# Popular Science Monthly/Volume 56/December 1899/Exact Methods in Sociology

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APPLETONS’
POPULAR SCIENCE
MONTHLY.
DECEMBER, 1899.
* EXACT METHODS IN SOCIOLOGY.
By FRANKLIN H. GIDDINGS, Ph. D.,
PROFESSOR OF SOCIOLOGY IN COLUMBIA UNIVERSITY.
THOSE who do pioneer work in science encounter not only the inherent difficulties of research and interpretation, but also the misapprehension of certain educated men whose distinctive gift is a fatal genius for applying false standards of measurement to the progress of thought. Seizing upon some branch of knowledge that is in a state of vigorous development, when its newer results are out of harmony with its earlier hypotheses, such critics love to point out these contradictions, and try to prove that the branch in question is no science at all, and that its teachers are hardly worthy of respectful consideration.
The history of science contains many interesting chapters pertaining to this kind of criticism and the fate that has invariably overtaken it. When Copernicus and Galileo showed the absurdity of the Ptolemaic astronomy, the theologians enjoyed themselves for a time, as they demonstrated—to their own entire satisfaction—the folly of all rationalistic attempts to explain what revelation only could make clear. When Darwin explained the origin of species through variation and natural selection, the pretensions of biology were completely exploded by its lay and clerical critics (they thought and said so) by the extremely simple device of the "deadly parallel column," Was not Cuvier a great anatomist, and had he ever taught this nonsense about the mutability of species? Was not Agassiz the most learned naturalist alive, and what had he to say about Darwinian vagaries? Had he not proved, over and over again, that the very concept of the species was the ​notion of a group of characteristics that could not possibly change or be changed from generation to generation? In more recent years we have again seen the same method of reducing science to a variety show for the entertainment of the tired general reader applied to both biology and psychology. Weismann has tried to prove that acquired characteristics are not transmitted in heredity, and that the germ plasm is distinct from the somatic cells. The neo-Lamarckians, Spencer, Cope, and some of the botanists have contended for the older interpretation. Is biology, then, a science? Forbid the thought! Heaven preserve our minds from such confusion!
If the sociologists have hoped that they alone might not be overtaken by easy annihilation, they deserve to be humiliated. But it is safe to say that they have cherished no such illusions. If the men who have devoted much time to the scientific explanation of society have had no other qualification for their task, they have at least shown some acquaintance with the history of thought. And so it is not likely that they have suffered deeply from disenchantment when they have been confronted with the regulation exposure of "the present position" of their science.
There is no need of wasting space to prove that the kind of criticism here referred to is without scientific value. The present position of any science can not be determined by arraying its contradictions and inconsistencies, irrespective of a serious attempt to ascertain which of its concepts and hypotheses have inherent vitality. It is precisely when a science is at its best, surely advancing year by year and full of promise for the future, that contradictions most abound in its monographs and text-books.
A true scientific criticism, then, must proceed by a different method. The present position of a science can be ascertained only by instituting three specific inquiries, namely: First, among the more or less contradictory conceptions and hypotheses which constitute its groundwork, what ones are surely displacing all others and gaining the wider acceptance among active students? Second, what progress is being made in the application of exact methods to research? Third, is there a practical or working harmony between the concepts that are gaining ground and the more exact methods of research that are being perfected? Do the concepts and hypotheses lend themselves to exact methods, and do they, on the whole, help to perfect methods? Do improving methods, on the whole, confirm or strengthen the concepts that are gaining wider acceptance?
If these inquiries are applied in the domain of sociology they bring to light unmistakable evidence of a steady and gratifying ​progress toward scientific consistency and rigor of method. Muck babble about social ills and possible reforms still masquerades as social science. A great deal of loose thinking and slipshod investigation is paraded as expert opinion on questions of social welfare. But no one who has seriously followed the efforts of scientifically trained minds to discover the natural laws of social evolution is in any danger of confounding the results thus far obtained with the chatter over every passing fad. In the more serious work itself there is found a vigorous and hopeful disagreement of opinion upon all unsettled questions. But the fact of real significance is that the disputation has become intensive. The debate no longer ranges over a wide field. A selective process has eliminated one after another the more loose and vague conceptions of the science, the irrelevant issues, and the superficial analogies. There has been a progressive concentration of attention upon a group of closely related and fundamental problems.
