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 cases 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 may 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.