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NAVIGATION (from Lat. navis, ship, and agere, to move), the science or art of conducting a ship across the seas. The term is also popularly used by analogy of boats on rivers, &c., and of flying-machines or similar methods of locomotion. Navigation, as an art applied properly to ships, is technically used in the restricted sense dealt with below, and has therefore to be distinguished from " seamanship " (q.v.), or the general methods of rigging a ship (see Rigging), or the management of sails, rudder, &c.

History. The early history of the rise and progress of the art of navigation is very obscure, and it is more easy to trace the gradual advance of geographical knowledge by its means than the growth of the practical methods by which this advance was attained. Among Western nations before the introduction of the mariner's compass the only practical means of navigating ships was to keep in sight of land, or occasionally, for short distances, to direct the ship's course by referring it to the sun or stars; this very rough mode of procedure failed in cloudy weather, and even in short voyages in the Mediterranean in such circumstances the navigator generally became hopelessly bewildered as to his position.

Over the China Sea and Indian Ocean the steadiness in direction of the monsoons was very soon observed, and by running directly before the wind vessels in those localities were able to traverse long distances out of sight of land in opposite directions at different seasons of the year, aided in some cases by a rough compass (q.v.). But it is surprising when we read of the progress made among the ancients in fixing positions on shore by practical astronomy that so many years should have passed without its application to solving exactly the same problems at sea, but this is probably to be explained by the difficulty of devising instruments for use on the unsteady platform of a ship, coupled with the lack of scientific education among those who would have to use them.

The association of commercial activity and nautical progress shown by the Portuguese in the early part of the 15th century marked an epoch of distinct progress in the methods of practical navigation, and initiated that steady improvement which in the 20th century has raised the art of navigation almost to the position of an exact science. Up to the time of the Portuguese exploring expeditions, sent out by Prince Henry, generally known as the " Navigator," which led to the discovery of the Azores in 141 9, the rediscovery of the Cape Verde Islands in 1447 and of Sierra Leone in 1460, navigation had been conducted in the most rude, uncertain and dangerous manner it is possible to conceive. Many years had passed without the least improvement being introduced, except the application of the magnetic needle about the beginning of the 14th century (see Compass and Magnetism). Prince Henry did all in his power to bring together and systematize the knowledge then obtainable upon nautical affairs, and also established an observatory at Sagres (near Cape St Vincent) in order to obtain more accurate tables of the declination of the sun. John II., who ascended the throne of Portugal in 1481, followed up the good work. He employed Roderick and Joseph, his physicians, with Martin de Bohemia, from Fayal, to act as a committee on navigation. They calculated tables of the sun's declination, and improved the astrolabe, recommending it as more convenient than the cross-staff. The Ordenanzas of the Spanish council of the Indies record the course of instruction prescribed at this time for pilots; it included the De Sphaera Mundi of Sacrobosco, the spherical triangles of Regiomontanus, the Almagest of Ptolemy, the use of the astrolabe and its mechanism, the adjustments of instruments, cartography and the methods of observing the movements of heavenly bodies.

The then backward state of navigation is best understood from a sketch of the few rude appliances which the mariner had, and even these were only intended for the purpose of ascertaining the latitude. The mystery of finding the longitude proved unfathomable for many years after the time of the Armada, and the very inaccurate knowledge existing of the positions of the heavenly bodies themselves fully justified the quaintly expressed advice given in a nautical work of repute at the time, where the writer observes, " Now there be some that are very inquisitive to have a way to get the longitude, but that is too tedious for seamen, since it requireth the deep knowledge of astronomy, wherefore I would not have any man think that the longitude is to be found at sea by any instrument; so let no seamen trouble themselves with any such rule, but (according to their accustomed manner) let them keep a perfect account and g reckonin of the way of their ship." Such record of the " way of the ship " appears to have been then and for many years later recorded in chalk on a wooden board (log board), which folded like a book, and from which each day a position for the ship was deduced, or from which the more careful made abstracts into what was termed the " journal." A compass, a cross-staff or astrolabe, a fairly good table of the sun's declination, a correction for the altitude of the pole star, and occasionally a very incorrect chart formed all the appliances of a navigator in the time of Columbus. For a knowledge of the speed of the ship one of the earliest methods of actual measurement in use was by what was known as the " Dutchman's log," which consisted in throwing into the water, from the bows of the ship, something which would float, and noting the interval between its apparently drifting past two observers standing on the deck at a known distance apart. No other method is mentioned until 1577, when a line was attached to a small log of wood, which was thrown overboard, and the length measured which was carried over in a certain interval of time; this interval of time was, we read, generally obtained by the repetition of certain sentences, which were repeated twice if the ship were only moving slowly. It is unfortunate that the words of this ancient shibboleth are unknown. This is mentioned by Purchas as being in occasional use in 1607, but the more usual method (as we incidentally see in the voyages of Columbus) was to estimate or guess the rate of progress. It was customary by one or other of these methods to determine the speed of a ship every two hours, " royal " ships and those with very careful captains doing so every hour. When a vessel had been on various courses during the two hours, a record of the duration on each was usually kept by the helmsman on a traverse board, which consisted of a board having 32 radial lines drawn on it representing the points of the compass, with holes at various distances from the centre, into which pegs were inserted, the mean or average course being that entered on the log board.

Some idea of the speed of ordinary ships in those days may be gathered from an observation in 1551 of a " certain shipp which, without ever striking sail, arrived at Naples from Drepana, in Sicily, in 37 hours " (a distance of 200 m.); the writer accounting for " such swift motion, which to the common sort of man seemeth incredible," by the fact of the occurrence of " violent floods and outrageous winds." In 1578 we find in Bourne's Inventions and Devices a description of a proposed patent log for recording a vessel's speed, the idea (as far as we can gather from its vague description) being to register the revolutions of a wheel enclosed in a case towed astern of a ship (see LoG).

