744 MR. p. H. CARPENTER ON THE [DcC. 19, 



Ex. Species B. of above scheme. 



/3. Two palmars, the axillary a syzygy ; the second joints be- 

 yond the palmar and all subsequent axillaries also have a 



syzygy- 



Ex. Act. multiradiata. 



Species A of the above scheme, with the first two brachials united 

 by syzygy, is an exception. 



6. Whenever any ray-division, distichal, palmar, or any other, 

 consists of three joints, the first two are articulated by ligaments, 

 the second bearing a pinnule, and the third (axillary) is a syzygy 

 just as in the first three brachials of Ant. rosacea and Act. echino- 

 ptera. When, however, there are only two joints, and the second 

 (axillary) is a syzygy, the first has a pinnule, just as in the arm-bases 

 of Act.fimbriata. 



7. The hypozygal of a syzygy is always united to the preceding 

 joint by a muscular articulation. 



Like Prof. Bell, I should use R to denote the syzygial union of 

 the two outer radials. When ten arms only are present, this is in- 

 dicated by 1 in the formula. This may be thought unnecessary, 

 as the absence of any signs for the distichals would indicate that the 

 primary arms remained undivided ; but I find that it is more con- 

 venient to indicate this character, which is generally a sharply 

 defined one, in a positive rather than in a negative manner. I also 

 assume, in accordance with Rules 3-5, that the first syzygy on the 

 arm is on the third brachial, unless otherwise stated. If it is on 

 the second brachial, I put 2 b at the end of the formula ; and if the 



first two brachials are united by syzygy, ^ is used. In like manner, 

 and in accordance with Rule 5, 2 d and 2 p would indicate that there 

 are two distichals or two palmars, of which the axillary is a syzygy ; 



and 2 *''' I that the two distichal or palmar joints are united by 



syzygy- . . 



The figures I or 2 alone would indicate that there is either only 

 a single axillary joint, or two which are united by ligament ; and a 

 3 would denote three joints, of which the axillary is a syzygy '. If 

 one figure occurs alone in a formula, it indicates the presence of 

 distichals only ; two figures, that palmars occur as well ; and so on, 

 an additional figure being added for each ray-division, e. g. Act- 

 alternans 3,2,3,2. 



This may be tabulated as follows : — 



Symbol used. 

 Character. Distichal. Palmar. 



One axillary joint 1 1. 



Two joints united by syzygy g !• 



Two articulated joints ... 2 2. 



1 It would, of course, be more consistent to write 3 d, or 3 p ; but the syzygial 

 nature of the third (axillary) joint is such a constant character (Rule 6) that, 

 until an exception is met with, I prefer to use the figure alone, for the sake of 

 brevity. 



