ZOOLOGY AND BOTANY, MICROSCOPY, ETC. 763 



(2) The second part of Haacke's paper contains an account of his 

 studies on abnormal Ambhjpneusfes, — (a) with four parameres ; (6) with 

 six ; (c) with differentiated median planes ; ((?) with hypertrophied 

 parameres ; (e) with two madreporic plates ; (/) with irregular peristomal 

 interambulacral plates. 



(3) The real question is whether the sea-urchin consists of five equiva- 

 lent portions, or only of two. It is evident that in all normal cases there 

 are five parameres, though many exhibit in the reduction of one a tendency 

 to become bilateral. The question is arithmetical, not geometrical. What- 

 ever be the geometric form, bilateral animals have two, and radial at least 

 three equivalent portions. That the geometric median plane in Clypeastroids 

 and Petalostichidae is different from that in Echinometra, and that again 

 different from the closely related Golobocentrotus, and that it occupies at 

 least four different positions in Ambhjpneustes are facts not to the point. 

 The question is arithmetical. 



Only radially symmetrical animals with an unequal number of para- 

 meres greater than two, can admit of a sudden and direct increase or 

 decrease in the number of their parameres. That is unknown in bilateral 

 animals. Even in Clypeasters with distinct and constant median planes, 

 the occurrence of forms with four and six rays, as noted by L. Agassiz and 

 Desor, shows how increase and reduction may even then occur. The 

 Clypeastroids and Petalostichidae are just as radial as the endocyclic 

 forms, in spite of the median plane present in the former. 



But by the gradual occurrence of paired symmetry throughout the 

 entire structure, a radial animal may become bilateral, and mutatis mutandis 

 vice versa. The difference between a bilateral with two, and a radial with 

 three parameres, is not greater than the difference between two radially 

 symmetrical animals with four and five parameres respectively. The 

 distinction has in fact been unwisely exaggerated out of proportion to its 

 real importance. 



Morphological Relations of Summit-plates in Blastoids, Orinoids, and 

 Cystids.* — Messrs. C. Wachsrauth and F. Springer discuss the views put 

 forward by Dr. P. H. Carpenter and Mr. E. Etheridge jun. in their recent 

 Catalogue of the Blastoids in the British Museum. The latter authors try 

 to show that the summit-plates of Blastoids exhibit a series of variations 

 in number and position in some degree corresponding with a similar but 

 more extensive series of variations among the Palaeocrinoidea — they both 

 exhibit a transition from five closely united plates fully covering the 

 summit to a set of six proximal plates surrounding a central one ; the six 

 proximal plates are regarded by Messrs. Carpenter and Etheridge as the 

 homologues of the five oral plates of the Neocrinoidea. Messrs. Wachsmuth 

 and Springer are, however, of opinion that the English authors have alto- 

 gether failed to point out a single case in which five primary plates cover 

 the peristome among Blastoids, and they think that the superficial resem- 

 blance in the form and position of the ventral plates oi Allagecriniis, Haplo- 

 crinus, &c., with the orals of certain Neocrinoids has led Dr. Carpenter to 

 regard them as orals. It may be pointed out that these plates agree equally 

 well with the interradials of the Cyathocrinidfe, and that, as interradials, 

 the genera just named do not present any exceptional type in the morpho- 

 logical conditions of these plates. The American critics refuse to look on 

 the " orocentral " as being anything more than a highly hypothetical plate, 

 and they refuse, therefore, to understand how five plates, without coming 

 into contact with the anus, were transformed into six plates or more. 



* Proc. Acad. Nat. Sci. Philad., 1887, pp. 82-114 (1 pi.). 



