The method to be adopted has been indicated by Alexander von Humboldt in his "Ansichten der Natur" ("Pictures of Nature"). His method consists in the comparison of the vegetable families whose numerical relations are _known_, with the number of species contained in our herbariums, or cultivated in our botanical gardens. But here, at the outset, a difficulty confronts us. Does any relation exist between the classification of plants by natural families and by their geographical distribution? To group plants according to their analogies of structure, we study them from an abstract point of view, and without any regard to the medium in which they flourish. The question grows complicated if we also take into consideration their characteristic conditions and their distribution over the terrestrial surface. Families are then split asunder, and the importance of our scientific classifications disappears. The gathering together of a small number of species, represented by innumerable individuals, confined within the same area, may suffice to communicate to a landscape its characteristic physiognomy: as, for example, is the case with the Asiatic steppes, the _landes_ of Brittany, the moors of Scotland, the palm-groves and the clumps of Cactaceæ of tropical America. By the side of species which impress us by their _mass_--that is, by the frequent reproduction of the same individuals at an infinitesimal distance from one another--are placed those much more numerous species which are everywhere very thinly sown. But do the plants themselves follow, from the equator to the poles, the same law of _decrease_ as obtains from the base to the summit of the loftiest equatorial mountains? Under identical isothermal lines, is the ratio of families known and identified to the probable aggregate of Phanerogams the same, in the temperate zone, on either side of the equator? What are the vegetable families which preponderate at the two extremes, represented by the torrid and the frigid zones? Under the same geographical latitude, or between the same isothermal lines, are the Synantheræ, the Gramineæ, the Leguminosæ, the Labiatæ, the Cruciferæ, the Umbelliferæ, more numerous in the Old than in the New World? What families, either through their mass of individuals or their number of species, take precedence of the other Phanerogams? How many species of one and the same family belong to any particular country? What groups or families are characteristic of each zone? Is the present classification of genera and species in all respects what could be desired? * * * * * These are questions that require to be considered, and to some of them we shall presently attempt replies.