Ernest Warren 
147 
as a criterion of the general size) has a correlation with the ratio of + '32, 
but if we accept the significance of the expression p — po, there is really a much 
larger organic relationship than is indicated by this number. 
(8) The variability of the race, measured by the coefficients of variation, was 
large (6 — 10), and there is apparently no significant difference between them and 
the coefficients found among sexual forms. 
(9) The mean of the coefficients, for aphis and daphnia, of the parental 
correlation was "41, and of the grandparental '24 ; thus here again there is no 
marked difference between parthenogenetic and sexual reproduction. 
(10) Two examples of cross-inheritance were examined: (1) frontal breadth of 
parent and length of antenna of offspring r = •30 ; and (2) frontal breadth of 
parent and the ratio of offspring ?' = "17. These results are in good accord with 
Prof Pearson's theorem for cross-inheritance. 
(11) The variability of arrays of offspring is by no means significantly small : 
and the variability of the individuals of a brood, measured by the mean of the 
standard deviations of the individual families, amounts to as much as 60 
of the racial variability. This may perhaps be rather less than in sexual repro- 
duction, but no very satisfactory direct comparison is at present possible. 
(12) A convenient measure of the similarity of brethren is afforded by the 
fraternal correlation. From numerous data Prof Pearson* regards '4.9 or "50 as 
the average fraternal correlation among sexual forms, while the mean coefficient 
for aphis and daphnia is "66 ; but it should be noticed that the ratio of aphis, on 
which the environment would have less effect, more nearly approaches the sexual 
value than do the absolute dimensions. The question as to whether we have 
here a real difference between parthenogenetic and sexual offspring can only 
be decided by further investigation both on aphis and other forms. 
(13) Concluding Remarks. 
The coefficient of correlation for a pair of organs must have a definite physical 
meaning, and if no spurious correlation be introduced, it should indicate the 
proportion of the manifold causes, affecting the two organs in question, which are 
common to each. 
The causes of inheritance are prohahly alike in nature to the causes of the corre- 
lation of parts of an individual. Thus the right and left organs of a bilateral 
animal are usually strongly correlated, and this fact translated into a physical 
meaning must imply that the numerous causes which build up the organ on the 
two sides are nearly identical. Now, it seems probable that a long comparative 
series of observations of the correlation between different parts of the numerous 
organisms and the cross-inJieritance between these various parts would throw a 
flood of light on the actual mechanism of both growth and inheritance. 
* Pearson, R. S. Proc. 1900, p. 157. Pearson and Lee, Phil. Trans. Roy. Soc. Vol. 195 (a), p. 119. 
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