AND THE WEST COASTS OF THE UNITED STATES. 



129 



should be associated with the size of the series. Accepting this view we may con- 

 clude that the variability of the rays of the Tampa and San Diego lots is sensibly the same. 

 2. Variability in the Transverse Half-diameter of the Shells ("Height" of Valve). 

 -The absolute " height" of the valve depends partly on the absolute size of the shell 

 and varies with the age of the scallop. In comparing the variability of the heights 

 of the two lots of shells from Tampa and San Diego we must, accordingly, compare 

 shells of the same dorso- ventral dimension (width). We may do this by means of 

 the usual correlation surface (see Appendix, Table I). In such a surface the various 

 heights for each width of shell is given. The average of the indices of variability of 

 height for the different widths is given by the formula 0'=< 7 \/.7-r 2 , in which r is 

 the coefficient of correlation as determined by the Galton-Pearson-Duncker method, 

 and a is the index of variability of widths in general. Since in graduated variates 



more significant than the index of variation, <*, 



we may substitute c in the above formula and obtain the average coefficient of varia- 

 tion, c f , of the heights corresponding to the different widths. A comparison of the 

 c's of the Tampa and the San Diego lots will give the best measure of the relative 

 variability of the height of the valve from the two places. The results are given 

 in the following table. 



the coefficient of variation ( C = ~T 



Expressed fully, these quantitative results' tell 'us "that, using the coefficient of 

 variation as a basis of comparison, the San Diego Pectens are from 1.8 to 0.5 times 

 as variable in "height" as those of Tampa; and San Diego Pectens of a constant 

 width are, on the average, 1.6 to 1.4 times as variable in "height" as the average 

 of Tampa Pectens. In a word, the San Diego Pectens are 50% more variable in 

 transverse half-diameter than those of Tampa. 



3. Variability in Symmetry of Single Valves. Comparison of Anterior and Posterior 

 Half-lengths. The following table gives, for the right valves only, the average dimen- 

 sion, in millimetres, of the anterior and posterior partial lengths; the corresponding 



