Vernier scale
A vernier scale is a visual aid to take an accurate measurement reading between two graduation markings on a linear scale by using mechanical interpolation. The vernier is a subsidiary scale replacing a single measured-value pointer, has for instance ten divisions equal in distance to nine divisions on the main scale; the interpolated reading is obtained by observing which of the vernier scale graduations is co-incident with a graduation on the main scale, easier to perceive than visual estimation between two points. Such an arrangement can go to higher resolution by using higher scale ratios, known as the vernier constant. A vernier may be used on straight scales where a simple linear mechanism is adequate. Examples are calipers and micrometers to measure to fine tolerances, on sextants for navigation, on theodolites in surveying, on scientific instruments; the Vernier principle of interpolation is used for electronic displacement sensors such as absolute encoders to measure linear or rotational movement, as part of an electronic measuring system.
Calipers without a scale originated in ancient China as early as the Xin dynasty. The secondary scale, which contributed extra precision, was invented in 1631 by French mathematician Pierre Vernier, its use was described in detail in English in Navigatio Britannica by mathematician and historian John Barrow. While calipers are the most typical use of Vernier scales today, they were developed for angle-measuring instruments such as astronomical quadrants. In some languages, the Vernier scale is called a nonius, a precursor to the Vernier scale developed by Portuguese mathematician, cosmographer Pedro Nunes, latinised as Petrus Nonius, it was known by this name in English until the end of the 18th century. The name "vernier" was popularised by the French astronomer Jérôme Lalande through his Traité d'astronomie; the use of the vernier scale is shown on a vernier caliper which measures the internal and the external diameters of an object. The vernier scale is constructed so that it is spaced at a constant fraction of the fixed main scale.
So for a vernier with a constant of 0.1, each mark on the vernier is spaced nine tenths of those on the main scale. If you put the two scales together with zero points aligned, the first mark on the vernier scale is one tenth short of the first main scale mark, the second two tenths short, so on up to the ninth mark—which is misaligned by nine tenths. Only when a full ten marks are counted is there alignment, because the tenth mark is ten tenths—a whole main scale unit—short, therefore aligns with the ninth mark on the main scale. Now if you move the vernier by a small amount, one tenth of its fixed main scale, the only pair of marks that come into alignment are the first pair, since these were the only ones misaligned by one tenth. If we move it two tenths, the second pair aligns, since these are the only ones misaligned by that amount. If we move it five tenths, the fifth pair aligns—and so on. For any movement, only one pair of marks aligns and that pair shows the value between the marks on the fixed scale.
The difference between the value of one main scale division and the value of one Vernier scale division is known as least count of the Vernier. It is known as Vernier constant. Let the measure of the smallest main scale reading, the distance between two consecutive graduations be S and the distance between two consecutive Vernier scale graduations be V such that the length of main scale divisions is equal to n Vernier scale divisions; the length of main scale divisions = the length of n vernier scale division or, S = nV or, nS-S = nV or, S = nS - nV or, S/n = or / = S/n and are both equal to the least count of vernier scale, are called the vernier constant. Vernier scales work so well because most people are good at detecting which of the lines is aligned and misaligned, that ability gets better with practice, in fact far exceeding the optical capability of the eye; this ability to detect alignment is called'Vernier acuity'. None of the alternative technologies exploited this or any other hyperacuity, giving the Vernier scale an advantage over its competitors.
Zero error is defined as the condition where a measuring instrument registers a reading when there should not be any reading. In case of vernier calipers it occurs when a zero on main scale does not coincide with a zero on vernier scale; the zero error may be of two types i.e. when the scale is towards numbers greater than zero it is positive else negative. The method to use a vernier scale or caliper with zero error is to use the formula: actual reading = main scale + vernier scale −. Zero error may arise due to knocks that cause the calibration to be thrown off at the 0.00 mm when the jaws are closed or just touching each other. Perfection is not equal to zero error. "Knocks" seem an excellent example of mathematical imperfection. Alignment of linear and rotational mathematics is a difficult but interesting task as described by Pierre Vernier and much elaborated in ages. Positive zero error refers to the case when the jaws of the vernier caliper are just closed and the reading is a positive reading away from the actual reading of 0.00mm.
