of enumerations for analogous aggregates is at our disposal, and the probability may be calculated from their average, it seems advisable to note the possible deviation of the actual number from this average. In the most extreme case the deviation can be supposed to equal the actual extremes in the series. When, however, we desire to find the probable deviation on one side or the 143 Annals of the American Academy. other, we can calculate the mean of the deviations from the average on each side. The extensive application of probabilities has led to cer- tain points of view which require more precise explanation, and a correct estimate of their relations to the whole field of probability. They are the so-called law of large num- bers and the so-called regularity of seemingly voluntary actions. § 84. THE SO-CALLED LAW OF LARGE NUMBERS. The so-called law of large numbers has often been treated as some mysterious force peculiar to large aggre- gates, through which large numbers establish regularity. The conception is more correct, that in a large number the actual relations are more accurately expressed than in a small number, and hence probability may be concluded much more safely from a large number. If there were any necessity for the phenomena found in large numbers, it would be equally well expressed in the small ones. And if this necessity were recognized, it might indeed be developed analytically and its results calculated. But this is not the case. The reason why the character of an aggregate and the circumstances at work in it are determined more readily from a large number of phenomena than from few observations, is simple. Every aggregate is composed of various things, and with general uniformity there may still be some ex- ceptional irregularities. If a small number of phenomena, that is, a portion of the aggregate only, is considered, it cannot be estimated whether accidental exceptions, causes of error, and unusual influences may not be. entirely lack- ing or especially concentrated in this portion, and hence any conclusions from it as to the erroneous nature of the whole. In a large number such exceptions must ap- pear in nearly the same relations as in the entire aggre- gates. A single case can only be either regular or Theory and Technique of Statistics. 149 exceptional, while in the whole regularities and exceptions assume their proper proportions. A large part approaches the whole much closer than a small one. In a derivative sense this might be called a law, because it is a truth uniform under all conditions, and a rule for the judgment of probability. But the rule has obviously no connection with the relations of the facts themselves, but only with the formal process of determining them. The phenomena and their effects occur in the same way whether few or many are observed. The law of large numbers has no more influence upon the facts than enu- meration itself. It is not a rule of causality, but simply a rule of perception. §85. THE REGULARITY OF SEEMINGLY VOLUNTARY ACTIONS. The doctrine of the regularity of the seemingly volun- tary actions was formulated by Condorcet, and has exercised an important influence upon the theory of statistics since the time of Quetelet (§51). It is based upon the fact that certain groups of human actions dependent upon the will show approximately the same numerical relations in their distribution in time and space. On this basis there has been postulated more or less emphatically a law governing with constraining force the will of man. In its elaboration this has led to the idea of laws ruling the entire historical development of the human race, capable of the same cal- culation as those governing inanimate matter. With this in view, some have broadly denied human liberty and moral responsibility, while others have admitted the free- dom of the will for individuals, but denied it for large groups of human beings. A law governing the will is in fact incompatible with responsibility to the individual conscience, or toward one's fellow-creatures or the State. Such a law would dissolve all religious convictions, the State and civil law. It must 150 Annals of the American Academy. either conform to the laws of the State, in which case the laws would be obeyed without being upon the statute books ; or it must be contrary to those laws, and in this case they would be brushed aside, but without criminality or redress. Whether or not such a position is admissible from an ethical, psychological, or anthropological point of view, cannot be decisive for statistical theory. If it were prova- ble by statistical means, the theory of statistics would have to be shaped in accordance with so weighty a fact. No end could be more worthy of statistics than to prove by its critical methods a definite cosmological system. An investigation of the facts shows, however, in the first instance that such uniformity of the numerical relations as would justify the conclusion of a constraining law can- not be conceded. Suicides, which are looked upon as the most decisive proof of the law, have, between 1836- 1875, in quinquennial periods, varied per 100,000 inhabit- ants as follows: Belgium, 3.65-7.01; Austria, 4.60-1 1.93; Germany, 4.83-9.16; England, 5.57-6.69; Sweden, 5.66- 8.49; Norway, 7.33-10.90; France, 7.62-14.55; Prussia, 10.28-13.28; Saxony, 16.00-28.10; Denmark, 21.40-28.60. If from these figures it is deduced that among 100, OOO inhabitants 100,000 suicides would have been possible, and only 3.65-28.60 have occurred, this would be a rea- sonable approximation. But if it is to be formulated as a law that among 100,000 inhabitants 3.65-28.60 must com- mit suicide, we cannot accord our assent. Even if in each State only the given figures were used, and the minima and maxima represented always a steady progression, and not ups and downs, there could be no conclusion of con- straining force. This becomes more and more evident in comparing lesser areas and periods. Similar results are to be obtained from a detailed examin- ation of the other means of proof, which relate chiefly to the illegitimate births and various kinds of criminals. The motives of the actions whose voluntary character Theory and Technique of Statistics. 151 has been questioned are in most cases known or capable of determination. They are fully conscious, and often contradictory, according to changing circumstances and situations of the persons. Certain motives of suicide and crimes, and also certain modes of carrying them into execution, increase with good or ill fortune, necessity or plenty, the quiet or disturbance of contemporary events. A law with different causes cannot be a natural law. The force of a natural law is permanently and uniformly inherent in all natural bodies. Its effects may be rendered difficult of perception by the action of opposing forces, but they cannot be changed. A law of nature cannot affect the aggregates and not the individual ; it works uncondi- tionally in each individual and in the aggregate only by virtue of this fact. Death is based upon a law of nature, and possibly also the fact that twenty-one boys are born for every twenty girls. But the natural law must be operative in every death and every birth, and not simply in a certain number of cases. Not a law of constraining force, but simply a similar combination of many and varying causes, is the reason for the approximately similar phenomena. But this basis is insufficient to support a doubt as to the existence of the freedom of the will. The expression is unhappily chosen, for the act of willing is always conceived as free. If ex- ternal law controlled without opposition the will of man, his existence as a rational being must cease. Numbers do not control his will but only his action. No one has claimed for man entire freedom of action. The sphere of / / free action is always very narrow. It is limited by multi- fold external circumstances, by the power of environment, by individuals, by the State, by nature, as well as by the powers and means of the individual himself. But for free and responsible choice a broad field in the wide possibility of decision remains open. The scope of the latter is shown not only by the difference between submitting to another's will and preferring to destroy one's own existence, but 152 Annals of the American Academy. also in the inexhaustible modifications in the mode of exe- cution and the ethical value of actions which differ but slightly. Finally, it cannot be overlooked that all the figures relied upon to overthrow the freedom of the will are drawn from civilized peoples. These live under like conditions, and it is not remarkable that there should here appear a similarity of the spontaneous actions of individuals. In itself human nature includes the uniformity of body and mind of the species ; in civilized States there are added similar classes of population, similar distribution of occu- pations, of education, and of income, similar principles of law and administration, similar protection, and similar perils ; and within the like classes, like views of life, like needs, like pleasures, and like habits. It cannot be disputed that under all these similar con- ditions like phenomena are more probable than unlike, and hence great disparity would appear according to all presumptions much more inexplicable than the existing uniformity with its slight variations. These approximat- ing results, which vary slightly according to the circum- stances, appear much more natural as the result of the liberty of the will than as a consequence of constraining law. Statistics finds within its own limits a satisfactory ex- planation of existing regularities, and does not need to borrow metaphysical or materialistic premises. On the contrary, it appears that the reversal of the law of proba- bilities leads conclusively to the same solution of this question. If the probability of similar averages is based upon the causality of like circumstances and relations, the conclu- sion is unavoidable that the uniform or uniformly changing figures of moral statistics must necessarily be founded upon a basis of uniform conditions and developments. One can say that the regularity of voluntary actions is Theory and Technique of Statistics. 153 explained most simply by concluding, from the fact, the same factors from whose existence the theory of proba- bility would assume the fact. § 86. STATISTICAL REGULARITY. Discarding all fantastical ideas of a law of large numbers or of unfreedom of the will, the regularity of phenomena is none the less a most important subject of statistical theory. " Rule " is our expression for the uniformity and arrangement of a number of analogous phenomena. Conformity to the rule is regularity. Hence we may properly call regularity things based upon ana- lytical rules calculated mathematically, or uniformities fol- lowing with necessity from natural typical premises {e. g. y that there are twice as many hands as men, or married persons as marriages). In the same way the necessary effect of a certain cause, or the same measure of effect with the same measure of cause; also the example of Sigwart (§ 58), when an object is found in relatively equal portions in the smaller sections of a State as in the whole, constitute regularity. These are not statistical regularities. Statistics does not investigate uniformities that are calculable because necessary, nor such as are typical or accidental. These are either known or else occur so that no more interest attaches to their uniformity than to their difference, as long as no conclusion is permitted that a similar number will be found in the next aggregate not yet observed. Statistics seeks regularities with the same end in view as in enumeration, i. e., of gaining knowledge of the confused and unclassified aggregates of concrete existence. Regu- larity has value for statistical methods only as expectation. Expectation depends, like all probability, upon the knowl- edge of causal connections. This knowledge may be based upon proof or it may be assumed, possibly erroneously, but must always be conscious. Sigwart's example (§58) 154 Annals of the American Academy. is applicable statistically only where there is an object in view. Conclusions as to regularities in statistics are conclu- sions as to probabilities, and are in a way an extension of the principle. Probabilities generally attempt to discover from the results of enumeration of analogous aggregates a number which in a special case has not been found by enumeration. Statistical rules, on the contrary, look for the numerical ratios for certain phenomena which may be expected for all aggregates, including those analogies which have not been observed. This inquiry cannot be conducted in any other way than by determining through enumeration the ratios of numerous analogous aggregates, and taking an average which may serve as a rule. The application in a single case is now much simpler. If the rule is once ascertained, it is no longer necessary to compare the figures for all the analogous aggregates, but simply to examine whether the aggregate is actually anal- ogous to those for which the rule is already ascertained. This reversal of the procedure facilitates so much all statistical efforts, that it is one of the chief aims to find such rules. If rules are established for special causes and special peculiarities of the aggregate, the scope of the rule is thereby limited. In applying it one must carefully in- quire whether all these pecularities and special causes are present in the aggregate. Such special regularities may be most frequently found in dealing with the same aggre- gate, but at different periods. In such a case the non- applicability of the rule would not be without value, as it would point to variations of certain causes But the more special the causes upon which the rule is based, the more they are apt to be variable and the more limited is the sphere of analogies. Hence the more difficult it becomes to find a sufficient number of analogies from which to gain the rule itself. The rules are taken, therefore, largely from such rela- tions as appear to be the result of the combined influence Theory and Technique of Statistics. 155 of manifold causes known only in a general way, such as the influence of human society generally or certain condi- tions of existence or of occupation, of rural and city life, etc. It is chiefly in the field of the statistics of popula- tion that such rules have been gained. In particular might be mentioned the group of voluntary actions and moral statistics, and also births, still-births, plural births, mar- riages, deaths, age classes, expectation of life, sickness, physical strength, causes of death, civil condition, occu- pations, and other conditions of human life in which simi- larity of the phenomena are observed, as in the voluntary actions, and which furnish proofs of the influence of com- mon circumstances leading to like results. When the rules are of such a general character it is much easier to apply them to the analogies. They have a double use. In each new problem they seem a probable solution, and when, on the other hand, these conjectures can be compared with the results of actual enumeration in a given case, they lead one to inquire the special causes of the deviations. C. THE FORM OF THE PROCESS. § 87. THE STEPS IN THE STATISTICAL INVESTIGATION. The minute consideration of the steps in the methodical statistical process has shown its strictly logical character, and the symmetry of its principles. The leading thoughts expressed in § 62 are the basis of the special phases of the mode of investigation seen in §§63-86. These rules are developed from a critical examination of the value of our experience. We may endeavor to form a conception of a concrete aggregate; we may attempt to compare it with what we have observed, or with the more or less vivid descriptions of others, but in 156 Annals of the American Academy. the final result we have only a conception of it as a col- lective idea. In it float various elements that we cannot perceive. We may notice details ; yet, however important they may appear to us, according to the subjective bent of our minds, they remain unrelated to the aggregate and purely accidental. This defect of our faculty of observation can only be overcome by organized effort. This is to be found in enu- meration, essentially the most general form of measure- ment. With a definite unit of enumeration the entire field of possibility is measured and the actual phenomena ascer- tained. The idea of gaining by systematic enumeration some knowledge of the confused and changing elements of an aggregate gives a fixed and definite course to the entire process. A deviation from the course involves an error. The enumeration has for its objects certain concrete things already defined. One or more units may be counted, and, indeed, distinct measures for the various units may be adopted. This will furnish a somewhat richer and more detailed result, but does not manifestly affect the mode of investigation. The enumeration must not take place within ill-defined limits of time and space. The aggregate examined must have the appearance of a compact definite concrete object. The results of the enu- meration are simply the totals of the things counted. These give some description, yet not such a one as would enable us to say that the totals were large or small. Such a judgment is the important thing attaching to the number gained. Other judgments could only be analytical ones derived from the ideas underlying the problem, and could furnish no contribution to our knowledge. To reach a judgment we must compare number with number, totals of like things found in analogous ag- gregates ; i. e. y such as have the same character for the purpose of the inquiry. It is not contended that this simi- larity exists concretely either for the units or aggregates. Theory and Technique of Statistics. 