744 MR. P. H. CARPENTER ON THE [Dec. 19, 
Ex. Species B. of above scheme. 
{. Two palmars, the axillary a syzygy ; the second joints be- 
yond the palmar and all subsequent axillaries also have a 
Shek 
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 10 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 2b at the end of the formula; and if the 
first two brachials are united by syzygy, B is used. In like manner, 
and in accordance with Rule 5, 2d and 2 p would indicate that there 
are two distichals or two palmars, of which the axillary is a syzygy ; 
and 2 or? that the two distichal or palmar joints are united by 
Syzygy: on 
The figures | 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. Aet- 
alternans 3,2,3,2. 
This may be tabulated as follows :-— 
Symbol used. 
Character. Distichal. Palmar. 
One ‘axillary jomit! - ec vawhie< os l i? 
d P 
Two joints united by syzygy...... 3 
Two articulated joints ........... 2 2. 
* It would, of course, be more consistent to write 3d, or 3 p; but thesyzygial 
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. 
