828 THE EQUIANGULAR SPIRAL [ch. 



a system of nearly symmetrical ellipses with the vertical axis about 

 twice the transverse; in Solen pellucidus, we have again a system 

 of lines of growth which are not far from being symmetrical eUipses, 



Ct 10 

 Fig. 402. 



in which however the transverse is between three and four times 

 as great as the vertical axis. In the great majority of cases, we 

 have a similar phenomenon with the further complication of slight, 

 but occasionally very considerable, lateral asymmetry. 



In the above account of the mathematical form of the bivalve shell, we 

 have supposed, for simplicity's sake, that the pole or origin of the system is 

 at a point where all the successive curves touch one another. But such an 

 arrangement is neither theoretically probable, nor is it actually the case; 

 for it would mean that in a certain direction growth fell, not merely to a 

 minimum, but to zero. As a matter of fact, the centre of the system (the 

 "umbo" of the conchologists) lies not at the edge of the system, but very 

 near to it; in other words, there is a certain amount of growth all round. 

 But to take account of this condition would involve more troublesome mathe- 

 matics, and it is obvious that the foregoing illustrations are a sufficiently near 

 approximation to the actual case. 



In certain little Crustacea (of the genus Estheria) the carapace 

 takes the form of a bivalve shell, closely simulating that of a 

 lamellibranchiate mollusc, and bearing lines of growth in all respects 

 analogous to or even identical with those of the latter. The explana- 

 tion is very curious and interesting. In ordinary Crustacea the 

 carapace, like the rest of the chitinised and calcified integument, is 

 shed off in successive moults, and is restored again as a whole. 

 But in Estheria (and one or two other small Crustacea) the moult is 



