New Inquiries into the Laws which are observed in the Distribution of Vegetable Forms. By Baron Alexander Humboldt . A separate copy of this memoir was sent to us by the author for insertion in our Journal, through Dr Marcet. The numerical proportions of vegetable forms may be viewed in two perfectly distinct lights. If we consider plants, grouped together in natural families, without having regard to their geographical distribution, we enquire what are the types of organization, according to which the greatest number of species are formed. Are there more Glumaceae than Compositae on the globe? Do these two tribes of vegetables constitute together the fourth part of Phaenogamous plants? What is the proportion of Monocotyledones to the Dicotyledones? These are questions of general Phytology--of the sciences which examine the organization and mutual connection of vegetables. If we view the species which we associate according to the analogy of their form, not in an abstract manner, but with regard to their climacteric relations, or their distribution over the surface of the globe, the questions which arise afford an interest highly varied. What are the families of plants which predominate over the other phaenogamous vegetables more within the torrid zone than under the polar circle? Are the Compositae more numerous, either in the same geographical latitude, or on the same isothermal band, in the new Continent than in the old? Do the types which predominate less in advancing from the equator to the pole, follow the same law of decrease, in proportion as they rise toward the summit of the equatorial mountains? Do not the mutual proportions of families vary, on isothermal lines of the same denomination, in the temperate zones, to the north and to the south of the equator? These questions belong to the geography of plants, properly so called: they are connected with the most important problems belonging to meteorology and the natural history of the globe in general. Upon the preponderance of certain families of plants, depends also the character of the landscape, the aspect of a country, whether of a beautiful or majestic nature. The abundance of the Gramineae, which form vast savannahs, and that of the Palms or the Coniferae, are much influenced by the social state of the people, by their manners, and by the more or less perfect development of the economical arts. In considering the geographical distribution of forms, we may attend to species, to genera, and to natural families, (Humboldt, Proleg. in Nov. Gen. vol. i. pp. xiii. li. & 33.). Often a single species of plants, especially among those which I have named social plants, covers a vast extent of country. Of this kind, in the north, are the heaths and forests of pines; in equinoctial America, the associations of Cactus, Croton, Bambusa, and Brathys of the same species. It is curious to examine the proportions of organic multiplication and development. We may demand what species in a given zone produces the greatest number of individuals;--we may point out the families to which in different climates belong the species which predominates over the others. Our imagination is peculiarly struck with the preponderance of certain plants, which we consider, on account of their easy reproduction, and the great number of individuals which present the same specific characters, as the more common plants of this or that zone. In a northern region, where the Compositae and the Ferns are to the phaenogamous plants in the proportion of 1:13, and of 1:25, (that is to say, where we find these proportions on dividing the total number of the phaenogamous plants by the number of the species of the Compositae and Ferns,) a single species of Fern may occupy ten times as much space as the whole species of Compositae together. In this case, the Ferns predominate over the Compositae by the mass,--by the number of individuals belonging to the same species of Pteris or of Polypodium; but they do not predominate, if we compare with the total sum of the species of phaenogamous plants the different forms which compose the two groups of Ferns and Compositae. As the multiplication of all the species does not follow the same laws, since they do not all produce the same number of individuals, the quotient obtained in dividing the total number of phaenogamous plants by the number of species of different families, does not of itself decide the aspect, I might almost say kind of monotony of nature in the different regions of the globe. If the traveller is struck with the frequent repetition of the same species,--with the sight of those which predominate by their mass,--he is not less so with the paucity of individuals of some other species useful to man. In the countries where the Rubiaceae, the Leguminosae, or the Terebinthaceae, compose the forests, we are surprised to see how rare are the trees of certain species of Cinchona, Haematoxylon, and the Balsamiferae. In turning our attention to species, we may also, without having regard to their multiplication, and to the greater or smaller number of individuals, compare in each zone, in an absolute manner, the species which belong to different families. This interesting comparison has been made in the great work of M. Decandolle, (Regni Vegetabilis Systema Naturae, vol. i. p. 128. 396. 439. 464. 510.). M. Kunth has attempted it with more than 3300 Compositae already known up to the present day, (Nova Genera, vol. iv. p. 238). It does not point out what family predominates in the same degree above the other indigenous phaenogamous plants, either by the mass of individuals, or by the number of species; but it presents the numerical proportions between the species of the same family belonging to a different country. The results of this method are generally more precise, because they are obtained without valuing the total mass of phaenogamous plants, after being freed with care from the study of each isolated family. The forms which are the most varied, the Ferns, for example, are found under the tropics: it is in the mountainous, temperate, humid and shady parts of the equatorial regions, that the family of Ferns produces the greatest number of species. In the temperate zone, there are not so many as under the tropics: their absolute number still diminishes as we advance toward the pole, but since the cold region, for example Lapland, produces species of Ferns which resist the cold better than the great mass of phaenogamous plants, the Ferns, by the number of species, predominate more over the other plants in Lapland than in France or Germany. The numerical proportions presented in the table