The Project Gutenberg eBook of Views of Nature, by Alexander Von Humboldt

83. p. 220—“Phanerogamic plants already recorded in herbariums.”

Three questions must be carefully distinguished from one another: 1. How many species of plants have been described in printed works? 2. How many of those discovered—that is to say included in herbariums—still remain undescribed? 3. How many species probably exist on the surface of the earth? Murray’s edition of the Linnæan system contains, including cryptogamic plants, only 10,042 species. Willdenow, in his edition of the Species Plantarum from 1797 to 1807, has described as many as 17,457 species of phanerogamia, reckoning from Monandria to Polygamia diœcia. If to these we add 3000 species of cryptogamic plants, we shall bring the number as given by Willdenow to 20,000. More recent investigations have shown how far this estimate of the species described, and of those preserved in herbariums, falls short of the truth. Robert Brown ^[NB] first enumerated above 37,000 phanerogamia, and I at that time attempted to describe the distribution of 44,000 species of phanerogamic and cryptogamic plants, over the different portions of the world already explored.^[NC] Decandolle finds, on comparing Persoon’s Enchiridium with his Universal System divided into twelve families, that more than 56,000 species of plants may be enumerated from the writings of botanists and European herbariums.^[ND] If we consider how many new species have been described by travellers since that time, (my expedition alone afforded 3600 of the 5800 collected species of equinoctial plants), and if we bear in mind that there are assuredly upwards of 25,000 phanerogamic plants, cultivated in all the different botanical gardens, we shall soon see how much Decandolle’s estimate is below the truth. 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. I was the first who passed from these principal divisions to the individual families, and considered the number of the species contained in each, in their ratio to the whole mass of phanerogamia belonging to one zone.^[NG]

The numerical relations of the forms of plants, and the laws observed in their geographical distribution, admit of being considered from two very different points of view. When we study plants in their arrangement according to natural families, without regard to their geographical distribution, the question arises: What are the fundamental forms or types of organization, in accordance with which the greater number of their species are formed? Are there more Glumaceæ than Compositæ on the earth’s surface? Do these two orders of plants combined, constitute one-fourth of the phanerogamia? What numerical relation do monocotyledons bear to dicotyledons? These are questions of general phytology, a science that investigates the organization of plants and their mutual connection, and therefore has reference to the now existing state of vegetation.

If, on the other hand, the species of plants that have been connected together according to their structural analogy, are considered not abstractedly, but in accordance with their climatic relations, and their distribution over the earth’s surface, these questions acquire a totally different interest. We then examine what families of plants predominate in the torrid zone more than towards the polar circle over other phanerogamia? We inquire, whether the Compositæ are more numerous in the new than in the old world, under equal geographical latitudes or between equal isothermal lines? Whether the forms which gradually lose their predominance in advancing from the equator to the poles, follow a similar law of decrease in ascending mountains situated in the equatorial region? Whether the relations of the different families to the whole mass of the phanerogamia differ under equal isothermal lines in the temperate zones on either side of the equator? These questions belong to the geography of plants properly so called, and are connected with the most important problems that can be presented by meteorology and terrestrial physics. Thus the predominance of certain families of plants determines the character of a landscape, and whether the aspect of the country is desolate or luxuriant, or smiling and majestic. Grasses, forming extended Savannahs, or the abundance of fruit-yielding palms, or social coniferous trees, have respectively exerted a powerful influence on the material condition, manners, and character of nations, and on the more or less rapid development of their prosperity.

