ABSTRACT 1. The cranial flexure, together with other features in the shape of the embryonic head skeleton in Teleosts, is probably a mechanical effect due to differences in the degree of distensibility between the dorsal and ventral surfaces of the brain, and to the presence of skeletal structures in close association with the latter (pp. 507—509). 2. The presence of an epiphysial bar, with consequent division of the large dorsal, cranial fontanelle into an anterior and a posterior portion, is a common feature among Teleosts during development (pp. 516, 517). 3. The Ostariophysi differ from all other Teleosts in the retention of this early developmental condition of the cranial roof in the adult (pp. 525, 526). 4. The intra-cranial notochord, so far from undergoing reduction, never at any stage ceases to grow (pp. 513, 516, 523). 5. In Gasterosteus, during embryonic life, those skeletal elements immediately concerned in the support of the jaws and operculum, and in the attachment of associated muscles, seem to undergo a considerable acceleration in the rate of development as compared with the rest of the head skeleton (pp. 534, 535). 6. Among Teleosts and the immediately related Ganoids, three types of palato-ethmoidal relationship exist (pp. 538, 539, 551—557). (a) The Panartete, in which the paiaume cartilage or its derivatives is attached to the ventral surface of the ethmoid for the whole length of this, from the parethmoid to the pre-ethmoid cornua, e. g. Amia, probably presented also by many Malacopterygii (Isospondyli). (b) The Disartete, in which the attachment is at the parethmoid and pre-ethmoid cornua, but not at any intermediate point, e. g. Esox, also presented by the Salmonidæ, Cyprinodontidæ, Acanthopterygii, and probably some Malacopterygii (Isospondyli). (c) The Acrartete, in which the attachment is confined solely to the pre-ethmoid cornua, e. g. Gasterosteus, and also presented by the Thoracostei, Scomberesoces, Plectognathi, Zanclidæ, Acronuridæ, and in a modified form by Lepidosteus. 7. The study of the adult anatomy and comparative ontogeny of the head skeleton in Elasmobranchs and Teleo-stomes seems to point to a common ancestral stock for these two great divergent branches of fishes. It presented among other features the following : A short embryonic life ; weak cranial flexure ; trabeculæ united to the extreme anterior end of the parachordals. A wholly cartilaginous cranium, possessing trabecular, parachordal, and occipital portions (pp. 560—562). A cranium having a large dorsal fontanelle, which may oi* may not have been divided by a transverse epiphysial bar. Also two lateral fontanelles for the passage of the optic, and possibly also the trigeminal and facial nerves. Also a ventral or pituitary fontanelle. Also a large opening between the cavum cranii and auditory capsule (pp. 562—568). A quadrate cartilage supporting a lower moveable jaw, formed by the union of two cartilages in the middle line, and bearing dorsally two, possibly three processes ; an anterior one, parallel to its fellow, and not united with it, but with the ethmoid plate, so that a moveable upper jaw did not exist; a middle one articulating with the trabeculæ, in the region lying between the optic and trigeminal nerves ; a posterior one articulating with the auditory capsule (pp. 568—573). A branchial apparatus consisting of at least five arches, already segmented into four parts. Balfour’s term Prolognathostoraata (81, p. 271) would be sufficiently expressive of such a type. 8. The manner of mandibular suspension in Teleosts is insufficiently described by the term Hyostylic (pp. 569, 570). 9. The Lophobranchii and Hemibranchii should no longer be kept in separate orders, for they together constitute a natural group, which may be designated the Thoracostei (pp. 575—579). 10. The Scomberesoces, through the Gasterosteoidei, approach more closely to the Thoracostei than do any other living Physoclisti, and seem to form with them a compact series, which may be provisionally spoken of as the Scomberesocine series (pp. 580, 581). 11. As judged by the study of the ethmoid and suspensorial regions, the Zanclidæ and Acronuridæ are closely allied to the Plectognathi, but the affinities of these forms must not be sought amongst living Physoclisti (pp. 582, 583).