332 GEORG DUNCKER [NOVEMBER 
able to find out whether there is correlation between these characters 
or not. 
For numerical characters there are now simple methods (Galton, 
Pearson) of calculating the degree of deviation of the real frequencies of 
the combinations of their variants from the probable ones. The results 
of these calculations are abstract numbers between zero (no deviation 
from probability) and one; the latter signifies the highest possible 
degree of deviation of the combination-frequencies from probability, 
inasmuch as each variant of the one character occurs only combined 
with a definite single variant of the other. These abstract numbers 
we call the coefficients of correlation of the investigated pairs of 
characters. The most convenient coefficient of correlation is that 
calculated according to Pearson’s method [15], and determined as the 
mean product of the individually combined relative deviations of the 
two characters from their average values, while the relative deviations 
are the absolute ones expressed in terms of their indices of variability. 
Like the indices of variability of homologous characters, the coefficients 
of correlation of homologous pairs of characters show a certain 
constancy even in different species (Warren [17]). This, again, I 
believe to be an expression of physiological relations between the 
correlated organs with regard to the respective characters. 
If on the average the combined variants lie either, on the one 
hand, both above or both below the mean values of the two characters, 
or, on the other hand, if the one is a positive, the other a negative 
deviation from these values, we get either a positive or a negative 
coefficient of correlation, and accordingly deal with positive or negative 
correlation. Series of variation between which there is positive 
correlation tend to form constant differences of the individually com- 
bined variants, while those between which there is negative correlation 
tend to form constant sums of the variants. The constancy of these 
sums or differences is the more remarkable, the higher the coefficient 
of correlation. The constancy of the sums of variants, that is, negative 
correlation, is mostly to be found in metamerically disposed characters 
(homoiotic variation), that of the differences of variants, that 1s, positive 
correlation, in antimerically disposed characters, especially in those with 
symmetrical variation. 
As it is possible to investigate the probability or the degree of 
correlation of the frequencies of the individual combinations of the 
variants of two or more characters, so it is reciprocally possible to treat 
the combinations of variants of one and the same character in two or 
more individuals which are connected by known relations in a similar 
manner. This might be, for instance, when we wish to decide if a 
character is important in sexual selection; or again, if a character is 
hereditary or not. In the former case the combination of variants, 
effected by mating, of one and the same character in males and females, 
must show correlation; in the latter the same is true for parent and 
