Centimeters 



Figure 22. — Two left shells of C. virginica grown on sticky mud. On the left side is the oyster from Karankawa Reef in 

 Matagorda Bay, Tex.; on the right is the oyster from Hadley Harbor, Naushon Island, near Woods Hole, Mass. 

 The dimensions of the Texas oyster are 1.3 by 11.5 cm. (.5.1 by 4.5 inclies) and for the Hadley Harbor oyster 15.5 by 

 14.5 cm. (6.1 by 5.7 inches). 



who in the book, "Biodynamique generale," at- 

 tributes mysterious and not well-defined meaning 

 to the "stereodynamics of vital vorte.x." These 

 speculations contributed nothing to the under- 

 standing of the processes which underlie the for- 

 mation of shells and other organic structures. 



In the earlier days of science the geometric 

 regularity of shells, particularly that of gastropods, 

 had been a favored object for mathematical 

 studies. Properties of curves represented by the 

 contours of shells, as well as those seen in horns, 

 in flower petals, in the patterns of distribution of 

 branches of trees, and in similar objects, were 

 carefully analyzed. An e.xcellent review of this 

 chapter of the history of science is given in a well- 

 known book "On growth and form" (Tliompson, 

 1942) in which the reader interested in nuithe- 

 matics and its application to the analysis of organic 

 forms will find many stimulating ideas. 



Among the array of curves known in matlie- 

 matics, the kind most fretiuently encountered in 

 the shells of mollusks is the logarithmic or equi- 

 angular spiral (fig. 23). The latter name refers to 

 one of its fundamental characteristics, described 

 by Descartes, namely, that the angle between 



tangent PG (fig. 23) and radius vector OP is con- 

 stant. Another property of tliis curve which may 

 be of interest tt) biologists is the fact that distances 

 along the ctu've intercepted by any radius vector 

 are proportional to the length of these radii. 

 D'Arcy Thompson showed that it is possible to 

 apply the mathematical characteristics of curves 

 to the interpretation of the growth of those shells 

 which follow the pattern of a logarithmic spiral. 

 According to his point of view, growtli along the 

 spiral contour is considered as a force acting at any 

 point P (fig. 23) which may be resolved into two 

 components PF and PK acting in directions per- 

 pendicular to each other. If the rates of growth 

 do not change, the angle the resultant force, i.e., 

 the tangent PG, makes with the radius vector re- 

 mains constant. This is the fundamental property 

 of the "equiangular" (logarithmic) spiral. The 

 idea forms the basis of Huxley's (1932) hypothesis 

 of tlie interaction of two differential growth ratios 

 in tlie bivalve shells and also underlies Owen's 

 (1953) concept of tlie role of the growth compo- 

 nents determining the shape of the valves. [ 

 .\nother important characteristic nf the growth " 

 of l)ivalves pointed out by Thompson is tliat 



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