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Show 732 MR. P. H. CARPENTER ON THE [Dec. 1 9, applies it to denote the varying characters of the cirri; and I shall have much pleasure in employing it to this extent. His idea of distinguishing Antedon and Actinometra by A and A' respectively is also a good one; though I should myself prefer A and a, as being less liable to printers' errors. He gives formula? for 58 species, 1 2 of which are M S . names of his own ; but of the remaining 46 formulae, no less than 12 would lead a collector who depended upon them for identification of a specimen to form a false conception of the corresponding species. In the case of Act. parvicirra and Act. novce guinea, the error is but a slight one. But the formulae given for Act. bennetti, Act. peroni, Act. schlegeli and other species denote a type of the genus which I have never met with, much less described ; and were it not that I am now prepared for nearly any freak of nature among these animals, I should almost venture to call it a " Comatulid impossibility." Eight of these twelve species (including the three -above mentioned) have been described by myself in the ' Notes from the Leyden Museum,' vol. iii.; and as these Notes have a far less wide circulation than the Proceedings of the Zoological Society, it is necessary to prevent other workers from forming the wrong conceptions of these types which would result from the exclusive use of Prof. Bell's formulas. The errors are in the parts of the formula? which denote the characters of the rays and their subdivisions, the remaining portions, which indicate the positions of the syzygies in the arm-bases and the characters of the cirri, requiring no alteration. As regards the former, Prof. Bell says:- " If (1) we use the letters R, D, P for the radials, distichals, and palmars respectively, and insert them in the formula whensoever the respective axillary is a syzygy, we may (2) distinguish which of the first three brachials (one of which is, with but with very rare exceptions, a syzygy) is a syzygy by simply making use of the number 1, 2, or 3. ... When a character frequently, though not always, obtains, the corresponding letter is put within brackets. . . . W h e n D or P appear in a formula it is clear the species must have more than 10 rays1, because of the meaning of the words those letters represent; where, however, neither distichals nor palmars present a syzygial joint, it will be necessary to make use of the mathematical sign for the square root to mark the fact of its being a multiradiate species" (pp. 531-532). 1 Prof. Bell has here confounded the ten primary arms with the rays proper, by the division of which tbese arms originate. This has led him into much confusion, as will be pointed out later. According to Miiller, " Radien nenne ich die auf dem Knopf aufgesetzten Suimme der Anne.... Auf jedem der 5 Ketch-radien sitzen 2 Arme, die entweder einfach bleiben oder sich noch einmal oder mehrmal wieder theileu." (" Ueber die Gattung Comatula, Lam., und ihre Arten," Abhandl. d. Berlin. Akad. 1849, p. 240.; Tbe arms therefore were clearly distinguished from the rays by Miiller ; and it is a pity that Prof. Bell has confounded them, especially as in the genus Promachocrinus there actually are ten rays springing directly from the centrodorsal. |