which was afterwards so cultivated by the Ptolemies, that Tyre and Carthage were forgotten.

Egypt being reduced to a Roman province, after the battle of Actium, its trade and navigation fell into the hands of Augustus, in whose time Alexandria was inferior only to Rome; aud the magazines of the capital of the world were wholly supplied from the capital of Egypt.

At length Alexandria itself underwent the fate of Tyre and Carthage; being surprised by the Saracens, who had overspread the northern coasts of Africa, &c.; and its commerce has ever since been in a languishing state, though it still has a considerable share of the trade which the Christian merchants carry on in the Levant.

The ancient Britons had inherited from their earliest ancestors many of the ruder arts of navigation. Their ships were large open boats, framed of light timbers, ribbed or wattled with hurdles and lined with hides, and furnished with masts and sails, the latter being formed of hides and the tackle of thongs. Among the Veneti they were of hides as late as the days of Cæsar; they were never furled, but bound to the mast. These slight sea-boats were, however, soon dismissed for the more substantial vessels and artificial sails of the Romans.

The fall of Rome and its empire involved the temporary ruin of all the arts of peace, the barbarians, into whose hands it fell, contenting themselves for some time with the spoils of the industry of their predecessors. But the more brave and active of these savage conquerors, the Turks in Gaul, the Goths in Spain, and the Lombards in Italy, soon perceived the advantages of navigation and commerce; and, learning the methods of practising them from the people whom they had subdued, they were speedily able to give new lessons on the subject, and set on foot new institutions for their promotion.

It is doubtful which of the European nations first again betook themselves to commerce, after the dissolution of the Roman empire; but on the whole the Italians, and particularly the Venetians and Genoese, seem best entitled to the glory of this restoration. Their situation for navigation was singularly advantageous. In the bottom of the Adriatic were a great number of marshy islands, separated by narrow channels, well screened, and almost inaccessible, the residence of some fishermen, who supported themselves by a little trade in fish and salt, the latter of which they found in some of the islands. Thither the Veneti, a people inhabiting that part of Italy along the shores 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 the little Archipelago continued a long time under its separate master, and each made a distinct commonwealth. When their commerce was become considerable enough to give 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 parts of the Mediterranean; and at last to those of Egypt, particularly Cairo, a new city, built by the Saracens on the east banks of the Nile, where they traded for the spices and other products of the Indies. Thus they flourished, increased their commerce, their navigation, and their conquests on the terra firma, till the league of Cambray in 1508, when a number of jealous princes conspired to 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 to navigation at the same time with Venice, and 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.

Jealousy soon began to break out; and, the two republics coming to blows, there was almost continual war for three centuries ere 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, at 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 revived 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 it was capable of, till the discovery of the East and West Indies, but also formed a new scheme of laws for the regulation thereof, which still obtain under the names of Uses and Customs of the Sea. This society is that famous league of the Hanse towns, commonly supposed to have begun about 1164. See HANSE TOWNS. For the modern state of navigation in England, Holland, France, Spain, Portugal, &c. COMPANY, TRADE, &c.

See

In examining the reasons why commerce has passed 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 or union between commerce and navigation is so intimate, that the fall of the one in evitably draws after it that of the other; and that they will always either flourish or dwindle together.

The art of navigation has been greatly im proved in modern times, both with respect to the form of the vessels and the method of working them. The use of rowers is now entirely superseded by the improvements made in the sails, rigging, &c., by which means they not only sail much faster than formerly, but can tack in any direction with the greatest facility. Ancient navigation indeed consisted of little more than coasting along shore. But the invention of the compass enabled the mariner to leave the land, and launch into the wide ocean with perfect confidence that he would find his way to his desired port; and it' is to the date of this invention that the rise of navigation as a science must be referred.

