ROYAL INSTITUTE OF FRANCE.

In the public sittings of the 22d of March 1819, a notice was read by M. Biot, on the continuation of the labours undertaken to determine the figure of the earth, and upon the results of the experiments on the pendulum, made in 1817, at the Shetland Islands, by himself and others.

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At first, it was merely known that the earth was of a round figure, which was easily ascertained by the circular form which its shadow presents when projected on the moon's disc during an eclipse. Newton afterwards discovered, by his calculations, that it was not completely round, but somewhat flattened at the poles, and protuberant at the equaThe methods of observation, yet imperfect, have, after great difficulty, established this truth, which has been at last obtained by measuring degrees of the meridian under the most distant latitudes, namely, at the equator and near the poles. The flatness of the poles was thus put beyond doubt. The operations prosecuted for the last fifty years in France, England, Sweden, America, and India, have succeeded in determining nearly its precise quantity. The measurement of the arc of the meridian comprehended between Dunkirk and Barcelona, and accomplished with infinite precision by MM. Mechain and Delambre, was the foundation upon which the new system of French measures was constructed. The desire of communicating greater precision to these results, caused this first arc to be prolonged across Spain as far as the Balearic Isles*; and it became a part of an immense triangle above the Mediterranean. In fine, the same

motive caused the French Government to seize with avidity the opportunity offered, two years ago, of seeing this operation, already so grand, extend itself towards the north to nearly equal extent, in uniting with a portion of the same meridian, which stretches from the southern coast of England as far as the Shetland Isles, to a higher latitude than St Petersburgh; a portion which the scientific men of England have been now twenty years occupied in measuring.

In order to terminate this immense arc, which comprehends almost the fourth part of the distance from the equator to the pole, there remained nothing, last year, but to construct some triangles between the Shetland Isles and Scotland, by the medium of the Orkneys, and to connect the operations of the English and the French at the point of junction, Dunkirk, by means of a system of combined operations, in which the instruments employed by the observers of the two nations should be made to co-operate.

This last labour was executed in the preceding autumn. MM. Arago and Biot went to receive, at Dunkirk, the English observers, MM. Mudge, Colby, and Gardner, who brought with them the grand astronomical sector constructed by Ramsden, which they had made use of in all their preceding operations and the French, on their part, brought one of their repeating circles.

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At Dunkirk this fine instrument was, by the desire of the observers, placed within the marine arsenal. The English brig the Investigator, which had conveyed it thither, was also to bring it by the docks to the place where it was to be employed,

and remain there ready to take it back. The French Mathematicians placed their little repeating circle at a short distance off, in a shed which the administration of marine had directed to be constructed for them. There, owing to a continuation of good weather, so little time was left for relaxation, that all the observations were finished in fifteen days; and when completed, were found to agree in a surprising manner, if the different nature of the processes be considered; and what is still more fortunate, they were found also to accord perfectly with those which M. Delambre had formerly made in the same place, at the commencement of his operations; whence results the double assurance, that the arcs of France and England are thus perfectly connected with each other; while the observations made on the other points of the two arcs, by similar processes, afford all the precision which can be desired.

As it was expedient that the point of junction of the English and French operations might always be re-ascertained, MM. Arago and Biot resolved to erect some lasting monument. The city of Dunkirk freed them from this care. A little marble column, surmounted with a spire, is to be erected in this place, and a short inscription will record the object of the operation, with the names of the observers of the two countries. At the Shetland Isles, the extremity of the great arc has been marked in like manner, in the garden of Mr Edmonstone, by a little monument which he has caused to be erected in the place where the observations were made. In Spain, in the isles called Balearic, the southern extremity of the arc is consecrated by a cross.

These operations refer to the first of the methods by which the figure of the earth may be determined. The

other method, which employs the measure of a pendulum, had, together with the preceding, been practised on all the points of the arc. An account had last year been given, of a tour made in England, Scotland, and the Shetland Isles, to carry the apparatus of the pendulum over the whole extent of the English arc. The English government, which had favoured this operation, naturally desired that it should be executed, in like manner, by an observer of their own nation. Captain Kater, member of the Royal Society London, an experimentalist singularly exact, and author of an excellent memoir on the length of the pendulum vibrating seconds in the latitude of London, was deputed for this purpose. With much precaution, he conveyed to Edinburgh and the Shetland Islands, a solid pendulum, of an invariable form, the diurnal rate of which he had previously determined at London; and the oscillations of which he had also observed in these different places. It is the same operation which Capt. Freycinet was to execute, in his voyage round the world, with pendulums constructed under the direction of M. Arago. Capt. Kater was received at the Shetland Islands by the same Mr Edmonstone who had received M. Biot with such obliging hospitality two years before. made his observations in the same place where M. Biot did, with the same assistance and with the same accommodations. The observations of Captain Kater have been found to accord in a remarkable degree with those of M. Biot, as was ascertained by mutual comparison. Having thus the lengths of the pendulum measured by an uniform process upon the same meridian from Formentera, the most southerly of the Balearic Islands, to Unst, the most northerly of the Shetland Islands, and not only in these two islands, and in a great

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number of intermediate points, the flatness of the earth can, by these lengths, be determined with great exactness. The amount resulting is found to be exactly the same as that derived from the lunar inequalities, or from the comparison of terrestrial degrees measured at very distant latitudes; so that all these methods, so different in their progress, so distinct in their processes, definitively terminate in this one result-the flatness of the earth; namely, the excess of the equatorial above the polar radius; the excess of the former above the latter amounting to a quantity intermediate between and The difference of these extreme values, between which the truth lies, will hardly give a hundred toises, more or less, on the half of the axis which passes through the poles of the earth; and from the number and exactness of the diversified observations by which this truth has been established, there can no longer be room for discussion on the subject.

