28 GEOLOGICAL MEMOIRS. 



which, as has been ah-eady shown, may be readily converted into 

 six, exactly similar and identical. Six lateral plates and six scapu- 

 lars form the cup, and six arms, three double and three single ones, 

 rise from its rim. Everything is entirely at variance, therefore, in 

 this respect, with what is seen in other Crinoidea ; and in none of 

 the latter is the base of the cup composed of four plates except in 

 the singularly formed and anomalous Melocrinus (Goldfuss, tab. 60. 

 fig. 1), while the number (^six) of the arms, proceeding from the 

 rim, is also peculiar and not met with elsewhere. 



Everything which is determined by the number five is developed 

 from within, and is directly connected with life ; but wherever the 

 number six dominates, the surface only is affected, the mere external 

 coating or enclosure, which stands in no other relation to the in- 

 ternal organs than simply as protecting and sheltering them. When 

 from a membrane at the surface a plate begins to be formed, a point 

 or a little hard particle being detached, it will increase by the con- 

 tinued detachment of hard particles in all directions, and will assume 

 a circular form. If during growth these circles touch one another, 

 they will be limited in their progress at the points of contact, and 

 will there be flattened, producing hexagonal plates only capable of 

 increase of size by increments at the edges, so that everything after- 

 wards formed at the surface, as the pores and striae, must necessarily 

 be disposed and determined according to this hexagonal form. 



In the Crinoidea, however, the five arms extending far over the 

 edge of the cup, are developed from the very basal plates, and the 

 determination of the number six is entirely limited to the plates 

 themselves. It does not however, in fact, affect their shape, for 

 from the very base of the cup and long before they make their ap- 

 pearance, the arms press the lateral plates together, raise them in the 

 middle, and give to the whole margin the prominent form of a pen- 

 tagon. For this reason has M. Miiller designated those plates which 

 announce as it were the existence of the arms so long before they 

 appear — radialia, calling those upon which the arm when developed 

 actually rests, radialia axillaria. The arms also, when they are put 

 forth, bring with them the ovaries so remarkable in these animals, 

 wliich till then were concealed within the margin of the cup, but 

 being now at liberty and attached far above the margin to the pin- 

 nules of the arms, they are no longer obliged to squeeze through a 

 narrow opening. In this way a new peculiarity is introduced, and 

 on it is based the essential difference between Crinoidea and Cy- 

 stidea. 



It will probably remain for a long time unknown what is the 

 nature of the mystery that exists in this number five, by which it 

 exercises so remarkable an influence over the whole of organic na- 

 ture. I would not presume to venture more than lift up the edge 

 of this dark veil; but the study of the liadiaria, in which the 

 subject appears so manifestly in its simplest form, has induced me 

 to suggest that the number five may be an augmentation of three in 

 the effort fully to complete the circle, these three being wrought out 



