THE SHELLS OF MOLLUSCS 



159 



Thus in most Ammonitoid and Gastropod shells with con- 

 stant angle between 8o° and 85 °, to produce contact between 

 the whorls the outer border must be growing between 3 and 

 17 times as fast as the inner. For spirals with lower con- 

 stant angle (i.e. those with high ratio of breadth-growth to 

 length-growth), the median growth-ratio must be much higher. 

 In open-coiled forms, however, the median growth-ratio will 

 be less, and does not have to increase so fast with decrease 

 of constant angle to preserve the same spacing. When the 

 median growth-ratio is very high, we shall get forms whose 

 whorls completely overlap, like Nautilus, if the constant angle 

 is high ; but if the constant angle is low we shall then get 

 types like Haliotis (or most Lamelli- 

 branch shells). 



(3) The lateral growth-ratio. If in 

 addition to the preceding two differ- 

 ential growth-ratios, we have also one 

 in a plane inclined (usually, it appears, 

 at right-angles) to the median, the result 

 will be what D'Arcy Thompson some- 

 what loosely speaks of as a " shear " in 

 the plane spiral, with as result a ' cork- 

 screw ' or turbinate spiral — i.e. a spiral 

 not confined to one plane. This is 

 prettily shown in the accompanying 

 sketches kindly given me by Miss M. 

 Lebour, of the Plymouth Laboratory, 

 illustrating the origin of this complex 

 spirality in a larval Pteropod. The 

 original shell is a hemispherical cap, 

 produced by growth which is uniform 

 all round. After a certain stage, how- 

 ever, a marked difference appears in the growth at the two 

 ends of the median axis, and a smaller difference in the 

 growth at the two sides ; and the shell at once begins to 

 ' corkscrew '. 



In terms of growth-gradients, what happens appears to be 

 as follows (Fig. 76) : If ABCD in (a) be the projection of the 

 growing edge of the mantle, with A the region of maximum 



(H — h)> C of minimum ( ) growth, with no lateral 



differential growth, then the corresponding gradient is shown in 

 (c). If, however, a lateral differential is established, the results 

 will be as shown in (b) and (d). The lateral differential growth- 



Fig. 75. 



Limacina retro- 

 versa. 



(a) shell of larva i day old ; the 

 shell is hemispherical ; (b) shell of 

 larva 3 days old. Differential 

 growth has begun, (c) Larva in 

 its shell, 4 days old. Differential 

 growth has proceeded further, and 

 the spiral shape of the shell is 

 apparent. 



