Navigation is the science of directing a craft by determining its postition, course, and distance travelled. It is concerned with finding the way, avoiding collision, conserving fuel, and meeting schedules. Navigation is derived from the Latin navis, "ship," and agere, "to drive." It originally denoted the art of ship driving, including steering and setting the sails. The skill itself is even more ancient than the word, and it has evolved over the course of many centuries into a science and a technology that encompasses the planning and execution of safe, timely, and economical operation of watercraft, aircraft, and spacecraft.

Early mariners who embarked on voyages of exploration gradually developed systematic methods of observing and recording their position, the distances and directions they travelled, the currents of wind and water, and the hazards and havens they encountered. The facts accumulated in their journals made it possible for them to find their way home and for them or their successors to repeat and extend their exploits. Each new landfall became a signpost along a route that could be retraced and integrated into a growing body of reliable information. For these pathfinders, the danger of running into another vessel was of negligible concern, but as heavy traffic developed along established routes, collision avoidance became a serious matter. In all fields of navigation, emphasis shifted from finding the way to maintaining an appropriate distance between craft moving in various directions at different speeds. The larger a ship is, the easier it is to see, but, by the same token, the larger a ship is, the more time it requires to change its speed or direction. When many ships are in a small area, an action taken by one to avoid colliding with another may endanger a third. This problem has been alleviated near busy seaports by confining incoming and outgoing ships to separate lanes, which are clearly marked and divided by the greatest practical distance.

The advent of steam-powered ships during the first half of the 19th century added the problem of fuel consumption to the navigator's duties. In the air as well as at sea, the need to carry large amounts of fuel for long trips reduces the cargo capacity; even if plenty of fuel is on board, economy requires that its consumption be kept to a minimum. Adherence to a predetermined schedule, a matter of vital importance in space navigation in connection with fuel consumption, has become important in sea and air navigation for a different reason. Today each voyage or flight is a single link in a coordinated network of transport that carries people and goods from any starting place to any chosen destination. The efficient operation of the whole system depends upon assurance that each journey will begin and end at the specified times. Modern navigation, in short, has to do with the whole of a preconceived passage, from start to finish, and is concerned with four basic objectives: selecting the course (and staying on it); avoiding collision with other moving ships and crashing into fixed obstacles; minimizing fuel consumption; and conforming to an established timetable.

Development of Marine Navigation.
The earliest navigators probably learned to steer their ships between distant ports by familiarizing themselves with the sequences of intervening landmarks. Keeping these reference points in view required them to stay quite close to shore, but they made the transition to ocean voyages well out of sight of land thousands of years ago in various parts of the world. Regular trade was carried on between the island of Crete and Egypt, a distance of approximately 300 miles (500 kilometres), more than 25 centuries before the Christian era. A passage in the Odyssey describes such a voyage from Crete: running before a north wind, sailing ships reached the mouth of the Nile in five days. Longer and longer routes became established by later sailors. By 600 BC the Phoenicians were routinely importing tin from Cornwall. Well before the 10th century AD, Irish seafarers successively reached the Shetland Islands, the Faeroe Islands, and Iceland, crossing 200 to 300 miles of the North Atlantic at each stage. The Vikings repeated those passages and ventured even farther, settling Greenland and visiting North America. In about AD 400, Polynesian navigators had reached Hawaii from the Marquesas Islands, 2,300 miles (3,700 kilometres) across the open Pacific.

