# Laplace Sentence Examples

- But the Cartesian theory, like the later speculations of Kant and
**Laplace**, proposes to give a hypothetical explanation of the circumstances and motions which in the normal course of things led to the state of things required by the law of attraction. - In preparation for these he spent the winter of 1877-1878 in reading up original treatises like those of
**Laplace**and Lagrange on mathematics and mechanics, and in attending courses on practical physics under P. G. - The application of this to telegraphic purposes was suggested by
**Laplace**and taken up by Ampere, and afterwards by Triboaillet and by Schilling, whose work forms the foundation of much of modern telegraphy. - In his Naturgeschichte des Himmels, in which he anticipated the nebular theory afterwards more fully developed by
**Laplace**, Kant sought to explain the genesis of the cosmos as a product of physical forces and laws. **Laplace**supposed the existence of a primeval nebula which extended so far out as to fill all the space at present occupied by the planets.- Considering that our sun is but a star, or but one of the millions of stars, it is of interest to see whether any other systems present indication of a nebulous origin analogous to that which
**Laplace**proposed for the solar system. **Laplace**, P. L.- Lavoisier and
**Laplace**, ante, § 1). - As the result of an examination conducted in September 1785 by
**Laplace**, Bonaparte was included among those who entered the army without going through an intermediate stage. - After serving for a short time in the artillery, he was appointed in 1797 professor of mathematics at Beauvais, and in 1800 he became professor of physics at the College de France, through the influence of
**Laplace**, from whom he had sought and obtained the favour of reading the proof sheets of the Mecanique celeste. **Laplace**is due the theoretical proof that this function is independent of temperature and pressure, and apparent experimental confirmation was provided by Biot and Arago's, and by Dulong's observations on gases and vapours.- Similarly, by putting one or more of the deleted rows or columns equal to rows or columns which are not deleted, we obtain, with
**Laplace**, a number of identities between products of determinants of complementary orders. - They remained untold, for he died two days later on the 10th of April, and was buried in the Pantheon, the funeral oration being pronounced by
**Laplace**and Lacepede. - This is especially the case between Lagrange and Euler on the one side, and between Lagrange and
**Laplace**on the other. **Laplace**owned that he had despaired of effecting the integration of the differential equations relative to secular inequalities until Lagrange showed him the way.- But
**Laplace**unquestionably surpassed his rival in practical sagacity and the intuition of physical truth. - Lagrange saw in the problems of nature so many occasions for analytical triumphs;
**Laplace**regarded analytical triumphs as the means of solving the problems of nature. - It deserves to be recorded as one of the numerous coincidences of discovery that
**Laplace**, on being made acquainted by Lagrange with his new method, produced analogous expressions, to which his independent researches had led him. - PIERRE SIMON
**LAPLACE**, MARQUIS DE (1749-1827), French mathematician and astronomer, was born at Beaumont-en-Auge in Normandy, on the 28th of March 1749. - The letters remained unnoticed, but
**Laplace**was not crushed by the rebuff. **Laplace**had not yet completed his twenty-fourth year when he entered upon the course of discovery which earned him the title of "the Newton of France."- The discordance of their results incited
**Laplace**to a searching examination of the whole subject of planetary perturbations, and his maiden effort was rewarded with a discovery which constituted, when developed and completely demonstrated by his own further labours and those of his illustrious rival Lagrange, the most important advance made in physical astronomy since the time of Newton. - Vii., 1776),
**Laplace**announced his celebrated conclusion of the invariability of planetary mean motions, carrying the proof as far as the cubes of the eccentricities and inclinations. - It was followed by a series of profound investigations, in which Lagrange and
**Laplace**alternately surpassed and supplemented each other in assigning limits of variation to the several elements of the planetary orbits. - The famous "nebular hypothesis" of
**Laplace**made its appearance in the Systeme du monde. - It is curious that
**Laplace**, while bestowing more attention than they deserved on the crude conjectures of Buffon, seems to have been unaware that he had been, to some extent, anticipated by Kant, who had put forward in 1755, in his Allgemeine Naturgeschichte, a true though defective nebular cosmogony. - The career of
**Laplace**was one of scarcely interrupted prosperity. - During the later years of his life,
**Laplace**lived much at Arcueil, where he had a country-place adjoining that of his friend C. L. - Biot relates that, when he himself was beginning his career,
**Laplace**introduced him at the Institute for the purpose of explaining his supposed discovery of equations of mixed differences, and afterwards showed him, under a strict pledge of secrecy, the papers, then yellow with age, in which he had long before obtained the same results. - With Lagrange, on the other hand, he always remained on the best of terms.
