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 



