122 THE POPULAR SCIENCE MONTHLY

phenomenon in which chance is involved, and that two events are equally likely, such as throwing head or tail with a coin. Suppose we have a vertical board in which are stuck horizontal pegs in a regular arrangement of rows and columns. Suppose a shot be dropped over the middle of this array of pegs, and assume that if it strikes a peg it is equally likely to drop to the right or the left. The next time it strikes a peg the chances are the same. It is obviously very unlikely that a shot will continually fall on the same side, while the likeliest thing that can happen is that it shall fall in the middle. Hence if a large number of shot are let fall they will be found, if caught where they fall, to be arranged in a form limited by a curve highest in the middle, and gradually falling symmetrically toward both sidrs, known as the curve of errors. This curve represents graphically the result of an infinite number of causes acting, each as likely to produce a certain effect as its opposite. Let us now take some biological subject of investigation, say the length of a certain kind of shell. Many thousands being measured, it is found that they vary from the average, but in such a way that very few differ very far from the mean. If the number having any given length is plotted vertically corresponding to the deviation from the mean laid off horizontally, we shall obtain a curve which will generally closely resemble the curve of errors. If this is the case we shall conclude that the causes of the variations in length are perfectly at random, but if we find that the curve is unsym- metrical, or for instance has two summits, we shall know that at least two sorts of causes are acting. Thus questions of heredity and varia- tion may be mathematically studied. This method has been greatly developed by the mathematician, Karl Pearson, who has now devoted himself to the study of evolution by mathematical means.

Finally, that apparently most remote of the sciences from the ex- actness of physical laws, economics, has been brought under the treat- ment of mathematics, not only by statistical methods like those just described, but by methods of the calculus. The distinguished mathe- matician and economist Cournot applied to the theory of wealth methods like those used in mechanics to treat of equilibria, so that very complicated economic principles were amenable to treatment by symbols.

I have, I think, said enough to show the power of science to trans- form the world, and to develop the mind of man. Is not this de- velopment of high spiritual value, and is not the pursuit of truth irre- spective of prejudice and authority a noble object, worthy of the devotion of a lifetime? Of the moral values of science it would be easy to give arguments. One has but to consider the self sacrifice of many of its devotees, who consider neither toil nor time if only the good of the race be advanced. Galileo was tortured, Giordano Bruno was burned, and to-day the daily papers bring us news of lives lost in

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