difficult, thus not only introducing the Cryptogams into the field of systematic investigation, but making them its starting-point. In this way morphology not only secured a foundation in exact historical development, but it assumed a different aspect, inasmuch as the morphological ideas hitherto drawn from the Phanerogams were now examined by the light of the history of development in the Cryptogams. This was one innovation; the second, closely connected with it, was the way in which Nägeli made the new doctrine of the cell the starting-point of morphology. Both the first commencement of organs and their further growth were carried back to the formation of the separate cells; and the remarkable result was to show, that in the Cryptogams especially, whose growth is intimately connected with cell-division, precise conformity to law obtains in the succession and direction of the dividing walls, and that the origin and further growth of every organ is effected by cells of an absolutely fixed derivation. The most remarkable thing was, that every stem and branch, every leaf or other organ has a single cell at its apex, and that all succeeding cells are formed by division of this one cell according to fixed laws, so that the origin of all cell-tissue can be traced back to an apical cell; and as early as the years 1845 and 1846 Nägeli described in the 'Zeitschrift für wissenschaftliche Botanik' the three main forms, according to which the segmentation of an apical cell proceeds, namely, in one, two, and three rows (Delesseria, Echinomitrium, Phascum, Jungermannia, Moss-leaves). In this way the separate points in the history of growth in the Cryptogams were brought out with unusual clearness and decision; but on the other hand, Nägeli showed in 1844 in the case of a genus of Algae (Caulerpa) that the growth of a plant may show the usual morphological differentiation into axis, leaf, and root, when the propagative cell undergoes no cell-divisions in the process of development and further growth, and similar conditions were for the first time demonstrated in 1847 in Valonia, Udotea, and Acetabularia. Beside other