In studying the geographical distribution of forms, we may consider the species, genera, and natural families of plants separately. A single species, especially among social plants, frequently covers an extensive tract of land. Thus we have in the north, Pine or Fir forests, and Heaths (ericeta); in Spain, Cistus groves; and in tropical America, collections of one and the same species of Cactus, Croton, Brathys, or Bambusa Guadua. It is interesting to study more closely these relations of individual increase, and of organic development; and here we may inquire, what species produces the greatest number of individuals in one certain zone; or, merely what are the families to which the predominating species belong in different climates. In a very high northern latitude, where the Compositæ and the Ferns stand in the ratios of 1 : 13 and 1 : 25 to the sum of all the phanerogamia (i. e., where these ratios are found by dividing the sum total of all phanerogamia by the number of species included in the family of the Compositæ, or in that of the Ferns); one single species of Fern may, however, cover ten times more space than all the species of the Compositæ taken together. In this case the Ferns predominate over the Compositæ by their mass, and by the number of the individuals belonging to the same species of Pteris, or Polypodium; but they will not be found to predominate, if we only compare the number of the different specific forms of the Filices, and of the Compositæ, with the sum total of all Phanerogamia. As, therefore, multiplication of plants does not follow the same laws in all species, and as all do not produce an equal number of individuals, the quotients obtained by dividing the sum of all phanerogamic plants by the species of one family, do not alone determine the leading features impressed on the landscape, or the physiognomy of nature peculiar to different regions of the earth. If the attention of the travelling botanist be arrested by the frequent repetition of the same species, by its mass, and the uniformity of vegetation thus produced, it will be still more forcibly arrested by the infrequency of many other species useful to man. In tropical regions, where the Rubiaceæ, Myrtles, Leguminosæ, or Terebinthaceæ, compose the forests, one is astonished to meet with so few trees of Cinchona, or of certain species of mahogany (Swietenia), of Hæmatoxylon, Styrax, or balsamic Myroxylon. I would also here refer to the scanty and detached occurrence of the precious febrifuge-bark trees (species of Cinchona) which I had an opportunity of observing on the declivity of the elevated plains of Bogota and Popayan, and in the neighbourhood of Loxa, in descending towards the unhealthy valley of the Catamayo, and to the river Amazon. The febrifuge-bark hunters (Cazadores de Cascarilla), as those Indians and Mestizoes are called at Loxa, who each year collect the most efficacious of all the medicinal barks, the Cinchona Condaminea, among the lonely mountains of Caxanuma, Uritusinga, and Rumisitana, undergo considerable danger in climbing to the summits of the highest forest-trees, in order to obtain an extended view, from which they may distinguish the scattered, slender, and aspiring trunks of the Cinchona, by the reddish tint of their large leaves. The mean temperature of this important forest region (between 4° and 4½° south lat.) varies from 60° to 68° Fahr., at an absolute height of from 6400 to 8000 feet above the level of the sea.^[NH]

In considering the distribution of species, we may also, independently of individual multiplication and mass, compare together the absolute number which belong to each family. Such a mode of comparison, which was employed by Decandolle,^[NI] has been extended by Kunth to more than 3300 of the species of Compositæ with which we are at present acquainted. It does not show what family preponderates by individual mass, or by the number of its species, over other phanerogamic forms, but it simply indicates how many of the species of one and the same family are indigenous in any one country or portion of the earth. The results of this method are, on the whole, more exact, because they are obtained by a careful study of the separate families, without requiring that the whole number of the phanerogamia of every country should be known. Thus, for instance, the most varied forms of Ferns are found in the tropical zone, each genus presenting the greatest number of species in the temperate, humid, and shaded mountainous parts of islands. While these species are less numerous in passing from tropical regions to the temperate zone, their absolute number diminishes still more in approaching nearer to the poles. Although the frigid zone, as, for instance, Lapland, supports species of the families which are best able to resist the cold, Ferns predominate more over other phanerogamia in Lapland than either in France or Germany, notwithstanding the absolute inferiority of the gross number of ferns indigenous to the northern zone, when compared with other countries. These relations are, in France and Germany, as ¹⁄₇₃ and ¹⁄₇₁, while in Lapland they are as ¹⁄₂₅. These numerical relations (obtained by dividing the sum total of all the phanerogamia of the different floras by the species of each family) were published by me in 1817, in my Prolegomena de distributione geographica Plantarum, and corrected in accordance with the great works of Robert Brown, in my Essay on the Distribution of Plants over the earth’s surface, which I subsequently wrote in French. These relations, as we advance from the equator towards the poles, necessarily vary from the ratios obtained by a comparison of the absolute number of the different species belonging to each family. We often see the value of the fractions increase by the decrease of the denominator, whilst the absolute number of the species is reduced. In the fractional method which I have followed as the most applicable to questions relating to the geography of plants, there are two variable quantities; for in passing from one isothermal line to another, we do not find the sum total of the phanerogamia change in the same proportion as the number of the species of one particular family.

