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The labours of M. Legendre will be felt in many branches of science besides our own; and the feeble notice to which we must here confine ourselves of those which more peculiarly relate to astronomy, will, we doubt not, be superseded by one more worthy of his fame, yet to come, from the country which his talents adorned and exalted. The author of the Elliptic Functions, and of the Theory of Numbers, and the extender of every branch of analysis, has unusual claims to the gratitude of the astronomer: but we must speak of those exertions which more directly appear to contribute to the advancement of our science.
From the year 1782 M. Legendre had turned his attention to the attraction exerted by an ellipsoid upon a point exterior to it. In 1790 he gained the prize of the Academy of Berlin for a paper on this subject. He was the first who proved that the spheroid is the only figure of equilibrium which a revolving mass of fluid can assume, under the laws which govern our system; and this both when the density is uniform and when the mass is composed of spheroidal strata of variable density. He also shewed that two spheroids about the same foci, attract an exterior point in the same direction, and with forces proportional to their masses.
The essay upon the determination of the elements of a comet's orbit, written in 1805, was the first in which the solution of that very difficult problem was attempted by all the resources of modern analysis. The method is long and intricate, but is distinguished by the power which it affords of introducing the effect of any errors in the original observations, without repeating the whole process. Some cases in which the method was found to fail, in consequence of it being necessary to determine a large quantity from a small one, induced M. Legendre to reconsider the question, and he was thus led to what has become known by the name of the method of least squares, since universally adopted, where use is to be made of discordant observations, and which has been since demonstrated by M. Laplace to give the most probable result.
In the year 1787, M. Legendre was appointed, in conjunction with MM. Méchain and Cassini, to extend the English survey, so as to connect the observatories of Greenwich and Paris by a chain of triangles. During this operation the repeating circle was for the first time applied to geodesical purposes. M. Legendre and his colleagues, after connecting the two coasts, deduced a base of 8167 toises at Dunkirk from triangulation, by which the latter place was subsequently connected with Paris. This operation was performed in spite of the greatest difficulties, arising from the weather; the whole was completed in 1787, on which occasion M. Legendre visited London. During the survey above mentioned he had made two additions, one to the practical, one to the theoretical branch of the inquiry. He then first employed the method of determining the intersections of the triangles with the meridian, instead of dropping perpendiculars upon it; and he then first investigated and made use of the now well-known theorem for the substitution of a plane triangle instead of a spherical triangle of small extent, by subtracting from each angle of the latter one-third of the spherical excess.
The establishment of the superiority of the repeating-circle over the instruments then in use, and the various theorems and methods employed by M. Legendre, were of especial use in the great measurement which followed. Though he took no part in the actual details of this celebrated operation, M. Legendre, in conjunction with M. Laplace, calculated the spheroid which most nearly agreed with the whole of the observations. He was also one of the commission specially appointed for the deduction of the whole meridian and the length of the metre.
In the construction of the great trigonometrical tables, M. Legendre superintended the choice and preparation of the formule employed, and on this occasion gave some elegant theorems for the direct determination of the successive differences of sines.
M. Legendre lived through a period in which science, speculative and experimental, made almost unprecedented advances, both in extent and power; and he was himself a principal agent in the great work. As the first investigator of elliptic functions, which have since been made useful in the processes of physical astronomy, he is, as it were, the Newton of a most profound and curious branch of the integral calculus. His name must last as long as science is respected, or its applications cultivated; his private worth must be remembered as long as a contemporary who knew him is alive: and your Council, in announcing the loss which science has sustained, feel that a life of fourscore years, distinguished by more than common success, and followed by more than common reputation, renders expressions of regret superfluous.
From the year 1782 M. Legendre had turned his attention to the attraction exerted by an ellipsoid upon a point exterior to it. In 1790 he gained the prize of the Academy of Berlin for a paper on this subject. He was the first who proved that the spheroid is the only figure of equilibrium which a revolving mass of fluid can assume, under the laws which govern our system; and this both when the density is uniform and when the mass is composed of spheroidal strata of variable density. He also shewed that two spheroids about the same foci, attract an exterior point in the same direction, and with forces proportional to their masses.
The essay upon the determination of the elements of a comet's orbit, written in 1805, was the first in which the solution of that very difficult problem was attempted by all the resources of modern analysis. The method is long and intricate, but is distinguished by the power which it affords of introducing the effect of any errors in the original observations, without repeating the whole process. Some cases in which the method was found to fail, in consequence of it being necessary to determine a large quantity from a small one, induced M. Legendre to reconsider the question, and he was thus led to what has become known by the name of the method of least squares, since universally adopted, where use is to be made of discordant observations, and which has been since demonstrated by M. Laplace to give the most probable result.
In the year 1787, M. Legendre was appointed, in conjunction with MM. Méchain and Cassini, to extend the English survey, so as to connect the observatories of Greenwich and Paris by a chain of triangles. During this operation the repeating circle was for the first time applied to geodesical purposes. M. Legendre and his colleagues, after connecting the two coasts, deduced a base of 8167 toises at Dunkirk from triangulation, by which the latter place was subsequently connected with Paris. This operation was performed in spite of the greatest difficulties, arising from the weather; the whole was completed in 1787, on which occasion M. Legendre visited London. During the survey above mentioned he had made two additions, one to the practical, one to the theoretical branch of the inquiry. He then first employed the method of determining the intersections of the triangles with the meridian, instead of dropping perpendiculars upon it; and he then first investigated and made use of the now well-known theorem for the substitution of a plane triangle instead of a spherical triangle of small extent, by subtracting from each angle of the latter one-third of the spherical excess.
The establishment of the superiority of the repeating-circle over the instruments then in use, and the various theorems and methods employed by M. Legendre, were of especial use in the great measurement which followed. Though he took no part in the actual details of this celebrated operation, M. Legendre, in conjunction with M. Laplace, calculated the spheroid which most nearly agreed with the whole of the observations. He was also one of the commission specially appointed for the deduction of the whole meridian and the length of the metre.
In the construction of the great trigonometrical tables, M. Legendre superintended the choice and preparation of the formule employed, and on this occasion gave some elegant theorems for the direct determination of the successive differences of sines.
M. Legendre lived through a period in which science, speculative and experimental, made almost unprecedented advances, both in extent and power; and he was himself a principal agent in the great work. As the first investigator of elliptic functions, which have since been made useful in the processes of physical astronomy, he is, as it were, the Newton of a most profound and curious branch of the integral calculus. His name must last as long as science is respected, or its applications cultivated; his private worth must be remembered as long as a contemporary who knew him is alive: and your Council, in announcing the loss which science has sustained, feel that a life of fourscore years, distinguished by more than common success, and followed by more than common reputation, renders expressions of regret superfluous.
Adrien-Marie Legendre's obituary appeared in Journal of the Royal Astronomical Society 3:4 (1834), 24-26.