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152-680: Zhangguangcai Range is divided into two branches, the west of the Jiaohe Basin (蛟河盆地) is the Xilaoye Range (西老爷岭), and the east of the Jiaohe Basin is the Weihu Range (威虎岭). Zhangguangcai Range runs northeast-southwest, with an average altitude of more than 800 meters , and the main peak, Laotudingzi Mountain (老秃顶子山), is 1,686.9 meters high. This article related to a mountain or hill in China

304-475: A polymath . He was born in the city of Pisa , then part of the Duchy of Florence . Galileo has been called the father of observational astronomy , modern-era classical physics, the scientific method , and modern science . Galileo studied speed and velocity , gravity and free fall , the principle of relativity , inertia , projectile motion and also worked in applied science and technology, describing

456-495: A second . After the 2019 revision of the SI , this definition was rephrased to include the definition of a second in terms of the caesium frequency Δ ν Cs . This series of amendments did not alter the size of the metre significantly – today Earth's polar circumference measures 40 007 .863 km , a change of about 200 parts per million from the original value of exactly 40 000  km , which also includes improvements in

608-609: A Central Office, located at the Prussian Geodetic Institute, whose management was entrusted to Johann Jacob Baeyer. Baeyer's goal was a new determination of anomalies in the shape of the Earth using precise triangulations, combined with gravity measurements. This involved determining the geoid by means of gravimetric and leveling measurements, in order to deduce the exact knowledge of the terrestrial spheroid while taking into account local variations. To resolve this problem, it

760-605: A book on the subject, encouraged by the election of Cardinal Maffeo Barberini as Pope Urban VIII in 1623. Barberini was a friend and admirer of Galileo, and had opposed the admonition of Galileo in 1616. Galileo's resulting book, Dialogue Concerning the Two Chief World Systems , was published in 1632, with formal authorization from the Inquisition and papal permission. Earlier, Pope Urban VIII had personally asked Galileo to give arguments for and against heliocentrism in

912-594: A brief treatise entitled Sidereus Nuncius ( Starry Messenger ). On 30 November 1609, Galileo aimed his telescope at the Moon . While not being the first person to observe the Moon through a telescope (English mathematician Thomas Harriot had done so four months before but only saw a "strange spottednesse"), Galileo was the first to deduce the cause of the uneven waning as light occlusion from lunar mountains and craters . In his study, he also made topographical charts, estimating

1064-605: A debate with Galileo, sending him an essay disputing the Copernican system. Galileo later stated that he believed this essay to have been instrumental in the action against Copernicanism that followed. Ingoli may have been commissioned by the Inquisition to write an expert opinion on the controversy, with the essay providing the basis for the Inquisition's actions. The essay focused on eighteen physical and mathematical arguments against heliocentrism. It borrowed primarily from Tycho Brahe's arguments, notably that heliocentrism would require

1216-473: A determination of the size of the Earth, then considered as a sphere, by Jean Picard through triangulation of Paris meridian . In 1671, Jean Picard also measured the length of a seconds pendulum at Paris Observatory and proposed this unit of measurement to be called the astronomical radius (French: Rayon Astronomique ). In 1675, Tito Livio Burattini suggested the term metro cattolico meaning universal measure for this unit of length, but then it

1368-409: A friend of Galileo, included a realistic depiction of the Moon in one of his paintings; he probably used his own telescope to make the observation. On 7 January 1610, Galileo observed with his telescope what he described at the time as "three fixed stars, totally invisible by their smallness", all close to Jupiter, and lying on a straight line through it. Observations on subsequent nights showed that

1520-487: A genuinely pious Catholic, Galileo fathered three children out of wedlock with Marina Gamba . They had two daughters, Virginia (born 1600) and Livia (born 1601), and a son, Vincenzo (born 1606). Due to their illegitimate birth, Galileo considered the girls unmarriageable, if not posing problems of prohibitively expensive support or dowries, which would have been similar to Galileo's previous extensive financial problems with two of his sisters. Their only worthy alternative

1672-537: A lutenist and composer who added to Galileo's financial burdens for the rest of his life. Michelangelo was unable to contribute his fair share of their father's promised dowries to their brothers-in-law, who later attempted to seek legal remedies for payments due. Michelangelo also occasionally had to borrow funds from Galileo to support his musical endeavours and excursions. These financial burdens may have contributed to Galileo's early desire to develop inventions that would bring him additional income. When Galileo Galilei

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1824-401: A method for measuring the apparent size of a star without a telescope. As described in his Dialogue Concerning the Two Chief World Systems , his method was to hang a thin rope in his line of sight to the star and measure the maximum distance from which it would wholly obscure the star. From his measurements of this distance and of the width of the rope, he could calculate the angle subtended by

1976-905: A metre "too short" compared to a more general definition taken from the average of a large number of arcs. As early as 1861, Johann Jacob Baeyer sent a memorandum to the King of Prussia recommending international collaboration in Central Europe with the aim of determining the shape and dimensions of the Earth. At the time of its creation, the association had sixteen member countries: Austrian Empire , Kingdom of Belgium , Denmark , seven German states ( Grand Duchy of Baden , Kingdom of Bavaria , Kingdom of Hanover , Mecklenburg , Kingdom of Prussia , Kingdom of Saxony , Saxe-Coburg and Gotha ), Kingdom of Italy , Netherlands , Russian Empire (for Poland ), United Kingdoms of Sweden and Norway , as well as Switzerland . The Central European Arc Measurement created

2128-625: A new value for the flattening of the Earth, which he determinated as ⁠ 1 / 299.15 ⁠ . He also devised a new instrument for measuring gravitational acceleration which was first used in Switzerland by Emile Plantamour , Charles Sanders Peirce , and Isaac-Charles Élisée Cellérier (8.01.1818 – 2.10.1889), a Genevan mathematician soon independently discovered a mathematical formula to correct systematic errors of this device which had been noticed by Plantamour and Adolphe Hirsch . This allowed Friedrich Robert Helmert to determine

2280-553: A pamphlet, An Astronomical Disputation on the Three Comets of the Year 1618 , which discussed the nature of a comet that had appeared late in November of the previous year. Grassi concluded that the comet was a fiery body that had moved along a segment of a great circle at a constant distance from the earth, and since it moved in the sky more slowly than the Moon, it must be farther away than

2432-687: A part of the Survey of the Coast. He compared various units of length used in the United States at that time and measured coefficients of expansion to assess temperature effects on the measurements. In 1832, Carl Friedrich Gauss studied the Earth's magnetic field and proposed adding the second to the basic units of the metre and the kilogram in the form of the CGS system ( centimetre , gram , second). In 1836, he founded

2584-627: A powerful argument against both the Ptolemaic system and the geoheliocentric system of Tycho Brahe. A dispute over claimed priority in the discovery of sunspots, and in their interpretation, led Galileo to a long and bitter feud with the Jesuit Christoph Scheiner . In the middle was Mark Welser , to whom Scheiner had announced his discovery, and who asked Galileo for his opinion. Both of them were unaware of Johannes Fabricius ' earlier observation and publication of sunspots. Galileo observed