Alexander Count Humboldt submitted to the Institute a curious paper, on the laws observed in the distribution of vegetable forms over the globe. Botany, long confined to the description of the external forms of plants, and their artificial classification, now presents several branches of study, which place it more on a foot ing with the other sciences. Such are the distribution of vegetables, according to a natural method founded upon the whole part of their structure; their physiology, which displays their internal organization; their botanical

geography, which assigns to each tribe of plants their height, limits, and climate. The terms alpine plants, plants of hot countries, plants of the seashore, are to be found in all languages, even in those of the most savage nations on the banks of the Oronoko, and prove that the attention of men has been constantly fixed on the distribution of vegetables, and on their connexion with the temperature of the air, the elevation of the soil, and the nature of the ground which they inhabit. It does not require much sagacity to observe, that on the slope of the high mountains of Armenia, vegetables of a different latitude follow each in succession, like the climates, superimposed, as it were, upon each other.

The vegetables, says M. Humboldt, which cover the vast surface of the globe, present, when we study their natural classes or families, striking differences in the distribution of their forms. On limiting them to the countries in which the number of the species is exactly known, and by divid ing this number by that of the glu maceæ, the leguminous plants, the labiated, and the compound, we find numerical relations which form very regular series. We see certain forms become more common, from the equator towards the pole, like the ferns, the glumaceæ, the ericeæ, and the rhododendra. Other forms, on the contrary, increase from the poles towards the equator, and may be considered in our hemisphere as southern forms: such are the rubiaceæ, the malvacea, the euphorbiaceæ, the leguminous, and the composite plants. Finally, others attain their

maximum even in the temperate zone, and diminish also towards the equator and the poles; such are the labiated plants, the amentaceæ, the cruciferæ, and the umbelliferæ. The grasses form in England 1-12th, in France 1-13th, in North America 1-10th, of all the phanerogamous plants. The glumaceæ form in Germany 1-7th, in France 1-8th, in North America 1-8th, in New Holland, according to the researches of Mr Brown, 1-8th, of the known phanerogamous plants. The composite plants increase a little in the northern part of the new continent; for, according to the new Flora of Pursch, there is between the parallels of Geor. gia and Boston 1-6th, whereas in Germany we find 1-8th, and in France 1-7th, of the total number of the species, with visible fructification. In the whole temperate zone, the glumaceæ and the composite plants form together nearly one-fourth of the phanerogamous plants; the glumacea, the compositæ, the cruciferæ, and the leguminosa, together, nearly one-third. It results from these researches, that the forms of organized beings are in a mutual dependence; and that the unity of nature is such, that the forms are limited, the one after the other, according to constant laws easy of determination.

The number of vegetable species described by botanists, or existing in European herbals, extends to 44,000, of which 6000 are agamous. In this number we had already included 3000 new phanerogamous species enumerated by M. Bonpland and myself. France, according to M. Decandolle, possesses 3645 phanerogamous plants, of which 460 are glumaceæ, 490 composite, and 230 leguminous, &c. In

Lapland there are only 497 phanero. gamous plants; among which are 124 glumaceæ, 58 composite, 14 leguminous, 23 amentaceous, &c.

Mr Pursch has made us acquainted with 2000 phanerogamous plants which grow between the parallels of 35° and 44°; consequently, under mean annual temperatures of 16° and 7°.

The Flora of North America is a mixture of several Floras. The southern regions give it an abundance of malvaceae and composite plants; the northern regions, colder than Europe, under the same parallel, furnish to this Flora abundance of rhododendra, amentaceæ, and coniferæ. The caryophylleæ, the umbelliferæ, and the cruciferæ, are in general more rare in North America, than in the temperate zone of the Old Continent.

These constant relations observed on the surface of the globe, in the plains from the equator to the pole, are again traced in the midst of perpetual snows on the summits of mountains. We may admit, in general, that on the Cordilleras of the torrid zone, the boreal forms become more frequent. It is thus that we see prevail at Quito, on the summit of the Andes, the ericea, the rhododendra, and the gramineous plants. On the contrary, the labiatæ, the ru biaceæ, the malvaceæ, and the euphorbiaceæ, then become as rare as they are in Lapland. But this analogy is not supported in the ferns and the composite plants. the composite plants. The latter abound on the Andes, whereas the former gradually disappear when they rise above 1800 fathoms in height. Thus the climate of the Andes resembles that of northern Europe only with respect to the mean temperature of the year. The repartition of