458 POPULAR SCIENCE MONTHLY. 



can be tested by experiment. It is not too much to say that the fre- 

 quency 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 under- 

 goes variation by itself alone. For the parts of the body are so knit 

 together, their morphological kinship or their physiological inter- 

 dependence 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 ex- 

 tinct form from one of its bones. Now, correlation is of great im- 

 portance 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 in- 

 dividual 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. ^Vhen 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.' 



