THE QUANTITATIVE STUDY OF VARIATION. 271 



important. Now how can we know anything definite concern- 

 ing the causes of specific change unless we can express exactly 

 the present condition of a form-unit and express exactly again 

 its condition after the working of a factor ? Descriptions based 

 on adjectives are inadequate for a precise expression either of 

 the present condition of a character or of a slight change in 

 it. The beautiful results on the change in form of the crabs 

 at Plymouth, which Weldon obtained by the quantitative 

 method, could hardly have been obtained without that method. 

 It has long been a reproach to biology that it could give so 

 few demonstrations of race differentiation going on in nature. 

 It has, indeed, been pointed out that we should not expect in 

 man's brief lifetime, nor even within historic times, to find such 

 changes ; but this defense is valid only if we rely upon adjec- 

 tives for specific descriptions. If specific descriptions are 

 given quantitatively, on the other hand, we can hope soon to 

 prove that many species are undergoing change and to deter- 

 mine the cause of the change. 



Again, correlation is an important biological conception ; it 

 is especially important for the determination of homologies, 

 for homologous organs exhibit, as is well known, a tendency to 

 vary correlatively, e.g., the right and left sides of the body ; the 

 series of teeth or ribs. Accordingly within certain limits one 

 can infer homology from correlation. A precise measure of cor- 

 relation consequently will serve as a measure of morphological 

 kinship. Such a precise measure is given by " Gallon's 

 function." 



Intimately associated with the study of correlation between 

 organs of the body is the quantitative study of heredity, or the 

 correlation between parent and offspring or between other 

 related individuals. In this field there are numerous matters 

 demanding thorough investigations. There is the confirmation 

 of Galton's law of Ancestral Inheritance, by which all the par- 

 ents of any (nth) degree of ancestry (the parents being of first 

 degree, grandparents of second, etc.) contribute together n 

 of the total heritage. There is the matter of prepotency in 

 breeding prepotency of one race or one sex. Prepotency is 

 the preponderating transmission from one parent. The very 



