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pays much attention to development. He describes the formation of the vertebrae in elasmobranch embryos; for the facts regarding other Vertebrates he relies largely on work by Rathke (_Blennius_, 1833) and Duges (1834). He recognises as the basis of his comparisons the homology of the notochord in all vertebrate embryos with the persistent notochord which forms the chief part or the whole of the vertebral column in the Cyclostomes. The notochord possesses an inner and an outer sheath and the outer sheath is continuous with the _basis cranii_ (p. 92). It is in the outer sheath that the vertebrae develop--from four separate pieces, in fish at least, plus an additional element which helps to form the centrum. The skull of Vertebrates consists, according to Mueller, of three vertebrae, whose centra are the basioccipital, the basisphenoid and the presphenoid. Other bones besides those belonging to the vertebrae are present, but this formation out of three vertebrae gives the essential schema for the skull. Now the brain capsule, like the sheath of the spinal cord, is a development from the outer sheath of the notochord. If the skull consists of vertebrae we should expect the centra of the skull-vertebrae to develop in the outer sheath at the sides of the cranial section of the notochord as two separate halves, just as do the bodies of the vertebrae; we should expect further the cartilaginous side-walls of the cranium to develop in the membranous brain-sheath just as the neural arches develop in the membranous sheath of the spinal column. In Rathke's discovery (!) of a segmentation of the _basis cranii_ into three parts, and of the isolated formation of the vomer, Mueller sees a confirmation of his view that the skull is composed of three and not four vertebrae. But there is nothing in Rathke's observations to support the idea that the centra of the cranial vertebrae are formed from separate halves. Mueller has to be content with a reference to the state of things in _Ammocoetes_ (which, by the way, he did not know to be the young of _Petromyzon_). In the simple skull of _Ammocoetes_ the base is formed chiefly by two cartilaginous bars lying more or less parallel with the longitudinal axis of the skull and embracing with their hinder ends the cranial portion of the notochord. These bars, declares Mueller, are clearly the still separate halves of the _pars basilaris cranii_, and represent the divided centra of the two hinder
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