Page:Popular Science Monthly Volume 59.djvu/458

448 We 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. Consequently, the laws of individual variation in a race may be relied on to illuminate the method of origin of the race or species under consideration. 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 quantitative method has been developed in biology. It will now be necessary 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 characteristic 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 comparable 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 consequently engineers, physicists, astronomers and others who aim at the greatest possible precision in the measurement of the individual