162 PROBLEMS OF RELATIVE GROWTH 



A rather different example is provided by the razor-shells 

 (Solen). In these, the normal symmetrical gradient of the 

 lamellibranch shell, wrdj^grQAvthrcentre opposite the hinge, is 

 completely distorted by the development of a second growth- 

 centre at the morphologically posterior (siphonal) margin of 

 the shell. This occurs, of course, in numerous other forms, 

 making the shell asymmetrical along the antero-posterior 

 axis ; but in Solen this ' secondary ' growth-centre has become 

 more important than the phylogenetically primary one, and 

 its markedly higher growth-ratio converts the shell into the 

 well-known elongated blade. 1 The margin of the shell at 

 this end is truncated, but the opposite margin is rounded, the 

 shell thus consisting of two markedly different but homologous 

 halves, the one conforming to the normal lamellibranch shape, 

 the other pulled out to ten or even twelve times the diameter 

 of the former. Still further examples, again of a somewhat 

 different type, are seen in the spines which beset the shell of 

 such forms as the Spiny Cockle {Cardium acidcatum) or various 

 Gastropods. These represent localized centres of excess 

 mantle-activity, which, however, are only active periodically. 

 Permanently^active fluctuations in growth-activity along the 

 gradient are revealed in such forms which have a crenellated 

 margin to the shell (e.g. Tridacna). It is not known whether 

 the presence of such special centres of high growth-ratio is 

 correlated, as in Crustacea, etc., with slight excess or defect 

 of growth in adjacent regions. 



As in multiplicative growth, these subsidiary regions of 

 special growth-activity are themselves constructed on the 

 usual plan, of growth-gradients — single or double — culminating 

 in a high point or growth-centre. 



The bivalve shell (Lamellibranch and Brachiopod) demands 

 a few words to itself. It_Dwes its form to the existence of 

 two separate gradients of accretionary growth, each forming 

 a shell of logarithmic-spiral form. "Typically, the two gradients 

 are equal but of opposite sign, each symmetrical about a line 

 drawn from the hinge to the ventral margin ; the growth- 

 ratio at the hinge is so close to zero as to be negligible, while 

 the component of growth in shell-width is relatively so large 

 that the spiral is a very high-angled one, and never forms 

 even one complete whorl. 



1 When distortion of this type occurs, it is usually the posterior 

 half which is enlarged ; but there are a number of genera which show 

 the opposite tendency (e.g. Donax). 



