The results of the investigations published in the ‘Vergleichende Untersuchungen’ in 1849 and 1851 were magnificent beyond all that has been achieved before or since in the domain of descriptive botany; the merit of the many valuable particulars, shedding new light on the most diverse problems of the cell-theory and of morphology, was lost in the splendour of the total result, which the perspicuity of each separate description revealed to the reader before he came to the conclusion of the work, and there a few words in plain and simple style gave a summary of the whole. Briefly to describe this result in all its importance for botanical science is a difficult task; the idea of what is meant by the development of a plant was suddenly and completely changed; the intimate connection between such different organisms as the Liverworts, the Mosses, the Ferns, the Equisetaceae, the Rhizocarps, the Selaginellae, the Conifers, the Monocotyledons, and Dicotyledons could now be surveyed in all its relations with a distinctness never before attained. Alternation of generations, lately shown to exist though in quite different forms in the animal kingdom, was proved to be the highest law of development, and to reign according to a simple scheme throughout the whole long series of these extremely different plants. It appeared most clearly in the Ferns and Mosses, though at the same time with a certain difference in each; in the Ferns and allied Cryptogams a small inconspicuous body grows out of the asexually produced spore, and immediately produces the sexual organs; from the fertilisation of these organs proceeds the root-bearing and leafy stem of the Fern, which in its turn again produces only asexual spores. In the Muscineae, on the other hand, a much differentiated and usually long-lived plant is developed from the spore, and this plant proceeds again after some time to form sexual organs, the product of which is the so-called Moss-plant. The first generation that arose from the spore, the sexual, is in the Muscineae the vegetative plant, while in the Ferns and their allies the whole fulness of vital activity and of morphological differentiation is unfolded in the second generation which is sexually produced. Here all was at once clear and obvious: but Hofmeister’s researches also showed that the same scheme of development holds good in the Rhizocarps and Selaginellae where two kinds of spores are formed; and it appeared plainly from their case that the recognition of the true relation between the production of spores and sexual organs is the guide to the morphological interpretation. When the processes in the large female spore of the most perfect of the Cryptogams was known, the formation of the seeds in the Conifers was at once understood; the embryo-sac in these answered to this large spore, while the endosperm represented the prothallium, and the pollen-grain the microspore; the last trace