those researches of Nägeli between the years 1844 and 1849, which have been already mentioned, and which are the first since Vaucher’s time that can be regarded as systematic. Nägeli studied especially the laws of cell-division in sexual multiplication and growth, but he considered the Florideae to be the only Algae that were sexually differentiated, and distinguished the rest as being without sexuality. Braun in his ‘Verjüngung’ (1850) made numerous contributions to the biology of the fresh-water Algae, affording many and most interesting glimpses into a connection still little understood between these forms; and in 1852 he gave an account of the history of growth in the Characeae, a work conceived in Nägeli’s spirit and a model of scientific research, in which the mode of derivation of every cell from the apical cell of the stem was shown, the sexual organs were minutely examined, and the relation established between the direction of the ‘streaming’ of the cell-contents and the morphology of the organs. Gustav Thuret had already made the zoospores of the Algae the subject of detailed examination. Such was the condition of affairs with respect to the Algae about the year 1850, when Hofmeister made the formation of the embryo in the Phanerogams, the Vascular Cryptogams, and the Muscineae the central point of investigation in morphology and systematic botany. He made it clear that a perfect insight into the whole cycle of development in the plant and into its affinities can only be obtained, if we succeed in making its sexual propagation, the first commencement of the embryo, the starting-point of the investigation. It was natural to expect as happy results from the embryology of the Algae, as had been obtained in the case of the higher plants; it was important therefore, that the observer should no longer rest satisfied with a knowledge of the sexual multiplication of the Algae; he must enquire into their asexual propagation, and by its aid discover the complete history of their development. Former observations suggested the probability that here too sexual propagation is the prevailing rule; but it was easy to foresee that it would be a task of great labour to make out a connected history of development, a task of which the collectors who liked to call themselves systematists had never formed a conception; but Nägeli’s and Hofmeister’s researches had made botanists familiar with the highest demands of this kind, and the men who were to gain new conquests for genuine science were already engaged in the work in 1850. A splendid result appeared in 1853, in Thuret’s account of the fertilisation of the genus Fucus; this was a simple process as a matter of embryology; but the sexual act was so clear, and even open to experimental treatment, that it threw light at once upon other cases more difficult to observe. Then followed discoveries of sexual processes in rapid succession; Pringsheim solved