CHARACTERS CHOSEK FOR MEASUREMENT 808 



differences in shape can be readily compared, l^oth in amount and direc- 

 tion of fluctuation, with mathematical precision. 



Muscular Scar of Pedicle Yalve 



Tlie other character chosen for measurement was the muscular scar of 

 the pedicle valve. This is a conspicuous, peculiar, and fluctuating char- 

 acter of the genus, and as it is well defined on good specimens and molds 

 of the interior, it furnishes a valuable second character for precise study. 



The muscular scar differs considerably in form and size in the various 

 described species of the genus, and these differences, of whatever kind, 

 have more or less direct effect on the proportion between width and 

 length. Hence each scar was measured for length and width, and from 

 the two measurements the value of index R^ was obtained, which ex- 

 presses in a single mathematical term the percentage ratio between the 

 width and length of the scar. 



Proportionate Rate of Growth of Parts 



A third relation, also expressing differences in the rate, the propor- 

 tionate rate in different parts, and the direction of growth, was obtained 

 by estimating the percentage ratio between the length of the muscular 

 scar and the length of the shell; this percentage gave the value of index 

 R2 for the several shells. 



Ratio Im)EXEs R^ R^, R^ 



METHOD OF PROCEDURE 



Thus were obtained three ratio indexes, represented by the values of 

 R"^, R2, R^. The values for each index should be alike for any two shells 

 presenting no variational differences; and the difference in value of the 

 indexes for different specimens expresses, on a common scale, the kind 

 and degree of difference in form, directly in three ways and indirectly 

 in a large number of ways not easily describable otherwise. If the shell 

 changed its form on passing from young to adult state, comparison of 

 the values of their indexes for small and for large specimens will show it. 

 Hence the law of ontogenic growth can be distinguished from and com- 

 pared with the law of the phylogenic modification by comparison of these 

 ratio indexes. 



Although I caught something of the drift of the evidence as I was 

 preparing the statistics, I deliberately put the specimens away in drawers, 

 after all the measurements had been recorded, and used only the recorded 



