The chorda sheath is the common matrix of the vertebræ and of a large part of the skull. The basilar plate and the trabeculæ, which are developed from the chorda sheath, give origin to three bones, which might possibly be considered equivalent to vertebral centra—the basioccipital, the basisphenoid, and the Riechbein (ethmoid). The Riechbein develops from the fused ends of the trabeculæ. The presphenoid might also be considered as a vertebral body, but it develops independently of the basilar plate and trabeculæ.

Now of these bones, the basioccipital is in every way equivalent to a vertebral centrum, for it develops in the basilar plate round the notochord. With the exoccipitals, which arise just like neural arches, it forms a true vertebra. The supraoccipital is an accessory bone developed in relation to bigger brains. The basisphenoid appears in the basilar plate, but in front of the notochord, nor does it arise in exactly the same way as the centrum of a vertebra. The basisphenoid with the alisphenoids, which develop independently in the side walls of the brain, may, however, still be considered as forming a vertebra, though the resemblance is not so great as in the case of the occipital ring. The presphenoid, being long and pointed, is very unlike a vertebral body. The orbitosphenoids develop separately from it. The ethmoid also differs from a vertebra, for it surrounds not the whole nervous axis as the two hinder "vertebræ" do, but only two prolongations of it, the olfactory lobes. In its development and final form it shows no particular resemblance to a vertebra. Its body, the pars perpendicularis (mesethmoid) shows no similarity with a vertebral centrum. Completing the three hinder cranial "vertebræ" and roofing in the brain are the supraoccipital, the parietals and the frontals. The premaxillaries, vomer, and nasals do not belong to the cranial scheme; they are covering bones connected with the ethmoid. So, too, the ear-capsule is not part of the cranial vertebræ, but is rather to be compared to the intercalary bones in the vertebral column of certain fish. Summing up as regards the cranial vertebræ Rathke writes, "We find that the four different groups of bones, consisting of the basioccipital with its intercalary (the supraoccipital), the basisphenoid with its intercalaries (parietals), the presphenoid with its intercalaries (frontals), and the ethmoid with its outgrowths (turbinals and cribriform plate), taking them in order from behind forwards, show an increasing divergence from the plan according to which vertebræ as commonly understood develop, so that the basioccipital shows the greatest resemblance to a vertebra, the ethmoid the least" (p. 30).

In a posthumous volume published in 1861 the same opinion is put forward. "In the head, too," he writes, "some vertebræ can be recognised, although in a more or less modified form. Yet at most only four cranial vertebræ can be assumed, and these differ from ordinary well-developed vertebræ in their manner of formation the more the farther forward they lie."[214]

Rathke was an able and careful critic of the vertebral theory of the skull, but he accepted it in the main. Actual attack on the theory upon embryological grounds was begun by C. Vogt, in his work on the development of Coregonus,[215] and in his paper on the development of Alytes.[216] He described for Coregonus an origin of the skull in the main similar to that established by Rathke for the adder. There was a "nuchal plate" in which the front end of the notochord was imbedded; the notochord ended at the level of the labyrinth; there were two lateral bands, comparable to Rathke's lateral trabeculæ; a "facial plate" was also formed, which seems on the whole equivalent to the plate formed by the fused anterior ends of the trabeculæ. A little later the cranium formed a complete cartilaginous box surrounding the brain, very similar to the adult cranium of a shark.

In his criticism of the vertebral theory of the skull, Vogt started by defining the vertebra as a ring formed round the chorda. Now since only the occipital segment of the skull is formed actually round the notochord, the parts of the skull lying in front of this cannot themselves be vertebræ, though they may be considered as prolongations of the occipital or nuchal vertebra. "We must regard the nuchal plate as a true vertebra, modified, it is true, in its formation and development by its particular functions. Now, since the notochord ends with the nuchal plate we can no longer regard as vertebræ the parts of the skull that lie beyond, such as the lateral processes of the cranium and the facial plate, for they have no relation with the notochord" (p. 123).

