1899] VARIATION-STATISTICS IN ZOOLOGY 333 



offspring. Galton and Pearson have shown this in anthropological 

 instances, but in zoology almost nothing has been as yet done. 1 



Statistical investigations may be applied to all sorts of characters ; 

 the immediate results acquaint us with the relative frequency of the 

 variants, and show, in addition, whether their variation depends upon 

 that of other characters or not. If w r e have to deal with numerical 

 characters, we discover furthermore the particular law according to 

 which their variants are distributed in the existing individuals of the 

 form-unit, and the coefficient of correlation according to which the 

 variants of several characters are individually combined. From the 

 mathematical analysis of series of variation we discover constitutional 

 factors, and the known external conditions of life differentiating the 

 species into form-units and their higher groups, which are characterised 

 in the first place by the mean values of their characters. Within the 

 form-unit numerous other causes of variation, which are not known, 

 produce by their combinations the individual differences of the 

 characters in typical proportions of frequency. According to their 

 physiological conditions the organs of different species react more or 

 less markedly to the causes of variation of their characters, so that the 

 physiological plasticity of the organs is indicated by the indices of 

 variability of their characters. 



The idea of investigating complexes of individuals statistically, in 

 order to discover series of variation, is not new. In ichthyology 

 especially, where nearly all systematic characters are dimensional or 

 numerical, as early as 1857 A. Czernay [5] published observations on 

 the variation of specific characters in freshwater fishes from the vicinity 

 of Charkow. From the period 1870-1880 Heincke's [10] papers on 

 the varieties of the herring may be named. All older publications, 

 however, deal with such a small amount of material, that the data are 

 without value for the mathematical analysis of series of variation. 



In 1890, in the Proceedings of the Royal Society of London, there 

 was published the first zoological paper where the results of statistical 

 observations of numerical characters were mathematically analysed. 

 W. F. E. Weldon [19] on the suggestion of F. Galton investigated 

 four dimensions of Crangon vulgaris in numerous individuals from 

 three different localities, and found that their variation follows the 

 Gauss' law of error, which is a frequently occurring special case of 

 Pearson's general probability-curve, and that each of the characters had 

 a different mean value in the different localities. Two years later, 

 using Galton's method, Weldon [21] showed the correlation between 

 several characters of Crangon. Then he made a series of investiga- 

 tions on variation and correlation in Carcinus macnas, treating differ- 



1 Since the above was written, "Warren [18] has published an interesting paper on 

 heredity in DapJmia. 



