Loudon’s useful work (Hortus britannicus) gives a general view of the species which now are or recently have been, cultivated in English gardens. The edition of 1832 enumerates, including indigenous plants, exactly 26,660 Phanerogamia. We must not confound with this large number of plants that either have been, or still are, cultivated in Great Britain, “all the living plants which may simultaneously be found in an individual botanic garden.” In this last respect the Botanic Garden of Berlin has long been regarded as one of the richest in Europe. The fame of its extraordinary riches rested formerly on a mere approximative estimate of its contents, and, as my old friend and fellow-labourer Professor Kunth, has very correctly remarked,[[NO]] “it was only by the completion of a systematic catalogue, based on the most careful examination of the species, that an actual enumeration could be undertaken. This enumeration gave somewhat more than 14,060 species; and when we deduct from these 375 cultivated ferns, there remain 13,685 Phanerogamia, among which there are 1600 Composite, 1150 Leguminosæ, 428 Labiatæ, 370 Umbelliferæ, 460 Orchideæ, 60 Palms, and 600 Grasses and Cyperaceæ. If we compare with these numbers the number of species given in recent works, as, for instance, Compositæ (according to Decandolle and Walpers), at about 10,000, Leguminosæ 8070, Labiatæ (Bentham) 2190, Umbelliferæ 1620, Grasses 3544, and Cyperaceæ 2000,[[NP]] we shall perceive that the Botanic Garden at Berlin cultivates only ⅐, ⅛, and ⅑ of the very large families (Compositæ, Leguminosæ, and Grasses), and as many as ⅕ and ¼ of the already described species belonging to the small families (Labiatæ and Umbelliferæ). If we estimate the number of all the different species of Phanerogamia simultaneously cultivated in all the botanical gardens of Europe at 20,000, we shall find, as they appear to constitute about the eighth part of those already described and contained in herbariums, that the whole number of Phanerogamia must amount to nearly 160,000. This estimate need not be regarded as too high, since scarcely the hundredth part of many of the larger families, as, for instance, Guttifereæ, Malpighiaceæ, Melastomeæ, Myrtaceæ, and Rubiaceæ, belong to our gardens.” If we take the number (26,660 species), given in Loudon’s “Hortus Britannicus,” as the basis, we shall find, from the well-grounded series of inferences drawn by Professor Kunth, and which I borrow from his manuscript notice above referred to, that the estimate of 160,000 will increase to 213,000 species; and even this is still very moderate, since Heynhold, in his “Nomenclator botanicus hortensis” (1846), estimates the species of Phanerogamia already cultivated at 35,600. On the whole, therefore,—and the conclusion is, at first sight, sufficiently striking,—the number of species of Phanerogamia at present known by cultivation in gardens, by descriptions, and in herbariums, is almost greater than that of known insects. According to the average estimates of several of the most distinguished entomologists, whose opinion I have been able to obtain, the number of insects at present described, or contained in collections without being described, may be stated as between 150,000 and 170,000 species. The rich collection at Berlin contains fully 90,000, among which there are about 32,000 beetles. Travellers have collected an immense quantity of plants in remote regions, without bringing with them the insects living upon them, or in the neighbourhood. If, however, we limit these numerical estimates to a definite portion of the earth’s surface that has been the best explored in regard to its plants and insects, as, for instance, Europe, we find the ratio between the vital forms of Phanerogamic plants and those of insects changed to such a degree, that while Europe counts scarcely 7000 or 8000 Phanerogamia, more than three times that number of European insects are at present known. According to the interesting contributions of my friend Dohrn in Stettin, more than 8700 insects have already been collected from the rich fauna of the neighbourhood, and yet there are still many MicroLepidoptera wanting; while the number of Phanerogamia found there scarcely exceeds 1000. The Insect-fauna of Great Britain is estimated at 11,600. Such a preponderance of animal forms will appear less surprising when we remember that several of the large classes of insects live only on animal substances, whilst others subsist on agamic plants (Fungi), and even on those which are subterranean. Bombyx Pini, the Pine Spider, the most destructive of all forest-insects, is infested, according to Ratzeburg, by no less than thirty-five parasitical Ichneumonidæ.

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.

