NAVIGATION.
Naviga- NAVIGATION is the art of conducting a ship from one tion. port or place to another.
HISTORY.
The profane poets refer the invention of the art of navigation to their heathen deities, though historians ascribe it to the Æginetes, the Phœnicians, the Tyrians, and the ancient inhabitants of Britain. Scripture refers the origin of so useful an invention to God himself, who gave the first specimen of navigation in the ark built by Noah under his direction.
However, profane history represents the Phœnicians, especially those of their capital Tyre, as the first navigators; being urged to seek a foreign commerce by the narrowness and poverty of a slip of ground they possessed along the coast, as well as by the convenience of two or three good ports, and by their natural genius for traffic. Accordingly, Lebanon and the other neighbouring mountains furnishing them with excellent wood for ship-building, they in a short time became masters of a numerous fleet; and constantly hazarding new navigations, and settling new trades, they soon arrived at an incredible pitch of opulence and populousness, inasmuch as to be in a condition to send out colonies. The principal of these was Carthage, which, keeping up the Phœnician spirit of commerce, in time not only equalled Tyre itself, but vastly surpassed it, sending its merchant fleets through the Straits of Gibraltar, along the western coasts of Africa and Europe, and even, if we may believe some authors, to America itself.
Tyre, whose immense riches and power are represented in such lofty terms both by sacred and profane authors, was destroyed by Alexander the Great, upon which its navigation and commerce were transferred by the conqueror to Alexandria, a new city, admirably situated for these purposes, and intended to form the capital of the empire of Asia, of which Alexander then meditated the conquest. And thus arose the navigation of the Egyptians, which was afterwards so much cultivated by the Ptolemies, that Tyre and Carthage were quite forgotten.
Egypt being reduced into a Roman province after the battle of Actium, its trade and navigation fell into the hands of Augustus, in whose time Alexandria was only inferior to Rome; and the magazines of the capital of the world were wholly supplied with merchandize from the commercial capital of Egypt.
At length Alexandria itself underwent the fate of Tyre and Carthage, being surprised by the Saracens, who, in spite of the Emperor Heraclius, overspread the northern coasts of Africa, whence the merchants being expelled, Alexandria has ever since been in a languishing state, though it still has a considerable share of the commerce of the Christian merchants trading to the Levant.
The fall of Rome and its empire drew along with it not only the overthrow of learning and the polite arts, but that of navigation; the barbarians, into whose hands it fell, contenting themselves with the spoils of the industry of their predecessors. But no sooner were the braver amongst those nations well settled in their new provinces, some in Gaul, as the Franks, others in Spain, as the Goths, and others in Italy, as the Lombards, than they began to learn the advantages of navigation and commerce, and the methods of managing them, from the people they had subdued; and this with so much success, that in a little time
some of them became able to give new lessons, and set on foot new institutions, for its advantage. Thus it is to the Lombards that we usually ascribe the invention and use of banks, book-keeping, exchanges, recharges, &c.
It does not appear which of the European people, after the settlement of their new masters, first betook themselves to navigation and commerce. Some think it began with the French, although the Italians seem to have the justest title to this distinction, and are accordingly regarded as the restorers of navigation, as well as of the polite arts, which had been banished together from the time the empire was torn asunder. It is the people of Italy, then, and particularly those of Venice and Genoa, who have the glory of this restoration; and it is to their advantageous situation for navigation that they in great measure owe their glory. In the bottom of the Adriatic were a great number of marshy islands, only separated by narrow channels, but these well screened, and almost inaccessible, the residence of some fishermen, who here supported themselves by a little trade in fish and salt, which they found in some of these islands. Thither the Veneti, a people inhabiting that part of Italy which stretches along the coasts of the gulf, retired, when Alaric king of the Goths, and afterwards Attila king of the Huns, ravaged Italy.
These new islanders, little imagining that this was to be their fixed residence, did not think of composing any body politic; but each of the seventy-two islands of this little archipelago continued a long time under its separate master, and each formed a distinct commonwealth. When their commerce had become considerable enough to occasion jealousy to their neighbours, they began to think of uniting into a body; and it was this union, first begun in the sixth century, but not completed till the eighth, that laid the sure foundation of the future grandeur of the state of Venice. From the time of this union, their fleets of merchantmen were sent to all the ports of the Mediterranean; and at last to those of Egypt, particularly Cairo, a new city, built by the Saracen princes, on the eastern bank of the Nile, where they traded for the spices and other products of the Indies. Thus they flourished, and increased their commerce, their navigation, and their conquests, till the league of Cambrai in 1508, when a number of jealous princes conspired to bring about their ruin; which was the more easily effected by the diminution of their East India commerce, of which the Portuguese had got one part and the French another.
Genoa, which had applied itself to navigation at the same time with Venice, and that with equal success, was a long time its dangerous rival, disputed with it the empire of the sea, and shared with it the trade of Egypt and other parts both of the east and west. But jealousy soon began to break out; and the two republics coming to an open rupture, there was almost continual war for three centuries before the superiority was ascertained, when, towards the end of the fourteenth century, the battle of Chioza ended the strife; the Genoese, who till then had usually the advantage, having now lost all, and the Venetians, almost become desperate, having, by one happy blow, beyond all expectation, secured to themselves the empire of the sea, and superiority in commerce.