which I have published in my Prolegomena de Distributione Geographica Plantarum, and which appears again here perfected by the great labours of Mr Robert Brown, differ entirely from the proportions given by an absolute comparison of the species which grow in the different zones. The variation which we observe in proceeding from the equator to the poles is not consequently the same in the result of the two methods. In this, two of the fractions used by Mr Brown and myself are variable, since, in changing the latitude , or rather the isothermal zone, the total number of phaenogamous plants is not seen to vary in the same proportion as the number of species which constitute the same family. When from species or individuals of the same form which are reproduced according to constant laws, we pass to divisions of the natural method, we may turn our attention to genera, to families, or to sections still more general. There are some genera and some families which belong exclusively to certain zones, to a particular association of climacteric conditions; but there is a great number of genera and of families which have representatives in all zones, and at all heights. The first researches which have been made regarding the geographical distribution of forms, those of M. Treviranus, published in his ingenious work on Biology, (vol. ii. p. 47. 63. 83. 129.), have for their object the dispersion of genera over the globe. That method is less proper for presenting general results than this, which compares the number of species of each family, or the large groups of the same family, with the total mass of phaenogamous plants. In the frigid zone, the variety of generie forms does not diminish in the same degree as the variety of species: we find more genera, with a smaller number of species, (Decandolle, Theorie Element. p. 190.; Humboldt, Nova Gen. vol. i. p. xvii. & l.). It is nearly the same on the summit of the lofty mountains, which receive colonists of a great number of genera, which we suppose to belong exclusively to the vegetation of the plains. I have deemed it necessary to show the different points of view from which the laws of the distribution of vegetables may be seen. It is in confounding them that we think the contradictions are to be found, which are not otherwise than apparent, and which are erroneously attributed to the uncertainty of observations. (Berliner Jahrbücher der Gewächskunde, Bd. i. p. 18. 21. 30.) When the following expressions are used: "this form or this family loses itself toward the frigid zone; it has its true native country in such and such a parallel; it is a southern form;" "it abounds in the temperate zone; we must expressly mention, if we consider the absolute number of species, the increase or decrease of their absolute frequency with the latitudes, or if we speak of families which predominate in the same degree over the rest of the phaenogamous plants. These expressions are correct: they afford a precise signification, if we distinguish the different methods according to which we consider the variety of forms. The Island of Cuba (to use an analogous case taken from political economy) contains a much greater number of individuals of the African than of the Martinique race; and yet the mass of these individuals predominates much more over the number of whites in this latter island than in that of Cuba. The rapid progress which the geography of plants has made within these twelve years, by the united labours of Messrs Brown, Wahlenberg, Decandolle, Leopold de Buch, Parrot, Ramond, Schouw and Hornemann, are owing in a great measure to the advantages of the natural method of M. de Jussieu. In following, I shall not say the artificial classifications of the sexual system, but the families founded upon vague and erroneous principles, ( Dumosae , Corydales, Oleraceae,) we no longer perceive the great physical laws in the distribution of vegetables on the globe. It was Mr Robert Brown, who, in a celebrated memoir on the vegetation of New Holland, first made known the true proportions between the great divisions of the vegetable kingdom, the Acotyledonous, Monocotyledonous, and Dicotyledonous plants. (Brown, in Flinders' Voyage to Terra Australis, vol. ii. p. 538; and Observations systematic and geographical on the Herbaries of the Congo, p. 3.) I made an attempt, in 1815, to pursue this kind of research, in extending it to the different orders or natural families. The natural history of the globe is, in its numerical elements, like the system of the world, and can be brought to perfection only by the joint efforts of botanical travellers, to discover the true laws of the distribution of vegetables. The collection of facts is not of itself sufficient: in order to obtain the most accurate approximations, (and we do not pretend to give any thing but approximations,) the different circumstances under which the observations have been made must be discussed. I think with Mr Brown, that we ought to prefer in general to calculations made upon incomplete lists of all the plants published, the examples taken from countries of considerable extent, and whose Flora is well known, such as France, England, Germany, and Lapland. It would be desirable to have still a complete Flora of two countries of 20,000 square leagues, destitute of lofty mountains and of platforms, and situated between the tropics in the Old and in the New Worlds. Until this shall be accomplished, we must be contented with the great herbaries formed by travellers, who have resided for some time in the two hemispheres. The habitations of plants are so vaguely and incorrectly pointed out, in the vast compilations known under the names of Systema Vegetabilium, and Species Plantarum, that it would be very dangerous to use them in an absolute manner. I have not employed these lists otherwise than in a subsidiary manner, to control and modify a little the results obtained by the Floras and the partial herbaries. The number of equinoctial plants which M. Bonpland and I have brought to Europe, and of which our learned colleague M. Kunth will have soon finished the publication, is perhaps numerically greater than any of the herbaries formed between the tropics; but it is composed of the vegetables of the plains and elevated platforms of the Andes. The alpine plants are even much more considerable than in the Floras of France, of England, and of the Indies, which associate also the productions of different climates belonging to the same latitude. In France, the number of species which vegetate exclusively at above 500 toises of height, does not appear to be more than [Formel] th of the entire