History of Early Oceanic Navigation.
The rise of oceanic navigation began when the basic Mediterranean trading vessel, the Venetian buss (a full-bodied, rounded two-masted ship), passed through the Strait of Gibraltar. At the time of Richard I of England (reigned 1189-99), whose familiarity with Mediterranean shipping stemmed from his participation in the Crusades, Mediterranean navigation had evolved in two directions: the galley had become a rowed fighting ship and the buss a sail-propelled trader's vessel. From Richard's crusading expeditions the value of the forecastle and aftercastle--giving enclosed deck houses and a bulging bow of great capacity--was learned, and this style became the basis of the English oceangoing trader. These crusading voyages also introduced the English to journeys longer than the coasting and North Sea navigation they had previously undertaken. The story of European navigation and shipbuilding is in large part one of interaction between technical developments in the two narrow boundary seas. It is thought that sailors from Bayonne in southwestern France introduced the Mediterranean carrack (a large three-masted, carvel-build ship using both square and lateen sails) to northern Europe and in turn introduced the double-ended clinker ship of the north to the Mediterranean. This crossfertilization took place in the 14th century, a time of considerable change in navigation in the Atlantic-facing regions of France, Spain, and Portugal.

Changes in shipbuilding during the Middle Ages were gradual. Among northern ships the double-ended structure began to disappear when sailing gained dominance over rowing. To make best use of sails meant moving away from steering oars to a rudder, first attached to the side of the boat and then, after a straight stern post was adopted, firmly attached to that stern. By 1252 the Port Books of Damme in Flanders distinguished ships with rudders on the side from those with stern rudders. The arts of navigation were improving at the same time. The compass was devised at the beginning of the 14th century, but it took time to understand how to use it effectively in a world with variable magnetic declinations. It was only about the year 1400 that the lodestone began to be used in navigation in any consistent manner.

Compass.
In navigation or surveying, it is the primary device for direction-finding on the surface of the Earth. Compasses may operate on magnetic or gyroscopic principles or by determining the direction of the Sun or a star. The oldest and most familiar type of compass is the magnetic compass, which is used in different forms in aircraft, ships, and land vehicles and by surveyors. Sometime in the 12th century, mariners in China and Europe made the discovery, apparently independently, that a piece of lodestone, a naturally occurring magnetic ore, when floated on a stick in water, tends to align itself so as to point in the direction of the polestar. This discovery was presumably quickly followed by a second, that an iron or steel needle touched by a lodestone for long enough also tends to align itself in a north-south direction. From the knowledge of which way is north, of course, any other direction can be found.
The reason magnetic compasses work as they do is that the Earth itself acts as an enormous bar magnet with a north-south field that causes freely moving magnets to take on the same orientation. The direction of the Earth's magnetic field is not quite parallel to the north-south axis of the globe, but it is close enough to make an uncorrected compass a reasonably good guide. The inaccuracy, known as variation (or declination), varies in magnitude from point to point upon the Earth. The deflection of a compass needle due to local magnetic influences is called deviation. Over the centuries a number of technical improvements have been made in the magnetic compass. Many of these were pioneered by the English, whose large empire was kept together by naval power and who hence relied heavily upon navigational devices. By the 13th century the compass needle had been mounted upon a pin standing on the bottom of the compass bowl. At first only north and south were marked on the bowl, but then the other 30 principal points of direction were filled in. A card with the points painted on it was mounted directly under the needle, permitting navigators to read their direction from the top of the card. The bowl itself was subsequently hung on gimbals (rings on the side that let it swing freely), ensuring that the card would always be level. In the 17th century the needle itself took the shape of a parallelogram, which was easier to mount than a thin needle.
During the 15th century navigators began to understand that compass needles do not point directly to the North Pole but rather to some nearby point; in Europe, compass needles pointed slightly east of true north. To counteract this difficulty, British navigators adopted conventional meridional compasses, in which the north on the compass card and the "needle north" were the same when the ship passed a point in Cornwall, England. (The magnetic poles, however, wander in a predictable manner--in more recent centuries Europeans have found magnetic north to be west of true north--and this must be considered for navigation.)
In 1745 Gowin Knight, an English inventor, developed a method of magnetizing steel in such a way that it would retain its magnetization for long periods of time; his improved compass needle was bar-shaped and large enough to bear a cap by which it could be mounted on its pivot. The Knight compass was widely used.
Some early compasses did not have water in the bowl and were known as dry-card compasses; their readings were easily disturbed by shocks and vibration. Although they were less affected by shock, liquid-filled compasses were plagued by leaks and were difficult to repair when the pivot became worn. Neither the liquid nor the dry-card type was decisively advantageous until 1862, when the first liquid compass was made with a float on the card that took most of the weight off the pivot. A system of bellows was invented to expand and contract with the liquid, preventing most leaks. With these improvements liquid compasses made dry-card compasses obsolete by the end of the 19th century.
Modern mariners' compasses are usually mounted in binnacles, cylindrical pedestals with provision for illuminating the compass face from below. Each binnacle contains specially placed magnets and pieces of steel that cancel the magnetic effects of the metal of the ship. Much the same kind of device is used aboard aircraft, except that, in addition, it contains a corrective mechanism for the errors induced in magnetic compasses when airplanes suddenly change course. The corrective mechanism is a gyroscope , which has the property of resisting efforts to change its axis of spin. This system is called a gyromagnetic compass. Gyroscopes are also employed in a type of nonmagnetic compass called the gyrocompass. The gyroscope is mounted in three sets of concentric rings connected by gimbals, each ring spinning freely. When the initial axis of spin of the central gyroscope is set to point to true north, it will continue to do so and will resist efforts to realign it in any other direction; the gyroscope itself thus functions as a compass. If it begins to precess (wobble), a pendulum weight pulls it back into line. Gyrocompasses are generally used in navigation systems because they can be set to point to true north rather than to magnetic north.

