We can best make this plain by examples. The wing of a bird and the wing of a butterfly are analogous organs. They have the same function--i. e., flying; and this function necessitates the same general form of a flat plane. But they are not at all homologous; they are not at all the same organ or part. They certainly have never been formed one out of the other by modification. But the wing of a bird, the fore-paw of a reptile or mammal, the wing of a bat, and the arm and hand of a man, though so different in form and function, are homologous parts. On close examination they are found to have the same general structure, to be composed of essentially the same pieces, although they are so greatly modified in order to adapt them to different functions, that the general or superficial resemblance is now lost. Their structure is precisely such as it would be if they had all originated from some archetypal fore-limb by modifications in different directions of its several parts. By extensive comparison in the taxonomic and ontogenic series, all the intermediate gradations between these extreme modifications may be picked up. [Illustration: FIG. 2.--Lepidosiren.] Another example. The lungs of a mammal and the gills of a fish are analogous organs, since they have the same function of aëration of the blood. But they are not at all homologous: they are not built on the same plan; by no effort of the mind can we imagine that the former could have come out of the latter by modification. On the contrary, we have positive proof that it did not so come. But there is an organ in the fish which is homologous with the mammalian lung, viz., the air-bladder, or swim-bladder. We know it--1. Because we can trace in the taxonomic series all the gradations from the one to the other. In most fishes the air-bladder is wholly cut off from the gullet, and only very feebly supplied with blood. It is used and can be used only for flotation. In others, as the gar-pike, the swim-bladder is quite vascular and opens by a tube into the throat. Through this opening air is gulped down from time to time into the bladder, and again from time to time expelled. In other words, this fish supplements its gill-breathing by an imperfect lung-breathing. We have here the beginning of a lung. In still other fishes, viz., the Dipnoi (_lepidosiren_ and _ceratodus_, Fig. 2), the air-bladder becomes a more perfect lung--i. e., a very vascular sacculated sac; and there is not only an opening into the throat, but also from the throat to the snout. In other words, we have for the first time _nostrils_. These fishes completely combine gill-breathing with lung-breathing. The step from these to the lowest amphibian reptiles is so small, that some have classed the lepidosiren among amphibians instead of fishes. The siredon or axolotl of New Mexico, the necturus or menobranchus of our Northern lakes, and the siren of our Southern swamps, have both gills and lungs,