The sociology of August Comte was little more than a highly intelligent and quickening talk about social order and progress. It convinced thoughtful men that there is a social order to be studied in a scientific spirit and by scientific methods, and that social progress conforms to laws that may be discovered. Mr. Spencer narrowed the field of sociological inquiry and gave precision of statement to all social problems by bringing them within the formulas of universal evolution. He still further narrowed the field by demonstrating the close relationship of social phenomena to the phenomena of organic evolution and by seizing upon certain psychological facts as chief factors in social causation. All fruitful later work in social interpretation has been a further concentration of investigation upon the psychic factors. While admitting that social as well as mental phenomena are subsumed under biological phenomena, and that the parallelism of social organization to biotic organization is real, the younger students of sociology have developed the science as an offshoot of psychology, and have dropped the biological analogy as unfruitful for purposes of research. The pioneer in this movement was Dr. Lester F. Ward, whose masterly analysis of the psychic factors of social phenomena gave the right direction for all time to sociological inquiry, and whose emphasis of the importance of reason and volition in the social process, although it has not yet received the attention that it merits, is destined to be fruitful in coming years.
To the further study of the psychological foundations of society practically all the valuable work on fundamental social problems has been given during the past ten years. Tarde has ​given us profound studies of imitation and invention; Gumplowicz and Le Bon, of the psychology of races and culture groups; Novicow, of the psychology of conflict and toleration; Le Bon and Durkheim, of the psychology of crowds, of co-operation, and of the division of labor; Baldwin, of the psychology of the social unit—the socius.
Thus it appears that while sharp disagreements of opinion still exist relative to the priority or the generality of one or another of these psychic factors in the social process, discussion has focused about the psychological phenomena themselves. There has been a progressive limitation of the field and an increasing definiteness of conception and hypothesis.
My own effort, if now I may be pardoned for referring to it, has been to restrict the field yet further, and to make the problems of sociology yet more specific. I have contended that these psychological phenomena which have been seized upon for purposes of sociological interpretation are still too vaguely conceived. They are often disclosed to the inquirer in purely individual as well as in social aspects. The lines of inquiry between the study of mind in general, of mind as individual, and of mind as manifesting itself socially in the concert or co-operation of a number of individual minds, have not been drawn with sufficient precision. I have tried to show that the psychological phenomena that Ward, Tarde, Gumplowicz, Novicow, Le Bon, Durkheim, Baldwin, and others have so admirably analyzed as psychic factors of society are social when, and only when, they have certain coefficients, namely: (1) The coefficient of resemblance—that is, a fundamental similarity of individuals to one another underlying and, on the whole, dominating their innumerable differences; (2) the coefficient of awareness or consciousness of resemblance—that is to say, certain feelings, perceptions, or thoughts of resemblance, which give rise to varied prejudices and preferences that facilitate or prevent effective co-operation. Whether this contention of mine will prevail, whether there will ultimately be a general agreement among sociologists that these coefficients of resemblance and consciousness of kind are the true differentia of social phenomena, time and further research must determine.
The second inquiry through which we may learn somewhat of the present position of sociology relates to the development of method. Exact method in social research is statistical. Wherever we can obtain numerical data within the domain of social phenomena, there we arrive at exact or quantitative knowledge. The development and application of statistical methods to social problems has been one of the most striking scientific achievements ​of the present century. When Quetelet, in 1835, published his great work, Sur l'Homme et le Développement de ses Facultés, he laid the foundation for a thorough statistical investigation of psychological and sociological no less than of anatomical phenomena. And after the publication, in 1846, of his work, Sur la Théorie des Probabilités appliquées aux Sciences morales et politiques, followed, in 1848, by Du Système social et des Lois qui le régissent, there was a rapid development of statistical methods in precision, and of attempts to extend the statistical method to groups of facts which had until then been studied only from a purely qualitative or, at best, a vaguely comparative point of view. At the present time every subdivision of descriptive sociology draws data from rich collections of statistical materials, and employs statistical methods for the further extension of knowledge.