157 Similarity exists only in the conception, in the character- istics necessary to it. All other characteristics of aggre- gate and unit can and must be very different. The comparison teaches how many things of the same kind are to be found in a series of aggregates of the same kind. The next result is the idea of variability, or the limits and relations of the fluctuations. Theoretically it would be erroneous to attach the variability to one aggregate. One is easily induced to this by the impression that an aggregate observed at different periods is really the same with slight changes of certain qualities. According to § 65 a thing to be counted cannot be the same when an essential character changes. And so an aggregate is not the same in which the number of units to be counted changes or may have changed. It requires two enumera- tions to find out a change, and for each enumeration the aggregate is different. The analogy may be closer when it relates to aggregates of different periods of time than to those locally distinct, yet theoretically they are as different in the one case as in the other. The idea of the aggregate itself, a confused and changeable complex, inaccessible in its inner details to inductive and deductive processes, is contradictory to the notion that it might be considered as unchanged in the period between two enumerations. All variability which is observed statistically relates not to one and the same aggregate, but to analogous aggregates, those of the same kind. It is simply the different fre- quency of the things whose proportions describe the aggregate more explicitly. Tracing further the statistical process, we find for all aggregates similar phases in forming judgments. The sums, when reduced to common terms, i. e., the possible differences in the occurrences of the phenomena, furnish a measure for the quantitative judgment of the results. This judgment is limited to the aggregates compared. They cannot furnish a general standard. It is a standard, how- 158 Annals of the American Academy. ever, suitable for the purposes of the problems, inasmuch as the aggregates compared are sufficiently well known indirectly in their general character. On this quantitative judgment we can solve the problem of causal connections upon the principle that the greater the quantity of things acting as causes the greater positively or negatively the number of things to be re- garded as effects. Like effects follow from like causes, and from the knowl- edge of causal connections it is but a step to the conclu- sion that the average relation between the quantities of cause and effect in analogous aggregates is to be looked upon as most probable in the aggregate under investiga- tion, and further that from the quantity of cause one may calculate the quantity of effect and vice versa. This con- clusion is so strengthened by numerous instances which confirm it, that regularity becomes one of the premises of statistical argument. § 88. predominance of statistical material. The sketch of statistical processes given in the fore- going section seems to have but little connection with ordinary statistical work. Most statistical investigations show only portions of it. This is accounted for in the purpose of the most com- mon phase of statistical work. Nearly all statistical bureaus are engaged in preparing matter for work on problems of the future. This is true of official bureaus, of corporations, and scientific institutions, perhaps in a still higher degree of private undertakings. It is in the nature of statistics that for special problems and sharp distinctions the analogy between the aggregates must be drawn very close. Hence for detailed investiga- tions aggregates differing only in time are preferable to those differing in space. It is manifest that an aggregate remains essentially the same at different periods, however Theory and Technique of Statistics. 159 it may vary in its parts. The fixed elements remain the same, and hence it is peculiarly adapted for tracing causal connections by statistical methods. Questions which arise from the practical necessities of administration are apt to be such as cannot be solved at once by observations and enumerations. They often deal with the changes which have taken place in the field of the administration, and can only be answered by compar- ing past and present conditions. The investigation requires constant or periodical observations in order to determine numerically the changes which have occurred. In all statistical bureaus a system of providing for future uses has been developed, which far exceeds in extent actual solutions, and forms the main contents of the publications described in §§ 50 and 75. At each point there are certain data which it is considered necessary to collect continu- ously or periodically. In no case do they approach in comprehensiveness the field which the Statistical Congress regarded proper for such statistics. (Appendix II.) The necessary restrictions of the field have already been noticed (§ 50). The great bulk of statistical publications belongs to the class of preparatory statistics. It is profitable to establish rules as to what material is the most desirable under given conditions. Such rules might be called rational statistics. But statistical practice, with its changing needs, is rarely dependent to any great degree upon such a theory. Not only in different coun- tries, but also in the same State, objects of enumeration and the treatment of them are only too often changed according to circumstances. But whatever view may be held in the matter, it cannot be doubted that this phase of statistical activity brings about a peculiar conception and treatment of the material. This must be examined, and its relation to the method of solving statistical problems explained. 160 Annals of the American Academy. § 89. the elaboration of systematic statistics. I The comprehensive labors of statistical bureaus which J /collect data in all fields of statistics for future use may well be termed systematic statistics. Such statistics col- lect material for the problems which experience tells us are the most frequent and important in the history of States. In following these facts regularly the material (§§ 1 and 60) itself becomes of interest. The observation and discussion of a single object is not based entirely on the problem to be solved, but each object is examined to find the best possible and most fruitful investigations which might be undertaken in connection with it. It is necessary to study carefully the phenomena, to examine its causes and effects and their connection, and thus form a judgment as to the nature and practicability of the observations which seem to promise the most information. Thus theories spring up as to how certain branches of statistics, as of population, industries, transportation, and the like, may be most effectively treated. These are ques- tions of methods, but lead also to investigations of the nature of the conditions and changes of population, popu- lar wealth and popular morals, public economy and na- tional strength. This is the reason that a large number I of influential statisticians hold that statistics is essentially ^ the science of human societies (§ 56). In opposition to this view one may justly object that a systematic knowl- edge of human society which did not at the same time include the historical, geograghical, anthropological, physi- ological, and, finally, also the philosophic consideration of it could not be, after all, a science. It can, none the less, be an important subject for instruction. This school of statisticians has produced, however, the practically and theoretically important branches of knowledge which we designate statistics of population, medicine, finance, eco- nomics, morals, and so forth. At the same time we should remember that we already possess a certain body of Theory and Technique of Statistics. 161 facts for each of these subjects. We know certain regu- larities, probabilities, causes and quantitative relations, and principles of determining these relations. If it should be asked how this conception and treatment of the material affect the features of the method described, it cannot be overlooked that, however exact and careful these statisticians have been, the methods of statistics require the same care and exactness for all problems. THE TENDENCIES OF SYSTEMATIC STATISTICS. Systematic statistics has given to statistical processes some peculiar features. Two things could not fail to affect the contents and mode of treatment. First, the observa^ i \ tions are confined to one country and to essentially the same group of objects. Secondly, they are governed not by the special needs of a particular problem, but by general . % considerations which take up the problems in a general \~- way, collecting materials for their solution, but not at- tempting a solution. Confining the observations to one State, and making them continuous or periodical, render almost wholly super- fluous one of the fundamental requirements, the determi- nation of the aggregate and its limits in time and space. These are, then, matters of course. On the contrary, the possibility of future use gives the highest importance to the distinctions between the smaller subdivisions of the State. Even when the problem might be solved by the totals of the entire State a great number of subdivisions is deemed advisable. A large number of subdivisions are made for the enumerators, and while it is not meant that all these are distinguished in the results, it is true of the most important of them, counties, townships, etc. 1 Not only the aggregates, but also the units, are deter- y mined by general considerations instead of special needs. The group of enumerated units is extended in view of their probable causal connection as far as possible without over- 1 62 Annals of the American Academy. burdening the enumeration. The choice is made so as to avoid counting the units of a general nature, and also others which are merely subdivisions of them. The subdivisions are counted so that the sums will give the total. In this manner a more correct enumeration of the qualified units is secured, and at the same time the totals for a larger group of units obtained. These may possibly be important. Absolute uniformity of the enumeration in the time, determination of ideas and organization increases its value for comparison. There is frequently combined with the systematic preparation of the data the calculation of ratios for some of the more usual comparisons. The entire system excels in clear distinctions between aggregate, unit, and ratio, and a plan of arrangement which furnishes easily understood results. This is also reflected in the presentation of the results. The fruit of all these labors are the great compilations of tables, in which the data are arranged with the greatest detail possible, but in which conclusions and definite problems are only excep- tionally included. This form does not, however, warrant any conclusion that there is any difference in principles. All the results, as far as no special questions are to be solved, are to be classed as statistical material (§§ 73 and / 78). It is not the final purpose of the investigations. §91. THE PROBLEMS OF SYSTEMATIC STATISTICS. Systematic statistics has been highly developed, and presents certain phases of statistical processes in a very favorable light. But it cannot be denied that it has done little to promote a correct conception of the real purpose of the process, and hence of the real character of- statistics generally. Its influence may be characterized, theoretically as tending to show that the investigation of I \ the units, and not of the masses, was the object of statis- tical inquiry. This misconception permits of ready expla*- nation. The aggregates have become fixed and appear to ll Theory and Technique of Statistics. 163 be always the same. The group of things observed is apt to be always the same. It comprises the persons and things which have the greatest value for the people and the nation, and which, when investigated, give the best characterization of the latter. These persons and things are in their essential qualities typical, and are so treated in every statistical observation. All that is asked is, Do they exist? and if so, have they certain qualities? In the same manner they are observed in the changes of their mutual relations. And as the result of all observations there appears to be no other result than a certificate of these changes. Hence it is not strange that attention should not be given to the aggregate, which is regarded as a matter of course, but that it should centre in the objects. It may appear to be more important and more useful to base any further investigation immediately on the persons and things. One may discover a gain for statistical processes in permitting an investigation of typical things with refer- ence to their variable elements. Unfortunately this apparently simple and attractive con- ception, however widely held, is inadmissible. For the correctness of statistical conclusions, as well as the appli- cation of results, it is confusing and in most cases danger- ous. It forms a generalization for which absolutely no foundation is to be found in statistics and for which statistics cannot be responsible. No statistical judgment deals with the unit, but strictly and only with the aggregate. The variable elements of persons and things otherwise typical, that are enumerated, are always counted in a specific aggregate and under cer- tain specific circumstances. The qualities of the objects themselves, so far as they are not typical, or the subject of the investigation, are completely unknown. There is absolutely no presumption that these other qualities are typical or permanent in the aggregate observed, and much less beyond its limits. 164 Annals of the American Academy. When the person or thing has no relation to an aggre- gate it is wholly immaterial whether the variable elements are observed statistically or in individual cases. A gene- ralization from them is inductive. If the quality is typical, statistical inquiry is unnecessary; if it is not typical, then it is only known where it is observed, or where a conclu- sion upon observations leads us to expect it upon the basis of probabilities. Even such a general rule that for 20 girls 21 boys are born, does not hold except within the range of the analogy, that is, within civilized States. Whether or not this condition exists in China nobody knows, and anybody who claims that it does places him- self upon an anthropological induction, not upon a statis- tical probability. §92. the form of the question in systematic statistics. Systematic statistics must have as a basis a definite aggregate in solving any problem, and its excellent and elaborate material occupies exactly the same position as any other. This may be shown again by an examination of the form of the question, which is the kernel of every problem. The form of the question is, in the operations of system- atic statistics, as a rule, peculiar. The questions raised in the preliminary observations to the compilations of tables, are not devoted, as a rule, to single aggregates. On the contrary, they discuss the aggregates having the phenom- ena in the greatest and least intensity and the relations between them in this respect. It would seem that with this peculiar manner of dis- cussing the material there must be some change in the nature of the problems arising from it. But closer con- sideration reveals the fact that the general theoretical scheme has not been departed from. One question appears at a certain phase of every sta- 1( Theory and Technique of Statistics. 165 tistical problem. It occurs first in the comparison of analogies. It is the question discussed in §87, of the J I variability of phenomena ; i. e. y the question of the rela- tions of the fluctuations. Upon this is based the deter- mination of the average, the consideration of the minima and maxima, and the entire conception of the progression of the series. This shows that the discussion, when ap- plied to the various aggregates, is only another form of treating the same subject. Any attempt to answer questions upon the basis of this combination will show that it admits of no use for any purposes not derived from the analogy of the aggregates in question. Thus, in the example of § 75, the question is permissible, which district has had the greatest growth of population, or whether it has been greatest for the dis- trict A. But if the question is whether all the districts or the district A have had a large growth of population, these data are worthless, because the question calls for a different analogy. In this case each district separately or the entire number must be compared with these conditions at an earlier period. But if we leave the field of quantitative judgments, w^iere there is a greater measure of freedom, and proceed to the judgment of causalities, it is evident that for the indication of causes we cannot proceed from a plurality of aggregates, but only from the single aggregate, unless, indeed, the plurality is regarded as a whole. The ques- tion why in district A the growth of population has been greatest separates immediately the different districts. It must, therefore, follow that unless the results obtained are to be useful simply in accidental cases, they must form part of some previously arranged problem. It is charac- teristic of systematic statistics that it takes such problems into consideration. To argue correctly and avoid all errors we must go back to the starting-point required by the method ; in other words, we must start from a single } \ aggregate, or what is the same thing, a total of them. 1 66 Annals of the American Academy. § 93. form of judgments of causality and probabilities. The form which the judgment of causality and proba- bility is apt to assume, has also a tendency to prevent the proper conception of the methodical process. It follows from the fact that the labor of collecting the data and preparing the returns for publication is out of all propor- tion to that required to formulate the conclusions arising out of them. Yet these are the final results. As a rule it is quite sufficient to prepare the material up to the quantitative comparison. This enables a specialist to form his conclusion in a short time. Hence a very large portion of the material is collected, and presented to the public in compilations, without any attempt at drawing conclusions. It does not seem advisable to do so until some necessity for it arises. When it is necessary to form a judgment one can seldom wait until some new special material for it has been gathered. By far the greater number of problems which arise must be answered from existing material. The publications of official statistics have therefore the character of store-houses of information. The same *Adty be said of private statistics which offer informati'' a for general use. Such are : Gothaische Genealogische Kalen- dar (§ 18); G. Fr. Kolb, Handbuch der Vergleichende Statistik, 1857; Brachelli, Staaten Europas, 1853; Martin, Statesman's Year-book, 1864; Brachelli, Statististische Skizze, 1868; Legoyt, La France et l'Etranger, 1864; Michael G. Mulhall, The Progress of the World, 1880, and the Dictionary of Statistics, London, 1884. When official statisticians discuss the conclusions to be drawn from data, they are apt to do so in periodicals and in historical or political works. In the bureaus themselves the discussion of such matters is limited to the needs of the organization. Nevertheless, there are statistical problems requiring Theory and Technique of Statistics. 