342 E. A. MINCHIN. 
which contain the optic axis and intersect at equal angles ; 
so that the triradiates of this class, if projected in-a trans- 
verse plane (that is to say, in a plane at right angles to the 
optic axis), appear as regular equiangular triradiates, what- 
ever their actual form may be.! In the secondary tri- 
radiates, on the other hand, the projection in a transverse 
plane gives a figure in which the angle between the paired 
rays is greater than 120°, usually 150°—180°, and the curva- 
ture of the paired rays is not confined to a plane of crystal- 
line symmetry which contains the optic axis. The secondary 
sagittal triradiates may be derived from the primary type 
by supposing that the paired rays rotate symmetrically 
away from each other, until they may come finally to he in 
the same straight line when projected in a transverse plane 
of crystalline symmetry. An extreme form of the secondary 
sagittal type is seen in the “ pseudo-regular ” triradiates of 
the gastral surface of Sycortis quadrangulata; spicules 
which appear morphologically to be regular equiangular tri- 
radiates, but which are entirely different crystallographically 
from the true regular forms, since one ray, the unpaired ray, 
has its morphological axis coincident with the optic axis, 
while its paired rays both he in one and the same plane of 
crystalline symmetry passing through the optic axis. 
From the discoveries of von Ebner it is seen that the 
primary sagittal triradiates of Leucosoleniide and Hetero- 
coela agree with the perregular triradiates of Clathrinide 
in so far, that both types alike appear equiangular when pro- 
jected in a plane lying at right angles to the crystalline optic 
axis. With regard to the secondary sagittal forms, it can also 
be stated that their morphological symmetry is in a definite 
and constant relation to their crystalline structure. Kbner’s 
investigations establish, so far as they go, the following 
1 This remarkable fact was also discovered by Bidder (1898), who regarded 
it as a universal law for all triradiate systems; Bidder was not aware, appa- 
rently, of the existence of von Ebner’s secondary sagittal forms. In my paper 
at the British Association at York (1906) I also overlooked von Ebner’s state- 
ments, and attributed the-discovery to Bidder. 
