742 MR. P. H. CARPENTER ON THE (Dee. 19, 
while the first arm-syzygy is not on the third, but on the second 
brachial, or between the first and second. 
Group. Actinometra. 8rd br. Sy. 2nd br. Sy. 1—2 br. Sy. 
7 3 distichals and 3 palmars, the 
axillaries SyZYQI€S .........+.-4+- parvicirra, 
8 distichals and 2 palmars, the : 
1,4  axillaries syzygies .........0...0.  seseeeees multiradiata. A. 
8 distichals, the axillary a sy- 
tase : and 2 palmars united by 
ZY8Y 
2 aectiakaley the axillary a sy- 
AEN) : and 2 palmars united by 
TI. 4 2 austichals and 2 palmars, the 
axillaries syzygies. 
2 distichals and 3 palmars, the 
axillaries syzygies. 
2 distichals united by syzygy; 
2 palmars united by syzygy. 
Til. 4 2 distichals united by syzygy; 
2 palmars, the axillary asyzygy. 
| 2 distichals united by syzygy; 
( 3 palmars, theaxillary a syzygy. 
Now, unless Rule 3 were known, how should any one, taking the cor- 
rected formula for a parvicirra (3A'D(P)™), or for Act. multi- 
radiata (2A'DP( pyr ;)> know that he could only have to deal with 
types belonging to one of the first two groups? And unless he were also 
acquainted with Rule 7, he could not know that Group II. represents 
a series of types that are as yet undiscovered. But within Group I. 
the chances of error would be two to one unless Rule 5 were known, 
according to which the third (or second) brachial is only a syzygy 
when there are three (or two) palmars, the axillary with a syzygy. 
There may, however, be two palmars with the axillary a syzygy, 
and yet the first two brachials be united by syzygy, as in species A 
of the scheme above. This exception, to which others will doubtless 
soon be added, also shows the weakness of Prof. Bell’s system, even 
supposing the following rules to be understood; for its formula 
would be 1DP, identical with that of another more regular species, 
B of the above scheme, to say nothing of half a dozen other possi- 
bilities in Groups II. and III. 
A working method of formulation, therefore, must be elastic 
enough to deal with such anomalies as A, and indicate exactly 
on what joint the syzygy comes in the distichals, palmars, and 
brachials. Further, when there are no syzygies in the ray- 
divisions, whether throughout them all (Ané. palmata) or in some 
only (Act. alternans), the number of joints in each division should 
be clearly indicated. Thus the formula 3 A’D, as understood by 
Prof. Bell, would stand for any one of the following existing types 
of Uctinametra apart from any number of possibilities. 
Act, Srna No palmars. : 
ante 1 palmar (axillary). All setae di a 
B. Se 1 palmar, and 1 axillary beyond it. Aaa Pas i 
wx 8 2 palmars. ae ae 
Act, iniltifida ‘.. 2 palmars, and another similar division.) ther axillary. 
