CLARK: THE STARFISHES OF THE GENUS HELIASTER. 65 



followed. But it can hardly be questioned that it indicates the usual 

 course and is a natural deduction from the facts already given. The 

 process is almost certainly continually modified by physiological condi- 

 tions, one of which, at least, after the individual is well grown, is very 

 possibly the amount and rate of calcification in the different interradii. 

 Such unknown factors often cause some striking deviations from the 

 suggested rule, as in the two cases previously mentioned, a canopus with 

 24 rays, where interradius 2-3 has only three accessory rays, while 4-5 

 has six, and a polybrachius with 20 rays, where interradius 2-3 has only 

 two accessory rays and 4-5 has five. 



If the above suggested rule is the usual course, we should expect to 

 find that in specimens with from 21 to 30 rays, those with an odd num- 

 ber would predominate, but that in those with from 31-40 rays, there 

 would be less tendency to an odd number, and the chances of odd or 

 even would have been about equal. And such proves to be the case ; for 

 of 163 mature specimens having 21-30 rays, 98 or 60 per cent have an 

 odd number, while of 170 specimens with 31-40 rays 86, or almost 

 exactly half, have an even number. It is interesting in this connection 

 to call attention to the fact mentioned on p. 45, that canopus has a 

 marked tendency to an even number of rays, although they range from 

 20 to 27. If canopus is omitted, there are 89 out of 136 specimens with 

 21-30 rays, or 66 per cent which have an odd number. The condition 

 in canopus is difficult to account for but it is apparently associated with 

 a peculiar tendency in interradius 2-3 to fall behind in the production 

 of new rays. In all of the six specimens examined with from 20-24 

 rays, that interradius has a smaller number of rays than 3-4, and in 

 four of the six, it has the smallest number of any of the four interradii. 

 In none of the ten specimens of canopus examined does interradius 2-3 

 have a larger number of rays than 3-4. The cause for this curious con- 

 dition is obscure and we need make no attempt here to determine it, 

 but it seems clear that it accounts for the tendency to an even number of 

 rays in canopus. It may be added that there is no very obvious reason 

 why interradius 5-1 develops no accessory rays, although it is very 

 probable that the presence of the stone-canal and axial organ in that in- 

 terradius is associated with the cause. 



In the light of all the facts here brought out with reference to ray 

 formation in Heliaster, it is, to say the least, unfortunate that Bitter 

 and Crocker (1900) should have said (p. 263): — "The inconstancy and 

 irregularity of the phenomena of new ray formation certainly finds 

 no support in what takes place in Pycnopodia and, as we have shown, 

 vol. li. — No. 2 5 



