22 



VARIATION AND CORRELATION IN THE CRAYFISH. 



terminal segment of a series such as that presented by the leg of the 

 crayfish would occupy an extreme position with respect to relative varia- 

 bility, but such does not appear to be the case. The propodite is neither 

 the most variable nor the least variable joint uniformly. 



We may next examine somewhat more in detail the facts regarding the 

 skewness in the different segments of the appendages. In table 8 the 

 data are arranged in convenient form for comparison. 



Table 8. — Skewness in variation of the different joints. 



Segment of Leo. 



Skewness (+ in all, Cases). 



Leg I. 



Leg II. 



Leg III. 



Meripodite . 

 Carpopodite 

 Propodite . . 



Mean. 



0.3077 

 .3144 

 .4139 



0.3530 

 .3619 

 .2406 



0.3158 

 .3293 

 .0994 



.3453 



.3185 



.2482 



We see from this table that — 



(a) Considering the means of the columns, leg i shows the greatest 

 skewness in its variation, and there is a steady decrease as we pass to legs 

 II and III. Great weight, however, is not to be laid on this conclusion 

 drawn from the means, for the reason that it is obvious that the excess of 

 the mean skewness for leg I over that for leg ii is due entirely to the influ- 

 ence of a single joint, the propodite of leg i. It was shown above that 

 the great chela was the most variable single segment, and it is now seen 

 that it also has the greatest skewness in its distribution. In other words, 

 the most specialized structure of those studied shows a maximum degree 

 not only of variability but also of skewness. 



(6) Leaving the great chela out of account, the segment which in each 

 leg gives the distribution with the greatest skewness is the carpopodite. 

 The difference between carpopodites and meripodites in skewness is not 

 large, but since in every case it is in the same direction, it is probably 

 safe to conclude that there is a slight tendency for the former to have 

 generally the more asymmetrical distributions. Here, as in (a), we 

 find degree of skewness and degree of variability going parallel, it having 

 been shown above (p. 16) that the carpopodite is the most variable of 

 the joints after the great chela is put aside. 



(c) The low degree of skewness in the distributions for the propodites 

 of legs II and iii is noteworthy. In fact, the propodite distribution for 

 leg III is, within the limits of error from random sampling, symmetrical. 