In proceeding from the consideration of these species to that of the divisions established in the natural system according to an ideal series of abstractions, we may direct our attention to genera or races, to families, or even to still higher classes of division. There are some genera, and even whole families, which exclusively belong to certain zones; not merely because they can only thrive under a special combination of climatic relations, but also because they first sprang up within very circumscribed localities, and have been checked in their migrations. The larger number of genera and families have, however, their representatives in all regions of the earth, and at all elevations. The earliest inquiries into the distribution of vegetable forms had reference to genera alone, and are to be found in the valuable work of Treviranus.^[NJ] This method is, however, less appropriate for yielding general results, than that which compares the number of the species of each family, or the great leading divisions (acotyledons, monocotyledons, and dicotyledons), with the sum total of the phanerogamia. In the frigid zone, the variety of forms, or the number of the genera, does not decrease in an equal degree with that of the species, there being in these regions relatively more genera and fewer species.^[NK] The case is almost the same on the summits of high mountain-chains, where are sheltered individual members of many different genera which one would be disposed to regard as belonging exclusively to the vegetation of the plain.

I have deemed it expedient to indicate the different points of view from which the laws of the distribution of vegetable forms may be considered. It is only when these points of view are confounded together, that we meet with contradictions, which have been unjustly attributed to uncertainty of observation.^[NL] When expressions like the following are employed: “This form, or this family diminishes as it approaches towards the cold zone,” or “the true habitat of this form is in such or such a parallel of latitude;” or “this is a southern form,” or, again, “it predominates in the temperate zone;” it should be definitely stated whether reference is made to the absolute number of the species, and the proportion of their predominance according to the increase or decrease of latitude; or whether the meaning conveyed is, that a family, when compared with the whole number of the phanerogamia of a flora, predominates over other families of plants. The impression conveyed to the mind of the predominance of forms, depends literally on the conception of relative quantity.

Terrestrial physics have their numerical elements as well as the cosmical system, and it is only by the united labours of botanical travellers that we can hope gradually to arrive at a knowledge of the laws which determine the geographical and climatic distribution of vegetable forms. I have already observed that in the temperate zone of the northern hemisphere, the Compositæ (Synanthereæ) and the Glumaceæ (in which latter division I place the three families of the Gramineæ, the Cyperoideæ, and the Juncaceæ) constitute the fourth part of all phanerogamia. The following numerical relations are the result of my investigations for seven great families of the vegetable kingdom in one and the same temperate zone:

Glumaceæ	⅛	(Grasses alone ¹⁄₁₂)
Compositæ	⅛
Leguminosæ	¹⁄₁₈
Labiatæ	¹⁄₂₄
Umbelliferæ	¹⁄₄₀
Amentaceæ (Cupuliferæ, Betulineæ, and Salicineæ)	¹⁄₄₅
Cruciferæ	¹⁄₁₉

The forms of organic beings are reciprocally dependent on one another. Such is the unity of nature, that these forms limit each other in obedience to laws which are probably connected with long periods of time. When we have ascertained the number of the species on any particular part of the earth’s surface belonging to one of the great families of the Glumaceæ, the Leguminosæ, or the Compositæ, we may with some degree of probability, form approximative conclusions regarding the number of all the phanerogamia, as well as of the species belonging to the other families of plants growing in the country. The number of the Cyperoideæ determines that of the Compositæ, and the number of the latter determines that of the Leguminosæ; and these estimates, moreover, enable us to ascertain in what classes and orders the Floras of a country are still incomplete, teaching us what harvests may still be reaped in the respective families, if we guard against confounding together very different systems of vegetation.