About the same time that navigation was retrieved in the southern parts of Europe, a new society of merchants was formed in the north, which not only carried commerce to the greatest perfection of which it was capable till the discovery of the East and West Indies, but also formed a
History. new scheme of laws for its regulation, which still obtain under the name of Uses and Customs of the Sea.
This society is that famous league of the Hanse Towns, commonly supposed to have been instituted about the year 1164. See HANSE TOWNS. For the modern state of navigation in England, Holland, France, Spain, Portugal, &c. see the articles COMMERCE, COMPANY, &c.
We shall only add, that in examining the causes of commerce passing successively from the Venetians, Genoese, and Hanse Towns, to the Portuguese and Spaniards, and from these again to the English and Dutch, it may be established as a maxim, that the relation between commerce and navigation, or their union, is so intimate, that the fall of the one inevitably draws after it that of the other; and that they will always either flourish or decline together. Hence so many laws, ordinances, statutes, and edicts for its regulation; and hence particularly that celebrated act of navigation, which an eminent foreign author calls the palladium or tutelar deity of the commerce of England, which was long considered as the standing rule, not only of the British amongst themselves, but also as that of other nations with whom they trafficked.
The art of navigation has been exceedingly improved in modern times, both with regard to the form of the vessels themselves, and also with respect to the methods of working them. The use of rowers is now entirely superseded by the improvements made in the formation of the sails, rigging, &c. by which means ships can not only sail much faster than formerly, but can tack in any direction with the greatest facility. It is also very probable that the ancients were neither so well skilled in finding the latitudes, nor in steering their vessels in places of difficult navigation, as the moderns. But the greatest advantage which the moderns possess over the ancients consists in the mariner's compass, by which they are enabled to find their way with more facility in the midst of an immeasurable ocean, than the ancients could have done by creeping along the coast, and never going out of sight of land. Some people indeed contend that this is no new invention, but that the ancients were acquainted with it. They say, that it was impossible for Solomon to have sent ships to Ophir, Tarshish, and Parvaim, which last they imagine to have been Peru, without this useful instrument. They insist, that it was impossible for the ancients to be acquainted with the attractive virtue of the magnet, and to be ignorant of its polarity; nay, they affirm that this property of the magnet is plainly mentioned in the book of Job, where the loadstone is mentioned by the name of topaz, or the stone that turns itself. But it is certain that the Romans who conquered Judea were ignorant of this instrument; and it is very improbable that such an useful invention, if it had once been commonly known to any nation, would have been forgotten, or perfectly concealed from such a prudent people as the Romans, who were so deeply interested in the discovery of it.
Amongst those who admit that the mariner's compass is a modern invention, it has been much disputed who was the inventor. Some attribute the honour of the discovery to Flavio Gioia of Amalfi in Campania,1 who lived about the beginning of the fourteenth century; whilst others contend that it came from the east, and was earlier known in Europe. But, at whatever time it was invented, it is certain, that the mariner's compass was not commonly used in navigation before the year 1420. In that year the science was considerably improved under the auspices of Henry duke of Visco, brother to the king of Portugal. In the year 1485, Roderick and Joseph, physicians to John II. king of Portugal, together with one Martin de Bohemia, a Portuguese native of the island of Fayal, and scholar
of Regiomontanus, calculated tables of the sun's declination for the use of sailors, and recommended the astrolabe for taking observations at sea. Of the instructions of Martin the celebrated Christopher Columbus is said to have availed himself, and to have improved the Spaniards in the knowledge of the art; for the further progress of which a lecture was afterwards founded at Seville by the Emperor Charles V.
The discovery of the variation is claimed both by Columbus and by Sebastian Cabot. The former certainly did observe the variation without having heard of it from any other person, on the 14th of September 1492, and it is very probable that Cabot might have done the same. At that time it was found that there was no variation at the Azores, where some geographers have thought proper to place the first meridian, though it has since been observed that the variation alters in time. The use of the cross staff now began to be introduced amongst sailors. This ancient instrument is described by John Werner of Nuremberg, in his annotations on the first book of Ptolemy's Geography, printed in the year 1514. He recommends it for observing the distance between the moon and some star, in order thence to determine the longitude.
