Pierre-Simon, marquis de Laplace (; ; 23 March 1749 – 5 March 1827) was a French

scholar A scholar is a person who pursues academic and intellectual activities, particularly academics who apply their intellectualism into expertise in an area of study. A scholar can also be an academic, who works as a professor, teacher, or researc ...

and

polymath A polymath ( el, πολυμαθής, , "having learned much"; la, homo universalis, "universal human") is an individual whose knowledge spans a substantial number of subjects, known to draw on complex bodies of knowledge to solve specific pro ...

whose work was important to the development of

engineering Engineering is the use of scientific method, scientific principles to design and build machines, structures, and other items, including bridges, tunnels, roads, vehicles, and buildings. The discipline of engineering encompasses a broad rang ...

mathematics Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ...

statistics Statistics (from German language, German: ''wikt:Statistik#German, Statistik'', "description of a State (polity), state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of ...

physics Physics is the natural science that studies matter, its fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge which r ...

astronomy Astronomy () is a natural science that studies astronomical object, celestial objects and phenomena. It uses mathematics, physics, and chemistry in order to explain their origin and chronology of the Universe, evolution. Objects of interest ...

, and

philosophy Philosophy (from , ) is the systematized study of general and fundamental questions, such as those about existence, reason, knowledge, values, mind, and language. Such questions are often posed as problems to be studied or resolved. Some ...

. He summarized and extended the work of his predecessors in his five-volume ''Mécanique céleste'' (''

Celestial Mechanics Celestial mechanics is the branch of astronomy that deals with the motions of objects in outer space. Historically, celestial mechanics applies principles of physics (classical mechanics) to astronomical objects, such as stars and planets, to ...

'') (1799–1825). This work translated the geometric study of

classical mechanics Classical mechanics is a physical theory describing the motion of macroscopic objects, from projectiles to parts of machinery, and astronomical objects, such as spacecraft, planets, stars, and galaxies. For objects governed by classical ...

to one based on

calculus Calculus, originally called infinitesimal calculus or "the calculus of infinitesimals", is the mathematical study of continuous change, in the same way that geometry is the study of shape, and algebra is the study of generalizations of arithm ...

, opening up a broader range of problems. In statistics, the Bayesian interpretation of probability was developed mainly by Laplace. Laplace formulated Laplace's equation, and pioneered the

Laplace transform In mathematics, the Laplace transform, named after its discoverer Pierre-Simon Laplace (), is an integral transform In mathematics, an integral transform maps a function from its original function space into another function space via integra ...

which appears in many branches of

mathematical physics Mathematical physics refers to the development of mathematics, mathematical methods for application to problems in physics. The ''Journal of Mathematical Physics'' defines the field as "the application of mathematics to problems in physics and t ...

, a field that he took a leading role in forming. The Laplacian differential operator, widely used in mathematics, is also named after him. He restated and developed the

nebular hypothesis The nebular hypothesis is the most widely accepted model in the field of cosmogony to explain the formation and evolution of the Solar System (as well as other planetary systems). It suggests the Solar System is formed from gas and dust orbitin ...

of the origin of the Solar System and was one of the first scientists to suggest an idea similar to that of a black hole. Laplace is regarded as one of the greatest scientists of all time. Sometimes referred to as the ''French Newton'' or ''Newton of France'', he has been described as possessing a phenomenal natural mathematical faculty superior to that of almost all of his contemporaries. He was Napoleon's examiner when

Napoleon Napoleon Bonaparte ; it, Napoleone Bonaparte, ; co, Napulione Buonaparte. (born Napoleone Buonaparte; 15 August 1769 – 5 May 1821), later known by his regnal name Napoleon I, was a French military commander and political leader who ...

attended the ''

École Militaire École may refer to: * an elementary school in the French educational stages normally followed by secondary education establishments (collège and lycée) * École (river), a tributary of the Seine flowing in région Île-de-France * École, Savo ...

'' in Paris in 1784. Laplace became a count of the

Empire An empire is a "political unit" made up of several territories and peoples, "usually created by conquest, and divided between a dominant center and subordinate peripheries". The center of the empire (sometimes referred to as the metropole) ex ...

in 1806 and was named a marquis in 1817, after the Bourbon Restoration.

Early years

Pierre-Simon de Laplace by Johann Ernst Heinsius (1775)

Some details of Laplace's life are not known, as records of it were burned in 1925 with the family

château A château (; plural: châteaux) is a manor house or residence of the lord of the manor, or a fine country house of nobility or gentry, with or without fortifications, originally, and still most frequently, in French-speaking regions. Nowaday ...

in Saint Julien de Mailloc, near

Lisieux Lisieux () is a commune in the Calvados department in the Normandy region in northwestern France. It is the capital of the Pays d'Auge area, which is characterised by valleys and hedged farmland. Name The name of the town derives from the ...

, the home of his great-great-grandson the Comte de Colbert-Laplace. Others had been destroyed earlier, when his house at

Arcueil Arcueil () is a commune in the Val-de-Marne department in the southern suburbs of Paris, France. It is located from the center of Paris. Name The name Arcueil was recorded for the first time in 1119 as ''Arcoloï'', and later in the 12th ...

near Paris was looted in 1871."Laplace, being Extracts from Lectures delivered by Karl Pearson", '' Biometrika'', vol. 21, December 1929, pp. 202–216. Laplace was born in

Beaumont-en-Auge Beaumont-en-Auge (, literally ''Beaumont in Auge'') is a commune in the Calvados department in the Normandy region in northwestern France. The town hosts one of the last kaleidoscope manufacturers in France. Population Personalities *Pierre-S ...

, Normandy on 23 March 1749, a village four miles west of Pont l'Évêque. According to

W. W. Rouse Ball Walter William Rouse Ball (14 August 1850 – 4 April 1925), known as W. W. Rouse Ball, was a British mathematician, lawyer, and fellow at Trinity College, Cambridge, from 1878 to 1905. He was also a keen amateur magician, and the founding ...

, his father, Pierre de Laplace, owned and farmed the small estates of Maarquis. His great-uncle, Maitre Oliver de Laplace, had held the title of Chirurgien Royal. It would seem that from a pupil he became an usher in the school at Beaumont; but, having procured a letter of introduction to

d'Alembert Jean-Baptiste le Rond d'Alembert (; ; 16 November 1717 – 29 October 1783) was a French mathematician, mechanician, physicist, philosopher, and music theorist. Until 1759 he was, together with Denis Diderot, a co-editor of the '' Encyclopé ...

, he went to Paris to advance his fortune. However, Karl Pearson is scathing about the inaccuracies in Rouse Ball's account and states: His parents, Pierre Laplace and Marie-Anne Sochon, were from comfortable families. The Laplace family was involved in agriculture until at least 1750, but Pierre Laplace senior was also a

cider Cider ( ) is an alcoholic beverage made from the fermented juice of apples. Cider is widely available in the United Kingdom (particularly in the West Country) and the Republic of Ireland. The UK has the world's highest per capita consumption, ...

merchant and '' syndic'' of the town of Beaumont. Pierre Simon Laplace attended a school in the village run at a

Benedictine , image = Medalla San Benito.PNG , caption = Design on the obverse side of the Saint Benedict Medal , abbreviation = OSB , formation = , motto = (English: 'Pray and Work') , foun ...

priory A priory is a monastery of men or women under religious vows that is headed by a prior or prioress. Priories may be houses of mendicant friars or nuns (such as the Dominicans, Augustinians, Franciscans, and Carmelites), or monasteries of ...

, his father intending that he be ordained in the

Roman Catholic Church The Catholic Church, also known as the Roman Catholic Church, is the largest Christian church, with 1.3 billion baptized Catholics worldwide . It is among the world's oldest and largest international institutions, and has played a ...

. At sixteen, to further his father's intention, he was sent to the

University of Caen The University of Caen Normandy (French: ''Université de Caen Normandie''), also known as Unicaen, is a public university in Caen, France. History The institution was founded in 1432 by John of Lancaster, 1st Duke of Bedford, the first rector ...

to read theology.*. Retrieved 25 August 2007 At the university, he was mentored by two enthusiastic teachers of mathematics,

Christophe Gadbled Christophe Gadbled (1734 – 11 October 1782) was a mathematics professor at the University of Caen. Gadbled was born in Saint-Martin-le-Bouillant. He is known to have been the mentor of Pierre-Simon Laplace Pierre-Simon, marquis de Laplace ...

and Pierre Le Canu, who awoke his zeal for the subject. Here Laplace's brilliance as a mathematician was quickly recognised and while still at Caen he wrote a memoir ''Sur le Calcul integral aux differences infiniment petites et aux differences finies''. This provided the first intercourse between Laplace and Lagrange. Lagrange was the senior by thirteen years, and had recently founded in his native city

Turin Turin ( , Piedmontese language, Piedmontese: ; it, Torino ) is a city and an important business and cultural centre in Northern Italy. It is the capital city of Piedmont and of the Metropolitan City of Turin, and was the first Italian capital ...

a journal named ''Miscellanea Taurinensia'', in which many of his early works were printed and it was in the fourth volume of this series that Laplace's paper appeared. About this time, recognising that he had no vocation for the priesthood, he resolved to become a professional mathematician. Some sources state that he then broke with the church and became an atheist. Laplace did not graduate in theology but left for Paris with a letter of introduction from Le Canu to

Jean le Rond d'Alembert Jean-Baptiste le Rond d'Alembert (; ; 16 November 1717 – 29 October 1783) was a French mathematician, mechanician, physicist, philosopher, and music theorist. Until 1759 he was, together with Denis Diderot, a co-editor of the '' Encyclopéd ...

who at that time was supreme in scientific circles. According to his great-great-grandson, d'Alembert received him rather poorly, and to get rid of him gave him a thick mathematics book, saying to come back when he had read it. When Laplace came back a few days later, d'Alembert was even less friendly and did not hide his opinion that it was impossible that Laplace could have read and understood the book. But upon questioning him, he realised that it was true, and from that time he took Laplace under his care. Another account is that Laplace solved overnight a problem that d'Alembert set him for submission the following week, then solved a harder problem the following night. D'Alembert was impressed and recommended him for a teaching place in the ''

