PARTIAL CORRELATIONS. 39 



part of the observed total correlations between the joints in the case of 

 leg I, and as we pass to more posterior legs the effect of this factor increases. 

 From the individual values we begin to get a closer insight into the rela- 

 tive effects of the different factors influencing the intercorrelations of the 

 joints of the legs. It is clear that leg i shows distinctly different rela- 

 tions than do legs ii and iii. In the case of legs ii and iii, a very con- 

 siderable proportion ( >50 per cent.) of the total correlation of joint pairs 

 involving the carpopodite as one variable arises from the fact that these 

 joints are correlated with the length of the cephalothorax. In the joint 

 pair which does not involve a carpopodite, a very small proportion of the 

 total correlation is due to this "general size" factor. On the other hand, 

 leg I shows exactly the opposite relation. There the net relation is least 

 in the joint pair which does not involve the carpopodite and greatest in 

 the cases where the carpopodite is included. Leg i follows an entirely 

 different rule in the correlation of its joints than legs ii and iii. In 

 leg I the bulk of the total correlation represents net organic relationship 

 between the joints, whereas in the other legs a very large portion of the 

 total correlation arises in an indirect way through the correlation of the 

 joints with the size of the body as a whole. 



Turning again to the values in table 18, we have calculated the mean 

 values of the net coeflBcients for the correlations between homologous 

 joints of the different legs with the following results: Mean net correla- 

 tion between homologous joints: Meripodites = 0.6926; carpopoditea 

 = 0.4227; propodites = 0.5299. 



For all possible pairs of non-homologous joints of contiguous legs 

 (12 cases) the mean net coefficient is 0.4789, while for the six cases of 

 non-homologous joints of non-contiguous legs the mean is 0.4457, or, in 

 other words, there is no evidence in these correlations of an effect of the 

 contiguity of metameres. From the means of the net correlations we see 

 that just as in the case of the total correlations there is clear evidence 

 that homologous segments tend to the more highly correlated than non- 

 homologous, but as before the carpopodite correlations form an exception. 

 These results point to the conclusion that the higher gross correlations of 

 contiguous parts arise through the growth correlation factor, while for 

 the higher correlation of homologous parts another explanation must 

 be sought. 