Whether the property of the lodestone was independently discovered in Europe or introduced from the East, it does not appear to have been generally utilized in Europe earlier than about A.D. 1400 (see Compass). In Europe the card or " flie " appears to have been attached to the magnet from the first, and the whole suspended as now in gimbal-rings within the " bittacle," or, as we now spell the word, " binnacle." The direction of a ship's head by compass was termed how she " capes." From the accounts extant of the stores supplied to ships in 1588, they appear to have usually had two compasses, costing 3s. 4d. each, which were kept in charge by the boatswain. The fact that the north point of a compass does not, in most places, point to the true pole but eastward or westward of it, by an amount which is termed by sailors " variation," appears to have been noticed at an early date; but that the amount of variation varied in different localities appears to have been first observed by either Columbus or Cabot about 1490, and we find it used to be the practice to ascertain this error when at sea either from a bearing of the pole star, or by taking a mean of the compass bearings of the sun at both rising and setting, the deviation of the compass in the ships of those days being too small a quantity to be generally noticed, though there is a very suggestive remark on the effect of moving the position of any iron placed near a compass, by a Captain Sturmy of Bristol in 1679. In order, partially to obviate the error of the compass (variation), the magnets, which usually consisted of two steel wires joined at both ends and opened out in the middle, were not placed under the north and south line of the compass card, but with the ends about a point eastward of north and westward of south, the variation in London when first observed in 1580 being about 11 ° E.; the change of the variation year by year at the same base was first noted by Gellibrand in 1635.

The " cross-staff " appears to have been used by astronomers at a very early period, and subsequently by seamen for measuring altitudes at sea. It was one of the few instruments possessed by Columbus and Vasco da Gama. The old cross-staff, called by the Spaniards " ballestilla," consisted of two light battens. The part we may call the staff was about I z in. square and 36 in. long. The cross was made to fit closely and to slide upon the staff at right angles; its length was a little over 26 in., so as to allow the " pinules " or sights to be placed exactly 26 in. apart. A sight was also fixed on the end of the staff for the eye to look through so as to see both those on the cross and the objects whose distance apart was to be measured. It was made by describing the angles on a table, and laying the staff upon it (fig. I). The scale of degrees was marked on the upper face. Afterwards shorter crosses were introduced, so that smaller angles could be taken by the same instrument. These angles were marked on the sides of the staff.

To observe with this instrument a meridian altitude of the sun the bearing was taken by compass, to ascertain when it was near the meridian; then the end of the long staff was placed close to the observer's eye, and the transversary, or cross, moved until one end exactly touched the horizon, and the other the sun's centre. This was continued until the sun dipped, when the meridian altitude was obtained.

Another primitive instrument in common use at the beginning of the 16th century was the astrolabe (q.v.), which was more convenient than the cross-staff for taking altitudes. Fig. 2 represents an astrolabe as described by Martin Cortes. It was made of copper or tin, about 4 in. in thickness and 6 or 7 in. in diameter, and was circular except at one place, where a projection was provided for a hole by which it was suspended. Weight was considered desirable in order to keep it steady when in use. The face of the metal having been well polished, a plumb line from the point of suspension marked the vertical line, from which were derived the horizontal line and centre. The upper left quadrant was divided into degrees. The second part was a pointer pt of the same metal and thickness as the circular plate, about 12 in. wide, and in length equal to the diameter of the circle. The centre was bored, and a line was drawn across it the full length, which was called the line of confidence. On the ends of that line were fixed plates, s, s, having each a small hole, both exactly over the line of confidence, as sights for the sun or stars. The pointer moved upon a centre the size of a goose quill. When the instrument was suspended the pointer was directed by hand to the object, and the angle read on the one quadrant only. Some years later the opposite quadrant was also graduated, to give the benefit of a second reading. The astrolabe was used by Vasco da Gama on his first voyage FIG. 2 round the Cape of Good Hope in 1 497; but the movement of a ship rendered accuracy impossible, and the liability to error was increased by the necessity for three observers. One held the instrument by a ring passed over the thumb, the second measured the altitude, and the third read off.

For finding latitude at night by altitude of the pole star taken by cross-staff or astrolabe, use was made of an auxiliary instrument called the " nocturnal." From the relative positions of the two stars in the constellation of the " Little Bear " farthest from the pole (known as the Fore and Hind guards) the position of the pole star with regard to the pole could be inferred, and tables were drawn up termed the " Regiment of the Pole Star," showing for eight positions of the guards how much should be added or subtracted from the altitude of the pole star; thus, " when the guards are in the N.W. bearing from each other north and south add half a degree," &c. The bearings of the guards, and also roughly the hour of the night, were found by the nocturnal, first described by M. Coignet in 1581.

The nocturnal (fig. 3) consisted of two concentric circular plates, the outer being about 3 in. in diameter, and divided into twelve equal parts corresponding to the twelve months, each being again subdivided into groups of five days. The inner circle was graduated into twenty-four equal parts, corresponding to the hours of the day, and again subdivided into quarters; the handle was fixed to the outer circle in such a way that the middle of it corresponded with the day of the month on which the guards had the same right ascension as the sun - or, in other words, crossed the meridian at noon. From the common centre of the two circles extended a long index bar, which, together with the inner circle, turned freely and independently about this centre, which was pierced with a round hole. To use the instrument, the projection at twelve hours on the inner plate was turned until it coincided with the day of the month of observation, and the instrument held with its plane roughly parallel to the equinoctial or celestial equator, the observer looking at the pole star through the hole in the centre, and turning the long central index bar until the guards were seen just touching its edge; the hour in line with this edge read off on the inner plate was, roughly, the time. Occasionally the nocturnal was constructed so as to find the time by observations of the pointers in the Great Bear.

The rough charts used by a few of the more expert navigators at the time we refer to will be more fully described later (see also MAP andGEOGRAPHY). Nautical maps or charts first appeared in Italy at the end of the 13th century, but it is said that the first seen in England was brought by Bartholomew Columbus in 1489.

