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Recherches 1.o. sur l'intégration des Équations différentielles aux différences finies, & sur leur usage dans la théorie des hasards. 2.o. sur le principe de la Gravitation universelle, & sur les inégalités séculaires des Planètes qui en dépendent.


(Paris, Imprimerie Royale, 1776). 4to. Extract from "Mémoires de Mathematique et de Physique, Présentés à l'Academie des Sciences par divers Savans", Année 1773. Pp. 37-232. a. 1 folded engraved plate. Clean and fine.

First printing of Laplace's famous double-memoir in which he made a coupling of probability theory with astronomy. The first memoir here is his third memoir on probability, a follow-up of his groundbreaking paper "Mémoire sur la Probabilité des Causes par les Évènemens" from the same year; the main portion of the paper deals with the theory of chances. He solves different problems, that of odd and even, a solid has p equal faces, which are numbered 2,2,....p: required the probability that in the course of n throws the faces will occur in the order of 1,2,...p., a complicate problem arising with more players, the Problem of Points in the case of two players and with 3 players, on Duration and Play..."The present memoir may be regarded as a collection of examples in the history of Finite Differences"(Todhunter).The second memoir constitutes Laplace's "FIRST COMPREHENSIVE PIECE ON THE MECHANICS OF THE SOLAR SYSTEM", and his theory of the gravitational force. His modifications of Newton's laws set forth here, became the foundation for his developed celestial mechanics."A close reading of the astronomical part of the dual memoir, Laplace’s first comprehensive piece on the mechanics of the solar system, serves to temper the conventional image of a vindicator of Newton’s law of gravity against the evidence for decay of motion in the planets. Nothing is said about apparent anomalies gathering toward a cosmic catastrophe;on the contrary, the state of the universe is assumed to be steady. The problem is not whether the phenomena can be deduced from the law of universal gravity, but how to do it. Since that appeared to be impossible on a strict Newtonian construction of the evidence, Laplace proposed modifying the law of gravity slightly. He proceeded to try out the notion that gravity is a force propagated in time instead of instantaneously. Its quantity at a given point would then depend on the velocity of bodies as well as on their mass and distance. Even more interesting, the reasoning in this argument was not that of normal ,mathematical astronomy but was of the type that he brought to physics in other, much later writings. Lastly, in a problem that he did handle in the tradition of theoretical astronomy, namely in the secular variations in the mean motions of Jupiter and Saturn, the conclusion is that the mutual attraction of the plants cannot account for them, contrary to what we expect from Mécanique céleste."(DSB).

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