Thus, in the study of the social population, statistical methods are employed not only to give the total number of inhabitants dwelling within a given territory and the degree of density of population per square mile, but also to show to what extent population increases by births in excess of deaths, to what extent by immigration in excess of emigration, and to what extent the composition of the population is rendered complex by the intermingling of many nationalities. The character of a population, also, and its social capacities are in a large measure statistically investigated. General intelligence is studied by means of statistics of literacy and illiteracy; industrial preferences by statistics of occupation; habits of industry by statistics of the number in every thousand of the total population who regularly follow gainful occupations; frugality by statistics of savings, insurance, and home ownership; and the amount of communication, whereby assimilation and cooperation are rendered possible, by statistics of travel, mail, and telegraphic service.
Passing to that study of concerted feeling, thought, and purpose which may be called a study of the social mind, and which constitutes the second great division of descriptive sociology, we find that it can be carried on, and that to a great extent it is prosecuted, by means of statistical research. We have statistics incomplete, but admitting of perfection, of those impulsive, emotional disturbances of masses of men which take the form of strikes, insurrections, lynchings, and revivals. The report of the United States Department of Labor on strikes, published in 1894, and a recently published monograph by Dr. Frederick S. Hall on Sympathetic Strikes, show the possibilities of this method whenever it shall be exhaustively applied. It could be successfully applied to the other phenomena mentioned. By painstaking effort and a sufficient ​expenditure of money the data could be obtained. Lombroso and Laschi, in their work, Le Crime politique et les Révolutions, have made a beginning toward the collection of statistics of insurrections and revolutions. More exact, at present, are our statistics of the rational working of the minds of large numbers of men in communication and co-operation. These we have in the familiar form of election returns, which show us the decisions that communities make on questions of public policy and administration. This information could be increased by the application of statistical analyses to the vast body of statute law and judicial decisions. A beginning of such work has been made in the valuable Bulletin of State Legislation, published by the New York State Library.
In the third division of descriptive sociology—that, namely, which treats of social organization—the application of statistical method is proceeding with great rapidity. We have not only statistics (yearly improving in quality) of marriage and divorce, of the organization of all governmental departments, military and civil, of chartered corporations, of religious and educational societies, but also of the thousands of associations formed for the promotion of special interests, recreation, scientific research, art and literature, and philanthropy. Every year the statistical information on these matters, included in such compilations as The World Almanac, becomes not only more extensive but more precise.
Yet more abundant are the statistical accumulations pertaining to that fourth and last division of descriptive sociology which treats of the social welfare—of the functioning of society, of the ends for which it exists. We have statistics of prosperity, of the accumulation and distribution of wealth, of the expansion and contraction of credit, and of business failures. We have statistics of longevity. We ascertain improving sanitary conditions by changes in the death rate. We learn by statistical methods of the increase or decrease of accident and death due to public disorder or maladministration. We ascertain through educational statistics the decrease of illiteracy and superstition. And by the same means we ascertain the dimensions of pauperism and of crime. Not only so, but, by a certain refinement of statistical method, applied by competent men like Sir Francis Galton, we ascertain the increase or decrease and the distribution of the higher manifestations of intellectual ability and moral character.
Thus the whole field of descriptive sociology is being more and more exhaustively studied by statistical methods that are yearly improving in precision. So far, then, as may be judged from the development of its methods, no science at the present time is making surer and better progress than sociology, and none is offering ​to the general public conclusions based upon more exact methods of induction.
Let us now look at the relations which the development of statistical method bears to that development of fundamental conceptions, which has already been described. Do we here discover increasing harmony, a tendency toward co-ordination, or have analyses of concepts, on the one hand, and developments of statistical method, on the other hand, followed diverging lines?