Charts.
A map designed and used primarily for navigation. A nautical chart presents most of the information used by the marine navigator, including latitude and longitude scales, topographical features, navigation aids such as lights and radio beacons, magnetic information, indications of reefs and shoals, water depth, and warning notices. Such information allows both plotting a safe course and checking progress while sailing.
The first navigation charts were made at the end of the 13th century. The appearance of the magnetic compass 100 years earlier is considered to have been the catalyst for the development of charts. Earlier, seamen had relied on the proximity of a familiar coast, on the position of celestial bodies, or on meteorological phenomena such as, in the Indian Ocean, the monsoon winds. The less-predictable winds and weather of the Mediterranean spurred the development there of the first charts. These were plane charts (they took no account of the Earth's curvature) that were regularly crossed by rhumb, or wind, lines that corresponded to the directions that the wind rose.
Plane maps were not suitable for navigation in far northern or southern latitudes and by the 17th century were replaced by Mercator-projection charts that showed compass directions as straight lines. Projections other than the Mercator are also used, especially in very high latitudes. Aeronautical charts are similar to nautical charts but emphasize such things as topography, heights of obstructions, airports, and airways. They are usually drawn on the Lambert conformal projection.

Radio Navigation.Direction Finders.
To avoid the hazards marked on the charts, a mariner needs to know the vessel's exact position. By means of a sight fitted to the compass, the direction of any visible landmark or buoy can be measured. This direction, called a bearing, can be marked on the chart as a line passing through the identified reference point. A similar line corresponding to a second bearing will intersect the first and fix the position of the vessel.