167 very extended and complicated calculations and estimates for the conclusions to be drawn from them. But this does not place them outside of the usual processes. In this num- ber should be classed, for instance, statistics of trade in commodities. The aggregate to be considered is the cus- toms limits, and totals have no other divisions than those of time, where months or quarters may be distinguished. The units are the different articles, which are further distinguished as goods exported, imported, in transit, warehoused, etc. The material is counted by pieces and weight, the results examined and grouped. From this we can compare the different units in time and compare their quantity. A simple change in quantity does not show certain essential matters sufficiently, unless there is some grouping by degrees of quality, and the value of the total of each group determined. This necessitates appraisement by experts, and for this purpose a comprehensive knowledge of prices is requisite with all the difficulties in its application which are pointed out in §65. The statistics of trade are, therefore, worked over in a double way, and are one of the most important tasks of statistics (Gesetz iiber die Statistik des Waaren- verkehrs des deutschen Zollgebiets mit dem Auslande, v. 20, 6. 1879; nebst Ausfuhrungsbest., 2 A. 1885 ; R. G. B., S. 261 ; Central Bl., p. 676; Stat. d. D. R., Bd. 43). Another example, very different, yet very complicated, is to be found in mortality tables. The simplest rudimen- tary forms have been discussed (§ 14). More exact forms give rise to intricate and delicate problems (Appendix VII.). The simplest, as well as the most complicated, is a judgment of probabilities. The combination of the year of birth or the age of the dying with the living persons of a given population, furnishes the probability of death. If one goes a step further, and from a single death table or a comparison of several arrives at the order of death of a large group of populations, we find a statistical regularity. It is not necessary to discuss the similar problems, only 1 68 Annals of the American Academy. slightly less complicated, which might be drawn from the statistics of agriculture, of finance, of trade, or of medicine. The requirements of the technique show also the definite internal workings of the method. V D. THE REQUIREMENTS QF THE TECHNIQUE. I. The Problem and the Plan. §94. THE SEPARATE PHASES OF THE TECHNICAL PROCESS. There are certain distinct processes which are to be observed in the solution of every problem of empirical investigation, and upon closer analysis even in all our synthetical judgments. They proceed from the develop- ment of the idea, to procuring the means of proof, to the examination of the latter, to the answering of objections, and finally to incorporating the result in our general knowledge. In statistical problems these phases appear with unusual distinctness. */ No matter what the statistical problem may be, it must proceed according to a frfjm* It is always a specific ques- tion which may be answered in several more or less ac- curate ways. The end in view and the resources which can be drawn upon will indicate in which manner and within which limits the answer is to be given. According to the choice made, it may be very simple or very com- plicated. But under all circumstances a definite plan pro- viding for all the details is an absolute prerequisite. The means of proof are collected according to this plan. They may be gathered from material in existence or by special observations and enumerations of greater or less compli- cation and extent. The means of proof must be subjected to a critical examination, they must be sifted, errors cor- rected, and compared with known facts. By this prepara- Theory and Technique of Statistics. 169 tion they are ready for use. The question must now be answered and presented in its details, so that it is summar- ized, and yet sufficiently clear to enable an expert to examine the premises. Finally, provision must be made that the knowledge gained shall not be lost. It is neces- sary to preserve not only the conclusion, but, as far as possible, all that leads up to it, for future reference. It is probable that it will be needed to solve future problems. §95. DEVELOPMENT OF THE PLAN. A statistical problem grows out of a practical or scientific \\ need. It is always a clear and distinct question as to some concrete relations. The answer to the question is always the number of times in which certain objects occur in a confused and changing aggregate, and, further, the rela- tions of a quantitative, causal, or probable nature which such objects bear to one another. The answer can only be obtained by comparing the number of objects in aggre- gates of a like nature. The range which remains open for the mode of answer is, as a glance at the method shows, very broad. The aggregate and the purpose of the problem are the only fixed elements. Within certain limits the choice of ob- jects to be counted is free. Theory shows that one unit may sometimes be used in place of another (§81). This is especially true when it is wished to judge of abstract peculiarities or qualities of the aggregate rather than actual phenomena. In this case the objects counted act only as indications, which are to be chosen with reference to the reliance which can be placed upon them. And, further, the characteristics of the object chosen may be clearly distinguished and sharply drawn, or, on the contrary, may be less well defined, giving less exact results. Such characteristics might be chosen because of the facility of enumerating them. The investigation can choose simple or complicated 170 Annals of the American Academy. methods in ascertaining the number. Instead of observa- tion and enumeration, easy or difficult according to cir- cumstances, estimates may be used. The use of estimates, particularly when they are based upon remote probabilities, is almost unlimited. It depends wholly on the degree of exactness required, or which can be considered satisfactory under the circumstances. Finally, the choice of the analogous aggregates to be drawn into the comparison is (§ 74) as to extent wholly at the discretion of the person who is forming the judgment. From all these considerations it follows that statistics is rarely at a loss for an answer to any question which may be put. Yet, in every case, with increased resources it can give a more satisfactory, more comprehensive and reliable answer. The most important question for the expert is whether the material at hand is sufficient for the answer, or whether new observations and enumerations are necessary and appropriate. New investigations require for most statistical problems an extensive organization of officials. As a rule, it is not the statistician who first proposes the question and pro- vides the means of answering it, but the State, corporations, economic or scientific bodies. Hence the plan of investigation depends largely on the means at the disposal of the expert. These means will depend on the judgment of a superior official, who must be convinced of the amount of expenditure necessary to obtain a satisfactory solution of the problem. The decision as to the mode of execution will depend upon the absolutely necessary requirements of the problem, the limit of time allowed, and the greatest pecuniary ex- penditure permissible. When this is determined, it may be considered whether the plan may be extended without interfering with the purpose or increasing the cost, so as to include further data of practical and scientific impor- tance. In any case, the entire plan will depend largely from the clearness with which the estimates of the time Theory and Technique of Statistics. 171 and cost for the different processes can be made and compared. §96. ESTIMATES OF TIME AND COST. Estimating the time and cost connected with statistical investigations is greatly facilitated by the fact that they consist of a repetition of exactly the same process for a large area. In a case of necessity it is practicable to make the enumeration for a small section in order to gain a basis of calculation. The costs of every statistical undertaking are distributed^ over the preparation, the enumeration, and the examina- tion of the results. The preparation includes complete organization, direction, and drill of the enumerators, the printing and distribution of the schedules for their use. The enumeration necessitates payments to the enumerators and other officials for their expenses and their labors. The examination brings with it the expenses for the services of more or less expert officials for the examination of returns, corrections, the tabulations, and in addition the cost of pub- lication. Schedules and publications are estimated by the amount of paper and printing, labor by time, and, besides these, packing, expressage, rent, furniture, heating, light- ing, and attendance, all at current prices. It is easily seen, for an undertaking such as the enumer- ation of population, how many schedules are necessary for 1000 inhabitants, either for lists or for cards. The time for the enumeration, the number of questions asked, the amount of cooperation on the part of those counted, will determine the number which can be finished by an enu- merator in a certain number of hours, and how much time will be required for reading for corrections. The chief point is always the examination. If lists or cards have been collected for 45 million persons, and there are 12 answers for each person, it will be necessary to make and calculate 540 million items. It can by trial 172 Annals of the American Academy. be easily ascertained how many seconds are necessary for a small number of items, and for their addition. Five sec- onds for each item would make 2700 million seconds, or 750,000 hours, or 125,000 days of six working hours each, which finally would equal the labor of 417 men for one year or 139 men for three years. In a similar manner the most complicated estimates may be calculated. Every combination of questions is at least equal to a further question. All necessary reductions must be calculated by the number of multiplications and divisions necessary. Hence one can decide beforehand whether it is not de- sirable to omit certain items, because their consideration would involve too great an expenditure of time and labor. In a similar fashion we may form from the details an accurate idea of the space which the printed tables will occupy. It is absolutely indispensable to form from the start a precise idea of the tables in which the chief results are to be grouped. The number of figures which will be required for each column and the number of columns are easily ascertained, and then the necessary breadth of the table. The number of lines depends altogether upon the number of subdivisions of the chief sum. The number of lines shows the length. Suppose the chief sum Prussia contains figures of 4 to 10 places in 50 columns, in all, for instance, 400 figures; and if this is to be divided according to the 54,000 boroughs, there will be required a breadth of 4 folio pages, and 1000 X 60 lines in length, i. e. t a work of 1000 sheets. The costs of composition and printing would come to about ioo,oco marks, and an edition of 1000 copies would require 2050 reams of paper. In this way it is simple to calculate by figures and pages how far the subdivisions may be entered into when the funds at disposal are limited in amount. What cannot be printed is, as a rule, worthless, and should not be examined or collected. (E. Engel, Die Kosten der Volkszahlung Zeitschr. des K. Preuss. Statist. Bureaus, X. Jahrg. 1870, p. 42; Preuss. Theory and Technique of Statistics. 173 Statistik, Heft XXIX., 2 Halfte Vorwort, p. VIII. ; Erfor- derniss an Drucksachen, Preuss. Statistik, Heft XXXIX., 2 Halfte, p. 50; Kostenanschlag der Berufsstatistik von 1882, Drucksachen des Deutschen Reichtages, 5 Leglper, I Sess. 1881-82, N. 27.) §97. FIRST DRAFT OF THE PLAN. The decision as to the plan to be pursued in solving the problem may favor the use of material already in exist- ence, supplemented by conclusions based on probabilities. It may be deemed advisable to furnish a basis for the conclusions by ascertaining certain data by means of the enquete or enumeration. All such methods are only means of facilitating the complete methodical processes which rest in principle upon enumeration. They are in part explained through the theory and technique of the process of enumeration. In using them one can never feel secure unless in a position to survey all the known data, and to examine whether it is based upon enumera- tions actually meeting all the requirements of the theory. We must in theory have a plan, by which it is proposed to collect the means of proof. The plan when elaborated must provide clearly for the collection of the material, and also for the proper use of it in forming conclusions. For the technical execution of the plan, the utilization of the results is for the present of minor importance. The char- acter of the data themselves will determine their use. CThe first technical requirement is the composition of the regulations for obtaining the actual data, by enumera- tion or other methods. The enumeration is a practical undertaking, the first step in the realization of the plan. Once commenced, it will not admit of change or variation without endangering completely the value of the results. Hence it is absolutely essential that the plan should in- clude a carefully worked-out scheme of the entire process of enumeration. As a rule, the execution of a plan is often 174 Annals of the American Academy. beyond the influence of the statistician who framed it. From it the enumerating official can only draw a few very general conclusions. Hence the statistician should never V [neglect to work out his plan into the last details, so that \ihe himself could, if called upon, furnish all the regulations ^necessary. Only when this is done can there be any * sufficient guaranty of the practicability of the plan. The notion of the aggregate and of the units of enumer- ation must be so clearly defined that absolutely no room for misapprehension remains, and every step of the pro- cess must be carefully prepared in order to avoid confusion. There must be no doubt of the suitability and practicability of the organization. Appropriate provision must be made for the organs of enumeration, the means of observation, and the manner in which the observations are to be pre- served and summarized. A schedule for the enumeration with the necessary explanations and directions must make M unmistakably clear what things are to be counted, what particular characteristics, and what distinctions and com- binations are to be noted. In the same manner it must be clearly understood exactly what result is expected. Hence no plan can dispense with a schedule for the tabulation showing at a glance all the elements which are to enter into the final result. It is only by comparison of these prospective totals with the questions upon the collection schedules that one can see how far the latter are com- plete. This comparison does much to make clear the nature of the whole operation. None of these requirements can be neglected without danger to the plan. The complete contents and final purpose may indeed remain a secret of the expert. But for the public in general there must necessarily be definite regulations for the business of enumeration. (Examples — Statistique des Deces, 1855, Compte rendu general (§ 48), p. 42 ; Statistique du Systeme et des Insti; tutions de Prevoyance, 1855, P- I 5 2 J Statistique des Finances, 1857, p. 245 ; Bericht, betr. Ermittelungen der Theory and Technique of Statistics. 175 landwirthschaftlichen Bodenbenutzung und Ernteertrage, 1871, Stat, des Deutsch. Reichs (§35), Bd. I. p. 102; Bericht, betr. die Statistik der See SchifFfahrt, 1871, Ibid. p. 229; Plan fur die Deutsche Forststatistik, 1874, Ibid. Bd. XIV. p. 52; Vorbereitung einer Deutschen Medizinal- statistik, 1874, Ibid. p. I. 156; Volks und Gewerbezahlung am 1 December, 1875, Ibid. Bd. XIV. p. I. 24, and Bd. XX. Th. I. p. 1, 51; Preussische Statistik, Heft XXXIX., 2 Feb. 1882; Gesetz iiber die Erhebung einer Deutschen Berufsstatistik von 5 Juni, 1882, Stat. d. Deutsch. Reichs, Bd. LIX. p. I. 2, and Neue Folge, Bd. I. p. 4; Centralbl. d. Deutsch. Reichs, 1882, p. 48.) §98. INSTRUCTIONS TO ENUMERATORS. The instructions to the enumerators must indicate clearly the methods and scope of the investigation. It cannot be advantageous to have plan and instructions drawn up by different persons. If the same person composes both, one acts as a check upon the other, and compels the most un- mistakable precision. If, on the other hand, a second per- son issues the instructions, it is clear that he cannot grasp so completely as its author the scope of the plan, and hence contradiction and confusion might ensue. The second person might not have the same feeling of responsibility for the imperfections of the work if the original plan were the work of another. (The instructions issued by the various German States for the carrying out of the census of industry of 1875 : Stat. d. D. R., Bd. XXXIV., Th. I. S. 129 ff.) The instructions require in every case the most pains- taking preparation and supervision. The process is here entirely bereft of any theoretical character which might be seen in the plan. The process acquires a concrete practical form. The logical character of the aggregates and units are not questions for the enumerators. The area is sub- divided into smaller portions, provinces, governmental 176 Annals of the American Academy. districts, tax districts, court districts, city, county, or election districts, districts of registration, districts of chambers of commerce, army districts, and others suffi- ciently numerous. Provision must be made that the limits are not misunderstood or overstepped. In excep- tional cases of common or disputed jurisdiction it may be necessary to come to some conclusion. (Stat. d. D. R., Bd. XIV., 1874, p. I. 24, §9.) The subdivision of time is the usual one of years, months, and weeks. When the condition at a given moment is to be ascertained, the point of time must be carefully noted. V Theoretically, a single instant is desired ; practically, this is only approximately attainable. Hence it becomes neces- sary in an enumeration of population, for instance, to fix rules for distribution and collection of the schedules, for noting the seamen, travellers, the newly-born, and dying, and also for later corrections and additions. (Stat. d. D. R., Bd. I. 1873, p. 75, §§8, 10, 13, 16, 17.) Just as little is there any conscious conception of the unit of enumeration as such. The things themselves are counted — persons, houses, and wares — they are distin- guished by sex, conjugal conditions, age, religion, occu- pation, education ; and as with persons, so also with houses and wares, cultivation and crops, phenomena of the sky, and, in fact, with every object of enumeration. It is, as a rule, the variable qualities of typical things which are concerned. Here are all the difficulties indicated in § 66. The idea which, in the plan, may be very clear, must be expressed as briefly and definitely as possible, yet so as to be com- monly understood without difficulty. This is the labor of the expert, and cannot be relegated to another person. In particular, provision must be made for the manner in which distinctions of measure, size, weight, and value are to be made, and how these are to be applied to the things to be rendered capable of enumeration by such distinctions (§ 65). Further, it is essential to consider Theory and Technique of Statistics. 