64 bulletin: museum of compakative zoology. 



definite relation to the plane and only certain, relatively few, individuals 

 reveal the symmetry. Theoretically, of course, any Heliaster with an odd 

 number of rays show this bilaterality but in none of those examined was 

 it shown, except those which had at least 25 rays. In all those with 

 just 25 rays, the plane of symmetry, with 10 accessory rays on each side, 

 is clearly indicated. Above 25, any odd number of rays may be accom- 

 panied by bilateral symmetry but it is not commonly, for of the 11 speci- 

 mens tabulated on page 61, it will be seen that only one, a helianthus 

 with 35 rays, can be considered truly symmetrical. 



It appears therefore that in Heliaster, the formation of new rays is 

 fundamentally different from that in Pycnopodia. This is well brought 

 out by a comparison of figure 1, plate 8, with Bitter's and Crocker's 

 (1900) figure 1, plate 13. In Heliaster the first three new rays are dis- 

 tributed one each in the three successive interradii to the left of the one 

 in which the madreporite lies, while in Pycnopodia all three (counting A 

 as the first accessory ray) lie in the single interradius 1-2. It is hard to 

 believe that the two methods have anything in common, the ray A is so 

 conspicuous and plays such an important part in Pycnopodia. In Heli- 

 aster the first accessory ray probably (?) appears in interradius 1-2, the 

 second in 2-3, and the third in 3-4. Then apparently, as is shown by 

 figure 2, plate 8, a new ray arises in 1-2, another in 2-3, another in 

 3-4, and then another in 1-2. Later on the process begins in inter- 

 radius 4-5 and by the time 25 rays are formed, it is going on at about an 

 equal rate in those four interradii. As we have already seen, it is only 

 very exceptionally that the interradius 5-1 takes part in ray formation. 

 It is not unfair to interpret the facts here brought out as showing that 

 the formation of new rays in Heliaster follows this rule : — 



Hie process begins in interradius 1-2, soon after larval life ends, and 

 goes on rapidly there until tivo or three accessory rays are formed, the 

 similar activity of interradii 2-3, 3-4, and 4-5 following in order. At 

 the time the process begins in 4-5, the rale of development in 1-2 has begun 

 to decrease, and by the time there are 25 rays, each of the four interradii 

 has formed five accessory rays, and the rate of development has greatly 

 decreased and become approximately equal in them all. Subsequent forma- 

 tion of new rays follows the same general order, the twenty-sixth ray ap- 

 pearing in interradius 1-2, but after 35 rays are formed further develop- 

 ment is sporadic. 



Of course it is not claimed for a moment that the above statement is 

 a "law" governing ray formation in all Heliasters, as the material exam- 

 ined has been too scanty to determine how generally any such rule is 