If the reading is 0.10mm, the zero error is referred to as +0.10 mm. Ne
Greenwich
Greenwich is an area of southeast London, located 5.5 miles east-southeast of Charing Cross. It is located within the Royal Borough of Greenwich. Greenwich is notable for its maritime history and for giving its name to the Greenwich Meridian and Greenwich Mean Time; the town became the site of a royal palace, the Palace of Placentia from the 15th century, was the birthplace of many Tudors, including Henry VIII and Elizabeth I. The palace fell into disrepair during the English Civil War and was rebuilt as the Royal Naval Hospital for Sailors by Sir Christopher Wren and his assistant Nicholas Hawksmoor; these buildings became the Royal Naval College in 1873, they remained an establishment for military education until 1998 when they passed into the hands of the Greenwich Foundation. The historic rooms within these buildings remain open to the public; the town became a popular resort in the 18th century and many grand houses were built there, such as Vanbrugh Castle established on Maze Hill, next to the park.
From the Georgian period estates of houses were constructed above the town centre. The maritime connections of Greenwich were celebrated in the 20th century, with the siting of the Cutty Sark and Gipsy Moth IV next to the river front, the National Maritime Museum in the former buildings of the Royal Hospital School in 1934. Greenwich formed part of Kent until 1889; the place-name ` Greenwich' is first attested in a Saxon charter of 918. It is recorded as Grenewic in 964, as Grenawic in the Anglo-Saxon Chronicle for 1013, it is Grenviz in the Domesday Book of 1086, Grenewych in the Taxatio Ecclesiastica of 1291. The name means'green wic or settlement'; the settlement became known as East Greenwich to distinguish it from West Greenwich or Deptford Strond, the part of Deptford adjacent to the Thames, but the use of East Greenwich to mean the whole of the town of Greenwich died out in the 19th century. However, Greenwich was divided into the registration subdistricts of Greenwich East and Greenwich West from the beginning of civil registration in 1837, the boundary running down what is now Greenwich Church Street and Crooms Hill, although more modern references to "East" and "West" Greenwich refer to the areas east and west of the Royal Naval College and National Maritime Museum corresponding with the West Greenwich council ward.
An article in The Times of 13 October 1967 stated: East Greenwich, gateway to the Blackwall Tunnel, remains solidly working class, the manpower for one eighth of London's heavy industry. West Greenwich is a hybrid: the spirit of Nelson, the Cutty Sark, the Maritime Museum, an industrial waterfront and a number of elegant houses, ripe for development. Royal charters granted to English colonists in North America used the name of the manor of East Greenwich for describing the tenure as that of free socage. New England charters provided that the grantees should hold their lands "as of his Majesty's manor of East Greenwich." This was in relation to the principle of land tenure under English law, that the ruling monarch was paramount lord of all the soil in the terra regis, while all others held their lands, directly or indirectly, under the monarch. Land outside the physical boundaries of England, as in America, was treated as belonging constructively to one of the existing royal manors, from Tudor times grants used the name of the manor of East Greenwich, but some 17c.
Grants named the castle of Windsor. Places in North America that have taken the name "East Greenwich" include a township in Gloucester County, New Jersey, a hamlet in Washington County, New York, a town in Kent County, Rhode Island. Greenwich, Connecticut was named after Greenwich. Tumuli to the south-west of Flamsteed House, in Greenwich Park, are thought to be early Bronze Age barrows re-used by the Saxons in the 6th century as burial grounds. To the east between the Vanbrugh and Maze Hill Gates is the site of a Roman temple. A small area of red paving tesserae protected by railings marks the spot, it was excavated in 1902 and 300 coins were found dating from the emperors Claudius and Honorius to the 5th century. This was excavated by the Channel 4 television programme Time Team in 1999, broadcast in 2000, further investigations were made by the same group in 2003; the Roman road from London to Dover, Watling Street crossed the high ground to the south of Greenwich, through Blackheath. This followed the line of an earlier Celtic route from Canterbury to St Albans.
