XI] OF THE MOLLUSCAN SHELL 785 



one another in a constant ratio or continued proportion*; and 

 Leopold von Buch and others accepted and even developed the 

 idea. 



Long before, Swammerdam had grasped with a deeper insight 

 the root of the whole matter; for, taking a few diverse examples, 

 such as Helix and Spirula, he shewed that they and all other spiral 

 shells whatsoever were referable to one common type, namely to 

 that of a simple tube, variously curved according to definite mathe- 

 matical laws; that all manner of ornamentation, in the way of 

 spines, tuberosities, colour-bands and so forth, might be superposed 

 upon them, but the type was one throughout and specific differences 

 were of a geometrical kind. "Omnis enim quae inter eas anim- 

 advertitur differentia ex sola nascitur diversitate gyrationum: 

 quibus si insuper externa quaedam adjunguntur ornamenta pin- 

 narum, sinuum, anfractuum, planitierum, eminentiarum, profundi- 

 tatum, extensionum, impressionum, circumvolutionum, colorumque : 

 . . . tunc deinceps facile est, quarumcumque Cochlearum figuras 

 geometricas, curvosque, obliquos atque rectos angulos, ad unicam 

 omnes speciem redigere : ad oblongum videhcet tubulum, qui 

 vario modo curvatus, crispatus, extrorsum et introrsum flexus, 

 ita concrevitf." 



Nay more, we may go back yet another hundred years and find 

 Sir Christopher Wren contemplating the architecture of a snail-shell, 

 and finding in it the logarithmic spiral. For AValhsf, after defining 

 and describing this curve with great care and simplicity, tells us 

 that Wren not only conceived the spiral shell to be a sort of cone 

 or pyramid coiled round a vertical axis, but also saw that on the 

 magnitude of the angle of the spire depended the specific form of 

 the shell: "Hanc ipsam curvam . . . fcontemplatus est Wrennius 

 noster. Nee tantum curvae longitudinem, partiumque ipsius, et 



* J. C. M. Reinecke, Maris protogaei Nautilos, etc., Coburg, 1818, p. 17: "In 

 eius forma, quae canalis spiram convoluti formam et proportiones simul sub- 

 ministrat, totius testae forma quoddammodo data est. Restaret solum scire, 

 quota cuj usque anfractus pars sequent! inclusa^it, ut testam geometrice construere 

 possimus." Cf. Leopold von Buch, Ueber die Ammoniten in den alteren Gebirgs- 

 schichten, Ahh. Berlin. Akad., Phys. Kl. 1830, pp. 135-158; Ann. Sc. Nat. xxvin, 

 pp. 5-43, 1833; cf. Elie de Beaumont, Sur I'enroulement des Ammonites, Soc. 

 Philom., Pr. verb. 1841, pp. 45-4^. 



t Biblia Naturae sive Historia Insectorum, Leydae,.1737, p. 152. 



X Job. Wallis, Tractatus duo, de Cydoide, etc., Oxon., 1659, pp. 107, 108. 



