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number of terms is 7, and the difference 3; the 7th term is, consequently, equal to the first with the addition of 6 times 3, or equal to 19. This property enables the scholar to obtain the amount of any term in the series, at any distance from the first, by a very simple proceeding. By this last property, we are enabled to show in what manner the sum of all the terms of an arithmetical progression can readily be found, for as the first and last terms make the same sum as the second and last but one, and as the third and last but two, &c., it thence follows, that the whole progression contains as many times the sum of the first and last as there are pairs of such terms. The number of pairs is, of course, equal to half the number of terms, and consequently, the sum of all the terms is equal to the sum of the first and last term, multiplied by half the number of terms.

Let us put the familiar instance of the man who picked up a hundred stones, one by one, placed in a straight line at one yard distance from each other, returning to a basket placed at a yard distance also from the first stone, one hundred times.

It is evident, that to pick up the first stone, and put it into the basket, the person must walk two yards, one in going, and one in returning; that for the second he must walk four yards, and so on, increasing by two as far as the hundredth, which will oblige him to walk two hundred yards, one hundred in going, and one hundred in returning.

It may easily be perceived also, that these numbers form an arithmetical progression, in which the number of terms is 100, the first term 2, and the last 200; by the rule already noticed, the number of yards he has walked is easily ascertained.

Yards.
2 distance walked for first stone.
200 distance walked for one hundredth stone.

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eighth column, seven being the number of counters, Then seek for the horizontal column of figures, whose distinguishing number is one more than the number of counters to be taken at one time, which in this instance is 3, the column, therefore, is numbered 4; by carrying the finger along these columns, until you come to their point of intersection at A, we find the number 35, the number of ways in which seven counters can be arranged by threes.

Two persons agree to choose, alternately, any number less than 11, and to add these numbers together until they shall make 100; by what means can one of them infallibly attain to that num

o - ber before the other ? - To effect this, subtract l l from 100, the num89 ber to be reached, as many times as possible;

ll this will give the remainders, 89, 78, 67, 56, 7S 45, 34, 23, 12, 1. By a knowledge of these ll numbers, the party who writes down the first 7: number is certain of reaching 100 first, if he 97 can count any one of these numbers. Let us 11 suppose, for example, that the first person who 56 knows the game, takes 1 for his first number; 11 it is evident that his adversary, as he must 15 count less than 11, can, at most, reach 11, by 11 adding 10 to it, the first will then take 1, which To will make 12; if the second takes 8, which ** will make 20, the first will take 3, which will 11 make 23; and, proceeding in this manner, he 23 will reach successively 34, 45, 56, 67, 78, 89; 1 1 when he attains the last number, it will be T2 impossible for the second player to prevent the 11 first reaching 100 before himself.

- It is evident that, if both parties understand

! the game, he who begins must inevitably win.

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NQ 358. SUPPLEMENT,

PRICE ONE PENNY,

JANUARY, 1838.

A BRIEF HISTORY OF

PART I. ON THE NAVIGATION OF THE ANCIENTS.

Rupe as their ships was navigation then,
No useful compass or meridian known
Coasting they kept the land within their ken,
And knew no North but when the pole-star shone.
‘DRYDEN.

EGYPTIAN POTTERY-FLOAT.

INTRoDUCTION.

The contemplative mind is supplied with matter for moral, and even sublime reflection, in viewing man in his more natural state, weak, savage, and untutored; clad in the skins of animals constituting his food, which are captured with toil and difficulty; inhabiting a rude hut, and confined within the narrow range of an island girt by the ocean, which to him is interminable; knowing no other land than that on which he dwells, and never daring to lose sight of that land, in the frail bark in which he moves along his native coast. Then if, by a rapid transition, we behold man civilized and highly cultivated as he now is, borne along byThe heaven-conducted prow Of Navigation bold, that fearless braves The burning line, or dares the wintry pole,

we feel the force of the oft-repeated truism, that man is a progressive being. Thus, it will furnish instruction to the reader, if we endeavour to fill up the long interval between these two conditions, in which we find man acting his part as a member of the human family, by tracing the progress of Navigation from the rude raft, or ill-constructed canoe, through the various stages of addition and improvement, until we reach that triumphant monument of human skill,— a ship of the line". An improvement, so vast, is of course only one of the results of the advancement of nations in the scale of civilization; and this advancement is accurately tested by their collateral progress in literature, art, and science. As the first ministers to the reflecting tastes of its members, so the two latter supply their actual wants and increasing desires; and there have been found, at all times, persons ready to devote their energies to carry out those subjects, which a few fortunate and gifted individuals have invented, or improved. But the great bulk of mankind does not the less further the progress of civilization, though all do not invent nor improve: they serve as the power for carrying on the work, which is contrived and