At this time the art of navigation was very imperfect, on account of the inaccuracies of the plane chart, which was the only one then known, and which, by its gross errors, must have greatly misled the mariner, especially in voyages far distant from the equator. Its precepts were probably at first only set down on the sea charts, as is the custom at this day; but at length two Spanish treatises were published in the year 1545, one by Pedro de Medina, and the other by Martin Cortes, which contained a complete system of the art, as far as it was then known. These seem to have been the oldest writers who fully handled the art; for Medina, in his dedication to Philip prince of Spain, laments that multitudes of ships daily perished at sea, because there were neither teachers of the art, nor books by which it might be learned; and Cortes, in his dedication, boasts to the emperor, that he was the first who had reduced navigation into a compendium, valuing himself much on what he had performed. Medina defended the plane chart; but he was opposed by Cortes, who showed its errors, and endeavoured to account for the variation of the compass, by supposing the needle to be influenced by a magnetic pole (which he called the point attractive), different from that of the world, which notion has been farther prosecuted by others. Medina's book was soon translated into Italian, French, and Flemish, and for a long time served as a guide to foreign navigators. However, Cortes was the favourite author of the English nation, and was translated in the year 1561; whilst Medina's work was entirely neglected, though translated also within a short time of the other. At that time the system of navigation consisted of an account of the Ptolemaic hypothesis, and the circles of the sphere; of the roundness of the earth, the longitudes, latitudes, climates, &c. and eclipses of the luminaries; a calendar; the method of finding the prime, equinox, moon's age, and tides; a description of the compass, an account of its variation, for the discovering of which Cortes said that an instrument might easily be contrived; tables of the sun's declination for four years, in order to find the latitude from his meridian altitude; directions to find the same by certain stars; of the course of the sun and moon; the length of the days; of time and its divisions; the method of finding the hour of the day and night; and, lastly, a description of the sea chart, on which, in order to discover where the ship was, they made use of a small table, which showed, upon an alteration of one degree of the latitude, how many
1 See the articles GIOIA and MAGNETISM.
History. leagues were run in each rhumb, together with the departure from the meridian. Besides, some other instruments were described, especially by Cortes; such as one to find the place and declination of the sun, with the days and place of the moon; certain dials, the astrolabe, and cross staff; together with a complex machine to discover the hour and latitude at once.
About the same time proposals were made for finding the longitude by observations of the moon. In 1530 Gemma Frisius advised the keeping of time by means of small clocks or watches, which were then, as he says, newly invented. He also contrived a new sort of cross staff, and an instrument called the nautical quadrant, which last was much praised by William Cunningham, in his Astronomical Glass, printed in the year 1559.
In the year 1537, Pedro Nunez, or Nonius, published a book in the Portuguese language, to explain a difficulty in navigation proposed to him by the commander Don Martin Alphonso de Susa. In this he exposed the errors of the plane chart, and likewise gave the solution of several curious astronomical problems, amongst which was that of determining the latitude from two observations of the sun's altitude and the intermediate azimuth. He observed, that although the rhumbs are spiral lines, yet the direct course of a ship will always be in the arc of a great circle, whereby the angle with the meridians will continually change; and hence all that the steersman can here do for the preserving of the original rhumb, is to correct these deviations as soon as they appear sensible. But in reality the ship will thus describe a course without the rhumb line intended; and therefore his calculations for assigning the latitude, where any rhumb line crosses the several meridians, will be in some measure erroneous. He invented a method of dividing a quadrant by means of concentric circles, which, after having been much improved by Dr Halley, is used at present, and is called a nonius.
In the year 1577, Mr William Bourne published a treatise, in which, by considering the irregularities in the moon's motion, he showed the error of the sailors in finding her age by the epoch, and also in determining the hour from observing on what point of the compass the sun and moon appeared. He advised, in sailing towards the high latitudes, to keep the reckoning by the globe, as there the plane chart was most erroneous. He despaired of our ever being able to find the longitude, unless the variation of the compass should be occasioned by some such attractive point as Cortes had imagined, of which, however, he doubted; but as he had shown how to find the variation at all times, he recommended to keep an account of the observations, as useful for finding the place of the ship; and this advice was prosecuted at large by Simon Stevin, in a treatise published at Leyden in 1599, the substance of which was the same year printed at London in English by Mr Edward Wright, entitled the Haven-finding Art. In this ancient tract is also described the method by which our sailors estimate the rate of a ship in her course, by an instrument called the log. This was so named from the piece of wood or log which floats in the water, whilst the time is reckoned during which the line that is fastened to it is veering out. The author of this contrivance is not known, neither was it taken notice of till 1607, in an East India voyage published by Purchas; but from that time it became famous, and was much taken notice of by almost all writers on navigation in every country; and it still continues to be used as at first, although many attempts have been made to improve it, and contrivances proposed to supply its place, many of which have succeeded in quiet water, but proved useless in a stormy sea.
In the year 1581 Michael Coignet, a native of Antwerp, published a treatise, in which he animadverted on Medina. In this he showed, that as the rhumbs are spirals, making
endless revolutions about the poles, numerous errors must arise from their being represented by straight lines on the sea charts; but although he hoped to find a remedy for these errors, he was of opinion that the proposals of Nonius were scarcely practicable, and therefore in a great measure useless. In treating of the sun's declination, he took notice of the gradual decrease in the obliquity of the ecliptic; he also described the cross staff with three transverse pieces, which he admitted were then in common use amongst the sailors. He likewise described some instruments of his own invention; but all of them are now laid aside, excepting perhaps his nocturnal. He constructed a sea table to be used by such as sailed beyond the sixtieth degree of latitude; and at the end of the book is delivered a method of sailing upon a parallel of latitude by means of a ring dial and a twenty-four hour glass. The same year the discovery of the dipping needle was made by Mr Robert Norman. In his publication on that subject he maintains, in opposition to Cortes, that the variation of the compass was caused by some point on the surface of the earth, and not in the heavens; and he also made considerable improvements on the construction of compasses themselves, showing especially the danger of not fixing, on account of the variation, the wire directly under the fleur de lis, as compasses made in different countries have it placed differently. To this performance of Norman's is prefixed a discourse on the variation of the magnetic needle, by Mr William Burrough, in which he shows how to determine the variation in many different ways, and also points out many errors in the practice of navigation at that time, speaking in very severe terms concerning those who had published upon it.