Among the earliest authors who touched upon navigation was John Werner of Nuremberg, who in 1514, in his notes upon Ptolemy's geography, describes the cross-staff as a very ancient instrument, but says that it was only then beginning to be generally introduced among seamen. He recommends measuring the distance between the moon and a star as a means of ascertaining the longitude; but this (though developed many years after into the method technically known as " lunars ") was at this time of no practical use owing to the then imperfect knowledge of the true positions of the moon and stars and the nonexistence of instrumental means by which such distances could be measured with the necessary accuracy.

Thirty-eight years after the discovery of America, when. long voyages had become comparatively common, R. Gemma Frisius wrote upon astronomy and cosmogony, with the use of the globes. His book comprised much valuable information to mariners of that day, and was translated into French fifty years later (1582) by Claude de Bossiere. The astronomical system adopted is that of Ptolemy. The following are some of the points of interest relating to navigation. There is a good description of the sphere and its circles; the obliquity of the ecliptic is given as 23° 30'. The distance between the meridians is to be measured on the equator, allowing 15° to an hour of time; longitude is to be found by eclipses of the moon and conjunctions, and reckoned from the Fortunate Islands (Azores). Latitude should be measured from the equator, not from the ecliptic, " as Clarean says." The use of globes is very thoroughly and correctly explained. The scale for measuring distances was placed on the equator, and 15 German leagues, or 60 Italian leagues, were to be considered equal to one degree. The Italian league was 8 stadia, or loon paces, therefore the degree is taken much too small. We are told that, on plane charts, mariners drew lines from various centres (i.e. compass courses), which were very useful since the virtue of the lodestone had become recognized; it must be remembered that parallel rulers were unknown, being invented by Mordente in 1584. Such a confusion of .lines has been continued upon sea charts till comparatively recently. Gemma gives rules for finding the course and distance correctly, except that he treats difference of longitude as departure. For instance, if the difference of latitude and difference of longitude are equal, the course prescribed is between the two principal winds - that is, 45°. He points out that the courses thus followed are not straight lines, but curves, because they do not follow the great circle, and that distances could be more correctly measured on the globe than on charts. The tide is said to rise with the moon, high water being when it is on the meridian and 12 hours later. From a table of latitudes and longitudes a few examples are here selected, by which it appears that even latitude was much in error. The figures in brackets FIG. I.

FIG. 3.

Alexandria .


o' N.



30' E.



Athens .


1 5


5 8)

5 2




Babylon .




3 2)





Dantzic .


3 0




1 5



London .

5 2



3 1)

1 9

1 5



Malta .





3 8




Rome .

4 1

5 0







represent the positions according to modern tables, counting the longitude from the western extremity of St Michael. (Flores is 5° 8' farther west.) The latitude of Cape Clear is given 34' in error, and the lo'ngi'tude 44°; the Scilly Islands are given with an error of one degree in latitude and 1° io' in longitude; while Madeira is placed 3° 8' too far south and 4° 20' too far west, and Cape St Vincent 1° 25' too far south and 6° too far west.

In 1534 Gemma produced an " astronomical ring," which he dedicated to the secretary of the king of Hungary. He admitted that it was not entirely his own invention, but asserted that it could accomplish all that had been said of quadrants, cylinders and astrolabes - also that it was a pretty ornament, worthy of a prince. As it displayed great ingenuity, and was followed by many similar contrivances during two centuries, a sketch with brief description is here given (fig. 4).

The outer and principal sustaining circle EPQ represents the meridian, and is about 6 in. in diameter; Per, are the poles. The upper quadrant is divided into degrees. It pended by fine cord or wire placed at the supposed latitude. The second circle EQ is fixed at right angles to the first, and represents the equinoctial line. The upper side divided into twenty-four parts, representing the hours from noon or midnight. On the inner side of that circle are marked the months and weeks. The third ring CC attached to the first at the poles, and revolves freely within it. On the interior are marked the months, and on another side the corresponding signs of the zodiac; another is gradu FIG. 4. ated in degrees. It is fitted with a groove carries two movable sights. On the fourth side are twenty-four unequal divisions (tangents) for measuring heights. Its use is illustrated by twenty problems, showing it capable of doing roughly all that any instrument for taking angles can. Thus, to find the latitude, set the sights C, C to the place of the sun in the zodiac, and shut the circle till it corresponds with 12 o'clock. Look through the sights and alter the point of suspension till the greatest elevation is attained; that time will be noon, and the point of suspension will be the latitude. The figure is represented as slung at lat. 40°, either north or south. To find the hour of the day, the latitude and declination being known: the sights C, C being set to the declination as before, and the suspension on the latitude, turn the ring CC freely till it points to the sun, when the index opposite the equinoctial circle will indicate the time, while the meridional circle will coincide with the meridian of the place.

There is in the museum attached to the Royal Naval College at Greenwich an instrument described as Sir Francis Drake's astrolabe. It is not an astrolabe, but may be a combination of astronomical rings as invented by Gemma with additions, probably of a later date. It has the appearance of a large gold watch, about 22 in. in diameter, and contains several parts which fall back on hinges. One is a sun-dial, the gnomon being in connexion with a graduated quadrant, by which it could be set to the latitude of the place. There are a small compass and an hour circle. It is very neat, but too small for actual use, and may be simply an ornament representing a larger instrument. There is a table of latitudes engraved inside one lid; that given for London is 51° 34', about 3 1n. too much.

Though clocks are mentioned in 1484 as recent inventions, watches were unknown till about 1530, when Gemma seized the idea of utilizing them for the purpose of ascertaining the difference of longitude between two places by a comparison between their local times at the same instant. They were too inaccurate, however, to be of practical use, and their advocate proposed to correct them by water-clocks cr sand-clocks. For rough purposes of keeping time on board ship sand glasses were employed, and it is curious to note that hour and half-hour glasses were used for this purpose in the British Navy until 1839. The outer margin of the compass card was early divided into twentyfour equal parts numbered as hours until the error of thus determining time by the bearings of the sun was pointed out by Davis in 1607.

