22 BULLETIN 82, UNITED STATES NATIONAL MUSEUM 



are to expand in the same plane, diverge at an angle greater than about 72. As a 

 consequence of this the distal angle of the axillary ought not to be less than 108. 

 It turned out, however, that among the forms examined Eycrinus carpenterii and 

 Monachometra cf. Jragilis only have an angle rising to any great extent above this 

 figure. In these two cases it reaches 162 and 145, respectively. All the other 

 types except two have a IBr axillary angle of less than 108 Comanthus japonica 

 88; Capiliaster sentosa, W5;AmphimetratesseUata, 106; Pontiometra andersoni, 105; 

 Tropiometra ajra macrodiscus, 105; Pectinometra flavopurpurea, 104; Diodontometra 

 bocki and Aster ometra anthus, 110; Notocrinus virilis, 83; Clarkometra elegans, 103; 

 Hypalometra dejecta, QQ;Antedon petasus, 78; Pleliometra glacialis, 68-72; Atelecrinus 

 helgae, 81; and Metacrinus nobilis tenuis, 98. In the 10-rayed Promachocrinus 

 kerguelensis the IBr axillary ought not to fall below 144; but in reality it is 107 here. 



Axillaries of higher rank, assuming the highest possible number of arms allowed 

 by the full number of the division series, would have angles as follows: IIBr axillary, 

 144+ ; IIIBr axillary, 162+ ; IVBr axillary, 171 + . The types examined, however, 

 gave the following figures: Comanthus japonica, IIBr axillary, 104, IIIBr axillary, 

 104; Capiliaster sentosa, IIBr axillary, 126; IIIBr axillary, 120; IVBr axillary, 131, 

 VBr axillary, 120; Pontiometra andersoni, IIBr axillary, 130, IIIBr axillary, 130, 

 IVBr axillary, 115; VBr axillary, 105; Pectinometra flavopurpurea, IIBr axillary, 

 126; Metacrinus nobilis tenuis, IIBr axillary, 104, IIIBr axillary, 102, IVBr axillary, 

 108. 



All the examples given above, other than the exceptions mentioned, have their 

 arms diverging far too rapidly. But owing to the first postaxillary ossicles being 

 longer on the outer side of the arms than on the inner this is counterbalanced. If the 

 arms were narrow proximally and not in lateral contact, the basal portions of the free 

 arms could certainly diverge at angles greater than those theoretically possible. 

 In such a case, however, the divergence must soon be lessened to prevent the arms 

 interfering in the more distal portions. 



If the distal angle of an axillary is smaller than the theoretically possible angle, 

 the sides of the brachials immediately following, in order to restore the arms to the 

 requisite angle, must be longer on the outside of the arms than on the inner side, and 

 the angle that the proximal and distal ends form with each other must reach at least 

 the difference between the actual distal angle of the axillary and the minimum possible. 

 It seems, however, to be a general rule that the divergence of the arms is still further 

 diminished, so that they become nearly parallel with each other. The earliest brachials 

 are usually so much longer on the outside than on the inner side that the distal end 

 of the first brachial forms almost a right angle with the longitudinal axis of the pre- 

 ceding axillary, and the distal end of the second brachial slopes somewhat downward 

 and inward. The too strong convergence of the arms resulting from this is compen- 

 sated by the first syzygial pair (composed of brachials 3+4) being longer on the 

 inner side of the arm than on the outer, so that the distal margin of the epizygal 

 (fourth brachial) is almost at right angles with the longitudinal axis of the arm. 

 The effect of the arm branching on the obliqueness of the brachials is thus counteracted. 



The conditions found in Clarkometra and in Hypalometra show that the presence 

 or absence of Pj and P a has no influence worth mentioning upon the obliqueness of the 

 first four brachials. 



