The Annelid theory of Dohrn and Semper was perhaps not so widely accepted as the rival Ascidian theory, but it counted not a few adherents and gave a certain stimulus to comparative morphology. F. M. Balfour, who pointed out about the same time as Semper the analogy between the nephridia of Annelids and the mesonephric tubules of Vertebrates,[405] while not accepting the actual theories of Dohrn and Semper, took up a distinctly favourable attitude to the general idea that Annelids and Vertebrates were descended from a common segmented ancestor. Discussing this question in his classical work on the development of Elasmobranch fishes,[406] Balfour came to the conclusion "that we must look for the ancestors of the Chordata, not in allies of the present Chætopoda, but in a stock of segmented forms descended from the same unsegmented types as the Chætopoda, but in which two lateral nerve-cords, like those of Nemertines, coalesced dorsally instead of ventrally to form a median nervous cord. This group of forms, if my suggestion as to their existence is well founded, appears now to have perished."[407]

He held that while there was much to be said for the interchange of dorsal and ventral surfaces postulated by Dohrn and Semper, the difficulties involved in the supposition were too great; he preferred, therefore, to assume that the present Vertebrate mouth was primitive, and not a secondary formation.

His views as to the phylogeny of the Chordata and the genetic relation of the various classes to one another are exhibited in the following schema,[408] names of hypothetical groups being printed in capitals, names of degenerate groups in italics:—

The hypothetical ancestral forms (Protochordata) possessed a notochord, a ventral suctorial mouth and numerous gill-slits, and were presumably descended from the common ancestor of Annelids and Vertebrates. Amphioxus and the Ascidians found their place in this schema as degenerate offshoots of the ancestral Protochordates, while the Cyclostomes were in the same way the degenerate modern representatives of the ancestral Protovertebrates.

Balfour's suggestion, that the nervous system in Annelids and Vertebrates might have arisen by the dorsal or ventral coalescence of the lateral nerve cords found in their common ancestor, bore fruit in the speculations of Hubrecht,[409] on the relation of Nemertines to Vertebrates.

The Annelid theory was firmly supported by Eisig, who in his elaborate monograph on the Capitellidæ[410] maintained against Fürbringer the genetic identity of the Annelidan nephridia with the kidney tubules of Vertebrates. The independent discovery by E. Meyer[411] and J. T. Cunningham,[412] of an internal segmental duct in Lanice, into which several nephridia opened, seemed to strengthen this view.

Following Ehlers,[413] Eisig found the homologue of the notochord in the accessory intestine of the Capitellidæ and Eunicidæ, which he supposed might easily be transformed, according to the principle of function-change, from a respiratory to a supporting organ. He finally disposed of the alternative notion that the notochord was represented in Annelids by the "giant-fibres" or neurochordal strands which lie close above the nerve-cord, a view held by Kowalevsky,[414] and for a time by Semper. These strands were shown by Eisig, and by Spengel, to be the neurilemmar sheaths of thick nerve fibres which had in many cases degenerated. The view that the content of the neurochordal tubes was nervous in nature was first promulgated by Leydig in 1864.

Much difference of opinion reigned as to the true homologies of the brain and mouth of Annelids and Vertebrates. Beard[415] and others got over the difficulty of the hæmal position of the cerebral ganglion in Annelids by supposing that it degenerated and disappeared altogether in the Annelidan ancestor of Vertebrates, and that accordingly it had no homologue in the Vertebrate nervous system. Beard put forward also the ingenious theory that the hypophysis represents the old Annelidan mouth.

Van Beneden and Julin[416] assumed that in the ancestors of Vertebrates the œsophagus shifted forward between the still unconnected lobes of the brain to open on the hæmal surface.