132 PROCEEDINGS OF THE AMERICAN ACADEMY. 



3. Ray Frequency. 



a. Correlation between Ray Frequency and the Dimensions of the Shell. 

 — The variability of the rays was determined by counting the grooves on 

 the inner face of each valve. This ordinarily presents no difficulty, but 

 occasionally the terminal groove of a series is so obscure that it is doubt- 

 ful whether it should be counted or not. The rule adopted was to 

 count any groove that had an appreciable elevation on two sides. An 

 elevation is determined by its ability to cast a shadow or to jar a pencil 

 point drawn across the inner face of the shell. 



The number of rays varies from 14 to 22, the prevailing numbers 

 being 17 and 18. It is important to determine whether the variability 

 in rays is correlated with the size of the shell, so that there are more or 

 possibly fewer rays as the shells become larger. The rays run roughly 

 dorso-ventrally in an antero-posterior series, much as a mammal's 

 ribs run, except that they start from a single dorsal point, the beak. 

 It might be expected that the greater the antero-posterior axis the 

 greater the number of rays. An inquiry into this relation will be at the 

 same time an inquiry into the relation between number of rays and size, 

 because the length of the antero-posterior axis is one index of size. 

 Again the breadth of the valve is, to a certain extent, independent of the 

 antero-posterior length ; and since broad shells have a greater area than 

 narrow shells of the same length of median axes, we might expect the 

 number of rays to be correlated with breadth. The appropriate correla- 

 tion surfaces having been prepared (Appendices G, H), the following 

 correlation coefficients were calculated : — 



Between number of rays and antero-posterior diameter . r — — 0.074 -J- .027 

 Between number of rays and breadth, right valve . . . r = — 0.057 ^ .027 



The departure of r from is negative, the relation being the reverse of 

 our expectations ; but as the departure from is only about twice the 

 probable error, it is quite probable that no relation whatever exists 

 between the number of rays and the size and form of the shell. The 

 number of rays is determined very early in the life of the individual and 

 is independent of environment. It follows from this that, for the com- 

 parison of races and the study of the effects of isolation, the number of 

 rays is an ideally good character. 



b. Variation in the Number of Rays from the Three Localities. — The 

 seriations of the number of rays for the lower valves from the three 

 localities are given in Table VII. (See also Fig. 1.) 