2736-502: A practical use for his discovery. Determining the east–west position of ships at sea required their clocks be synchronized with clocks at the prime meridian . Solving this longitude problem had great importance to safe navigation and large prizes were established by Spain and later Holland for its solution. Since eclipses of the moons he discovered were relatively frequent and their times could be predicted with great accuracy, they could be used to set shipboard clocks and Galileo applied for

2888-542: A prototype metre bar, distribute national metric prototypes, and maintain comparisons between them and non-metric measurement standards. The organisation distributed such bars in 1889 at the first General Conference on Weights and Measures (CGPM: Conférence Générale des Poids et Mesures ), establishing the International Prototype Metre as the distance between two lines on a standard bar composed of an alloy of 90% platinum and 10% iridium , measured at

3040-487: A remarkably accurate value of ⁠ 1 / 298.3 ⁠ for the flattening of the Earth when he proposed his ellipsoid of reference in 1901. This was also the result of the Metre Convention of 1875, when the metre was adopted as an international scientific unit of length for the convenience of continental European geodesists following the example of Ferdinand Rudolph Hassler . In 1790, one year before it

3192-644: A series of international conferences was held to devise new metric standards. When a conflict broke out regarding the presence of impurities in the metre-alloy of 1874, a member of the Preparatory Committee since 1870 and Spanish representative at the Paris Conference in 1875, Carlos Ibáñez e Ibáñez de Ibero intervened with the French Academy of Sciences to rally France to the project to create an International Bureau of Weights and Measures equipped with

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3344-609: A standard metre made in Paris to the United States in October 1805. He designed a baseline apparatus which instead of bringing different bars in actual contact during measurements, used only one bar calibrated on the metre and optical contact. Thus the metre became the unit of length for geodesy in the United States. In 1830, Hassler became head of the Office of Weights and Measures, which became

3496-558: A standard of length. By 1925, interferometry was in regular use at the BIPM. However, the International Prototype Metre remained the standard until 1960, when the eleventh CGPM defined the metre in the new International System of Units (SI) as equal to 1 650 763 .73   wavelengths of the orange - red emission line in the electromagnetic spectrum of the krypton-86 atom in vacuum . To further reduce uncertainty,

3648-423: A standard would be independent of any changes in the dimensions of the earth, and should be adopted by those who expect their writings to be more permanent than that body. Charles Sanders Peirce 's work promoted the advent of American science at the forefront of global metrology. Alongside his intercomparisons of artifacts of the metre and contributions to gravimetry through improvement of reversible pendulum, Peirce

3800-514: A thing. Compounding this problem, other astronomers had difficulty confirming Galileo's observations. When he demonstrated the telescope in Bologna, the attendees struggled to see the moons. One of them, Martin Horky, noted that some fixed stars, such as Spica Virginis , appeared double through the telescope. He took this as evidence that the instrument was deceptive when viewing the heavens, casting doubt on

3952-505: Is a stub . You can help Misplaced Pages by expanding it . Meters The metre (or meter in US spelling ; symbol: m ) is the base unit of length in the International System of Units (SI). Since 2019, the metre has been defined as the length of the path travelled by light in vacuum during a time interval of ⁠ 1 / 299 792 458 ⁠ of a second , where the second

4104-478: Is currently one limiting factor in laboratory realisations of the metre, and it is several orders of magnitude poorer than that of the second, based upon the caesium fountain atomic clock ( U = 5 × 10 ). Consequently, a realisation of the metre is usually delineated (not defined) today in labs as 1 579 800 .762 042 (33) wavelengths of helium–neon laser light in vacuum, the error stated being only that of frequency determination. This bracket notation expressing

4256-545: Is defined by a hyperfine transition frequency of caesium . The metre was originally defined in 1791 by the French National Assembly as one ten-millionth of the distance from the equator to the North Pole along a great circle , so the Earth's polar circumference is approximately 40 000  km . In 1799, the metre was redefined in terms of a prototype metre bar, the bar used was changed in 1889, and in 1960

4408-797: Is derived from the Proto-Indo-European root *meh₁- 'to measure'. The motto ΜΕΤΡΩ ΧΡΩ ( metro chro ) in the seal of the International Bureau of Weights and Measures (BIPM), which was a saying of the Greek statesman and philosopher Pittacus of Mytilene and may be translated as "Use measure!", thus calls for both measurement and moderation. The use of the word metre (for the French unit mètre ) in English began at least as early as 1797. Galileo discovered gravitational acceleration to explain

4560-565: The British Crown . Instead of the seconds pendulum method, the commission of the French Academy of Sciences – whose members included Borda , Lagrange , Laplace , Monge , and Condorcet – decided that the new measure should be equal to one ten-millionth of the distance from the North Pole to the Equator , determined through measurements along the meridian passing through Paris. Apart from

4712-579: The Committee Meter in the United States and served as standard of length in the United States Coast Survey until 1890. According to geodesists, these standards were secondary standards deduced from the Toise of Peru. In Europe, except Spain, surveyors continued to use measuring instruments calibrated on the Toise of Peru. Among these, the toise of Bessel and the apparatus of Borda were respectively

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4864-543: The Dialogue , his final interrogation, in July 1633, concluded with his being threatened with torture if he did not tell the truth, but he maintained his denial despite the threat. The sentence of the Inquisition was delivered on 22 June. It was in three essential parts: According to popular legend, after recanting his theory that the Earth moved around the Sun, Galileo allegedly muttered

5016-533: The Duchy of Florence ) on 15 February 1564, the first of six children of Vincenzo Galilei , a leading lutenist , composer, and music theorist , and Giulia Ammannati , the daughter of a prominent merchant, who had married two years earlier in 1562, when he was 42, and she was 24. Galileo became an accomplished lutenist himself and would have learned early from his father a skepticism for established authority. Three of Galileo's five siblings survived infancy. The youngest, Michelangelo (or Michelagnolo), also became

5168-613: The Florentine Academy , he presented two lectures, On the Shape, Location, and Size of Dante's Inferno , in an attempt to propose a rigorous cosmological model of Dante's hell . Being inspired by the artistic tradition of the city and the works of the Renaissance artists , Galileo acquired an aesthetic mentality . While a young teacher at the Accademia, he began a lifelong friendship with

5320-581: The Milky Way , previously believed to be nebulous , and found it to be a multitude of stars packed so densely that they appeared from Earth to be clouds. He located many other stars too distant to be visible to the naked eye. He observed the double star Mizar in Ursa Major in 1617. In the Starry Messenger , Galileo reported that stars appeared as mere blazes of light, essentially unaltered in appearance by

5472-628: The North Sea and the Baltic Sea in the north. In his mind, the cooperation of all the States of Central Europe could open the field to scientific research of the highest interest, research that each State, taken in isolation, was not able to undertake. Spain and Portugal joined the European Arc Measurement in 1866. French Empire hesitated for a long time before giving in to the demands of

5624-557: The Roman Inquisition by Father Niccolò Lorini , who claimed that Galileo and his followers were attempting to reinterpret the Bible, which was seen as a violation of the Council of Trent and looked dangerously like Protestantism . Lorini specifically cited Galileo's letter to Castelli. Galileo went to Rome to defend himself and his ideas. At the start of 1616, Francesco Ingoli initiated

