The doctrine of phyllotaxis of Schimper and Braun, as it appeared after 1830, had clearly presented only one side of the theory of metamorphosis; what other elements there were in it capable of being turned to speculative account were further cultivated by ALEXANDER BRAUN between the years 1840 and 1860. In this period fresh points of view were asserting themselves in botanical research; the founding of the doctrine of cells, the study of the more delicate anatomy of plants and of the history of development, and increased methodical knowledge of the Cryptogams were enlarging the repertory of botanical facts, while the physico-mechanical method of investigation was being more and more adopted. Braun, who took an active part by his own researches in this revolution in morphological botany, remained true nevertheless to idealistic views; and in his frequent and comprehensive discussions of the general results of the new investigations in accordance with these views he has shown how far the idealistic platonising contemplation of nature is in a condition to do justice to the results of exact inductive enquiry. The opposition between his point of view and that of the most eminent representatives of the inductive method became more and more pronounced as years went on, and must be treated here as a historical fact. But if the new tendency in botany pursued especially by von Mohl, Schleiden, Nägeli, Unger, and Hofmeister may be called inductive in the absence of a better term, and be contrasted with the idealistic tendency represented by Braun and his school, it must not be supposed that the latter did not equally contribute in matters of detail to the enriching of the science by the method of induction; on the contrary, Braun himself was the author of a series of important works conceived in this spirit. When the new method is here called inductive, it should be understood that the word is used in a higher than the usual sense, and some explanation of this point will not be superfluous in this place. Idealistic views of nature of all times, whether they present themselves as Platonism, Aristotelian logic, Scholasticism or modern Idealism, have all of them this in common, that they regard the highest knowledge attainable by man as something already won and established; the highest axioms, the most comprehensive truths are supposed to be already known, and the task of inductive enquiry is essentially that of verifying them; the results of observation serve to elucidate already received views, to illustrate already known truths; inductive enquiry has only to establish individual facts. But in the sense in which inductive enquiry was understood by Bacon, Locke, Hume, Kant, and Lange, its task is one that goes essentially farther than this; it must not be content with establishing individual facts, but it must employ them in the critical examination of the most general notions that have come down to us,