mass of phaenogamous plants. (Decandolle, in the Mem. de Arcueil, vol. iii. p. 295.). It will be useful to consider at a future period the vegetation of the tropics and that of the temperate region between the parallels of 40° and 50°, according to two different methods, either in searching the numerical proportions in the whole of the plains and the mountains, which nature presents over a great extent of country, or in determining these proportions in the plains alone of the temperate zone and of the torrid zone. As our herbaries are the only ones that point out, according to barometrical measurement, in more than 4000 plants of the equinoctial region, the height of each station above the level of the sea, the numerical proportions of the table which I have already published may be rectified, when our work, the Nova Genera, shall be finished, by taking away from the 4000 phaenogamous plants which M. Kunth has employed in this work (Prolegom. p. 16.), the plants which grow at above 1000 toises, and by dividing the total number of plants which are not alpine, of each family, by that of plants which live in the cold and temperate regions of equinoctial America. This mode of proceeding should affect more, as we shall show by and bye, the families which abound in alpine species, for example, the Gramineae and the Compositae. At 1000 toises of elevation, the mean temperature of the air is still, on the back of the equatorial Andes, 17° centigr., which is equal to that of the month of July at Paris. Although on the platform of the Cordilleras, we find the same annual temperature as in the high latitudes, (because the isothermal line of 8°, for example, is the track marked in the plains by the intersection of the isothermal surface of 8°, with the surface of the earth's spheroid,) it is not too much to generalise these analogies of the temperate climates of the equatorial mountains, with the low regions of the circumpolar zone. These analogies are not so great as might be thought; they are modified by the influence of the partial distribution of the heat in the different parts of the year. (Proleg. p. 54., and my Memoire sur les Lignes Isothermes , p. 137.) The quotients do not change, however, in ascending from the plains toward the mountains, in the same manner as they change in approaching the pole: this is the case with the Monocotyledones, considered in a general view, as well as with the Ferns and Compositae. (Proleg. p. 51. and 52.; Brown on Congo, p. 5.) A translation of this valuable Memoir will be found in this Journal, vol. III. pp. 1, 256.; IV. pp. 23, 262.; V. p. 28. It may further be remarked, that the development of vegetables of different families, and the distribution of forms, depend not on isothermal latitudes, nor on geographical latitudes alone; but that the quotients are not always similar on the same isothermal line of the temperate zone, in the plains of America and of the Old Continent. There exists, under the tropies, a very remarkable difference between America, India, and the west coasts of Africa. The distribution of organic beings on the globe, depends not only on very complicated climatic circumstances, but also on geological causes, with which we are entirely unacquainted, because they are connected with the original state of our planet. The great Pachydermata are wanting at the present day in the New World, although we find them still in abundance in analogous climates, in Africa, and in Asia. In the equinoctial zone of Africa, the family of palms is far from numerous, compared with the great number of species of equinoctial America. These differences, far from deterring us from the scrutiny of the laws of nature, ought to excite us to study these laws in all their complications. The lines of equal heat are not parallel to the equator. They have, as I have tried to prove elsewhere, convex summits, and concave summits, which are distributed with great regularity over the globe, and form different systems along the eastern and western coasts of the two worlds, in the centre of continents, and in the neighbourhood of the ocean. It is probable, that when philosophical botanists have travelled over a larger extent of the globe, we shall find, that often the lines of the maxima of agroupment (the lines taken from the points where the fractions are reduced to the smallest denominator,) become isothermal lines. In dividing the globe by longitudinal bands comprehended between two meridians, and in comparing the numerical proportions under the same isothermal latitudes, we perceive the existence of different systems of agroupment. We can already, with the actual state of our knowledge, distinguish four systems of vegetation, those of the New Continent, of Western Africa, of India, and of New Holland. Since, notwithstanding the regular increase of the mean heat from the pole to the equator, the maximum of heat is not identical in the different regions at different degrees of longitude, there exist also places where certain families attain a more perfect development than at any other: this is the case with the family of Compositae in the temperate region of North America, and especially at the southern extremity of Africa. These partial accumulations determine the physiognomy of the vegetation, and are what we call vaguely the characteristic features of the landscape. In the whole temperate zone, the Glumaceae and Compositae form together more than the fourth part of the phaenogamous plants. We find, from the same inquiries, that the forms of organised beings have a mutual dependence. The unity of nature is such, that the forms are universally limited according to constant and immutable laws. When we know at any point of the globe the number of species which a great family presents, (for example, that of the Glumaceae, the Compositae, or the Leguminosae,) we can estimate with much probability both the total number of phaenogamous plants, and the number of species which compose the other vegetable families. It is thus, that, on knowing the number of Cyperaceae or of Compositae in the temperate zone, we can form an estimate of that of the Gramineae or Leguminosae. These estimates enable us to see in what tribes of vegetables the Floras of a country are still deficient: they are so far from being uncertain, as to enable us to avoid confounding the quotients which belong to the different systems of vegetables. The labour which I have bestowed upon plants, will no doubt one day be applied with success to the different classes of vertebral animals. In the temperate zones, there are nearly five times as many birds as mammalia, and the latter