In 1537 Pedro Nunez (Nonius), cosmographer to the king of Portugal, published a work on astronomy, charts and some points of navigation. He recognized the errors in plane charts, and tried to rectify them. Among many astronomical problems given is one for finding the latitude of a place by knowing the sun's declination and altitude when on two bearings, not less than 40 apart. Gemma did a similar thing with two stars; therefore the problem now known as a " double altitude " is a very old one. It could be mechanically solved on a large globe within a degree. To Nunez has been erroneously attributed the present mode of reading the exact angle on a sextant, the scale of a barometer, &c., the credit of which is due, however, to Vernier nearly a hundred years later. The mode of dividing the scale which Nunez published in 1542 was the following. The arc of a large quadrant was furnished with forty-five concentric segments, or scales, the outer graduated to 90°, the others to 89, 88, 87, &c., divisions. As the fine edge of the pointer attached to the sights passed among those numerous divisions it touched one of them, suppose the fifteenth division on the sixth scale, then the angle was It of 90°= 15° 52' 56". This was a laborious method; Tycho Brahe tried it, but abandoned it in favour of the diagonal lines then in common use, and still found on all scales of equal parts.

In 1545 Pedro de Medina published Arte de navigar at Valladolid, dedicated to Don Philippo, prince of Spain. This appears to be the first book ever published professedly entirely on navigation. It was soon translated into French and Italian, and many years after into English by John Frampton. Though this pretentious work came out two years after the death of Copernicus, the astronomy is still that of Ptolemy. The general appearance of the chart given of the Mediterranean, Atlantic, and part of the Pacific is in its favour, but examination shows it to be very incorrect. A scale of equal parts, near the centre of the chart, extends from the equator to what is intended to represent 75° of latitude; by this scale London would be in 55° instead of 5 1 2 °, Lisbon in 374° instead of 38° 42'. The equator is made to pass along the coast of Guinea, instead of being over four degrees farther south. The Gulf of Guinea extends 14° too far east, and Mexico is much too far west. Though there are many vertical lines on the chart at unequal distances they do not represent meridians; and there is no indication of longitude. A scale of boo leagues is given (German leagues, fifteen to a degree). By this scale the distance between Lisbon and the city of Mexico is 1740 leagues, or 6960 miles; by the vertical scale of degrees it would be about the same; whereas the actual distance is 4820 miles. Here two great wants become apparent - a knowledge of the actual length of any arc, and the means of representing the surface of the globe on flat paper. There is a table of the sun's declination to minutes; on June 12th and December 11th (o.s.) it was given as 23° 33'. The directions for finding the latitude by the pole star and pointers appear good. For general astronomical information the book is inferior to that of Gemma.

In 1556 Martin Cortes published at Seville Arte de navigar. He gives a good drawing of the cross-staff and astrolabe, also a table of the sun's declination for four years (the greatest value being 23° 33'), and a calendar of saints' days. The motions of the heavens are described according to the notions then prevalent, the earth being considered as fixed. He recommends which the altitude of the pole being found frequently, as the estimated distance run was imperfect. He devised an instrument whereby to tell the hour, the direction of the ship's head, and where the sun would set. A very correct table is given of the distances between the meridians at every degree of latitude, whereby a seaman could easily reduce the difference of longitude to departure. In the rules for finding the latitude by the pole star, that star is supposed to be 3° from the pole. Martin Cortes attributes the tides entirely to the influence of the moon, and gives instructions for finding the time of high water at Cadiz, when by means of a card with the moon's age on it, revolving within a circle showing the hours and minutes, the time of high water at any other place for which it was set would be indicated. Directions are given for making a compass similar to those then in common use, also for ascertaining and allowing for the variation. The east is here spoken of as the principal point, and marked by a cross.

The third part of Martin Cortes's work is upon charts; he laments that wise men do not produce some that are correct, and that pilots and mariners will use plane charts which are not true. In the Mediterranean and " Channel of Flanders" the want of good charts is (he says) less inconvenient, as they do not navigate by the altitude of the pole.

As some subsequent writers have attributed to Cortes the credit of first thinking of the enlargement of the degrees of latitude on Mercator's principle, his precise words may be cited. In making a chart, it is recommended to choose a well-known place near the centre of the intended chart, such as Cape St Vincent, which call 37°, " and from thence towards the Arctic pole the degrees increase; and from thence to the equinoctial line they go on decreasing, and from the line to the Antarctic pole increasing." It would appear at first sight that this implied that the degrees increased in length as well as being called by a higher number, but a specimen chart in the book does not justify that conclusion. It is from 34° to 40°, and the divisions are unequal, but evidently by accident, as the highest and lowest are the longest. He states that the Spanish scale was formed by counting the Great Berling as 3° from Cape St Vincent (it is under 22°). Twenty English leagues are equal to 172 Spanish or 25 French, and to 1 ° of latitude. Cortes was evidently at a loss to know the length of a degree, and consequently the circumference of the globe. The degrees of longitude are not laid down, but for a first meridian we are told to draw a vertical line " through the Azores, or nearer Spain, where the chart is less occupied." It is impossible in such circumstances to understand or check the longitudes assigned to places at that period. Martin Cortes's work was held in high estimation in England for many years, and appeared in several translations. A reprint, with additions, of Richard Eden's (1561), by John Tapp and published in 1609, gives an improved table of the sun's declination from 1609 to 1625 - the maximum value being 23° to 30'. The declinations of the principal stars, the times of their passing the meridian, and other improved tables, are given, with a very poor traverse table for eight points. The cross-staff, he said, was in most common use; but he recommends Wright's sea quadrant.

William Cuningham published in 1559 a book called his Astronomical Glass, in which he teaches the making of charts by a central meridional line divided into equal parts, with other meridians on each side, distant at top and bottom in proportion to the departure at the highest and lowest latitude, for which purpose a table of departures is given very correctly to the third place of sexagesimals. The chart would be excellent were it not that the parallels are drawn straight instead of being curved. In another example, which shows one-fourth of the sphere, the meridians and parallels are all curved; it would be good were it not that the former are too long. The hemisphere is also shown upon a projection approaching the stereographic; but the eighteen meridians cut the equator at equal distances apart instead of being nearer together towards the primitive. He gives the drawing of an instrument like an astrolabe placed horizontally, divided into 32 points and 360 degrees, and carrying a small magnetic needle to be used as a prismatic compass, or even as a theodolite.