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Some ascribe the invention of the mariner's compass to Flavio Gioia, of Amalfi in Campania, in the fourteenth century; while others affirm that it came from the east, and that it was earlier known in Europe. It is certain, however, that it was not in common use in navigation till about 1410, when, under the auspices of Henry duke of Visco, brother of the king of Portugal, considerable improvements were made in this art. In 11485 Roderic and Joseph physicians to king 2 John II. of Portugal, aided by one Martin of › Bohemia, a Portuguese native of the island of Fayal, a pupil of Regiomontanus calculated tables of the sun's declination for the use of sailors, and recommended the astrolabe for taking observations at sea. Columbus is said to have benefited by the instructions of Martin, and to have been himself useful in improving the knowledge of the Spaniards in the art. Charles V. of 1. Spain, afterwards founded a lecture at Seville, whose coject was to diffuse a knowledge of naviagation.

The variation of the compass could not long remain a secret. Columbus, as his son Ferdinand asserts, observed it on the 14th of September, 1492. Sebastian Cabot is said also to have observed it. It was found by Gonzales d'Oveida that there was no variation at the Azores; but it is now known that the variation alters in time, and at the Azores at the time we write it is about 20° westerly. The use of the cross staff began now to be introduced among seamen. This ancient instrument is described by John Werner of Nuremberg in his notes on the first book of Ptolemy's Geography, printed in 1514. He recommends it for measuring the angular distance between the moon and some stars for the purpose of determining the longitude. The recommendation of such an instrument for such a purpose is curious, as marking the state of practical science at that period, and the indefinite conception of the difficulties attending the longitude problem which its first proposer Werner entertained.

Much as had been done in navigation, it must still be admitted that at this period it was still in a rude state. Even the construction of charts was not at all understood, the only ones in use being plane charts, which in places distant from the equator must often have greatly misled those who confided in them. At length there were published two Spanish treatises on this art, in 1545, one by Peter de Medina, the other by Martin Cortes, which contained a system of navigation as it was then understood. These two authors appear to have valued themselves very highly on their performances, and they were no doubt of use in their time. Medina defended the plane chart, but Cortes pointed out very clearly its errors. He speculated too on the variation of the compass, and endeavoured to account for it, by supposing the needle to be influenced by a magnetic pole, different from that of the world; an hypothesis which has lately been revived, with the additional supposition that the magnetic pole moves from east to west round the pole, in, or nearly in, the same parallel of latitude. Whether this hypothesis may ultimately be found to be the true one or not, it certainly accounts both

for the variation itself and the changes which it has been observed to undergo. (See Barlow on Magnetic Attractions).

Medina's being the earliest book on the subject was soon translated into Italian, French, and Flemish, and long served as a guide to the mariners of those countries. But both with respect to science and practice it was vastly inferior to the work of Cortes who was long the favorite of our English seamen. It was translated into English in 1561, and about twenty years after Medina's was also translated, but it never attained any popularity.

A system of navigation at that time consisted of the following and similar subjects.-An account of the Ptolemaic hypothesis and the circles of the sphere; of the roundness of the earth, longitudes, latitudes, climates, &c.;-the eclipses of the sun and moon; a calendar; the method of finding the prime epact, moon's age, and tides; a description of the compass, and an account of its variation, for discovering which Cortes said an instrument might easily be contrived; tables of the sun's declination for four years, to find the latitude by his meridian altitude; directions for finding the latitude 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, to discover a ship's place, they made use of a small table which showed, upon an alteration of 1° of lat., how many leagues they were to run on each rhumb; and their departure from the meridian. This table in its form and use was precisely the same as the common and useful table of difference of latitudes and departures still given in works of navigation. Some instruments were described, particularly by Cortes, such as one to find the declination of the sun, with the age and place of the moon; certain dials, the astrolabe and cross staff; and a complex machine to discover both the hour and latitude at once.

As Werner had proposed to find the longitude by observations on the moon, so Gemma Frisius in 1530 advised the keeping of time for the same purpose by means of small clocks, or watches, then as he says newly invented. Thus the two leading practical methods of finding the longitude at sea which have only been perfected in our own days were clearly enough understood 300 years ago, though it has required all the science and mechanical skill that the enlightenment of modern times has called into action to bring these ancient schemes to any practical bearing. Frisius also contrived a new sort of crossstaff, and an instrument called the nautical quadrant which was much praised by William Cunningham in his Astronomical Class, printed in 1559.

