816 THE EQUIANGULAR SPIRAL [ch. 



illustrations of this ratio in particular cases, in addition to those 

 which we have already studied. 



Ratio of breadth of consecutive whorls 



Pointed Turbinates 



Telescopium fuscum ... 1-14 



Terebra suhulata ... ... 1-16 



* Turritella terebellata ... 1-18 

 *Turritella imbricata... ... 1-20 



Cerithium palustre ... ... 1 "22 



Turritella duplicata ... ... 1-23 



Melanopsis terebralis ... 1-23 



Cerithium nodulosum ... 1-24 



* Turritella car inata ... ... 1-25 



Terebra crenulata ... ... 1-25 



Terebra maculata (Fig. 397) 1-25 



*Cerithium lignitarum ' ... 1-26 



Terebra dimidiata 1-28 



Cerithium sulcatum ... ... 1-32 



Fusus longissimus ... ... 1*34 



*Pleurotomaria conoidea ... 1-34 



Trochus niloticus (Fig. 398) 1-41 



Mitra episcopalis ... ... 1-43 



Fusus antiquus ... ... 1 -50 



Scalaria pretiosa ... ... 1-56 



Fusus colosseus ... ... 1-71 



PhasiaTvella australis ... 1-80 



Helicostyla polychroa ... 2-00 



Obtuse Turbinates and Discoids 



Conus virgo ... ... ... 1-25 



XClymenia laevigata ... ... 1-33 



Conus litteratus ... ... 1*40 



Conus betulinus ... ... 1-43 



XClymenia arietina ... ... 1-50 



%Goniatites bifer ... ... 1-50 



* Helix nemoralis ... ... 1-50 



* Solarium perspectivum ... 1*50 

 Solarium trochleare ... 1-62 

 Solarium magnificum ... 1-75 



*Natica aperta ... ... 2-00 



Euomphalus pentangulatus 2-00 



Planorbis corneus ... ... 2-00 



Solaropsis pellis-serpentis ... 2-00 



Dolium zondtum ... ... 2-10 



XGoniatites carinatus ... 2-50 



*Natica glaucina ... ... 3-00 



Nautilus pompilius ... 3-00 



Haliotis excavatus ... ... 4-20 



Hal^otis parvus ... ... 6*00 



Delphinula atrata ... ... 6-00 



Haliotis rugoso-plicata ... 9-30 



Haliotis viridis ... ... 10-00 



Those marked * from Naumann; J from Miiller; the rest from Macalisterf. 



In the case of turbinate shells, we muSt take into account the 

 angle y^, in order to determine the spiral angle a from the ratio 

 of the breadths of consecutive whorls; for the short table given 

 on p. 791 is only applicable to discoid shells, in which the angle fi 

 is an angle of 90°. Our formula, as mentioned on p. 771, now 

 becomes 



J^ _ ^27rsin/?cota 



For this formula, I have worked out the following table. 



f Alex. Macahster, Observations on the mode of growth of discoid and turbinated 

 shells, Proc. R.S. xviii, pp. 529-532, 1870; Ann. Mag. N.H. (6), iv, p 160, 1870. 

 Cf. also his Law of Symmetry as exemplified in animal form, Journ. B. Dublin Soc. 

 1869, p. 327. 



