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.’ 
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 we 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. R. 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 maenas, treating differ- 
1 Since the above was written, Warren [18] has published an interesting paper on 
heredity in Daphnia. 
