SPERRY ON METAClilNUS. 197 



The normal uiimber of distichals in rotundus is given as 8, in 

 interruptiis 8, and in the '*Vega" specimen 10. The normal number of 

 palmars in rottindus is 12-14, in interruptus 12-16. The accompanying 

 diagrams, tabulated from sixteen individuals are of interest, showing that 

 in both distichals and palmars there may be a considerable variation 

 between different individuals and different arms of the same individual. 

 The two curves also show another interesting fact, a tendency in both 

 distichals and palmars to seek an even number. 



The most plausible theory for the double curve in the variation of 

 number of joints in the distichals and palmars seemed to be one which 

 arose from a study of the relation of the pinnules to the arm joints. In 

 each branching every joint but the last, i. e. the axillary, bears a pinnule, 

 but the pinnules do not arise one directly above the other from the 

 middle of the ventral surface of the arm. They arise alternately on 

 either size of the food groove, so that the first, third, fifth, etc., lie in the 

 same vertical plane, while the second, fourth, sixth, etc., lie in a similar 

 plane on the other side of the groove. 



It is obvious that when a branching occurs, as for instance the division 

 of the radial ray into two sets of distichals, that if the two resulting 

 branches be comparatively close together, as in Metacrinus rotundus 

 there will be more room for the growth and function of the pinnules on 

 the outer side of the two branches than on the inner. An examination of 

 a specimen will show that the pinnules on the inner side of the two sets 

 of distichals or palmars arising from a common axillary, are much more 

 crowded than the outer sets of pinnules of two adjacent arms which arise 

 from different axillaries. Now when there is an even number of joints 

 in the whole ray division there is always one less to bear a pinnule, as 

 there are no pinnules on the axillary. If, then, we have an odd number 

 of pinnule-bearing joints, it is evident that there can not be the same 

 number of pinnules on each side of the arm, i. e. if there are seven 

 joints to bear pinnules, the normal number in the distichals, there will 

 be four on one side and three on the other. All the specimens examined 

 showed invariably, that the larger number are found on the outside and 

 the smaller on the inside, allowing greater chance for the growth and 

 functioning of those on the inside, whose room is much more limited. 



If there is an increase or a decrease in the normal number of joints, 

 the tendency seems to be to add not a single joint, which would throw 

 the one extra pinnule on the inside, with but the added space of a single 

 joint to function in, but to add or subtract two joints, which would add 

 two pinnules to the normal number or take them from it, keeping the 

 larger number still on the outside and giving the extra pinnule on the in- 

 side the length of two joints instead of one to function in. The fact that in 

 the radials where the branching from the basals is very sharp and there is 

 room for equal development on all sides, there seems to be no such 

 tendency to seek an even number of joints, but that we have a simple 

 curve rising to and falling from the normal number, six, without any 

 regard to either an odd or even number seems to substantiate this theory. 



The average number of arms in the specimens under consideration is 

 about 48, varying from 42-64. The radials all divide three times, with 

 often a fourth axillary beyond the palmar axillary and in one case a 

 fifth division. There were 42 arms in interruptus and 40-50 in rotundus, 

 so that this is probably merely a matter of individual variation. The 



