Decembee 7, 1900.] 



SCIENCE. 



869 



margin. The expectation, then, that quan- 

 titative studies would quickly demonstrate 

 that evolution is going on rapidly in certain 

 instances to-day has been realized. 



Another of Weldon's pupils, Warren, has 

 provided statistical data on variation in the 

 crab Portunus, and on the variation of an- 

 cient, barbarous races as compared with 

 modern civilized ones. More recently he 

 has measured quantitatively the effects on 

 the little crustacean Daphnia of various ex- 

 ternal conditions. Vernon, likewise, has 

 given quantitative data on the effects of 

 external conditions on the development of 

 echinoid larvse and on echinoid hybrids. 

 Finally, the recent confirmation by Galton 

 of his law of Ancestral Inheritance de- 

 mands brief mention. 



The continental school of variation stu- 

 dents includes chiefly botanists. Very 

 early (1887) F. Ludwig, of Greiz, began to 

 make quantitative studies on the variation 

 in the number of ray flowers of the white 

 daisy. These studies he continued and ex- 

 tended to other species, and has published 

 the results in a series of papers appearing 

 in the Botanisches Centralblatt from 1895 to 

 the present time. He finds that the varia- 

 tion curves of plants are more frequently 

 multimodal than are those of animals. 

 Ludwig has published two comprehensive 

 papers, in 1898 and 1900 respectively, which 

 have served to extend a knowledge of the 

 new method. At Amsterdam, de Vries has 

 applied statistics to his experimental, chiefly 

 selective, plant breeding. He has produced 

 new races of certain very variable species 

 within two to four years. Verschaffelt, a 

 student of de Vries, did good service in 

 calling attention to the importance of the 

 coefBcient of variation (or the index of 

 variation divided by the average) for com- 

 parative purposes. Verschaffelt also sug- 

 gested an ingenious measure of skewness, 

 which is very simple but has been largely 

 replaced by Pearson's index. Important 



work has also been done by L. MacLeod, 

 of Ghent, Belgium, and his pupils, in papers 

 published in Dutch in the Botanish Jahrboek. 



Among the continental zoologists Heincke 

 was the first in the field. He has applied 

 statistics especially to questions relating 

 to the existence of local races of fishes, 

 and especially the herring. George Dunc- 

 ker, a student of fishes, has been occu- 

 pied with biological statistics since the 

 early part of the decade. He has written 

 an excellent general treatise on the subject, 

 (1899) in which the more important 

 methods of Pearson are simplified and thus 

 made more generally available. In Italy, 

 Camerano has made a beginning with the 

 quantitative methods. 



In America quantitative studies of h uman 

 variation have been made by anthropolo- 

 gists incited by the work of Galton. Promi- 

 nent among these are Bowditch, Porter and 

 Boaz. Minot also has made use of Gal- 

 ton's methods. Within late years Bumpus 

 (1897-1899) has applied Galton's methods 

 to variation of Necturus, and to the problem 

 of the relation of variation to environment 

 and to selection. Eigenmann and his stu- 

 dent, Moenkhaus, have given data on the 

 differences in the mode of certain fish char- 

 acters in successive years and in different 

 environments. The writer and his pupils, 

 Blankinship, Brewster, Bullard and Field, 

 have contributed certain quantitative data 

 upon some of Darwin's laws of variation 

 and upon correlation. The writer has also 

 published a small book on the newer 

 methods which, containing the principal 

 formulae and tables for calculating curve 

 constants, it is hoped may be found useful 

 by students of the new methods. 



To sum up, the quantitative study of 

 biology, the modern impulse to which we 

 owe to Galton, has been furnished with 

 good methods by Pearson. Already the 

 application of these methods has borne 

 fruit in our knowledge of the types of bio- 



