The Paraphysis is a projection from the roof of the primitive fore-brain near its anterior end. It is well seen in Dipnoans[42] (_Lepidosiren_ and _Protopterus_) where in the larva (exactly as in the urodele larva) it forms a blindly ending tube sloping upwards and forwards between the two hemispheres. In the adult it becomes mixed with the two lateral plexuses and is liable to be confused with them. In the other groups--except the Teleosts where it is small (_Anguilla_) or absent (most Teleosts)--the paraphysis is by no means such a definite structure, but generally there is present a more or less branched and divided diverticulum of the brain wall, frequently glandular, which is homologized with the paraphysis. The morphological significance of the paraphysis is uncertain. It may represent the remains of an ancient sense organ, or it may simply represent the last connexion between the brain and the external ectoderm from which it was derived. An important derivative of the primitive fore-brain is seen in the pair of cerebral hemispheres which in the higher vertebrates become of such relatively gigantic dimensions. The hemispheres appear to be primitively associated with the special sense of smell, and they are prolonged anteriorly into a pair of olfactory lobes which come into close relation with the olfactory organ. From a consideration of their adult relations and of their development--particularly in those groups where there is no disturbing factor in the shape of a large yolk sac--it seems probable that the hemispheres are primitively paired outpushings of the lateral wall of the primitive fore-brain[43]--in order to give increased space for the increased mass of nervous matter associated with the olfactory sense. They are most highly developed in the Dipneusti amongst fishes. They are there (cf. fig. 29, C) of relatively enormous size with thick nervous floor (corpus striatum) and side walls and roof (pallium) surrounding a central cavity (lateral ventricle) which opens into the third ventricle. At the posterior end of the hemisphere a small area of its wall remains thin and membranous, and this becomes pushed into the lateral ventricle by an ingrowth of blood-vessel to form the huge lateral plexus ( = _plexus hemisphaerium_). In this great size of the hemispheres[44] and also in the presence of a rudimentary cortex in the Dipnoi we see, as in many other features in these fishes, a distinct foreshadowing of conditions occurring in the higher groups of vertebrates. The Cyclostomes possess a distinct though small pair of hemispheres. In the Selachians the relatively archaic _Notidanidae_[45] possess a pair of thick-walled hemispheres, but in the majority of the members of the group the paired condition is obscured (fig. 29, A).