5776-554: The Sun would cause its illuminated hemisphere to face the Earth when it was on the opposite side of the Sun and to face away from the Earth when it was on the Earth-side of the Sun. In Ptolemy's geocentric model , it was impossible for any of the planets' orbits to intersect the spherical shell carrying the Sun. Traditionally, the orbit of Venus was placed entirely on the near side of the Sun, where it could exhibit only crescent and new phases. It

5928-519: The Tychonic , Capellan and Extended Capellan models, each either with or without a daily rotating Earth. These all explained the phases of Venus without the 'refutation' of full heliocentrism's prediction of stellar parallax. Galileo's discovery of the phases of Venus was thus his most empirically practically influential contribution to the two-stage transition from full geocentrism to full heliocentrism via geo-heliocentrism. In 1610, Galileo also observed

6080-490: The luminiferous aether in 1905, just as Newton had questioned Descartes' Vortex theory in 1687 after Jean Richer 's pendulum experiment in Cayenne , French Guiana . Furthermore, special relativity changed conceptions of time and mass , while general relativity changed that of space . According to Newton, space was Euclidean , infinite and without boundaries and bodies gravitated around each other without changing

6232-525: The thermometer , and, in 1586, published a small book on the design of a hydrostatic balance he had invented (which first brought him to the attention of the scholarly world). Galileo also studied disegno , a term encompassing fine art, and, in 1588, obtained the position of instructor in the Accademia delle Arti del Disegno in Florence, teaching perspective and chiaroscuro . In the same year, upon invitation by

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6384-514: The 17th CGPM in 1983 replaced the definition of the metre with its current definition, thus fixing the length of the metre in terms of the second and the speed of light : This definition fixed the speed of light in vacuum at exactly 299 792 458  metres per second (≈ 300 000  km/s or ≈1.079 billion km/hour ). An intended by-product of the 17th CGPM's definition was that it enabled scientists to compare lasers accurately using frequency, resulting in wavelengths with one-fifth

6536-602: The 1860s, at the initiative of Carlos Ibáñez e Ibáñez de Ibero who would become the first president of both the International Geodetic Association and the International Committee for Weights and Measure , to remeasure the arc of meridian from Dunkirk to Formentera and to extend it from Shetland to the Sahara . This did not pave the way to a new definition of the metre because it was known that

6688-580: The 19th century by the modernist impetus of Muhammad Ali who founded in Sabtieh, Boulaq district, in Cairo an Observatory which he was keen to keep in harmony with the progress of this science still in progress. In 1858, a Technical Commission was set up to continue, by adopting the procedures instituted in Europe, the cadastre work inaugurated under Muhammad Ali. This Commission suggested to Viceroy Mohammed Sa'id Pasha

6840-536: The Aristotelian belief in the immutability of the heavens. Perhaps based only on descriptions of the first practical telescope which Hans Lippershey tried to patent in the Netherlands in 1608, Galileo, in the following year, made a telescope with about 3x magnification. He later made improved versions with up to about 30x magnification. With a Galilean telescope , the observer could see magnified, upright images on

6992-640: The Association, which asked the French geodesists to take part in its work. It was only after the Franco-Prussian War , that Charles-Eugène Delaunay represented France at the Congress of Vienna in 1871. In 1874, Hervé Faye was appointed member of the Permanent Commission which was presided by Carlos Ibáñez e Ibáñez de Ibero. The International Geodetic Association gained global importance with

7144-619: The Central European Arc Measurement (German: Mitteleuropaïsche Gradmessung ) on the initiative of Johann Jacob Baeyer in 1863, and by that of the International Meteorological Organisation whose president, the Swiss meteorologist and physicist, Heinrich von Wild would represent Russia at the International Committee for Weights and Measures (CIPM). In 1834, Hassler, measured at Fire Island

7296-583: The Church, the majority of educated people subscribed to the Aristotelian geocentric view that the Earth is the centre of the Universe and the orbit of all heavenly bodies, or Tycho Brahe's new system blending geocentrism with heliocentrism. Opposition to heliocentrism and Galileo's writings on it combined religious and scientific objections. Religious opposition to heliocentrism arose from biblical passages implying

7448-586: The Earth was the unit to which all celestial distances were to be referred. Indeed, Earth proved to be an oblate spheroid through geodetic surveys in Ecuador and Lapland and this new data called into question the value of Earth radius as Picard had calculated it. After the Anglo-French Survey , the French Academy of Sciences commissioned an expedition led by Jean Baptiste Joseph Delambre and Pierre Méchain , lasting from 1792 to 1798, which measured

7600-665: The Earth—it was what is commonly known as a terrestrial telescope or a spyglass. He could also use it to observe the sky; for a time he was one of those who could construct telescopes good enough for that purpose. On 25 August 1609, he demonstrated one of his early telescopes, with a magnification of about 8x or 9x, to Venetian lawmakers. His telescopes were also a profitable sideline for Galileo, who sold them to merchants who found them useful both at sea and as items of trade. He published his initial telescopic astronomical observations in March 1610 in

7752-456: The Equator . When the final result was known, a bar whose length was closest to the meridional definition of the metre was selected and placed in the National Archives on 22 June 1799 (4 messidor An VII in the Republican calendar) as a permanent record of the result. In 1816, Ferdinand Rudolph Hassler was appointed first Superintendent of the Survey of the Coast . Trained in geodesy in Switzerland, France and Germany , Hassler had brought

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7904-546: The Florentine painter Cigoli . In 1589, he was appointed to the chair of mathematics in Pisa. In 1591, his father died, and he was entrusted with the care of his younger brother Michelagnolo . In 1592, he moved to the University of Padua where he taught geometry, mechanics , and astronomy until 1610. During this period, Galileo made significant discoveries in both pure fundamental science (for example, kinematics of motion and astronomy) as well as practical applied science (for example, strength of materials and pioneering

8056-424: The French Academy of Sciences a report drafted by Otto Wilhelm von Struve , Heinrich von Wild , and Moritz von Jacobi , whose theorem has long supported the assumption of an ellipsoid with three unequal axes for the figure of the Earth, inviting his French counterpart to undertake joint action to ensure the universal use of the metric system in all scientific work. In the 1870s and in light of modern precision,

8208-472: The German born, Swiss astronomer, Adolphe Hirsch conformed to the opinion of Italy and Spain to create, in spite of French reluctance, the International Bureau of Weights and Measures in France as a permanent institution at the disadventage of the Conservatoire national des Arts et Métiers . At that time, units of measurement were defined by primary standards , and unique artifacts made of different alloys with distinct coefficients of expansion were

8360-410: The Greek verb μετρέω ( metreo ) ((I) measure, count or compare) and noun μέτρον ( metron ) (a measure), which were used for physical measurement, for poetic metre and by extension for moderation or avoiding extremism (as in "be measured in your response"). This range of uses is also found in Latin ( metior, mensura ), French ( mètre, mesure ), English and other languages. The Greek word

8512-449: The Magnetischer Verein, the first international scientific association, in collaboration with Alexander von Humboldt and Wilhelm Edouard Weber . The coordination of the observation of geophysical phenomena such as the Earth's magnetic field, lightning and gravity in different points of the globe stimulated the creation of the first international scientific associations. The foundation of the Magnetischer Verein would be followed by that of

