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.