Page:Popular Science Monthly Volume 59.djvu/468

458 can be tested by experiment. It is not too much to say that the frequency polygon is the key to the first door that has barred true progress in the difficult subject of the origin of organic diversity.

In what has gone before we have considered variation of single organs or qualities of a species. Yet, although we have to study the variation of organs taken one at a time, in nature no organ undergoes variation by itself alone. For the parts of the body are so knit together, their morphological kinship or their physiological interdependence is such, that when one organ deviates from the mode many others deviate also. This fact has long been known as correlation of variation. A recognition of the law by Cuvier was the justification, slight though it was, of his premature attempts to reconstruct an extinct form from one of its bones. Now, correlation is of great importance in the origin of species; it makes it easier to understand how evolution can take place. For example, when it was objected that natural selection by acting on one part at a time could hardly build up so complex a structure as the eye with so many mutually dependent parts, Darwin was able to rejoin that the principle of correlation comes in to ensure that when any one part is improved all other parts shall vary to meet the new conditions. And in general, a knowledge of correlation is necessary in order to complement the study of individual variation and to perfect our investigations upon the origin of species. And correlation must be studied quantitatively. A proper method has been afforded by Galton and Pearson. That method may be briefly stated. Let us suppose that we desire to find the degree of correlation in variation, or deviation from the mean, between an organ A, called subject, and a second organ B, called relative. We first take all the individuals of one (subject) class; that is, individuals whose subject organ deviates from the mean by a constant quantity, p. We next find for those individuals the average deviation-from-the-mean of the organ B, and call it q. We then find the ration q/p; this is the partial index of correlation. We find this ratio for every subject class. The average of the ratios is the index of correlation sought. The ratio will not exceed unity; because q is bound in the long run not to exceed p. When q $$=$$ p, correlation is perfect and is equal to 1. When the index of correlation is zero, correlation is absent; when the index is negative, correlation is inverse and a large organ is associated with a small one. A good example of organs with strong positive correlation is the right and left arm. Inverse correlation is rarer; an example is stature and cephalic index. The results of studying correlation quantitatively are interesting, as showing how intimately bound together the most remote parts of the body are. Take for example the following table of correlation of parts of the human skeleton, from Pearson's 'Grammar of Science.'