34 SMITHSONIAN INSTITUTION 



the connecting ridges crossing the sutures from plate to plate, and of the sunken 

 areas at the angles, forming pits or rhombs between them, as already explained 

 (PL IV, fig. 3). Owing to fixation and loss of function, the shape of the pinnu- 

 lars is more or less modified and often irregular, which adds to the difficulty 

 of identifying them. In some cases, the reticulate or banded surface com- 

 mences abruptly; in others, the sculpturing passes from the finely costate 

 marking of the lower calyx plates through an intermediate stage of stelliform 

 plates. This is sometimes much accentuated by erosion of the plates sufficient 

 to expose strong radiating channels in the substance of the plates crossing the 

 sutures (PI. Ill, fig. 3; PI. IV, fig. 2; PL VIII, figs. 2a, b). 



Inspection of figure 1 of Plate IV shows that while the relation of the fixed 

 pinnules to the tertibrachs as stated by Bather is confirmed, there is a further 

 definite relation, not only with the distal secundibrachs, which he found it not 

 so easy to trace, but also with the lower secundibrachs, as to which he thought 

 it probable that the plates uniting them are true interbrachials. As to all these 

 it now appears that there is a fixed rule in the position and sequence of the 

 pinnules. 



The sequence of pinnules. — The number of secundibrachs in these speci- 

 mens, as already stated, is quite uniformly about 18 to 20. They begin with 

 fairly large plates, resembling the primibrachs which precede them, with a 

 gradually increasing rugosity of sculpturing in the first five, beyond which the 

 surface is usually plain; there is also a gradual diminution in size, and a change 

 in proportions from about equal length and width in the lowest ones, to that 

 of extremely short and wide plates above. At about the fifth plate an increas- 

 ing convexity begins, marking the origin of a strong median elevation which 

 passes rapidly into the arms. At this point there is always a plainly noticeable 

 change of direction, or " jog," in the brachials of each ramus toward the 

 outside of the dichotom (PL V, fig. 1). Above this the plates rapidly become 

 shorter and wider, changing from a proportion of about 1:1.6 to about 1:12 

 next to the axillary; and they gradually become cuneiform and alternating. 

 This " jog " is a reliable guide in counting the number of secundibrachs in 

 imperfect specimens ; we know that there are always four or five plates in the 

 series below it. For example, in Plate VI, figure $d, with only a small fragment 

 of the ray preserved, we can tell that there were about 16 secundibrachs. 



The IIBr 2 gives off a strong pinnule toward the outer side of the dichotom, 

 composed of elongate, more or less hexagonal plates extending to the distal 

 margin of the calyx; IIBn gives off a similar pinnule to the inside of the 

 dichotom; IIBr 5 another to the outside. And from the fifth plate on, alter- 

 nating from side to side, each brachial bears a pinnule upon its wider end, 

 which may also abut upon the narrow end of the alternate brachial. The first 

 three to seven pinnules are more or less separated at their bases by interpinnu- 