The comparison of the numerical proportions of families in the different zones which have as yet been well explored, has led me to a knowledge of the laws which determine the numerical increase or decrease of vegetable forms constituting a natural family, in proceeding from the equator to the poles, when compared, for instance, with the whole mass of phanerogamia peculiar to each zone. We must here have regard not only to the direction, but also to the rapidity or measure of the increase. We see the denominator of the fraction, which expresses the ratio, increase or diminish. Thus, for instance, the beautiful family of the Leguminosæ diminishes in proportion as it recedes from the equinoctial zone to the north pole. If we find its ratio for the torrid zone (from 0° to 10° of latitude) ⅒, we shall have for the part of the temperate zone (lying between 45° and 52°) ¹⁄₁₈, and for the frigid zone (between 67° and 70° lat.) only ¹⁄₃₅. The direction followed by the great family of the Leguminosæ (viz., increase towards the equator) is also that of the Rubiaceæ, the Euphorbiaceæ, and especially the Malvaceæ. On the other hand, the Gramineæ and the Juncaceæ (the latter more than the former), the Ericeæ, and Amentaceæ, diminish towards the torrid zone. The Compositæ, Labiatæ, Umbelliferæ, and Cruciferæ, diminish from the temperate zone towards the pole and the equator, and the two latter families most rapidly in the direction of the equatorial region; whilst in the temperate zone the Cruciferæ are three times more abundant in Europe than in the United States of North America. In Greenland the Labiatæ are reduced to only one species, and the Umbelliferæ to two, while the whole number of the phanerogamia still amounts, according to Hornemann, to 315 species.

It must at the same time be observed that the development of plants of different families, and the distribution of their forms, do not depend alone on the geographical, or even on the isothermal latitude; the quotients not being always equal on one and the same isothermal line in the temperate zone, as for instance in the plains of America and in those of the Old Continent. Within the tropics there is a very marked difference between America, the East Indies, and the western coast of Africa. The distribution of organic beings over the surface of the earth does not depend solely on the great complication of thermic and climatic relations, but also on geological causes which continue almost wholly unknown to us, since they have been produced by the original condition of the earth, and by catastrophes which have not affected all parts of our planet simultaneously. The large pachydermata are no longer found in the New Continent, while they still exist under analogous climates in Asia and Africa. These differences, instead of deterring us from the investigation of the laws of nature, should rather stimulate us to study them in all their intricate modifications.

The numerical laws of families, the frequently striking agreement between the ratios, where the species constituting these families are for the most part different, lead us into that mysterious obscurity which envelopes everything connected with the fixing of organic types in the different species of animals and plants, and with all that refers to formation and development. I will take as examples two neighbouring countries—France and Germany—which have both been long since explored. In France many species of Gramineæ, Umbelliferæ, Cruciferæ, Compositæ, Leguminosæ, and Labiatæ are wanting, which are some of the commonest in Germany, and yet the ratios of these six large families are almost identical in both countries. Their relations, which I here give, are as follows:

Families.	Germany.	France.
Gramineæ.	¹⁄₁₃	¹⁄₁₃
Umbelliferæ.	¹⁄₂₂	¹⁄₂₁
Cruciferæ.	¹⁄₁₈	¹⁄₁₉
Compositæ.	⅛	⅐
Leguminosæ.	¹⁄₁₈	¹⁄₁₆
Labiatæ.	¹⁄₂₆	¹⁄₂₄