* See Saturday Magazine, Vol. III., p. 36. Vol. XII

NAVIGATION.

begun by that limited number of great minds, on which Nature has poured down her choicer gifts. While thus laborious crowds Ply the tough oar, Philosophy directs The ruling helm. In the present and succeeding papers it is our purpose, therefore, to trace the progress of Navigation from its earliest principles and practice, to its present comparatively perfect condition; and in doing so, it will be found convenient to adopt the following arrangement, and treat— 1st. Of the Navigation of the Ancients. 2nd. Of the Navigation of the Middle Ages. 3rd. Of Modern Navigation. The first division will comprehend, as to time, all the period between the creation of the world and the downfall

I of Rome; that is, a space of about 4500 years.

oN THE RUDIMENTs of NAVIGATION, To THE FoRMATION OF THE BOAT.

- | WHEN speaking of Navigation in the earliest stages of the

world, the idea of the ark, used by Noah and his family, will readily enter into the minds of our readers. But we cannot consider the formation and use of the ark, in the seventeenth century of the world, as a commencement or link in the chain of nautical invention. The entire direction and means for accomplishing this stupendous work, were afforded by God, to effect a saving purpose in the midst of the miraculous destruction of the human race; when the power and skill of man would have been, in those times at least, impotent to withstand or elude the watery havoc of Nature. In addition to this, we must notice the absence from the ark of any means, or of any necessity, for its occupants navigating it from one place to another; which is essentially necessary to make it belong to our present subject. No intention of this sort is alluded to; the ark being merely a vast shelter rendered capable of floating on the water. For these two reasons, therefore, we conclude against assigning to this event in the sacred history, a place in this treatise. We come, then, to regard the ocean as a part of the arrangement of the Almighty power for His own wise purposes; as among the creatures, which have been committed to the use of man; beneficial in various ways, which it is not our province to consider here, but only as it serves the purpose of a great high-way for the nations of the world; pre-eminent among which, and may it ever be, is our own country. Our subject takes not in its view a supernatural state of the floods of the ocean, but that, wherein there is “set a bound that they may not pass over; that they turn not again to cover the earth".” We contemn, therefore, the quailing lament of the heathen poet, Horace, who thus delivers himself:— Jove has the realms of earth in vain Divided by the unhabitable main, If ships profane, with fearless pride, Bound o'er the inviolable tide. We see how ill-timed is this awe of the sea, when we remember as readers of the Inspired Volume, that it is written, “They that go down to the sea in ships, that do business in great waters; These see the works of the Lord, and his wonders in the deep t :” and, when we call to mind, that, by means of ships, this Inspired Volume was brought to us, and has been carried out again to all parts of the habitable earth. In the youthful condition of the world, and when all was new and untried, the innate love of exploring that which had not yet been seen, gradually extended the locality of the human race. Brooks, and such like streams, were soon forded, when new pastures, the impulse of hunting, and the

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desire of novelty, prompted a change; and a mode of crossing the deeper stréams was soon suggested to the observation of the savage, whose condition seems, by the testimony of Homel, to have been at its lowest pitch, when in ignorance of any means whatever, for crossing the water, which, though seeming, at first sight, to bar intercourse, does, in reality, promote it. The buoyancy of wood in, the water is the germ of all his subsequent proceedings. Accident shows him that wood invariably floats; and on the fallen trunk of a tree he ventures, beyond his own depth, away from the land. The trunk of a tree, hollowed out, for a more convenient position of the body, (an idea derived, we are,told, from a split reed, seen floating on the water.) forms the canoe, which is usually found among the most uncivilized of the human species. From this rude beginning to the noble vessels of our day, how great the interval of time, how slow the pace of improvement, and how absolutely necessary, for any permanent and comprehensive effect, the application of elements, which seemed at one time out of the reach and cognizance of man.

ANCIENT Picture of an EGYPTIAN ship.

