ent 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 stud-
