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Simeon Denis Poisson (born June 21, 1781, died April 25, 1840) was placed, by common consent, at the head of European analysts on the death of Laplace. He was of humble birth, and was admitted in 1793 a student of the Ecole Polytechnique, then newly established. It is stated, by the historian of this school, that, at the age of eighteen, he submitted to his professor some ameliorations in the method of demonstrating the binomial theorem; which that teacher, who was no other than Lagrange, read publicly at his next lecture, and which he declared his intention of adopting in future.
The life of Poisson was one of quiet and uninterrupted study. He never held any situation connected with politics, nor was in any way, during thirty years, prevented from pursuing his one great object, the application of the most abstruse and newest developements of the integral calculus to problems of physics. The number of his memoirs is enormous; to which must be added his elementary treatise on mechanics (which stands at the head of all elementary writings on the application of pure analysis to the properties of matter), his treatises on capillary attraction, on heat, and on the theory of probabilities.
It is well known that the energies of Euler, Clairaut, D'Alembert, and the younger Bernoullis, had organised the application of mathematics in a manner which made the subsequent triumphs of Lagrange and Laplace seem almost beyond expectation. The power of the pure mathematics seemed to flag, when Fourier first came forward with his applications of definite integrals and periodic series to questions of physics, which seemed to be unconquerable, and of which the difficulties seemed to be altogether inexpressible, by ordinary analysis. A new school of mathematicians was rapidly formed, in whose hands the mode of expression by definite integrals added one more to the instances in which the happy enunciation of questions was all but their solution. Poisson was one of the first of this school in point of time, and by far the greatest in power. Throughout the major part of his writings we trace the same capability of explaining the most abstruse points with fluent clearness and rigid accuracy, combined with that of conquering the physical difficulties of his problem by the most happy art of adaptation.
Many of his memoirs are on the great questions of physical astronomy, and it is here that he shews that he was not the accident of a fortunate epoch, but that he could handle the instruments of his two great predecessors with skill resembling their own. Perhaps his greatest achievement in this line is the extension of our knowledge respecting the stability of the solar system, as far as it may be affected by perturbations of the mean orbital motions, or of the axical rotations. This question does not, as many imagine, owe all its interest either to the predictive power which is sought, or to the grandeur of the problem considered as the path to such a power. It is to be remembered that the connecting constants between the oldest and most recent astronomy are the lengths of the sidereal year and of the day; and that we cannot assume to talk a common language with Hipparchus and Ptolemy, unless we have reason to know that these elements continue sensibly unaltered. In addition to the imperfect presumptions derived from observation (imperfect on account of the large liability to error of the older astronomers) Lagrange had shewn that the mean motions have no secular inequalities depending on the first power of the disturbing forces; or, so far as this first power was concerned, or any powers of the eccentricities or inclinations. Laplace had shewn that a certain secular equation, which should in theory be applied to the sidereal day, would always be too small to be of any importance. Poisson extended the conclusions of Lagrange to the second power of the disturbing forces, and, relatively, to any powers of the eccentricities and inclinations; or rather, we may say, that he shewed any secular equation of the mean motions to depend only on the fourth power of disturbing forces: for, in the course of the investigation, it appears that no such equation of any odd order can exist. As far as the fourth powers of eccentricities and inclinations, he actually shews the mutual destruction of an infinite number of non-periodic disturbing terms; the rest of the powers are completed by a general and different investigation. In the problem of the rotation of the earth, he generalises the investigation of Laplace, by taking into consideration the actual change of the axis on the earth; the former investigation considering only the change of the axis, supposed to be fixed in the earth, relatively to the stars. The result agrees with that of Laplace as to the non-existence of any sensible secular inequality.
Poisson belongs to a class of investigators of whom many are always wanted, but one is permanently indispensable.
The life of Poisson was one of quiet and uninterrupted study. He never held any situation connected with politics, nor was in any way, during thirty years, prevented from pursuing his one great object, the application of the most abstruse and newest developements of the integral calculus to problems of physics. The number of his memoirs is enormous; to which must be added his elementary treatise on mechanics (which stands at the head of all elementary writings on the application of pure analysis to the properties of matter), his treatises on capillary attraction, on heat, and on the theory of probabilities.
It is well known that the energies of Euler, Clairaut, D'Alembert, and the younger Bernoullis, had organised the application of mathematics in a manner which made the subsequent triumphs of Lagrange and Laplace seem almost beyond expectation. The power of the pure mathematics seemed to flag, when Fourier first came forward with his applications of definite integrals and periodic series to questions of physics, which seemed to be unconquerable, and of which the difficulties seemed to be altogether inexpressible, by ordinary analysis. A new school of mathematicians was rapidly formed, in whose hands the mode of expression by definite integrals added one more to the instances in which the happy enunciation of questions was all but their solution. Poisson was one of the first of this school in point of time, and by far the greatest in power. Throughout the major part of his writings we trace the same capability of explaining the most abstruse points with fluent clearness and rigid accuracy, combined with that of conquering the physical difficulties of his problem by the most happy art of adaptation.
Many of his memoirs are on the great questions of physical astronomy, and it is here that he shews that he was not the accident of a fortunate epoch, but that he could handle the instruments of his two great predecessors with skill resembling their own. Perhaps his greatest achievement in this line is the extension of our knowledge respecting the stability of the solar system, as far as it may be affected by perturbations of the mean orbital motions, or of the axical rotations. This question does not, as many imagine, owe all its interest either to the predictive power which is sought, or to the grandeur of the problem considered as the path to such a power. It is to be remembered that the connecting constants between the oldest and most recent astronomy are the lengths of the sidereal year and of the day; and that we cannot assume to talk a common language with Hipparchus and Ptolemy, unless we have reason to know that these elements continue sensibly unaltered. In addition to the imperfect presumptions derived from observation (imperfect on account of the large liability to error of the older astronomers) Lagrange had shewn that the mean motions have no secular inequalities depending on the first power of the disturbing forces; or, so far as this first power was concerned, or any powers of the eccentricities or inclinations. Laplace had shewn that a certain secular equation, which should in theory be applied to the sidereal day, would always be too small to be of any importance. Poisson extended the conclusions of Lagrange to the second power of the disturbing forces, and, relatively, to any powers of the eccentricities and inclinations; or rather, we may say, that he shewed any secular equation of the mean motions to depend only on the fourth power of disturbing forces: for, in the course of the investigation, it appears that no such equation of any odd order can exist. As far as the fourth powers of eccentricities and inclinations, he actually shews the mutual destruction of an infinite number of non-periodic disturbing terms; the rest of the powers are completed by a general and different investigation. In the problem of the rotation of the earth, he generalises the investigation of Laplace, by taking into consideration the actual change of the axis on the earth; the former investigation considering only the change of the axis, supposed to be fixed in the earth, relatively to the stars. The result agrees with that of Laplace as to the non-existence of any sensible secular inequality.
Poisson belongs to a class of investigators of whom many are always wanted, but one is permanently indispensable.
Siméon Denis Poisson's obituary appeared in Journal of the Royal Astronomical Society 5:1 (1841), 84-86.