CORRELATION AND HOMOLOGY. 35 



While the figures set forth in the tables of this section show that in 

 general there is some tendency for homologous joint pairs to be more 

 highly correlated together than are non-homologous, yet they equally 

 show that this influence may be quite outweighed by special factors 

 influencing particular joints. The carpopodite correlations are clear 

 illustrations of this point. Now, there can be little doubt that these other 

 factors which come in to influence correlations are in general factors con- 

 nected with the functional relations of the parts ; that is, in a broad sense, 

 physiological factors. Perhaps the most obvious of such physiological 

 factors is growth. In the next section it will be shown that on the 

 average more than 50 per cent, of the observed gross correlations between 

 the joints of the crayfish appendages is due to a true growth correlation 

 factor. In comparison with such an effect as this it is obvious that the 

 influence of homology on correlation is practically a negligible one. From 

 these facts we are compelled to conclude that in comparison with physio- 

 logical factors the influence of morphological relationship, as implied in 

 homology, on correlation is relatively insignificant. This conclusion is 

 in entire agreement with certain results which have been obtained by 

 Davenport (1903, p. 130). Studying the correlation between the antero- 

 posterior diameter and the dorso-ventral diameter of the lower valve of 

 Pecten opercularis, he finds a very high degree of correlation between 

 them. These axes are morphologically independent, but by the position 

 which the animal takes they are brought into the same relation to the 

 bottom. The coefficient of correlation between these two axes is in each 

 of three samples > 0.969. Regarding this result Davenport says: 



Here the correlation coefficients of non-bilateral dimensions are extremely high, as 

 high as in many of the highest human coefficients between bilateral dimensions. As 

 a result of the newly assumed position of the scallop, two formerly largely independent 

 axes have come to vary simultaneously just because they have similar relations to the 

 bottom. Pecten has gained a new kind of symmetry; namely, a radial symmetry. 

 The fact points very forcibly to another conclusion; namely, that physiological factors 

 are much more important in determining correlations than morphological relationship 

 when the two come into conflict. 



Though the influence of homology on correlation is a relatively slight 

 one, that it is nevertheless a real one is evidenced by the fact that work 

 on other organisms than the crayfish has shown its existence. In his 

 memoir on the variation and correlation of the human skeleton Warren 

 (1897) includes a section on "The Correlation of Homologous Parts" (pp. 

 179182) in which he discusses the relative degree of correlation between 

 pairs of homologous and non-homologous limb bones. He finds that the 