As late as Henry V, Greenwich was only a fishing town, with a safe anchorage in the river. During the reign of Ethelred the Unready, the Danish fleet anchored in the River Thames off Greenwich for over three years, with the army being encamped on the hill above. From here they attacked Kent and, in the year 1012, took the city of Canterbury, making Archbishop Alphege their prisoner for seven months in their camp at Greenwich, at that time within the county of Kent, they stoned him to death for his refusal to allow his ransom to be paid. For this miracle his body was released to his followers, he achieved sainthood for his martyrdom and, in the 12th century, the parish church was dedicated to him; the present church on the site west of the town centre is St Alfege's Church, designed by Nicholas Hawksmoor in 1714 and completed in 1718. Some vestiges of the Danish camps may be traced in the nam
Parallax
Parallax is a displacement or difference in the apparent position of an object viewed along two different lines of sight, is measured by the angle or semi-angle of inclination between those two lines. Due to foreshortening, nearby objects show a larger parallax than farther objects when observed from different positions, so parallax can be used to determine distances. To measure large distances, such as the distance of a planet or a star from Earth, astronomers use the principle of parallax. Here, the term parallax is the semi-angle of inclination between two sight-lines to the star, as observed when Earth is on opposite sides of the Sun in its orbit; these distances form the lowest rung of what is called "the cosmic distance ladder", the first in a succession of methods by which astronomers determine the distances to celestial objects, serving as a basis for other distance measurements in astronomy forming the higher rungs of the ladder. Parallax affects optical instruments such as rifle scopes, binoculars and twin-lens reflex cameras that view objects from different angles.
Many animals, including humans, have two eyes with overlapping visual fields that use parallax to gain depth perception. In computer vision the effect is used for computer stereo vision, there is a device called a parallax rangefinder that uses it to find range, in some variations altitude to a target. A simple everyday example of parallax can be seen in the dashboard of motor vehicles that use a needle-style speedometer gauge; when viewed from directly in front, the speed may show 60. As the eyes of humans and other animals are in different positions on the head, they present different views simultaneously; this is the basis of stereopsis, the process by which the brain exploits the parallax due to the different views from the eye to gain depth perception and estimate distances to objects. Animals use motion parallax, in which the animals move to gain different viewpoints. For example, pigeons down to see depth; the motion parallax is exploited in wiggle stereoscopy, computer graphics which provide depth cues through viewpoint-shifting animation rather than through binocular vision.
Parallax arises due to change in viewpoint occurring due to motion of the observer, of the observed, or of both. What is essential is relative motion. By observing parallax, measuring angles, using geometry, one can determine distance. Astronomers use the word "parallax" as a synonym for "distance measurement" by other methods: see parallax #Astronomy. Stellar parallax created by the relative motion between the Earth and a star can be seen, in the Copernican model, as arising from the orbit of the Earth around the Sun: the star only appears to move relative to more distant objects in the sky. In a geostatic model, the movement of the star would have to be taken as real with the star oscillating across the sky with respect to the background stars. Stellar parallax is most measured using annual parallax, defined as the difference in position of a star as seen from the Earth and Sun, i. e. the angle subtended at a star by the mean radius of the Earth's orbit around the Sun. The parsec is defined as the distance.
Annual parallax is measured by observing the position of a star at different times of the year as the Earth moves through its orbit. Measurement of annual parallax was the first reliable way to determine the distances to the closest stars; the first successful measurements of stellar parallax were made by Friedrich Bessel in 1838 for the star 61 Cygni using a heliometer. Stellar parallax remains the standard for calibrating other measurement methods. Accurate calculations of distance based on stellar parallax require a measurement of the distance from the Earth to the Sun, now based on radar reflection off the surfaces of planets; the angles involved in these calculations are small and thus difficult to measure. The nearest star to the Sun, Proxima Centauri, has a parallax of 0.7687 ± 0.0003 arcsec. This angle is that subtended by an object 2 centimeters in diameter located 5.3 kilometers away. The fact that stellar parallax was so small that it was unobservable at the time was used as the main scientific argument against heliocentrism during the early modern age.