8664-475: The Moon. Grassi's arguments and conclusions were criticised in a subsequent article, Discourse on Comets , published under the name of one of Galileo's disciples, a Florentine lawyer named Mario Guiducci , although it had been largely written by Galileo himself. Galileo and Guiducci offered no definitive theory of their own on the nature of comets, although they did present some tentative conjectures that are now known to be mistaken. (The correct approach to

8816-413: The North Pole to the Equator was then extrapolated from the measurement of the Paris meridian arc between Dunkirk and Barcelona and was determined as 5 130 740  toises. As the metre had to be equal to one ten-millionth of this distance, it was defined as 0.513074 toise or 3 feet and 11.296 lines of the Toise of Peru, which had been constructed in 1735 for the French Geodesic Mission to

8968-401: The Pope and the Jesuits , who had both strongly supported Galileo up until this point. He was tried by the Inquisition, found "vehemently suspect of heresy", and forced to recant. He spent the rest of his life under house arrest. During this time, he wrote Two New Sciences (1638), primarily concerning kinematics and the strength of materials . Galileo was born in Pisa (then part of

9120-558: The Spanish standard had been compared with Borda 's double-toise N° 1, which served as a comparison module for the measurement of all geodesic bases in France, and was also to be compared to the Ibáñez apparatus. In 1954, the connection of the southerly extension of the Struve Geodetic Arc with an arc running northwards from South Africa through Egypt would bring the course of a major meridian arc back to land where Eratosthenes had founded geodesy . Seventeen years after Bessel calculated his ellipsoid of reference , some of

9272-535: The Sun or even the orbit of the Earth. It would not be until much later that astronomers realized the apparent magnitudes of stars were caused by an optical phenomenon called the airy disk , and were functions of their brightness rather than true physical size (see Magnitude#History ). Galileo defended heliocentrism based on his astronomical observations of 1609 . In December 1613, the Grand Duchess Christina of Florence confronted one of Galileo's friends and followers, Benedetto Castelli , with biblical objections to

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9424-416: The Swiss physicist Charles-Edouard Guillaume , was granted the Nobel Prize in Physics in 1920. Guillaume's Nobel Prize marked the end of an era in which metrology was leaving the field of geodesy to become a technological application of physics . In 1921, the Nobel Prize in Physics was awarded to another Swiss scientist, Albert Einstein , who following Michelson–Morley experiment had questioned

9576-501: The Toise of Peru, one for Friedrich Georg Wilhelm von Struve , a second for Heinrich Christian Schumacher in 1821 and a third for Friedrich Bessel in 1823. In 1831, Henri-Prudence Gambey also realized a copy of the Toise of Peru which was kept at Altona Observatory . In the second half of the 19th century, the creation of the International Geodetic Association would mark the adoption of new scientific methods. It then became possible to accurately measure parallel arcs, since

9728-413: The Two Chief World Systems the Dialogue on the Ebb and Flow of the Sea . The reference to tides was removed from the title by order of the Inquisition. For Galileo, the tides were caused by the sloshing back and forth of water in the seas as a point on the Earth's surface sped up and slowed down because of the Earth's rotation on its axis and revolution around the Sun. He circulated his first account of

9880-416: The accession of Chile , Mexico and Japan in 1888; Argentina and United-States in 1889; and British Empire in 1898. The convention of the International Geodetic Association expired at the end of 1916. It was not renewed due to the First World War . However, the activities of the International Latitude Service were continued through an Association Géodesique réduite entre États neutres thanks to

10032-461: The accuracy of measuring the circumference. Metre is the standard spelling of the metric unit for length in nearly all English-speaking nations, the exceptions being the United States and the Philippines which use meter . Measuring devices (such as ammeter , speedometer ) are spelled "-meter" in all variants of English. The suffix "-meter" has the same Greek origin as the unit of length. The etymological roots of metre can be traced to

10184-457: The book, and to be careful not to advocate heliocentrism. Whether unknowingly or deliberately, Simplicio, the defender of the Aristotelian geocentric view in Dialogue Concerning the Two Chief World Systems , was often caught in his own errors and sometimes came across as a fool. Indeed, although Galileo states in the preface of his book that the character is named after a famous Aristotelian philosopher ( Simplicius in Latin, "Simplicio" in Italian),

10336-410: The chandelier took the same amount of time to swing back and forth, no matter how far it was swinging. When he returned home, he set up two pendulums of equal length and swung one with a large sweep and the other with a small sweep and found that they kept time together. It was not until the work of Christiaan Huygens , almost one hundred years later, that the tautochrone nature of a swinging pendulum

10488-406: The condemned opinions, and initially he denied even defending them. However, he was eventually persuaded to admit that, contrary to his true intention, a reader of his Dialogue could well have obtained the impression that it was intended to be a defence of Copernicanism. In view of Galileo's rather implausible denial that he had ever held Copernican ideas after 1616 or ever intended to defend them in

10640-412: The creation of the Office of Standard Weights and Measures in 1830. In continental Europe , Napoleonic Wars fostered German nationalism which later led to unification of Germany in 1871. Meanwhile, most European countries had adopted the metre. In the 1870s, German Empire played a pivotal role in the unification of the metric system through the European Arc Measurement but its overwhelming influence

10792-470: The creation of the Office of Standard Weights and Measures as an office within the Coast Survey contributed to the introduction of the Metric Act of 1866 allowing the use of the metre in the United States, and preceded the choice of the metre as international scientific unit of length and the proposal by the European Arc Measurement (German: Europäische Gradmessung ) to establish a "European international bureau for weights and measures". In 1867 at

10944-406: The data available at the time, Ritter came to the conclusion that the problem was only resolved in an approximate manner, the data appearing too scant, and for some affected by vertical deflections , in particular the latitude of Montjuïc in the French meridian arc which determination had also been affected in a lesser proportion by systematic errors of the repeating circle . The definition of

11096-418: The difference in longitude between their ends could be determined thanks to the invention of the electrical telegraph . Furthermore, advances in metrology combined with those of gravimetry have led to a new era of geodesy . If precision metrology had needed the help of geodesy, the latter could not continue to prosper without the help of metrology. It was then necessary to define a single unit to express all

11248-607: The distance between a belfry in Dunkirk and Montjuïc castle in Barcelona at the longitude of the Paris Panthéon . When the length of the metre was defined as one ten-millionth of the distance from the North Pole to the Equator , the flattening of the Earth ellipsoid was assumed to be ⁠ 1 / 334 ⁠ . In 1841, Friedrich Wilhelm Bessel using the method of least squares calculated from several arc measurements

11400-634: The efforts of H.G. van de Sande Bakhuyzen and Raoul Gautier (1854–1931), respectively directors of Leiden Observatory and Geneva Observatory . After the French Revolution , Napoleonic Wars led to the adoption of the metre in Latin America following independence of Brazil and Hispanic America , while the American Revolution prompted the foundation of the Survey of the Coast in 1807 and