There can be no possible doubt of the answer that must be made to these questions. Conceptions and methods are in as perfect accord as can be discovered in any branch of science. The merest glance over the field of social statistics shows that, for the most part, they record and classify phenomena that are essentially psychological. In working from the general theory of evolution through the biological parallelism down to psychological premises, analytical sociology has been doing in one way precisely what statistics have been doing in another. The moment we pass from statistics of density and distribution of population we find ourselves dealing next with groups of facts that are biological (the facts, namely, of distribution according to sex and age periods), through facts that are partly biological and partly psychological in character (the facts, namely, of nationality), and then, leaving these behind, we deal henceforth entirely with facts that belong to the mental and moral categories. To name them would be only to repeat the categories already enumerated: the statistics of intelligence, industry, and moral character, of emotional or rational social action, of various forms of organization for the achievement of as many different purposes, and of the development of the conscious personality of man as a result of his social relations and activities.
Not only is this true, but the further interesting fact may be discovered that social statistics of every category employed or known are based upon a frank recognition of that coefficient of resemblance, physical or mental, which I have contended is a mark of social phenomena. The first step in statistical tabulation is classification, and classification invariably starts from an assumption of real or supposed resemblance. Not to dwell on such fundamental distinctions as those of color, race, and nationality, we encounter the more special resemblances of agreement in religious belief, agreement in industrial preference, agreement in political conviction (as shown in election returns), similar susceptibility to emotionalism, similar capacities for rational comprehension, similar imperfections of nature, which result in lives of crime or ​pauperism. Remove from social statistics this postulate that blood kinship or mental resemblance between one social unit and another is the basis of social phenomena, and the statistics themselves would cease to exist.
Statistics reveal also the consciousness which men have of their resemblances and their differences. It is statistically known that the geographical distribution of nationalities is not accidental or capricious. Immigrant Italians, Germans, and Scandinavians find their way to those parts of the country where men of their own blood and speech are already established. Intermarriages of men and women of different nationalities are statistically known to be frequent where no differences of religion exist, and infrequent where different nationalities profess different faiths. The statistics of political elections are quite as much statistics of the consciousness of kind as of differences of mental type itself.
The most significant fact of all, however, has still to be named. It is this: From the first known beginnings of statistical research to the present time every extension of statistical inquiry has been in a large measure due to the consciousness of kind. The first statistical surveys of communities of which we have any record were such tribal enumerations as those recorded in the book of Numbers, the avowed object of which was to ascertain the strength and resources of the various tribes by clans, lesser gentile groups, and households, not more for utilitarian reasons than for the gratification of gentile and tribal pride. The census taken in Greece in 594 B.C. was for the purpose of dividing the people into four classes and levying taxes according to wealth. The constitution of Servius Tullius, 550 B.C., distinguished six property classes, and the attempt to determine these statistically was one of the earliest experiments in census-making at Rome. The Domesday Book of William I (1086) is the first great statistical document in English history, and its origin was due to a desire to know not only the military and fiscal strength of the nation, but also its class distinctions and feudal relationships. The great stimulus given to statistical investigation by the Trench Revolution was an obvious product of class feeling. Most of the refinements of statistical inquiry in later years have had a like origin. Such, for example, was the cause of the discrimination in our own census of the foreign born from the native born, and of the native born of foreign parents from both native and foreign born. Such has been the cause of the attempt to get more exact statistics of religious denominations, of labor organizations, and of the distribution of wealth. Had there been no reason for including these costly inquiries in statistical investigations, except that of their general ​utility and scientific interest, the appropriation for them would have been denied in Congress without an instant's hesitation. They have been included because of the political deference given to class feeling and to various forms of religious and educational prejudice.
Thus there is seen to be a remarkable interdependence of statistical method and psychological analysis in the development of sociological research. Analysis and method have converged upon the same postulates, and it is apparently by the development of methods frankly founded upon these postulates that our sociological knowledge is to be further increased.
It would be a great mistake, however, to assume that sociological knowledge is to be increased only by the further collection and interpretation of numerical data. Careful monographic description and historical research must continue to be important sources of both information and hypothesis. The great defects of monographic work, both descriptive and historical, are, first, a certain lack of precision, attributable to the large part played in investigation by the individual judgment of the student (the lack of objective tests by which his subjective impressions may be critically examined); second, a certain incompleteness, attributable to a failure to separate each inquiry into all its scientific subdivisions and to attempt to obtain desired data under each subdivision, as is done in statistical investigation where, in every table, as many topics as there are scientific subdivisions of the general subject are represented by columns, and an entry of some kind is made in every column.
