8 



VARIATION AND CORRELATION IN THE CRAYFISH. 



TABLE 2. Coefficients of variation in Crustacea. 



ORGANISM. 



CHARACTER. 



COEFFICIENT 

 OF VARIATION. 



AUTHORITY. 



Eupagurus prideauxi: 



Deep water, male 



Shallow water, male. 



Deep water, male 



Shallow water, male. 

 Gelasimus pugilator: 



Lefts, male 



Do 



Do.. 



Do. 



Do. 

 Do. 

 Do. 

 Do. 

 Do. 

 Do. 

 Do. 



Do. 



Palaemonetes vulgaris 



Both sexes 



Do 



Do 



Do.. 



Right chela length 



do do. . . 



Carapace length . . 

 . .do. . . do. . 



Frontal breadth 



Median length 



Lateral margin, great che- 



lar side 



Lateral margin, small che- 



lar side 



Meripodite of great chela. 

 Carpopodite of great chela 

 Propodite of great chela. . 

 Meripodite of small chela 

 Carpopodite of small chela 

 Propodite of small chela. . 

 Meripodite of second leg, 



great chelar side 



Meripodite of second leg, 



small chelar side 



Dorsal spine of rostrum . . . 

 Ventral spine of rostrum . 

 Dorsal spine of rostrum . . 

 Ventral spine of rostrum. 



26.313 0.609 

 23.434 .502 

 19.446 .438 

 17.746 .372 



7.471 



7.598 



8.880 



9.000 



9.657 

 10.472 

 10.255 



9.920 

 11.139 



8.898 



9.660 

 9.160 



9.83 

 15.03 

 IIO.OO 

 28.26 



Schuster (1903) 

 Do. 

 Do. 

 Do. 



Yerkes (1901) 

 Do. 



Do. 



Do. 

 Do. 

 Do. 

 Do. 

 Do. 

 Do. 

 Do. 



Do. 



Do. 



Duncker (1900) 

 Do. 

 Do. 

 Do. 



(6) The variation in all the characters shows a distinct skewness in 

 the positive direction. The value of the constant measuring the skew- 

 ness ranges from 0.10 to 0.45, being lowest in the case of the propo- 

 dite of leg in, and highest for the length of the cephalothorax. That 

 the distributions all deviate significantly from the symmeti'ical conditions 

 given by the normal or Gaussian law is evident if we compare the values 

 of the skewness and the modal divergence with the probable errors of 

 these constants for the normal curve. In a normal distribution where N, 

 the total number of individuals, is 283 we have 



Probable error of skewness = 0.0491 



The probable error of the "modal divergence" for each case, on the 

 assumption of normality, is given in table 1. From these values we 

 see that in only one case (the propodite of leg in) is the value of the 

 skewness or the modal divergence less than three times the probable 

 error. For this character the constant is in each case almost exactly 

 twice the probable error. Now, if these distributions were to be regarded 



