866 THE SPIRAL SHELLS [ch. 



We may also conceive, among other conditions, the very curious 

 case in which the protoplasm may entirely overspread the surface 

 of the shell without reaching a position of equilibrium; in which 

 case a new shell will be formed enclosing the old one, whether 

 the old one be in the form of a single, solitary chamber, or have 

 already attained to the form of a chambered or spiral shell. This 

 is precisely what often happens in the case of Orbulina, when within 

 the spherical shell we find a small, but perfectly formed, spiral 

 ''Globigerina*.'^ 



The various Miliolidae (Fig. 425) only differ from the typical 

 spiral, or rotaline forms, in the large angle subtended by each 

 chamber, and the consequent abruptness of their inclination to each 

 other. In these cases the outward appearance of a spiral tends to 

 be lost; and it behoves us to recollect, all the more, that our spiral 

 curve is not necessarily identical with the outline of the shell, but 

 is always a line drawn through corresponding points in the successive 

 chambers of the latter. 



We reach a limiting case of the logarithmic spiral when the 

 chambers are arranged in a straight Line ; and the eye will tend to 

 associate with this limiting case the much more numerous forms in 

 which the spiral angle is small, and the shell only exhibits a gentle 

 curve with no succession of enveloping whorls. This constitutes 

 the Nodosarian type (Fig. 134, p. 421); and here again, we must 

 postulate some force which has tended to keep the chambers in 

 a rectilinear series : such for instance as gravity, acting on a system 

 of "hanging drops." 



In Textularia and its allies (Fig. 431) we have a precise parallel 

 to the helicoid cyme of the botanists (cf. p. 767): that is to say we 

 have a screw translation, perpendicular to the plane of the underlying 

 logarithmic spiral. In other words, in tracing a genetic spiral 

 through the whole succession of chambers, we do so by a continuous 

 vector rotation through successive angles of 180° (or 120° in some 

 cases), while the pole moves along an axis perpendicular to the 

 original plane of the spiral. 



Another type is furnished by the "cyclic" shells of the Orbi- 

 tolitidae, where small and numerous chambers tend to be added 



* Cf. G. Schacko, Ueber Glohigerina-^in^chluBS bei Orbulina, Wiegmann's 

 Archiv, XLix, p. 428, 1883; Brady, Chall. Rep. 1884, p. 607. 



