Abstract
Summary: 1. A mode of origin of cephalopod buoyancy, by withdrawal of the animal from the apex of the shell followed by withdrawal of liquid from the resulting space, is suggested.2. Buoyancy, once evolved, gave cephalopods an immediate advantage over contemporary animals and evolutionary radiation in the early Ordovician was a consequence of this.3. The earliest cephalopods probably had curved (cyrtocone) shells. Tightly coiled shells evolved from cyrtocones in at least two separate lineages and were in the first place adapted to a benthonic existence. Straight shells (orthocones) were adapted for efficient swimming. They usually had apical counterweights to maintain a horizontal position, but in forms without counterweights, liquid‐filled chambers could have served the same purpose.4. Six evolutionary branches are described, which were distinct by the end of the Canadian (Lower Ordovician). Each branch is believed to be monophyletic, and up to a point each is characterized by certain structures or trends.5. Increased efficiency in jet propulsion became possible in one orthocone group, consequent on loss of the ventral wall of the body‐chamber, so that the mantle cavity wall could become muscular and contractile. This group gave rise to the living di‐branchiates, or Coleoidea.6. The primitive septum, which was concave forwards, remained standard in most orthocones and in some coiled shells. Folded septal edges, giving rise to more or less complex septal sutures, evolved independently in a number of coiled lineages. Their significance is unknown.7. The siphuncle is simple and small in all coiled shells and in some orthocones. In some cyrtocones and other orthocones large siphuncles of complex structure were evolved. They usually contain deposits which are interpreted as counterweights.8. Existing classifications of cephalopoda stem from subdivisions recognized in the nineteenth century when knowledge of fossils was inadequate. They are ill‐balanced and should be abandoned.9. A classification based on phylogeny is now possible. The six branches already described may be regarded as major subdivisions. In addition, it may be desirable to subdivide branches on the basis of important evolutionary changes. The strongest case is for the separation of Coleoidea on the grounds of the loss of the shell.

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