I wish now to point out the possibility of giving greater precision to monographic work in sociology by the introduction of quasi-statistical methods—methods that are essentially quantitative in an algebraic sense, though they are not numerical.
Social phenomena have the interesting characteristic that small forces, while never lost in that composition of forces which determines the ultimate equilibrium of the social system, often count for absolutely nothing in the practical affairs of a given generation. If, for example, Mr. Bryan and a Democratic Congress had been elected in 1896, the practical consequences for the United States would have been much the same whether the Democratic plurality had been one hundred thousand, half a million, or two or three millions. This is but one example of a large class of facts. Social phenomena are more often than not determined by a mere matter of more or less, rather than by the exact amount or degree of more or less. The determination is algebraic rather than arithmetical. Is the element under investigation a positive ​or a negative quantity? Is its sign plus or minus? That is usually the important question for the sociological student.
Now it happens that a great many investigations in descriptive sociology do not as yet admit of the introduction of exact statistical—that is, arithmetical—inquiries which, nevertheless, do admit the use of algebraically quantitative methods. In the monographic description of a community many questions arise which can not be answered by the entry of figures in a column, but which could be answered by entering in a column a symbol indicating that a certain trait, habit, or choice could be predicated of a large majority, or of a small majority, or of only a large minority, or of only a small minority of the entire population. That is to say, it often happens that an observer who can not take a perfect census (getting answers to all his questions from every individual in the community), and who therefore can not fill out his columns with arithmetical values, can, by such interviewing as is possible to him and by such an examination of the objective products of social activity as are open to the inspection of any one who chooses to observe them critically, determine with absolute certainty whether certain things are true of majorities or only of minorities.
Suppose, for example, that a traveler is studying an out-of-the-way settlement, or a tribe, which presents many points of interest that are comparatively novel. All who are familiar with the narratives of travel and exploration which Mr. Spencer has used as data for his Descriptive Sociology are aware that they are almost totally devoid of system. The reader is told that such marriage customs, such clan relationships, such political institutions, such industrial operations, have been observed. The all-important coefficient is left out. What the student of sociology would most of all like to know is how many individuals in the community manifest such or such a trait; how many have such or such a habit; how many profess such or such a belief; how many adhere to this organization, how many to that. But since this exact arithmetical knowledge usually can not be obtained within the limited time and under the circumstances of a traveler's researches, he should try to get at least partially quantitative results by noting in every instance whether the phenomenon observed is true of a majority or only of a minority of the people under investigation.
This simple method admits of a high degree of refinement by the obvious device of subdividing the total human mass under observation into enumeration units. If, for example, we are studying the social character and activities of the people of the United States, we may take the fifty Commonwealths and Territories as enumeration units. Making out a tabular form, we may enter ​in the left-hand column the names of the several States and Territories. At the top of successive columns, counting from left to right, we may enter words designating the social phenomena to be observed. Then, taking the States and Territories in order, we may enter opposite the name of each a symbol indicating that a majority large or small, or a minority large or small, of the inhabitants of the State or Territory in question manifests the trait or follows the activity, or belongs to the social organization designated at the top of the column. The symbols that I have found most convenient in use are these: For a large majority, a double plus sign thus, ⧺; for a small majority, a single plus sign thus, +; for a large minority, a double plus sign in a circle thus, ⨭⨮; for a small minority, a single plus sign in a circle thus, ⊕.