In 1581 Michael Coignet of Antwerp published sea charts, and also a small treatise in French, wherein he exposes the errors of Medina, and was probably the first who said that rhumb lines form spirals round the pole. He published also tables of declination of the sun and observed the gradual decrease in the obliquity of the ecliptic. He described a cross-staff with three transverse pieces, which was then in common use at sea. Coignet died in 1623.

The Dutch published charts made up as atlases as early as 1584, with a treatise on navigation as an introduction. In 1585 Roderico Zamorano, who was then lecturer at the naval college at Seville, published a concise "and clearly-written compendium of navigation; he follows Cortes in the desire to obtain better charts. Andres Garcia de Cespedes, the successor of Zamorano at Seville, published a treatise on navigation at Madrid in 1606. In 1592 Petrus Plancius published his universal map, containing the discoveries in the East and West Indies and. towards the north pole. It possessed no particular merit; the degrees of latitude are equal, but the distances between the meridians are varied. He made London appear in 51° 32' N. and long. 22°, by which his first meridian should have been more than 3° east of St Michael.

For Mercator's great improvements in charts at about this date see MAP; from facsimiles of his early charts in Jomard, Les Monuments de la geographie, the following measurements have been made. A general chart in 156 9 of North America, from lat. 25° to lat. 79°, is 2 ft. long north and south, and 20 in. wide. Another of the same date, from the equator to 60° south lat. is 15.8 in. long. The charts agree with each other, a slight allowance being made for remeasuring. As compared with J. Inman's table of meridional parts, the spaces between the parallels are all too small. Between o° and 10° the error is 8'; at 20° it is 5'; at 30 16'; at 40°, 39'; at 50°, 61'; at 60°, 104'; at 70°, 158'; and at 79°, 182' - that is, over three degrees upon the whole chart. As the measures are always less than the truth it is possible that Mercator was afraid to give the whole. In a chart of Sicily by Romoldus Mercator in 158 9, on which two equal degrees of latitude, 36° to 38°, extend 92 in., the degree of longitude is quite correct at one-fourth from the top; the lower part is 1 m. too long. One of the, north of Scotland, published in 1595, by Romoldus, measures 102 in. from 58° 20' to 61°; the divisions are quite equal and the lines parallel; it is correct at the centre only. A map of Norway, 15 9 5, lat. 60° to 70° - 9 4 in., has the parallels curved and equidistant, the meridians straight converging lines; the spaces between the meridians at 60° and 70 are quite correct.

In 1594 Blundeville published a description of Mercator's charts and globes; he confesses to not having known upon what rule the meridians were separated by Mercator, unless upon such a table as that given by Wright, whose table of meridional parts is published in the same book, also an excellent table of sines, tangents and secants - the former to seven figures, the latter to eight. These are the tables made originally by Regiomontanus and improved by Clavius.

In 1594 the celebrated navigator John Davis published a pamphlet of eighty pages, in black letter, entitled The Seaman's Secrets, in which he proposes to give all that is necessary for sailors - not for scholars on shore. He defines three kinds of sailing: horizontal, paradoxical and great circle. His horizontal sailing consists of short voyages which may be delineated upon a plain sheet of paper. The paradoxical or cosmographical embraces longitude, latitude and distance - the combining many horizontal courses into one " infallible and true," i.e. what is now called traverse and Mercator's sailings. His " paradoxical course " he describes correctly as a rhumb line which is straight on the chart and a curve on the globe. He points out the errors of the common or plane chart, and promises if spared to publish a " paradoxall chart." It is not known whether such appeared or not, but he assisted Wright in producing his chart on what is known as Mercator's projection a few years later. Great circle sailing on a globe is clearly described by Davis, and to render it more practicable he divides a long distance into several short rhumb lines quite correctly. From the practice of navigators in using globes the principles of such sailing were not unknown at an earlier date; indeed it is said that S. Cabot projected a voyage across the North Atlantic on the arc of a great circle in 1495.

The list of instruments given by Davis as necessary to a skilful seaman comprises the sea compass, cross-staff, chart, quadrant, astrolabe, an " instrument magnetical " for finding the variation of the compass, a horizontal plane sphere, a globe and a paradoxical compass. The first three are said to be sufficient for use at sea, the astrolabe and quadrant being uncertain for sea observations. The importance of knowing the times of the tides when approaching tidal or barred harbours is clearly pointed out, also the nn p nde of ascertaining them by the moon's age. A table of the sun's d..2clination is given for noon each day during four years 1593-1597, fpom the ephemerides of J. Stadius. The greatest given value is 2,3° 28'. Several courses and distances, with the resulting differer;ce of latitude and departure, are correctly worked out. A specimen log-book provides one line only for each day, but the columns are arranged similarly to those of a modern log. Under the head of remarks after leaving Brazil, we read, " the compass varied 9°, the south point westward." He states that the first meridian passed through St Michael, because there was no variation at that place, and therefore that this meridian passed through the magnetic pole as well as the pole of the earth. He makes no mention of Mercator's chart by name nor of Cortes or other writers on navigation. Rules are given for finding the latitude by two altitudes of the sun and intermediate azimuth, also by two fixed stars, using a globe. There is a drawing of a quadrant, with a plumb line, for measuring the zenith distance, and one of a modification of a cross-staff using which the observer stands with his back to the sun, looking at the horizon through a sight on the end of the staff, while the shadow of the top of a movable projection, falls on the sight; this, known as the back-staff, was an improvement on the cross-staff. It was fitted with a reflector, and was thus the first rough idea of the principle of the quadrant and sextant. This remained in common use till superseded in 1731 by Hadley's quadrant. The eighth edition of Davis's work was printed in 1657.

Edward Wright, of Caius College, Cambridge, published in 1 599 a valuable work entitled Certain Errors in Navigation Detected and Corrected. One part is a translation from Roderico Zamorano; there is a chapter from Cortes and one from Nunez. A year later appeared his chart of the world, upon which both capes and the recent discoveries in the East Indies and America are laid down truthfully and scientifically, as well as his knowledge of their latitudes and longitudes would admit. Just the northern extremity of Australia is shown.