During this time the Spaniards continued to publish treatises on the art. In 1585 an excellent compendium was published by Roderico Zamorano, and contributed greatly towards the improvement of the art, particularly in the sea charts. Globes of an improved kind, and of a much larger size than those formerly used, were now constructed, and many improvements were made in other instruments; nevertheless, the plane chart continued still to be followed, though its errors were frequently complained of. Methods of removing these errors had indeed been sought after; and Gerard Mercator seems to have been the first who found the true method of effecting this, so as to answer the purposes of seamen. His method was to represent the parallels, both of latitude and longitude, by parallel straight lines, but gradually to augment the former as they approached the pole. Thus the rhumbs, which otherwise ought to have been curves, were now also extended into straight lines; and thus a straight line drawn between any two places marked upon the chart formed an angle with the meridians, expressing the rhumb leading from the one to the other. But although in 1569 Mercator published an universal map constructed in this manner, it does not appear that he was acquainted with the principles upon which this proceeded; and it is now generally believed, that the true principles on which the construction of what is called Mercator's chart depends were first discovered by an Englishman, Mr Edward Wright.
Mr Wright supposed, but, according to the general opinion, without sufficient grounds, that this enlargement of the degrees of latitude was known and mentioned by Ptolemy, and that the same thing had also been spoken of by Cortes. The expressions of Ptolemy alluded to relate indeed to the proportion between the distances of the parallels and meridians; but instead of proposing any gradual enlargement of the parallels of latitude in a general chart, he speaks only of particular maps, and advises not to confine a system of such maps to one and the same scale, but to plan them out by a different measure, as occasion might require; with this precaution, however, that the degrees of
History. longitude in each should bear some proportion to those of latitude, and this proportion was to be deduced from that which the magnitude of the respective parallels bore to a great circle of the sphere. He added, that, in particular maps, if this proportion be observed with regard to the middle parallel, the inconvenience will not be great, although the meridians should be straight lines parallel to each other. But here he is understood only to mean, that the maps should in some measure represent the figures of the countries for which they are drawn. In this sense Mercator, who drew maps for Ptolemy's tables, understood him; thinking it, however, an improvement not to regulate the meridians by one parallel, but by two, one distant from the northern, the other from the southern extremity of the map, by a fourth part of the whole depth; by which means, in his maps, although the meridians are straight lines, yet they are generally drawn inclining to each other towards the poles. With regard to Cortes, he speaks only of the number of degrees of latitude, and not of the extent of them; nay, he gives express directions that they should all be laid down by equal measurement in a scale of leagues adapted to the map.
For some time after the appearance of Mercator's map, it was not rightly understood, and it was even thought to be entirely useless, if not detrimental. However, about the year 1592 its utility began to be perceived; and seven years afterwards, Mr Wright printed his famous treatise entitled the Correction of certain Errors in Navigation, where he fully explained the reason of extending the length of the parallels of latitude, and the uses thereof to navigators. In 1610 a second edition of Mr Wright's book was published, with improvements. An excellent method was proposed of determining the magnitude of the earth; and at the same time it was judiciously proposed to make our common measures in some proportion to a degree on its surface, that they might not depend on the uncertain length of a barleycorn. Amongst his other improvements may be mentioned the Table of Latitudes for Dividing the Meridian computed to Minutes, whereas it had been only divided to every tenth minute. He also published a description of an instrument which he calls the sea rings, by which the variation of the compass, the altitude of the sun, and the time of the day, may at once readily be determined in any place, provided the latitude is known. He also showed how to correct the errors arising from the eccentricity of the eye in observing by the cross staff. In the years 1594, 1595, 1596, and 1597, he amended the tables of the declinations and places of the sun and stars from his own observations made with a six-feet quadrant, a sea quadrant to take altitudes by a forward or backward observation, and likewise with a contrivance for the ready finding of the latitude by the height of the pole star, when not upon the meridian. To this edition was subjoined a translation of Zamorano's Compendium, above mentioned, in which he corrected some mistakes in the original; adding a large table of the variation of the compass observed in different parts of the world, in order to show that it was not occasioned by any magnetical pole.
These improvements soon became known abroad. In 1608 a treatise entitled Hypomnemata Mathematica was published by Simon Stevin, for the use of Prince Maurice. In the portion of the work relating to navigation, the author having treated of sailing on a great circle, and shown how to draw the rhumbs on a globe mechanically, set down Wright's two tables of latitudes and of rhumbs, in order to describe these lines more accurately, pretending even to have discovered an error in Wright's table. But all Stevin's objections were fully answered by the author him-
self, who showed that they arose from the rude method of calculating made use of by the former. History.
In 1624 the learned Willebrordus Snellius, professor of the mathematics at Leyden, published a treatise of navigation on Wright's plan, but somewhat obscurely; and as he did not particularly mention all the discoveries of Wright, the latter was thought by some to have taken the hint of all his discoveries from Snellius. But this supposition has been long ago refuted; and Wright now enjoys the honour of those discoveries, which is justly his due.