177 how far an estimate of the aggregate may take the place of the actual measurement of such qualities, or whether estimate may be used at all in place of enumeration. Precise instructions are particularly requisite in. dealing with things which are susceptible only of estimates and not of actual enumeration. (Stat. d. D. R., Bd. XLIII. Th. I. p. 57, and Centralbl. fur d. Deutsch Reich., 1879, p. 855 : Distinctions of wares, and tare percentages in sta- tistics of trade. Bd. I., p. 102 : Estimate of area and crops in agricultural statistics.) All these things are best given as explanations and directions for the use of the enumeration schedule. The body which directs the enumeration immediately or in- directly cannot dispense with instructions covering the entire field, giving necessary provisions for the extent, organization, the initial steps, and time-limits of the pro- cess. When intermediate bodies summarize the results, in whole or in part, a schedule of tabulations is necessary. The directions and instructions for officials and enumer- ators assume necessarily the character and structure of a law or regulation. (Examples, § 95.) They must prevent dubious or conflicting interpretation in all details, and form an objective standard for those who make and those who use the enumeration. Whoever undertakes to carry out the plan or to use the material gained must be careful not to depart from the instructions and the characterizations of the objects given therein. Criticism is directed to the in- terpretation of the contents, and we recognize very properly the ability of the statistical expert in his preparation of exhaustive unmistakable instructions. (Mittheilung der In- struktionen § 21 der Allgemeinen Bestimmungen in betr. der Volkszahlung im D. R., Stat. d. D. R., Bd. I., p. 75 ; Neue Folge, Bd. I., p. 2, § 18.) 178 Annals of the American Academy. II. Enumeration. • § 99. ORGANIZATION OF THE PROCESS. The process is thoroughly concrete. It requires a fixed organization, observations, and the summarization and tabulation of the results. The phases of the process are different according as we make an observation of a fixed condition or a movement. The distinction is to be seen at the outset in the organ- ization of the more important undertakings. If the sta- tistical bureau does not itself undertake the enumeration, it takes place through the agency of various organs of the general administration. Those which make the observa- tions directly are often very various and often difficult to select. The enumeration of a fixed condition, as of population, cattle, ships, etc., must arrange to investigate the entire field in a certain limit of time. The mobility of the ob- jects requires a rapid — as nearly as possible an instantane- ous observation. Close relations to less mobile objects (buildings, industries, farms) lead to the enumeration of the latter at the same time. Hence, such undertakings assume large proportions and require large numbers of observers. They are repeated periodically. In conse- quence they cannot furnish regular employment, and it cannot be avoided that persons without preparation and practice should be employed. Hence there is great neces- sity for some preparation and instruction. The plan has recently been adopted, where the degree of general intelli- gence would permit, that each house-owner or mill-owner, and, indeed, all heads of families should write their own answers upon a list or card containing the printed ques- tions. The enumerator has in this case only a secondary function : he lends his assistance in case of doubt, and merely revises the results. (Stat. d. D. R., Bd. XIV. p. Theory and Technique of Statistics. 179 I. 24, §§ 4-13, 18 ; Bd. XX., p. I., 72, §§ 7-9). The greater the division of labor, the simpler is the work of each indi- vidual. It may, therefore, be possible, as in Germany, to secure this labor from persons who, in consideration of the public utility of the work, do it without remuneration. The chief reliance for the correctness of the data is in any case the good-will and interest of those concerned. Means to facilitate this correctness are good schedules, the cooperation and supervision of experts, rewards which may be forfeited by neglect, and penalties for refusals to make returns or for intentionally false returns. (Reichs- gesetz betr. Berufsstatistik vom 13 Februar, 1882, § 5, R. G. Bl. 9.) Finally, we must include in many cases the self-interest of the participants as members of the com- munity. (Preussische Gewerbesteuerollen, Gesetz. vom 30 Mai, 1820, Ges. S. 133. Gutereinschatzungen der land- wirthschaftlichen Kreditvereine). Observations of movements requiring a much longer time must be made from one or more stations. They have a more complicated character, and are as a rule conducted by permanent and therefore expert observers. (Registra- tion, Tax, Customs, Signal Service officials.) The observation is greatly facilitated when the phenom- enon appears periodically, or may be so observed, as in the case of meteorological and river-depth observations. It is necessary to arrange that, at every point when an occurrence of the phenomena is possible there should be an observer present, whose attention is called to the matter either at once or subsequently. These observers must have fixed districts in order to avoid omissions and dupli- cations, and it must also be determined whether the double occurrence of the same thing is to be noted once or twice. (Statistik des Seeverkehrs, Stat. d. D. R., Bd. L, p. 240, § 5, 15.) In the first case it would be necessary to distinguish each individual by name or mark of some kind (§ 67). In addition to proper organization and supervision, good 180 Annals of the American Academy. results may often be secured by the requirements of the business of administrative bureaus. Such are obligations which must be satisfied by money payments (taxes), regis- tration, which, if neglected, entails fines or other losses (births, deaths, etc., or losses which are to be made good by insurance); finally, also, automatic registers, which require only periodical supervision (meteorological and hydrographic stations). (Examples of very ingenious aids in the organization under the most difficult circumstances are to be found in the census and registration in East India : Report on the Census of British India, 1881, Vol. 3, 1883.) § IOO. THE OBSERVATION IN ENUMERATIONS. The observation is the decisive point of the process. It must permeate into the facts, find the occurrence of the phenomena, make the necessary distinctions, count with- out omission or duplication, so that a correct total may be obtained. The observation is based upon a direct and sub- jective act of perception. Theoretically, the statistical process consists of a succession of such acts with sharp and clear distinctions, but the technical practice assumes a very different form. There is only a relatively small number of investigations in which the enumerator searches for the phenomenon and decides what shall be counted. Under ordinary cir- cumstances it includes only the census of population and domestic animals, and these only in the most primitive form of direct observation. Nowadays, when the owners and heads of families make out the lists there is little for the enumerator to do. The observation is made by those who answer the questions, and is hardly liable to mistakes as to the facts, but only to misapprehension of the ques- tions. In many matters the same person makes the observa- tion who makes the statistical tabulation. But these per- Theory and Technique of Statistics. 181 sons, clergymen, registrars, assessors, receivers of taxes, meteorologists, make these observations independently of the statistical problems, and are led by very different mo- tives to devote a higher degree of attention and care than would appear were statistical considerations the only reason for their labors. By far the greater part of the data, from the simplest to those of the automatic registers, which are useful for statistical purposes, do not belong in the first instance to statistical work. Statistics does not, as a rule, participate in the observation, but makes only a critical examination of the results. Hence statistical instructions rarely devote space to the act of observation. They are concerned more with the proper classification of objects already observed in order to increase their usefulness or statistical problems. Certain phenomena (houses, horses, storms), which can readily be distinguished, may be simply counted by rely- ing upon the memory, and the giving the total for the area or period. Objects of a more variable nature cannot be properly counted without more precise methods. This precision may be obtained simply by rubrics in which each unit when observed is noted, so that the sum of the nota- tions will give the sum of the corresponding units. If we have a special column for female, for single, for married, or divorced persons, the number of dots or lines in each column will give the number of each class. It may be desired to sum up the distinctive' qualifications not alone but in connection with each larger class of units (e.g., divorced women). In this case a direct count is possible only for the larger class and not the special class. The observation of the distinctions would require another sepa- ration. Accordingly, there must be different forms of schedules (§ 68). If qualifying characteristics are introduced in the sched- ules, and the number of each is found, we have a sum- marized view of the observation. The final summarization is not commenced. All these things are independent of 13 1 82 Annals of the American Academy. the source whence the data are gathered, whether from direct observation, from reports of the enumerated, or from the numberless lists required for the ordinary purposes of administration. § 10 1, the observation in estimates. When estimates and calculations are brought into use instead of enumerations, the observation assumes a totally different aspect. The abridgment of the statistical process under certain circumstances by the use of substitutes for enumeration has already been discussed. It is possible, and, in some cases, even unavoidable (§ 69). Theory always requires much the same thing, that is, the determination of the units in the aggregate. Technically the difference is very great if enumeration is employed or a substitute. In one case the estimate attaches to a certain grouping in the condition of the units, which is supposed to be seen, so that in a certain sense the sums are observed and counted. Whether the groups are seen or remembered, in every case a portion of the operation of enumeration is dispensed with. Yet the object is considered directly. Indirect methods may be employed and more liberty allowed in making the estimate. The most common form is the conclusion of probability, already discussed (§§ 83, 86). The known results in analogous cases form the basis of the conclusion which judges the relation of the unit to the aggregate in the analogous aggregates to be identi- cal with that of the aggregate to be investigated, even when nothing is known of the latter but the analogy. Such estimates are of universal application. No one hesitates, when conditions do not change, to estimate the taxes, crops, prisoners, railroad traffic, etc., of a coun- try by the figures of the year before. Condorcet very properly declares that this is the calculation of the healthy human intellect. Nevertheless, he underestimates the im- Theory and Technique of Statistics. 183 portance of complete conformity with the conditions of the method for absolute accuracy. Estimates may also be made without a complete chain of analogies. In those cases where enumeration presents very great difficulties there are not apt to be any enumer- ations for analogous aggregates. Probability cannot be employed where the interest of the problem attaches to the variations within the same individual. Hence, esti- mates can be made on the testimony of experts. The broad field of economic statistics is especially de- pendent upon such estimates. While it would not be impossible to determine by measurement, by enumeration, the area cultivated with the different agricultural products, it would be wholly impracticable. Estimates are usually required from local authorities, who may employ more or less complicated methods. But it is impossible to know by enumeration the harvest by grain and straw, roots, or hay. This would require for each large and small farm, data which the farmer himself could not furnish with any accuracy. For such purposes there is no other resource than the average estimates of experts. (Stat. d. D. R., Bd. I., S. 103; Motive, p. 116.) Similar conditions apply in the statistics of industry and trade. The product of manu- factures and the profits of tradesmen could be enumerated, for they are in the books. But like the tax office, statis- tics must be content with estimates. Even when the ques- tion is asked directly of the producers, their replies are largely estimates or supplemented by estimates (e. g. y Montanstatistik, Stat. d. D. R., Bd. I., p. 302, Bd. XXX., L. 12, 55; Bd. I., Neue Folge, p. 53). Consumption and production, wages, prices charged by mechanics, small traders, carriers, etc., are susceptible only of estimate. The process is apparently most simple, for the expert is simply asked his opinion. But this opinion is the fruit of complicated processes. Unless he can base it upon enu- meration, a direct survey of the groupings or analogies, he must resort to indirect methods. He may find some 1 84 Annals of the American Academy. support in the numerical relations of some other object which includes the object in question, or bears some causal relation to it, or is in some other way symptomatic of it. Experience or experiment will guide him in estab- lishing a relation for the usual connection of the two ob- jects, as, for instance, a relation of the harvest to the kinds of crop, or of the product in a spinnery to the spindles when the area of cultivation and the number of spindles is known. As the application to the absolute total is simple, the main question is often as to the rela- tion. The expert knows by calculation that x distilled liquor tax indicates y mash mass. Hence, he infers that in a given district the distilleries use potatoes of z quality, with / exploitation. Hence, from the amount of tax, he can tell the consumption of potatoes for the given district and period. It is to be noted that his judgment holds good only for the given district and year. Yet in this method there is always a certain definite course which the expert must pursue in his observation. He must give an average relation. He must have sufficient knowledge not only of one or of some cases, but of so many that he may assume, as in the case of probabilities, to have a just appreciation of the fluctuations between the maximum and minimum and of their approximate rela- tion. According to circumstances this feeling may be justified as based upon causal technical or economic con- nections of a very definite nature, and thus the estimate be very accurate. On the contrary, accuracy in the esti- mate may require such a series of observations, that, like an enumeration, all the phenomena in question must be drawn into consideration singly, or at least in groups. This shows the limits of the application of the processes of estimate and enquete (§ 69). It is impossible even from the most accurate observation of single cases, or of a por- tion of the field to be investigated, to form a judgment of the totality of the phenomena or of the entire field, unless it may be shown, and this ought, as a rule, to be proven, Theory and Technique of Statistics'. 185 that the totality of the phenomena and the entire field possess everywhere like conditions and relations. § 102. SUMMARIZING. The result of the observation, by whatever method it may have been gained, is expressed in the number of units found in the aggregate. The summarization must include the sums and all the distinct subdivisions required by the instructions. When, in simple cases, the observer simply gives the total for his district, or they are gathered from his lists, the summarization consists only in the complete total of all the districts. In some cases the units cannot be added in the collec- tion schedules, as they require separation for the distinc- tions. In this case a large schedule in shape of the tabu- lation schedule is prepared, and the data from the lists gathered under the proper titles by scoring for each case a vertical line with the customary horizontal line for the fifth or tenth case, so that the total can readily be obtained. If the distinctions are very numerous this process is very inconvenient and tedious. The paper is large, the proper column must be found, errors are apt to be frequent and the method therefore unreliable. Since i860, therefore, enumeration cards have come into use. They were originally introduced in Italy, and 1867 in Prussia (Zeitschr. d. Preuss. Stat. Bureaus VII., 1867, p. 305) in the following form : For each unit in the collection schedule a card was prepared from the lists giving all the qualifications in the shortest possible form. A further step was to give such cards to the heads of families for them to fill out, one for each member of the household. This was introduced into the general German census of 1871 for Prussia, Lauenburg, Brunswick, and Hamburg, through the efforts of Engel. The simplification of the clerical work has led to its use in various fields (Stat. d. D. R., Bd. 1 86 Annals of the American Academy. II. p. 112; Nessmann, in Zeitschr. d. Preus. Stat. Bureaus, i8;i,p. 271). With the cards the distinctions are summarized simply by placing cards with like data in piles, and then counting the cards. In this placing and counting it is easy to attain great manual dexterity. Each pile can now be used for any number of other distinctions. The more numerous such combinations the greater must be the economy of time and cost which is gained by cards in preference to the older method. (Appendix IV. shows seven comparatively simple combi- nations as to population. Including the ten columns omitted for women, it would require in an ordinary schedule 823 columns to be filled and counted. In these there would be for every 1000 persons 9000 entries. By the card method a single sorting and counting for each combination, i. e., by sorting and counting 7000 cards the same result can be obtained more accurately and in one-third of the time. The explanations in the Appendix show how the cards are to be grouped and counted, after which counts they are to be thrown together again.) As is shown by Appendix V., cards may be made which give not only the sums by counting them off, but which also give the sums in such a way that by placing one over the other they may be added up without further additional writing. In all summarization, from the simplest to the most com- plex, the rule holds that no opportunity should be lost to prove the results obtained. The figures should be so arranged that sums of certain lines when added give the same results as the sums of certain columns, and thus all error avoided. (See Appendix IV.) The grand total gives the final results as to the aggre- gate enumerated. It must always be looked upon as a desirable elaboration of the result when the aggregate is divided (§ 90) in the summarization into as many as pos- sible appropriate portions. It has already been seen (§ 74) Theory and Technique of Statistics. 