2io THE POPULAR SCIENCE MONTHLY. 



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 succes- 

 sion 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 commit- 

 ted 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 ap- 

 plied, thus disclose a marked difference in the fact that the average 

 of many games shows a very small margin of departure from calcu- 

 lated 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 phe- 

 nomena 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 be- 

 yond 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 cal- 

 culation 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 thou- 

 sand 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 in- 

 clination. He says : 



"It thus appears probable that there have been many glacial 

 periods in each hemisphere, and that the ocean, like a mighty pen- 

 dulum, vibrates from pole to pole." 



* " The Logic of Chance," by John Venn, M. A., p. 6. 



\ Published in " The Popular Science Monthly," October, 1879. 



