—that resulting special aggregates, differing widely in number, show a narrow margin of difference when combined into an average of many such aggregates. "Let us suppose," he says, "that we toss up a penny a great many times; the results of the successive throws may be said to form a series. The separate throws of this series seem to occur in utter disorder. . . . But when we consider the result of a long succession we find a marked distinction; a kind of order begins gradually to emerge, and at last assumes a distinct and striking aspect."
It is claimed that at one time about two hundred persons committed suicide annually in London, but it is possible that the increase of prosperity or the extension of moral influence might lessen the number. Human actions, when compared with games in which no skill is applied, thus disclose a marked difference in the fact that the average of many games shows a very small margin of departure from calculated uniformity, while during long periods human actions arising from like causes differ widely, owing to the evolution of intelligence, which gradually establishes extensive differences. Many natural phenomena go through long periods of growth and decline. But this method in nature may be far more difficult to trace than that in a game of cards. It is completely beyond our power to arrange the star systems in even a theoretical way that would seem in the slightest degree complete. In phenomena repeated at conceivable intervals, however, we may find the average as steadily maintained as that of great numbers of games. This is seen in the slight variations in the average of rainfall during a decade. If we extend the problem beyond the range of our short lives, we again find that apparently fixed averages slowly change. It would, therefore, require inconceivable lapses of time to discern the uniformity of average in these gradual changes during many centuries. As an illustration of this, there are good reasons for believing that the temperatures of the north and south temperate zones vary so greatly in ten thousand five hundred years that large portions of the globe now under cultivation will be covered by glaciers. Mr. H. B. Norton, in a lecture delivered before the Kansas Academy of Science, makes a careful mathematical calculation based on the precession of the equinoxes. He thus estimates that the greatest variation in length between winters of the northern and southern hemispheres occurs at recurring periods of twenty thousand nine hundred and thirty-seven years. These great lapses of time are, he claims, accompanied by alternate deep submergence of the poles in accordance with the gradual change of the earth's axial inclination. He says:
"It thus appears probable that there have been many glacial periods in each hemisphere, and that the ocean, like a mighty pendulum, vibrates from pole to pole."
- "The Logic of Chance," by John Venn, M. A., p. 6.
- Published in "The Popular Science Monthly," October, 1879.