448 POPULAR SCIENCE MONTHLY. 



AVe all know that a lot of people, taken at random, show individual 

 physical differences. Even when the people form a homogeneous lot 

 and are of one sex, are all adults, and are of one race, and when such 

 individuals as are very pathological or freaks are excluded, we still find 

 that they differ in stature, weight, proportions of trunk and appendages, 

 color of hair and eyes, proportions of facial features and various other 

 characters. These differences are so slight and multitudinous that the 

 language of adjectives fails to indicate them; measurements must he 

 made in order that they may be expressed numerically. 



But how can these numbers tell us anything about the evolution 

 of the human species? The general principle is this: The differences 

 between the races of man are of the same kind as, and differ only in 

 degree from the differences between the individuals of a race. Conse- 

 quently, the laws of individual variation in a race may be relied on to 

 illuminate the method of origin of the race or species under consider- 

 ation. Just how, will be clearer after we have considered the sorts of 

 individual variation. 



The laws of nature are got at only with the key of the proper 

 method. And it is only within recent years that an adequate quan- 

 titative method has been developed in biology. It will now be neces- 

 sary to consider this method. 



Imagine a file of 40 men arranged in order of stature — the tallest 

 at the head of the column. The crown of their heads will form a 

 flowing curve, nearly level in the middle of its course and becoming 

 more oblique at the ends. The reason for this is that the middle 

 statures are much m.ore common than the extreme ones. Half the 

 people have a stature within two inches of the average (Fig. 1). 

 The general features of such a curve are common to all classes of 

 men, but the details differ in different classes of men. The character- 

 istic differences are measured by what are called the constants of the 

 curve. 



The stature of the middle man in the file will give us very nearly 

 the first constant, the mean or average. The average is obtained exactly 

 by adding all the individual statures together and dividing by the 

 number of men (e. g., by 40). The average is used constantly and as 

 a matter of course by nearly every one who wishes to compare two com- 

 parable series of numbers. It is awkward to compare all the separate 

 data so we let the average stand for the lot. The average is, however, 

 an entirely ideal quantity which need not agree with the measurement 

 of any individual ; and it is a little curious that it is so universally used 

 in statistics. Of a series of measurements made on one and the same 

 dimension, the average is demonstrably nearest the true value, and con- 

 sequently engineers, physicists, astronomers and others who aim at the 

 greatest possible precision in the measurement of the individual 