11552-544: The error is explained in the article on measurement uncertainty . Practical realisation of the metre is subject to uncertainties in characterising the medium, to various uncertainties of interferometry, and to uncertainties in measuring the frequency of the source. A commonly used medium is air, and the National Institute of Standards and Technology (NIST) has set up an online calculator to convert wavelengths in vacuum to wavelengths in air. As described by NIST, in air,

11704-481: The existence of the moons. Christopher Clavius 's observatory in Rome confirmed the observations and, although unsure how to interpret them, gave Galileo a hero's welcome when he visited the next year. Galileo continued to observe the satellites over the next eighteen months, and by mid-1611, he had obtained remarkably accurate estimates for their periods—a feat which Johannes Kepler had believed impossible. Galileo saw

11856-410: The fall of bodies at the surface of the Earth. He also observed the regularity of the period of swing of the pendulum and that this period depended on the length of the pendulum. Kepler's laws of planetary motion served both to the discovery of Newton's law of universal gravitation and to the determination of the distance from Earth to the Sun by Giovanni Domenico Cassini . They both also used

12008-566: The first baseline of the Survey of the Coast, shortly before Louis Puissant declared to the French Academy of Sciences in 1836 that Jean Baptiste Joseph Delambre and Pierre Méchain had made errors in the meridian arc measurement , which had been used to determine the length of the metre. Errors in the method of calculating the length of the Paris meridian were taken into account by Bessel when he proposed his reference ellipsoid in 1841. Egyptian astronomy has ancient roots which were revived in

12160-461: The fixed nature of the Earth. Scientific opposition came from Brahe, who argued that if heliocentrism were true, an annual stellar parallax should be observed, though none was at the time. Aristarchus and Copernicus had correctly postulated that parallax was negligible because the stars were so distant. However, Brahe countered that since stars appear to have measurable angular size , if the stars were that distant, they would have to be far larger than

12312-480: The fourth on 13 January. Galileo named the group of four the Medicean stars , in honour of his future patron, Cosimo II de' Medici, Grand Duke of Tuscany , and Cosimo's three brothers. Later astronomers, however, renamed them Galilean satellites in honour of their discoverer. These satellites were independently discovered by Simon Marius on 8 January 1610 and are now called Io , Europa , Ganymede , and Callisto ,

12464-453: The heights of the mountains. The Moon was not what was long thought to have been a translucent and perfect sphere, as Aristotle claimed, and hardly the first "planet", an "eternal pearl to magnificently ascend into the heavenly empyrian", as put forth by Dante . Galileo is sometimes credited with the discovery of the lunar libration in latitude in 1632, although Thomas Harriot or William Gilbert may have done so before. The painter Cigoli,

12616-507: The idea of buying geodetic devices which were ordered in France. While Mahmud Ahmad Hamdi al-Falaki was in charge, in Egypt, of the direction of the work of the general map, the viceroy entrusted to Ismail Mustafa al-Falaki the study, in Europe, of the precision apparatus calibrated against the metre intended to measure the geodesic bases and already built by Jean Brunner in Paris. Ismail Mustafa had

12768-460: The legal basis of units of length. A wrought iron ruler, the Toise of Peru, also called Toise de l'Académie , was the French primary standard of the toise, and the metre was officially defined by an artifact made of platinum kept in the National Archives. Besides the latter, another platinum and twelve iron standards of the metre were made by Étienne Lenoir in 1799. One of them became known as

12920-582: The legal heir of Galileo and married Sestilia Bocchineri. Although Galileo seriously considered the priesthood as a young man, at his father's urging he instead enrolled in 1580 at the University of Pisa for a medical degree. He was influenced by the lectures of Girolamo Borro and Francesco Buonamici of Florence. In 1581, when he was studying medicine, he noticed a swinging chandelier , which air currents shifted about to swing in larger and smaller arcs. To him, it seemed, by comparison with his heartbeat, that

13072-421: The length of a metre in the 1790s was founded upon Arc measurements in France and Peru with a definition that it was to be 1/40 millionth of the circumference of the earth measured through the poles. Such were the inaccuracies of that period that within a matter of just a few years more reliable measurements would have given a different value for the definition of this international standard. That does not invalidate

13224-592: The main references for geodesy in Prussia and in France . These measuring devices consisted of bimetallic rulers in platinum and brass or iron and zinc fixed together at one extremity to assess the variations in length produced by any change in temperature. The combination of two bars made of two different metals allowed to take thermal expansion into account without measuring the temperature. A French scientific instrument maker, Jean Nicolas Fortin , had made three direct copies of

13376-452: The meantime, the commission of the French Academy of Sciences calculated a provisional value from older surveys of 443.44 lignes. This value was set by legislation on 7 April 1795. In 1799, a commission including Johan Georg Tralles , Jean Henri van Swinden , Adrien-Marie Legendre and Jean-Baptiste Delambre calculated the distance from Dunkirk to Barcelona using the data of the triangulation between these two towns and determined

13528-651: The measurements of terrestrial arcs and all determinations of the gravitational acceleration by means of pendulum. In 1866, the most important concern was that the Toise of Peru, the standard of the toise constructed in 1735 for the French Geodesic Mission to the Equator , might be so much damaged that comparison with it would be worthless, while Bessel had questioned the accuracy of copies of this standard belonging to Altona and Koenigsberg Observatories, which he had compared to each other about 1840. This assertion

13680-680: The measuring devices designed by Borda and used for this survey also raised hopes for a more accurate determination of the length of this meridian arc. The task of surveying the Paris meridian arc took more than six years (1792–1798). The technical difficulties were not the only problems the surveyors had to face in the convulsed period of the aftermath of the French Revolution: Méchain and Delambre, and later Arago , were imprisoned several times during their surveys, and Méchain died in 1804 of yellow fever, which he contracted while trying to improve his original results in northern Spain. In

13832-462: The melting point of ice. The comparison of the new prototypes of the metre with each other involved the development of special measuring equipment and the definition of a reproducible temperature scale. The BIPM's thermometry work led to the discovery of special alloys of iron–nickel, in particular invar , whose practically negligible coefficient of expansion made it possible to develop simpler baseline measurement methods, and for which its director,

13984-454: The meridian arcs the German astronomer had used for his calculation had been enlarged. This was a very important circumstance because the influence of errors due to vertical deflections was minimized in proportion to the length of the meridian arcs: the longer the meridian arcs, the more precise the image of the Earth ellipsoid would be. After Struve Geodetic Arc measurement, it was resolved in

14136-428: The metre in any way but highlights the fact that continuing improvements in instrumentation made better measurements of the earth’s size possible. It was well known that by measuring the latitude of two stations in Barcelona , Méchain had found that the difference between these latitudes was greater than predicted by direct measurement of distance by triangulation and that he did not dare to admit this inaccuracy. This

14288-539: The metre in replacement of the toise of Bessel, the creation of an International Metre Commission, and the foundation of a World institute for the comparison of geodetic standards, the first step towards the creation of the International Bureau of Weights and Measures . Hassler's metrological and geodetic work also had a favourable response in Russia. In 1869, the Saint Petersburg Academy of Sciences sent to