Mr Wright having shown how to find the place of the ship upon his chart, observed that the same might be performed more accurately by calculation; but considering, as he says, that the latitudes, and especially the courses at sea, could not be determined so precisely, he forbore setting down particular examples, as the mariner may be allowed to save himself this trouble, and only to mark out upon his chart the ship's way, after the manner then usually practised. However, in 1614, Mr Raphe Handson, amongst the nautical questions he subjoined to a translation of Pitiscus's Trigonometry, solved very distinctly every case of navigation, by applying arithmetical calculations to Wright's Table of Latitudes, or of Meridional Parts, as it has since been called. Although the method discovered by Wright for finding the change of longitude by a ship sailing on a rhumb is the proper way of performing it, Handson also proposes two methods of approximation without the assistance of Wright's division of the meridian line. The first was computed by the arithmetical mean between the cosines of both latitudes; and the other by the same mean between the secants as an alternative, when Wright's book was not at hand; although this latter is wider of the truth than the former. By the same calculations also he showed how much each of these compendiums deviates from the truth, and also how widely the computations on the erroneous principles of the plane chart differ from them all. The method generally used by our sailors, however, is commonly called the middle latitude, which, although it errs more than that by the arithmetical mean between the two cosines, is preferred on account of its being less op-erose; yet in high latitudes it is more eligible to use that of the arithmetical mean between the logarithmic cosines, equivalent to the geometrical mean between the cosines themselves; a method since proposed by Mr John Bassat. The computation by the middle latitude will always fall short of the true change of longitude, that by the geometrical mean will always exceed; but that by the arithmetical mean falls short in latitudes of about 45 degrees, and exceeds in lesser latitudes. However, none of these methods will differ much from the truth when the change of latitude is sufficiently small.
About this period logarithms were invented by John Napier, baron of Merchiston in Scotland, and proved of the utmost service to the art of navigation. From these Mr Edmund Gunter constructed a table of logarithmic sines and tangents to every minute of the quadrant, which he published in 1620. In this work he applied to navigation, and other branches of mathematics, his admirable ruler known by the name of Gunter's scale,1 on which are described lines of logarithms, of logarithmic sines and tangents, of meridional parts, &c.; and he greatly improved the sector for the same purposes. He also showed how to take a back observation by the cross staff, by which the error arising from the eccentricity of the eye is avoided. He likewise described another instrument, of his own invention, called the cross boss, for taking altitudes of the sun or stars, with some contrivances for the more readily collecting the latitude from the observation. The discoveries concerning logarithms were carried into France in
1 See Gunter's Scale.
History. 1624 by Mr Edmund Wingate, who published two small tracts in that year at Paris. In one of these he taught the use of Gunter's scale; and in the other, that of the tables of artificial sines and tangents, as modelled according to Napier's last form, erroneously attributed by Wingate to Briggs.
Gunter's rule was projected into a circular arch by the Reverend Mr William Oughtred in 1633, and its uses were fully shown in a pamphlet entitled the Circles of Proportion, where, in an appendix, several important points in navigation are well treated. It has also been made in the form of a sliding ruler.
The logarithmic tables were first applied to the different cases of sailing by Mr Thomas Addison, in his treatise entitled Arithmetical Navigation, printed in the year 1625. He also gave two traverse tables, with their uses; the one to quarter points of the compass, and the other to degrees. Mr Henry Gellibrand published his discovery of the changes of the variation of the compass, in a small quarto pamphlet, entitled a Discourse Mathematical on the Variation of the Magnetical Needle, printed in 1635. This extraordinary phenomenon he found out by comparing the observations which had been made at different times near the same place by Mr Burrough, Mr Gunter, and himself, all persons of great skill and experience in these matters. This discovery was likewise soon known abroad; for Athanasius Kircher, in his treatise entitled Magnes, first printed at Rome in the year 1641, informs us, that he had been told of it by Mr John Greaves, and then gives a letter of the famous Marinus Mersennus, containing a very distinct account of the same.
