DAVENPORT. — EVOLUTION OF PECTEN. 141 



Pacific, to be, like them, semi-tropical species in origin, then the Eddy- 

 stone scallops will lie nearest the centre of distribution and the Firth of 

 Forth will be in an extreme position ; i. e., nearest to the northern limit 

 of the species, — the Lofoten Islands (where it occurs, however, only at a 

 great depth). The high correlations of the Forth form unit likewise 

 indicate that it is highly specialized ; hence not primitive but an out- 

 lying branch. 



V. General Discussion. 

 1. The Inconstancy of the Coefficient of Correlation in Allied Races. 



The view that the coefficients of correlation of any two organs of a 

 species will be constant for all form units of the species, or even for 

 distinct but closely related species, has been long maintained. Weldon 

 (1892, p. 9) was led by a suggestion of Galton to compare the coefficient 

 of correlation between length of carapace and length of post-spinous 

 portion of Crangon vulgaris from five localities, and he found that they 

 varied between .81 and .85, which, considering the roughness of the 

 methods then in use, was an approximately uniform result. In 1893 he 

 determined a large number of coefficients between organs in Carcinus 

 maznas from Naples and from Plymouth. Here the results were not 

 very close (e.g., .60 ± .01 : .70 ± .01 ; .50 : .55 ; .71 : .78, etc.), but 

 Weldon concluded that, on the whole, they spoke for the identity of the 

 coefficients. Nevertheless, the differences were often greater than the 

 probable errors, as calculated by Warren (1896) ; the Plymouth shells 

 appearing, on the whole, the more closely correlated. Warren finds, 

 moreover, that the correlations of corresponding organs of a different 

 genus (Portunus) hardly differ more from those of Carcinus mamas thau 

 do the correlations of the Carcinus from the two localities. 



Pearson (1896, pp. 267, 280) pointed out that Weldon's values of r 

 proved rather the fact of variation of the correlation coefficient; and he 

 obtained the following values of r between the length and the breadth of 

 human skulls: Naquada race, r = 0.2705; modern Germans, r = 0.2849 ; 

 modern Parisians, r = 0.0474; modern French peasants, r = 0.1265. 

 Also in Dr. Lee's paper on the skull (1901) we find such discrepancies 

 as these: capacity and length: r for Aino, 0.89 ± .01; for Germans, 

 0.52 ± .05; length and height: r for Aino, 0.50 ± .05; for Germain, 

 -.10 ± .07. 



In the present paper the coefficients run quite close, but sometimes 

 the difference is several times the probable error. Thus between d-v. 



