276 Proceedings of the Royal Irish Academy. 
here, although differently arranged by other authors. Wm. Smith, 
recognising the affinity between Biddulphia and Amphitetras, placed 
them close together, but assigned to Triceratium a widely different 
position in his system of arrangement. Kiitzing distributes the in- 
cluded genera in two distinct groups—the Angulifere and Angulate, 
between which he interposed the Biddulphiee and Tripodiscus argus 
= Eupodiscus argus. The Angulifere, he says, ‘‘are easily distin- 
guished by means of their angular side view;”’ but of the Angulate, 
which embraces only the single genus Triceratium, he gives no other 
diagnosis than that contained in the description of that genus, ‘‘ indi- 
viduals free, with the bivalve lorica triangular, not concatenated,”’ 
Ralfs omits Trinacria, a genus established by Heiberg subsequently to 
the publication of the ‘‘ History of the Infusoria,”’ and along with the 
other genera placed in the present group includes Euodia, and Hemi- 
discus. Of Hemidiscus I have never seen a specimen, and, therefore, 
can express no opinion regarding it; but as to Euodia, from the cuneate 
outline of its transverse section, it plainly should be excluded from this 
group, with which it has little, if any, affinity. Ralfs indicates two 
features by which the forms in this group may be distinguished from 
the Biddulphiee: ‘‘The angles on the front view are usually less 
elongated, and the intervening margin less lobed.’? Of these charac- 
ters the latter can scarcely be sustained in all cases; and as to the 
former, if Trinacria, in which the processes at the angles are very 
long, is to be admitted here, this, too, must be regarded as by no 
means a satisfactory diagnosis. Grunow does not refer to Trinacria, 
for the same reason as Ralfs, but includes the other forms of this group 
under the Biddulphiex, which he thus defines: ‘‘ Valves on side view 
longish, or three, four, or more angled,” no reference being made to the 
processes springing from the angles which constitute so remarkable a 
feature of these forms. According to this author, the characteristic 
distinction between Amphitetras and Triceratium is the possession of 
four angles by the former, while the latter has but three. The fact 
that specimens of the former occur with five angles, and of the latter 
with four or more angles, evinces how untenable is this distinction asa 
generic diagnosis. 
Heiberg includes Amphitetras and Triceratium in the Biddulphiee, 
and his genus Trinacria in another group, namely, the Hemiaulide ; 
the main distinction of which rests on the form and position of the 
processes, which are triangular, and spring at right angles from the 
basal plane of the valve. But these differences, though sufficient to 
establish generic distinction, seem scarcely to justify the establishment 
of a distinct group to receive the forms. It will thus appear that, in 
consequence of the projection of the processes from the angles of the 
valves, the relationship of this group to the Biddulphiez is recognised 
by most authors: but no more satisfactory distinction between Am- 
phitetras and Triceratium has been suggested than that in the former 
the frustules are concatenate, and in the other free. This distinction 
I adopt, not because I consider the supposed fact on which it rests in 