It is clear from Euclid's geometry that the effect would be undetectable if the stars were far enough away, but for various reasons such gigantic distances involved seemed implausible: it was one of Tycho's principal objections to Copernican heliocentrism that in order for it to be compatible with the lack of observable stellar parallax, there would have to be an enormous and unlikely void between the orbit of Saturn and the eighth sphere. In 1989, the satellite Hipparcos was launched for obtaining improved parallaxes and proper motions for over 100,000 nearby stars, increasing the reach of the method tenfold. So, Hipparcos is only able to measure parallax angles for stars up to about 1,600 light-years away, a little more than one percent of the diameter of the Milky Way Galaxy; the European Space Agency's Gaia mission, launched in December 2013, will be able to measure parallax angles to an accuracy of 10 microarcseconds, thus mapping nearby stars up to a distance of tens of thousands of ligh
Nautical almanac
A nautical almanac is a publication describing the positions of a selection of celestial bodies for the purpose of enabling navigators to use celestial navigation to determine the position of their ship while at sea. The Almanac specifies for each whole hour of the year the position on the Earth's surface at which the sun, moon and first point of Aries is directly overhead; the positions of 57 selected stars are specified relative to the first point of Aries. In Great Britain, The Nautical Almanac has been published annually by HM Nautical Almanac Office since the first edition was published in 1767. In the United States, a nautical almanac has been published annually by the US Naval Observatory since 1852, it was titled American Ephemeris and Nautical Almanac. Since 1958, the USNO and HMNAO have jointly published a unified nautical almanac, the Astronomical Almanac for use by the navies of both countries. Almanac data is now available online from the US Naval Observatory. Commercial almanacs were produced that combined other information.
A good example would be Brown's — which commenced in 1877 – and is still produced annually, its early twentieth century subtitle being "Harbour and Dock Guide and Advertiser and Daily Tide Tables". This combination of trade advertising, information "by permission... of the Hydrographic Department of the Admiralty" provided a useful compendium of information. More recent editions have kept up with the changes in technology – the 1924 edition for instance had extensive advertisements for coaling stations. Meanwhile, the Reeds Nautical Almanac, published by Adlard Coles Nautical, has been in print since 1932, in 1944 was used by landing craft involved in the Normandy landings; the "Air Almanac" of the United States and Great Britain tabulates celestial coordinates for 10-minute intervals for the use in aerial navigation. The Sokkia Corporation's annual "Celestial Observation Handbook and Ephemeris" tabulated daily celestial coordinates for the Sun and nine stars. To find the position of a ship or aircraft by celestial navigation, the navigator measures with a sextant the apparent height of a celestial body above the horizon, notes the time from a marine chronometer.
That height is compared with the height predicted for a trial position. American Practical Navigator Nautical Almanac, Board of Longitude Collection Her Majesty's Nautical Almanac Office Online Nautical Almanac A free nautical Almanac in PDF format Navigation Spreadsheets: Almanac data History of the Nautical Almanac
Three-body problem
In physics and classical mechanics, the three-body problem is the problem of taking the initial positions and velocities of three point masses and solving for their subsequent motion according to Newton's laws of motion and Newton's law of universal gravitation. The three-body problem is a special case of the n-body problem. Unlike two-body problems, no closed-form solution exists for all sets of initial conditions, numerical methods are required; the first specific three-body problem to receive extended study was the one involving the Moon, the Earth, the Sun. In an extended modern sense, a three-body problem is any problem in classical mechanics or quantum mechanics that models the motion of three particles; the mathematical statement of the three-body problem can be given in terms of the Newtonian equations of motion for vector positions r i = of three gravitationally interacting bodies with masses m i: r ¨ 1 = − G m 2 r 1 − r 2 | r 1 − r 2 | 3 − G m 3 r 1 − r 3 | r 1 − r 3 | 3, r ¨ 2 = − G m 3 r 2 − r 3 | r 2 − r 3 | 3 − G m 1 r 2 − r 1 | r 2 − r 1 | 3, r ¨ 3 = − G m 1 r 3 − r 1 | r 3 − r 1 | 3 − G m 2 r 3 − r 2 | r 3 − r 2 | 3.
Where G is the gravitational constant. This is a set of 9 second-order differential equations; the problem can be stated equivalently in the Hamiltonian formalism, in which case it is described by a set of 18 first-order differential equations, one for each component of the positions r i and momenta p i: d r i d t = ∂ H ∂ p i, d p i d t = − ∂ H ∂ r i, {\displaystyle =,\qquad =-{\frac {\partial
Pacific Ocean
The Pacific Ocean is the largest and deepest of Earth's oceanic divisions. It extends from the Arctic Ocean in the north to the Southern Ocean in the south and is bounded by Asia and Australia in the west and the Americas in the east. At 165,250,000 square kilometers in area, this largest division of the World Ocean—and, in turn, the hydrosphere—covers about 46% of Earth's water surface and about one-third of its total surface area, making it larger than all of Earth's land area combined; the centers of both the Water Hemisphere and the Western Hemisphere are in the Pacific Ocean. The equator subdivides it into the North Pacific Ocean and South Pacific Ocean, with two exceptions: the Galápagos and Gilbert Islands, while straddling the equator, are deemed wholly within the South Pacific, its mean depth is 4,000 meters. The Mariana Trench in the western North Pacific is the deepest point in the world, reaching a depth of 10,911 meters; the western Pacific has many peripheral seas. Though the peoples of Asia and Oceania have traveled the Pacific Ocean since prehistoric times, the eastern Pacific was first sighted by Europeans in the early 16th century when Spanish explorer Vasco Núñez de Balboa crossed the Isthmus of Panama in 1513 and discovered the great "southern sea" which he named Mar del Sur.
