Gegenbaur, in his excellent “Outlines of Comparative Anatomy,”(21) has lately endeavoured to explain the origin of the Tracheata by an ingenious hypothesis. The system of tracheæ, or air pipes, and the modifications of organization dependent upon it, distinguish Flies, Centipedes, and Spiders so much from other animals, that the conception of its first origin presents no inconsiderable difficulties to phylogeny. According to Gegenbaur, of all living Tracheate Insects, the Primæval Flies, or Archiptera, are most closely allied to the common primary form of the Tracheata. These insects—among which we may especially mention the delicate Day flies (Ephemera), and the agile dragon-flies (Libellula)—in their earliest youth, as larvæ, frequently possess _external tracheate gills_ which lie in two rows on the back of the body, and are shaped like a leaf or paint-brush. Similar leaf or paint-brush shaped organs are met with as real water-breathing organs or gills, in many crabs and ringed worms, and, moreover, in the latter as real dorsal appendages or limbs. The “tracheate gills,” found in the larvæ of many primæval winged insects, must in all probability be explained as “_dorsal limbs_,” and as having developed out of the corresponding appendages of the Annelida, or possibly as having really arisen out of similar parts in Crustacea long since extinct. The present tracheal respiration of the Tracheata developed at a later period out of respiration through the “tracheate gills.” The tracheate gills themselves, however, have in some cases disappeared, and in others become transformed into the _wings_ of the Flies. They have disappeared entirely in the classes of Spiders and Centipedes, and these groups must accordingly be conceived of as degenerated or peculiarly developed lateral branches of the Fly class, which at an early period branched off from the common primary form of Flies; Spiders probably did so at an earlier period than Centipedes. Whether that common primary form of all Tracheata, which in my General Morphology I have named Protracheata, did develop directly out of genuine Ringed worms, or at first out of Crustacea of the Zoëa form (Zoëpoda, p. 177) will probably be settled at some future time by a more accurate knowledge and comparison of the ontogeny of the Tracheata, Crustacea, and Annelida. However, the root of the Tracheata, as well as that of the Crustacea, must in any case be looked for in the group of Ringed worms.