108 SIDERASTREA RADIANS. 



the hexameral multiple of the last cycle of entosepta, the same number 

 will be lacking from the exosepta. The third complete cycle, as understood 

 by Milne-Edwards and Verrill, is really made up of both tertiary entosepta 

 and of tertiary exosepta. The two kinds of septa are of very different value 

 in their development and relations to the polyp, and, as a matter of fact, 

 will be scarcely of the same thickness and radial length to justify their 

 being regarded as a cycle. 



The cyclic formula, as above understood, may be written 6, 6, 12, x, 

 where x will represent any number from i to 24. Formulated in this way 

 the number 12 conveys the impression that the third cycle is really com- 

 pleted, and that all the additions made will belong to the next or fourth 

 cycle, whereas they will belong to both the third and fourth cycles. Beyond 

 the two first cycles the septa do not arise a cycle at a time, but the penulti- 

 mate and last cycles are formed concurrently, or almost so. Incomplete 

 cyclic hexamerism, as met with in S. radians, is an intermediate condition 

 in the establishment of two adult hexameral cycles, not of one alone, and 

 attention should be drawn to this in the septal formula. 



According to the relationships now established the morphological septal 

 formula for S. radians should be written 6, 6, x, 6 + 6 + x. In this 

 formula, 6, 6, x will represent the number of septa in the two completed 

 entocycles, x being the number in the last entoseptal or penultimate cycle 

 which does not yet complete the hexameral sequence ; while 6 -j- 6 + x will 

 represent the total number of exosepta, x being the same number as before ; 

 some of the exosepta will be tertiaries and some will be quaternaries, the 

 number of the latter being always double the number of tertiary entosepta. 

 The formula for a corallite having 36 septa would, according to the ordinary 

 cyclic formula, be written 6, 6, 12, 12, whereas, considered as entosepta and 

 exosepta, the formula will be 6, 6, 6, 18, the three first numerals indicating 

 the entosepta and the last the exosepta ; the usual cyclic formula of a corallite 

 with 40 septa would be 6, 6, 12, 1 6, and the morphological formula 6, 6, 8, 20. 

 In the first case 12 of the exosepta will be quaternaries and 6 will be ter- 

 tiaries ; in the second 16 will be quaternaries and 4 tertiaries. 



Where the relationships of the septa to the mesenteries are clearly known 

 the morphological formula will more nearly express the real value of the septa 

 than the ordinary cyclic formula ; the latter has little significance unless the 

 hexameral sequence is fully completed. One can not say that a cycle is 

 really complete unless its constituents all have the same morphological value, 

 which is not the case where some are entosepta and some are exosepta. 



The bilaterality of the polyp during development may be looked upon 

 as associated in turn with each cycle individually. Any cycle tends to attain 



