From our complete ignorance of the interior of South America (Mato-Grosso, Paraguay, the eastern declivity of the Andes, Santa-Cruz de la Sierra, and all the countries lying between the Orinoco, the Rio Negro, the Amazon, and Puruz), of Africa, of Madagascar, and Borneo, and of Central and Eastern Asia, the idea involuntarily presents itself to the mind that we are not yet acquainted with one third, or probably even with one fifth part of the plants existing on the earth. Drège has collected 7092 phanerogamic species in Southern Africa alone; and he believes that the flora of that region consists of more than 11,000 phanerogamic species, seeing that in Germany and Switzerland, on an equal area (192,000 square miles,) Koch has described only 3300, and Decandolle only 3645 phanerogamia in France. I would here also instance the new genera, consisting partly of high forest trees, which are still being discovered in the neighbourhood of large commercial towns in the lesser Antilles, although they have been visited by Europeans for the last three hundred years. Such considerations, which I purpose developing more fully at the close of this illustration, seem to verify the ancient myth of the Zend-Avesta, that “the creating primeval force called forth 120,000 vegetable forms from the sacred blood of the bull.” If therefore no direct scientific solution can be afforded to the question, how many vegetable forms—leafless cryptogamia (water algæ, fungi, and lichens), characeæ, liverworts, foliaceous mosses, marsilaceæ, lycopodiaceæ, and ferns—exist on the dry land, and in the wide basin of the sea, in the present condition of the organic terrestrial life of our planet, it only remains for us to employ an approximative method for ascertaining with some degree of probability certain “extreme limits” (numerical data of minima). Since the year 1815, I have, in my arithmetical considerations on the geography of plants, calculated the numbers expressing the ratio which the aggregate of species of different natural families bears to the whole mass of the phanerogamia in those countries where the latter is sufficiently determined. Robert Brown,[NE] the greatest botanist of our age, had, prior to my researches, already determined the numerical proportion of the principal divisions of vegetable forms, as for instance of acotyledons (_Agamæ_, cryptogamic or cellular plants) to cotyledons (_Phanerogamia_, or vascular plants), and of monocotyledons (_Endogenæ_) to dicotyledons (_Exogenæ_). He finds the ratio of monocotyledons to dicotyledons in the tropical zone as in the proportion of 1 to 5, and in the frigid zone, in the parallels of 60° north, and 55° south lat. as 1 to 2½.[NF] The absolute numbers of the species are compared together in the three great divisions of the vegetable kingdom, according to the method developed in Brown’s work.