The ocean's current name was coined by Portuguese explorer Ferdinand Magellan during the Spanish circumnavigation of the world in 1521, as he encountered favorable winds on reaching the ocean. He called it Mar Pacífico, which in both Portuguese and Spanish means "peaceful sea". Important human migrations occurred in the Pacific in prehistoric times. About 3000 BC, the Austronesian peoples on the island of Taiwan mastered the art of long-distance canoe travel and spread themselves and their languages south to the Philippines and maritime Southeast Asia. Long-distance trade developed all along the coast from Mozambique to Japan. Trade, therefore knowledge, extended to the Indonesian islands but not Australia. By at least 878 when there was a significant Islamic settlement in Canton much of this trade was controlled by Arabs or Muslims. In 219 BC Xu Fu sailed out into the Pacific searching for the elixir of immortality. From 1404 to 1433 Zheng He led expeditions into the Indian Ocean; the first contact of European navigators with the western edge of the Pacific Ocean was made by the Portuguese expeditions of António de Abreu and Francisco Serrão, via the Lesser Sunda Islands, to the Maluku Islands, in 1512, with Jorge Álvares's expedition to southern China in 1513, both ordered by Afonso de Albuquerque from Malacca.
The east side of the ocean was discovered by Spanish explorer Vasco Núñez de Balboa in 1513 after his expedition crossed the Isthmus of Panama and reached a new ocean. He named it Mar del Sur because the ocean was to the south of the coast of the isthmus where he first observed the Pacific. In 1519, Portuguese explorer Ferdinand Magellan sailed the Pacific East to West on a Spanish expedition to the Spice Islands that would result in the first world circumnavigation. Magellan called the ocean Pacífico because, after sailing through the stormy seas off Cape Horn, the expedition found calm waters; the ocean was called the Sea of Magellan in his honor until the eighteenth century. Although Magellan himself died in the Philippines in 1521, Spanish Basque navigator Juan Sebastián Elcano led the remains of the expedition back to Spain across the Indian Ocean and round the Cape of Good Hope, completing the first world circumnavigation in a single expedition in 1522. Sailing around and east of the Moluccas, between 1525 and 1527, Portuguese expeditions discovered the Caroline Islands, the Aru Islands, Papua New Guinea.
In 1542–43 the Portuguese reached Japan. In 1564, five Spanish ships carrying 379 explorers crossed the ocean from Mexico led by Miguel López de Legazpi, sailed to the Philippines and Mariana Islands. For the remainder of the 16th century, Spanish influence was paramount, with ships sailing from Mexico and Peru across the Pacific Ocean to the Philippines via Guam, establishing the Spanish East Indies; the Manila galleons operated for two and a half centuries, linking Manila and Acapulco, in one of the longest trade routes in history. Spanish expeditions discovered Tuvalu, the Marquesas, the Cook Islands, the Solomon Islands, the Admiralty Islands in the South Pacific. In the quest for Terra Australis, Spanish explorations in the 17th century, such as the expedition led by the Portuguese navigator Pedro Fernandes de Queirós, discovered the Pitcairn and Vanuatu archipelagos, sailed the Torres Strait between Australia and New Guinea, named after navigator Luís Vaz de Torres. Dutch explorers, sailing around southern Africa engaged in discovery and trade.