''.Gillispie (1997), pp. 3–4 With a secure income and undemanding teaching, Laplace now threw himself into original research and for the next seventeen years, 1771–1787, he produced much of his original work in astronomy.Rouse Ball (1908). Calorimeter of Lavoisier and La Place plate xi the s1784m49j 3f462600t dl full size

Calorimeter of Lavoisier and La Place plate xi the s1784m49j 3f462600t dl full size

From 1780 to 1784, Laplace and French chemist

Antoine Lavoisier Antoine-Laurent de Lavoisier ( , ; ; 26 August 17438 May 1794), When reduced without charcoal, it gave off an air which supported respiration and combustion in an enhanced way. He concluded that this was just a pure form of common air and th ...

collaborated on several experimental investigations, designing their own equipment for the task. In 1783 they published their joint paper, ''Memoir on Heat'', in which they discussed the kinetic theory of molecular motion. In their experiments they measured the

specific heat In thermodynamics, the specific heat capacity (symbol ) of a substance is the heat capacity of a sample of the substance divided by the mass of the sample, also sometimes referred to as massic heat capacity. Informally, it is the amount of heat t ...

of various bodies, and the expansion of metals with increasing temperature. They also measured the boiling points of

ethanol Ethanol (abbr. EtOH; also called ethyl alcohol, grain alcohol, drinking alcohol, or simply alcohol) is an organic compound. It is an Alcohol (chemistry), alcohol with the chemical formula . Its formula can be also written as or (an ethyl ...

and

ether In organic chemistry, ethers are a class of compounds that contain an ether group—an oxygen atom connected to two alkyl or aryl groups. They have the general formula , where R and R′ represent the alkyl or aryl groups. Ethers can again be c ...

under pressure. Laplace further impressed the Marquis de Condorcet, and already by 1771 Laplace felt entitled to membership in the French Academy of Sciences. However, that year admission went to

Alexandre-Théophile Vandermonde Alexandre-Théophile Vandermonde (28 February 1735 – 1 January 1796) was a French mathematician, musician and chemist who worked with Bézout and Lavoisier; his name is now principally associated with determinant theory in mathematics. He was b ...

and in 1772 to Jacques Antoine Joseph Cousin. Laplace was disgruntled, and early in 1773 d'Alembert wrote to Lagrange in Berlin to ask if a position could be found for Laplace there. However, Condorcet became permanent secretary of the ''Académie'' in February and Laplace was elected associate member on 31 March, at age 24.Gillispie (1997), p. 5 In 1773 Laplace read his paper on the invariability of planetary motion in front of the Academy des Sciences. That March he was elected to the academy, a place where he conducted the majority of his science. On 15 March 1788, at the age of thirty-nine, Laplace married Marie-Charlotte de Courty de Romanges, an eighteen-year-old girl from a "good" family in

Besançon Besançon (, , , ; archaic german: Bisanz; la, Vesontio) is the prefecture of the department of Doubs in the region of Bourgogne-Franche-Comté. The city is located in Eastern France, close to the Jura Mountains and the border with Switzer ...

. The wedding was celebrated at

Saint-Sulpice, Paris , image = Paris Saint-Sulpice Fassade 4-5 A.jpg , image_size = , pushpin map = Paris , pushpin label position = , coordinates = , location = Place Saint-Sulpice 6th arrond ...

. The couple had a son, Charles-Émile (1789–1874), and a daughter, Sophie-Suzanne (1792–1813).

Analysis, probability, and astronomical stability

Laplace's early published work in 1771 started with differential equations and

finite differences A finite difference is a mathematical expression of the form . If a finite difference is divided by , one gets a difference quotient. The approximation of derivatives by finite differences plays a central role in finite difference methods for the ...

but he was already starting to think about the mathematical and philosophical concepts of probability and statistics.Gillispie (1989), pp. 7–12 However, before his election to the ''Académie'' in 1773, he had already drafted two papers that would establish his reputation. The first, ''Mémoire sur la probabilité des causes par les événements'' was ultimately published in 1774 while the second paper, published in 1776, further elaborated his statistical thinking and also began his systematic work on

celestial mechanics Celestial mechanics is the branch of astronomy that deals with the motions of objects in outer space. Historically, celestial mechanics applies principles of physics (classical mechanics) to astronomical objects, such as stars and planets, to ...

and the stability of the

Solar System The Solar SystemCapitalization of the name varies. The International Astronomical Union, the authoritative body regarding astronomical nomenclature, specifies capitalizing the names of all individual astronomical objects but uses mixed "Solar S ...

. The two disciplines would always be interlinked in his mind. "Laplace took probability as an instrument for repairing defects in knowledge."Gillispie (1989). pp. 14–15 Laplace's work on probability and statistics is discussed below with his mature work on the analytic theory of probabilities.

Stability of the Solar System

Sir

Isaac Newton Sir Isaac Newton (25 December 1642 – 20 March 1726/27) was an English mathematician, physicist, astronomer, alchemist, theologian, and author (described in his time as a "natural philosopher"), widely recognised as one of the grea ...

had published his '' Philosophiae Naturalis Principia Mathematica'' in 1687 in which he gave a derivation of

Kepler's laws In astronomy, Kepler's laws of planetary motion, published by Johannes Kepler between 1609 and 1619, describe the orbits of planets around the Sun. The laws modified the heliocentric theory of Nicolaus Copernicus, replacing its circular orbi ...

, which describe the motion of the planets, from his laws of motion and his law of universal gravitation. However, though Newton had privately developed the methods of calculus, all his published work used cumbersome geometric reasoning, unsuitable to account for the more subtle higher-order effects of interactions between the planets. Newton himself had doubted the possibility of a mathematical solution to the whole, even concluding that periodic

divine intervention Divine intervention is an event that occurs when a deity (i.e. God or a god) becomes actively involved in changing some situation in human affairs. In contrast to other kinds of divine action, the expression "divine ''intervention''" implies that ...

was necessary to guarantee the stability of the Solar System. Dispensing with the hypothesis of divine intervention would be a major activity of Laplace's scientific life.Whitrow (2001) It is now generally regarded that Laplace's methods on their own, though vital to the development of the theory, are not sufficiently precise to demonstrate the

stability of the Solar System The stability of the Solar System is a subject of much inquiry in astronomy. Though the planets have been stable when historically observed, and will be in the short term, their weak gravitational effects on one another can add up in unpredictable ...

, and indeed, the Solar System is understood to be

chaotic Chaotic was originally a Danish trading card game. It expanded to an online game in America which then became a television program based on the game. The program was able to be seen on 4Kids TV (Fox affiliates, nationwide), Jetix, The CW4Kid ...

, although it happens to be fairly stable. One particular problem from

observational astronomy Observational astronomy is a division of astronomy that is concerned with recording data about the observable universe, in contrast with theoretical astronomy, which is mainly concerned with calculating the measurable implications of physical ...

was the apparent instability whereby Jupiter's orbit appeared to be shrinking while that of Saturn was expanding. The problem had been tackled by

Leonhard Euler Leonhard Euler ( , ; 15 April 170718 September 1783) was a Swiss mathematician, physicist, astronomer, geographer, logician and engineer who founded the studies of graph theory and topology and made pioneering and influential discoveries in ma ...

in 1748 and

Joseph Louis Lagrange Joseph-Louis Lagrange (born Giuseppe Luigi LagrangiaWhittaker (1949b) In 1776, Laplace published a memoir in which he first explored the possible influences of a purported

luminiferous ether Luminiferous aether or ether ("luminiferous", meaning "light-bearing") was the postulated medium for the propagation of light. It was invoked to explain the ability of the apparently wave-based light to propagate through empty space (a vacuum), so ...

or of a law of gravitation that did not act instantaneously. He ultimately returned to an intellectual investment in Newtonian gravity.Gillispie (1989). pp. 29–35 Euler and Lagrange had made a practical approximation by ignoring small terms in the equations of motion. Laplace noted that though the terms themselves were small, when integrated over time they could become important. Laplace carried his analysis into the higher-order terms, up to and including the cubic. Using this more exact analysis, Laplace concluded that any two planets and the Sun must be in mutual equilibrium and thereby launched his work on the stability of the Solar System.Gillispie (1989), pp. 35–36

Gerald James Whitrow Gerald James Whitrow (9 June 1912 – 2 June 2000) was a British mathematician, cosmologist and science historian. Biography Whitrow was born on 9 June 1912 at Kimmeridge in Dorset, the elder son of William and Emily (née Watkins) Whitrow. Af ...

described the achievement as "the most important advance in physical astronomy since Newton". Laplace had a wide knowledge of all sciences and dominated all discussions in the ''Académie''. Laplace seems to have regarded analysis merely as a means of attacking physical problems, though the ability with which he invented the necessary analysis is almost phenomenal. As long as his results were true he took but little trouble to explain the steps by which he arrived at them; he never studied elegance or symmetry in his processes, and it was sufficient for him if he could by any means solve the particular question he was discussing.

