822 THE EQUIANGULAR SPIRAL [ch. 



The angle of retardation (y ) is very small in . Dentalium and 

 Patella ; it is very large in Haliotis ; it becomes infinite in Argonauta 

 and in Cypraea. Connected with the angle of retardation are the 

 various possibilities of contact or separation, in various degrees, 

 between adjacent whorls in the discoid shell, and between both 

 adjacent and opposite whorls in the turbinate. But with these 

 phenomena we have already dealt sufficiently. 



The beautiful shell of the paper-nautilus {Argonauta argo L.) differs 

 in sundry ways both from the Nautilus and from ordinary univalves. 

 Only the female Argonaut possesses it; it is not attached to its 

 owner, but is (so to speak) worn loose; it is rather a temporary 

 cradle for the young than a true shell or bodily covering; and it 

 is not secreted in the usual way, but is plastered on from the outside 

 by two of the eight arms of the Uttle Octopus to which it belongs. 

 The shell shews a single whorl, or but Httle more; and the spiral 

 is hard to measure, for this reason. It ha« been supposed by some 

 to obey a law other than the logarithmi-c spiral. For my part I have 

 made no special study of it, nor has any one else, to my knowledge, 

 of recent years; but the simple fact that it conserves its shape as it 

 grows, or that each increment is a gnomon to the rest, is enough to 

 shew that this dehcate and beautiful shell is mathematically, though 

 not morphologically, homologous with all the others. 



Of bivalve shells 



Hitherto we have dealt only with univalve shells, and it is in 

 these that all the mathematical problems connected .with the spiral, 

 or hehco-spiral, configuration are best illustrated. But the case of 

 the bivalve shell, whether of the lamelHbranch or the brachiopod, 

 presents no essential difference, save only that we have here to do 

 with two conjugate spirals, whose two axes have a definite relation 

 to one another, and some independent freedom of rotatory movement 

 relatively to one another. 



The bivalve or lamelHbranch moUusca are very different creatures 

 from the rest. The univalves or gastropods, hke their cousins the 

 cephalopods, go about their business and get their living in an 

 ordinary way; but the bivalves are linintelHgent, "acephalous" 

 animals, and imbibe the invisible plankton-food which ciliary 

 currents bring automatically to their mouths. There is something 