In 1537 Peter Nunez, or Nonius, published a book in the Portuguese language, to explain a difficulty in navigation that had been proposed to him by the commander Don Martin Alphonso de Susa. He there exposes the errors of the plane chart, and gives the solution of some curious astronomical problems, amongst which is that of determining the latitude from two altitudes of the sun and the intermediate change of

azimuth. He observes that though the rhumbs are spiral lines, yet the direct course of a ship is always on the arch of a great circle, whence the angle with the meridian will continually change; all that the steersman can do, for keeping the ship on a rhumb line, being to correct those deviations when they appear sensible. But the ship will thus describe a sort of polygon without the rhumb line; and the computations for the latitude, &c., founded on the supposition that the ship has sailed on a rhumb line, will in consequence be in some measure erroneous. Nonius also invented the method of subdividing the divisions on circular instruments by means of a moveable concentric circle, on which the divisions have a given difference in value from those on the circle on which it moves. This admirable contrivance is still sometimes called a nonius from the name of its inventor, and on nautical instruments is still in universal use, though on large fixed instruments it has been superseded. The method of Nonius, however, was much improved by Dr. Halley.

In 1577 Mr. William Bourne published a treatise, in which, by considering the irregularities in the moon's motion, he shows the errors of the sailor in finding her age by the epact, and also in determining the hour from observing on what point of the compass the sun and moon appeared. He advises, in sailing towards the high latitudes, to keep the reckoning by the globe, as there the plane chart is most erroneous. He despairs of our ever being able to find the longitude, unless the variation of the compass should be occasioned by some such attractive power as Cortes had imagined; of which, however, he doubts: but, as he had shown how to find the variation at all times, he advises to keep an account of the observations, as useful for finding the place of the ship; which advice was prosecuted at large by Simon Stevin, in a treatise published at Leyden in 1599; the subject of which was the same year printed at London in English by Mr. Edward Wright, entitled the Haven-finding Art.

In this ancient tract also is described the way by which our sailors estimate the rate of a ship in her course, by the log. This was so named from the piece of wood or log that floats in the water, while 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 this 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, hough 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 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, though 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, and which he owned to have been then in common use among the sailors. He likewise gave some instruments of his own invention; but all of them are now laid aside. He constructed a sea-table to be used by such as sailed beyond 60° of lat. ; and at the end of the book is delivered a method of sailing on 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 art 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; he also made considerable improvements in 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 placed it differently. To this performance of Forman's is prefixed a discourse on the variation of the magnetical needle, by Mr. William Burrough, in which he shows how to determine the variation in many different ways. points out many errors in the practice of navigation at that time, and speaks in very severe terms concerning those who had written upon it.

He also

All this time the Spaniards had continued to publish treatises on the art. In 1585 an excellent compendium was published by Roderick Zamorano; which 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; however 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 doing 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 would make an angle with the meridians, expressing the rhumb leading from the one to the other. But though, in 1569, Mercator published a universal map constructed in this manner, it does not appear that he was acquainted with the principles on 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 supposes, but, according to the general opinion, without sufficient grounds, that this enlargement of the degrees of latitude was

known and mentioned by Ptolemy, ano 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: only with this precaution, that the degrees of longitude in each should bear some proportion to those of latitude; and this proportion is to be deduced from that which the magnitude of the respective parallels bears to a great circle of the sphere. He adds, that in particular maps, if this proportion be observed with regard to the middle parallel, the inconvenience will not be great, though the meridians should be straight parallels to each other. Here he is said 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, though 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 on 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 1592 its utility began to be perceived; and seven years after 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 of it 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; 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 barley corn. Some of his other improvements were, The table of latitudes for dividing the meridian computed to minutes;' whereas it had only been divided to every tenth minute. He also published a description of an instrument which he calls the sea-rings; and by which the variation of the compass, altitude of the sun, and time of the day, may be determined readily at once in any place, provided the latitude is known. He showed also how to correct the errors arising from the eccentricity of the eye in observing by the cross-staff. Ile made a total amendment in the tables of the declinations and places of the sun and stars from his own observations, made VOL. XV.

with a six foot quadrant, in the years 15941597. A sea-quadrant to take altitudes by a foreward or backward observation; and likewise with a contrivance for readily finding the latitude by the height of the pole-star, when not upon the meridian. To this edition was subjoined a translation of Zemorano'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 very different parts of the world, 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 that part relating to navigation the author having treated of sailing on a great circle, and shown how to draw the rhumbs on a globe mechanically, sets down Wright's two tables of latitude and rhumbs, in order to describe these lines more accurately, pretending even to have discovered an error in Wright's table. But all these objections were fully answered by the author himself, who showed that they arose from the gross way of calculating made use of by Stevin.