As altitudes of the sun are taken on shipboard by observing his elevation above the visible horizon, to obtain from these the sun's true altitude with correctness, Wright observed it to be necessary that the dip of the visible horizon below the horizontal plane passing through the observer's eye should be brought into the account, which cannot be calculated without knowing the magnitude of the earth. Hence he was induced to propose different methods for finding this; but he complains that the most effectual was out of his power to execute, and therefore he contented himself with a rude attempt, in some measure sufficient for his purpose. The dimensions of the earth deduced by him corresponded very well with the usual divisions of the log line; nevertheless, as he wrote not an express treatise on navigation, but only for the correcting such errors as prevailed in general practice, the log line did not fall under his notice. Mr Richard Norwood, however, put in execution the method recommended by Mr Wright as the most perfect for measuring the dimensions of the earth, with the true length of the degrees of a great circle upon it; and, in 1635, he actually measured the distance between London and York; from which measurement, and the summer solstitial altitudes of the sun observed on the meridian at both places, he found a degree on a great circle of the earth to contain 367,196 English feet, equal to 57,300 French fathoms or toises, which is very exact, as appears from many measurements that have been made since that time. Of all this Mr Norwood gave a full account in his treatise called the Seaman's Practice, published in 1637. He there showed the reason why Snellius had failed in his attempt; and he also pointed out various uses of his discovery, particularly for correcting the gross errors hitherto committed in the divisions of the log line. But necessary amendments have been little attended to by sailors, whose obstinacy in adhering to established errors has been complained of by the best writers on navigation. This improvement, however, has at length made its way into practice, and few navigators of reputation now make use of the old measure of forty-two feet to a knot. In this treatise Mr Norwood also describes his
own excellent method of setting down and perfecting a sea reckoning, by using a traverse table, which method he had followed and taught for many years. He likewise shows how to rectify the course by the variation of the compass being considered; as also how to discover currents, and to make proper allowance on their account. This treatise, and another on trigonometry, were continually reprinted, as the principal books for learning scientifically the art of navigation. What he had delivered, especially in the latter of them, concerning this subject, was abridged as a manual for sailors, in a very small piece called an Epitome, which useful performance has gone through a great number of editions. No alterations were ever made in the Seaman's Practice till the twelfth edition in 1676, when the following paragraph was inserted in a smaller character: "About the year 1672, Monsieur Picart has published an account in French, concerning the measure of the earth, a breviary whereof may be seen in the Philosophical Transactions, No. 112, wherein he concludes one degree to contain 365,184 English feet, nearly agreeing with Mr Norwood's experiment;" and this advertisement is continued through the subsequent editions as late as the year 1732.
About the year 1645 Mr Bond published in Norwood's Epitome a very great improvement of Wright's method, from a property in his meridian line, whereby the divisions are more scientifically assigned than the author himself was able to effect; it resulted from this theorem, that these divisions are analogous to the excesses of the logarithmic tangents of half the respective latitudes augmented by forty-five degrees above the logarithm of the radius. This he afterwards explained more fully in the third edition of Gunter's works, printed in 1653, where he observed that the logarithmic tangents from 45° upwards increase in the same manner as the secants do added together, if every half degree be accounted as a whole degree of Mercator's meridional line. His rule for computing the meridional parts belonging to any two latitudes, supposed to be on the same side of the equator, is to the following effect: "Take the logarithmic tangent, rejecting the radius, of half each latitude, augmented by forty-five degrees; divide the difference of those numbers by the logarithmic tangent of 45° 30', the radius being likewise rejected, and the quotient will be the meridional parts required, expressed in degrees." This rule is the immediate consequence of the general theorem, that the degrees of latitude bear to one degree (or sixty minutes, which in Wright's table stands for the meridional parts of one degree), the same proportion as the logarithmic tangent of half any latitude augmented by forty-five degrees, and the radius neglected, to the like tangent of half a degree augmented by forty-five degrees, with the radius likewise rejected. But here there was still wanting the demonstration of this general theorem, which was at length supplied by Mr James Gregory of Aberdeen, in his Exercitationes Geometricæ, printed at London in 1668; and afterwards more concisely demonstrated, together with a scientific determination of the divisor, by Dr Halley, in the Philosophical Transactions for 1695 (No. 219), from the consideration of the spirals into which the rhumbs are transformed in the stereographic projection of the sphere upon the plane of the equinoctial, and which is rendered still more simple by Mr Roger Cotes, in his Logometria, first published in the Philosophical Transactions for 1714 (No. 388). It is moreover added in Gunter's book, that if th of this division, which does not sensibly differ from the logarithmic tangent of 45° 1' 30", with the radius subtracted from it, be used, the quotient will exhibit the meridional parts expressed in leagues, and this is the divisor set down in Norwood's Epitome. After the same manner the meridional parts will be found in minutes, if the like logarithmic tangent of 45° 1' 30", diminished by the radius, be
Theory. taken; that is, the number used by others being 12633, when the logarithmic tables consist of eight places of figures besides the index.
In an edition of a book called the Seaman's Kalender, Mr Bond declared that he had discovered the longitude by having found out the true theory of the magnetic variation; and to gain credit to his assertion, he foretold, that at London in 1657 there would be no variation of the compass, and from that time it would gradually increase the other way; which happened accordingly. Again, in the Philosophical Transactions for 1668 (No. 40), he published a table of the variation for forty-nine years to come. Thus he acquired such reputation, that his treatise entitled The Longitude Found, was in the year 1676 published by the special command of Charles II. and approved by many celebrated mathematicians. It was not long, however, before it met with opposition; and in the year 1678, another treatise, entitled The Longitude not Found, made its appearance, and as Mr Bond's hypothesis did not in any manner answer its author's sanguine expectations, the affair was undertaken by Dr Halley. The result of his speculation was, that the magnetic needle is influenced by four poles; but this wonderful phenomenon seems hitherto to have eluded all our researches. (See MAGNETISM.) In 1700, however, Dr Halley published a general map, with curve lines expressing the paths where the magnetic needle had the same variation; which was received with universal applause. But as the positions of these curves vary from time to time, they should frequently be corrected by skilful persons, as was done in 1644 and 1756, by Mr William Mountain, and Mr James Dodson. In the Philosophical Transactions for 1690, Dr Halley also gave a dissertation on the monsoons, containing many very useful observations for such as sail to places subject to these winds.
