II. parallels of Barcelona and Dunkirk. These two celebrat- BOOK. ed geometricians measured the angles of 90 triangles with the new repeating circles which Borda had constructed; they observed with these instruments, 5 latitudes at Dunkirk, Paris, Evaux, Carcassone, and Barcelona. The two bases near Melun and Perpignan were measured with platina and copper rules, and were found to agree, to a few inches, with the measures calculated. Minute attention prevented or rectified the smallest errors. The most eminent of the French mathematicians, together with a number of others sent from different countries, verified and sanctioned all the calculations. No farther doubt, therefore, can be entertained respecting the results of this vast enterprise, which commenced in 1792, and terminated, as to the measurement, in 1798. It has been proved, that the degrees of the meridian Results. diminish towards the south, and increase towards the north. But this augmentation of the terrestrial degrees does not follow a regular and constant progression. Therefore no meridian whatever can be a regular ellipse. It is probable, that the earth itself is not a solid of revolution, that is, circumscribed by the revolution of an individual ellipse round its centre. However, those irregularities which appear extremely small in comparison with the mass of the earth, may, without inconvenience, be overlooked. of the de pression, The meridian of France, which Messrs. Biot and Arago Quantity have lately prolonged, by a very tedious operation, as far as the isles of Ivica and Fromentera* gives, if we consider it apart, for the quantity of the depression ʊ, and, by comparing it with the degree of Peru, it would give • This latter result, adopted by the commission of weights Accords and measures, coincides with what was found by observing the pendulum. It agrees also with several celestial phenomena, the cause whereof is the non-sphericity of the earth; for this planet being swelled towards the equator, the attraction of the sun and moon is there more powerful than *Notice of the operations carried on in Spain. Mercury, Jan. 7, 1810. + Laplace, Système du Monde, p. 62. with phe nomena. II. BOOK towards the poles; and, as the plane of the equator is inclined to the ecliptic and lunar orbit, this additional attraction communicates to the axis a progressive motion, which causes the equinoctial points to retrograde, and an alternate motion, by which it oscillates around the position it would have by virtue of the first motion. The latter is called the precession of the equinoxes, and the former the nutation. M. Burg, a celebrated German astronomer, having calculated, at the request of M. de Laplace, the causes of those perturbations, and the influence of the earth's depression, found the latter to be New measurement by the Swedish astrono mers. Accords with the French measure. The degree measured at the polar circle by the French academicians in 1737, was that which differed the most from the general result deduced from all the other data. We have already mentioned, that considerable errors were suspected in the operation, and this has been since demonstrated. M. Melanderheilm, a learned Swedish astronomer, undertook to get a new degree measured by M. Svanberg, one of his pupils, and for that purpose the repeating circle was employed, and all the delicate methods of modern geodesia. The French academicians had measured only an arc of 57', but M. Svanberg extended the operation to 1° 37'. By the definitive result of this measure, a degree of the meridian is found to be 57,209 toises, or 60,970 fathoms, in latitude 66° 20', or 196 toises, shorter than that which was measured in 1737. This, compared with the French degree, gives for the depression 17, and with that of Peru • We may also, by different hypotheses, combine this measure with a depression of. Thus there is no essential difference between this result and that which was adopted by the French mathematicians.‡ Laplace, Système du Monde, p. 218. + Svanberg, Exposition of the Operations carried on in Lapland. Stockholm, 1805, p. 164, 92. Since the publication of this work, the king of Denmark, full of zeal for the progress of the sciences, has ordered an arc of the meridian to be measured which passes through Jutland, Fienia, Holstein, and Lauenbourg, and which contains 4 degrees of latitude. This measurement it entrusted to one of the ablest modern astronomers, M. Schumacher of Copenhagen. At the same time, Observations made on the planets, which are several mil- BOOK lions of leagues distant from us, have concurred to esta- II. blish our ideas respecting the oblate figure of the terrestrial spheroid. The alteration of the spherical figure, resulting Depression from the rotation of a celestial body on its own axis, apof Jupiter. pears also in the planet Jupiter, where it is so sensible that the differences of both diameters of