In 1624 the learned Wellebrord Snell, professor of 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 his discoveries from Snellius. But this supposition was long ago refuted; and Wright enjoys the honor of those discoveries, which is justly his due.

Mr. Wright having shown how to find the place of the ship on his chart, observed that the same might be performed more accurately by circulation; but considering, as he says, that the latitudes, and especially the courses at sea, could not be determined so precisely, he forebore setting down particular examples; as the mariner may be allowed to save himself this trouble, and only mark out upon his chart the ship's way after the manner then usually practised. How ever, in 1614, Mr. Raphe Handson, among h.nautical questions subjoined to a translation o. 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.

Though 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 proposes two ways of approximation to it 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; the other by the same mean between the secants, as an alternate, when Wright's book was not at hand; though this latter is farther from the truth than the first. 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, however, generally used by our sailors is commonly called the

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middle latitude; which, though it errs more than that by the arithmetical mean between the two cosines, is preferred, on account of its being less operose; 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 above 45°, and exceeds in lesser latitudes. However, none of these methods will differ much from the truth when the change of latitude is small.

About this time logarithms were invented by John Napier, baron of Merchiston in Scotland, and proved of the utmost service to the art of navigation. They were first applied by Mr. Edward Gunter in 1620. He constructed a table of artificial sines and tangents to every minute of the quadrant. These were applied according to Wright's table of meridional parts, and have been found extremely useful in other branches of the mathematics. He contrived, also, a most excellent ruler, commonly called Gunter's scale, on which were inscribed the logarithmic lines for numbers, and the sines and tangents of arches. He also greatly improved the sector for the same purposes. He showed also how to take a back observation by the cross-staff, whereby the error arising from the eccentricity of the eye is avoided. He described, likewise, another instrument of his own invention, called the cross-bow, for taking altitudes of the sun or stars, with some contrivances for more readily deducing the latitude from the observation. The discoveries concerning the logarithms were carried to France in 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 of the tables of artificial sines and tangents, as modelled according to Napier's last form, erroneously attributed by Wingate to Briggs.

Gunter's ruler was projected into a circular arch by the Rev. William Oughtred in 1633, and its uses fully shown in a pamphlet entitled The Circles of Proportion; where, in an appendix, several important points in navigation are ably discussed. 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 1625. He also gives two traverse tables, with their uses; the one to quarter points of the compass, 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 Variations of the Magnetical Needle, printed in 1635. This extraordinary phenomenon he found out by comparing the observations 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 F. Athanasius Kircher, in his treatise entitled Magnes, first printed at Rome in 1641, informs us, that he had been told 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 collect thence the sun's true altitude with correctness, Wright observes it to be necessary that the dip of the horizon below 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 the different methods for finding this; but complains that the most effectual was out of his power to execute; and therefore contented himself with a rude attempt, in some measure sufficient for his purpose; and the dimensions of the earth deduced by him corresponded so well with the usual divisions of the log-line, that as he wrote not an express treatise on navigation, but only for the correcting such errors as prevailed in general practice, the logline 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; whence, 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 measures 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 shows the reason why Snell had failed in his attempt; he points out also various uses of his discovery, particularly for correcting the gross errors hitherto committed in the divisions of the log-line. These necessary amendments, however, were little attended to by the sailors. whose obstinacy in adhering to established errors has been complained of by the best writers on navigation; but at length they found their way into practice, and no navigator of any skill now uses the old measure of forty-two feet to a knot. In that treatise also Mr. Norwood 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 shows also how to rectify the course by the variation of the compass being considered; 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, concerning the subject, was contracted as a manual for sailors, in a very small piece called his Epitome; a useful performance, which 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