After the true principles of the art were settled by Wright, Bond, and Norwood, the authors who wrote on navigation became so numerous that it would be impossible to enumerate them. New improvements were daily made, and every thing relative to it was settled with an accuracy not only unknown to former ages, but which would have been reckoned utterly impossible. The earth being found to be a spheroid, and not a perfect sphere, with the shortest diameter passing through the poles, a tract was published in 1741 by the Reverend Doctor Patrick Murdoch, wherein he accommodated Wright's sailing to such a figure; and the same year Mr Colin Maclaurin, in the Philosophical Transactions (No. 461), gave a rule for determining the meridional parts of a spheroid; which speculation is farther treated of in his book of Fluxions, printed at Edinburgh in 1742, and in Delambre's Astronomy (t. iii. ch. xxxvi.).
Amongst the later discoveries in navigation, that of finding the longitude both by lunar observations and by time-keepers is the principal. It is owing chiefly to the rewards offered by the British parliament that this has attained the present degree of perfection. We are indebted to Dr Maskelyne for putting the first of these methods in practice, and for other important improvements in navigation. The time-keepers constructed by Harrison for this express purpose were found to answer so well that he obtained the parliamentary reward. These have been improved by Arnold, Earnshaw, and many others, so as now to be almost in common use.
The works which have latterly appeared on navigation are those on the longitude and navigation by Dr Mackay, Dr Inman, Mr Riddle, Mr Norie, and others, and which contain every necessary requisite to form the practical navigator.
THEORY OF NAVIGATION.
The motion of a ship in the water is well known to depend on the action of the wind upon its sails, regulated by the direction of the helm. As the water is a resisting medium, and the bulk of the ship very considerable, it thence follows that there is always a great resistance on her fore-part; and when this resistance becomes sufficient to balance the moving force of the wind upon the sails, the ship attains her utmost degree of velocity, and her motion is no longer accelerated. This velocity is different according to the different strength of the wind; but the stronger the wind, the greater resistance is made to the ship's passage through the water; and hence, although the wind should blow ever so strongly, there is also a limit to the velocity of the ship, for the sails and ropes can bear but a certain force of air; and when the resistance on the fore-part becomes more than equivalent to their strength, the velocity can no longer be increased, and the rigging gives way.
The direction of a ship's motion depends upon the position of her sails with regard to the wind, combined with the action of the rudder. The most natural direction of the ship is, when she runs directly before the wind, the sails being then disposed so as to be at right angles thereto. But this is not always the case, both on account of the variable nature of the winds, and the situation of the intended port, or of intermediate headlands or islands. When the wind, therefore, happens not to be favourable, the sails are placed so as to make an oblique angle both with the direction of the ship and with the wind; and the sails, together with the rudder, must be managed in such a manner that the direction of the ship may make an acute angle with that of the wind; and the ship, making boards on different tacks, will by this means arrive at the intended port.
The reason of the ship's motion in this case is, that the
water resists the side more than the fore-part, and that in the same proportion as her length exceeds her breadth. This proportion is so considerable, that the ship continually flies off where the resistance is least, and that sometimes with great swiftness. In this way of sailing, however, there is a great limitation; for if the angle made by the keel with the direction of the wind be too acute, the ship cannot be kept in that position; neither is it possible for a large ship to make a more acute angle with the wind than about six points, though small sloops, it is said, may make an angle of about five points with it or less. In all these cases, however, the velocity of the ship is greatly retarded, and that not only on account of the obliquity of her motion, but by reason of what is called her lee-way. This is occasioned by the yielding of the water on the lee-side of the ship, by which means the vessel acquires a compound motion, partly in the direction of the wind, and partly in that which is necessary for attaining the desired port.
It is perhaps impossible to lay down any mathematical principles on which the lee-way of a ship could be properly calculated; only we may observe in general that it depends on the strength of the wind, the roughness of the sea, and the velocity of the ship. When the wind is not very strong, the resistance of the water on the lee-side bears a very great proportion to that of the current of air, and therefore it will yield but very little; however, supposing the ship to remain in the same place, it is evident, that the water having once begun to yield, will continue to do so for some time, even though no additional force were applied to it; but as the wind continually applies the same force as at first, the lee-way of the ship must go on constantly increasing till the resistance of the water upon the lee-side balances the force applied on the other, when it will become uniform, as does the motion of a ship sailing
Mariner's before the wind. If the ship change her place with any degree of velocity, then every time she moves her own length, a new quantity of water is to be put in motion, which has not yet received any momentum, and which of consequence will make a greater resistance than it can do when the ship remains in the same place. In proportion to the swiftness of the ship, then, the lee-way will be the less; but if the wind be very strong, the velocity of the ship will bear but a small proportion to that of the current of air, and the same effects must follow as though the ship moved slowly and the wind was gentle, that is, the ship must make a great deal of lee-way. The same thing happens when the sea rises high, whether the wind be strong or not; for then the whole water of the ocean, as far as the swell reaches, has acquired a motion in a certain direction, and that to a very considerable depth. The mountainous waves will not fail to carry the ship very much out of her course; and this deviation will certainly be according to their velocity and their magnitude. In all cases of a rough sea, therefore, a great deal of lee-way is made. Another circumstance also occasions a variation in the quantity of the lee-way, namely, the lightness or heaviness of the ship; it being evident, that when the ship sinks deep in the water, a much greater quantity of that element is to be put in motion before she can make any lee-way, than when she swims on the surface. As, therefore, it is impossible to calculate all these things with mathematical exactness, it is plain that the real course of a ship is exceedingly difficult to be found, and frequent errors must occur, which can only be corrected by means of celestial observations.