This correspondence in the number of species of one family compared to the whole mass of the phanerogamia of Germany and France would not exist, if the absent German species were not replaced in France by other types of the same families. Those who delight in conjectures respecting the gradual transformation of species, and who regard the different parrots, peculiar to islands situated near each other, as merely transformed species, will ascribe the remarkable uniformity presented by the above numerical ratios to a migration of the same species, which having been altered by climatic influences, continuing for thousands of years, appear to replace each other. But why have our common Heath, (Calluna vulgaris,) and our Oaks not penetrated to the east of the Ural Mountains, and passed from Europe to northern Asia? Why is there no species of the genus Rosa in the southern, and scarcely any Calceolaria in the northern hemisphere? These are points that cannot be explained by peculiarities of temperature. The present distribution of forms (fixed forms of organization) is no more explained by thermal relations alone, than by the hypothesis of migrations of plants radiating from certain central points. Thermal relations are scarcely sufficient to explain the phenomenon why certain species have fixed limits beyond which they cannot pass, either in the plains towards the pole, or in vertical elevation on the declivities of mountains. The cycle of vegetation of each species, however different may be its duration, requires a certain minimum of temperature to enable it to arrive at the full stage of its development.^[NM] But all the conditions necessary to the existence of a plant, either within its natural sphere of distribution or cultivation—such as geographical distance from the pole, and elevation of the locality—are rendered still more complicated by the difficulty of determining the beginning of the thermic cycle of vegetation; by the influence which the unequal distribution of the same quantity of heat among days and nights succeeding each other in groups, exerts on the irritability, the progressive development, and the whole vital process; and lastly, by the secondary influence of the hygrometric and electric relations of the atmosphere.

My investigations regarding the numerical laws of the distribution of vegetable forms may, perhaps, at some future time, be applied successfully to the different classes of vertebrate animals. The rich collections of the Muséum d’histoire naturelle in the Jardin des Plantes at Paris, contained in 1820, at a rough estimate, above 56,000 species of phanerogamic and cryptogamic plants in the herbariums, 44,000 insects (probably below the actual number, although they were thus given me by Latreille), 2500 species of fishes, 700 reptiles, 4000 birds, and 500 mammalia. Europe possesses about 80 mammalia, 400 birds, and 30 reptiles; there are, therefore, five times as many birds as mammalia in the northern temperate zone, (as there are in Europe five times as many Compositæ as Amentaceæ and Coniferæ, and five times as many Leguminosæ as Orchideæ and Euphorbiaceæ). In the southern temperate zone the ratio of the Mammalia bears a sufficiently striking accord with that of Birds, being as 1 : 4·3. Birds (and reptiles even to a greater extent), increase more than mammalia in advancing towards the torrid zone. We might be disposed to believe, from Cuvier’s investigations, that this ratio was different in the earlier age of our planet, and that the number of mammalia that perished by convulsions of nature was much greater than that of birds. Latreille has shown the different groups of insects that increase in advancing towards the pole, or towards the equator, and Illiger has indicated the native places of 3800 birds, according to the quarters of the globe;—a far less instructive method than if they had been given according to zones. We may easily comprehend how, on a given area, the individuals of one class of plants or animals may limit each other’s numbers, and how, after the long-continued contests and fluctuations engendered by the requirements of nourishment and mode of life, a condition of equilibrium may have been at length established; but the causes which have determined their typical varieties, and have circumscribed the sphere of the distribution of the forms themselves, no less than the number of individuals of each form, are shrouded in that impenetrable obscurity which still conceals from our view all that relates to the beginning of things and the first appearance of organic life.

If, therefore, as I have already observed at the beginning of this illustration, we attempt to give an approximative estimate of the numerical limit (“le nombre limite” of the French mathematicians), below which we cannot place the sum of all the phanerogamia on the surface of the earth; we shall find that the surest method will be by comparing the known ratios of the families of plants with the number of the species contained in our herbariums, or cultivated in large botanical gardens. As I have just remarked, the herbariums of the Jardin des Plantes at Paris were, in 1820, already estimated at 56,000 species. I will not hazard a conjecture as to the number that may be contained in the herbariums of England, but the great Paris herbarium, which Benjamin Delessert with the noblest disinterestedness has given up to free and general use, was estimated, at the time of his death, to contain 86,000 species, a number almost equal to that which Lindley, even in 1835,^[NN] regarded as the probable number of all the species existing “on the whole earth.” Few herbariums are numbered with care, according to a complete, severe, and methodical separation of the different varieties; while, moreover, we often find no inconsiderable number of plants wanting in the large so-called general herbariums, which are contained in some of the smaller ones. Dr. Klotzsch estimates the whole number of Phanerogamic plants in the Great Royal Herbarium at Schöneberg, near Berlin, of which he is curator, at 74,000 species.

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.”