The great possibilities in this method of giving precision to observations and records of the facts of social psychology and activity become daily more obvious to students who practice it with reasonable care. Almost any desired degree of accuracy can be attained by taking smaller and smaller enumeration units. Thus, if I wish to form and to record my judgment as to whether the people of the United States as a whole manifest a high, a medium, or a low degree of general intelligence, I seem to be raising a question that admits of little better answer than a statement of vague impressions. But let me take a concrete measure of high general intelligence—for example, the general intelligence of a town noted for its large proportion of scientific and professional men, its graded schools, its satisfactory school attendance, and its low percentage of illiteracy. Let me then subdivide the United States into fifty parts—namely, the Commonwealths and Territories—and let me enter in a column opposite the name of each a symbol indicating that, as compared with the general intelligence of the town which I have taken as a standard, a large majority or a small majority, or a large minority or only a small minority, of the people in that Commonwealth are of the high general intelligence; that a large majority or a small majority, or a large minority or only a small minority, are of medium intelligence; and that a large majority or a small majority, or a large minority or a small minority, are of low intelligence. Obviously, when I have completed this process I have subjected my vague general impression that the people of the United States as a whole are of high, medium, or low general intelligence to a certain correction and measure. I count up the entries in my columns. I discover that I have made, let us say, nine entries indicating that a large majority of the people in each of nine States are of high intelligence. I find that I have made, let us say, eighteen entries indicating that in each of ​eighteen States a small majority of the people are of low general intelligence; and this mere counting of the entries may show me that, when taking the States one by one, I have made a somewhat different estimate of the general intelligence of the people of the entire country from that which I made when looking at all the people of the country as an undivided mass.
If still unsatisfied with my judgment, I may proceed to subdivide each State into its counties, and take the counties as enumeration units. I may go through the process of recording my judgments by entering symbols in the several columns of my table, and at the end I may again count up my totals of high, medium, and low intelligence. Obviously, I can do this work only if I am able to travel through every county in the United States, and, by interviews with people, by forming general impressions and by visiting schools, get a fairly definite idea of the relative intelligence of each civil division; or if, being unable to make this personal inquiry, I resort to printed information—namely, educational reports, miscellaneous public documents, historical records, newspapers, and other objective data throwing light upon the intellectual status of these various divisions. This, I find, is an enormous labor; but if I conscientiously perform it I correct my subjective impressions, and there is a fair presumption that my final result is a judgment vastly nearer the truth than was my first general impression of the intelligence of the whole undivided mass of the American population.
Thus the conscientious use of the method which I have suggested insures, in the interest of precision, two important modifications of ordinary sociological description: First, it subjects the purely subjective processes of judgment to a certain correction and measurement; secondly, it leads the observer step by step, and almost unconsciously, to resort more and more to definite objective data in place of first impressions.
Essentially the same method, by slight modifications of detail, may be extended to historical inquiries. How often do we encounter in historical monographs the statement that, since a certain date, there has been a marked increase of this or that activity, or that such a trait or such a habit, occasionally observed half a century ago, is now characteristic of whole sections or populations! To the credit of the historians, it must be said that careful men seldom make such statements without offering in substantiation of them a certain amount of objective evidence. But the method is loose, and it has the radical defect of permitting such terms as "increase" and "decrease," "great increase" and "great decrease" to stand for different quantities when applied to ​different phenomena under examination in the same treatise. There is no uniformity of measurement. Now, it is easy to introduce uniformity, even where arithmetical values are not known. It is possible to know that we are applying the same method of measurement when we say that, since 1850, there has been a "great" multiplication of lynchings in the United States that we apply when we say that there has been a "great" increase of population, although, in the case of the lynchings, we have not arithmetical values, while in the case of the increase of population we have.
This can be done in the following way: Distinguish and designate degrees of increase or decrease by symbols thus: No change, = 0; absolute increase but relative decrease, = +1; absolute increase with no relative decrease, = +2; great absolute increase without relative decrease, = +3; absolute and relative increase, = +4; absolute decrease but relative increase, =-1; absolute decrease without relative increase, =-2; great absolute decrease without relative increase, =-3; absolute and relative decrease, =-4.
Now let the historian who wishes to pass in review the quantitative changes that have occurred since a given time—for example, 1850—before he puts on paper his impressions, based upon such evidence as he has been able to collate, put down all these symbols against the name of each of the social phenomena which he is studying. He will instantly see that he is trying to apply to each of the phenomena whose changes he wishes to record a certain scale of measurement, and he at once asks himself: What do I really mean by such a term as "relative" increase or decrease when contrasted with "absolute" increase or decrease; and what do I mean by such a term as "great" increase or decrease when contrasted with such a term as "increase" or "decrease" without a modifying word? The moment he puts these questions before his mind he will feel a sinking of heart as he reviews the pages in which he has confidently told his readers that such "absolute" and "relative" changes have from time to time occurred, and reflects that he has seldom been consistent in his use of these terms.
