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ventral edge of a part of the sphenoid bone that is preformed in 

 membrane, enters the cranial cavity as the arteria cerebralis. Imme- 

 diately dorsal to the point where it pierces the sphenoid there arises 

 from the inner surface of that bone a short horizontal bracket, or 

 shelf, of connective tissue. Whether this tissue is continued across the 

 cranial cavity, beneath the brain, to meet the corresponding shelf on 

 the opposite side, or not, I could not determine. But, as the opticus 

 nerves have their origin from the ventral surface of the brain in this 

 immediate region, this fact, together with the relations to the artery 

 and the point of origin of the recti muscles, strongly suggests that 

 this little shelf must be in some way related to the presphenoid. wall 

 of Amia, and hence to the basisphenoid bone of teleosts. 



Immediately in front of the foramen for the arteria cerebralis, 

 the opticus pierces the sphenoid, also in the portion of membrane 

 origin, and enters the orbit. In the adult these two independent 

 foramina of my larva are fused, the foramen for the arteria cerebralis 

 being simply a notch in the hind edge of the opticus foramen. 



The internal carotid, as it turns upward to enter the cranial 

 cavity as the arteria cerebralis gives off three branches. One of these 

 branches runs outward, and perforating the posterior surface of the 

 sclerotic enters the eye ball. A second branch is the arteria retinalis, 

 which pierces the sclerotic not far from the optic nerve. The third 

 branch continues forward along the floor of the orbit, as a prolon- 

 gation of the artery posterior to this point, sending, among other 

 branches, one branch outward to pierce the anterior surface of the 

 sclerotic. The artery itself, when it reaches the anterior end of the 

 orbit, pierces the side wall of the skull, accompanied by the orbito- 

 nasal vein, and enters the cranial cavity in the region of the olfactory 

 lobe ; running forward from there into the nasal sac. This long branch 

 of the internal carotid is accordingly an orbito-nasal artery, apparently 

 strictly homologous with that of teleosts. I could not determine whether 

 or not the cerebral branch of the internal carotid was connected by 

 commissure with its fellow of the opposite side, thus completing an 

 intracranial circulus cephalicus ; but it doubtless is so connected. The 

 internal carotids themselves are certainly not so connected by extra- 

 cranial commissure. 



Polypterus thus differs, in the arrangement of its pseudobranchial 

 and carotid arteries, from all the fishes considered in my earlier work, 

 but it presents nothing either irregular or especially primitive, the 

 arrangement being one that might naturally arise in a fish in which 

 the choroid and mandibular gills had been wholly and early suppressed. 



