402 Prof. Beyrich on the Base {Pelvis) 



The base in both genera is exceptionally small, and for the 

 most part covered by the stem ; its composition was unknown 

 to or misunderstood by the founders of the genera. That 

 Taxocrimis possesses a dicyclic tripartite base was first esta- 

 blished by Johannes Mliller ; in Forbes iocrinus it was first 

 observed by Hall in species from the Carboniferous Limestone 

 of America. Among the materials in the Berlin Museum, the 

 composition of the base was visible in a well-preserved Taxo- 

 crimis tuber culatiis, and in two isolated calycine bases from the 

 Carboniferous Limestone of Bollandand of Altwasser,in Silesia, 

 of which the first probably belongs to Forbes iocrinus nohilis^ 

 and the other to a still unknown species of the same genus. In 

 the two calycine bases the inner basal circle is very small, and 

 visible with distinctly preserved sutures only on the inside of 

 the base ; on the outside, in the surface of attachment of the 

 stem, no sutures presented themselves, even on the applica- 

 tion of acids ; so that in perfectly preserved heads the com- 

 position of the base in these species would hardly be demon- 

 strable. 



In the three observed cases the sutures of the inner basal 

 circle exhibited the position shown 

 in the annexed figure. As the 

 segments of the second basal cir- 

 cle alternate with those of the 

 first, the pentagon, compared with 

 that of the monocyclic base of 

 PlatycrinuSj has received a re- 

 versed position, and the sides now 

 correspond with the interradial, 

 the angles with the radial, direc- 

 tions of the calyx. The segments 

 and the sutures of the symmetri- 

 cally divided lower basal circle Taj-ocn'nu'^. 

 have acquired a totally difterent 



position ; but the direction of the dorsal axis has remained 

 precisely the same ; as in Platj/crinus, it passes from the 

 right adjacent radius to the left abjacent interradius. 



In order to review the simple foundation of this phenomenon 

 the more easily, we must start from the geometrical condition 

 that a symmetrical tripartition of the regular pentagon may 

 take place in two different ways, as the unpaired suture be- 

 tween two larger segments might issue from any one of the 

 five angles or from the middle of any one of the five sides. 

 As the division takes place in a pentagon the segments of 

 which alternate with the superjacent ones, the divisions start- 

 ing from the angles are excluded, and five modes of division 