Wright said of himself that he had striven beyond his ability to mend the errors in chart, compass, cross-staff and declination of sun and stars. He considered that the instruments which had then recently come in use " could hardly be amended," as they were growing to " perfection " - especially the sea chart and the compass, though he expresses a hope that the latter may be " freed from that rude and gross manner of handling in the making." He gives a table of magnetic declinations (variation) and explains its geometrical construction. He states that Medina utterly denied the existence of variation, and attributed it to bad construction and bad observations. Wright expresses a hope that a right understanding of the dip of the needle would lead to a knowledge of the latitude, " as the variation did of the longitude." He gives a table of declination of the sun for the use of English mariners during four years - the greatest given value being 23° 31' 30". The latitude of London he made 51° 32'. For these determinations a quadrant over 6 f t. in radius was used. He also treats of the " dip " of the sea horizon, refraction, parallax and the sun's motions. With all this knowledge the earth is still considered as stationary - although Wright alludes to Copernicus, and says that he omitted to allow for parallax. Wright ascertained the declinations of thirty-two stars, and made many improvements or additions to the art of navigation, considering that all the problems could be performed trigonometrically, without globe or chart. He devised sea rings for taking observations, and a sea quadrant to be used by two persons, which is in some respects similar to that by Davis. While deploring the neglected state which navigation had been in, he rejoices that the worshipful society at the Trinity House (which had been established in 1514), under the favour of the king (Henry VIII.), had removed " many gross and dangerous enormities." He joins the brethren of the Trinity House in the desire that a lectureship should be established on navigation, as at Seville and Cadiz; also that a grand pilot should be appointed, as Sebastian Cabot had been in Spain, to examine pilots (i.e. mates) and navigators. Wright's desire was partially fulfilled in 1845, when an Act of Parliament paved the way for the compulsory qualification of masters and mates of merchant ships; but such was the opposition by shipowners that it was even then left voluntary for a few years. England was in this respect more than a century behind Holland. It has been said that Wright accompanied the earl of Cumberland to the Azores in 1589, and that he was allowed £5 0 a year by the East India Company as lecturer on navigation at Gresham College, Tower Street.

The great mark which Wright made was the discovery of a correct and uniform method of dividing the meridional line and making charts which are still called after the name of Mercator.

He considered such charts as true as the globe itself; and so they were for all practical purposes. He commenced by dividing a meridional line, in the proportion of the secants of the latitude, for every ten minutes of arc, and in the edition of his work published in 1610 his calculations are for every minute. His method was based upon the fact that the radius bears the same proportion to the secant of the latitude as the difference of longitude does to the meridional difference of latitude - a rule strictly correct for small arcs only. One minute is taken as the unit upon the arc and io,000 as the corresponding secant, 2' becomes 20,000, 3' = 30,000, &c., increasing uniformly till 49', which is equal to 490,001; 1° is 600,012. The secant of 20° is 12,251,192, and for 20° 1' it will be 12,251,192+10,642 - practically the same as that used in modern tables.

The principle is simply explained by fig. 5, where b is the pole and bf the meridian. At any point a a minute of longitude: a min. of lat.:: ea (the semi-diameter of the parallel): kf (the radius). Again ea: kf:: kf: ki: : radius: sec. akf (sec. of lat). To keep this proportion on the chart, the distances between points of latitude must increase in the same proportion as the secants of the arc contained between those points and the equator, which was then to be done by the " canon of triangles." Wright gave the following excellent popular description of the principle of Mercator's charts " Suppose a spherical globe (representing the world) inscribed in a concave cylinder to swell like a bladder equally in every part (that is as much in longitude as in latitude) until it joins itself to the concave surface of the cylinder, each parallel increasing successively from the equator towards either pole until it is of equal diameter to the cylinder, and consequently the meridians widening apart until they are everywhere as distant from each other as they are at the equator. Such a spherical surface is thus by extension made cylindrical, and consequently a plane parallelogram surface, since the surface of a cylinder is nothing else but a plane parallelogram surface wound round it. Such a cylinder on being opened into a flat surface will have upon it a representation of a Mercator's chart of the world." This great improvement in the principle of constructing charts was adopted slowly by seamen, who, putting it as they supposed to a practical test, found good reason to be disappointed. The positions of most places in the world had been originally laid down erroneously, by very rough courses and estimated distances upon the plane chart, and from this they were transferred to the new projection, so that errors in courses and distances, really due to erroneous positions, were wrongly attributed to the new and accurate form of chart.

When Napier's Canon Mirificus appeared in 1614, Wright at once recognized the value of logarithms as an aid to navigation, and undertook a translation of the book, which he did not live to publish (see Napier). Gunter's tables (1620) made the application of the new discovery to navigation possible, and this was done by Addison in his Arithmetical Navigation (1625), as well as by Gunter in his tables of 1624 and 1636, which gave logarithmic sines and tangents, to a radius of 1,000,000, with directions for their use and application to astronomy and navigation, and also logarithms of numbers from 1 to 10,000. Several editions followed, and the work retained its reputation over a century. Gunter invented the sector, and introduced the meridional line upon it, in the just proportion of Mercator's projection.

The means of taking observations correctly, either at sea or on shore, was about this time greatly assisted by the invention bearing the name of Pierre Vernier, the description of which was published at Brussels in 1631. As Vernier's quadrant was divided into half degrees only, the sector, as he called it, spread over 141 degrees, and that space carried thirty equal divisions, numbered from o to 30. As each division of the sector contained 29 min. of arc, the vernier could be read to minutes. The verniers now commonly adapted to sextants can be read to Io secs. Shortly after the invention it was recommended for use by P. Bouguer and Jorge Juan, who describe it in a treatise entitled La Construction, &c., du quadrant nouveau. About this period Gascoigne applied the telescope to the quadrant as used on shore; and Hevelius invented the tangent screw, to give slow and steady motion when near the desired position. These practical improvements were not applied to the rougher nautical instruments until the invention of Hadley's sextant in 1731.

