30 VAKIATION AND CORKELATION IN THE CRAYFISH. 



Table 13 shows perfect regularity in the trend of the "excess," but 

 it is of a quite different kind from that observed in table 12. Here 

 there is no uniform rule that the homologous joints show the higher 

 correlations. Instead there appears to be a special factor governing the 

 carpopodite correlations which leads to a rule which may be formulated 

 in the following way : ( I ) The carpopodite of any given leg is correlated 

 to a relatively high degree with the meripodite and propodite of each of 

 the legs which lie posterior to it, and further, the correlations of carpopo- 

 dite with meripodite and propodite are practically equal; (n) the car- 

 popodite of any given leg is correlated to a relatively low degree with 

 the meripodite and propodite of each of the legs anterior to it, and again 

 these correlations are substantially equal. Consequently we find that 

 the "homologous joint" carpopodite correlations are higher than the non- 

 homologous joint correlations when the latter are directed anteriorly (by 

 u), and lower when they are directed posteriorly (by i). Consequently, 

 as a result of special factors influencing carpopodite correlations, the effect 

 of homology is in part overshadowed. It is clear from the figures in 

 parentheses in the excess column that the minus ( ) differences are 

 relatively, as well as absolutely, greater than the plus ( + ) . 



The data for the propodite correlations are given in table 14. 



The results here are rather more irregular than one could wish. There 

 is clearly no uniform tendency for the homologous joint correlations to 

 be higher than the non-homologous. In both the contiguous metamere 

 and non-contiguous metamere groups there is a mixture of plus ( + ) and 

 minus ( ) entries in the excess column. Consequently, in order to get a 

 notion of the general trend of the results, we are thrown back on an estimate 

 of the relative magnitude of the plus and minus differences. From the 

 figures in the excess column it is evident that on the whole the plus 

 differences run distinctly larger than the minus. The average of all the 

 plus difference ratios is 5.32, while for the minus ratios it is 1.62. From 

 this it appears reasonable to conclude that on the whole there is a distinct, 

 though very slight, tendency for the correlations of homologous propo- 

 dite segments to be higher than those of non-homologous joint pairs 

 involving a propodite as one variable. 



Putting all the results set forth in tables 12 to 14 together, we may 

 conclude that in general, so far as indicated by our present material, 

 there is a slight but distinct tendency for homologous pairs of joints to 

 be more closely correlated than non-homologous pairs. In the case of 



