Terms in Crinotd Morphology. 61 



bein£^ represented by " Ax " instead of " ax," and hy the use 

 of Arabic instead of Roman numerals. 



We are now in a position to express in tlie formulre tlie 

 number of bracliials in any series. To say that tlic Quartaxil 

 is tlie fifth ossicle of its series is obviously the same thing as 

 saying that there are five quartibrachs ; while to say that the 

 third nnunaxil (or Tctraxil) is the fourth ossicle of its scries 

 is obviously the same thing as saying that there are four 

 tetrastichals. These facts may be expressed symbolically 

 thus — IV ax.,, and 3 Ax, ; which symbols come to mean just 

 the same as IV Br-5 and 4 St- 1, or as IVBr5=IVax, and 

 4St4 = 3 Ax. Applying this method to the formulas we get 

 such results as these : — 



Thenarocrinus callipygus. 



I axg . II aX(,) . Ill ax^_i^ . IV-VIII ax^.^g .f^, 



which being interpreted is, Primibrachs 3, Secundibrachs 4 

 as a rule, Tertiobrachs from 4 to 10, Quartibrachs, Qiiiuti- 

 brachs, Sextibrachs, Septimibrachs, and Octavlbrachs from 6 

 to 18, inmiber of finials uncertain. It also conveys the infor- 

 mation that the arms branch eight times, that they are nou- 

 pinnulate, and that none of the bracliials enter into the 

 dorsal cup. 



Botryocrinus pinnulatus. 



Iax4.2St-35 + , 



which indicates that there are four primibrachs, which are 

 free, that there are two arms to each ray, which do not branch 

 again but which bear pinnules, and that the number of ossicles 

 in each of these arms is uncertain, but exceeded 35. 



Botryocrinus decadactylus. 



I aX(3.,) . (II ax2 & III Br) . 2 St. 



The facts expressed by this are somewhat more compli- 

 cated. Primibrachs are usually 3 or 4, but may be more or 

 less ; they are free. It is clear from the symbol 2 St that 

 the arm bifurcates on the primaxil ; but the signs in brackets 

 that precede 2 St show that the earlier ossicles of this distichal 

 series do not all bear pinnules, there being first a simple 

 secundibrach, then a secundibrach bearing either a pinnule or 

 armlet, then a simple ossicle which is morphologically a 

 tevtiobrach, and then the series of pinnuliferous distichals of 

 which the number is uncertain. 



