398 Prof. Beyrich oa the Base {Pehns) 



its pentagonal form; but the sutures are displaced, and no 

 longer strike tlie middle of the sides. A similar equalization 

 of the inner angles might also be possible in the tripartite 

 pentagon by the displacement of the two sutures bounding 

 the unpaired segment ; but this appears to occur but rarely. 



In the preceding three figures, a shows the symmetrically 

 tripartite and h the symmetrically quadripartite pentagon ; 

 c the latter with the inner angles equalized. The dotted lines 

 in c are in the position of the undisplaced sutures. 



Simple as these conditions are, they were not, when first 

 observed, either correctly interpreted or parti cidarly valued. 

 We may see this from the erroneously indicated divisions, 

 such as are represented in the figures in Goldfuss, Petr. Germ. 

 Taf. 58. fig. 3, or in Johannes Muller, I. c. Taf. 6. fig. 1 a. 

 That both the tripartite and the quadripartite pentagon are 

 only modifications of the quinquepartite, and formed in ac- 

 cordance with a definite law, Avas first explained by L. von Buch 

 in his memoir on the Cystidea ; at first, also, he had a notion 

 that there might be a certain connexion between the occurrence 

 of a sjnnmetrically divided base and a lateral position of the 

 vertical aperture ; but by the further carrying out of this idea, 

 he arrived at false conclusions. His opinion was that the 

 axis in accordance with which the base is divisible into two 

 similar halves, if prolonged meridionally round the Crinoid, 

 must strike the excentrically placed vertical aperture ; and he 

 went so far as to believe that a central vertical aperture can 

 occur only where the base is of regular quinquepartite struc- 

 ture (Ueber Cystideen, p. 5). It would almost appear that at 

 the time when he was endeavouring to decypher the nature of 

 the Cystidea, this observer, otherwise so acute, had never seen 

 the Avell-preserved calyx of a Brachiate Crinoid with a penta- 

 gonal tripartite base. He depends chiefly upon the genus 

 Actinocrimis (Cystideen, Taf. 2. fig. 9), which, however, does 

 not possess the pentagonal base ascribed to it, but an hexa- 

 gonal one ; and for Platycrinus he refers to the figures of 

 Johannes Muller, in the memoir on Pentacnnus (Taf. 6), in 

 Avhich there is nothing to be seen but an erroneously figured 