increase much less toward the equator than the birds and reptiles. The geography of plants may be considered as a part of the natural history of the globe. If the laws which nature has followed in the distribution of vegetable forms, should prove to be more complicated than they appear at first sight, still, we ought not on this account to be deterred from submitting them to accurate investigation. We do not relinquish the tracing of a map, when we perceive the sinuosities of rivers, and the irregular form of coasts. The laws of magnetism become intelligible to him who has commenced with tracing the lines of equal inclination and declination, and who has compared a great number of observations, which, at first sight, might seem contradictory. He who thinks that it is not yet time to search the numerical elements of the geography of plants, forgets the progressive march by which the physical sciences have elevated themselves to determinate results. In examining a complicated phenomenon, we commence with a general scrutiny of the circumstances by which it is determined or modified; but, before discovering certain proportions, we find, that the first results to which we attend, are not sufficiently free from local influence: it is then that we modify and correct the numerical elements, and discover the regularity in the very effects of partial disturbances. Criticism exercises itself on whatever has been prematurely announced as a general result; and the spirit of criticism once excited, becomes favourable to the investigation of truth, and accelerates the progress of human knowledge. Acotyledones. Cryptogamous plants (fungi, lichens, mosses, and ferns); Agames celluleuses et vasculaires of M. Decandolle. On uniting the plants of the plains with those of the mountains, we have found them to be under the tropics [Formel] ; but their number ought to be much greater. Mr Brown has rendered it very probable, that, in the torrid zone, the proportion is in the plains [Formel] , on the mountains [Formel] . (Congo, p. 5.) In the temperate zone, the agamous plants are generally to the phaenogamous as 1:2; in the frigid zone they attain the same number, and often exceed it considerably. In this article, the fractions [Formel] , [Formel] , [Formel] , indicate the proportions between the species of a family and the total number of Phaenogamous plants which vegetate in the same country. The abbreviations Trop. Temp. Frig., signify Tropies or Torrid Zone, Temperate Zone, Frigid Zone. On dividing the agamous plants into three groups, we observe that the ferns are more frequent (the denominator of the fraction being less) in the frigid zone than in the temperate zone, (Berl. Jahrb., bd. i. p. 32.), and the lichens and mosses also increase towards the frigid zone. The geographical distribution of ferns depends upon the union of the local circumstances of shade, humidity, and moderate heat. Their maximum (that is to say, the place where the denominator of the normal fraction of a group becomes the least possible,) is found in the mountainous parts of the tropics, particularly in islands of small extent, where the proportion rises to [Formel] , and upwards. When the plains and mountains were not separated, Mr Brown found the ferns of the torrid zone to be [Formel] . In Arabia, India, New Holland, and Western Africa, (between the tropics,) they are [Formel] : our herbaries of America do not give more than [Formel] ; but the ferns are rare in the great valleys and on the dry platforms of the Andes, where we were forced to remain a long time. (Congo, p. 43., and Nova gen. , vol. i. p. 33.) In the temperate zone, the ferns are [Formel] ; in France, [Formel] ; in Germany, according to late inquiries, [Formel] . (Berl. Jahrb., b. i. p. 26.) The group of ferns is extremely rare on the Atlas mountains, and almost completely disappears in Egypt. In the frigid zone, the ferns appear to rise to [Formel] . Monocotyledones. The denominator becomes progressively smaller in proceeding from the equator toward the 62d degree of North Latitude; it increases again in the regions still farther north, on the coast of Greenland, where the Gramineae are very scanty. (Congo, p. 10.) In the different parts of the tropics, the proportion varies from [Formel] to [Formel] . In 3880 phaenogamous plants of equinoctial America, found by M. Bonpland and me, in flower and in fruit, there are 654 monoctyledonous, and 3226 dicotyledonous; hence the great division of the Monocotyledones would be [Formel] of the phaenogamous plants. According to Mr Brown, the proportion in the Old Continent (in India, equinoctial Africa, and New Holland,) is [Formel] ; in the temperate zone we find [Formel] . (France, 1:4 [Formel] ; Germany, 1:4 [Formel] ; North America, according to Pursh, 1:4 [Formel] ; Kingdom of Naples, 1:4 [Formel] ; Switzerland, 1:4 [Formel] ; British Isles, 1:3 [Formel] ); in the frigid zone, [Formel] . Glumaceae. (The three families of Junceae, Cyperaceae, and Gramineae, united). = Trop., [Formel] . Temp., [Formel] . Frig., [Formel] . The increase toward the north is owing to the Junceae and Cyperaceae being very rare compared with the other Phaenogamous plants, in the temperate and torrid zones. On comparing the species belonging to the three families, we find that the Gramineae, the Cyperaceae, and the Junceae, are under the tropics, as 25, 7, 1; in the temperate region of the Old Continent, as 7, 5, 1; in the polar circle, as 2 [Formel] , 2 [Formel] , 1. In Lapland the Gramineae and Cyperaceae are equal: toward the equator the Cyperaceae and Junceae diminish much more than the Gramineae; the junceal form disappears almost entirely under the tropics, (Nova Gen. vol. i. p. 240.). Junceae alone. = Trop., [Formel] . Temp., [Formel] . Frig., [Formel] , (Germany, [Formel] ; France, [Formel] .) Cyperaceae alone. = Trop. America, nearly [Formel] ; Western Africa, [Formel] ; India, [Formel] ; New Holland, [Formel] . (Congo, p. 9). Temp., probably [Formel] . (Germany, [Formel] ; France, according to the works of M. Decandolle, [Formel] ; Denmark, [Formel] .) Frig. [Formel] . This is the proportion found in Lapland, and as far as Kamtschatka. Gramineae alone. Trop. I have allowed as much as [Formel] . Mr Brown found in Western Africa, [Formel] ; in India, [Formel] . (Congo, p. 41.) M. Hornemann fixed this part of Africa at [Formel] . (De Indole Plant. Guineensium, 1819, p. 10.) Temp. Germany, [Formel] ; France, [Formel] . Frig. [Formel] . Compositae. On blending the plants of the plains with those of the mountains, we have found in equinoctial America [Formel] and [Formel] ; but, of 534 Compositae of our herbaries, there