**Laplace**left a son, Charles Emile Pierre Joseph**Laplace**(1789-1874), who succeeded to his title, and rose to the rank of general in the artillery. - It might be said that
**Laplace**was a great mathematician by the original structure of his mind, and became a great discoverer through the sentiment which animated it. **Laplace**was, moreover, the first to offer a complete analysis of capillary action based upon a definite hypothesis - that of forces "sensible only at insensible distances"; and he made strenuous but unsuccessful efforts to explain the phenomena of light on an identical principle.**Laplace**treated the subject from the point of view of the gradual aggregation and cooling of a mass of matter, and demonstrated that the form which such a mass would ultimately assume must be an ellipsoid of revolution whose equator was determined by the primitive plane of maximum areas.- Legendre, in 1783, extended Maclaurin's theorem concerning ellipsoids of revolution to the case of any spheroid of revolution where the attracted point, instead of being limited to the axis or equator, occupied any position in space; and
**Laplace**, in his treatise Theorie du mouvement et de la figure elliptique des planetes (published in 1784), effected a still further generalization by proving, what had been suspected by Legendre, that the theorem was equally true for any confocal ellipsoids. - Finally, in a celebrated memoir, Theorie des attractions des spheroides et de la figure des planetes, published in 1785 among the Paris Memoirs for the year 1782, although written after the treatise of 1784,
**Laplace**treated exhaustively the general problem of the attraction of any spheroid upon a particle situated outside or upon its surface. - By his discovery that the attracting force in any direction of a mass upon a particle could be obtained by the direct process of differentiating a single function,
**Laplace**laid the foundations of the mathematical sciences of heat, electricity and magnetism. **Laplace**nowhere displayed the massiveness of his genius more conspicuously than in the theory of probabilities.- The theory of probabilities, which
**Laplace**described as common sense expressed in mathematical language, engaged his attention from its importance in physics and astronomy; and he applied his theory, not only to the ordinary problems of chances, but also to the inquiry into the causes of phenomena, vital statistics and future events. - The device known as the method of least squares, for reducing numerous equations of condition to the number of unknown quantities to be determined, had been adopted as a practically convenient rule by Gauss and Legendre; but
**Laplace**first treated it as a problem in probabilities, and proved by an intricate and difficult course of reasoning that it was also the most advantageous, the mean of the probabilities of error in the determination of the elements being thereby reduced to a minimum. **Laplace**published in 1779 the method of generating functions, the foundation of his theory of probabilities, and the first part of his Theorie analytique is devoted to the exposition of its principles, which in their simplest form consist in treating the successive values of any function as the coefficients in the expansion of another function with reference to a different variable.- The first formal proof of Lagrange's theorem for the development in a series of an implicit function was furnished by
**Laplace**, who gave to it an extended generality. - In 1842, the works of
**Laplace**being nearly out of print, his widow was about to sell a farm to procure funds for a new impression, when the government of Louis Philippe took the matter in hand. - A grant of 40,000 francs having been obtained from the chamber, a national edition was issued in seven 4to vols., bearing the title Ouvres de
**Laplace**(1843-1847). - An edition entitled Les Ouvres completes de
**Laplace**(1878), &c., which is to include all his memoirs as well as his separate works, is in course of publication under the auspices of the Academy of Sciences. - Meanwhile the astronomical theories of development of the solar system from a gaseous condition to its present form, put forward by Kant and by
**Laplace**, had impressed men's minds with the conception of a general movement of spontaneous progress or development in all nature. - Thus he carried on the narrative of orderly development from the point at which it was left by Kant and
**Laplace**- explaining by reference to the ascertained laws of physics and chemistry the configuration of the earth, its mountains and seas, its igneous and its stratified rocks, just as the astronomers had explained by those same laws the evolution of the sun and planets from diffused gaseous matter of high temperature. - In 1826 Fourier became a member of the French Academy, and in 1827 succeeded
**Laplace**as president of the council of the Ecole Polytechnique. - P. 211, Paris, 1869) proposed an equation of the form (p+po)(v - b) =RO, in which the effect of the size of the molecules is represented by subtracting a quantity b, the " covolume," from the volume occupied by the gas, and the effect of the mutual attractions of the molecules is represented by adding a quantity po, the internal pressure, to the external pressure, p. This type of equation, was more fully worked out by van der Waals, who identified the internal pressure, po, with the capillary pressure of
**Laplace**, and assumed that it varied directly as the square of the density, and could be written a/v 2 . - Its coefficient of expansion for each degree between o° and Ioo C. is 0.000014661, or for gold which has been annealed 0.000015136 (
**Laplace**and Lavoisier). - 1875); Examples of Analytical Geometry of Three Dimensions (1858, 3rd ed., 1873); Mechanics (1867), History of the Mathematical Theory of Probability from the Time of Pascal to that of Lagrange (1865); Researches in the Calculus of Variations (1871); History of the Mathematical Theories of Attraction and Figure of the Earth from Newton to
**Laplace**(1873); Elementary Treatise on**Laplace's**, Lame's and Bessel's Functions (1875); Natural Philosophy for Beginners (1877). - Newton found 979 ft./sec. But, as we shall see, all the determinations give a value of Uo in the neighbourhood of 33, 000 cm./sec., or about 1080 ft./sec. This discrepancy e was not explained till 1816, when
**Laplace**(Ann. **Laplace**; though even here it appeared, in the hands of Young, and in complete fulness afterwards in those of C. F.- In this memoir also the function which is now called the potential was, at the suggestion of
**Laplace**, first introduced. - During forty years the resources of analysis, even in the hands of d'Alembert, Lagrange and
**Laplace**, had not carried the theory of the attraction of ellipsoids beyond the point which the geometry of Maclaurin had reached. **Laplace**also justified the method by means of the principles of the theory of probability; and this led Legendre to republish the part of his Nouvelles Methodes which related to it in the Memoires de l'Academie for 1810.- Late in 1793, Bailly quitted Nantes to join his friend Pierre Simon
**Laplace**at Melun; but was there recognized, arrested and brought (November 10) before the Revolutionary Tribunal at Paris. - The chemistry of Lavoisier, the zoology of Lamarck, the astronomy of
**Laplace**and the geology of Lyell. - He not only agrees with
**Laplace**and Lyell about the evolution of the solar system, but also supposes that the affinities, pointed out by Lothar Meyer and Mendeleeff, between groups of chemical elements prove an evolution of these elements from a primitive matter (prothyl) consisting of homogeneous atoms. These, however, are not ultimate enough for him; he thinks that everything, ponderable and imponderable or ether, is evolved from a primitive substance, which condenses first into centres of condensation (pyknatoms), and then into masses, which when they exceed the mean consistency become ponderables, and when they fall below it become imponderables. - Pursuing the investigations of
**Laplace**, he demonstrated with greater rigour the stability of the solar system, and calculated the limits within which the eccentricities and inclinations of the planetary orbits vary.