mortality and a few other similar subjects, without much attempt at generalizing from them.
Political arithmetic had come into existence in England in the middle of the 17th century. The earliest example of this class of investigation is the work of Captain John Graunt of London, entitled Natural and Political Annotations made upon the Bills of Mortality, which was first published in 1666. This remarkable work, which dealt with mortality in London only, ran through many editions, and the line of inquiry it suggested was followed up by various other writers, of whom the most distinguished was Sir William Petty, who published in 1683 his Five Essays in Political Arithmetick. Other writers, of whom Halley, the celebrated mathematician and astronomer, was one, entered on similar investigations, and during the greater part of the 18th century the number of persons who devoted themselves to " arithmetical " inquiries into problems of the class now known as statistical was steadily increasing. Much attention was given to the construction of tables of mortality. Attempts were also made to deal with figures as the basis of political and fiscal discussion by Arthur Young, Hume and other historical writers, as well as by the two Mirabeaus.
It is now necessary to return to Siissmilch, who, as already mentioned, endeavoured to form a general theory of society, based on what were then termed " arithmetical " premises. In modern language, he made use of quantitative aggregateobservation as an instrument of social inquiry. It is true he did not enter on hit, investigation' with an " open mind." He desired to support a foregone conclusion, as the title of his work shows. But nevertheless his work was a most valuable one, since it pointed out a road which others who had no desire to procure evidence in favour of a particular system of thought were not slow to follow. Although for many years after the appearance of Siissmilch's book there was a good deal of resistance to the introduction of " arithmetic " as the coadjutor of moral and political investigations, yet, practically there was a tacit admission of the usefulness of figures, even by the chiefs of the socalled " descriptive " school. On the other hand, Siissmilch's success was the origin of a "mathematical" school of statisticians, some of whom carried their enthusiasm for figures so far that they refused to allow any place for mere " descriptions " at all. These two schools have now coalesced, each admitting the importance of the point of view urged by the other. They were, however, still perceptibly distinct even as late as 1850, and the ignorant hostility with which many people even among the cultivated classes still regard statistical inquiries into the nature of human society may be regarded as a survival of the much stronger feeling which showed itself among " orthodox " professors of law and economics on the publication of Siissmilch's treatise.
To the impulse given by the great Belgian, Quetelet, must he attributed the foundation in 1834 of the Statistical Society of London, a body which, though it has contributed little to the theory of statistics, has had a considerable influence on the practical work of carrying out statistical investigations in the United Kingdom and elsewhere. Quetelet was above all things an exponent of the " laws of large numbers." He was especially fascinated with the tendency to relative constancy of magnitude displayed by the figures of moral statistics, especially those of crime, which inspired him with a certain degree of pessimism. His conception of an average man (l'homme moyen) and his disquisition on the " curve of possibility " were most important contributions to the technical development of the statistical method.
The influence exercised by Quetelet on the development of statistics is clearly seen from the fact that, though there is still considerable controversy among statisticians, the old controversy between the " descriptive " and arithmetical schools has disappeared, or perhaps we should say has been transformed into a discussion of another kind, the question now at issue being whether there is a science of statistics as well as a statistical method. It is true that a few books were published between 1830 and 1850 in which the politico-geographical description of a country is spoken of as " statistics," which is thus distinguished from " political arithmetic." The title of Knies's great work, Die Statistik als selbstandige Wissenschaft (Cassel, 1850), is especially noteworthy as showing that the nature of the controversy was changing. Knies claimed that the really " scientific " portion of statistics consisted of the figures employed. As Haushofer says, " his starting point is political arithmetic." Some eminent statisticians of the latter half of the igth century accepted the view of Knies, but the majority of modern writers on the theory of statistics, especially in Germany, have adopted a slightly different standpoint according to which statistics is at once a science relating to the social life of man and a method of investigation applicable to all sciences. This view was ably maintained by von Mayr, Haushofer, Gabaglio and Block, whose views, published fifteen to twenty years before the close of last century, still substantially represent the opinions held by the majority of statisticians in Germany, and probably on the European continent. In France, however, several writers of importance have recently published works on the subject in which, in spite of the influence of M. Block, the claim of statistics to be considered as an independent sociological science has been rejected. There has been little systematic exposition of the subject in the United Kingdom. Isolated dicta have been furnished by authorities on the practice of statistics, such as the late Dr W. A. Guy, Professor J. K. Ingram, Sir Rawson W. Rawson, Sir Robert Giffen and others, Professor Foxwell has lectured on statistics at University College, London. The most important English work dealing with the matter is that of Mr A. L. Bowley. His volume, Elements of Statistics (first published in 1901), is intended as a practical handbook for teaching the principles on which statistics should be handled. The nature of Mr Bowley's book is, indeed, an indication of the fact that in the United Kingdom the study of statistics has been, in the main, of a practical character, the investigation of the theoretical basis of the statistical method attracting little interest. On the other hand, numerous monographs have been published by English writers on particular points connected with the technique of statistical investigation, as was natural considering the excellence of the practical use made of statistics in the United Kingdom.
With regard to the few earlier invasions of the domain of theory attempted by English writers, it may be observed that the authorities above mentioned were not unanimous. Dr Guy as well as Sir Rawson W. Rawson both claim that statistics is to be regarded as an independent science, apart from sociology, while Professor Ingram maintained that statistics cannot occupy a position co-ordinate with that of sociology, and that they " constitute only one of the aids or adminicula of science." Sir Robert Giffen has also expressed himself adversely to the continental doctrine that there is an independent science of statistics, and this opinion appears to be the correct one, but, as Dr Guy and Sir Rawson W. Rawson had the support of the great body of systematic teaching emanating from distinguished continental statisticians in support of their view, while their opponents have so far only the obiter dicta of a few eminent men to rely upon, it appears needful to examine closely the views held by the continental authorities, and the grounds on which they are based.
The clearest and shortest definition of the science of statistics as thus conceived is that of M. Block, who describes it as " la science de l'homme vivant en societ y en tant qu'elle peut titre exprimee par les chiffres." He proposes to give a new name to the branch of study thus defined, namely " demography." Von Mayr's definition is longer. He defines the statistical science as " die systematische Darlegung and Erdrterung der thatsachlichen Vorgange and der aus diesen sich ergebendcn Gesetze des gesellschaftlichen menschlichen Lebens auf Grundlage quantitativer Massenbeobachtungen" (the systematic statement