14440-401: The metre was redefined in terms of a certain number of wavelengths of a certain emission line of krypton-86 . The current definition was adopted in 1983 and modified slightly in 2002 to clarify that the metre is a measure of proper length . From 1983 until 2019, the metre was formally defined as the length of the path travelled by light in vacuum in ⁠ 1 / 299 792 458 ⁠ of

14592-495: The motion of the Earth. Prompted by this incident, Galileo wrote a letter to Castelli in which he argued that heliocentrism was actually not contrary to biblical texts and that the Bible was an authority on faith and morals, not science. This letter was not published but circulated widely. Two years later, Galileo wrote a letter to Christina that expanded his arguments previously made in eight pages to forty pages. By 1615, Galileo's writings on heliocentrism had been submitted to

14744-498: The name "Simplicio" in Italian also has the connotation of "simpleton". This portrayal of Simplicio made Dialogue Concerning the Two Chief World Systems appear as an advocacy book: an attack on Aristotelian geocentrism and defence of the Copernican theory. Most historians agree Galileo did not act out of malice and felt blindsided by the reaction to his book. However, the Pope did not take

14896-432: The names given by Marius in his Mundus Iovialis published in 1614. Galileo's observations of the satellites of Jupiter caused controversy in astronomy: a planet with smaller planets orbiting it did not conform to the principles of Aristotelian cosmology , which held that all heavenly bodies should circle the Earth, and many astronomers and philosophers initially refused to believe that Galileo could have discovered such

15048-402: The number of wavelengths of laser light of one of the standard types that fit into the length, and converting the selected unit of wavelength to metres. Three major factors limit the accuracy attainable with laser interferometers for a length measurement: Of these, the last is peculiar to the interferometer itself. The conversion of a length in wavelengths to a length in metres is based upon

15200-455: The obvious consideration of safe access for French surveyors, the Paris meridian was also a sound choice for scientific reasons: a portion of the quadrant from Dunkirk to Barcelona (about 1000 km, or one-tenth of the total) could be surveyed with start- and end-points at sea level, and that portion was roughly in the middle of the quadrant, where the effects of the Earth's oblateness were expected not to have to be accounted for. Improvements in

15352-525: The opinion that the sun stands still at the centre of the world and the Earth moves, and henceforth not to hold, teach, or defend it in any way whatever, either orally or in writing." The decree of the Congregation of the Index banned Copernicus's De Revolutionibus and other heliocentric works until correction. For the next decade, Galileo stayed well away from the controversy. He revived his project of writing

15504-529: The painting, Stillman Drake wrote "there is no doubt now that the famous words were already attributed to Galileo before his death". However, an intensive investigation by astrophysicist Mario Livio has revealed that said painting is most probably a copy of an 1837 painting by the Flemish painter Roman-Eugene Van Maldeghem. After a period with the friendly Ascanio Piccolomini (the Archbishop of Siena ), Galileo

15656-473: The planet Saturn , and at first mistook its rings for planets, thinking it was a three-bodied system. When he observed the planet later, Saturn's rings were directly oriented to Earth, causing him to think that two of the bodies had disappeared. The rings reappeared when he observed the planet in 1616, further confusing him. Galileo observed the planet Neptune in 1612. It appears in his notebooks as one of many unremarkable dim stars. He did not realise that it

15808-605: The portion of the distance from the North Pole to the Equator it represented. Pierre Méchain's and Jean-Baptiste Delambre's measurements were combined with the results of the Spanish-French geodetic mission and a value of ⁠ 1 / 334 ⁠ was found for the Earth's flattening. However, French astronomers knew from earlier estimates of the Earth's flattening that different meridian arcs could have different lengths and that their curvature could be irregular. The distance from

15960-421: The positions of these "stars" relative to Jupiter were changing in a way that would have been inexplicable if they had really been fixed stars . On 10 January, Galileo noted that one of them had disappeared, an observation which he attributed to its being hidden behind Jupiter. Within a few days, he concluded that they were orbiting Jupiter: he had discovered three of Jupiter's four largest moons . He discovered

16112-459: The previous decade, Barberini, the future Urban VIII, had come down on the side of Galileo and the Lincean Academy . Galileo's dispute with Grassi permanently alienated many Jesuits, and Galileo and his friends were convinced that they were responsible for bringing about his later condemnation, although supporting evidence for this is not conclusive. At the time of Galileo's conflict with

16264-472: The prizes. Observing the moons from a ship proved too difficult, but the method was used for land surveys, including the remapping of France. From September 1610, Galileo observed that Venus exhibits a full set of phases similar to that of the Moon . The heliocentric model of the Solar System developed by Nicolaus Copernicus predicted that all phases would be visible since the orbit of Venus around

16416-472: The properties of the pendulum and " hydrostatic balances". He was one of the earliest Renaissance developers of the thermoscope and the inventor of various military compasses . With an improved telescope he built, he observed the stars of the Milky Way , the phases of Venus , the four largest satellites of Jupiter , Saturn's rings , lunar craters and sunspots . He also built an early microscope . Galileo's championing of Copernican heliocentrism

16568-493: The pseudonym Lothario Sarsio Sigensano, purporting to be one of his own pupils. The Assayer was Galileo's devastating reply to the Astronomical Balance . It has been widely recognized as a masterpiece of polemical literature, in which "Sarsi's" arguments are subjected to withering scorn. It was greeted with wide acclaim, and particularly pleased the new pope, Urban VIII , to whom it had been dedicated. In Rome, in

16720-483: The rebellious phrase " And yet it moves ". There was a claim that a 1640s painting by the Spanish painter Bartolomé Esteban Murillo or an artist of his school, in which the words were hidden until restoration work in 1911, depicts an imprisoned Galileo apparently gazing at the words "E pur si muove" written on the wall of his dungeon. The earliest known written account of the legend dates to a century after his death. Based on

16872-442: The relation Galileo Galileo di Vincenzo Bonaiuti de' Galilei (15 February 1564 – 8 January 1642), commonly referred to as Galileo Galilei ( / ˌ ɡ æ l ɪ ˈ l eɪ oʊ ˌ ɡ æ l ɪ ˈ l eɪ / , US also / ˌ ɡ æ l ɪ ˈ l iː oʊ -/ ; Italian: [ɡaliˈlɛːo ɡaliˈlɛːi] ) or mononymously as Galileo , was a Florentine astronomer , physicist and engineer, sometimes described as

17024-415: The result of several secondary causes including the shape of the sea, its depth, and other factors. Albert Einstein later expressed the opinion that Galileo developed his "fascinating arguments" and accepted them uncritically out of a desire for physical proof of the motion of the Earth. Galileo also dismissed the idea, known from antiquity and by his contemporary Johannes Kepler, that the Moon caused

17176-401: The same length, confirming an hypothesis of Jean Le Rond d'Alembert . He also proposed an ellipsoid with three unequal axes. In 1860, Elie Ritter, a mathematician from Geneva , using Schubert's data computed that the Earth ellipsoid could rather be a spheroid of revolution accordingly to Adrien-Marie Legendre 's model. However, the following year, resuming his calculation on the basis of all

17328-454: The scientific means necessary to redefine the units of the metric system according to the progress of sciences. The Metre Convention ( Convention du Mètre ) of 1875 mandated the establishment of a permanent International Bureau of Weights and Measures (BIPM: Bureau International des Poids et Mesures ) to be located in Sèvres , France. This new organisation was to construct and preserve

17480-630: The second General Conference of the International Association of Geodesy held in Berlin, the question of an international standard unit of length was discussed in order to combine the measurements made in different countries to determine the size and shape of the Earth. According to a preliminary proposal made in Neuchâtel the precedent year, the General Conference recommended the adoption of

17632-443: The sense of Holy Scripture". The Inquisition found that the idea of the Earth's movement "receives the same judgement in philosophy and ... in regard to theological truth, it is at least erroneous in faith". Pope Paul V instructed Cardinal Bellarmine to deliver this finding to Galileo, and to order him to abandon heliocentrism. On 26 February, Galileo was called to Bellarmine's residence and ordered "to abandon completely ...