187 that such portions have the value and character of smaller aggregates, only when in them exactly the same units have been observed as in the general aggregate. If there are 1 data which do not unite to form aggregates, they are important only as accessory numbers for calculations. Every complete summarization needs, according to the (^ requirements of the theory, an explanatory statement as to the instructions, the mode of carrying them out, the effect of any deviation from the rules, and the presumptive de- gree of correctness of the result. This is necessary for the critique. The latter can be much more effective when the original data are given. (Preuss. Statistik, Heft XXXIX., 2 Februar, 1882, p. 65 ; Gutachten der K. Bezirksverwal- tungsbehorden, Stat. d. D. R., Neue Folge, Bd. I. p. 53; Montanstatistik Bestimmungen, § 5 et seq.) III. Examination of Returns. Qp § IO3. EXAMINATION, CORRECTION, AND CRITICISM OF THE RESULT. The examination of the returns is necessary in order to assimilate the matter to the plan, so that the conclusions necessary to answer the question may be drawn from it. It requires that the result of the new enumeration be\ critically examined and ascertained exactly, that the anal- ogous aggregates suitable for comparison should be ex- amined and arranged for that purpose, and finally that the results be reduced to ratios. The basis of all further discussion is the degree of ac- curacy which may properly be ascribed to the results of the enumeration. It is indispensable therefore to determine from the standpoint of the most rigid practical statistician whether in reality the process has conformed to the plan and instructions, whether also the instructions issued have entirely agreed with the intentions of the plan; further, 1 88 Annals of the American Academy. whether the organization and capacity of enumerators and experts was adequate to a proper and reliable observation, and finally, whether, in counting up, no deficiencies and ambiguities have crept into the result. It is necessary, as far as the material allows, to test the clearness of each return and the mathematical accuracy of each calcu- lation. Besides such formal investigation there must be a con- tinuous and attentive criticism of the figures, testing at every step their probability. A basis for such compari- son may be found by calculation from typical relations. Within the results of the same enumeration a careful sifting of the matter will show deviating relations which were to be expected, and also concentration or scarcity for which there is no explanation. Finally, the compari- son with the results for earlier years, or for analogous aggregates, even those only remotely related, leads us to be sceptical of particularly large differences for which no reason is apparent. Such matters must be cleared up by subsequent re- search and the mistakes corrected. Any subsequent enu- meration which may be necessary for such corrections must obviously take place with reference to the same period as the chief enumeration. (Stat. d. D. R., Bd. I., Neue Folge, p. 2, § 12.) Unquestionable errors can only be omitted; or, when no other means are at hand, be removed by proper explanations. After careful application of all these sifting processes it remains to ascertain the totals which are to be considered the final results. Errors are in any case unavoidable. It has often been proposed to express this in. the numbers themselves by giving only round numbers. Without doubt the feeling of security is increased by using only the unquestionable figures, e. g., the first three places of every number. This would indicate that possible mistakes were considered as less than one per cent. But even if such percentages Theory and Technique of Statistics. 189 could always be given, the correctness of the number would obviously not be enhanced. Rounding-off the numbers always brings an increase or decrease, and the actual number seems preferable to this, and has greater probability. Nevertheless, as already shown (§ 70), a judgment must be made as to the presumptive possibility of error in order to use the number's at all for the present problem. How far this may be necessary for other problems should, unless the possibility of error is very small, be definitely explained and recorded for the future student of the material. Up to a certain point it is necessary to accord a certain amount of credence to the authority of the expert who prepares a statistical investigation. He should therefore be fully alive to the responsibilities of his position. § IO4. THE COMPARISON WITH ANALOGIES. When, possibly after considerable labor, the numbers have been obtained, no further progress has been made than the indefinite description pointed out in § 73. There is as yet no fixed method by which a judgment may be formed until a comparison with other and analogous aggregates has been made. The comparison is the same, no matter what kind of judgment the problem requires. Preceding paragraphs (§§ 82 and 86) have shown that all probability depends upon previously ascertained causality, and this upon quantity. Hence, whatever the ultimate end may be, the first step in drawing conclusions from the data is a judgment of quantitative relations. Yet this first step is partially conditioned by the ultimate purpose. Every series of analogous masses in which like units have been counted will enable us to establish quan- titative ratios which are unimpeachable in their form. They may have a value for certain judgments. For this reason caution is needed in using the large mass of the 190 Annals of the American Academy. systematic material described in §90. While ratios and comparisons are frequently prepared for the aggregates and units of these comprehensive schemes, it should be remembered that a slight variation of the question (§91) often suffices to change the analogy completely and render the former comparison useless. In a special problem there is always a special question which must be precisely stated and clearly comprehended. This shows where we must look for the materials for the comparison necessary in quantitative judgments. Unless complete agreement in the analogy of the masses is se- cured the agreement of the units will not fit them for comparison. Whether the analogies belong to a large number of simultaneously counted aggregates or are drawn from widely different periods or localities is of no consequence, either for the underlying idea and method of comparison or for its technical treatment. If quantitative relations may be judged from such com- parisons the second question of causality may perhaps be answered. It requires for its conclusions certain additional independent premises, for which the analogies must be found, examined, and compared, even though they may exist in the same aggregate. In similar fashion the judg- ment of probability or regularity requires a third technically distinct arrangement of the problem. Each of these forms corresponds to a certain syllogism. They depend upon the enumeration of exactly the same units in entirely analogous aggregates and upon sufficient accuracy in the process. They all need critical examina- tion of the results. This examination must go over all the points which would be important for a new enumera- tion, and must test particularly whether the method of enumeration or estimate, applied possibly with a totally different end in view, does not contain too large a margin of error for the problem in hand. However large or small the group of analogies applica- ble to the comparison, it should always admit technically Theory and Technique of Statistics. 191 of a systematic review, in which the aggregates and units, with their distinctions and their limitations, and with their totals, should clearly appear. § IO5. REDUCTION TO RATIOS FOR COMPARISON. Once decided that the aggregates and units are capable of comparison, the only further step is to reduce them to common terms (§ 76). For each comparison the series in which the maxima, minima, and fluctuations may be rec- ognized and the average made, can only be derived from the same measure. This reduction is a purely arithmetical operation, and it is entirely immaterial whether the final purpose may be a judgment of quantitative relations or a search for causality and probability among more complex conditions. But it is an essential factor, a connecting link between the ma- terial and the solution. As a rule, all these reductions determine the number in which the units are found on an average in equal divisions of time or space, or how many units of one kind are found for a fixed number of another in the aggregates compared. The mode of calculation in the principal cases has already been indicated in § j6. Very complicated calculations may be necessary in these reductions. Theoretically all ele- ments of the reduction, e. g. y the area of the aggregates, must be collected with the fundamental material. This is not always the case in fact, for it may be necessary to make a special inquiry for certain elements to make the reduc- tion complete. Technically this is important, as it is not probably the concern of the usual organization (§ 99), but requires a special process to be united, as a rule, with the labors of the statistical organs. Such special inquiries are all the more necessary, as it is not always easily foreseen what points of view may be most suitable for comparison in conclusions of causality 192 Annals of the American Academy. and probability. In some larger undertakings (production, trade, and similar subjects) series of units may occur, some of which are noted by weight, some by piece, some by measure, and which can be compared only when reduced to value or some other common term. Thus arises the necessity of the determination of price, value, or other matters, the possible intricacy of which was indicated in the allusion to the statistics of trade in § 93. The similarity of the units may be so conceived, that though obtainable from the material, they may require very extensive calculations. An example is to be found in the death tables mentioned in §93, when the problem is to compare the average life of the populations of differ- ent States and periods. A similar case is the comparison of different districts with reference to the medical aid within the reach of each inhabitant. (Stat. d. D. R., Bd. XXV.. 1877, § 57-) Even when these complicated methods do not enter into the question, the reduction of a large number of totals may require a multitude of multiplications and divisions, and involve the expenditure of a great deal of labor. Hence various technical devices are employed to facilitate the work. Multiplication tables are useful when the same figures are used often as multipliers or divisors. For variable figures the Calculation Tables of A. L. Crelles (1858), " which save all multiplication and division of figures less than 1000," are of service; also tables of logarithms, with seven figures (v. Vega, Bremiker), or five figures (Bremi- ker, Albrecht, Schloemilch), or even four figures (Witt- stein). Calculating machines render good service. Various constructions have been tried ; the most satisfactory is the Arithmometer. It was invented by Thomas, of Strassburg, in 1820; produced at a moderate price in 185 1 (240 mark), and has since 1880 been quite generally adopted in the more important bureaus.' Theory and Technique of Statistics. 193 IV. The Presentation of the Results. § 106. requirements of the presentation. Whoever has examined the material, and compared the analogous aggregates after their reduction to common terms, is in a position to give, if possible, a solution of the problem. The ratios show at once the quantitative relations for the aggregate investigated, what causalities may be considered as predominant, and in what number the phenomena are to be expected. On the basis of these simple mathematical relations the statistician is frequently able to solve at a glance many statistical problems. This depends, of course, on the na- ture and accessibility of the material. No scientific propo- sitions can be based on the conclusions of a single observer, however capable he may be. The specialist is often able to answer the questions from his general knowledge of the premises, and frequently he would hardly need the reduction to ratios. But if his labors are to be beyond question, and to have lasting value, he cannot omit to present his material and the whole process of proof in such a way that any sufficiently informed person might convince himself of the correctness and reliability of the conclusions, and find the solution himself. This presentation is essentially a report on such portions of the process as may be necessary to establish the proof and furnish the means of testing it. The facts must be brought out as completely as possible, so arranged as to show their connection with the problem. The entire means of proof should be exhibited, and with them the calcula- tions upon which it is based. The wealth of material even for the most ordinary problems would make de- mands almost impossible of fulfilment in meeting these requirements, were it not that the method of statistics furnishes peculiar simplifications whose importance seems to be scarcely adequately appreciated. 194 Annals of the American Academy. The strictly logical character of statistical investigation permits the presentation of statistics in an admirably clear and simple form. Statistical investigation deals with real facts, but by mean's of familiar ideas. On the basis of these ideas it measures, sifts, and systematizes the object investigated. Nothing not included in these ideas attracts attention, and just as the scheme groups the ideas with their distinctions, their species and genera, so the conclu- sions can also be similarly collected. Nothing in the ideas is changed. All that is new is the number of things corresponding to each found by observation. Hence a special form for statistical proof is possible which presents with the utmost precision and brevity the enormous num- ber of varying qualities which have been ascertained. This is done by representing the logical interdependence of the ideas in the manner of presentation. This gives rise to tabulation and graphical representation. § 107. TABULATION. The tabular presentation gives a complete account of the entire process by giving concisely the results of each step. The table gives briefly the ideas outlined in the plan. The tabular system is best applied when the hori- zontal lines are devoted to the aggregates, the vertical columns to the various units. The various aggregates are named at the beginning of the line, the units at the head of the column. When the meaning of the terms used to designate the units needs further explanation, a note containing extracts from the instructions serves the purpose best. The numbers for units of the same sort are therefore placed one above the other. There can be no doubt of the meaning of the totals, and the eye detects differences readily in the figures where units, tens, hundreds are in the same vertical line. If reduced to ratios, the latter may be introduced into parallel columns of the same Theory and Technique of Statistics. 195 scheme, and the comparison made without further effort. It is useful also to place in the table the area or size of the aggregates, and this occurs generally in the column im- mediately after the names. Logically also a fixed portion of the area is like an enumerated unit, and the total area a total of enumerated units. All columns except those containing ratios furnish totals. These are the total number of the units of the same kind found in all the aggregates compared. Brought into a ratio with a total of the sizes, we have the average of the ratios by which the individual ratios may be measured. In the same way units which form part of a larger unit may be compared, and the percentual relations of their totals to the total of the larger unit determined. All tabular presentations have similar contents. It is only a difference of form when the aggregates are in the columns, the units on the lines, but it is not so clear. The case is different when the aggregate is divided by position and size on the lines and by time in the columns. In this case the table can only include the figures for a single unit. In like manner the columns may be occupied by various units and the lines by their distinctions, or the reverse. In this case the table can only include a single aggregate, and the comparison is more difficult, as each aggregate needs a separate table. Such tables, however, show more clearly the influences of changes in the aggregates and the special relations of the same units. § 108. GRAPHICAL PRESENTATION. Graphical presentation is a modification of the idea under- lying the tables. It uses geometrical instead of numerical methods. It often shows the results in their geographical distribution instead of merely naming the sections as in a table. The object is to gain greater clearness and simplify the drawing of conclusions. It is perfectly clear that, for every unit or 100 units, a 196 Annals of the American Academy. point, a line, or a small surface might be placed in the system of coordinates. (Appendix VI. b. c. a.) If the number is to be expressed by a line, it is, as a rule, measured upon a vertical line from a fixed horizontal line, and for the sake of greater clearness the points are united. One can distinguish subdivisions of a larger unit by differ- ent color or shading of the proportionate part of the line or surface. Instead of drawing the lines perpendicular to a fixed line, they can be drawn from one point as radii and the surfaces may be colored. Surfaces may be indicated in squares, and shading or coloring be employed to indicate subdivisions. In each square a system of coordinates may be placed. But the further this goes the more the simplicity which is the prime object is lost. All such methods of indicating sizes are called diagrams. Hexagrams and chronograms are similar plans of show- ing the intensity of a phenomenon at various periods of time, by the rise and fall of a curve within a system of coordinates expressing a measure and time. If this occurs in an automatic register, observation and representation take place simultaneously. But the hexagram may also be constructed later. A chorogram is the result when different aggregates are indicated by surfaces, showing the size of each, and por- tions of the surface are colored or shaded differently to indicate the result of the enumeration in each aggregate. It can be profitably employed to show the different degrees of the occurrence of a single phenomenon in different aggregates. Cartograms are representations in which the geographi- cal map shows the totals or the ratios of the different units by various inserted diagrams and hexagrams. The dia- grams may here show a certain number of distinctions, but the limit is soon reached. (G. Mayr: Marey, § 57.) In recent times solids have been used for these purposes. They have the advantage of three dimensions instead of Theory and Technique of Statistics. 