Determining Position by Intersection of Compass Bearings to Known Points.
The invention of radio transmission and reception led to an improvement in this navigational technique, making it possible to obtain bearings from reference points obscured by fog or darkness. The signals picked up by a loop antenna are weakest when the plane of the loop is perpendicular to the direction in which the radio waves are traveling. If the receiver is tuned to the frequency of a particular transmitter and the loop is rotated for minimum signal pickup, the direction to the transmitter can be found and plotted. A second position line then fixes the navigator's position, as before.
Soon after ships were first equipped with radio, direction-finding stations were placed on shore at strategic points along navigational routes and near harbour approaches. Upon receiving a request by radio from a ship, two or more shore stations determined the directions from which the ship's signal arrived and transmitted this information to the vessel. The navigator then could fix his position. The limitation of this service to one vessel at a time, however, was a serious drawback in bad weather, when demands were heavy. Beginning in 1921, continuously operating transmitters were placed ashore and the direction finder on the ship to eliminate the possibility of overloading the system and to give the navigator two further advantages: that of taking continuous or frequent bearings on any shore beacon and that of taking bearings of any receivable signal, such as transmissions from commercial broadcasting stations and from other vessels. This change in the system was roughly coincident with the initial growth of aviation, and the airborne direction finder immediately became a valuable aid to air navigation.
Under ideal conditions a well-designed direction finder will provide bearings within 1° or 2° of the true value. The uncertainty can be considerably increased, however, if the direction of the radio waves is altered by reflection from the ionosphere or refraction in the atmosphere. The loop-antenna radio direction finder, almost as old as radio itself, developed into a device in which a motor turned the loop, and electronic circuitry identified the direction of the source of the signals. This instrument, originally called a radio compass, could guide the navigator toward any detectable transmitter. It was often linked to a compass so as to display not merely the direction of the radio station compared to the heading of the craft but the actual direction as plotted on a chart.

The Inductor Compass.
Whereas the pivoted-needle magnetic compass indicates direction by aligning itself with the horizontal component of the Earth's magnetic field, the inductor compass measures, in effect, the strength of this horizontal component and indicates the direction in which the strength is greatest. One such instrument, the saturable-inductor compass, makes use of magnetic materials that are easily saturated--that is, materials in which it is easy to build up the maximum number of lines of magnetic flow, or flux. The amount of flux through such a material depends on its orientation in the Earth's field, being greatest when it is aligned in the magnetic north-south direction. By means of suitable electronic circuitry, it is possible to determine the exact orientation of a bar of such material and thus indicate precisely the direction of magnetic north. Compasses of this type require no rotating parts. Several can be installed at various points aboard a craft and their outputs combined electronically.

The Marine Chronometer.
Latitude could be determined by measuring the altitude of the Sun at noon or the altitude of any tabulated star when it crossed the local meridian, but the determination of longitude at sea remained a serious problem. By the Middle Ages, astronomers knew that the local time of an eclipse depended on the longitude, and in the 16th century they pointed out the principle of determining longitude by comparing the local time with the reading of a clock that reliably kept the time of a known meridian. No such clock was then available, but in 1714 the British Parliament offered a prize of 20,000 pounds to anyone who could discover a method of finding the longitude within 30 miles during a sea voyage. The English inventor John Harrison eventually was awarded the prize for a chronometer tested in 1761-62. His success heralded the practice of making timed observations of heavenly bodies at sea.

John Harrison.
b. March 1693, Foulby, Yorkshire, Eng. d. March 24, 1776, London .
English horologist who invented the first practical marine chronometer, which enabled navigators to compute accurately their longitude at sea. Harrison, the son of a carpenter and a mechanic himself, became interested in constructing an accurate chronometer in 1728. Several unfortunate disasters at sea, caused ostensibly by poor navigation, prompted the British government to create a Board of Longitude empowered to award 20,000 pounds to the first man who developed a chronometer with which longitude could be calculated within half a degree at the end of a voyage to the West Indies. Harrison completed his first chronometer in 1735 and submitted it for the prize. He then built three more instruments, each smaller and more accurate than its predecessor. In 1762 Harrison's famous No. 4 marine chronometer was found to be in error by only five seconds (1 1/4' longitude) after a voyage to Jamaica. Although his chronometers all met the standards set up by the Board of Longitude, he was not awarded any money until 1763, when he received 5,000 pounds, and not until 1773 was he paid in full. The only feature of his chronometers retained by later manufacturers was a device that keeps the clock running while it is being wound. A copy of Harrison's design, made by a watchmaker Larcum Kendall was used on Cook's epic survey of the Pacific 1772 - 1775.