are only 94 which grow to 500 toises above the plains, (the height at which the mean temperature is still 21°.8; equal to that of Cairo, of Algiers, and of the Island of Madeira.) From the equatorial plains to 1000 toises of height (where we have still the mean temperature of Naples), we have collected 265 Compositae. This last result gives the proportion of Compositae, in the regions of equinoctial America, beneath 1000 toises, from [Formel] to [Formel] . This result is very remarkable, because it proves, that between the tropics in the lowest and warmest region of the New Continent, there are fewer Compositae, in the subalpine and temperate regions more, than under the same circumstances in the Old World. Mr Brown found on the Rio-Congo, and in Sierra- Leone, [Formel] ; in India and New Holland [Formel] . (Congo, p. 26; Nova Gen. vol. iv. p. 239.) In the temperate zone, the Compositae are in America, [Formel] , (this is probably also in equinoctial America the proportion of the Compositae of the highest mountains to the whole mass of alpine phaenogamous plants); at the Cape of Good Hope, [Formel] ; in France, [Formel] (correctly [Formel] ); in Germany [Formel] . Under the frigid zone the Compositae are, in Lapland, [Formel] ; in Kamtschatka, [Formel] . (Hornemann, p. 18.; Berl. Jahrb. b. i. p. 29.) Leguminosae. = Trop. America, [Formel] ; India, [Formel] ; New Holland, [Formel] ; Western Africa, [Formel] , (Congo, p. 10.) Temp. France, [Formel] ; Germany, [Formel] ; North America, [Formel] ; Siberia, [Formel] , (Berl. Jahrb. b. i. p. 22.) Frig. [Formel] . Labiatae. = Trop. [Formel] . Temp. North America, [Formel] ; Germany, [Formel] ; France, [Formel] . Frig. [Formel] . The rarity of Labiatae and Cruciferae in the temperate zone of the New Continent is a very remarkable phenomenon. Malvaceae. = Trop. America, [Formel] ; India and Western Africa, [Formel] , (Congo, p. 9.); on the coast of Guinea alone, [Formel] , (Hornemann, p. 20.) Temp. [Formel] . Frig. 0. Cruciferae. Almost wanting under the tropics, on taking away the mountains to within from 1200 to 1700 toises. (Nova Gen. p. 16.) France, [Formel] ; Germany, [Formel] ; North America, [Formel] . Rubiaceae. Without dividing the family into sections, we find beneath the tropics, in America, [Formel] ; in Western Africa, [Formel] : under the temperate zone in Germany, [Formel] ; in France, [Formel] : under the frigid zone, in Lapland, [Formel] . Mr Brown separates the great family of Rubiaceae into two groups, which present very distinct climatic proportions. The group of Stellatae without interposed stipules, belong chiefly to the temperate zone: it almost disappears between the tropics, excepting at the summit of the mountains. The group of Rubiaceae with opposite leaves and stipules, belong very peculiarly to the equinoctial region. M. Kunth has divided the great family of Rubiaceae into eight groups, one of which, that of the Coffeaceae, forms in our herbaries a third part of the whole Rubiaceae of equinoctial America. (Nov. Gen. vol. iii. p. 341.) Euphorbiaceae. = Trop. America, [Formel] ; India and New Holland, [Formel] ; Western Africa, [Formel] . (Congo, p. 25.) Temp. France, [Formel] ; Germany, [Formel] . Frig. Lapland, [Formel] . Ericeae and Rhododendra. = Trop. America, [Formel] . Temp. France, [Formel] ; Germany, [Formel] ; North America, [Formel] . Frig. Lapland, [Formel] . Amentaceae. = Trop. America, [Formel] . Temp. France, [Formel] ; Germany, [Formel] ; North America, [Formel] . Frig. Lapland, [Formel] . Umbelliferae. = almost none under the tropics to the height of 1200 toises; but, on taking both the plains and high mountains in equinoctial America, [Formel] ; under the temperate zone much more numerous in the Old than in the New Continent. France, [Formel] ; North America, [Formel] ; Lapland, [Formel] . On comparing the two worlds, we find in general in the New World, under the equatorial zone, fewer Cyperaceae and Rubiaceae, and more Compositae; under the temperate zone, fewer Labiatae and Cruciferae, and more Compositae, Ericae, and Amentaceae, than in the corresponding zones of the Old World. The families which increase from the equator toward the pole (according to the fractional method), are the Glumaceae, the Ericeae, and the Amentaceae. The families which decrease from the pole toward the equator are the Leguminosae, the Rubiaceae, the Euphorbiaceae, and the Malvaceae. The families which appear to attain the maximum under the temperate zone, are the Compositae, the Labiatae, the Umbelliferae, and the Cruciferae. I have thrown together the principal results of this work in one table; but I enjoin naturalists to have recourse to illustrations of the several families, whenever any of the numbers seem doubtful. The quotients of the tropics are modified in such a manner that they are proportioned to regions whose mean temperature is from 28° to 20°, (from the level of the sea to 750 toises of height). The quotients of the temperate zone are adapted to the central part of that zone, between 13° and 10° of mean temperature. In the frigid zone, the mean temperature is from 0° to 1°. To this table of quotients or fractions, which indicate the proportions of each family to the total mass of phaenogamous plants, might be added another, in which the absolute number of species might be compared. We here present a fragment which comprehends only the temperate and frigid zones. France. North America. Lapland. Glumaceae, - - 460 365 124 Compositae, - - 490 454 38 Leguminosae, - - 230 148 14 Cruciferae, - - 190 46 22 Umbelliferae, - 170 50 9 Caryophylleae, - 165 40 29 Labiatae, - - 149 78 7 Rhinantheae, - - 147 79 17 Amentaceae, - - 69 113 23 These absolute numbers are taken from the works of Messrs Decandolle, Pursh, and Wahlenberg. The mass of plants described in France is to that of North America in the proportion of 1 [Formel] :1; to that of Lapland in the proportion of 7:1 . A series of additional observations on this subject, so highly interesting to the philosophical botanist and the geologist, also by Baron Humboldt, will appear in our next Number. Groups, founded on the Analogy of Forms. Proportions to the whole mass of Phaenogamous Plants. Signs indicating the direction of Increase. Equatorial Zone, Lat. 0°--10°. Temperate Zone, Lat. 45°--52°. Frigid Zone, Lat. 67°--70°. Agamous Plants, Plains, - - - [Formel] Mountains, - - - [Formel] / Ferns alone. Country slightly Mountainous, [Formel] Country very Mountainous, [Formel] -- [Formel] - - Monocotyledonous Plants. Old Continent, - - [Formel] New Continent, - - [Formel] / Glumaceae, / Junceae alone. / Cyperaceae alone. Old Continent, - - [Formel] New Continent, - - [Formel] / Gramineae alone. / Compositae. Old Continent, - - [Formel] New Continent, - - [Formel] Old Continent, - [Formel] New Continent, - [Formel] - - Leguminosae. / Rubiaceae. Old Continent, - - [Formel] New Continent, - - 1 / Euphorbiaceae. / Labiatae. America, - - [Formel] Europe, - - [Formel] - - Malvaceae. 