In conformity with this natural division of Amphibious animals into two classes, the whole tribe of Vertebrate animals was divided into two main groups. The first main group, containing Amphibious animals and Fishes, breathe throughout their lives, or in early life, by means of gills, and are therefore called _gilled Vertebrata_ (Branchiata, or Anallantoida). The second main group—Reptiles, Birds, and Mammals—breathe at no period of their lives through gills, but exclusively through lungs, and hence may appropriately be called Gill-less, or _Vertebrata with lungs_ (Abranchiata, or Allantoida). However correct this distinction may be, still we cannot remain satisfied with it if we wish to arrive at a true natural system of the vertebrate tribe, and at a right understanding of its pedigree. In this case, as I have shown in my General Morphology, we are obliged to distinguish three other classes of Vertebrate animals, by dividing what has hitherto been regarded as the class of fishes into four distinct classes. (Gen. Morph. vol. ii. Plate VII. pp. 116-160.) The first and lowest of these classes comprises the _Skull-less_ animals (Acrania), or animals with _tubular hearts_ (Leptocardia), of which only one representative now exists, namely, the remarkable little Lancelet (Amphioxus lanceolatus). Nearly allied to this is the second class, that of the _Single-nostriled_ animals (Monorrhina), or _Round-mouthed_ animals (Cyclostoma), which includes the Hags (Myxinoida) and Lampreys (Petromyzonta). The third class contains only the genuine Fish (Pisces): the Mud-fishes (Dipneusta) are added to these as a fourth class, and form the transition from Fish to Amphibious animals. This distinction, which, as will be seen immediately, is very important for the genealogy of the Vertebrate animals, increases the original number of Vertebrate classes from four to eight. In most recent times a ninth class of Vertebrata has been added to these eight classes. Gegenbaur’s recently published investigations in comparative anatomy prove that the remarkable class of _Sea-dragons_ (Halisauria), which have hitherto been included among Reptiles, must be considered quite distinct from these, and as a separate class which branched off from the Vertebrate stock, even before the Amphibious animals. To it belong the celebrated large Ichthyosauri and Plesiosauri of the oolitic and chalk periods, and the older Simosauri of the Trias period, all of which are more closely allied to Fish than to Amphibious animals.