Latitude and Longitude.
Latitude is a measurement on a globe or map of location north or south of the Equator. Technically there are different kinds of latitude--geographic, astronomical, and geocentric--but there are only minor differences between them. In most common references, geographic latitude (the kind used in mapping) is implied. Given in degrees, minutes, and 0.000 min. Geographic latitude is the arc subtended by an angle at the centre of the Earth and measured in a north-south plane poleward from the Equator. Thus, a point at 30°15.20' N subtends an angle of 30°15.20' at the centre of the globe; similarly, the arc between the Equator and either geographic pole is 90 (one-fourth the circumference of the Earth, or 1/4 360), and thus the greatest possible latitudes are 90° N and 90° S. As aids to indicate different latitudinal positions on maps or globes, equidistant circles are plotted and drawn parallel to the Equator and each other; they are known as parallels, or parallels of latitude. Different methods are used to determine geographic latitude, as by taking angle-sights on certain polar stars or by measuring with a sextant the angle of the noon Sun above the horizon. The length of a degree of arc of latitude is approximately 111 km ( 69 miles), varying, because of the nonuniformity of the Earth's curvature, from 110.567 km ( 68.706 miles) at the Equator to 111.699 km ( 69.41 miles) at the poles.

Longitude.
Is a measurement of location east or west of the prime meridian at Greenwich, the specially designated imaginary north-south line that passes through both geographic poles and Greenwich, London. Measured also in degrees, minutes, and seconds, longitude is the amount of arc created by drawing first a line from the centre of the Earth to the intersection of the Equator and the prime meridian and then another line from the centre of the Earth to any point elsewhere on the Equator. Longitude is measured 180° both east and west of the prime meridian. As aids to locate longitudinal positions on a globe or map, meridians are plotted and drawn from pole to pole where they meet. The distance / degree of longitude at the Equator is about 111.32 km ( 69.18 miles) and at the poles, 0.
The combination of meridians of longitude and parallels of latitude establishes a framework or grid by means of which exact positions can be determined in reference to the prime meridian and the Equator: a point described as 40° N, 30° W, for example, is located 40° of arc north of the Equator and 30° of arc west of the Greenwich meridian.

History of Latitude Measurements.
Portuguese seamen determined latitude by observing the altitude of the polestar (Polaris), that is, the angle between its direction and the horizontal. They knew from astronomical studies that the star does not lie exactly on the extension of the Earth's axis, so that it appears to move daily in a small circle around the celestial pole, but the necessary correction (as much as 3 1/2 deg. in the 15th century) could be applied by noting the position of the nearby star Kochab. When the navigators got close to the Equator, these stars fell below the horizon; there it became necessary to rely on observing the altitude of the noonday Sun and calculating latitude with the aid of an almanac.The first instruments used at sea for altitude measurements seem to have been the quadrant and the astrolabe, long known to astronomers. For both devices the reference direction was the vertical, rather than the horizontal, but conversion of the readings was an elementary matter.
The mariner's astrolabe, however, was less widely used than its 16th-century successor, the cross-staff, a simple device consisting of a staff about three feet long fitted with a sliding crosspiece. The navigator, holding the staff to one eye, would move the crosspiece until its lower end coincided with the horizon and its upper end with the polestar. The desired altitude could then be read from the intersection of the crosspiece with the staff, on which a scale was marked in degrees. The cross-staff remained in use until the 18th century despite several drawbacks, the most serious being that it required the observer to look directly into the Sun. Coloured shades were fitted to the crosspiece, but the decisive improvement was made in 1594 by the English navigator John Davis. His instrument, called the backstaff because it was used with the observer's back to the Sun, remained common even after 1731 when the octant (an early form of the modern sextant) was demonstrated independently by John Hadley of England and Thomas Godfrey of Philadelphia. In the octant and the sextant, two mirrors--one fixed, the other movable--bring the image of the Sun into coincidence with the horizon. In the hands of the practiced observer, the modern sextant can be used to measure altitudes with an accuracy of 10 seconds of arc, that is, closely enough to determine a ship's north-south position within a few hundred metres.