To support this view he adduced the fact that the vertebral divisions (primitive vertebræ) visible in the trunk do not extend into the head. He used precisely the same arguments in his paper on Alytes to destroy the vertebral theory of the skull. We quote the following passage translated by Huxley (1864, p. 295) from this paper. "It has therefore become my distinct persuasion that the occipital vertebra is indeed a true vertebra, but that everything which lies before it is not fashioned upon the vertebrate type at all, and that efforts to interpret it in such a way are vain; that, therefore, if we except that vertebra (occipital) which ends the spinal column anteriorly, there are no cranial vertebræ at all."

L. Agassiz, himself a pupil of Döllinger, in the general part (1844) of his Recherches sur les Poissons fossiles (Neuchâtel, 1833-43), repeats in the main his pupil Vogt's criticism of the vertebral theory (vol. i., pp. 125-9).

These arguments of Vogt and Agassiz were not considered by Müller to dispose of the theory,[217] which maintained a firm hold even upon embryologists. It was still upheld by Reichert, and Kölliker in 1849 showed himself convinced of its general validity.

A useful step in the analysis of the concept "vertebra" was taken by Remak,[218] who showed what a complex affair the formation of vertebræ really is, involving as it does a complete resegmentation (Neugliederung) of the vertebral column, whereby the original vertebral bodies were replaced by the secondary definitive bodies (p. 143). Remak showed, as he thought, that the protovertebral segmentation of the dorsal muscle-plates did not extend into the head, and he denied Reichert's assertion (1837) that the cranial basis in mammals showed transverse grooves delimiting three cranial vertebræ (p. 36). The gill-slits, he considered, could not possibly be regarded as marking the limits of head vertebræ.

In 1858 appeared Huxley's well-known Croonian Lecture, On the Theory of the Vertebrate Skull,[219] in which he stated with great clearness and force the case for the embryological method of determining homologies, and criticised with vigour the vertebral theory of the skull. By this time the two rival methods in morphology had become clearly differentiated, and Huxley was able to contrast them, or at least to show how necessary the new embryological method was as a corrective and a supplement to the older anatomical, or, as he calls it, "gradation" method. Applied to the "Theory of the Skull," the gradation method consists in comparing the parts of the skull and vertebral column in adult animals with respect to their form and connections. "Using the other method, the investigator traces back skull and vertebral column to their earliest embryonic states and determines the identity of parts by their developmental relations" (p. 541). This second method is the final and ultimate. "The study of the gradations of structure presented by a series of living beings may have the utmost value in suggesting homologies, but the study of development alone can finally demonstrate them" (p. 541). As an example of the utility and, indeed, the necessity of applying the embryological method Huxley takes the case of the quadrate bone in birds. This bone had been generally regarded by anatomists as the equivalent of the tympanic of mammals, on account of its connection with the tympanum; but Reichert showed (1837) that the same segment of the first visceral arch developed into the incus in mammals, and into the quadrate in birds, and that therefore the quadrate was homologous with the incus. Similarly, on developmental grounds, the malleus or hammer of mammals is the homologue of the articular of birds, since both are developed from a portion of Meckel's cartilage identical in form and connections in the two groups. The homologies of the bones connected with the jaws in bony fishes had long been a subject of contention among comparative anatomists; Huxley shows from his personal observations how the development of the visceral arches throws light upon these difficulties. The mandibular arch in the developing fish is abruptly angled, as in the embryo of Tetrapoda; the upper prong of it ossifies into the palatine and pterygoid; at the angle is formed the quadrate (jugal, Cuvier), and to the quadrate is articulated the lower jaw, which ossifies round the lower prong or Meckel's cartilage. The scheme of development of the jaws is accordingly similar in fish to what it is in other Vertebrates, and this similarity of development enables Huxley to recognise what are the true homologues of the quadrate, the palatine and the pterygoid in adult bony fish, and to prove that the symplectic and the metapterygoid (tympanal, Cuvier) are bones peculiar to fish. In developing Amphibia Huxley found a suspensorium of hyoid and mandibular arches similar to the hyomandibular of fish.