This branch of science developed considerably in the second half of the nineteenth century. It has now its methods, its technique, its chairs at the universities, its laboratories, and its literature. It has particularly applied itself to the study of the “material changes” or the _metabolism_ of living beings, and with that object in view it has done two things. In the first place, it has determined the composition of the constituent materials of the organism; then analyzing qualitatively and quantitatively all that penetrates into that organism in a given time—that is to say, all the alimentary or respiratory ingesta, and all that issues from the organism, _i.e._, all the excreta, all the _egesta_,—it has drawn up _nutritive balance sheets_, corresponding to the various conditions of life, whether naturally or artificially created. And thus we can determine the alimentary régimes which give too much, and which give too little, and which finally restore equilibrium. We do not propose to give a detailed account of this scientific movement. This may be done in monographs. All we wish to indicate here is the most general result of these laborious researches—that is to say, the laws and the doctrines which are derived from them, and the theories to which they have given birth. It is by this alone that they are brought into relation with general science, and may therefore interest the reader. The facts of detail are never lacking to the historian; it is more profitable to show the movement of ideas. The theories of alimentation bring into conflict very different conceptions of the vital functional activity. And here we find a confused medley of opinions on which it is not without interest to endeavour to throw some light. § 1. FOOD, A SOURCE OF ENERGY AND MATTER. _Definitions of Food._—Before the introduction into physiology of the notion of energy, no one had succeeded in giving an exact idea and a precise definition of food and alimentation. Every physiologist and medical man who attempted it had failed, and this for various reasons. The general cause of this failure was that most definitions, popular or technical, interposed the condition that the food must be introduced into the digestive apparatus. “It is,” said they, “a substance which when introduced into the digestive tube undergoes, etc., etc.” But plants draw food from the soil, and they possess no digestive apparatus; many animals have no intestinal tube; and in the case of certain rotifera, the females possess a digestive apparatus, while the males have none. Nevertheless all animals feed. On the other hand, there are other substances than those which use the digestive tract for the purpose of entering the organism, and which are eminently useful or necessary to the maintenance of life. In particular we may mention oxygen.