334 GEORG DUNCKER [ 



[NOVEMBER 



ences of age, sex, locality, in certain dimensions, and partly explaining 

 them by selective processes [22, 23]. Further, he found a dimorphism 

 of the females in the Naples race, which Giard [9] tried to explain 

 by parasitic influences. In the meantime Thompson and Warren, 

 inspired by Weldon, worked on variation and correlation in the 

 dimensions of Palaemon serratus [15], Carcinus maenas [16], and 

 Portunus depurator [17]. Warren first discovered the fact, afterwards 

 several times confirmed, that the coefficients of correlation of homo- 

 logous characters remain fairly constant not only within the form- 

 units of the same, but also within those of allied but different species. 

 Warren also was the first zoologist to follow Pearson's improved method 

 in analysing series statistically. Thompson demonstrated distinctly 

 determined changes of mean value and index of variability in the 

 characters of the same form-unit in different years, which result 

 Weldon has investigated further, and has recently [24] considered as a 

 proof of the reality of natural selection. 



While the leader of the English biological-statistical school is 

 especially interested in the problem of natural selection, the North 

 American school, led by C. B. Davenport, works especially on morpho- 

 logical problems. First, Davenport in association with Bullard [6] 

 investigated in a very rich material (4000 individuals) the influence 

 of sex on the constants of variation and correlation. On Davenport's 

 suggestion Brewster [1] and Field [8], the first in mammals, the 

 second in insects, investigated the relation between the variability of 

 certain characters and their systematic importance. The result tended 

 to show that the two correspond. But the material basis of these 

 investigations appears to me too small to settle this question definitely. 



Besides mathematical-statistical researches there have been pub- 

 lished, since statistical methods came into vogue, some others of a non- 

 analytical sort based upon large numbers of individuals. Among 

 these I wish to call especial attention to Bumpus' papers on variation 

 and mutation in two very different species introduced from Europe to 

 North America, the sparrow (Passer) [2], and the periwinkle (Littorina) 

 [3]. In each of these instances the great increase of variability in 

 the American forms, compared with the European ones, is remarkable. 



In Germany Heincke and I are still alone among zoologists in 

 applying statistical methods to problems of variation. Heincke is 

 chiefly interested in the existence of local races within the species, and 

 one of his most important results is, I think, his method of determining 

 the racial character of any given individual as well as its specific 

 character [11]. Among botanists the number of fellow - workers 

 increases every year. Besides foreign naturalists, H. de Vries and 

 G. Verschaeffelt, who have published German papers, F. Ludwig has 

 for several years been statistically investigating the law of Fibonacci 

 in plants, while recently H. Voechting has published a splendid paper 

 on abnormalities of flowers. There is a great advantage in botanical 



