THE QUANTITATIVE STUDY OF VARIATION. 269 



measured ; practically to all qualities of form and color which 

 an organism possesses. The thorough application of the quan- 

 titative method often takes time, practice, and ingenuity, but 

 the results are worth the cost. 



As stated above, the distribution of frequencies in the several 

 classes gives a measure of the stability or variability of an 

 organ. Let us consider what this single result enables us 

 to do. It enables us to express the laws of normal variation 

 quantitatively instead of loosely, as heretofore. Thus we can 

 now compare the relative variability of the sexes ; we can 

 determine whether wide-ranging species are especially varia- 

 ble ; whether specific characters are more variable than generic 

 ones ; whether parts developed to an extraordinary degree are 

 especially variable ; whether in serially repeated organs those 

 standing at the ends of the series vary most ; and whether 

 secondary sexual characters are more unstable than other 

 somatic ones. All these and other "laws" can be established 

 only by quantitative methods. 



Again, in systematic zoology this method will be of great 

 use. I know that systematic zoology is much decried in some 

 schools, and unquestionably it has suffered from the adherence 

 of some unphilosophic workers. On the other hand, many of 

 the workers in this department of zoology have been brought 

 face to face with the great problem of the origin of species, 

 have seen their opportunity, and have contributed valuable data. 

 If they have failed to do more, it is because the methods they 

 have used — the methods of adjective descriptions — have been 

 wholly inadequate to the task. What headway can one make 

 on the classification of the American Unios by saying that the 

 individuals from one river differ from those of another by being 

 more elongated, or rounder, or browner, or by having a lower 

 beak, or sharper radiating lines. Not until these qualities and 

 others are reduced to numbers can we hope to disentangle 

 this maze of varying communities. After we shall have a 

 number of studies made in this fashion upon wide-ranging 

 species or genera, we shall have gained some adequate notion 

 of the relation of the origin of species to geographic distri- 

 bution. 