How, then, shall he attain consistency and precision? To be consistent and precise in the use of the word "relative" it is necessary to make at the outset an arbitrary choice of a term of comparison, just as in making comparative judgments of such a phenomenon as general intelligence it is necessary to take as a standard the phenomenon as observed in a particular community. The most suitable term of comparison for all judgments of increase or decrease in social phenomena is the increase or decrease of population per square mile within the area and during the period ​studied. The increase of population is arithmetically measured, and it stands in relations of direct causation to every social change. The historian, therefore, in forming his judgments of relative increase or decrease should always take the increase or decrease of population per square mile as his term of comparison.
What meaning, finally, shall be attached to the word "great" when the historian wishes to distinguish "great" increase or "great" decrease from "increase" or "decrease" in general, and absolute statistics are not available? There is one, and, as far as I can see, only one, perfectly satisfactory procedure.
Let the investigator subdivide the community which he is studying into enumeration units according to the method suggested above for the descriptive monograph. Let him then make as many tables as there are ten-year periods in the general historical period that he is investigating. That is to say, let him make a table for 1850, for 1860, for 1870, for 1880, and for 1890. Let him then proceed according to the method laid down for the descriptive monograph, entering opposite each Commonwealth the symbol for majority or minority, thus showing by States, for each of the ten-year periods, the prevalence of the trait or activity under investigation. Suppose, for example, that the phenomenon studied is the growth of popular interest in prize fighting since 1850. The historian should begin by asking. In what States, if any, in 1850 were large majorities of the people interested in prize fights to the extent of countenancing them and eagerly following their progress? In what States were only small majorities so interested, in what States only large minorities, and in what ones only small minorities? The best answers that the historian can make to these questions, after examining all the evidence that he can command, he should record by entering the proper symbol against each State, after which he should repeat the procedure for the date 1860, for the date 1870, and so on. When his tables are thus completed, he should count up the number of entries of each symbol in each table. If then he finds that in less than half of his enumeration units—i.e., in less than half of all the States and Territories—small minorities have become large minorities, large minorities have become small majorities, or small majorities have become large, he will be justified in concluding that there has been an increase, but not a "great" increase, in popular interest in prize fighting. If, however, he discovers that these changes have occurred in more than half of his enumeration units, he can say with reason that the increase of interest in prize fighting has been "great."
Cases may arise in which a correction of the judgment thus ​formed may be necessary. It might be erroneous to say that there had been no great increase of interest in prize fighting if it were discovered that the increase had occurred in two or three Commonwealths only, but that in them it had been phenomenal. The method itself, however, reveals the necessity for correction in such eases and measures the error; for, obviously, a phenomenal increase or decrease in any one enumeration unit would be disclosed by a dropping of the intermediate symbols between ⊕ and ⧺. That is to say, small minorities would become majorities, or great majorities would become small minorities, within an interval during which lesser changes were occurring elsewhere.
Thus, by taking a little trouble, the historian can apply one constant measure to his judgments of increase and decrease, as he reviews social changes. He must subdivide his community into enumeration units, and against each unit, at each convenient date, he must enter a record of his judgment that the trait, activity, interest, or relation under investigation can be predicated of a large or of only a small majority, of a large or of only a small minority, of the individuals composing the enumeration unit. He must then count up the changes from minority to greater minority or to majority, or from majority to minority. Conscientiously following this method, the historian; nay often make comparisons of great precision, when otherwise his comparisons, made without reference to a common measure, would be little more than suppositions.
Following such methods as these, the writers of descriptive and historical monographs can increase our approximately exact sociological knowledge. Constructing and filling out such tables as have been described, they can bring to light serious gaps in our numerical statistics, and they can thereby suggest and stimulate new statistical inquiries. Thus co-operating, the descriptive writers, the historians, and the statisticians can in time perfect our descriptive sociology, and, co-operating with those students who are completing the analysis of fundamental concepts, they can gradually give precision to our formulations of sociological law.