0 / Ericeae and Rhododendra. Europe, - - [Formel] America, - - [Formel] / Amentaceae. Europe, - - [Formel] America, - - [Formel] / Umbelliferae. - - Cruciferae. Europe, - - [Formel] America, - - [Formel] - - Explanation of the Signs: / The denominator of the fraction diminished from the Equator toward the North Pole: / The denominator diminished toward the Equator: - - The denominator diminished toward the Equator and toward the North Pole: - - The denominator diminished from the North Pole, and from the Equator toward the Temperate Zone. Ferns, Lichens, Mosses, Fungi, Junceae, Cyperaceae, Gramineae, New Inquiries into the Laws which are observed in the Distribution of Vegetable Forms. By Baron Alexander Humboldt . (Continued from Vol. VI. p. 289.) This continuation is taken from a Memoir read before the Academy of Sciences on the 19th February 1821. It is with the distribution of organic beings as with all the other phenomena of the physical world. In the midst of apparent disorder, which seems to arise from the influence of a multitude of local causes, we discover the immutable laws of Nature, as soon as we cast our eyes over a great extent of country, or employ a mass of facts with which the partial disturbances mutually agree. I have had the satisfaction to see this work completed by a minute examination made in Germany, England, Italy, and of late in Denmark. One of the greatest botanists of our times, and indeed of any age, Mr Robert Brown, has compared each of the numerical results with those given by the rich herbaries which he has had the opportunity of consulting. Many of the numbers have been rectified, while the others have been confirmed by an agreement somewhat unexpected. The mass of facts is increased by the very desire of invalidating or corroborating the results to which I have applied myself. It is thus that, in the progress of the physical sciences, general ideas, which at first have only been deduced from a small number of facts, compel observers to multiply the partial results. Enriched by these materials, profiting daily by whatever truth or utility is contained in the most severe criticism of my works, I have been enabled to give to the numerical results of which the table of vegetable forms consists, a degree of exactness which I have not till now been able to attain. It is in the nature of these researches, that we are not able to rectify the co-efficients otherwise than progressively, in proportion as the observations accumulate. I have attended here only to the general development of principles. As this kind of botanical arithmetic demands more minute discussions of the proportions of each family of vegetables to the whole mass of phaenogamous plants, I have thrown together these discussions in the notes which I have published separately . See Dictionnaire des Sciences Naturelles, arranged by the Professors of the Garden of Plants, vol. xviii. p. 423,--436. We may foresee, that the labour which I have bestowed on the families of plants, will one day be applied with success to most of the classes of vertebral animals. The immense collections which are to be seen at Paris, in the Museum of Natural History, show that we are already acquainted with nearly 56,000 species of Plants, cryptogamous and phaenogamous; 44,000 Insects, 2500 Fishes; 700 Reptiles; 4000 Birds; and 500 species of Mammalia. Agreeably to the inquiries which M. Valenciennes and I have made, there exist in Europe alone nearly 80 Mammalia, 400 Birds, and 30 Reptiles: it follows, that, in this northern temperate zone, there are five times as many species of Birds as of Mammalia, as there are (in Europe) five times as many Compositae as Amentaceae and Coniferae; five times as many Leguminosae as Orchideae and Euphorbiaceae. The beautiful collections lately brought from the Cape of Good Hope by M. De Lalande prove, (if we compare them with the works of MM. Temminik and Le Vaillant), that in that part of the southern temperate zone, the Mammalia are to the Birds in the proportion of 1:4,3. Such an agreement between two opposite zones is abundantly striking. The Birds, and especially the Reptiles, increase towards the equatorial zone in a much more considerable degree than the Mammalia. According to the discoveries of M. Cuvier regarding fossil bones, we may be induced to believe, that these proportions have not been the same in all ages, and that, amid the ancient catastrophes of our planet, a much greater number of Mammalia has been lost than of Birds. M. Latreille, in an excellent memoir on the Geographical Distribution of Insects, has not compared the number of articulated animals with the number of plants, and with that of the different classes of vertebral animals which inhabit the same climates; but he has exhibited, in an interesting manner, a view of the increase or diminution of the particular groups of insects, in advancing from the pole towards the equator. I pass over in silence the laborious researches of M. Illiger on the Geography of Birds . The author has discussed the habitation of upwards of 3800 species; but he has contented himself with viewing them according to their distribution among the five divisions of the world,--a method by no means philosophical, and altogether improper for investigating the influence of climate over the development of organized beings. All the continents, with the exception of Europe, extend from the temperate to the equatorial zone: the laws of Nature cannot, therefore, manifest themselves, when we group the phenomena according to divisions which are arbitrary, and which depend, so to speak, simply upon the difference of meridians. It is not my intention to push to a greater extent these considerations regarding the numerical proportions of animals of different classes. I am satisfied with having called the attention of the learned to a branch of natural philosophy which has appeared to me very worthy of investigation. We conceive how, in a given space of country, the individuals belonging to different tribes of plants and of animals may be numerically limited,--how, after an obstinate struggle, and long wavering, a state of equilibrium is established, which results from the necessity of food, and the habitudes of life; but the causes which have limited the forms, are hidden