STRUCTURE OF CERTAIN PALAEOZOIC DIPNOI. 171 
underside to a hollowed and polished surface. Four o£ the commonest 
patterns (of each of which there are several duplicates) are represented in 
iig. 5, p. 169. It wi\l be noticed that the radius of curvature of the orbital 
notches is far from uniform, apart from questions of size of bones, which 
seems to indicate that the orbit cannot have been circular. One skull in the- 
Atthey Collection (fig. 18, A, p. 183), several in the Royal Scottish Museum 
{e.g. fig. 6, A, B, p. 170), and one fragment from Ohio in the British- 
Museum (fig. 6, 0, p. 170), show some of the orbital and other marginal 
bones in top view in articulation with the skull-roof, but no specimen we have 
yet seen gives much help in reconstructing the orbit itself. The hypothetical 
arrangement which we suggest in fig. 20, p. 186, is chiefly based on an 
examination of the bones themselves, taking account of the edges bearing 
orbital notches, the edges with articular faces, and the edges which were 
evidently free. It accounts for all the recognizable types of eircumorbitals^ 
which occur in the Atthey Collection. Some of the skulls referred to above- 
show that the smaller marginal bones articulating with the nasals and with 
the fore-part of the frontals did not enter into the orbit, and we have 
accordingly represented them as intermediate roofing ossicles. 
Tlie Palate. 
Neither we nor previous workers have found indications of any kind of 
ossification of the brain-case, which must have been as completely cartila- 
ginous as it is in Ceratodus. Where the skull-roof and the palate are 
undisturbed they lie directly one upon the other, usually with hardly a trace 
even of the matrix between them. 
The bones of the palate have been well known for many years, and the 
additional observations that we have to make refer mainly to certain details^ 
of their relations to one another. Like all the other bones of Sagenodus, the 
parasphenoid is very variable in form within definite limits, and especially 
so in regard to the development of a median ridge on the buccal face of its 
main " lozenge " and in the shape and prominence of the lozenge at its 
hinder angle. Common types are represented in fig. 9, p. 174. The para- 
sphenoids collected at Newsham were supposed by Hancock and Atthey to 
belong to about half-a-dozen distinct species, a view which Miall dissented 
from, though.it is not without some measure of support. 
Even before the existing Ceratodus became known, it was seen in a general 
way how the pterygoids with their tooth-plates must have fitted round the 
lozenge of the parasphenoid. Attempts to depict the bones in their natural 
position have not, however, been altogether happy. Miall's restoration 
(1874, pi. 47), which is based on the similar palate of Ctenodus, is the most 
successftil, but he shows the hinder ends of the pterygoids projecting as loose 
frills beyond the lozenge. Williston's figure (1899, pi. 37. fig. 2) has the 
same defect, and in addition his pterygoids lack most of their hinder wing,. 
