These considerations have led us to the proportion borne by the number of species growing in gardens to the gross number of those already described and preserved in herbariums; it now remains for us to consider the proportion of the latter to the conjectural number of species existing on the whole earth, or, in other words, to test their minimum by the relative numbers of the different families—_i. e._ by variable _multipla_. A test of this kind gives, however, such low results for the _lower_ amount, as plainly to show that even in the large families, which appear to have been the most strikingly enriched in recent times by the researches of descriptive botanists, our knowledge is still limited to a very small portion of the treasure actually existing. The _Repertorium_ of Walpers which completes Decandolle’s _Prodromus_ of 1825 to 1846, gives 8068 species of the family of the Leguminosæ. We may assume the mean ratio to be ¹⁄₂₁; since it is ⅒ in the tropical zone, ¹⁄₁₈ in the middle temperate zone, and ¹⁄₃₃ in the cold northern zone. The _described_ Leguminosæ would therefore only lead us to assume that there were 169,400 species of Phanerogamia existing on the earth, whereas the Compositæ, as already shewn, testify to the existence of more than 160,000 known Phanerogamia, _i. e._ such as have been described or are contained in herbariums. This discrepancy is instructive, and will be further elucidated by the following analogous considerations.