148 BULLETIN 82, UNITED STATES NATIONAL MUSEUM. 



For purely mechanical reasons a radially symmetrical animal in which the 

 divisions between the radii are formed by sutures or other lines of weakness will 

 always be divided into three, five or seven parts, so that none of the lines of weak- 

 ness will pass through the center and thus subject the organism to danger of dis- 

 ruption through a shearing strain; but if the divisions between the radii are formed 

 by lines of increased strength, as in the coelenterates, the animal will be divided 

 into an even number of parts, the continuation of the lines of strength across the 

 center to the opposite periphery giving an added rigidity which would be lost 

 were the divisions uneven in number. 



A comparative study of the crustaceans indicates that five is the most com- 

 mon number of fully developed thoracic metameres. The coincidence of the 

 number of available metameres and the number of radial somatic divisions offering 

 the maximum resistance to external forces doubtless played an important part in 

 the evolution of, and the establishment of pentaradiate symmetry in, the echino- 

 derms. 



The lateral body wall of the crinoid and of the echinoid is the body wall 

 of half of each of five metameres of the insects or crustaceans, the other halves, on 

 the opposite side of the body, having become atrophied so that each of the five 

 developed half metameres have become curved about into a circle, the free anterior 

 edge of the first joining with the free posterior edge of the fifth and forming a crea- 

 ture with perfect radial symmetry. In this transformation the five remaining half 

 metameres have become most curiously altered ; the ventral portion of the five half 

 metameres have in some way become dissociated from the dorsal portion so that 

 when the final equilibrium of the adult is attained the ventral structures of each 

 of the five half metameres are found to be alternating in position with the dorsal 

 structures of the same half metameres instead of, as naturally would be expected, 

 lying in the same radial planes. 



During this process the mouth and the peristomal region have become turned 

 upward so that they now occupy a circular area delimited by what was originally 

 the middorsal line of the body; in the crinoids the anal opening occurs in the same 

 area, but in the urchins it occupies a circular area at the opposite pole delimited 

 by what was originally the midventral line of the body. 



The ventral disk of the crinoid is composed of both the anterior and posterior 

 portions of the animal, united in one; the column arises from the midventral area; 

 the area between is true lateral, corresponding in all ways to the sides of insects 

 and crustaceans. 



The peristome of the echinoid is anterior and the periproct posterior; but the 

 intervening area corresponds as in the crinoids to one side of an insect or a crustacean. 



Briefly stated the relation between the bilateral crustacean type and the 

 pentaradiate echinoderm type is as follows: the echinoderm consists of one-half 

 of a five segmented crustacean thorax from which the head, abdomen, and left 

 side have disappeared by atrophy; as the left side became atrophied the right halves 

 of the five metameres curved about until at last the anterior and posterior ends 

 met, so that a radial body with five similar and equal radial divisions was formed ; 

 in some manner during this process the ventral and the dorsal portions of each 