History of Longitude Measurements.
Almanacs and tables.
One of the earliest tabulations of the day-to-day positions of the heavenly bodies was Ephemerides, compiled by the German astronomer Regiomontanus and published by him in Nürnberg in 1474. This work also set forth the principle of determining longitude by the method of lunar distances, that is, the angular displacement of the Moon from other celestial objects. This method, which was destined to become the standard for a time during the 19th century, remained impracticable for more than three centuries because of the inaccuracy of the existing lunar tables, and because special knowledge and tedious computations were necessary in its use. Meanwhile, during the 16th and 17th centuries, working from translations of Portuguese and Spanish manuals, a flourishing school of instrument makers, chart makers, and teachers grew in England. This group rapidly improved the theory of navigation and compiled tables of increasing accuracy. In 1675 the Royal Observatory was established at Greenwich with the specific object of providing the sailor with astronomical data of the required precision. At Paris the Connaissance des temps, the first national almanac, was founded in 1679; it contained tables for the crude determination of longitude from observations of the eclipses of Jupiter's satellites, first seen by Galileo in 1610. (Galileo himself had advocated the preparation of such tables for this purpose, but the method, though sound in principle, could not be made practical.) In 1755 Johann Tobias Mayer, a German astronomer, published remarkably accurate tables of the motion of the Moon. To make them useful to navigators, however, it was necessary to prepare from them an ephemeris of the Moon for every noon and midnight. The English astronomer royal, Nevil Maskelyne, supervised this task; the results were published in the annual Nautical Almanac, which was inaugurated in 1766.

The Mercator Chart.
When the Portuguese, under the leadership of Prince Henry the Navigator, ventured farther south along the west coast of Africa, they encountered navigational difficulties by assuming that the charts used in the Mediterranean could simply be extended. Over long distances the rhumb lines could not be taken as straight, and the charts bore no relation to the new methods of checking the dead reckoning that Portuguese astronomers and mathematicians had devised. These methods required a chart on which positions were expressed as latitudes and longitudes rather than bearings and distances. Such a chart had to embody a practical method of representing the curved meridians and parallels on a flat surface. Even for an area as large as the Mediterranean, this can be done without grossly falsifying either distances or directions, but for larger regions some distortions are inevitable, and a choice has to be made between alternative mapping techniques. On certain types of charts, distances can be shown accurately, but directions cannot; on other types, directions are reliably presented, but the scale of distance varies greatly between different parts of the chart. The navigator accepts the second type because the risk of lengthening the voyage is preferable to that of missing the target.
In 1569 the Flemish cartographer Gerardus Mercator published a world map that he had composed using a "projection suitable for navigation," the details of which he did not disclose. On a Mercator chart the meridians of longitude are represented by equally spaced vertical lines, and the parallels of latitude are represented by horizontal lines that are closer together near the Equator than near the poles. The uneven spacing of the parallels compensates for the increasing exaggeration of the east-west distance between adjacent meridians at higher latitudes; this distance decreases on the Earth but remains the same on the chart. In 1599 the English mathematician Edward Wright supplied a rational explanation of Mercator's projection and provided tables by which the distorted distances could be corrected.
Virtually all navigational charts are constructed on the ordinary Mercator projection; the only navigational charts not on ordinary Mercator projections are great-circle charts and charts of the polar regions. Great-circle charts, which are maps of large areas, such as the entire Pacific Ocean, are ordinarily on very small scales with Gnomonic projection. The navigator uses them to lay out a track between ports perhaps thousands of miles apart and then transfers the latitudes corresponding, for example, to each 5° of longitude, to his ocean sailing chart. He thus arrives at a series of short rhumb-line courses, each of which makes the same angle with all meridians, that closely approximate the shortest distance between the two ports.