Tidal dynamics

Dynamic theory of tides

While Newton explained the tides by describing the tide-generating forces and

Bernoulli Bernoulli can refer to: People *Bernoulli family of 17th and 18th century Swiss mathematicians: ** Daniel Bernoulli (1700–1782), developer of Bernoulli's principle **Jacob Bernoulli (1654–1705), also known as Jacques, after whom Bernoulli numbe ...

gave a description of the static reaction of the waters on Earth to the tidal potential, the ''dynamic theory of tides'', developed by Laplace in 1775, describes the ocean's real reaction to

tidal force The tidal force is a gravitational effect that stretches a body along the line towards the center of mass of another body due to a gradient (difference in strength) in gravitational field from the other body; it is responsible for diverse phenomen ...

s. Laplace's theory of ocean tides took into account

friction Friction is the force resisting the relative motion of solid surfaces, fluid layers, and material elements sliding against each other. There are several types of friction: *Dry friction is a force that opposes the relative lateral motion of ...

resonance Resonance describes the phenomenon of increased amplitude that occurs when the frequency of an applied Periodic function, periodic force (or a Fourier analysis, Fourier component of it) is equal or close to a natural frequency of the system ...

and natural periods of ocean basins. It predicted the large

amphidromic An amphidromic point, also called a tidal node, is a geographical location which has zero tidal amplitude for one harmonic constituent of the tide. The tidal range (the peak-to-peak amplitude, or the height difference between high tide and low ...

systems in the world's ocean basins and explains the oceanic tides that are actually observed. The equilibrium theory, based on the gravitational gradient from the Sun and Moon but ignoring the Earth's rotation, the effects of continents, and other important effects, could not explain the real ocean tides. Newton's three-body diagram

Since measurements have confirmed the theory, many things have possible explanations now, like how the tides interact with deep sea ridges and chains of seamounts give rise to deep eddies that transport nutrients from the deep to the surface. The equilibrium tide theory calculates the height of the tide wave of less than half a meter, while the dynamic theory explains why tides are up to 15 meters. Satellite observations confirm the accuracy of the dynamic theory, and the tides worldwide are now measured to within a few centimeters. Measurements from the CHAMP satellite closely match the models based on the

TOPEX TOPEX/Poseidon was a joint satellite altimeter mission between NASA, the U.S. space agency; and CNES, the French space agency, to map ocean surface topography. Launched on August 10, 1992, it was the first major oceanographic research satellite. ...

data. Accurate models of tides worldwide are essential for research since the variations due to tides must be removed from measurements when calculating gravity and changes in sea levels.

Laplace's tidal equations

In 1776, Laplace formulated a single set of linear

partial differential equation In mathematics, a partial differential equation (PDE) is an equation which imposes relations between the various partial derivatives of a Multivariable calculus, multivariable function. The function is often thought of as an "unknown" to be sol ...

s, for tidal flow described as a barotropic two-dimensional sheet flow.

Coriolis effect In physics, the Coriolis force is an inertial or fictitious force that acts on objects in motion within a frame of reference that rotates with respect to an inertial frame. In a reference frame with clockwise rotation, the force acts to the ...

s are introduced as well as lateral forcing by gravity. Laplace obtained these equations by simplifying the

fluid dynamic In physics and engineering, fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids— liquids and gases. It has several subdisciplines, including ''aerodynamics'' (the study of air and other gases in motion) an ...

equations. But they can also be derived from energy integrals via Lagrange's equation. For a fluid sheet of

average In ordinary language, an average is a single number taken as representative of a list of numbers, usually the sum of the numbers divided by how many numbers are in the list (the arithmetic mean). For example, the average of the numbers 2, 3, 4, 7 ...

thickness ''D'', the vertical tidal elevation ''ζ'', as well as the horizontal velocity components ''u'' and ''v'' (in the

latitude In geography, latitude is a coordinate that specifies the north– south position of a point on the surface of the Earth or another celestial body. Latitude is given as an angle that ranges from –90° at the south pole to 90° at the north pol ...

''φ'' and

longitude Longitude (, ) is a geographic coordinate that specifies the east–west position of a point on the surface of the Earth, or another celestial body. It is an angular measurement, usually expressed in degrees and denoted by the Greek letter l ...

''λ'' directions, respectively) satisfy Laplace's tidal equations: :

\frac &+ u \left( 2 \Omega \sin( \varphi ) \right) + \frac \frac \left( g \zeta + U \right) =0, \end

where ''Ω'' is the

angular frequency In physics, angular frequency "''ω''" (also referred to by the terms angular speed, circular frequency, orbital frequency, radian frequency, and pulsatance) is a scalar measure of rotation rate. It refers to the angular displacement per unit tim ...

of the planet's rotation, ''g'' is the planet's gravitational acceleration at the mean ocean surface, ''a'' is the planetary radius, and ''U'' is the external gravitational tidal-forcing

potential Potential generally refers to a currently unrealized ability. The term is used in a wide variety of fields, from physics to the social sciences to indicate things that are in a state where they are able to change in ways ranging from the simple r ...

. William Thomson (Lord Kelvin) rewrote Laplace's momentum terms using the curl to find an equation for

vorticity In continuum mechanics, vorticity is a pseudovector field that describes the local spinning motion of a continuum near some point (the tendency of something to rotate), as would be seen by an observer located at that point and traveling along wi ...

. Under certain conditions this can be further rewritten as a conservation of vorticity.

On the figure of the Earth

During the years 1784–1787 he published some memoirs of exceptional power. Prominent among these is one read in 1783, reprinted as Part II of ''Théorie du Mouvement et de la figure elliptique des planètes'' in 1784, and in the third volume of the ''Mécanique céleste''. In this work, Laplace completely determined the attraction of a

spheroid A spheroid, also known as an ellipsoid of revolution or rotational ellipsoid, is a quadric surface obtained by rotating an ellipse about one of its principal axes; in other words, an ellipsoid with two equal semi-diameters. A spheroid has ...

on a particle outside it. This is memorable for the introduction into analysis of

spherical harmonics In mathematics and physical science, spherical harmonics are special functions defined on the surface of a sphere. They are often employed in solving partial differential equations in many scientific fields. Since the spherical harmonics form ...

or Laplace's coefficients, and also for the development of the use of what we would now call the

gravitational potential In classical mechanics, the gravitational potential at a location is equal to the work (energy transferred) per unit mass that would be needed to move an object to that location from a fixed reference location. It is analogous to the electric ...

Spherical harmonics

In 1783, in a paper sent to the ''Académie'',

Adrien-Marie Legendre Adrien-Marie Legendre (; ; 18 September 1752 – 9 January 1833) was a French mathematician who made numerous contributions to mathematics. Well-known and important concepts such as the Legendre polynomials and Legendre transformation are name ...

had introduced what are now known as associated Legendre functions. If two points in a

plane Plane(s) most often refers to: * Aero- or airplane, a powered, fixed-wing aircraft * Plane (geometry), a flat, 2-dimensional surface Plane or planes may also refer to: Biology * Plane (tree) or ''Platanus'', wetland native plant * ''Planes' ...

have

polar co-ordinates In mathematics, the polar coordinate system is a two-dimensional coordinate system in which each point on a plane is determined by a distance from a reference point and an angle from a reference direction. The reference point (analogous to the ...

(''r'', θ) and (''r'' ', θ'), where ''r'' ' ≥ ''r'', then, by elementary manipulation, the reciprocal of the distance between the points, ''d'', can be written as: :

\frac = \frac \left 1 - 2 \cos (\theta' - \theta) \frac + \left ( \frac \right ) ^2 \right^.

This expression can be expanded in powers of ''r''/''r'' ' using Newton's generalised binomial theorem to give: :

\frac = \frac \sum_^\infty P^0_k ( \cos ( \theta' - \theta ) ) \left ( \frac \right ) ^k.

The

sequence In mathematics, a sequence is an enumerated collection of objects in which repetitions are allowed and order matters. Like a set, it contains members (also called ''elements'', or ''terms''). The number of elements (possibly infinite) is calle ...

of functions ''P''⁰_''k''(cos φ) is the set of so-called "associated Legendre functions" and their usefulness arises from the fact that every

function Function or functionality may refer to: Computing * Function key, a type of key on computer keyboards * Function model, a structured representation of processes in a system * Function object or functor or functionoid, a concept of object-oriente ...

of the points on a circle can be expanded as a

series Series may refer to: People with the name * Caroline Series (born 1951), English mathematician, daughter of George Series * George Series (1920–1995), English physicist Arts, entertainment, and media Music * Series, the ordered sets used in ...

of them. Laplace, with scant regard for credit to Legendre, made the non-trivial extension of the result to

three dimensions Three-dimensional space (also: 3D space, 3-space or, rarely, tri-dimensional space) is a geometric setting in which three values (called ''parameters'') are required to determine the position of an element (i.e., point). This is the informa ...

to yield a more general set of functions, the

or Laplace coefficients. The latter term is not in common use now.

Potential theory

This paper is also remarkable for the development of the idea of the

scalar potential In mathematical physics, scalar potential, simply stated, describes the situation where the difference in the potential energies of an object in two different positions depends only on the positions, not upon the path taken by the object in trav ...

. The gravitational

force In physics, a force is an influence that can change the motion of an object. A force can cause an object with mass to change its velocity (e.g. moving from a state of rest), i.e., to accelerate. Force can also be described intuitively as a p ...

acting on a body is, in modern language, a

vector Vector most often refers to: *Euclidean vector, a quantity with a magnitude and a direction *Vector (epidemiology), an agent that carries and transmits an infectious pathogen into another living organism Vector may also refer to: Mathematic ...

, having magnitude and direction. A potential function is a

scalar Scalar may refer to: *Scalar (mathematics), an element of a field, which is used to define a vector space, usually the field of real numbers * Scalar (physics), a physical quantity that can be described by a single element of a number field such ...

function that defines how the vectors will behave. A scalar function is computationally and conceptually easier to deal with than a vector function.

Alexis Clairaut Alexis Claude Clairaut (; 13 May 1713 – 17 May 1765) was a French mathematician, astronomer, and geophysicist. He was a prominent Newtonian whose work helped to establish the validity of the principles and results that Sir Isaac Newton had ou ...

had first suggested the idea in 1743 while working on a similar problem though he was using Newtonian-type geometric reasoning. Laplace described Clairaut's work as being "in the class of the most beautiful mathematical productions". However, Rouse Ball alleges that the idea "was appropriated from

Joseph Louis Lagrange Joseph-Louis Lagrange (born Giuseppe Luigi Lagrangia The term "potential" itself was due to Daniel Bernoulli, who introduced it in his 1738 memoire ''Hydrodynamica''. However, according to Rouse Ball, the term "potential function" was not actually used (to refer to a function ''V'' of the coordinates of space in Laplace's sense) until George Green's 1828 An Essay on the Application of Mathematical Analysis to the Theories of Electricity and Magnetism.W.W. Rouse Ball ''A Short Account of the History of Mathematics'' (4th edition, 1908)
/ref> Laplace applied the language of calculus to the potential function and showed that it always satisfies the

differential equation In mathematics, a differential equation is an equation that relates one or more unknown functions and their derivatives. In applications, the functions generally represent physical quantities, the derivatives represent their rates of change, an ...