In the 16th and 17th centuries Spain considered the Pacific Ocean a mare clausum—a sea closed to other naval powers. As the only known entrance from the Atlantic, the Strait of Magellan was at times patrolled by fleets sent to prevent entrance of non-Spanish ships. On the western side of the Pacific Ocean the Dutch threatened the Spanish Philippines; the 18th cen
Josef de Mendoza y Ríos
Josef de Mendoza y Ríos was a Spanish astronomer and mathematician of the 18th century, famous for his work on navigation. The first work of Mendoza y Ríos was published in 1787: his treatise about the science and technique of navigation in two tomes, he published several tables for facilitating the calculations of nautical astronomy and useful in navigation to calculate the latitude of a ship at sea from two altitudes of the sun, the longitude from the distances of the moon from a celestial body. In the field of the nautical instruments, he improved the reflecting circle. In 1816, he was elected a foreign member of the Royal Swedish Academy of Sciences. Tratado de Navegación. Tomo I y tomo II, Imprenta Real, 1787. Memoria sobre algunos métodos nuevos de calcular la longitud por las distancias lunares: y aplication de su teórica á la solucion de otros problemas de navegacion. Madrid, Imprenta Real, 1795. Colección de tablas. Madrid, Imprenta Real, 1800.. Table des latitudes croissantes Connoissance des Temps… pour l’annee comune 1793: 303.
Mémoire sur la methode de trouver la latitude par le moyen de deux hauteurs du soleil, del’intervalle de tems écoule entre les deux observations, et de la latitude estimée. Connoissance des Temps pour l’année comune 1793: 289-302. Mémoire sur la méthode de trouver la latitude par le moyen de deux hauteurs du soleil, de l'intervalle de temps écoulé entre les deux observations et de la latitude estimée, ….8°, 14 p. et planche. Memoire sur le calcul de la longitude en mer, par les distances de la lune au soleil et aux étoiles. Connaissance des Temps…: 258-284. Recherches sur les solutions des principaux problemes de l'astronomie nautique. Philosophical Transactions, 87: 43-122. Recherches sur les solutions des principaux problemes de l´astronomie nautique. London, 1797.4º, 4 + 85 p. Tables to correct the observed altitudes of the sun and the stars. London, 4º, 92 p. On an improved reflecting circle. Philosophical Transactions, 91: 363-374. On an improved reflecting circle London, W. Bulmer, 1801.4º, 14 p. Tables for facilitating the calculations of nautical astronomy, of the latitude of a ship at sea from two altitudes of the sun, that the longitude from the distances of the moon from the sun or a star, of the latitude of a ship at sea from two altitudes of the sun, that of the longitude from the distances of the moon from the sun or a star.
London, R. Faulder, 1801. 4º, 8 + 311 + 77 p. Appendix, containing tables for clearing the apparent distances of the moon from the sun or a star, from the effects of parallax and refraction. By H. Cavendish: 77 p. at end. A complete collection of tables for navigation and nautical astronomy, with simple and accurate methods for all the calculation useful at sea. London, printed by T. Bensley, sold by R. Faulder, etc. 1805. Folio, 12 + 47 + 670 p. + 1 h. A Complete Collection of Tables for Navigation and Nautical Astronomy. With simple and accurate methods for all the calculation useful at sea. Connaissance des Temps… pour l’an 1808: 443-447. A Complete Collection of Tables for Navigation and Nautical Astronomy. With simple and accurate methods for all the calculation useful at sea. 2nd ed. improved. London, T. Bensley, 1809. 4º, 6 p. + 1 h. + 604 p. + 58 p. + 1 h. Tables for facilitating the calculation of nautical astronomy. London, 1812. Forms for the ready calculation of the longitude... with the Tables published by Joseph de Mendoza Ríos.
London, Parry, & Co, 1814.4º, + p. American Practical Navigator Celestial navigation Haversine History of longitude Lunar distance Marine sandglass Nautical almanac Navigational Algorithms Sextant Reflecting instrument Media related to José de Mendoza y Ríos at Wikimedia Commons On an Improved Reflecting Circle — Philosophical Transactions. Joseph de Mendoza y Rıos- Teorıa, observacion y tablas IMMR LA COLECCIÓN DE MENDOZA Y RÍOS EN EL MUSEO NAVAL DE MADRID Los mapas de la Colección Mendoza - Biblioteca Nacional de España Navigational Algorithms http://sites.google.com/site/navigationalalgorithms/ facsimile of the Latitude and Lunar Distance chapters. Tratado de Navegación. Tome I http://www.google.es/books?id=egw6EJqi3rYC Tratado de Navegación. Tome II http://www.google.es/books?id=GunvU8qfXzYC