Celestial Navigation.
Is the use of the observed positions of celestial bodies to determine a navigator's position. At any moment some celestial body is at the zenith of any particular location on the Earth's surface. This location is called the ground position (GP). GP can thus be stated in terms of celestial coordinates, with the declination of the celestial object equal to latitude and the Greenwich hour angle equal to longitude. Almanacs such as those published by the Nautical Almanac Office of the U.S. Naval Observatory provide these coordinates for the Sun, Moon, and planets (or navigator's stars); the tabulations are given in terms of Greenwich Civil Time. From this information a line of position can be plotted. In principle, the line could be drawn on a very large sphere, but, in practice, a Mercator chart, or plotting sheet, is used. The navigator then uses a sextant or bubble octant to measure the altitude of the celestial object and records this altitude using Greenwich Civil Time. The navigator estimates his position, this being the dead-reckoning position. The altitude and the bearing that the celestial object would have at this position are calculated or taken from tables. The dead-reckoning position is marked on the plotting sheet and a line drawn in the direction of the celestial object's calculated bearing. From this information and from the difference between the observed and computed altitudes of the celestial object, known as the intercept, the position of the navigator can be calculated.

Sextant.
An instrument for determining the angle between the horizon and a celestial body such as the Sun, the Moon, or a star, used in celestial navigation to determine latitude and longitude. The device consists of an arc of a circle, marked off in degrees, and a movable radial arm pivoted at the centre of the circle. A telescope, mounted rigidly to the framework, is lined up with the horizon. The radial arm, on which a mirror is mounted, is moved until the star is reflected into a half-silvered mirror in line with the telescope and appears, through the telescope, to coincide with the horizon. The angular distance of the star above the horizon is then read from the graduated arc of the sextant. From this angle and the exact time of day as registered by a chronometer, the latitude can be determined (within a few hundred metres) by means of published tables. The name comes from the Latin sextus, or "one-sixth," for the sextant's arc spans 60°, or one-sixth of a circle. Octants, with 45° arcs, were first used to calculate latitude. Sextants were first developed with wider arcs for calculating longitude from lunar observations, and they replaced octants by the second half of the 18th century.

Hour angle.
The angle between an observer's meridian (a great circle passing over his head and through the celestial poles) and the hour circle (any other great circle passing through the poles) on which some celestial body lies. This angle, when expressed in hours and minutes, is the time elapsed since the celestial body's last transit of the observer's meridian. The hour angle can also be expressed in degrees, 15° of arc being equal to one hour.

Loxodrome.
Also called RHUMB LINE, OR SPHERICAL HELIX, curve cutting the meridians of a sphere at a constant nonright angle. Thus, it may be seen as the path of a ship sailing always oblique to the meridian and directed always to the same point of the compass. Pedro Nunes, who first conceived the curve (1550), mistakenly believed it to be the shortest path joining two points on a sphere (see great circle route). Any ship following such a course would, because of convergence of meridians on the poles, travel around the Earth on a spiral that approaches one of the poles as a limit. On a Mercator projection such a line (rhumb line) would be straight. Rhumb lines are used to simplify small-scale charting.

Great Circle.
The shortest course between two points on the surface of a sphere. It lies in a plane that intersects the sphere's centre and was known by mathematicians before the time of Columbus. Until the 19th century ships generally sailed along rhumb lines, which made use of prevailing winds and fixed compass headings. The development of steamships in the 19th century allowed complete independence from the winds, removing the major uncertainty for sailors trying to follow a geometrically prescribed route.

Great circle routes, which require constantly changing headings, are most useful beyond the equatorial regions and for distances greater than several hundred miles. Long-distance air traffic uses great circle routes routinely, saving time and fuel. Navigational radio signals also follow great circle paths.
Great circle routes are usually plotted on charts based on the gnomonic projection, on which great circles appear as straight lines.