: :

\nabla^2V= +
 +
 = 0.

An analogous result for the velocity potential of a fluid had been obtained some years previously by

. Laplace's subsequent work on gravitational attraction was based on this result. The quantity ∇²''V'' has been termed the concentration of ''V'' and its value at any point indicates the "excess" of the value of ''V'' there over its mean value in the neighbourhood of the point. Laplace's equation, a special case of

Poisson's equation Poisson's equation is an elliptic partial differential equation of broad utility in theoretical physics. For example, the solution to Poisson's equation is the potential field caused by a given electric charge or mass density distribution; with t ...

, appears ubiquitously in mathematical physics. The concept of a potential occurs in

fluid dynamics In physics and engineering, fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids— liquids and gases. It has several subdisciplines, including ''aerodynamics'' (the study of air and other gases in motion) an ...

electromagnetism In physics, electromagnetism is an interaction that occurs between particles with electric charge. It is the second-strongest of the four fundamental interactions, after the strong force, and it is the dominant force in the interactions of ...

and other areas. Rouse Ball speculated that it might be seen as "the outward sign" of one of the ''

a priori ("from the earlier") and ("from the later") are Latin phrases used in philosophy to distinguish types of knowledge, justification, or argument by their reliance on empirical evidence or experience. knowledge is independent from current ...

'' forms in Kant's theory of perception. The spherical harmonics turn out to be critical to practical solutions of Laplace's equation. Laplace's equation in

spherical coordinates In mathematics, a spherical coordinate system is a coordinate system for three-dimensional space where the position of a point is specified by three numbers: the ''radial distance'' of that point from a fixed origin, its ''polar angle'' meas ...

, such as are used for mapping the sky, can be simplified, using the method of

separation of variables In mathematics, separation of variables (also known as the Fourier method) is any of several methods for solving ordinary and partial differential equations, in which algebra allows one to rewrite an equation so that each of two variables occurs ...

into a radial part, depending solely on distance from the centre point, and an angular or spherical part. The solution to the spherical part of the equation can be expressed as a series of Laplace's spherical harmonics, simplifying practical computation.

Planetary and lunar inequalities

Jupiter–Saturn great inequality

Laplace presented a memoir on planetary inequalities in three sections, in 1784, 1785, and 1786. This dealt mainly with the identification and explanation of the perturbations now known as the "great Jupiter–Saturn inequality". Laplace solved a longstanding problem in the study and prediction of the movements of these planets. He showed by general considerations, first, that the mutual action of two planets could never cause large changes in the eccentricities and inclinations of their orbits; but then, even more importantly, that peculiarities arose in the Jupiter–Saturn system because of the near approach to commensurability of the mean motions of Jupiter and Saturn. In this context ''commensurability'' means that the ratio of the two planets' mean motions is very nearly equal to a ratio between a pair of small whole numbers. Two periods of Saturn's orbit around the Sun almost equal five of Jupiter's. The corresponding difference between multiples of the mean motions, , corresponds to a period of nearly 900 years, and it occurs as a small divisor in the integration of a very small perturbing force with this same period. As a result, the integrated perturbations with this period are disproportionately large, about 0.8° degrees of arc in orbital longitude for Saturn and about 0.3° for Jupiter. Further developments of these theorems on planetary motion were given in his two memoirs of 1788 and 1789, but with the aid of Laplace's discoveries, the tables of the motions of Jupiter and Saturn could at last be made much more accurate. It was on the basis of Laplace's theory that

Delambre Jean Baptiste Joseph, chevalier Delambre (19 September 1749 – 19 August 1822) was a French mathematician, astronomer, historian of astronomy, and geodesist. He was also director of the Paris Observatory, and author of well-known books on th ...

computed his astronomical tables.

Books

Laplace now set himself the task to write a work which should "offer a complete solution of the great mechanical problem presented by the Solar System, and bring theory to coincide so closely with observation that empirical equations should no longer find a place in astronomical tables." The result is embodied in the ''Exposition du système du monde'' and the ''Mécanique céleste''. The former was published in 1796, and gives a general explanation of the phenomena, but omits all details. It contains a summary of the history of astronomy. This summary procured for its author the honour of admission to the forty of the French Academy and is commonly esteemed one of the masterpieces of French literature, though it is not altogether reliable for the later periods of which it treats. Laplace developed the

of the formation of the Solar System, first suggested by

Emanuel Swedenborg Emanuel Swedenborg (, ; born Emanuel Swedberg; 29 March 1772) was a Swedish pluralistic-Christian theologian, scientist, philosopher and mystic. He became best known for his book on the afterlife, ''Heaven and Hell'' (1758). Swedenborg had a ...

and expanded by

Immanuel Kant Immanuel Kant (, , ; 22 April 1724 – 12 February 1804) was a German philosopher and one of the central Enlightenment thinkers. Born in Königsberg, Kant's comprehensive and systematic works in epistemology, metaphysics, ethics, and ...

, a hypothesis that continues to dominate accounts of the origin of planetary systems. According to Laplace's description of the hypothesis, the Solar System had evolved from a globular mass of

incandescent Incandescence is the emission of electromagnetic radiation (including visible light) from a hot body as a result of its high temperature. The term derives from the Latin verb ''incandescere,'' to glow white. A common use of incandescence is ...

gas rotating around an axis through its

centre of mass In physics, the center of mass of a distribution of mass in space (sometimes referred to as the balance point) is the unique point where the weighted relative position of the distributed mass sums to zero. This is the point to which a force may ...

. As it cooled, this mass contracted, and successive rings broke off from its outer edge. These rings in their turn cooled, and finally condensed into the planets, while the Sun represented the central core which was still left. On this view, Laplace predicted that the more distant planets would be older than those nearer the Sun.Owen, T. C. (2001) "Solar system: origin of the solar system", ''

Encyclopædia Britannica The (Latin for "British Encyclopædia") is a general knowledge English-language encyclopaedia. It is published by Encyclopædia Britannica, Inc.; the company has existed since the 18th century, although it has changed ownership various time ...

'', Deluxe CDROM edition As mentioned, the idea of the nebular hypothesis had been outlined by

in 1755, and he had also suggested "meteoric aggregations" and

tidal friction Tidal acceleration is an effect of the tidal forces between an orbiting natural satellite (e.g. the Moon) and the primary planet that it orbits (e.g. Earth). The acceleration causes a gradual recession of a satellite in a prograde orbit away f ...

as causes affecting the formation of the Solar System. Laplace was probably aware of this, but, like many writers of his time, he generally did not reference the work of others. Laplace's analytical discussion of the Solar System is given in his ''Mécanique céleste'' published in five volumes. The first two volumes, published in 1799, contain methods for calculating the motions of the planets, determining their figures, and resolving tidal problems. The third and fourth volumes, published in 1802 and 1805, contain applications of these methods, and several astronomical tables. The fifth volume, published in 1825, is mainly historical, but it gives as appendices the results of Laplace's latest researches. Laplace's own investigations embodied in it are so numerous and valuable that it is regrettable to have to add that many results are appropriated from other writers with scanty or no acknowledgement, and the conclusions — which have been described as the organised result of a century of patient toil — are frequently mentioned as if they were due to Laplace.

Jean-Baptiste Biot Jean-Baptiste Biot (; ; 21 April 1774 – 3 February 1862) was a French physicist, astronomer, and mathematician who co-discovered the Biot–Savart law of magnetostatics with Félix Savart, established the reality of meteorites, made an early ba ...

, who assisted Laplace in revising it for the press, says that Laplace himself was frequently unable to recover the details in the chain of reasoning, and, if satisfied that the conclusions were correct, he was content to insert the constantly recurring formula, "''Il est aisé à voir que ... ''" ("It is easy to see that ..."). The ''Mécanique céleste'' is not only the translation of Newton's '' Principia'' into the language of the differential calculus, but it completes parts of which Newton had been unable to fill in the details. The work was carried forward in a more finely tuned form in

Félix Tisserand François Félix Tisserand (13 January 1845 – 20 October 1896) was a French astronomer. Life Tisserand was born at Nuits-Saint-Georges, Côte-d'Or. In 1863 he entered the École Normale Supérieure, and on leaving he went for a month as profes ...

's ''Traité de mécanique céleste'' (1889–1896), but Laplace's treatise will always remain a standard authority. In the years 1784–1787, Laplace produced some memoirs of exceptional power. The significant among these was one issued in 1784, and reprinted in the third volume of the ''Méchanique céleste''. In this work he completely determined the attraction of a spheroid on a particle outside it. This is known for the introduction into analysis of the potential, a useful mathematical concept of broad applicability to the physical sciences.

Black holes

Laplace also came close to propounding the concept of the black hole. He suggested that there could be massive stars whose gravity is so great that not even light could escape from their surface (see

escape velocity In celestial mechanics, escape velocity or escape speed is the minimum speed needed for a free, non- propelled object to escape from the gravitational influence of a primary body, thus reaching an infinite distance from it. It is typically ...

). However, this insight was so far ahead of its time that it played no role in the history of scientific development.

Arcueil

In 1806, Laplace bought a house in

, then a village and not yet absorbed into the Paris

conurbation A conurbation is a region comprising a number of metropolises, cities, large towns, and other urban areas which through population growth and physical expansion, have merged to form one continuous urban or industrially developed area. In most ca ...