17784-496: The smaller sizes were not small enough to answer Tycho's argument. Cardinal Bellarmine had written in 1615 that the Copernican system could not be defended without "a true physical demonstration that the sun does not circle the earth but the earth circles the sun". Galileo considered his theory of the tides to provide such evidence. This theory was so important to him that he originally intended to call his Dialogue Concerning

17936-433: The standard both for the unit of length and for the second. These two quantities could then be used to define the unit of mass. About the unit of length he wrote: In the present state of science the most universal standard of length which we could assume would be the wave length in vacuum of a particular kind of light, emitted by some widely diffused substance such as sodium, which has well-defined lines in its spectrum. Such

18088-436: The star at his viewing point. In his Dialogue , he reported that he had found the apparent diameter of a star of first magnitude to be no more than 5 arcseconds , and that of one of sixth magnitude to be about / 6 arcseconds. Like most astronomers of his day, Galileo did not recognise that the apparent sizes of stars that he measured were spurious, caused by diffraction and atmospheric distortion, and did not represent

18240-422: The stars as they appeared to be much larger than the Sun. The essay also included four theological arguments, but Ingoli suggested Galileo focus on the physical and mathematical arguments, and he did not mention Galileo's biblical ideas. In February 1616, an Inquisitorial commission declared heliocentrism to be "foolish and absurd in philosophy, and formally heretical since it explicitly contradicts in many places

18392-479: The structure of space. Einstein's theory of gravity states, on the contrary, that the mass of a body has an effect on all other bodies while modifying the structure of space. A massive body induces a curvature of the space around it in which the path of light is inflected, as was demonstrated by the displacement of the position of a star observed near the Sun during an eclipse in 1919. In 1873, James Clerk Maxwell suggested that light emitted by an element be used as

18544-570: The study of comets had been proposed at the time by Tycho Brahe.) In its opening passage, Galileo and Guiducci's Discourse gratuitously insulted the Jesuit Christoph Scheiner , and various uncomplimentary remarks about the professors of the Collegio Romano were scattered throughout the work. The Jesuits were offended, and Grassi soon replied with a polemical tract of his own, The Astronomical and Philosophical Balance , under

18696-626: The surname "Galilei") derives from the Latin "Galilaeus", meaning "of Galilee ". The biblical roots of Galileo's name and surname were to become the subject of a famous pun. In 1614, during the Galileo affair , one of Galileo's opponents, the Dominican priest Tommaso Caccini , delivered against Galileo a controversial and influential sermon . In it he made a point of quoting Acts 1:11 : "Ye men of Galilee, why stand ye gazing up into heaven?". Despite being

18848-550: The suspected public ridicule lightly, nor the Copernican advocacy. Galileo had alienated one of his biggest and most powerful supporters, the Pope, and was called to Rome to defend his writings in September 1632. He finally arrived in February 1633 and was brought before inquisitor Vincenzo Maculani to be charged . Throughout his trial, Galileo steadfastly maintained that since 1616 he had faithfully kept his promise not to hold any of

19000-451: The task to carry out the experiments necessary for determining the expansion coefficients of the two platinum and brass bars, and to compare the Egyptian standard with a known standard. The Spanish standard designed by Carlos Ibáñez e Ibáñez de Ibero and Frutos Saavedra Meneses was chosen for this purpose, as it had served as a model for the construction of the Egyptian standard. In addition,

19152-573: The telescope). His multiple interests included the study of astrology , which at the time was a discipline tied to the studies of mathematics, astronomy and medicine. Tycho Brahe and others had observed the supernova of 1572 . Ottavio Brenzoni's letter of 15 January 1605 to Galileo brought the 1572 supernova and the less bright nova of 1601 to Galileo's notice. Galileo observed and discussed Kepler's Supernova in 1604. Since these new stars displayed no detectable diurnal parallax , Galileo concluded that they were distant stars, and, therefore, disproved

19304-440: The telescope, and contrasted them to planets, which the telescope revealed to be discs. But shortly thereafter, in his Letters on Sunspots , he reported that the telescope revealed the shapes of both stars and planets to be "quite round". From that point forward, he continued to report that telescopes showed the roundness of stars, and that stars seen through the telescope measured a few seconds of arc in diameter. He also devised

19456-439: The theoretical definition of the metre had been inaccessible and misleading at the time of Delambre and Mechain arc measurement, as the geoid is a ball, which on the whole can be assimilated to an oblate spheroid , but which in detail differs from it so as to prohibit any generalization and any extrapolation from the measurement of a single meridian arc. In 1859, Friedrich von Schubert demonstrated that several meridians had not

19608-687: The tides in 1616, addressed to Cardinal Orsini . His theory gave the first insight into the importance of the shapes of ocean basins in the size and timing of tides; he correctly accounted, for instance, for the negligible tides halfway along the Adriatic Sea compared to those at the ends. As a general account of the cause of tides, however, his theory was a failure. If this theory were correct, there would be only one high tide per day. Galileo and his contemporaries were aware of this inadequacy because there are two daily high tides at Venice instead of one, about 12 hours apart. Galileo dismissed this anomaly as

19760-514: The tides—Galileo also took no interest in Kepler's elliptical orbits of the planets . Galileo continued to argue in favour of his theory of tides, considering it the ultimate proof of Earth's motion. In 1619, Galileo became embroiled in a controversy with Father Orazio Grassi , professor of mathematics at the Jesuit Collegio Romano . It began as a dispute over the nature of comets, but by

19912-567: The time Galileo had published The Assayer ( Il Saggiatore ) in 1623, his last salvo in the dispute, it had become a much wider controversy over the very nature of science itself. The title page of the book describes Galileo as a philosopher and "Matematico Primario" of the Grand Duke of Tuscany. Because The Assayer contains such a wealth of Galileo's ideas on how science should be practised, it has been referred to as his scientific manifesto. Early in 1619, Father Grassi had anonymously published

20064-526: The time, surnames were optional in Italy, and his first name had the same origin as his sometimes-family name, Galilei. Both his given and family name ultimately derived from an ancestor, Galileo Bonaiuti , an important physician, professor, and politician in Florence in the 15th century. Galileo Bonaiuti was buried in the same church, the Basilica of Santa Croce in Florence , where about 200 years later, Galileo Galilei

