He published eight folio volumes of Greenwich Observations, translated Laplace's Systeme du monde (in 2 vols.
As notable instances may be mentioned Laplace's discoveries relating to the velocity of sound and the secular acceleration of the moon, both of which were led close up to by Lagrange's analytical demonstrations.
The year 1787 was rendered further memorable by Laplace's announcement on the 19th of November (Memoirs, 1786), of the dependence of lunar acceleration upon the secular changes in the eccentricity of the earth's orbit.
With these brilliant performances the first period of Laplace's scientific career may be said to have closed.
To this task the second period of Laplace's activity was devoted.
4to, Paris, 1799) contains methods for calculating the movements of translation and rotation of the heavenly bodies, for determining their figures, and resolving tidal problems; the second, especially dedicated to the improvement of tables, exhibits in the third and fourth volumes (1802 and 1805) the application of these formulae; while a fifth volume, published in three instalments, 1823-1825, comprises the results of Laplace's latest researches, together with a valuable history of progress in each separate branch of his subject.
Expressions occur in Laplace's private letters inconsistent 3 Mee.
This instance of abnegation is the more worthy of record that it formed a marked exception to Laplace's usual course.
These researches derive additional importance from having introduced two powerful engines of analysis for the treatment of physical problems, Laplace's coefficients and the potential function.
The expressions designated by Dr Whewell, Laplace's coefficients (see Spherical Harmonics) were definitely introduced in the memoir of 1785 on attractions above referred to.
An enumeration of Laplace's memoirs and papers (about one hundred in number) is rendered superfluous by their embodiment in his principal works.
Laplace's first separate work, Theorie du mouvement et de la figure elliptique des planetes (1784), was published at the expense of President Bochard de Saron.
Some of Laplace's results in the theory of probabilities are simplified in S.
Laplace's treatise on specific heat was published in German in 1892 as No.
Sary to satisfy Laplace's equation is also one which makes the potential energy a minimum and therefore the energy stable.
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).
That is to say, instead of using Boyle's law, which supposes that the pressure changes so exceedingly slowly that conduction keeps the temperature constant, we must use the adiabatic relation p = kpy, whence d p /d p = y k p Y 1= yp/p, and U = (yp/p) [Laplace's formula].
In the first of these, entitled " Recherches sur l'attraction des spheroides homogenes," published in the Memoires of the Academy for 1785, but communicated to it at an earlier period, Legendre introduces the celebrated expressions which, though frequently called Laplace's coefficients, are more correctly named after Legendre.
The introduction of the coefficients now called Laplace's, and their application, commence a new era in mathematical physics."
The third memoir relates to Laplace's theorem respecting confocal ellipsoids.
For the first time we have a correct and convenient expression for Laplace's nth coefficient."
His well-known correction of Laplace's partial differential equation for the potential was first published in the Bulletin de la societe philomatique (1813).
In the theory of surfaces, in hydrokinetics, heat-conduction, potentials, &c., we constantly meet with what is called " Laplace's operator," viz.
And we now see that the square of V is the negative of Laplace's operator; while V itself, when applied to any numerical quantity conceived as having a definite value at each point of space, gives the direction and the rate of most rapid change of that quantity.
Leslie's theory was afterwards treated according to Laplace's mathematical methods by James Ivory in the article on capillary action, under "Fluids, Elevation of," in the supplement to the fourth edition of the Encyclopaedia Britannica, published in 1819.
He proceeded to an investigation of the equilibrium of a fluid on the hypothesis of uniform density, and arrived at the conclusion that on this hypothesis none of the observed capillary phenomena would take place, and that, therefore, Laplace's theory, in which the density is supposed uniform, is not only insufficient but erroneous.
In particular he maintained that the constant pressure K, which occurs in Laplace's theory, and which on that theory is very large, must be in point of fact very small, but the equation of equilibrium from which he concluded this is itself defective.
Hence we may write p = P +Ap2, where A is a constant [equal to Laplace's intrinsic pressure K.
The expression for the intrinsic pressure is thus simply K= 2 iro 2 f 1,G(z)dz (28) In Laplace's investigation o- is supposed to be unity.
From this consideration we may derive Laplace's expression, as has been done by Dupre (Theorie mecanique de la chaleur, Paris, 1869), and Kelvin (" Capillary Attraction," Proc. Roy.
Since 0(o) is finite, proportional to K, the integrated term vanishes at both limits, and we have simply f 0(z)dz f: (z)dz, (34) and T= ref: z1,1,(z)dz (35) In Laplace's notation the second member of (34), multiplied by 27r, is represented by H.
For further calculations on Laplace's principles, see Rayleigh, Phil.
(" Laplace's Theory of Capillarity," Rayleigh, Phil.
Mag., 1883, P. 315) According to Laplace's hypothesis the whole energy of any number of contiguous strata of liquids is least when they are arranged in order of density, so that this is the disposition favoured by the attractive forces.
So far the results of Laplace's hypothesis are in marked accordance with experiment; but if we follow it out further, discordances begin to manifestthemselves.
Laplace's mathematical theory of the form of Saturn's rings.