. The chemist

Claude Louis Berthollet Claude Louis Berthollet (, 9 December 1748 – 6 November 1822) was a Savoyard-French chemist who became vice president of the French Senate in 1804. He is known for his scientific contributions to theory of chemical equilibria via the mecha ...

was a neighbour – their gardens were not separatedFourier (1829). – and the pair formed the nucleus of an informal scientific circle, latterly known as the Society of Arcueil. Because of their closeness to

, Laplace and Berthollet effectively controlled advancement in the scientific establishment and admission to the more prestigious offices. The Society built up a complex pyramid of

patronage Patronage is the support, encouragement, privilege, or financial aid that an organization or individual bestows on another. In the history of art, arts patronage refers to the support that kings, popes, and the wealthy have provided to artists su ...

. In 1806, Laplace was also elected a foreign member of the Royal Swedish Academy of Sciences.

Analytic theory of probabilities

In 1812, Laplace issued his ''Théorie analytique des probabilités'' in which he laid down many fundamental results in statistics. The first half of this treatise was concerned with probability methods and problems, the second half with statistical methods and applications. Laplace's proofs are not always rigorous according to the standards of a later day, and his perspective slides back and forth between the Bayesian and non-Bayesian views with an ease that makes some of his investigations difficult to follow, but his conclusions remain basically sound even in those few situations where his analysis goes astray. In 1819, he published a popular account of his work on probability. This book bears the same relation to the ''Théorie des probabilités'' that the ''Système du monde'' does to the ''Méchanique céleste''. In its emphasis on the analytical importance of probabilistic problems, especially in the context of the "approximation of formula functions of large numbers," Laplace's work goes beyond the contemporary view which almost exclusively considered aspects of practical applicability. Laplace's Théorie analytique remained the most influential book of mathematical probability theory to the end of the 19th century. The general relevance for statistics of Laplacian error theory was appreciated only by the end of the 19th century. However, it influenced the further development of a largely analytically oriented probability theory.

Inductive probability

In his ''Essai philosophique sur les probabilités'' (1814), Laplace set out a mathematical system of inductive reasoning based on

probability Probability is the branch of mathematics concerning numerical descriptions of how likely an Event (probability theory), event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and ...

, which we would today recognise as

Bayesian Thomas Bayes (/beɪz/; c. 1701 – 1761) was an English statistician, philosopher, and Presbyterian minister. Bayesian () refers either to a range of concepts and approaches that relate to statistical methods based on Bayes' theorem, or a followe ...

. He begins the text with a series of principles of probability, the first six being: # Probability is the ratio of the "favored events" to the total possible events. # The first principle assumes equal probabilities for all events. When this is not true, we must first determine the probabilities of each event. Then, the probability is the sum of the probabilities of all possible favoured events. # For independent events, the probability of the occurrence of all is the probability of each multiplied together. # For events not independent, the probability of event B following event A (or event A causing B) is the probability of A multiplied by the probability that, given A, B will occur. # The probability that ''A'' will occur, given that B has occurred, is the probability of ''A'' and ''B'' occurring divided by the probability of ''B''. # Three corollaries are given for the sixth principle, which amount to Bayesian probability. Where event exhausts the list of possible causes for event ''B'', . Then :::

\Pr(A_i \mid B) = \Pr(A_i)\frac.

One well-known formula arising from his system is the

rule of succession In probability theory, the rule of succession is a formula introduced in the 18th century by Pierre-Simon Laplace in the course of treating the sunrise problem. The formula is still used, particularly to estimate underlying probabilities when ...

, given as principle seven. Suppose that some trial has only two possible outcomes, labelled "success" and "failure". Under the assumption that little or nothing is known ''a priori'' about the relative plausibilities of the outcomes, Laplace derived a formula for the probability that the next trial will be a success. :

\Pr(\text) = \frac

where ''s'' is the number of previously observed successes and ''n'' is the total number of observed trials. It is still used as an estimator for the probability of an event if we know the event space, but have only a small number of samples. The rule of succession has been subject to much criticism, partly due to the example which Laplace chose to illustrate it. He calculated that the probability that the sun will rise tomorrow, given that it has never failed to in the past, was :

\Pr(\text) = \frac

where ''d'' is the number of times the sun has risen in the past. This result has been derided as absurd, and some authors have concluded that all applications of the Rule of Succession are absurd by extension. However, Laplace was fully aware of the absurdity of the result; immediately following the example, he wrote, "But this number .e., the probability that the sun will rise tomorrowis far greater for him who, seeing in the totality of phenomena the principle regulating the days and seasons, realizes that nothing at the present moment can arrest the course of it."

Probability-generating function

The method of estimating the ratio of the number of favourable cases to the whole number of possible cases had been previously indicated by Laplace in a paper written in 1779. It consists of treating the successive values of any

as the coefficients in the expansion of another function, with reference to a different variable. The latter is therefore called the

probability-generating function In probability theory, the probability generating function of a discrete random variable is a power series representation (the generating function) of the probability mass function of the random variable. Probability generating functions are oft ...

of the former. Laplace then shows how, by means of interpolation, these coefficients may be determined from the generating function. Next he attacks the converse problem, and from the coefficients he finds the generating function; this is effected by the solution of a

finite difference equation A finite difference is a mathematical expression of the form . If a finite difference is divided by , one gets a difference quotient. The approximation of derivatives by finite differences plays a central role in finite difference methods for the ...

Least squares and central limit theorem

The fourth chapter of this treatise includes an exposition of the

method of least squares The method of least squares is a standard approach in regression analysis to approximate the solution of overdetermined systems (sets of equations in which there are more equations than unknowns) by minimizing the sum of the squares of the res ...

, a remarkable testimony to Laplace's command over the processes of analysis. In 1805 Legendre had published the method of least squares, making no attempt to tie it to the theory of probability. In 1809

Gauss Johann Carl Friedrich Gauss (; german: Gauß ; la, Carolus Fridericus Gauss; 30 April 177723 February 1855) was a German mathematician and physicist who made significant contributions to many fields in mathematics and science. Sometimes refer ...

had derived the normal distribution from the principle that the arithmetic mean of observations gives the most probable value for the quantity measured; then, turning this argument back upon itself, he showed that, if the errors of observation are normally distributed, the least squares estimates give the most probable values for the coefficients in regression situations. These two works seem to have spurred Laplace to complete work toward a treatise on probability he had contemplated as early as 1783.Stigler, 1975 In two important papers in 1810 and 1811, Laplace first developed the

characteristic function In mathematics, the term "characteristic function" can refer to any of several distinct concepts: * The indicator function of a subset, that is the function ::\mathbf_A\colon X \to \, :which for a given subset ''A'' of ''X'', has value 1 at points ...

as a tool for large-sample theory and proved the first general

central limit theorem In probability theory, the central limit theorem (CLT) establishes that, in many situations, when independent random variables are summed up, their properly normalized sum tends toward a normal distribution even if the original variables themsel ...

. Then in a supplement to his 1810 paper written after he had seen Gauss's work, he showed that the central limit theorem provided a Bayesian justification for least squares: if one were combining observations, each one of which was itself the mean of a large number of independent observations, then the least squares estimates would not only maximise the likelihood function, considered as a posterior distribution, but also minimise the expected posterior error, all this without any assumption as to the error distribution or a circular appeal to the principle of the arithmetic mean. In 1811 Laplace took a different non-Bayesian tack. Considering a linear regression problem, he restricted his attention to linear unbiased estimators of the linear coefficients. After showing that members of this class were approximately normally distributed if the number of observations was large, he argued that least squares provided the "best" linear estimators. Here it is "best" in the sense that it minimised the asymptotic variance and thus both minimised the expected absolute value of the error, and maximised the probability that the estimate would lie in any symmetric interval about the unknown coefficient, no matter what the error distribution. His derivation included the joint limiting distribution of the least squares estimators of two parameters.

Laplace's demon

In 1814, Laplace published what may have been the first scientific articulation of

causal determinism Determinism is a philosophical view, where all events are determined completely by previously existing causes. Deterministic theories throughout the history of philosophy have developed from diverse and sometimes overlapping motives and cons ...

: This intellect is often referred to as ''Laplace's demon'' (in the same vein as '' Maxwell's demon'') and sometimes ''Laplace's Superman'' (after Hans Reichenbach). Laplace, himself, did not use the word "demon", which was a later embellishment. As translated into English above, he simply referred to: ''"Une intelligence ... Rien ne serait incertain pour elle, et l'avenir comme le passé, serait présent à ses yeux."'' Even though Laplace is generally credited with having first formulated the concept of causal determinism, in a philosophical context the idea was actually widespread at the time, and can be found as early as 1756 in

Maupertuis Pierre Louis Moreau de Maupertuis (; ; 1698 – 27 July 1759) was a French mathematician, philosopher and man of letters. He became the Director of the Académie des Sciences, and the first President of the Prussian Academy of Science, at the ...

' 'Sur la Divination'. As well,

Jesuit , image = Ihs-logo.svg , image_size = 175px , caption = ChristogramOfficial seal of the Jesuits , abbreviation = SJ , nickname = Jesuits , formation = , founders ...

scientist Boscovich first proposed a version of scientific determinism very similar to Laplace's in his 1758 book ''Theoria philosophiae naturalis''.

Laplace transforms

As early as 1744, Euler, followed by Lagrange, had started looking for solutions of

s in the form: :

z = \int X(x) e^ \,dx\textz = \int X(x) x^a \,dx.

The Laplace transform has the form: :

F(s) = \int f(t) e^\,dt

This integral operator transforms a function of time (

t

) into a function of a complex variable (

s

), usually interpreted as

complex frequency In mathematics, the Laplace transform, named after its discoverer Pierre-Simon Laplace (), is an integral transform that converts a function of a real variable (usually t, in the ''time domain'') to a function of a complex variable s (in the compl ...