The larger number of the Compositæ, of which Linnæus knew only 785 species, and which have now increased to 12,000, appear to belong to the Old Continent. At least Decandolle described only 3590 American, while he estimated the European, Asiatic, and African species at 5093. This abundance of Compositæ in our vegetable systems is however deceptive, and only apparently considerable; for the quotient of this family (which within the tropical zone is ¹⁄₁₅, in the temperate zone ⅐, and in the frigid zone ¹⁄₁₃) shows that more species of Compositæ than of Leguminosæ have hitherto eluded the diligent research of travellers; for even when multiplied by 12 we only obtain the improbably small number of 144,000 for the sum total of the Phanerogamia! The families of the Grasses and of the Cyperaceæ give still lower results, because a proportionally smaller number of species have been described and collected. We need only cast a glance at the map of South America, and remember that the vast extent of country occupied by the grassy plains of Venezuela the Apure and the Meta, as well as to the south of the woody region of the Amazon, in Chaco, in Eastern Tucuman, and in the Pampas of Buenos Ayres and Patagonia, has either been very imperfectly or not at all explored in relation to botany. Northern and Central Asia present an almost equally extensive territory occupied by steppes; but here a larger proportion of dicotyledonous plants is intermixed with the Gramineæ. If we had sufficient grounds for believing that one-half of all the phanerogamic plants existing on the surface of the earth are known, and if we estimate this number at only 160,000 or at 213,000 known species; we must give to the family of grasses, whose general ratio appears to be ¹⁄₁₂, in the former case at least 26,000, and in the latter 35,000 different species, of which in the first case ⅛, and in the second ⅒ are known.

The following considerations oppose the hypothesis that we are already acquainted with half the Phanerogamia on the earth’s surface. Several thousand species of Monocotyledons and Dicotyledons, and among them lofty arborescent forms, have recently been discovered (I would remind the reader of my own expedition) in districts of a very large extent, which had already been explored by distinguished botanists. Yet that portion of the great continents which has never been visited by botanical observers far exceeds the extent of the parts even superficially traversed. The greatest variety of phanerogamic vegetation, i. e. the greatest number of species on an equal area, is to be met with in the tropical or subtropical zones. It is therefore the more important to bear in mind that we are almost wholly unacquainted, north of the equator, in the New Continent, with the floras of Oaxaca, Yucatan, Guatimala, Nicaragua, the Isthmus of Panama, the Choco, Antioquia, and the Province de los Pastos; while south of the equator, we are equally ignorant of the floras of the boundless forest-region between the Ucayale, the Rio de la Madura, and the Toncantin (three mighty tributaries of the Amazon), as well as of those of Paraguay and the Province de las Missiones. In Africa, we know nothing of the vegetation of the whole of the interior, between 15° north and 20° south lat.; and in Asia we are unacquainted with the floras of the south and south-east of Arabia, where the highlands rise to an elevation of 6400 feet; as also with the floras between the Thian-schan, the Kuen-Lün, and the Himalaya; those of Western China; and those of the great portion of the countries beyond the Ganges. Still more unknown to botanists are the interior portions of Borneo and New Guinea, and of some districts of Australia. Further to the south the number of the species decreases in a most remarkable manner, as Joseph Hooker has ably shown, from his own observation, in his Antarctic Flora. The three islands which constitute New Zealand extend from 34½° to 47¼° of latitude, and as they have besides snow-crowned mountains more than 8850 feet in height, they must exhibit considerable differences of climate. The most northern island has been explored with tolerable accuracy from the time of Banks and Solander’s voyage (with Capt. Cook), to the visits of Lesson, the brothers Cunningham, and Colenso; and yet in more than seventy years, the number of Phanerogamia with which we have become acquainted is below 700.[[NQ]] This paucity of vegetable species corresponds with the paucity of animal forms. Dr. Joseph Hooker has observed that “Iceland, proverbially barren as it is, and upon which no tree, save a few stunted birches, is to be found, possesses five times as many flowering plants as Lord Auckland’s group and Campbell’s Islands together, although these are situated at from 8° to 10° nearer the equator in the southern hemisphere. The antarctic flora is at once characterised by uniformity and great luxuriance of vegetation, which is attributable to the influence exerted by an uninterruptedly cool and humid climate. In Southern Chili, Patagonia, and Tierra del Fuego (from 45° to 56° lat.) this uniformity is strikingly manifested on the mountains and their declivities no less than in the plains. How great is the difference of species when we compare the flora of the south of France, in the same latitude as the Chonos Islands off the coast of Chili, with the Scottish flora of Argyleshire, in the parallel of Cape Horn. In the southern hemisphere the same types of vegetation pass through many degrees of latitude. In the regions near the north pole ten flowering plants have been collected on Walden Island (80½° north lat.), while there is scarcely a solitary grass to be met with in the South Shetland Islands, although situated 63° south latitude.”[[NR]] These considerations on the distribution of plants prove that the great mass of the still unobserved, uncollected, and undescribed phanerogamia belong to the tropical zone, and to the contiguous regions extending from twelve to fifteen degrees from it.

