Figure 31. — Diagram of a shell of adult C. virginica. 

 Radii extend from the umbo to the periphery of the 

 generating curve. The principal axis AGF shows the 

 change in the direction of growth at G. The length of 

 radii is proportional to the rate of shell growth at the 

 edge. 



sides of it along growth radii AC, AB, and Ad, 

 ABi. 



Circular shells in C. virginica may be found only 

 in very young oysters (fig. 32a). Within a few 

 weeks after setting the shell becomes elliptical, 

 and as elongation (increase in height) continues 

 the principal vector of growth shifts to one side 

 (fig. 32b). 



A series of curves noticeable on round shells 

 (fig. 32) clearly illustrate the differential rate of 

 growth along the periphery of the valve, whicli 

 increases in size without altering in configuration. 

 Tliompson (1942) found an interesting analogy 

 between tills type of growth, radiating from a 

 single focal point (the umbo), and the theorem 

 of Galileo. Imagine that we have a series of 

 planes or gutters originating from a single point 

 A (fig. 30) and sloping down in a vertical plane 



MORPHOLOGY AND .STRUCTURE OF SHELL 



at various angles along the radii AB, AC, ACi, 

 and ABi which end at the peripheiy of a circle. 

 Balls placed one in each gutter and simultaneously 

 released will roll down along the vectors B, Bi, C, 

 Ci, and D. If there is no friction or other form 

 of resistance, all the balls will reach the peripheiy 

 at the same time as the ball dropping vertically 

 along AD. The acceleration along any of the 

 vectors, for instance, AB, is found from the 

 formula t^ = 2/g AD where t is time and g is 

 acceleration of gravity. 



A similar law, involving a more complex 

 formula, applies to cases in which the generating 

 curve is nearly elliptical, for instance, in the 

 shells of adult oysters. The rate of growth at 

 different sectors of the periphery of the shell 

 obviously has nothing to do with the acceleration 

 of gravity, but the similarity between the length 

 of the radii which represent the rate of growth 

 along a given direction of the shell and the accelera- 

 tion along the vectors in the theorem of Galileo 

 is striking. It appears reasonable to expect that 

 the Galileo formula may be applicable to the 

 physiological process taking place near the edge 

 of the valve. One may assume, for instance, that 

 the rate of physiological activities is afTected by 

 the concentration of growth promoting sub- 

 stances or by enzymes involved in the calcification 

 of the shell and that these factors vary at different 

 points of tlie mantle edge in conformity with 

 Galileo's formula. Experimental exploration of 

 the possibilities suggested by mathematical paral- 

 lelism may be, therefore, profitable in finding the 

 solution to the mysteiy of the formation of shell 

 patterns. 



CHANGES IN THE DIRECTION OF 

 PRINCIPAL AXES OF SHELL 



Tlie principal axes of shells of C. virghvica are 

 not as permanent as they are in clams, scallops, 

 and other bivalves in which the shape of the 

 valves remains fairly constant and is less afl'ected 

 by environment than in the oyster. The plasticity 

 of oysters of the species Crassasfrea is so great 

 that their shape cannot be determined geometri- 

 cally (Lison, 1949). This inability to maintain 

 a definite shape is proba])ly the result of the 

 sedentary living associated with complete loss 

 of the power of locomotion. 



In some species of oysters the shells are circular 

 or nearly circular. In such cases the ratio of 

 the heiglit of tlie valve to its length is ecjual to 



27 