Other discoveries and accomplishments

Mathematics

Among the other discoveries of Laplace in pure and applied mathematics are: * Discussion, contemporaneously with

, of the general theory of

determinant In mathematics, the determinant is a scalar value that is a function of the entries of a square matrix. It characterizes some properties of the matrix and the linear map represented by the matrix. In particular, the determinant is nonzero if and ...

s, (1772); * Proof that every equation of an odd degree must have at least one

real Real may refer to: Currencies * Brazilian real (R$) * Central American Republic real * Mexican real * Portuguese real * Spanish real * Spanish colonial real Music Albums * ''Real'' (L'Arc-en-Ciel album) (2000) * ''Real'' (Bright album) (2010) ...

quadratic factor; *

Laplace's method In mathematics, Laplace's method, named after Pierre-Simon Laplace, is a technique used to approximate integrals of the form :\int_a^b e^ \, dx, where f(x) is a twice-differentiable function, ''M'' is a large number, and the endpoints ''a'' an ...

for approximating integrals * Solution of the

linear partial differential equation In mathematics, a partial differential equation (PDE) is an equation which imposes relations between the various partial derivatives of a multivariable function. The function is often thought of as an "unknown" to be solved for, similarly to ...

of the second order; * He was the first to consider the difficult problems involved in equations of mixed differences, and to prove that the solution of an equation in finite differences of the first degree and the second order might always be obtained in the form of a

continued fraction In mathematics, a continued fraction is an expression obtained through an iterative process of representing a number as the sum of its integer part and the reciprocal of another number, then writing this other number as the sum of its integer ...

; * In his theory of probabilities: **

de Moivre–Laplace theorem In probability theory, the de Moivre–Laplace theorem, which is a special case of the central limit theorem, states that the normal distribution may be used as an approximation to the binomial distribution under certain conditions. In particu ...

that approximates binomial distribution with a normal distribution ** Evaluation of several common definite integrals; ** General proof of the

Lagrange reversion theorem In mathematics, the Lagrange reversion theorem gives series or formal power series expansions of certain implicitly defined functions; indeed, of compositions with such functions. Let ''v'' be a function of ''x'' and ''y'' in terms of another fu ...

Surface tension

Laplace built upon the qualitative work of Thomas Young to develop the theory of

capillary action Capillary action (sometimes called capillarity, capillary motion, capillary rise, capillary effect, or wicking) is the process of a liquid flowing in a narrow space without the assistance of, or even in opposition to, any external forces li ...

and the

Young–Laplace equation In physics, the Young–Laplace equation () is an algebraic equation that describes the capillary pressure difference sustained across the interface between two static fluids, such as water and air, due to the phenomenon of surface tension or w ...

Speed of sound

Laplace in 1816 was the first to point out that the

speed of sound The speed of sound is the distance travelled per unit of time by a sound wave as it propagates through an elastic medium. At , the speed of sound in air is about , or one kilometre in or one mile in . It depends strongly on temperature as w ...

in air depends on the

heat capacity ratio In thermal physics and thermodynamics, the heat capacity ratio, also known as the adiabatic index, the ratio of specific heats, or Laplace's coefficient, is the ratio of the heat capacity at constant pressure () to heat capacity at constant volu ...

. Newton's original theory gave too low a value, because it does not take account of the adiabatic

compression Compression may refer to: Physical science *Compression (physics), size reduction due to forces *Compression member, a structural element such as a column *Compressibility, susceptibility to compression * Gas compression *Compression ratio, of a ...

of the air which results in a local rise in temperature and

pressure Pressure (symbol: ''p'' or ''P'') is the force applied perpendicular to the surface of an object per unit area over which that force is distributed. Gauge pressure (also spelled ''gage'' pressure)The preferred spelling varies by country and e ...

. Laplace's investigations in practical physics were confined to those carried on by him jointly with Lavoisier in the years 1782 to 1784 on the

of various bodies.

Politics

Minister of the Interior

In his early years Laplace was careful never to become involved in politics, or indeed in life outside the ''Académie des sciences''. He prudently withdrew from Paris during the most violent part of the Revolution. In November 1799, immediately after seizing power in the coup of 18 Brumaire, Napoleon appointed Laplace to the post of

Minister of the Interior An interior minister (sometimes called a minister of internal affairs or minister of home affairs) is a cabinet official position that is responsible for internal affairs, such as public security, civil registration and identification, emergency ...

. The appointment, however, lasted only six weeks, after which

Lucien Bonaparte Lucien Bonaparte, 1st Prince of Canino and Musignano (born Luciano Buonaparte; 21 May 1775 – 29 June 1840), was French politician and diplomat of the French Revolution and the Consulate. He served as Minister of the Interior from 1799 to 1800 ...

, Napoleon's brother, was given the post. Evidently, once Napoleon's grip on power was secure, there was no need for a prestigious but inexperienced scientist in the government.Grattan-Guinness (2005), p. 333 Napoleon later (in his ''Mémoires de Sainte Hélène'') wrote of Laplace's dismissal as follows: Grattan-Guinness, however, describes these remarks as "tendentious", since there seems to be no doubt that Laplace "was only appointed as a short-term figurehead, a place-holder while Napoleon consolidated power".

From Bonaparte to the Bourbons

Although Laplace was removed from office, it was desirable to retain his allegiance. He was accordingly raised to the senate, and to the third volume of the ''Mécanique céleste'' he prefixed a note that of all the truths therein contained the most precious to the author was the declaration he thus made of his devotion towards the peacemaker of Europe. In copies sold after the Bourbon Restoration this was struck out. (Pearson points out that the censor would not have allowed it anyway.) In 1814 it was evident that the empire was falling; Laplace hastened to tender his services to the

Bourbons The House of Bourbon (, also ; ) is a European dynasty of French origin, a branch of the Capetian dynasty, the royal House of France. Bourbon kings first ruled France and Navarre in the 16th century. By the 18th century, members of the Spani ...

, and in 1817 during the

Restoration Restoration is the act of restoring something to its original state and may refer to: * Conservation and restoration of cultural heritage ** Audio restoration ** Film restoration ** Image restoration ** Textile restoration * Restoration ecology ...

he was rewarded with the title of marquis. According to Rouse Ball, the contempt that his more honest colleagues felt for his conduct in the matter may be read in the pages of

Paul Louis Courier Paul Louis Courier (; 4 January 177210 April 1825), French Hellenist and political writer, was born in Paris. Life Brought up on his father's estate of Méré in Touraine, he conceived a bitter aversion for the nobility, which seemed to strengt ...

. His knowledge was useful on the numerous scientific commissions on which he served, and, says Rouse Ball, probably accounts for the manner in which his political insincerity was overlooked. Roger Hahn in his 2005 biography disputes this portrayal of Laplace as an opportunist and turncoat, pointing out that, like many in France, he had followed the debacle of Napoleon's Russian campaign with serious misgivings. The Laplaces, whose only daughter Sophie had died in childbirth in September 1813, were in fear for the safety of their son Émile, who was on the eastern front with the emperor. Napoleon had originally come to power promising stability, but it was clear that he had overextended himself, putting the nation at peril. It was at this point that Laplace's loyalty began to weaken. Although he still had easy access to Napoleon, his personal relations with the emperor cooled considerably. As a grieving father, he was particularly cut to the quick by Napoleon's insensitivity in an exchange related by

Jean-Antoine Chaptal Jean-Antoine Chaptal, comte de Chanteloup (5 June 1756 – 30 July 1832) was a French chemist, physician, agronomist, industrialist, statesman, educator and philanthropist. His multifaceted career unfolded during one of the most brilliant periods ...

: "On his return from the rout in Leipzig, he apoleonaccosted Mr Laplace: 'Oh! I see that you have grown thin—Sire, I have lost my daughter—Oh! that's not a reason for losing weight. You are a mathematician; put this event in an equation, and you will find that it adds up to zero.'"

Political philosophy

In the second edition (1814) of the ''Essai philosophique'', Laplace added some revealing comments on politics and

governance Governance is the process of interactions through the laws, social norm, norms, power (social and political), power or language of an organized society over a social system (family, tribe, formal organization, formal or informal organization, a ...

. Since it is, he says, "the practice of the eternal principles of reason, justice and humanity that produce and preserve societies, there is a great advantage to adhere to these principles, and a great inadvisability to deviate from them". Noting "the depths of misery into which peoples have been cast" when ambitious leaders disregard these principles, Laplace makes a veiled criticism of Napoleon's conduct: "Every time a great power intoxicated by the love of conquest aspires to universal domination, the sense of liberty among the unjustly threatened nations breeds a coalition to which it always succumbs." Laplace argues that "in the midst of the multiple causes that direct and restrain various states, natural limits" operate, within which it is "important for the stability as well as the prosperity of empires to remain". States that transgress these limits cannot avoid being "reverted" to them, "just as is the case when the waters of the seas whose floor has been lifted by violent tempests sink back to their level by the action of gravity".Hahn (2005), p. 185 About the political upheavals he had witnessed, Laplace formulated a set of principles derived from physics to favour evolutionary over revolutionary change: In these lines, Laplace expressed the views he had arrived at after experiencing the Revolution and the Empire. He believed that the stability of nature, as revealed through scientific findings, provided the model that best helped to preserve the human species. "Such views," Hahn comments, "were also of a piece with his steadfast character." In the ''Essai philosophique'', Laplace also illustrates the potential of probabilities in political studies by applying the law of large numbers to justify the candidates’ integer-valued ranks used in the Borda method of voting, with which the new members of the Academy of Sciences were elected. Laplace’s verbal argument is so rigorous that it can easily be converted into a formal proof.

Death

Laplace died in Paris on 5 March 1827, which was the same day

Alessandro Volta Alessandro Giuseppe Antonio Anastasio Volta (, ; 18 February 1745 – 5 March 1827) was an Italian physicist, chemist and lay Catholic who was a pioneer of electricity and power who is credited as the inventor of the electric battery and the ...

died. His brain was removed by his physician,

François Magendie __NOTOC__ François Magendie (6 October 1783 – 7 October 1855) was a French physiologist, considered a pioneer of experimental physiology. He is known for describing the foramen of Magendie. There is also a ''Magendie sign'', a downward ...

