84 SIDERASTREA RADIANS. 



colonial polyps arising asexually as buds. Fortunately, in any colony, 

 individuals of various sizes occur, and thus all the stages in the growth of the 

 third cycle can be secured. As already traced, the mesenteries consist of 

 six equal pairs of protocnemes all united with the stomodaeum, the fifth and 

 sixth pairs having become complete, and six smaller, incomplete pairs of 

 metacnemes, alternating with the former. Following the laws of hexactinian 

 cyclic symmetry the third cycle of mesenteries should consist of twelve equal 

 pairs situated within the exocceles formed by the first and second cycles; 

 the problem is to determine their order of appearance. 



The earliest stage obtained in the formation of the third cycle of mesen- 

 teries is diagrammatically represented in fig. 8, ^, p. 81, taken from one 

 of the small bud polyps of a colony. In addition to the primary and second- 

 ary cycles an isocnemic pair of mesenteries has appeared on each side of the 

 median axis, in the exoccele between the dorsal directives and the dorsal pair 

 of second-cycle mesenteries. Such an early stage would be expected on the 

 dorso-ventral succession already established for the second cycle. The 

 chamber within which the next pair of mesenteries will arise is, however, 

 one of much significance. The succeeding exoccelic chamber on each side 

 is between the dorsal pair of second-cycle mesenteries and the dorso-lateral 

 pair of first-cycle mesenteries, and it might be supposed that the new mesen- 

 teries would occupy the exocceles in regular succession, from one border of 

 the polyp to the other. Instead of this it is found that the pairs arise succes- 

 sively within only the dorsal of the two exocceles of each system. This 

 condition is shown in fig. 8, h, p. 81, the next stage available, where a third- 

 cycle pair (in) is found within the dorsal exoccele of each of the six systems. 



A later stage secured in the establishment of the twelve third-cycle 

 mesenteries is given in fig. 8,/, p. 82, where an additional pair (in, d) has 

 appeared, this time within the ventral exoccele of the two dorsal systems. 

 Clearly, if the succession here indicated were followed with perfect regu- 

 larity, other pairs would appear within the ventral exocceles of the middle 

 and ventral systems, and the cycle would then be completed according to 

 fig. 8, k, p. 82. No stage exactly corresponding with this figure, however, 

 has been obtained, as the polyps of S. radians very rarely, if ever, complete 

 the third cycle of mesenteries. 



The stages above presented prove that in the establishment of the third 

 cycle of mesenteries the dorso-ventral succession is twofold : First, a series 

 of six pairs within the dorsal exocceles, and then a similar series within the 

 ventral exocceles of each system. 



The regularity in the sequence, represented by fig. 8, g-k, was secured 



