In spite of the real and apparent differences between Goethe’s doctrine of metamorphosis and De Candolle’s doctrine of a plan of symmetry, these writers agreed in this, that they set out alike from the doctrine of the constancy of species, and led up equally to the result, that alongside of manifold physiological differences in the organs of plants certain points of formal agreement can be discovered, which are expressed chiefly in the order of their succession and in their relative positions. In this distinction lay the good kernel of the doctrine of metamorphosis in Goethe, and Wolff, and even in Linnaeus and Cesalpino: it was only necessary to set this free from the dross with which the nature-philosophy had surrounded it, and to make the relations of position in organs the subject of earnest investigation, in order to secure important results in this branch of morphology. The first step in this direction was taken by Carl Friedrich Schimper, who was followed by Alexander Braun; both adopted the main idea of the doctrine of metamorphosis in the form in which it can be reconciled with the doctrine of constancy, that is, in a purely idealistic sense. Both liberated themselves from the gross errors of the nature-philosophers, and thus gave a more logical expression to the purely idealistic morphological consideration of form in plants. KARL FRIEDRICH SCHIMPER[46] founded before the year 1830 the theory of the arrangement of leaves which is named after him, and which he expounded to the naturalists assembled at Stuttgart in 1834 as a complete and perfected system. Alexander Braun, in a review of Schimper’s exposition in ‘Flora’ of 1835, gave a clear and simple account of the theory, having already himself published an excellent and comprehensive treatise on the same subject. The doctrine of phyllotaxis appeared in these publications with a formal completeness which could not fail to attract the attention of the botanical world and indeed of a larger audience; and justly so, for, as unfortunately so very seldom happens in botanical subjects, a scientific idea was in this case not merely incidentally suggested, but was worked out in all its consequences as a complete structure, and this structure gained in external splendour from the circumstance that its propositions, dealing with geometrical constructions, could be expressed in numbers and formulae,—a thing hitherto unknown in botanical science.