38 



VARIATION AND CORRELATION IN THE CRAYFISH. 



The most striking fact about these coefficients which one notices at 

 once is that they are uniformly considerably smaller than the correspond- 

 ing gross correlation coefficients. This means that in a group of indi- 

 viduals all having the same length of cephalothorax the correlation is 

 much less close between different segments of the legs than when indi- 

 viduals of all sizes are considered together. Or, in other words, the result 

 shows that a considerable portion of the high gross correlations between 

 joints arises from the fact that both the joints of the given pair are corre- 

 lated with the length of the cephalothorax. When we get rid of the 

 effect of these general "size" correlations by making cephalothorax length 

 a constant we have left the measure of the net relationship between parts. 

 This net correlation measures the true organic relationship which exists 

 between a given pair of organs, quite apart from the fact that both the 

 organs have their dimensions correlated with the size of the body as a 

 whole. The biological interpretation of the excess of gross over partial 

 correlation coefficients appears to us to be that it measures the portion 

 of the total correlation, which is a true growth correlation. 



It is of interest to see what proportion the partial bears to the total 

 correlation in the case of the different legs and segments. This may be 

 done by expressing the partial coefficient as a percentage of the total. 

 Doing this for the three possible joint pairs of each leg, we have the result 

 set forth in table 19. 



Table 19. — Proportion of net to total correlation in the different legs. 



From this table, considering first the means of the columns, we see 

 that on the average the net correlation forms the largest proportion out 

 of the total correlation in the case of leg i, less in leg ii, and least in leg 

 III. Or, put in another way, the fact that the joints are correlated with 

 cephalothorax length measuring size of body accounts for the smallest 