, and kept for many years, eventually being displayed in a roving anatomical museum in Britain. It was reportedly smaller than the average brain. Laplace was buried at

Père Lachaise A name suffix, in the Western English-language naming tradition, follows a person's full name and provides additional information about the person. Post-nominal letters indicate that the individual holds a position, educational degree, accredit ...

in Paris but in 1888 his remains were moved to Saint Julien de Mailloc in the canton of Orbec and reinterred on the family estate. The tomb is situated on a hill overlooking the village of St Julien de Mailloc, Normandy, France. Tomb of Pierre-Simon Laplace

Religious opinions

''I had no need of that hypothesis''

A frequently cited but potentially apocryphal interaction between Laplace and Napoleon purportedly concerns the existence of God. Although the conversation in question did occur, the exact words Laplace used and his intended meaning are not known. A typical version is provided by Rouse Ball: An earlier report, although without the mention of Laplace's name, is found in Antommarchi's '' The Last Moments of Napoleon'' (1825): In 1884, however, the astronomer

Hervé Faye Hervé Auguste Étienne Albans Faye ( – ) was a French astronomer, born at Saint-Benoît-du-Sault (Indre) and educated at the École Polytechnique, which he left in 1834, before completing his course, to accept a position in the Paris Obser ...

Faye, Hervé (1884), ''Sur l'origine du monde: théories cosmogoniques des anciens et des modernes''. Paris: Gauthier-Villars, pp. 109–111Pasquier, Ernest (1898)
"Les hypothèses cosmogoniques (''suite'')"
''Revue néo-scholastique'', 5^o année, N^o 18, pp. 124–125, footnote 1. affirmed that this account of Laplace's exchange with Napoleon presented a "strangely transformed" (''étrangement transformée'') or garbled version of what had actually happened. It was not God that Laplace had treated as a hypothesis, but merely his intervention at a determinate point: Laplace's younger colleague, the astronomer François Arago, who gave his eulogy before the French Academy in 1827, told Faye of an attempt by Laplace to keep the garbled version of his interaction with Napoleon out of circulation. Faye writes: The Swiss-American historian of mathematics

Florian Cajori Florian Cajori (February 28, 1859 – August 14 or 15, 1930) was a Swiss-American historian of mathematics. Biography Florian Cajori was born in Zillis, Switzerland, as the son of Georg Cajori and Catherine Camenisch. He attended schools first ...

appears to have been unaware of Faye's research, but in 1893 he came to a similar conclusion. Stephen Hawking said in 1999, "I don't think that Laplace was claiming that God does not exist. It's just that he doesn't intervene, to break the laws of Science." The only eyewitness account of Laplace's interaction with Napoleon is from the entry for 8 August 1802 in the diary of the British astronomer Sir

William Herschel Frederick William Herschel (; german: Friedrich Wilhelm Herschel; 15 November 1738 – 25 August 1822) was a German-born British astronomer and composer. He frequently collaborated with his younger sister and fellow astronomer Caroline ...

: Since this makes no mention of Laplace's saying, "I had no need of that hypothesis," Daniel Johnson argues that "Laplace never used the words attributed to him." Arago's testimony, however, appears to imply that he did, only not in reference to the existence of God.

Views on God

Raised a Catholic, Laplace appears in adult life to have inclined to deism (presumably his considered position, since it is the only one found in his writings). However, some of his contemporaries thought he was an atheist, while a number of recent scholars have described him as agnostic. Faye thought that Laplace "did not profess atheism", but Napoleon, on

Saint Helena Saint Helena () is a British overseas territory located in the South Atlantic Ocean. It is a remote volcanic tropical island west of the coast of south-western Africa, and east of Rio de Janeiro in South America. It is one of three constitu ...

, told General

Gaspard Gourgaud Gaspard, Baron Gourgaud (September 14, 1783 – July 25, 1852), also known simply as Gaspard Gourgaud, was a French soldier, prominent in the Napoleonic wars. Biography He was born at Versailles; his father was a musician of the royal chapel. At s ...

, "I often asked Laplace what he thought of God. He owned that he was an atheist." Roger Hahn, in his biography of Laplace, mentions a dinner party at which "the geologist

Jean-Étienne Guettard Jean-Étienne Guettard (22 September 1715 – 7 January 1786), French naturalist and mineralogist, was born at Étampes, near Paris. In boyhood, he gained a knowledge of plants from his grandfather, who was an apothecary, and later he qualif ...

was staggered by Laplace's bold denunciation of the existence of God". It appeared to Guettard that Laplace's atheism "was supported by a thoroughgoing materialism". But the chemist Jean-Baptiste Dumas, who knew Laplace well in the 1820s, wrote that Laplace "provided materialists with their specious arguments, without sharing their convictions".Kneller, Karl Alois. ''Christianity and the Leaders of Modern Science: A Contribution to the History of Culture in the Nineteenth Century'', translated from the second German edition by T.M. Kettle. London: B. Herder, 1911
pp. 73–74
Hahn states: "Nowhere in his writings, either public or private, does Laplace deny God's existence." Expressions occur in his private letters that appear inconsistent with atheism. On 17 June 1809, for instance, he wrote to his son, "''Je prie Dieu qu'il veille sur tes jours. Aie-Le toujours présent à ta pensée, ainsi que ton père et ta mère'' pray that God watches over your days. Let Him be always present to your mind, as also your father and your mother" Ian S. Glass, quoting Herschel's account of the celebrated exchange with Napoleon, writes that Laplace was "evidently a deist like Herschel". In ''Exposition du système du monde'', Laplace quotes Newton's assertion that "the wondrous disposition of the Sun, the planets and the comets, can only be the work of an all-powerful and intelligent Being". This, says Laplace, is a "thought in which he ewtonwould be even more confirmed, if he had known what we have shown, namely that the conditions of the arrangement of the planets and their satellites are precisely those which ensure its stability". By showing that the "remarkable" arrangement of the planets could be entirely explained by the laws of motion, Laplace had eliminated the need for the "supreme intelligence" to intervene, as Newton had "made" it do. Laplace cites with approval Leibniz's criticism of Newton's invocation of divine intervention to restore order to the Solar System: "This is to have very narrow ideas about the wisdom and the power of God." He evidently shared Leibniz's astonishment at Newton's belief "that God has made his machine so badly that unless he affects it by some extraordinary means, the watch will very soon cease to go". In a group of manuscripts, preserved in relative secrecy in a black envelope in the library of the ''Académie des sciences'' and published for the first time by Hahn, Laplace mounted a deist critique of Christianity. It is, he writes, the "first and most infallible of principles ... to reject miraculous facts as untrue". As for the doctrine of

transubstantiation Transubstantiation (Latin: ''transubstantiatio''; Greek: μετουσίωσις '' metousiosis'') is, according to the teaching of the Catholic Church, "the change of the whole substance of bread into the substance of the Body of Christ and of ...

, it "offends at the same time reason, experience, the testimony of all our senses, the eternal laws of nature, and the sublime ideas that we ought to form of the Supreme Being". It is the sheerest absurdity to suppose that "the sovereign lawgiver of the universe would suspend the laws that he has established, and which he seems to have maintained invariably". Laplace also ridiculed the use of probability in theology. Even following Pascal's reasoning presented in Pascal's wager, it is not worth making a bet, for the hope of profit – equal to the product of the value of the testimonies (infinitely small) and the value of the happiness they promise (which is significant but finite) – must necessarily be infinitely small. In old age, Laplace remained curious about the question of GodHahn (2005), p. 202. and frequently discussed Christianity with the Swiss astronomer Jean-Frédéric-Théodore Maurice. He told Maurice that "Christianity is quite a beautiful thing" and praised its civilising influence. Maurice thought that the basis of Laplace's beliefs was, little by little, being modified, but that he held fast to his conviction that the invariability of the laws of nature did not permit of supernatural events. After Laplace's death, Poisson told Maurice, "You know that I do not share your eligiousopinions, but my conscience forces me to recount something that will surely please you." When Poisson had complimented Laplace about his "brilliant discoveries", the dying man had fixed him with a pensive look and replied, "Ah! We chase after phantoms 'chimères''" These were his last words, interpreted by Maurice as a realisation of the ultimate "

vanity Vanity is the excessive belief in one's own abilities or attractiveness to others. Prior to the 14th century it did not have such narcissistic undertones, and merely meant ''futility''. The related term vainglory is now often seen as an archaic ...

" of earthly pursuits.Hahn (2005), p. 204. Laplace received the

last rites The last rites, also known as the Commendation of the Dying, are the last prayers and ministrations given to an individual of Christian faith, when possible, shortly before death. They may be administered to those awaiting execution, mortall ...

from the

curé A curate () is a person who is invested with the ''care'' or ''cure'' (''cura'') ''of souls'' of a parish. In this sense, "curate" means a parish priest; but in English-speaking countries the term ''curate'' is commonly used to describe clergy w ...

of the Missions Étrangères (in whose parish he was to be buried) and the curé of Arcueil. According to his biographer, Roger Hahn, it is "not credible" that Laplace "had a proper Catholic end", and he "remained a skeptic" to the very end of his life. Laplace in his last years has been described as an agnostic.

Excommunication of a comet

In 1470 the

humanist Humanism is a philosophical stance that emphasizes the individual and social potential and agency of human beings. It considers human beings the starting point for serious moral and philosophical inquiry. The meaning of the term "human ...

scholar Bartolomeo Platina wrote that

Pope Callixtus III Pope Callixtus III ( it, Callisto III, va, Calixt III, es, Calixto III; 31 December 1378 – 6 August 1458), born Alfonso de Borgia ( va, Alfons de Borja), was head of the Catholic Church and ruler of the Papal States from 8 April 1455 to his ...

had asked for prayers for deliverance from the Turks during a 1456 appearance of

Halley's Comet Halley's Comet or Comet Halley, officially designated 1P/Halley, is a short-period comet visible from Earth every 75–79 years. Halley is the only known short-period comet that is regularly visible to the naked eye from Earth, and thus the on ...