197 two. But the difficulty of constructing them, reproducing and preserving them, make an extended use of them impracticable. (Perozzo, § 57.) § IO9. DEMONSTRATION OF THE QUANTITATIVE JUDGMENTS. The demonstration follows almost mathematically from the presentation. It is based upon the certainty that an analogy exists between the aggregate which has been in- vestigated and those with which it is compared, and that in all of them the things in question have been counted or estimated sufficiently accurately. This must be beyond a doubt, or else any further step is impossible. No one should omit to elucidate the means of examination by an explanation of the plan, of the instructions, the results, and the possibility of error. Under the supposition that all requisites are complied with, the aggregates and the totals of enumerated things become merely quantities whose concrete character is not drawn into consideration. Conclusions are based on num- ber and measure, on the mutual connections and relations of these comparable quantitative notions. The regular statistical process advances from the de- scriptive material to a judgment of quantity, of causality, and probability. Practical demonstrations must follow the same course. In each special case it is a question at what point the problem in hand receives the solution desired. Circumstances may make the path longer or shorter, but its direction is always the same. The demonstration finds a like expression in every ex- ample, but is perhaps clearest in the graphic presentation.. For our explanation a case in which, as in Appendix VI.,, prominent extremes occur, will render the most efficient service. Suppose that for the investigation presented in Appendix VI. attention were called to the phenomena of the week ending June 10, 1876, in the city B, and that within the limits of time and space thus indicated, the 14 198 Annals of the American Academy. deaths be considered worthy of special observation. We find in the delineation of the problem in column 23 not only the unit d, deaths of all kinds, but a number of others which have been subject to observation and enumeration. Such are in the first instance parts of the unit d specially noted, as i deaths of children under one year of age, / deaths from zymotic and epidemic diseases (typhoid fevers, dysentery, diphtheria, measles, etc.), and finally as a sub- division of the last, m the deaths from measles alone. Other contemporaneous phenomena are also observed, evidently with the idea that they might have some con- nection with the deaths. Such are : a, the rainfall ; b, in- tensity of the wind, and c, the direction of the wind; e, the atmospheric pressure ; f, the atmospheric temperature; g, the level of flowing water ; h, of subterranean water ; and finally, k, the price of rye. That the winds, observed three times daily as to direction, and the price of rye are not observed specially for the week in column 23, but only for the month of June, is a defect. These data refer to a larger aggregate, the portion of which belonging to the aggregate 23 cannot be determined. Yet it must be assumed that any possible connection between the aggre- gate 23 and these factors is to be considered sufficiently characterized by the figures for the month. It needs no further explanation to demonstrate that from the total d, observed for the aggregate 23, or from the sum of the units a to e t no one could know whether they were large or small. This question could only be answered by comparison with the aggregates 1 to 52. Here it is clear that it is a question of the place of the week June 4- 10 in relation to the rest of the year. If one wished to compare the week June 4-10 with previous years in the same city or of other cities in respect to the units, the analogy would be quite different, and hence also the standard of com- parison. A survey of the unit d in the various aggregates to be compared shows at once that 23 has the maximum num- Theory and Technique of Statistics. 199 ber. The final column shows the average for the year. By extending this average line across the page the fluc- tuations to each side would be apparent. The question of the quantity of the unit d in the aggregate 23 may be answered, therefore, by saying that it exceeds the average by nearly half; that like extremes occur only in the aggre- gates 31 to 34, while, as a rule, the fluctuations including those toward the minimum are much smaller. In a similar manner the other units may be measured by reference to the standard given by the average for each, noting the deviation from the mean. Thus, it ap- pears that in 23, besides d, the units a, 5,/, i, /, and m occur in unusual strength, whereas the deviation from the average for the units c, e, g, h, and k is scarcely appreci- able. This is the basis of an exact, if not very far-reaching judgment as to the quantitative relation of the units. The treatment of the material could not differ essentially if the aggregate 23 represented a year of large exports, a district with large or small crops, or any other field of observation. Whether the data for the various aggregates are the result of systematic statistical efforts collected for a special purpose, possibly even by means of estimate, would not, apart from the possibility of error, affect the mode of rea- soning in the slightest. Nor would it be changed if instead of a single aggregate the entire field were the subject of the judgment (§ 90). § 1 10. THE DEMONSTRATION OF JUDGMENTS OF CAUSALITY AND PROBABILITY. If the problem is not limited merely to quantity but includes also causality, the demonstration must consider the different sets of phenomena in turn. Suppose the question to be the cause of the extreme phenomena of the aggregate 23. One might at first look for k, the price 200 Annals of the American Academy. of rye, which might possibly indicate scarcity of food, and if so a probable cause of high death-rate. A close exam- ination excludes this presumption entirely. The price of rye is subject to slight variations, and it is observed that in the aggregates compared the mortality is lowest when the price is highest. The influence of epidemics is a possible cause. But the unit m does not prove it. It does show the maximum of deaths from measles, which may be considered epidemic. It shows the relation of this disease to all diseases of the class. The deaths, /, caused by epidemic and zymotic dis- eases, have, apart from the deaths from measles, a compara- tively uniform and slight relation to the general mortality from the beginning of January to the middle of July, and again from the middle of September to the end of Decem- ber. It is only for the aggregates 29 to 35 that an exces- sive increase of the zymotic and epidemic mortality is noticed, but it is observed that measles have no part in it. If, however, we consider the causality of the sum m for the sum d in the aggregate 23, it is plain that m, mortality from measles, gives no satisfactory explanation. Thirty- six deaths in m subtracted from 235 in d, leave still 47 in excess of the average 154, a difference almost equivalent to the extreme minimum (154-93). Further explanation is necessary, and it may, perhaps, be found in the infant mortality. With an average of 62 it shows in 23 the large number of 102. But it is com- monly known that measles are fatal chiefly to children. If we subtract the mortality from that source we find that the infant mortality has not appreciably increased. Instead, therefore, of special influences, we must look to more general climatic relations. From the units g and h t which indicate the humidity of the soil, it appears that there is no reason to suppose miasmatic influences, which would have shown themselves in an increase of zymotic and epidemic diseases. The subterranean water at 47.8 dm. above low- water mark is higher than the average, 46.2. Theory and Technique of Statistics. 201 This, with the flowing water, which at 59.9 dm. is higher than the average, 50.5, prevents the dangerous drying-up of the ground. The atmospheric pressure e is evidently indifferent, as it corresponds exactly to the average, 331, Parisian scale, or 29.397+ inches. 1 Observing the direc- tion of the wind, it is noticeable that no southwest wind occurred, yet the others are all in about the average pro- portion. Of more weight is the fact that, as shown by b t it was less intense than in the other summer months. On the other hand it is not markedly below the average. The rainfall, a, of the week 23 is slight, only one-sixth of the average. But it can scarcely be looked upon as a cause of sickness, for though the preceding week had only one-third of the average, the one before that had had a precipitation of three times the average of 9.3 Parisian scale. Among all the elements prepared for this investi- gation there remains only the atmospheric temperature. This does, indeed, show very extreme conditions. The weekly average is the highest of all. The maximum of 23. 9 R. is only once exceeded, in the 30th week, which shows 26.2 R., and the minimum of -f-io.6° R. is only a little less than the minimum of week 30. A peculiar feat- ure is that the high temperature was developed very rap- idly from a comparatively low one. In the middle of May the mean temperature was less than the yearly average — the minimum was — 1° R. and the maximum only -f- 12.2 R. Hence, the change was very sudden. The effect of this abrupt change seems to be indicated by the increase of measles. This investigation would evidently be defective if the in- ductive or experimental knowledge which has been called in so largely to furnish premises could point out any other more probable general or special circumstance as the cause of the increase of mortality in the week in question. It would then have been necessary to measure these influ- 1 In the Parisian scale 405.3425 =36 inches. 202 Annals of the American Academy. ences by enumeration either directly or by means of symptoms. If a critique does not indicate such circum- stances, it must be admitted that the quantitative relations adduced in the presentation clearly show the rapidly in- creasing temperature to be the cause of the great mortality in the aggregate 23. It is perfectly clear that the material which is prepared for such a proof of causality is capable of furnishing other similar proofs. The Appendix VI. shows in the extremes 31 and 34, already mentioned, another easily perceptible causality. A general view of the course of the lines shows that here the zymotic and epidemic diseases are the cause, and more precisely, among children under one year. In spite of the enormous increase of the mortality, the deaths of those of more advanced years show great regu- larity from the week 24 to the end of the year. All fluc- tuations in this part of the year are caused by the infant mortality, which is zymotic — epidemic, yet not attributable to measles. We must exclude as a cause of the fatality of disease in 31 to 34, apart from dearness (k), also atmos- pheric pressure (e) and wind (b, c). On the contrary, the subterranean water (k) shows an obviously unfavorable status. It has sunk from a level above the average to 2 dm. below, and at the same time the flowing water shows the lowest position, 2 dm. below the level of the subterranean water. Dangerous miasmas are highly probable. Never- theless, the first extreme of high mortality precedes this sinking of the water-level. Yet the second extreme may have been partly due to this cause. Again, the chief cause appears to be the temperature, rendered less endurable by long drought and feeble winds. The deaths are distin- guishable from those of the week 23 in having a zymotic and epidemic character, but without measles. Besides these causal connections the presentation illus- trates in the 34th week another. It is in the obvious reason for the remarkably rapid decrease of zymotic and epidemic mortality, which with the infant mortality sinks Theory and Technique of Statistics. 203 in the three weeks 34, 35 and 36, the greatest extreme, to a point below the average. The reason is the excessive rainfall of the week 34. The temperature does not seem to have been cooled off enough to account for the decrease. The explanation is the direct purification of the atmosphere and the closing of the pores of the earth by the great amount of rain. If it is possible by such means to arrive not only at a negative result, that causes cannot be proved, but, in spite of the highly hypothetical character of the conclusions, to reach a satisfactory positive result, there is no need of any special demonstration that it is possible and desirable to pursue the matter further to conclusions of probability. Under like conditions for two aggregates, a cause proved to , be operative in the one may properly be supposed to cause the like effect in the other, and its intensity may be meas- ured by the intensity of the effect, compared with analo- gous aggregates. No one can doubt that an increased dry heat will increase the fatality of sickness, or that sharp and continuous rains will purify the air more effectually than weaker ones. According to the nature of the causal connection and the thing in question, the expression of such a relation in a definite number is more or less ven- turesome, yet if it is a question of using it statistically it must be done, always making ample reservation for the possible margin of error. With properly prepared mate- rial this is always possible. The entire presentation deals with definite quantities, and a relatively most probable quantity can, of course, be calculated from them. The causality in Appendix III. shows that with rye at 9.6 mk. a hectolitre, an average of 861 marriages per 100,000 in- habitants is the most probable for the four countries. By interpolation, according to the scale of absolute fig- ures, the most probable number can be deduced for other rye prices, provided that with such defective material as the determination of price can (§ 65) furnish, they may seem to have value. To develop from probabilities the 204 Annals of the American Academy. regularities cannot be considered the concern of the single problem and its proof. § III. CHARACTER OF THE SOLUTION. Presentation and proof furnish the answer which is the solution of the problem. The importance of the solution must not be overestimated. The peculiar processes of statistical methods fix very definite limits for the result. The problem requires an observation from a certain point of view of a variable and confused aggregate, definite only in its limits. Corresponding observations were made in similar aggregates. Whether the question concerns a single aggregate or a great number making up a total is wholly unimportant. It is only essential that the observa- tion should be made with the use of the same logical premises. These observations furnish the basis for all conclusions which have facilitated in any way the solution. Hence, it is clear that the latter is limited, as already seen (§91), to these fundamental premises. It rests strictly within the definite boundaries of time and space of the compared aggregates and of the characteristics of the things ob- served, forming the units of enumeration. This holds also in the field of probability. It cannot extend beyond the limits traced by the conditions. This limitation fol- lows, as a matter of course, from §§ 82 and 86, for proba- bilities are only a species of proportion, where three known factors furnish a fourth. In like manner every- thing claiming to be a regularity is, as explained in § $6, always dependent on the analogy of the aggregates. Rules for the occurrence of qualities of things may be estab- lished inductively and experimentally with more or less precision, and the mutual relations of different things may be marked out. Such rules are derived from the general nature of the things, as shown by observation and experi- ment. Such a rule is not statistical. Statistics can only Theory and Technique of Statistics. 