670 HERRI CK E. WILSON 



No. 6) ; that of the second theory is xa — b — c — d — e — -, while those 

 of the third theory are ax — b—c — d — e — for lateral enlargement 

 of the left side, and xa — b — c — d — e — for lateral enlargement of the 

 right side. 



b) Development of the quadripartite base. — In the evolution of 

 the four-basal, hexagonal base there can be no disagreement, as 

 but one pair of basals, the anterior pair, is anchylosed. Anchylosis 

 in this type of base is generally accompanied by symmetrical 

 reduction of the compound plate and an asymmetrical and com- 

 pensating enlargement of the apposed basals. The formula for 

 the four-basal type, based upon the theory of symmetrical enlarge- 

 ment of the posterior basal, is a — b — cd — e — (Fig. 9, No. 7) ; that 

 of Wachsmuth and Springer, xa — b — cd — e — (Fig. 1, No. 7). 



c) Development of the tripartite base. — In the discussion of the 

 evolution of the tripartite base three theories will be considered: 

 (i) the tortional theory of Wachsmuth and Springer; (ii) the 

 bisection theory; and (iii) theory of atrophy and compensating 

 hypertrophy. 



i. Tortion theory: Wachsmuth and Springer's theory may be 

 stated as follows: The equally tripartite base of the hexagonal 

 Camerata originated from an unequally tripartite base of the 

 Platycrinus type by the addition of an anal plate, which caused 

 (1) a spreading of the posterior interradius; (2) a tortion of the 

 base which brought the right-posterior and anterior basal sutures 

 respectively into contact with the anal plate and the right-anterior 

 radial; and (3) the addition of a lateral-growth factor (x), to the 

 right of the left-anterior basal. The evolution of the base upon 

 this theory may be expressed in formula as follows: ab — c — de — 

 to ab — ex — de — (Fig. 1, Nos. 3, 9, 10). 



Since this theory was thought to have been confirmed by an 

 abnormal example of Teleiocrinus umbrosus in which the anal plate 

 is missing and the base, supposedly, reduced to the Platycrinus 

 type (ab — c — de — ), it assumes (1) that the subequally tripartite 

 base did not originate from the hexagonal five- or four-basal forms, 

 but from another line, or (2) that it did originate from them and 

 that an intermediate form existed in which the anal plate was 

 temporarily lost and the base was like that of Platycrinus. This 