20216-520: The true sizes of stars. However, Galileo's values were much smaller than previous estimates of the apparent sizes of the brightest stars, such as those made by Brahe, and enabled Galileo to counter anti-Copernican arguments such as those made by Tycho that these stars would have to be absurdly large for their annual parallaxes to be undetectable. Other astronomers such as Simon Marius, Giovanni Battista Riccioli , and Martinus Hortensius made similar measurements of stars, and Marius and Riccioli concluded

20368-437: The uncertainties in characterising the medium are dominated by errors in measuring temperature and pressure. Errors in the theoretical formulas used are secondary. By implementing a refractive index correction such as this, an approximate realisation of the metre can be implemented in air, for example, using the formulation of the metre as 1 579 800 .762 042 (33) wavelengths of helium–neon laser light in vacuum, and converting

20520-570: The uncertainty involved in the direct comparison of wavelengths, because interferometer errors were eliminated. To further facilitate reproducibility from lab to lab, the 17th CGPM also made the iodine-stabilised helium–neon laser "a recommended radiation" for realising the metre. For the purpose of delineating the metre, the BIPM currently considers the HeNe laser wavelength, λ HeNe , to be 632.991 212 58  nm with an estimated relative standard uncertainty ( U ) of 2.1 × 10 . This uncertainty

20672-436: The wavelengths in vacuum to wavelengths in air. Air is only one possible medium to use in a realisation of the metre, and any partial vacuum can be used, or some inert atmosphere like helium gas, provided the appropriate corrections for refractive index are implemented. The metre is defined as the path length travelled by light in a given time, and practical laboratory length measurements in metres are determined by counting

20824-419: Was a planet, but he did note its motion relative to the stars before losing track of it. Galileo made naked-eye and telescopic studies of sunspots . Their existence raised another difficulty with the unchanging perfection of the heavens as posited in orthodox Aristotelian celestial physics. An apparent annual variation in their trajectories, observed by Francesco Sizzi and others in 1612–1613, also provided

20976-409: Was a way to determine the figure of the Earth , whose crucial parameter was the flattening of the Earth ellipsoid . In the 18th century, in addition of its significance for cartography , geodesy grew in importance as a means of empirically demonstrating the theory of gravity , which Émilie du Châtelet promoted in France in combination with Leibniz's mathematical work and because the radius of

21128-536: Was also buried. When he did refer to himself with more than one name, it was sometimes as Galileo Galilei Linceo, a reference to his being a member of the Accademia dei Lincei , an elite science organization founded in the Papal States . It was common for mid-16th century Tuscan families to name the eldest son after the parents' surname. Hence, Galileo Galilei was not necessarily named after his ancestor Galileo Bonaiuti. The Italian male given name "Galileo" (and thence

21280-416: Was also possible to place it entirely on the far side of the Sun, where it could exhibit only gibbous and full phases. After Galileo's telescopic observations of the crescent, gibbous and full phases of Venus, the Ptolemaic model became untenable. In the early 17th century, as a result of his discovery, the great majority of astronomers converted to one of the various geo-heliocentric planetary models, such as

21432-508: Was determined astronomically. Bayer proposed to remeasure ten arcs of meridians and a larger number of arcs of parallels, to compare the curvature of the meridian arcs on the two slopes of the Alps , in order to determine the influence of this mountain range on vertical deflection . Baeyer also planned to determine the curvature of the seas, the Mediterranean Sea and Adriatic Sea in the south,

21584-429: Was discovered that the length of a seconds pendulum varies from place to place. Christiaan Huygens found out the centrifugal force which explained variations of gravitational acceleration depending on latitude. He also mathematically formulated the link between the length of the simple pendulum and gravitational acceleration. According to Alexis Clairaut , the study of variations in gravitational acceleration

21736-477: Was eight, his family moved to Florence , but he was left under the care of Muzio Tedaldi for two years. When Galileo was ten, he left Pisa to join his family in Florence, where he came under the tutelage of Jacopo Borghini. He was educated, particularly in logic, from 1575 to 1578 in the Vallombrosa Abbey , about 30 km southeast of Florence. Galileo tended to refer to himself only by his first name. At

21888-486: Was later explained by clearance in the central axis of the repeating circle causing wear and consequently the zenith measurements contained significant systematic errors. Polar motion predicted by Leonhard Euler and later discovered by Seth Carlo Chandler also had an impact on accuracy of latitudes' determinations. Among all these sources of error, it was mainly an unfavourable vertical deflection that gave an inaccurate determination of Barcelona's latitude and

22040-526: Was met with opposition from within the Catholic Church and from some astronomers. The matter was investigated by the Roman Inquisition in 1615, which concluded that his opinions contradicted accepted Biblical interpretations. Galileo later defended his views in Dialogue Concerning the Two Chief World Systems (1632), which appeared to attack and ridicule Pope Urban VIII , thus alienating both

22192-714: Was mitigated by that of neutral states. While the German astronomer Wilhelm Julius Foerster , director of the Berlin Observatory and director of the German Weights and Measures Service boycotted the Permanent Committee of the International Metre Commission, along with the Russian and Austrian representatives, in order to promote the foundation of a permanent International Bureau of Weights and Measures ,

22344-467: Was necessary to carefully study considerable areas of land in all directions. Baeyer developed a plan to coordinate geodetic surveys in the space between the parallels of Palermo and Freetown Christiana ( Denmark ) and the meridians of Bonn and Trunz (German name for Milejewo in Poland ). This territory was covered by a triangle network and included more than thirty observatories or stations whose position

22496-452: Was particularly worrying, because when the primary Imperial yard standard had partially been destroyed in 1834, a new standard of reference was constructed using copies of the "Standard Yard, 1760", instead of the pendulum's length as provided for in the Weights and Measures Act of 1824, because the pendulum method proved unreliable. Nevertheless Ferdinand Rudolph Hassler 's use of the metre and

22648-467: Was the first to tie experimentally the metre to the wave length of a spectral line. According to him the standard length might be compared with that of a wave of light identified by a line in the solar spectrum . Albert Michelson soon took up the idea and improved it. In 1893, the standard metre was first measured with an interferometer by Albert A. Michelson , the inventor of the device and an advocate of using some particular wavelength of light as

22800-460: Was the religious life. Both girls were accepted by the convent of San Matteo in Arcetri and remained there for the rest of their lives. Virginia took the name Maria Celeste upon entering the convent. She died on 2 April 1634, and is buried with Galileo at the Basilica of Santa Croce, Florence . Livia took the name Sister Arcangela and was ill for most of her life. Vincenzo was later legitimised as

22952-441: Was ultimately decided that the metre would be based on the Earth quadrant (a quarter of the Earth's circumference through its poles), Talleyrand proposed that the metre be the length of the seconds pendulum at a latitude of 45°. This option, with one-third of this length defining the foot , was also considered by Thomas Jefferson and others for redefining the yard in the United States shortly after gaining independence from

23104-399: Was used to create an accurate timepiece. Up to this point, Galileo had deliberately been kept away from mathematics, since a physician earned a higher income than a mathematician. However, after accidentally attending a lecture on geometry, he talked his reluctant father into letting him study mathematics and natural philosophy instead of medicine. He created a thermoscope , a forerunner of

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