Figure 23. — Logarithmic or equiangular spiral. Expla- 

 nation in text. 



increase in size is not accompanied by any change 

 in shape of the shell; the proportions of the latter 

 remain constant, and the shell increases only in 

 size (gnomonic growth). This general rule holds 

 true for many free-moving gastropods and bi- 

 valves. It is not, however, applicable to sessile 

 forms like oysters, in which the shape of the shell 

 changes somewhat with size, particularly at the 

 early stages of growth, and is greatly modified 

 by contact with the substratum upon which the 

 niollusks rest. The plasticity and variability of 

 attached forms are probably associated with their 

 inability to escape the eflfects of proximate 

 environment. 



The contour of oyster shell may be either circular 

 (young C. virginica, 0. edulis) or elongated and 

 irregular. Spiral curvature may be noticed, 

 however, on a cross section of the lower (concave) 

 valve cut along its height perpendicular to the 

 hinge. The curve can be reproduced by covering 

 the cut surface with ink or paint and stamping 

 it on paper. The upper valve is either flat or 

 convex. 



The curvature of bivalve shells is sometimes 

 called conchoid. The term may be found in 



general and popular books dealing with bivalve 

 shells, but the author who introduced it in scien- 

 tific literature could not be traced. The Greek 

 word "conchoid", derived from "conch" — shell 

 and "eidos" — resembling or similar to, implies 

 the similarity of the cinwe to the contour of a 

 molluscan shell. 



The curve is symmetric with respect to the 90° 

 polar axis (fig. 24). It consists of two branches, 

 one on each side of the fixed horizontal line CD 

 to which the branches approach asymptotically 

 as the curve extends to infinity. The curve, 

 known us conchoid of Nicomedes, is constructed by 

 drawing a line through the series of points P and 

 Pi which can be found in the following way: from 

 the pole draw a line OP which intersects the 

 fixed line CD at any point Q. Lay off segments 

 QP=QPi = b along the radius vector OP. Repeat 

 the process along the radii originating from the pole 

 O and draw the two branches of the curve by 

 joining the points. The cmwe has tliree distinct 

 forms depending on whether "a" (a distance OQ 

 from the pole to the point of intersection of the 

 polar axis with the fixed line CD) is greater, equal 

 to or less than b. The formula of the cm-ve if 

 b<a, is r = a sec ^±b, where r is the locus of the 

 equation and sec 6 is secant of the vectorial angle B. 

 Sporn (1926) made a detailed mathematical 

 analysis of the conchoid curve and considered 

 that the curvatures of bivalve shells conform to 

 this geometrical type. Lison (1942) rejected this 

 conclusion as not supported by observations and 

 experimental evidence. He quite correctly stated 

 that Sporn 's work deals exclusively with abstract 

 mathematical analyses of curves which in reality 

 are Tiot those found in molluscan shells. If one 

 cuts a bivalve shell at any angle to the plane of 

 closure of the valves, one obtains the curved 

 lines of the two valves (fig. 25) which only remotely 

 resemble the conchoid of Nicomedes and touch 



Figure 24. — Construction of the conchoid curve of 

 Xicomedes. Explanation in text. 



MORPHOLOGY AND STRUCTURE OF SHELL 



23 



