196 MARINE BIOLOGY OF THE SUDANESE RED SEA. 
the whole spicule behaves as a single crystal, with its optic axis lying perpen- 
dicularly to its facial plane. Similarly, the optic axis of a quadriradiate lies 
perpendicular to its facial plane, and therefore corresponds with the morpho- 
logical axis of its apical ray. It should, however, be noted, as von Hbner 
points out, that, owing to the curvature of the surface of the sponge and of 
the chambers in those species possessing a syconoid canal-system, the facial 
rays of a spicule rarely lie in one plane, but are usually in the form of an 
extremely low and widespread tripod. References to the facial plane must 
therefore be taken to refer to the plane containing the apices of the three rays, 
whether or not this should also contain the other portions of the ravs. There 
must therefore also be distinguished the true oral angle from the angle seen 
between the paired rays when the spicule is viewed as though projected in 
the facial plane, as is the case in ordinary microscopic examination. The true 
oral angle is the angle between the paired rays measured in the plane containing 
those rays. 
When examining sagittal triradiates, spicules are very frequently found 
whose true orai angle is 170° and whose oral rays lie in a plane perpendicular 
to the optic axis. The basal ray of these spicules is usually somewhat 
inclined to the optic axis, usually from 10°-50°. 
Among the sagittal triradiates whose true oral angle is greater than 120°, 
von Ebner found that in a large number of cases, when the spicule was viewed 
as a projection in a plane at right angles to the optic axis, that the angle then 
seen between the oral rays was one of 120°. In many cases, however, he 
found that the projection of the oral angle in such a plane produced an angle 
greater than 120°, usually from 150° to 180°. 
He therefore divided all sagittal triradiates into two classes distinguished 
by the size of the “ Projections Oralwinkel”’ in a plane at right angles to the 
optic axis: (a) those in which the angle was 120°; () those in which it was 
greater. 
The very close similarity of this optical series‘of modifications with the 
morphological modifications here described in Grantilla can at once be seen. 
Viewing the tubar triradiates of Grantilla in the primitive facial plane, they 
can be divided into those in which the primitive oral angle is less than, 
equal to, or greater than 120°. The first two of these divisions includes the 
prochiacts, while all the secondary triradiates will be placed in the other. 
It must, however, he observed that the two cases are not equivalent, since 
in one case the spicule is orientated with regard to its optic axis, and in the 
other case with regard to its morphological axis. 
If the theory put forward in this paper is accepted, the prochiacts and 
secondary sagittal triradiates of Grantilla are derived directly from an already 
formed spicule by an actual change in the morphological orientation of the 
spicule during its growth. Such a change, whether of the whole spicule 
or of one ray, must obviously cause a similar change in the position of the 