In many places of the ocean there are currents, or places where the water, instead of remaining at rest, runs with a very considerable velocity for a considerable way in some particular direction, and which will certainly carry the ship greatly out of her course. This occasions an error of the same nature with the lee-way; and therefore, whenever a current is perceived, its direction and velocity ought to be determined, and the proper allowances made.
Another source of error in reckoning the course of a ship proceeds from the variation of the compass. There are few parts of the world where the needle points exactly north; and in those where the variation is known, it is subject to very considerable alterations. By these means the course of the ship is mistaken; for as the sailors have no other standard to direct them than the compass, if the needle, instead of pointing due north, should point north-east, a prodigious error would be occasioned during the course of the voyage, and the ship would not come near the port to which she was bound. To avoid errors of this kind, the only method is to observe the sun's amplitude and azimuth as frequently as possible, by which the variation of the compass will be perceived, and the proper allowances can then be made for errors in the course which this may have occasioned.
Errors will arise in the reckoning of a ship, especially when she sails in high latitudes, from the spheroidal figure of the earth; for as the polar diameter of our globe is found to be considerably shorter than the equatorial one,
it thence follows, that the farther we remove from the equator, the longer are the degrees of latitude. Of consequence, if a navigator assigns any certain number of miles for the length of a degree of latitude near the equator, he must vary that measure as he approaches towards the poles, otherwise he will imagine that he has not sailed so far as he has actually done. It would therefore be necessary to have a table containing the length of a degree of latitude in every different parallel from the equator to either pole; as, without this, a troublesome calculation must be made at every time the navigator makes a reckoning of his course. Such a table, however, has not yet appeared; neither indeed does it seem to be an easy matter to make it, on account of the difficulty of measuring the length even of one or two degrees of latitude in different parts of the world. Sir Isaac Newton first discovered this spheroidal figure of the earth; and showed, from theory originally suggested by experiments on pendulums, that the polar diameter was to the equatorial one as 229 to 230. This proportion, however, has not been admitted by succeeding calculators. The French mathematicians, who measured a degree of the meridian in Lapland, made the proportion between the equatorial and polar diameters to be as 1 to 0.9891; those who measured a degree at Quito in Peru made the proportion as 1 to 0.99624, or 266 to 265; M. Bouguer makes the proportion to be as 179 to 178; and M. Buffon, in one part of his theory of the earth, makes the equatorial diameter exceed the polar one by th of the whole. According to M. du Séjour, this proportion is as 321 to 320; and M. de Laplace, in his Memoir upon the Figure of Spheroids, has deduced the same proportion. Later investigations, however, show that the polar axis is to the equatorial diameter in the ratio of 300 to 301 nearly. From these variations, it appears that the point is not exactly determined, and, consequently, that any corrections which can be made with regard to the spheroidal figure of the earth must be very uncertain.
It is of consequence to navigators, in a long voyage, to take the nearest way to their port; but this is scarcely possible to be done. The shortest distance between any two points on the surface of a sphere is measured by an arc of a great circle intercepted between them; and therefore it is advisable to direct the ship along a great circle of the earth's surface. But this is a matter of considerable difficulty, because there are no fixed marks by which it can be readily known whether the ship sails in the direction of a great circle or not. For this reason the sailors commonly choose to direct their course by the rhumbs, or the bearing of the place by the compass. These bearings do not point out the shortest distance between places; because, upon a globe, the rhumbs are spirals, and not arcs of great circles. However, when the places lie directly under the equator, or exactly under the same meridian, the rhumb then coincides with the arc of a great circle, and of consequence shows the nearest way. The sailing on the arc of a great circle is called great circle sailing; and the cases of it depend all upon the solution of problems in spherical trigonometry.
MARINER'S COMPASS.
A ship is enabled to keep her course at sea by means of an instrument called the mariner's compass. It consists of a magnetic steel bar attached to the under side of a card divided into points and quarter points, and supported by a fine pin, on which it turns freely within a box covered with glass. By reason of the directive property of the magnet, the north point, which is commonly denoted by a fleur de lis, is readily known. The circumference of the card is generally divided into thirty-two points, which
in the best compasses are again subdivided into half points and quarters. These are reckoned sufficient for nautical purposes. On the inside of the box is drawn a dark vertical line called lubber's point. This point, or rather line, and the pin on which the card turns, are in the same line or plane with the keel of the ship; and hence the point on the circumference of the card opposite to lubber's point shows the angle which the ship's course makes with the magnetic meridian, called the course of the ship.