205 be based upon the fact that a given combination of things has been observed under like conditions in a great number of aggregates, and hence under essentially unchanged conditions the same combination may be expected in an- alogous aggregates. Where definite concrete things, such as cultivation and crops, trade, transportation, finance, tax statistics, and the like are concerned, this limitation is at once apparent. But in problems of a somev/hat more abstract character the tendency to generalize is always dangerous. For the validity of a rule the confirmation of numerous examples is more decisive, but the presumption of a regu- larity appears admissible from such problems and presen- tations as Appendix III. In this problem the price of rye is properly taken as a symptom of the cost of daily sub- sistence, and the rule is that cheap bread renders marriage easier. But whoever would conclude, for instance, that with 900 marriages per 100,000 inhabitants cheap subsist- ence, and with 700 dear subsistence, were to be inferred, would entirely overlook the fact that the question, whether the average 861 marriages per 100,000 inhabitants was many or little, was at the most answered only for the four states in question ; that for other countries they furnish no stan- dard. That the price of rye is not claimed to be a standard for the cost of living in remote lands hardly needs to be mentioned. Anyone who would conclude from the decrease of the price of rye, an increase for example of marriages among peasants, might be taught exactly the opposite by actual enumeration. The problem concerns only the total population, and does not indicate how the price of rye may affect single classes. That no characteristics of the unit may be changed, that none may be neglected and none added, and that every more abstract or general conception includes such change, is more obvious. Much difficulty arises, for instance, from the use of the term city instead of city district, in enu- merations of population and the like. 206 Annals of the American Academy. Just as little should the great importance of the solu- tions obtained be underestimated. The entire history of statistics is a steadily increasing testimony to its useful- ness and indispensability. Its utility has been shown only within the limits in which alone it can be true. It is no fault that it cannot fulfil demands and expectations which have no foundation in those simple and logical premises which should be clear to everyone. Its methods and technique have always been aimed at the mark of reliable observations. Every empirical science seeks to increase its treasure, and each finds it, in spite of progress, poorer than desirable. Like the controversy of 1806 (§27), it would only be an illusion to see in this limitation of sta- tistics an abandonment of ideal aims. The demands of that day were simply that the judgment of statistical ag- gregates might not be extended to combinations of phan- tasy until it stood firmly on the ground of measured facts. V. Preservation and Application of the Results. § 1 1 2. COLLECTION OF THE RICHEST POSSIBLE MATERIALS. The last requisite of statistical technique is the proper preservation of the results attained in the treatment of statistical problems. The solution of every scientific problem is of permanent value. It does not disappear with the immediate occasion for it, and so statistics must furnish lasting achievements for the further development of systematic knowledge. This is all the more indispens- able in statistics, as its technique requires so frequently the use of earlier results, which cannot be obtained by subsequent inquiries. This demand may mean preserving the original mate- rial ; i. e., the original lists, schedules of arrangement, and collation, with the necessary explanations (§ 68), and in many cases this must suffice. But the purpose can only Theory and Technique of Statistics. 207 be satisfactorily obtained by printing. Only by such mul- tiplication of the results obtained is a proper use of the material possible, a comprehensible and handy form at- tained, and the occasional whole or partial destruction with which manuscripts are always threatened averted. The presentation (§§ 106, 107) takes into consideration the printing with reference to the contents and form. With the publication the work becomes public property. Just as with the collection of the material, so with its preservation, systematic provision has very fruitful results. The useful results of one's own investigations, as well as those of other persons and other periods, are collected, and placed in readiness for possible use. So far as practicable, scholars and scientific and private institutions should attempt this for the material in which they are in- terested. But it is the province of the State, which in the nature of things has far the greater number of statistical needs and functions, to provide also for the preservation of statistical material. There are some general maxims to be considered for the organization of these official collec- tions of materials. §113. THE ARCHIVES OF OFFICIAL BUREAUS. Each State endeavors to build up a system of official statistics, as explained in § 88, which shall be appropriate to its own conditions, as extensive and as logically con- nected as possible. At the same time the official bureau must endeavor not to lose any statistical results which are carried through by correct methods and are capable of critical estimate. This must extend to private statistics and the more important publications of foreign States. It is necessary in the first place that the appropriate ma- terial which may exist at home or abroad should be known to the bureau. The greater part of the statistical publica- tions does not come into the book trade, or excites so little attention that it is not noticed in advertisements and 208 Annals of the American Academy. catalogues. The reason is the very general custom of exchanges between the various institutions, which has the effect that few copies are sold. It would be wholly unde- sirable to change this. But attention must be given first to such publications as are not exchanged, and second to the regularity and extension of the exchanges. Instruc- tions to the various public organs to send in their publi- cations may be necessary. At the same time the purchase of works of reference and compendiums upon all branches of economics and technology, technical dictionaries and lexica of foreign languages, also copies of statutes and regulations, and particularly of the best and most complete topographic charts, is indispensable. This material in- creases from year to year in bulk, and the older material has lasting value for statistics. Provision must always be made for an appropriate space for the reception and classi- fication of the material and its storage. Not only the collection of the material, but provision for its easy accessibility, is very important. Catalogues should include not only the title but also the main points of the contents, which are often very much mixed and dissimilar in the same work ; also the more important essays, and so forth, that they may be easily found. (Preussisch. Statist. Bureau, Katalog, see § 50; Zeitschrift, Jahrgang XX., 1880. Beilage.) The less the official statistician is, as a rule, in a position to draw conclusions from the statistical matter on account of the necessary work of preparation, correction, and pub- lication, the more he must desire to see such scientific treatment accomplished by private persons and scholars. Yet such investigations need not be expected, and are for the greater part impossible if the archives are merely open to investigators, but like ordinary libraries presuppose a knowledge of the works in those who look for them. They should rather be arranged like historical archives. There should be well-informed persons who are, if desired, will- ing to point out the material, and when necessary to ex- Theory and Technique of Statistics. 209 plain it. (v. Scheel, Organisation der amtlichen Statistik, 1869). §114. APPLIED STATISTICS, POLITICAL ARITHMETIC. The limits of exact data and of the conclusions which may be drawn from statistical problems have been shown in § 1 1 1. It may, however, appear that the limits of the statis- tical field have been drawn too closely, if certain combina- tions commonly designated as applied statistics or political arithmetic are not drawn into consideration. These are based essentially upon the union of numerical results and other empirical maxims, with strictly statistical data. It would, however, be hopeless to look here for any peculiar form of knowledge. Inductive and experimental knowl- edge as well as deductions come into play. From the interweaving of such typical relations and comprehensive abstractions with statistical results, rich and fertile fields of inquiry may arise. What is understood by political arithmetic founded by Petty (§ 13) is chiefly an extension of statistical enumera- tions and probabilities by calculations based upon techni- cally necessary or typical relations. When the number and variety of the ships of a nation have been statistically ascertained, any seaman can easily tell how large must be the crews and also the seafaring population of the nation. The technical expert can tell easily the consumption of raw material, the necessary machines, the approximate produc- tion, the circulating capital, and other essential conditions of the enterprise from the number of spindles. Obviously all these data come by calculation from the empirical knowledge of the person who makes them and from the premise that the conditions estimated have necessary and typical relations. The combinations can, on the other hand, be of a more abstract nature. Say said, that without the aid of statistics political economy would scarcely be an empirical science. 210 Annals of the American Academy. This is not correct, as Say meant it, that if statistics gives the causes or effects of its facts, it becomes political econ- omy. Yet political economy has two sources whence its principles are drawn. Either the typical characteristics of a number of private economies which have been observed are applied to the nation, a course which, on account of the differences of economic and ethical qualities of individuals, is ambiguous and unreliable, or it gains them by the enu- meration or estimate of direct or symptomatic phenomena within the entire nation or of so much as is concerned, i. e. t statistically. The latter can alone give an exact basis for further abstractions. In the same way geography, history, and other sciences include facts statistically ascer- tained and abstractions from these facts. The scientific conception of statistics is of the utmost importance in this union of inductive and statistical con- clusions. If it is considered the science of a certain object one must either include all objects participating in such combinations in the limits of statistics, or else draw a line when the consideration of an object ceases to be statistical and belongs to another science, and the statistical data utilized are to be looked upon as subsidiary to the latter. If we consider statistics from a standpoint of a method which examines its objects from a point of view closed to other methods, then the single problem of applied statistics becomes simply a portion of empirical knowledge investi- gated more or less by statistical processes. CONCLUSION. §115. THE CHARACTER OF STATISTICAL THEORY. It has been demonstrated that ever since the beginning of history extensive statistical investigations were requisites of political and social life, and how in consequence an- Theory and Technique of Statistics. 211 tiquity and the middle ages show in various fields of prac- tice some empirical skill. Scientific statistics is also the immediate outgrowth of the practical needs of State and Church in modern times. They existed for a long time as a mass of unconnected and partly heterogeneous matter, until it came within the mighty revolution of ideas, which since the beginning of our century has permeated and clarified all scientific knov/ledge. The idea of unity in the entire field of scientific statistical activity brought with it also the consciousness of a peculiar statistical method. The tre- mendous development of statistics in public administration, as well as in many departments of economics and other sciences, went hand in hand with a clearer perception of correct and exact processes. In spite of the most diver- gent views as to the scientific position of statistics, there exists entire unanimity among statisticians as to the de- mands and conditions of the statistical method] Our presentation of the subject has aimed to explain this method in its logical foundation and in its technical application, in order thus to gain the principles of an un- ambiguous and complete theory of statistics. The result of thjs treatment m ay be briefly sum marized. Theoretical statistics is the doctrine of a strictly systematic process of investigation which can be properly applied to every con- crete object conceived as complex and changeable. Sta- tistics is capable of furnishing knowledge attainable in no other way as to the connections and relations of things in this changing aggregate. This doctrine constitutes a well ordered system of ideas, demands, and principles which have definite relations to the general theory of perception. Whatever position may therefore be accorded to statistics in a system of the sciences, it cannot be denied that un- less it is considered, with Sigwart (§ 58), as a part or branch of logic, it must be classed properly with logic and mathe- matics, or at least, as is done by Rumelin (§ 57) and Haushofer, with the methodical sciences of critique and hermeneutics. 212 Annals of the American Academy. A peculiarity of the method is the fact that its compre- \ hension is not based upon a particular portion of previous knowledge. Although for many problems it may be neces- sary to have very exact knowledge of political and legal matters, or of technical purposes and conditions, kinds and denominations of means, tools, and materials em- ployed, and also of the decisive relation of the events, it is not in all these cases any special technical knowledge that is required, but simply just such ideas and points of view as are not inaccessible to a man of general education and common sense. But just from this fact very appreciable difficulties arise. Because statistics operates almost exclusively with the ideas of everyday life and combinations of numbers, which are very simple, it makes very extraordinary demands upon the specialist. It is unfavorable in the first place that the purpose of the problem is abstract, that it is not connected with the direct operations of daily life. It cer- tainly is very interesting to compose a plan, to propose problems, or to draw or substantiate conclusions — but these operations are rare exceptions. As a rule, one is concerned simply with the treatment of the material, col- lation, sifting, and correction of the results, continued for years. One list looks like another; there are the same ideas, the same sets of figures through hundreds of sheets, always the same common-place things and everyday dis- tinctions. At the same time we must not overlook any possible misapprehension of the idea of the unit of enu- meration, whatever form it may assume, nor any improba- bility in the data which may include errors. Assistants may indeed be charged with the discovery of false or changing designations of things, of errors of calculation, of writing, etc. But all more serious doubts are the con- cern of the interest, attention, and continued patience of the specialist properly so-called. Hence it is obvious that any proposed lightening of these labors involves not a merely personal question, but possibly the value of the result. Theory and Technique of Statistics. 213 On the other hand, because it deals in ideas plain to everybody and in figures which are easily comprehended, statistics is, more than other sciences, subjected to mislead- ing and trivial use and criticism. Because of its simple elements, its conclusion and data always assume a form of expression apparently comprehensible. Interpreted solely by one's general knowledge, changed in its form and re- peated in this new shape, it can only be a case of luck that the careful choice and limitation of the ideas still is applicable. Yet the entire system of conclusions is based upon this fact. Often when doubt arises as to the correct- ness of such traditions, the means of corroboration are lacking, and even when these are known nothing is easier than falling into new errors by small mistakes which so easily occur, unless there is a certain consciousness of the requirements of criticism and the mode in which the data are presented. Hence arises that peculiar contradiction in the opinions held as to the value of statistics, that one doubts completely the value of the figures, and another expects from statistics what is unattainable. The means of decreasing these unfavorable conditions are worthy, finally, of our attention. §Il6. THE WORK OF THE PROFESSIONAL STATISTICIAN. That statistics in its methods makes great demands upon the professional statistician is due partly to the necessity of completely comprehending the purpose of practical problems arising in the most varied fields of political and economic life and scientific research, in order to make them susceptible to statistical treatment. Everything to be considered must either directly or by symptoms assume the form of things capable of enumeration, possibly of such as have qualities which can be measured. The indefinite ideas and conjectures from examples, which fill our ordinary thought, can never take the place of the complete obser- vation with its numerical results. To determine what is 214 Annals of the American Academy. aggregates may be considered analogous and compared, and whether their enumerations are of value, requires sharp discrimination and often comprehensive knowledge and research. Causality and probability cannot always be ascertained without a profound penetration into actual and historical premises and conditions. But the real difficulties are not to be found here. On the contrary, these demands when they arise only stimu- late and interest. The chief requirement is to keep up the interest, the continued tension, which enables the sta- tistician to handle each of these endless repetitions of the same ideas and totals with the same energy. There are no means of attaining this except the change of the de- mands and the increase of responsibility for their fulfilment. The tedium of monotony and the consciousness of not making personally the finishing touches, are the greatest enemies of good achievements and capacity. It is therefore highly desirable to make the specialist as far as possible head of the statistics for a certain district, so that he, himself, with not more than one scientific as- sistant, can attend to all special matters which cannot be considered merely mechanical, and hence all the problems engage his attention in comparatively rapid variation, and lead him to the desire and necessity of carrying on these works originally, intensively, and definitely. The organization of bureaus for smaller districts is to be preferred to the establishment of a single centralized institution for other reasons. From the centre of a small State or a province or a district there remains a possibility of that local and personal knowledge which is of the utmost importance for estimating the value of different organs and their mode of procedure, for detecting errors, and for ascertaining the reliability of the conclusions drawn. The examination of the returns is also essentially facilitated. They are not in such an enormous number as to escape the supervision of the director, and they do not come from places and conditions so distant and different Theory and Technique of Statistics. 