I have deemed it not unimportant to draw attention to the imperfect state of our knowledge in this slightly cultivated department of numerical botany, and to treat such questions in a more definite manner than has hitherto been possible. In all conjectures regarding relative numbers, we must first examine the practicability of obtaining the lowest limit; as in the question, of which I have treated elsewhere, regarding the ratio of the gold and silver coined to the quantity of the precious metals existing in a wrought state; or as in the question of how many stars, from the tenth to the twelfth magnitude, are scattered over the heavens, and how many of the smallest telescopic stars may be contained in the Milky Way?[[NS]] It is an established fact, that if it were possible to ascertain completely by observation the number of species of the large phanerogamic families, we should at the same time obtain an approximate knowledge of the sum-total of all the phanerogamia on the surface of the earth (that is, the numbers included in every family). The more therefore we are enabled, by the progressive exploration of unknown districts, gradually to determine the number of species belonging to any one great family, the higher will be the gradual rise of the lowest limit, and the nearer we shall arrive at the solution of a great numerical vital problem, since the forms, in accordance with still unexplained laws of universal organism, reciprocally limit each other. But is the number of the organisms a constant number? Do not new vegetable forms spring from the ground after long intervals of time, whilst others become more and more rare, and finally disappear? Geology confirms the latter part of this question by means of the historical memorials of ancient terrestrial life. “In the primitive world,” to use the expression of the intellectual Link,[[NT]] “elements remote from each other blend together in wondrous forms, indicating, as it were, a higher degree of development and articulation in a future period of the world.”

[84]. p. 222—“Whether the height of the aërial ocean and its pressure have always been the same.”

The pressure of the atmosphere has a decided influence on the form and life of plants. This life, owing to the fulness and abundance of the leafy organs provided with interstitial openings, is principally directed outwards. Plants mainly live in and through their surfaces, and hence their dependence on the surrounding medium. Animals are more dependant on internal stimuli; they generate and maintain their own temperature, deriving from muscular movements their electric currents, and the chemical vital processes which arise from and re-act upon those currents. A kind of cutaneous respiration constitutes an active vital function of plants, and depends, so far as it is an evaporation, inhalation, and exhalation of fluids, on atmospheric pressure. Hence Alpine plants are more aromatic and hirsute than others, and more amply provided with numerous exhalants.[[NU]] Zoonomic experiments teach us, as I have shown in another work, that organs are more abundant and more perfectly developed in proportion to the facility with which their functional requirements are fulfilled. The disturbance occasioned in the respiration of their external integuments, by increased barometric pressure, renders it, as I have elsewhere shewn, very difficult for Alpine plants to thrive in the plain.

Whether the aërial ocean surrounding the earth has always exerted the same mean pressure is a question wholly undecided. We do not even know for certain whether the mean barometric height has remained the same during a hundred years at any one given spot. According to the observations of Poleni and Toaldo, this pressure appeared variable. Doubts were long entertained regarding the accuracy of these views, but the more recent investigations of the astronomer Carlini render it almost probable that in Milan the mean barometric pressure is on the decrease. Perhaps the phenomenon is very local, and dependent on periodic variations in descending currents of air.

[85]. p. 223—“Palms.”

It is remarkable, that of this majestic form of plants—the Palms—some of which rise to more than twice the height of the Royal Palace at Berlin, and which the Indian, Amarasinha, has very characteristically called “kings among grasses,”—only fifteen species had been described up to the time of the death of Linnæus. The Peruvian travellers, Ruiz and Pavon, added only eight; whilst Bonpland and myself, traversing a greater extent of country, from 12° south lat. to 21° north lat., described twenty new species, and distinguished as many more which we named, without however being able to procure their blossoms in a perfect state.[[NV]] At present (forty-four years after my return from Mexico) more than 440 species of palms, from both continents, have already been scientifically described, including the East Indian species arranged by Griffith. The “Enumeratio Plantarum” of my friend Kunth, which appeared in 1841, contains no fewer than 356 species.