THEORY. The United States Census reported in 1890 22,329,990 persons in the country over 15 years of age and married; in 1900 this class of the population numbered 27,765.707. On computing the ratios it is found that among each 1000 adults 553 were married in 1890 and 557 in 1900. The same authority reported at the Eleventh Census S75.521 deaths during the pre ceding year, of which 6756 were caused by rail road accidents, and at the Twelfth Census 1,030, 091 deaths, of which 9930 were due to the same cause, so that railroad accidents caused in 1890 657 deaths and in 1900 667 deaths out of each 100,000 reported. The foregoing will serve to illustrate a regularity or uniformity often, but not always, traceable in the distribution of con ditions o• the recurrence of events in society. Upon this uniformity in the characteristics of, and this regularity in the events occurring in, so cial groups, which has been not very felicitously called 'the law of large numbers,' the statistical method rests. These uniformities and regulari ties do not exist in the individual o• even in the small group, and if they could not he traced in the large group the laborious and uninviting statistical method would add nothing to the in formation obtainable from examination of a few individuals o• instances, and therefore, however important for political ends, would have no sig nificance for science. It is this 'law of large numbers,' or the permanence of numerical rela tions in social life, that makes it possible to de scribe human societies with accuracy in quantita tive terms, to frame inductions from their past, which are found to hold for their future, to fore cast the influence of a given change upon their life and so in multitudinous ways to control that life. Perhaps the hest illustration of the im portance of the 'law of large numbers' is found in the business of insurance, which could not exist were it not for that law as a foundation. This principle stands in somewhat the same rela tion to the possibility of a science of society that the principle of the uniformity of nature does to the possibility of natural science. In social phe nomena it is seldom if ever possible to carry the isolation of causes to the degree of perfection it has reached in the natural world. The presence of a few drops of hydrochloric acid is practically the only difference between a transparent solu tion of nitrate of silver and a turbid white fluid, so the acid is said to cause the precipitate. But
the marriage of an individual man or woman is influenced by so many complex considerations that it is impossible to perceive in the vast ma jority of marriages taken separately any effect of so subsidiary a cause as the price of bread or the spread of business depression. What this subsidiary cause loses, however, in power over each individual instance it gains by the number of individuals it reaches and the fact that its effect is uniformly in the same direction, while the influence of age, of example, of personal af fection, of gain or loss of property, etc., though in many individual cases far more powerful, is felt sometimes in one direction and sometimes in another. Such causes, therefore, are as power less on the aggregate as they are potent on the individual, and, on the contrary, the society as a whole betrays the undeniable effects of slight causes, which perhaps few individuals therein would admit to have swayed their action. The `law of large numbers' thus assumes that the causes of any social phenomenon may be divided into two groups, the individual, accidental, or disturbing causes, and the essential or pri mary causes, and that causes of the former sort have no constant tendency to act in one direc tion rather than another, and. accordingly, no tendency to move the group as a whole in any one direction. If a. sufficiently large number of instances be taken, the disturbing or individual causes cancel and allow the influence of the essen tial or group causes to be traced. How large a member of instances must be enumerated to elim inate these individual causes with any specified degree of completeness is a mathematical prob lem dealt with by the calculus of probabilities.
BIBLIOGRAPHY. Fo• the only survey of the hisBibliography. Fo• the only survey of the his- tory in English, see Falkner's translation of Melt zen's Gcschichte, Theorie and Tcchnik der Statis tik, published by the American Academy of Po litical and Social Science in 1891. To• the theory of the subject, see the latter part of the foregoing book; Bowley, Men/cats of Statistics (London, 1901), strong in English methods, in wage statis tics, and in the mathematical basis of the subject ; and \Vestergaard, Theorie der Sta-tistik (Jena, 1390). See also Mayo-Smith, Statistics and So ciology and Statistics and Economies.