- [Footnote: countries, and in the latitudes from 12° to 15° distant from
the tropics.
It has appeared to me not unimportant to show the imperfect state of our knowledge in this still little cultivated department of arithmetical botany, and to propound numerical questions in a more distinct and determinate manner than could have been previously done. In all conjectures respecting numerical relations we must seek first for the possibility of deducing the lower or minimum limits; as in a question treated of by me elsewhere, on the proportion of coined gold and silver to the quantity of the precious metal fabricated in other ways; or as in the questions of how many stars, from the 10th to the 12th magnitude, are dispersed over the sky, and how many of the smallest telescopic stars the Milky Way may contain. (John Herschel, Results of Astron. Observ. at the Cape of Good Hope, 1847, p. 381.) We may consider it as established, that if it were possible to know completely and thoroughly by observation all the species belonging to one of the great families of phanerogamous or flowering plants, we should learn thereby at the same time, approximatively, the entire sum of all such plants (including all the families). As, therefore, by the progressive exploration of new countries we progressively and gradually exhaust the remaining unknown species of any of the great families, the previously assigned lowest limit rises gradually higher, and since the forms reciprocally limit each other in conformity with still undiscovered laws of universal organisation, we approach continually nearer to the solution of the great numerical problem of]*
