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 results it was established by these facts, that morphological differentiation during growth must not be regarded as an effect of cell-divisions, and from such cases as these the conception of the cell experienced a notable expansion. Moreover, Nägeli was not satisfied with seeking instructive examples for general morphological axioms in the lower Cryptogams; he devoted special study to the Algae for systematic and descriptive purposes; and his ‘Neuen Algensysteme,’ which appeared in 1847, and ‘Gattungen einzelliger Algen,’ of 1849, were the first successful attempts to substitute serious investigation for the mere zeal of the collector in this part of the vegetable kingdom, which had not indeed been hitherto neglected, but had not been systematically worked since the time of Vaucher. In the same spirit Alexander Braun also in his ‘Verjüngung’ contributed a rich material of new observations on the mode of life of the Algae and the morphological conditions connected with it, and his labours were followed in the succeeding years by the important researches of Thuret, Pringsheim, De Bary, and others, to which we shall recur in a later portion of this history.