In 1635 Henry Gellibrand published his discovery of the annual change in variation of the needle, which was effected by comparing the results of his own observations with those of W. Borough and Edmund Gunter. The latter was his predecessor at Gresham College.

In 1637 Richard Norwood, a sailor, and reader in mathematics, published an account of his most laudable exertions to remove one of the greatest stumbling-blocks in the way of correct navigation, that of not knowing the true length of a degree or nautical mile, in a pamphlet styled The Seaman's Practices. Norwood ascertained the latitude of a position near the Tower of London in June 1633, and of a place in the centre of York in June 1635, with a sextant of more than 5 ft. radius, and, having carefully corrected the declination of the sun and allowed for refraction and parallax, made the difference of latitude 2° 28'. He then measured the distance with a chain, taking horizontal angles of all windings, and made a special table for correcting elevations and depressions. A few places which he was unable to measure he paced. His conclusion was that a degree contained 367,176 English feet; this gives 2040 yds. to a nautical mile - only about 12 yds. too much. Norwood's work went through numerous editions, and retained its popularity over a hundred years. In a late edition he says that, as there is no means of discovering the longitude, a seaman must trust to his reckoning. He recommends the knots on the log-line to be placed 51 ft. apart, as the just proportion to a mile when used with the half-minute glass. To Norwood is also attributed the discovery of the " dip " of the magnetic needle in 1576.

The progress of the art of navigation was and is still of course inseparably connected with that of map and chart drawing and the correct astronomical determinations of positions on land. While as we have seen at an early period simple practical astronomical means of finding the latitude at sea were known and in use, no mode could be devised of finding longitude except by the rough method of estimating the run of the ship, so that the only mode of arriving at a port of destination was to steer so as to get into the latitude of such a port either to the eastward or westward of its supposed position, and then approach it on the parallel of its latitude. The success of this method would of course greatly depend upon the accuracy with which the longitude of such port was known. Even with the larger and more accurate instruments used in astronomical observatories on shore the means of ascertaining latitude were far in advance of those by which longitude could be obtained, and this equally applied to the various heavenly bodies themselves upon which the terrestrial positions depended, the astronomical element of declination (corresponding to latitude) being far more accurately determined than that of right ascension (corresponding to longitude) .

Almanacs were first published on the continent of Europe in 1 457, but the earliest printed work of that kind in England is dated 14 9 7. The only portions of their contents of use to seamen were tables of the declination of the sun, rough elements of the positions of a few stars, and tables for finding latitude by the pole star.

No accurate predictions of the positions of the moon, stars and planets could, however, be made until the laws governing their movements were known, such laws of course involving a knowledge of their actual positions at different widely separated epochs.

In 16 99 Edmund Halley (subsequently astronomer royal), in command of the " Paramour," undertook a voyage to improve the knowledge of longitude and of the variation of the compass. The results of his voyage were the construction of the first variation chart, and proposals for finding the longitude by occultations of fixed stars.

The necessity for having more correct charts being equalled by the pressing need of obtaining the longitude by some simple and correct means available to seamen, many plans had already been thought of for this purpose. At one time it was hoped that the longitude might be directly discovered by observing the variation of the compass and comparing it with that laid down on charts. In 1674 Charles II. actually appointed a commission to investigate the pretensions of a scheme of this sort devised by Henry Bond, and the same idea appears as late as 1777 in S. Dunn's Epitome. But the only accurate method of ascertaining the longitude is by knowing the difference of time at the same instant at the meridian of the observer and that of Greenwich; and till the invention and perfecting of chronometers this could only be done by finding at two such places the apparent time of the same celestial phenomenon.

A class of phenomena whose comparative frequency recommended them for longitude observations, viz. the eclipses of Jupiter's satellites, became known through Galileo's discovery of these bodies (1610). Tables for such eclipses were published by Dominic Cassini at Bologna in 1688, and repeated in a more correct form at Paris in 1693 by his son, who was followed by J. Pound, J. Bradley, P. W. Wargentin, and many other astronomers. But this method, though useful on land, is not suited to mariners; when W. Whiston, for example, in 1737 recommended that the satellites should be observed by a reflecting telescope, he did not sufficiently consider the difficulty of using a telescope at sea.

Another method proposed was that of comparing the local time of the moon's crossing the meridian of the observer with the predicted time of the same event at Greenwich, the difference of the two depending upon the moon's motion during the time represented by the longitude; thus Herne's Longitude Unveiled (1678), proposes to find the time of the moon's meridian passage at sea by equal altitudes with the cross-staff, and then compare apparent time at ship with London time. The accuracy of this, as in the case of lunar problems, would obviously depend upon a more perfect knowledge of the laws of the moon's motion than then existed.

The celebrated problem of finding longitude by lunars (or by measurement of " lunar distances ") occupied the attention of astronomers and sailors for many years before being superseded by the more simple and accurate modern method by the use of chronometers, and was the principal reason for establishing the Royal Observatory at Greenwich and the subsequent publication of the Nautical Almanac. The principle was simple, depending upon the comparatively rapid movement of the moon with regard to the heavenly bodies lying in her immediate path in the heavens. It is evident that if the theory of this movement were perfectly understood and the positions of such heavenly bodies accurately determined, the distances of the moon from those at any instant of time at Greenwich could be accurately foretold so that if such predictions were published in advance, an observer at any place in the world, by simply measuring such distances, could accurately determine the Greenwich time, a comparison of which with the local time (which in clear weather can be frequently and simply determined) would give the longitude. This, as previously mentioned, was foreseen by J. Werner as early as 1514, but very great difficulties attended its practical application for many years. Until the establishment of national astronomical observatories it was impossible to accumulate the vast number of observations necessary to fulfil the astronomical conditions, and until the invention of the sextant no instrument existed capable of use at sea which would measure the distances required with the necessary accuracy, while even up to the time when the problem had attained its greatest practical accuracy the calculations involved were far too intricate for general use among those for whom it was chiefly intended. The very principles of a theory of the movements of the moon were unknown before Newton's time, when the lunar problem begins to have a chief place in the history of navigation; the places of stars were formerly derived from various and widely discrepant sources.

