So gorgeous a picture as Hofmeister had designed of the genetic connection of the vegetable kingdom, except the Thallophytes, could not possibly be completely perfect and correct in all its separate features; there were still many gaps to fill up and particular observations to correct. Hofmeister himself continued his labours; the remarkable genera Isoetes and Botrychium were in the following years more carefully studied by himself, the fertilisation and embryology of the Equisetaceae by himself and Milde, and those of Ophioglossum by Mettenius, and all were fitted into their place in the system. To the present day it is always a profitable task to submit the different forms of the Muscineae, the Vascular Cryptogams, and the Gymnosperms to exact investigation in order to ascertain all the details in the process of development in these plants, the formation of the embryo, the succession of cells at the apex, the first appearance and further growth of the lateral organs; and the more careful the observation, the more clearly even to its farthest results does the correctness of the alternation of generations asserted by Hofmeister everywhere appear. It does not fall within the limit of this history to pursue the subject further, and to show how the doctrine of alternation of generations and the knowledge of the morphology of the Cryptogams were further advanced by later and distinguished researches, such as those of Cramer on the Equisetaceae, of Pringsheim on Salvinia (1862), of Nägeli and Leitgeb on the formation of roots in the Cryptogams, of Hanstein on the germination of the Rhizocarps, and of others. THALLOPHYTES. The method of investigation which starts from the first steps towards the formation of the embryo before and after fertilisation, and follows the advancing segmentation and growth through all the stages of development up to the final completion of the embryo-plant, has led since 1850 in the case of the Muscineae, Vascular Cryptogams, and Phanerogams to great certainty in the morphological explanation of the organs, while the determination of affinities has ceased to be arbitrary and insecure; the way was now known which would lead to the desired end, whenever it was sought to establish the affinities of a genus of Cryptogams or of the larger groups of Phanerogams; the day of ingenious guessing and trying was over; the only plan was patient investigation, and this always yielded a result of lasting value.