Vol. 54.] MR. F. A. BATHER ON PETALOCRINUS. 411 



The grooves on the ventral surface of the arm -fan are proved by 

 their mode of branching, and by various structures described in 

 due course, to represent the ventral grooves of originally separate 

 arm-branches. 



The grooves do not simply radiate from the proximal end, as do 

 the grooves of a fan or of the test of some brachiopods, but dicho- 

 tomize according to a plan that is approximately the same for all 

 species, and still more the same for all individuals of each species. 

 This dichotomy may be described in language similar to that used 

 in describing ordinary free arms, the difference being that one is 

 unable to insert the numbers of the brachials in each series, since 

 no trace of the original joints is retained. 



In P. mirabilis, P. visbycensis, and P. inferior the grooves (or 

 arm-branches) divide almost immediately on entering the fan, so 

 that a distinct ridge runs down the middle of each fan, dividing it 

 into two similar halves. The secundibrach region is quite short, 

 and the groove forks again almost at once. 



In fans of P. miralilis, nearly, if not absolutely, without excep- 

 tion, the two main divisions of the fan are almost precisely similar, 

 that is, the arm-fan is bilaterally symmetrical. Moreover, so far 

 as number is concerned, the branching is perfectly regular or ' iso- 

 tomous ' ; there are always 2 IIBr grooves, 4 IIIBr, 8 IVBr, and 

 16 YBr, these last being the finials; or, as Mr.Weller puts it, there 

 are ' 16 ambulacral grooves at the distal edge of each arm.' This 

 number is stated by Mr. Weller in a letter to be invariable ; and 

 the specimens submitted to me confirm his statement. Though 

 isotomous in respect of number and bilateral symmetry, the forking 

 of the III, IV, and Y Br series takes place at unequal levels. Por 

 example, confining our attention to the right-hand half of any fan 

 (as viewed from the ventral surface), we see that the right-hand or 

 outer IIIBr groove forks before the left-hand or inner groove ; 

 whereas, of the two lYBr branches springing from the latter, it is 

 always that on the left which forks first. This may be reduced to 

 rule. In any crinoid arm all the portion borne by any one axillary 

 may be termed a ' dichotom,' and the line bisecting that axillary 

 may be regarded as the median axis of the said dichotom ; branches 

 next to the median axis will be mediad with respect to that par- 

 ticular dichotom. If these terms be applied to Petalocrinus^ the 

 law governing the branching maybe stated thus : in each dicho- 

 tom that groove is first to branch which is farthest 

 from the median axis of the preceding dichotom. This, 

 though subject to minor modifications in the various species, is the 

 law for the whole genus. It is but another mode of expressing 

 the law that governs the branching of ail primitive, non-pinnulate, 

 simply dichotomous arms, and is the regular law for all Cyatho- 

 crinoidea that have more than two arm-branches. On p. 156 of 

 ' The Crinoidea of Gotland: Part I.,' the law was thus expressed : 

 ' the series towards the middle of each dichotom contain more 

 ossicles than the outer branches.' The facts upon which the law 

 was based are given in various parts of that paper, and on p. 219 of 