under the impenetrable veil which conceals from our sight all that extends from the origin of things to the first development of organic life. Memoirs of the Academy of Berlin for the years 1812 and 1813, p. 221,-- 237. On examining in detail all that we already know regarding the proportion of monocotyledonous to dicotyledonous plants, we find that the denominator becomes gradually smaller (and this with a very great degree of regularity), in proceeding from the equator toward the 62d degree of N. Lat. It increases probably anew in regions still more northern, on the coast of Greenland, where the Gramineae have become very rare (Congo, p. 4.). The proportion varies from [Formel] to [Formel] in the different parts of the tropics. In upwards of 3880 phaenogamous plants of Equinoctial America, found by M. Bonpland and myself in flower and in fruit, there were 654 monocotyledones, and 3226 dicotyledones: hence the great division of monocotyledones would be [Formel] of the phaenogamous plants. According to Mr Brown, the proportion is generally in the Old Continent (in India, Equinoctial Africa, and New Holland,) [Formel] . In the temperate zone, we find (according to my Proleg. p. xii. and the partial results published by M. Decandolle, Dict. des Sciences Nat. vol. xviii. p. 594,--597.) that the monocotyledones are to the dicotyledones, In Barbary, - - = 1:4,8 Egypt. - - = 1:5,0 Caucasus and Crimea, = 1:6,0 Kingdom of Naples, = 1:4,7 The State of Venice, = 1:4,0 In France, - - - = 1,4,7 Germany, - - = 1:4,0 Switzerland, - - = 1:4,3 The British Isles, - = 1:3,6 North America, - = 1:4,6 In the frigid zone, the proportion is, In Lapland, - - - = 1:2,8 Iceland, - - = 1:2,8 We see, that, from the tropics to the pole, the relative increase of the monocotyledones is very regular. As the monocotyledones affect moisture, they are more numerous in the British Isles, and more rare in Egypt and on the dry mountains of Caucasus. I have already observed, that in the Alps of Switzerland, up to the region of the Rhododendra, the monocotyledones are to the phaenogamous plants as 1:7, while in the plains, they are, at the foot of the Alps, as 1:4,3, (Prolegomena, p. lii.) In the most fertile part of Europe, at the centre of the temperate zone, an extent of country of 30,000 square leagues produces about 6000 species of plants, of which 2200 are acotyledonous or cryptogamous, and 3800 phaenogamous. Among the last there are nearly 500 Compositae, 300 Gramineae, (exclusive of the Cyperaceae and Junceae), 250 Leguminosae, and 200 Cruciferae; but only 70 Amentaceae, 50 Euphorbiaceae, and 25 Malvaceae. The great families constitute from [Formel] to [Formel] , the small ones about [Formel] of the total mass of phaenogamous plants. This is, so to speak, the mean state of the vegetation in Europe, in the fertile countries, between 42° and 50° of N. Lat. To convince the most incredulous of the reality of fixed proportions, or of the regularity to be observed in Europe in the distribution of forms in a particular zone, I shall here present the proportions given by two neighbouring countries, France and Germany. The figures marked in the following Table may be regarded as the coefficients of each family; for, on multiplying the number of phaenogamous plants of the temperate zone of Europe by 0.076 or 0.053, the number of species which compose the families of Gramineae or Cruciferae may be found. Compositae, / Fr. [Formel] Ger. [Formel] Glumaceae, / Fr. [Formel] Ger. [Formel] Gramineae alone, / Fr. [Formel] Ger. [Formel] Leguminosae, / Fr. [Formel] Ger. [Formel] Cruciferae, / Fr. [Formel] Ger. [Formel] Umbelliferae, / Fr. [Formel] Ger. [Formel] Labiatae, / Fr. [Formel] Ger. [Formel] Cyperaceae alone, / Fr. [Formel] Ger. [Formel] Amentaceae, / Fr. [Formel] Ger. [Formel] Orchideae, / Fr. [Formel] Ger. [Formel] Boragines, / Fr. [Formel] Ger. [Formel] Rubiaceae. / Fr. [Formel] Ger. [Formel] Euphorbiaceae, / Fr. [Formel] Ger. [Formel] Junceae, / Fr. [Formel] Ger. [Formel] Ericeae, / Fr. [Formel] Ger. [Formel] Malvaceae, / Fr. [Formel] Ger. [Formel] Coniferae, / Fr. [Formel] Ger. [Formel] This agreement in the greater part of the results is the more striking, that the coefficients have been obtained from very unequal masses of plants. In France 3645, in Germany only 1844 phaenogamous plants have been employed, in order to determine the particular proportions of the families. Since the two countries border on each other, the species should in like manner be much the same. The agreement of the results within limits thus marked (the greater part commonly within [Formel] of difference), prove two facts equally remarkable: 1st, That the 1700 to 1800 species of phaenogamous plants which the French catalogue has more than the excellent catalogue of M. Schrader employed for Germany, are distributed among the different families almost in the same proportions which we observe among the plants common to the two countries: 2d, That the species of Leguminosae, of Cruciferae, and of Umbelliferae, which Germany would appear to possess exclusively, are substituted in France by a nearly equal number of species belonging to the same families. In general, where the greatest discrepancies are observed, they may be attributed to the circumstance, that Germany is situate more to the north than France is. We know that the Cyperaceae and the Ericeae increase so rapidly towards the north pole, that, while in the temperate zone the Cyperaceae are [Formel] , and the Ericeae [Formel] , in the frigid zone there is [Formel] of Cyperaceae, and [Formel] of Ericeae. On the other hand, the proportions of the Orchideae, of the Malvaceae, and of the Euphorbiaceae, increase with equal rapidity towards the south. On comparing the preceding table with the table of the three zones, (the torrid, the temperate, and frigid), we observe the same laws. I have added to this comparative table of the vegetation of France and Germany the arrows which, in the general table, indicate the directions of increase, from the pole to the equator, and from the equator to the pole. It is a very remarkable circumstance, also, that the coefficients of the families do not change so much, if, instead of examining extensive countries which have from 2600 to 3800 species of phaenogamous plants, we confine our researches to an extent of some square leagues; for example, to the Flora of Berlin, which, according to the work of M. Kunth, comprehends only 900 species. In that small extent of land, the Leguminosae are [Formel] , (in the whole of France [Formel] , in the whole of Germany [Formel] ); the Glumaceae [Formel] , (in France [Formel] , in Germany [Formel] ,) of the whole mass of phaenogamous plants. In the same way that the system of climates of the New Continent differs essentially from that of the Old, on account of the unequal distribution of the heat among the different parts of the year, so also the system of agroupment of American plants has its peculiar features. It is to the new researches of botanical arithmetic that we owe the knowledge of these contrasts between the temperate zones of the two worlds. I have thrown together in the following Table the results of the American Flora of Pursh and of the French Flora of M. Decandolle. I have added certain coefficients of the European frigid region, in order to show how much of a boreal character the American temperate region presents in the five families of Ericeae (and Rhododendra), Coniferae, Amentaceae, Umbelliferae, and Labiatae. Temp. America. France. Lapland. Compositae, 0 Glumaceae, 0 Gramineae alone, 0 Junceae alone, 0 Cyperaceae alone, 0 Cruciferae, 0 Leguminosae, 0 Temp. America. France. Lapland. Malvaceae, 0 Labiatae, Ericeae and Rhododendra,} Umbelliferae, Amentaceae, Coniferae, The differences which are manifested in this table between the two continents, bear, not merely upon the five last families, which might be called boreal forms, but also upon the Cruciferae, the Junceae, and the Cyperaceae, which are equally rare in the torrid zone and in the temperate zone of the New Continent. It is conceived that the inquiries regarding the numerical proportions of vegetable families, will present results much more interesting when the Floras of different countries shall be circumscribed within more precise geographical limits, and when botanists shall attend more particularly to the principles according to which varieties and species ought to be distinguished. The catalogues which we see under the vague name of Flora of the United States of America, comprehend countries placed in very different climates, from 18° to 9° of mean temperature. Here we have a difference of climate as great as in Europe between Calabria and Austria. When the vegetation of South Carolina, of Pennsylvania, and of New England, shall be described individually, and with the same degree of exactness, we shall notice a regular increase and decrease in the numerical proportions of families from south to north. At present, we only know the general mean of these partial proportions. Many countries seem richer in plants, because the botanists have inconsiderately elevated varieties to the rank of species. In another country, the travellers often neglect the plants which they believe to be the same as those of their own country. But when we attend to the great divisions, and when the number of species which we compare is very considerable, our researches are favoured with happy compensations. It is thus that the new Floras, much more complete of America and Lapland, published by Messrs Pursh and Wahlenberg, have not sensibly altered the numerical proportions which we find on confining ourselves to the old Floras of Michaux and Linnaeus, (Berl. Jahrb. der Gew. b. i. s. 24.). Whatever may be the corrections which shall be made in my work, I am persuaded beforehand, that the more that exact observations are accumulated, and the more we look beyond the same hemisphere, the same system of agroupment, the partial variations of the coefficients will be found not to be made by sudden starts, but according to invariable laws. It may be that the tropical proportion of the Malvaceae is [Formel] or [Formel] , instead of [Formel] , but it is not the less certain, that the Leguminosae and the Malvaceae increase toward the equator, while the Junceae and the Ericeae increase toward the pole. One may recall in doubt the quantities of the variations, the rapidity of the increase, but not its direction. On comparing the coefficients which belong to the same families, in different zones, we find, in the rapidity of the increase, contrasts strongly marked. In the Old Continent, the proportions of the Gramineae, the Leguminosae, and the Euphorbiaceae, change much less from the temperate zone to the equator, than from the temperate zone to the pole. Those who are accustomed to consider each phenomenon in an absolute and irrelative point of view,--who regard the mean temperature of places, the laws which are observed in the variations of terrestrial magnetism, with the proportions between births and deaths, as daring hypotheses, and as vague, theoretical speculations,--will probably look with contempt on the discussions which form the principal object of this memoir. Those, on the other hand, who delight to contemplate the mutual concatenation of organized beings,--who are aware that the numerical results correct themselves by the accumulation and the careful investigation of particular facts,--will cherish a kind of research, which throws light upon the economy of Nature,--on the connection which is observed between the climates and the form of beings,--on the distribution of plants and of animals in the different regions of our planet. It is only by the numerical examination and the comparison of species, that we can form a correct idea of the state of the vegetation of a given country;-- of the general influence which the temperature exercises over the frequency of certain forms, near the equator, in the mean parallel, and towards the polar circle;--of the characteristic features which distinguish, in isothermal zones, the two systems of agroupment of the Old and the New World . For the use of such as have not made descriptive botany their particular study, and who are yet desirous of acquiring a knowledge of the investigations which have been attempted in the different branches of the natural sciences, we shall add in this place the names of some of the most common plants which characterise, if we may so speak, the tribes or families which are frequently the subject of discussion in this memoir. (The translation of the following is modified so as to give an English reader an idea of the families). Junceae (Rushes); Cyperaceae (Hard or Moor Grasses, Cotton-Grass); Gramineae (Corn, Grasses); Compositae (Dandelion, Thistles, Sunflower); Leguminosae or Papilionaceae (Vetches, Pease, Clover); Rubiaceae (Rennet, Madder); Euphorbiaceae (Sun-spurge, Dogs' Mercury); Labiatae (Mint, Thyme, Rosemary); Malvaceae (Mallows, Hollyhock); Umbelliferae (Carrot, Hemlock, Chervil, Carraway); Cruciferae (Mustard, Cresses, Radish, Turnip). The great mass of plants which cover the globe is divided by botanists into Phaenogamous (those having visible flowers), and Cryptogamous or Agamous (Ferns, Lichens, Mushrooms).