. Platina's account does not accord with Church records, which do not mention the comet. Laplace is alleged to have embellished the story by claiming the Pope had "

excommunicated Excommunication is an institutional act of religious censure used to end or at least regulate the communion of a member of a congregation with other members of the religious institution who are in normal communion with each other. The purpose ...

" Halley's comet. What Laplace actually said, in ''Exposition du système du monde'' (1796), was that the Pope had ordered the comet to be "

exorcised Exorcism () is the religious or spiritual practice of evicting demons, jinns, or other malevolent spiritual entities from a person, or an area, that is believed to be possessed. Depending on the spiritual beliefs of the exorcist, this may be ...

" (''conjuré''). It was Arago, in ''Des Comètes en général'' (1832), who first spoke of an excommunication.

Honors

* Correspondent of the Royal Institute of the Netherlands in 1809. * Foreign Honorary Member of the

American Academy of Arts and Sciences The American Academy of Arts and Sciences (abbreviation: AAA&S) is one of the oldest learned societies in the United States. It was founded in 1780 during the American Revolution by John Adams, John Hancock, James Bowdoin, Andrew Oliver, a ...

in 1822. * The asteroid

4628 Laplace 46 may refer to: * 46 (number) * 46 (album), ''46'' (album), a 1983 album by Kino (band), Kino * "Forty Six", a song by Karma to Burn from the album ''Appalachian Incantation'', 2010 * One of the years 46 BC, AD 46, 1946, 2046 {{Number disambiguat ...

is named for Laplace. * A spur of the

Montes Jura Montes Jura is a mountain range in the northwest part of the near side of the Moon. The selenographic coordinates of this range are 47.1° N 34.0° W. It has a diameter of 422 km, with mountains rising to approximately 3800m above the level ...

on the Moon is known as

Promontorium Laplace Promontorium Laplace is a raised mountainous cape situated at the end of Montes Jura in Mare Imbrium on the near side of the Moon. Its selenographic coordinates are 46.8° N, 25.5° W and it is 2600 meters high. It forms the northeast boundary of ...

. * His name is one of the 72 names inscribed on the Eiffel Tower. * The tentative working name of the

European Space Agency , owners = , headquarters = Paris, Île-de-France, France , coordinates = , spaceport = Guiana Space Centre , seal = File:ESA emblem seal.png , seal_size = 130px , image = Views in the Main Control Room (1205 ...

Europa Jupiter System Mission Europa may refer to: Places * Europe * Europa (Roman province), a province within the Diocese of Thrace * Europa (Seville Metro), Seville, Spain; a station on the Seville Metro * Europa City, Paris, France; a planned development * Europa Clif ...

is the "Laplace"

space probe A space probe is an artificial satellite that travels through space to collect scientific data. A space probe may orbit Earth; approach the Moon; travel through interplanetary space; flyby, orbit, or land or fly on other planetary bodies; or ent ...

. * A train station in the

RER B RER B is one of the five lines in the Réseau Express Régional (English: Regional Express Network), a hybrid commuter rail and rapid transit system serving Paris, France and its Île-de-France suburbs. The RER B line crosses the region from no ...

bears his name. * A street in Verkhnetemernitsky (near

Rostov-on-Don Rostov-on-Don ( rus, Ростов-на-Дону, r=Rostov-na-Donu, p=rɐˈstof nə dɐˈnu) is a port city and the administrative centre of Rostov Oblast and the Southern Federal District of Russia. It lies in the southeastern part of the East Eu ...

Russia Russia (, , ), or the Russian Federation, is a List of transcontinental countries, transcontinental country spanning Eastern Europe and North Asia, Northern Asia. It is the List of countries and dependencies by area, largest country in the ...

Quotations

* I had no need of that hypothesis. ("Je n'avais pas besoin de cette hypothèse-là", allegedly as a reply to

, who had asked why he hadn't mentioned God in his book on

.) * It is therefore obvious that ... (Frequently used in the ''Celestial Mechanics'' when he had proved something and mislaid the proof, or found it clumsy. Notorious as a signal for something true, but hard to prove.) * "We are so far from knowing all the agents of nature and their diverse modes of action that it would not be philosophical to deny phenomena solely because they are inexplicable in the actual state of our knowledge. But we ought to examine them with an attention all the more scrupulous as it appears more difficult to admit them." ** This is restated in Theodore Flournoy's work ''From India to the Planet Mars'' as the Principle of Laplace or, "The weight of the evidence should be proportioned to the strangeness of the facts." ** Most often repeated as "The weight of evidence for an extraordinary claim must be proportioned to its strangeness." (see also:

Sagan standard The Sagan standard is a neologism abbreviating the aphorism that "''extraordinary claims require extraordinary evidence''" (ECREE). It is named after science communicator Carl Sagan who used the exact phrase on his television program ''Cosmos'' ...

) * This simplicity of ratios will not appear astonishing if we consider that all the effects of nature are only mathematical results of a small number of immutable laws. * Infinitely varied in her effects, nature is only simple in her causes. * What we know is little, and what we are ignorant of is immense. (Fourier comments: "This was at least the meaning of his last words, which were articulated with difficulty.") * One sees in this essay that the theory of probabilities is basically only common sense reduced to a calculus. It makes one estimate accurately what right-minded people feel by a sort of instinct, often without being able to give a reason for it.

List of works

* * * * * * * File:Laplace-1.jpg, Volumes 1-5 of Pierre-Simon Laplace's " Traité de mécanique céleste" (1799) File:Laplace-2.jpg, Title page to Volume I of " Traité de mécanique céleste" (1799) File:Laplace-3.jpg, Table of contents to Volume I of " Traité de mécanique céleste" (1799) File:Laplace-4.jpg, First page of Volume I of " Traité de mécanique céleste" (1799)

Bibliography

*
Œuvres complètes de Laplace
', 14 vol. (1878–1912), Paris: Gauthier-Villars (copy from Gallica in French) * ''Théorie du movement et de la figure elliptique des planètes'' (1784) Paris (not in ''Œuvres complètes'') *
Précis de l'histoire de l'astronomie
' * Alphonse Rebière, ''Mathématiques et mathématiciens'', 3rd edition Paris, Nony & Cie, 1898.

English translations

Bowditch, N. (trans.) (1829–1839) ''Mécanique céleste'', 4 vols, Boston ** New edition by Reprint Services * – 829–1839(1966–1969) ''Celestial Mechanics'', 5 vols, including the original French * Pound, J. (trans.) (1809) ''The System of the World'', 2 vols, London: Richard Phillips * _ ''The System of the World (v.1)'' * _ ''The System of the World (v.2)'' * –

809 __NOTOC__ Year 809 (Roman numerals, DCCCIX) was a common year starting on Monday (link will display the full calendar) of the Julian calendar. Events By place Byzantine Empire * Spring – Siege of Serdica (809), Siege of Serdica: ...

(2007) ''The System of the World'', vol.1, Kessinger, * Toplis, J. (trans.) (1814) A treatise upon analytical mechanics Nottingham: H. Barnett * , translated from the French 6th ed. (1840) ** * , translated from the French 5th ed. (1825)

References

Citations

General sources

* * * * – (2006) "A Science Empire in Napoleonic France", ''History of Science'', vol. 44, pp. 29–48 * * David, F. N. (1965) "Some notes on Laplace", in Neyman, J. & LeCam, L. M. (eds) ''Bernoulli, Bayes and Laplace'', Berlin, pp. 30–44. * * * * * * , delivered 15 June 1829, published in 1831. * * * Grattan-Guinness, I., 2005, "'Exposition du système du monde' and 'Traité de méchanique céleste'" in his ''Landmark Writings in Western Mathematics''. Elsevier: 242–57. * Gribbin, John. ''The Scientists: A History of Science Told Through the Lives of Its Greatest Inventors''. New York, Random House, 2002. p. 299. * * – (1981) "Laplace and the Vanishing Role of God in the Physical Universe", in Woolf, Henry, ed., ''The Analytic Spirit: Essays in the History of Science''. Ithaca, NY: Cornell University Press. . * * * * * (1999) * * Rouse Ball, W.W.

908 __NOTOC__ Year 908 ( CMVIII) was a leap year starting on Friday (link will display the full calendar) of the Julian calendar. Events By place Byzantine Empire * May 15 – The three-year-old Constantine VII, the son of Emperor L ...

(2003) "Pierre Simon Laplace (1749–1827)", in ''A Short Account of the History of Mathematics'', 4th ed., Dover, Als
available at Project Gutenberg
* * * Whitrow, G. J. (2001) "Laplace, Pierre-Simon, marquis de", ''

'', Deluxe CDROM edition * * * *

External links

* *
Pierre-Simon Laplace
in the MacTutor History of Mathematics archive. *
Guide to the Pierre Simon Laplace Papers
at

The Bancroft Library The Bancroft Library in the center of the campus of the University of California, Berkeley, is the university's primary special-collections library. It was acquired from its founder, Hubert Howe Bancroft, in 1905, with the proviso that it retai ...

*
English translation
of a large part of Laplace's work in probability and statistics, provided b

Pierre-Simon Laplace – Œuvres complètes
(last 7 volumes only) Gallica-Math * "Sur le mouvement d'un corps qui tombe d'une grande hauteur" (Laplace 1803), online and analysed on
BibNum
' (English). {{DEFAULTSORT:Laplace, Pierre Simon 1749 births 1827 deaths People from Calvados (department) 18th-century French mathematicians 19th-century French mathematicians Counts of the First French Empire Determinists Enlightenment scientists French agnostics French deists 18th-century French astronomers French marquesses French physicists Fluid dynamicists Grand Officiers of the Légion d'honneur Mathematical analysts Linear algebraists Members of the Académie Française Members of the French Academy of Sciences Members of the Royal Netherlands Academy of Arts and Sciences Members of the Royal Swedish Academy of Sciences Fellows of the Royal Society Probability theorists French interior ministers Theoretical physicists Fellows of the American Academy of Arts and Sciences University of Caen Normandy alumni