Page:American Journal of Sociology Volume 8.djvu/626

 6o6 THE AMERICAN JOURNAL OF SOCIOLOGY

consciousness, the object is distinguished from the subject by the primary sensation of size or extent, which arrests our attention, and, by this resistance, at the same time traces relationships, limits, and a distinction between the me and the not-me. From the mathematical point of view, the simultaneous or successive order of the appearance of natural phenomena, whether physical, vital, psychic, or social, is subject to laws which the theory of probabilities makes known to us. The basis of this mathe- matical theory is that the quantitative variations in the appear- ance or disappearance of phenomena are limited by the conditions or chances which are favorable or unfavorable to the production of the phenomena. Thus, if six hundred balls, of which four hundred are white and two hundred black, are placed at random in a ballot box, the law of the appearance of the balls will be as four is to six or as two is to three. It is apparent that the variations in this case are limited by the very law of probabilities.

When the chances are limited and always the same, the prob- lem is easy. The mathematical probability is estimated by dividing the number of chances favorable to an event by the total number of chances. Thus, in the example given above, the probability of the appearance of a white ball is $-$-, or f ; that is to say, the chances are two divided by three that a white ball will come out. The variations will be so much the less frequent as they differ more from this norm, from this mathematical limit.

The problem becomes more difficult when the task is to investigate what are the chances of the reappearance of a peri- odical phenomenon which has been observed many times in suc- cession. Then the probability is great in proportion as the number of times that the event has been observed is increased and as our previsions extend a short distance into the future. With these conditions, in order to calculate the chances of the reappearance of the phenomenon, the number of observations increased by unity is divided by the same number increased by two units. If, for example, we have observed for ten successive days the periodical rising of the sun, the chances are eleven