the disc may be discerned by means of a telescope. This difference is almost th; and when we compare the exact measure of this depression, the dimensions of Jupiter, and the time of his rotation with those of the earth,* we find for this latter planet a flatness proportional to; which still coincides with the grand French measure. measures, It must not be dissembled, that this accord, which appa- English rently ought to have been universal, was affected by some new doubts suggested by two German mathematicians, by Doubts. reason of the geodesical operations of the English. The two measurements in the East Indies, the one by Burrow, under the tropic, the other by Lambton at 12° north latitude, have furnished results which combine tolerably well with those of the French measures, though they are still more favourable to Newton's theory.† But the measure of 3 degrees by Major Mudge‡ in England, gives, according to the German mathematicians, considered by itself, a depression under the equator of th. This singular result seems to prove decidedly, that the spheroidal figure of the the celebrated M. Gauss of Gottingen, is directed to measure an arc of the meridian of 3 degrees in Hanover. This operation will likely be connected with that of the Danes. It is known that, since the publication of this volume in 1812, (second edition,) the English and French mathematicians have connected together the grand and magnificent geodesical operations of France and England. By these measures, the curvature of the earth is exactly determined from the Shetland islands to the island of Fromentera. See the Notice published by M. Biot.-Author's note. Laplace, Système du Monde, 253. + Zach. Corresp. xii. 488-493. Phil. Trans. 1803, part ii. p. 383. Comp. Lindenau in Zach. Corresp. xiv. 137, et seq. BOOK earth is subject to irregularities which can only be deter- cal conclu sions. We may therefore consider the quantity of the earth's Geopraphi- depression as sufficiently determined for geographical purposes. There are few geographers indeed, who, in the construction of maps on a small scale, have paid attention to the depression or ellipticity of the earth. Maupertuis, Murdoch, and others, have indeed calculated tables, which give the increase of the degrees of longitude on an elliptic spheroid. The geographer Bonne demonstrated to Rizzi Zannoni,‡ that in his large map of Europe, he ought to have made allowance for the effect of ellipticity, which was then presumed to be. But the measures and calculations have now changed one of the elements of this question. The depression of the earth, reduced to the 33 of the equatorial diameter, not producing between this diameter and that which passes through the poles more than a difference of about 7 leagues, would give for a spheroid, the major axis of which would be 3 feet, a difference of only 14 line, or about 4th of an inch, a quantity which it would be extremely difficult to observe with precision in the construction of globes. They may therefore be made perfectly spherical. In topography and special hydrography the effect of ellipticity is perceptible not only in the degrees of latitude, but also in those of longitude; it is the duty of a careful geographer to attend to it, by following the methods which several late works give for express *Laplace, Mecan. Céleste, ii. 144. Since the publication of this work, few memoirs have appeared on this subject, at least to our knowledge; but the opinion, supported by so many physical probabilities, that the earth is composed of two unequal hemispheres, seems to have been rejected by Laplace. Note of the Author.-Much light will be thrown on this subject by the labours of Mudge, Colby, Kater, Macculloch, &c. who have been employed lately in extending the British arc of the meridian to Shetland, combining it with the French arc, and determining the length of the pendulum at different points. Maupertuis, Elem. de Géograph. Comp. Mem. de l'Acad. des Sciences, 1744, p. 466. Refutation of a work of M. Rizzi Zannoni, entitled, Dissertation on different points of Geography, by M. Bonne, a rare work, communicated by M. de Lalande to M. de Zach. Corresp. i. 136. II. ing those differences.* The tables annexed to this volume BOOK give all the necessary details for ascertaining the absolute value of each degree of longitude and latitude, as also for the comparison of the new metrical system with the ancient measures. However, we cannot terminate this short historical account of the investigations relative to the figure of the globe, without placing before the reader the principal results of the great French measure. Note. The French metre is 39.371 English inches; the toise, according to General Roy, is 1.0657 English fathoms. * Puissant, Traité de Géodésie, p. 125, et seq. Dubourguet, Traité de Nav. The name adopted is Kilometre; but it is a barbarism: the proper expression is Kiliometre, |