215 that mistakes cannot be much more easily detected, and corrections much more easily undertaken with promise of better results. Such a small bureau can give assistance and instructions within its district in a way impossible to a large central institution. The local officials can apply directly to it for explanations, which it would be difficult to obtain from the general publications. The small bureau can also apply itself to problems of local importance which a central bu- reau could not properly supervise, though it should under- take them. (v. Scheel (§ 1 1 3), Zeitschrift f. d. gesammt. Staatswissenchaft, 1869, 1 Heft.) The cost of statistics is in no sense greater for decen- tralized than centralized organization, since the same labor is to be accomplished. At the introduction of the modern card system it was supposed that it would be cheaper in large factories. But this was only until its conditions had been learned by trial. When all the steps and all the accessories of the work are fully known, when uniform instructions and schedules have been distributed to the smaller bureaus, we must consider their less expensive office rent and salaries, the immediate supervision of the director, as well as the greater demands which a centralized organization makes upon the general administration. There must of course be a central institution superior to the local bureaus. It provides the uniform plan and for the uniformity and collation of results. In § 50 attention has already been called to the benefits which have resulted from the position of the German Statistical office as erected by the resolutions of the Bundesrath, as compared with the numerous statistical bureaus of the single States, chiefly in promoting the method. But it would not do to conclude from the recognized superiority of the growing labors of this bureau peculiar advantages in centralization. This would overlook, on the one hand, that the German Empire was so fortunate as to possess in the first director of sta- tistics a man of extraordinary critical endurance and acute- 216 Annals of the American Academy. ness, and of remarkable clearheadedness in the conception of the technical requirements of the work ; and it would overlook, upon the other hand, that the most admirable achievements of a centralized institution cannot make up for the loss of those advantages which the lack of smaller bureaus necessarily entails. §117. THE POSITION OF STATISTICS IN GENERAL CULTURE. The means of promoting the proper appreciation and use of statistics, outside of statistical bureaus, must, as a matter of course, consist in spreading correct knowledge, and in the increase of the number of those who have been instructed in theoretical statistics. In this connection it is highly desirable to have a certain number of young administrative officials pass as assistants through the statistical bureaus. This would involve con- siderable inconvenience for the director, for he would have to instruct them, and it would require some time before they could furnish sufficiently useful and reliable work. Their occupation could not therefore be calculated for a very short period, but should be placed at from four to five years. It could, however, be counted to their credit, like any other administrative work, for they would receive great benefit from it, and take with them a knowledge and experience and a critical insight into statements of fact, which would be of service in any office to which they might be assigned, and promote generally the proper comprehension of statistics. Such an arrangement would aid in discovering the per- sons, who are by no means numerous, especially qualified for statistical work, and thus variety in the labors of the directors of statistical institutions could be more easily introduced. For such preparation statistical seminaries have been created. One was established by a Ministerial Rescript of August 18, 1862 (Preuss. Minist. Blatt. f. d. innere Verw., Theory and Technique of Statistics. 217 1862, p. 257), in connection with the Prussian Statistical Bureau. Other seminaries have been established by pro- fessors of political science at universities, such as Halle, Leipzig, and Strassburg. It is important whether such institutions are conducted with the intention of schooling statistical specialists or for the instruction of students. The first requires, besides the usual scientific preparation, ex- tensive practice from occupation with the first material to the conception of definite problems. It is presumably to be attained best when it is looked upon as a profession, and gained by work as a clerk and then as assistant in a bureau. For the purpose of instructing students of political economy and others who are not looking forward to a statistical career, the seminar cannot attempt extensive undertakings which would occupy the student for some time, and thus draw his attention from his studies. Such seminars are limited to smaller essays, usually to discus- sion of examples and demonstrations. Nevertheless it is just as fruitful for theoretical education as it is indispens- able. It differs chiefly from the statistical exercises which form the practical part of the lectures only by certain appliances, such as a regularly accessible library, working- rooms, collection of schedules, diagrams, means for calcula- tion and drawing, and the like, which are very desirable. Yet the question of the preparation of specialists is by no means the all-absorbing topic. The demand for them is not so great but that a substitute may be found. This will be all the more easy if the effort to bring into the general culture a clearer conception and comprehension of statistics, which stands obviously in the foreground, is successful. In this effort the burden of the task falls upon the uni- versities. It is important to spread as far as possible the theory of statistics, for theoretical education does not mean anything else than gaining knowledge from sys- tematically arranged principles and illustrations, in con- 2i 8 Annals of the American Academy. trast to the experience gained by a practice of the art. For it is evident that the numerical results of statistics without reference to the fields of knowledge which they serve — geography, anthropology, political economy, his- tory, etc. — cannot be subjects of instruction except as examples of method and of its possible results. The method itself can, however, be presented as a connected body of thought. It is indeed a body of doctrine preeminently adapted as preparation and support of a general scientific education. It is closely united to the first bases of human percep- tion and logical thought, and, unlike theoretical logic, does not develop from these ideas an apparently abstract and abstruse system of syllogisms, but shows directly and clearly how these logical connections are turned to account in problems of economic and political life, of a thoroughly practical and indispensable character. In every new ex- planation it shows in a new form how the slightest error of an idea or smallest logical mistake can render large undertakings useless, and in their consequences mislead- ing and even dangerous for the judgment of important facts of political and social existence. The theory of statistics shows also the value and appli- cation of logic, and must heighten the interest in critical thought. It leads to a comprehension of the earnest and firm purpose of statistical endeavor, to a consciousness that requires strict truth and love of the truth, that the proper treatment of the conclusions or data, which will not permit or excuse any self-deception, involves a serious responsi- bility, that may properly be designated as a demand of the public conscience. For the youth of all professions, particularly those of official position, the theory of statistics is a very appro- priate field of study. When its way is opened more and more among students we may expect a reaction upon political bodies, the press, public opinion, and general culture. We shall then become accustomed to a more Theory and Technique of Statistics. 210 critical treatment of statistical questions; ambiguities of conception, of interpretation, and proposals will decrease; statistics will be more exactly applied in their true fields, and, with proofs of their value, the general estimate of them will be higher. y* Note. Appendices III., IV., and VI. are placed opposite the paragraphs to which they refer, in order to facilitate comparison with the text. APPENDIX. Appendix I. (to \ 14) Halley's Tables of Mortality. Halley's Report — An Estimate of the Degrees of the Mortality of Mankind, Drawn from Curious Tables of the Births and Funerals of the City of Breslau, with an Attempt to Ascertain the Price of Annui- ties upon Lives (Philosophical Transactions, Vol. XVII., for the year 1693, 15 pp. in No. 196, and 3 pp. in No. 198) — says that in the tables under consideration for the five years 1687 to 1691, the age and sex of all who died in the city of Breslau is registered with all possible care and exactness, and that the figures are given by months and compared with the births. Complete materials for the year 1691 were also preserved. It would appear, however, that Halley's observations are based mainly on the following table, which, as the main result of Neumann's work, had been transmitted to him with the other papers. The upper line gives the age, and the one just below the number of persons of that age who died in each year. Where no number is given in the upper line the lower figure indicates the number of per- sons who died each year in the period between the previous and suc- ceeding ages : 7 8 9 . 14 . 18 . 21 . 27 28 . 35 * "H " " 6 5i 2 3J 5 6 4 $ 6\ 9 877 36 . 42 . 45 • 49 "• I 54 8 9i 8 9 7 7 10 LiojJ 11 55 56 .63 9 9 10 12 9$ 70 71 72 . 77 . 81 . 84 14 9 11 9i 6 7 3 4 2 . 90 91 r.i 98 1 1 1 LiJ ° 99 IOO \ \ The two points in brackets are not to be found in the essay, but this must be a printer's error, for, as Knapp has pointed out, they must be supplied. (Theorie des Bevolkerungswechsels, 1874, p. 125.) (221) 222 Annals of the American Academy. Halley has, as shown in his calculations, supplemented this table with other observations, so as to secure a regular progression, which might serve as a general scale, as follows : 7 • 9 • 14 . 18 . 21 • 27 28 . 35 12 10 9 6| 6 6 6 6 6 6f 7 7 8J 9 36 42 45 . 49 54 . 56 63 9 9 10 10 10 10 11 11 10 10 10 10 10 10 70 . 72 77 81 84 N 11 11 11 ioi 10 8 6 4 2 UJ The principal change is in the number of deaths between the 9th and 1 8th years. He increased this, as he held the small number in the table to be merely accidental. He was correct in this, but went too high on his part. Halley says that it appears from the Breslau tables that in the years in question there were 6198 births and 5896 deaths (1 173^ yearly, there- fore). Hence the growth of the population is about 64 in each year, or about one-twentieth, but this is probably equalized by recruiting for the Imperial military service. But as this is problematical, the num- ber of births, however, well known, it may be supposed that the popu- lation of Breslau grows by 1238 births annually. It appears further, from the same tables, that on an average 348 die in the first year of their age ; that only 890 reach the age of 1 year ; that between the completion of the 1st and that of the 6th year, 198 die on the aver- age, and hence only 692 survive the sixth year. On this basis he constructed the following table. This, he says, shows the number of the population of Breslau in all ages from birth to old age, and shows, therefore, the probability of death at each age. This shows how annuities may be calculated, which until then had only an imaginary basis, and also shows what are the chances that a person of one age should reach some more advanced age. In his language, "this table does show the number of persons at the age current annexed thereto, as follows :" Theory and Technique of Statistics. 223 Age cur- rent Per- sons. Age cur- rent. Per- sons. Age cur- rent. Per- sons. Age cur- rent. Per- sons. Age cur- rent. Per- sons. Age cur- rent. Per- sons. I 2 3 4 5 6 7 IOOO 855 798 760 732 710 692 8 9 IO II 12 13 14 680 670 661 653 646 640 634 15 16 17 18 19 20 21 628 622 616 6lO 604 598 592 22 23 24 25 26 27 28 586 579 573 567 560 553 546 29 30 31 32 33 34 35 539 531 523 515 507 499 490 36 37 38 39 40 41 42 481 472 463 454 445 436 427 43 417 5o 346 57 272 64 202 7i 131 78 58 44 407 5i 335 58 262 65 192 72 120 79 49 45 397 52 324 59 252 66 182 73 109 8p 4i 46 387 53 3i3 60 242 67 172 74 98 81 34 47 377 54 302 61 232 68 162 75 88 82 28 48 367 55 292 62 222 69 152 76 78 83 23 49 357 56 282 63 212 70 142 77 68 84 20 Age. I 14 21 28 35 42 49 56 Persons. 5,547 4.584 4,270 3.964 3.604 3,178 2,709 2,194 Age. 63 70 77 84 100 Total Persons. 1,694 1,204 692 253 107 34,000 The first series shows how many of 1238 persons born in Breslau die in each age class. The second series shows a general order of mortality, as Halley called it, based on the former. If to explain the two series we assume that the 1000 persons noted by Halley in the age current 1 represent the births of the 1st year, then the entire calculation must be reduced to 1000 instead of 1238, and this reduction must appear in the further figures. But, since for 1238 persons born, 890 are said to survive the 1st and 692 the 6th year, the number at the age current 2 must be not 855, but 719, and hence all the following figures must be too high. Hence the population of Breslau could not be counted, as is done above in the second series, by adding together the first. If, on the other hand, it should be sup- posed that the number of persons opposite each age current repre- sented the average number of persons living in each year, it would be seen that 1000 instead of 1238 was not appropriate in view of the greater mortality of the early months. Hence it would be seen that, though the following numbers might be averages, it would not agree 224 Annals of the American Academy. with Halley's statement, that 692 survive the 6th year, to find the same figures in the middle of the 7th year. All subsequent figures would, therefore, disagree. If the figures opposite each age current are not those living at the beginning of the year or at the middle of it, they can only represent those who survive each age. This agrees with the supposition that of 1238 persons born 692 survive the 6th year to find this figure opposite the age current 7. Hence, working backwards, we find surviving the 5th year 710; the 4th, 732 ; the 3d, 760 ; the 2d, 798, and the 1st 855. On the other hand, Halley gives this last at 890, and the number 1000 could only be the average number during the first year. Although Halley laid no great weight on these calculations of esti- mates, we have still no ground to suppose that he made any mistakes in his figuring, and the difficulties in his niethods cannot be solved with such material as has been preserved. (G. F. Knapp: Theorie des Bevolkerungswechsels, 1874. J. Graetzer: Edmund Halley und Caspar Neumann, Breslau, 1883. E. Rehnisch : Review of the last work in Gottinger Gelehrten An- zeigen, 1883, p. 1576.) Theory and Technique of Statistics. 225 Appendix II. (to $ 48) System of Resolutions of the Inter- national Statistical Congress. (Compte-rendu general, St. Petersburg, 1872.) A. THEORETICAL AND GENERAL STATISTICS. 1. Theory and Technique of Statistics, General treatment of methods. Graphical methods and cartography. Uniformity of terminology. Statistical instruction. 2. Statistical Organization. General principles of organization ; central commissions ; scope of statistical organs. Statistical publications. Exchange of the same. 3. Organization of the Congress. Resolutions on organization, statutes, and work of later Con- gresses (temporary regulations). Plan for comparative international statistics. B. PRACTICAL OR SPECIAL STATISTICS. 1. Territory and Nature of the Country, Cartography in relation to catasters and the transfer of property. Hydrography. Application of natural sciences to statistics. Meteorology. 2. Place of Residence. Statistics of large cities. v 3. Population. Census : data to be collected, methods of enumeration. Subsidiary questions to enumeration of population, necessary for a general view of the nation. Population registers. Movement of the population. Death tables. Emigration. Basis of ethnographic statistics. 4. Health and Sickness. Statistics of geographical influences on health. Statistics of deaths. Statistics of epidemics. 226 Annals of the American Academy. Statistics of mental diseases. Statistics of institutions for the sick. Military medical statistics. Comparative statistics of health and mortality of the civil and military population. Statistics of accidents in transportation, factories, mines, and furnaces. 5. Real Property. General resolutions, division, and extent of property in land. Modes of ownership. Transfer of ownership, prices, and indebtedness. Catasters. Buildings. 6. Agriculture and Grazing. Agricultural investigations, data to be collected, and methods to be pursued. 7. Fisheries. Statistics of fisheries. 8. Mines and Furnaces. General resolutions. 9. Industry. General statistics of labor. Special statistics of industries. 10. Production and Consumption. General resolutions. 11. Laboring Classes, Prices, Wages, General resolutions. Budgets of the laboring classes. Prices and wages. 12. Public Charity. Resolutiors on statistics of the systems and arrangements for public charity. 13. Money, Weights, and Measures. Uniformity of money, weights, and measures. 14. Commerce. General resolutions. Foreign commerce. 15. Transportation, Shipping. Statistics of country roads. Statistics of railroads. Statistics of inland navigation. Statistics of maritime navigation. Statistics of postal service. Statistics of telegraphs. Theory and Technique of Statistics. 227 16. Banks and Institutions of Credit. Statistics of stock corporations. Statistics of banks. Land credit. Circulation of bank notes and paper money. 17. Insurance. Resolutions on the statistics of insurance. 18. Charity and Care of the Poor. Statistics of the poor. « Dependent persons. 19. Public Education , Art, and Science. Schools and public education. Institutions for instruction in the fine arts. Institutions for the preservation of scientific collections. Institutions for the preservation of collections of the fine arts. 20. Justice. General resolutions, judiciary organization. Statistics of criminal courts. Statistics of civil and commercial causes. 21. Prisons and Police. Statistics of prisons. 22. Army and Navy. General statistics of land and naval forces. Special statistics of marines. Medical statistics of army and navy. 23. Finance. General statistics of finance. Yearly income of the nation. Statistics of expenditure. Finances of cities, the church, corporations. 24. Statistics of Municipalities. General resolutions. 25. Statistics of Colonies. General resolutions. Appendix V. 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