The study of the lunar problem was stimulated by the reward of woo crowns offered by Philip III. of Spain in 1598 for the discovery of a method of finding longitude at sea; the States-general followed with an offer of Io,000 florins. But for a long time nothing practical came of this; a proposal by J. B. Morin, submitted to Richelieu in 1633, was pronounced by commissioners appointed to judge of it to be impracticable through the imperfection of the lunar tables, and the same objection applied when the question was raised in England in 1674 by a proposal of St Pierre to find the longitude by using the altitudes of the moon and two stars to find the time each was from the meridian. When the king was pressed by St Pierre, Sir J. Moore and Sir C. Wren to establish an observatory for the benefit of navigation, and especially that the moon's exact position might be calculated a year in advance, Flamsteed gave his judgment that the lunar tables then in use were.quite useless, and the positions of the stars erroneous. The result was that the king decided upon establishing an observatory in Greenwich Park, and Flamsteed was appointed astronomical observer on March 4, 1675, upon a salary of ioo a year, for which also he was to instruct two boys from Christ's Hospital. While the small building in the Park was in course of erection he resided in the Queen's House (now the central part of Greenwich Hospital school), and removed to the house on the hill on the 10th of July 1676, which came to be known as " Flamsteed House." The institution was placed under the surveyor-general of ordnance - perhaps because that office was then held by Sir Jonas Moore, himself an eminent mathematician. Though this was not the first observatory in Europe, it was destined to become the most useful, and has amply fulfilled the important duties for which it was XIX. I O designed. It was established to meet the exigencies of navigation, as was clearly stated on the appointment of Flamsteed, and on several subsequent occasions; we see now what an excellent fostermother it has been to the higher branches of that science. This has been accomplished by much labour and patience; for, though originally the most suitable man. in the kingdom was placed in charge, it was so starved and neglected as to be almost useless during many years. The government did not provide a single instrument. Flamsteed entered upon his important duties with an iron sextant of 7 ft. radius, a quadrant of 3 ft. radius, two telescopes and two clocks, the last given by Sir Jonas Moore. Tycho Brahe's catalogue of 777 stars, formed in about 1590, was his only guide. In 1681 he fitted a mural arc which proved a failure. Seven years after another mural arc was erected at a cost of £120, with which he set to work in earnest to verify the latitude, and to determine the position of the equinoctial point, the obliquity of the ecliptic and the right ascensions and declinations of the stars; he obtained the positions of 2884 which appeared in the " British catalogue " in 1723 (see Flamsteed, and Astronomy).

Flamsteed died in 1719, and was succeeded by Halley, who paid particular attention to the motions of the moon with a view to the longitude problem. A paper which he published in the Phil. Trans. (1731) shows what had been accomplished up to that date, and proves that it was still impossible to find the longitude correctly by any observation depending upon the predicted position of the moon. He repeats what he had published twenty years before in an appendix to Thomas Street's Caroline tables, which contained observations made by him (Halley) in1683-1684for ascertaining the moon's motion, which he thought to be the only practical method of " attaining " the longitude at sea. The Caroline tables of Street, though better than those before his time as well as those of Tycho, Kepler, Bullialdus and Horrox, were uncertain; sometimes the errors would compensate one another; at others when they fell the same way the result might lead to a position being 100 leagues in error. He hopes that the tables will be so amended that an error may scarce ever exceed 3 minutes of arc (equal to 12 ° of longitude). Sir Isaac Newton's tables, corrected by himself (Halley) and others up to 1713, would admit of errors of 5 minutes, when the moon was in the third and fourth quarters. He blames Flamsteed for neglecting that portion of astronomical work, as he was at the observatory more than two periods of eighteen years. He himself had at this time seen the whole period of the moon's apogee - less than nine years - during which he observed the right ascensions at her transit, with great exactness, almost fifteen hundred times, or as often as Tycho Brahe, Hevelius and Flamsteed together. He hoped to be able to compute the moon's position within 2 minutes of arc with certainty, which would reduce errors of position to 20 leagues at the equator and 15 in the Channel; he thought Hadley's quadrant might be applied to measure lunar distances at sea with the desired accuracy.' The rise of modern navigation may be fairly dated from the invention of the sextant in 1731 and of the chronometer in 1735; the former a complete nautical observatory in itself, and the latter an instrument which in its modern development has become an almost perfect time-keeper. It was a curious coincidence that these two invaluable instruments were invented at so nearly the same time. Until 1731 all instruments in use at sea for measuring angles either depended on a plumb line or required the observer to look in two directions at once.

Their imperfections are clearly pointed out in a paper by Pierre Bouguer (1729) which received the prize of the Paris Academy of Sciences for the best method of taking the altitude of stars at sea. Bouguer himself proposes a modification of what he calls the English quadrant, probably the one suggested by Wright and improved by Davis. Fig. 6 represents the instrument as proposed, capable of measuring fully 90° from E to N. A fixed pinule was recommended to be placed at E, through which a ray from the sun would pass to the sight C. The sight F was movable. The observer, standing with his back to the sun would look through F and C at the horizon, shifting the sight F up or down till the ray from the sun coincided with the horizon. The space from E to F would represent the altitude, and the remaining part F to N the zenith distance. The English quadrant which this was to supersede differed in having about half the arc from E towards N, and, instead of the pinule being fixed at E, it was on a smaller arc represented by the dotted line eB, and movable. It was placed on an even number of degrees, considerably less than the altitude; the remainder was measured on the larger arc, as described.

' Halley's observations were published posthumously in 1742, and in 1765 the commissioners of longitude paid his daughter £ ioo for MSS. supposed to be useful to navigation. As the moon passes the stars lying in her course through the heavens at the mean rate of 33" in one minute of time, it is obvious that an erro

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Bibliography Information
Chisholm, Hugh, General Editor. Entry for 'Navigation'. 1911 Encyclopedia Britanica. 1910.

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