We seem to learn from contemplating the first materials of antiquity, that man derived, from the natural objects which surrounded him, a notion of the forms and fashions of things which conduce to his benefit. The pitcher-flower, (Nepenthes distillatoria,) * presented to him a graceful and convenient form for his cups and vases; the leaf-covered grottoes infused into him the idea of arranging his architectural principles on the patterns of nature; and the movements of the finny tribe developed the secret of directing his path on the water with nearly the same ease as on land; the trunk of the tree hollowed out, as a receptacle for the navigator, accords with the body of the fish; the forepart of this trunk, when sharpened off to an edge, in order to cleave the waters the more easily, is assimilated to the head of the animal, while the forcible motion of its tail shadows out the rudder, which, by its lateral movements, serves the purpose of steering the boat, as the tail of the animal directs the motion of the fish. This step in Navigation is completed by adopting a method for propelling the vessel onwards, which method is furnished by seeing the use of the fins of the fish in forming a passage through the waters. When oars, sculls, or paddles came into operation at the instance of Atlas, an ancient African monarch, the boat was essentially complete.

The foregoing illustration condenses into one view the various traditions, which have been handed down respecting the first decided step in Navigation; for it matters little from what other quarter-the swan, or any other aquatic fowl, the suggestion arises to the human mind, so it agree with the beauty of nature in its physical utility.

The raft, or floor of wood, formed by the lashing together of two or more planks, seems to have been an early, as it is one of the readiest modes for passing and conveying rough goods along upon the water. In time of shipwreck, or for any temporary purpose of transport, its facility of make recommends it, when other modes fail. Thus Hannibal used rafts for transporting his horses and elephants across the Rhone. The Egyptians, in very early times, used the raft on the Nile. An improved sort of raft was found in use among the Peruvians, tapered at the prow, in order to pass through the water more easily; the planks were fastened together with leather thongs, by the unnoticed decay of which the bark would oftentimes fall to pieces,

* See Saturday Magazine, Wol. II., p. 159,

and its mariner and goods, disappear under the waves. The celebrated timber-raft which floats down the Rhine to Dort, in the Netherlands, from the forests of Germany, is oftentimes 1000 feet long, and 80 or 90 feet wide, consisting of trees fastened together with iron spikes and crosstimber—a floating island with a village at the top, and o: nearly 500 labourers to manage it. When the raft is broken up and sold, it sometimes fetches a sum of £30,000. The same practice is used on the coast of Norway, thereby saving the trouble and expense of landcarriage. On a board, or slight raft, the surf-swimmers of the Sandwich Islands, in the Pacific Ocean, pursue their pastime. They swim out to sea on this raft through a violent surf, plunging under every wave, and rising beyond it. In returning they are carried swiftly on the top of a large wave towards #. shore, when they steer among the rocks, taking care not to lose their planks, for such a loss is deemed to be very disgraceful. Somewhat superior in contrivance and effect is the construction of the pottery-floats of Egypt. Jars and various earthen vessels are made in great quantities in Upper Egypt; a large number of them are fastened together with cords and twigs into a triangular shape, having the mouths of the vessels upwards; É. are then covered with bulrushes, and, being empty, are rowed as need may be, and steered down the §. to Cairo, where the raft is taken apart and the articles are sold. Some remarks on these earthenware boats may be found in Vol. IX., p. 164, of this work. It appears that, in very ancient times, a vessel was in use on the Nile, made from the planks of acanthus wood, so laid together as to lap over in the manner of tiling, and fastened with wooden pegs, the seams being tightened with leaves. It was also covered over with flags of the papyrus, and properly cemented, to keep out the water. In process of time an acanthus mast was added, to which was apended a sail, formed of papyrus leaves. This was the case in the infancy of Moses, and to such the prophet Isaiah alludes in the second verse of the 18th chapter of his book. In ascending the Nile the vessel was towed along; in its descent, it was steadied against the effects of the N.E. winds by a hurdle of wood let i. from the prow. By the term canoe is generally meant a single tree hollowed out boat-like, propelled onwards in the direction of the view of the Indian, who urges its course with paddles, which are worked perpendicularly in the water. The Macedonians, who saw the natives at the mouth of the Indus paddling in their canoes, thought they were digging the water with spades. Canoes are of various lengths, from 10 to 50 feet. But the make and build of all the early naval structures depended simply upon the use they were put to, and the means at hand for their formation. We have from Herodotus the description of a vessel for conveying goods down the Euphrates to Babylon. A frame-work of willow was covered with skins, forming, when complete, a sort of large tub, which was managed by two men with long poles, without any regard to stem or stern. They were of various sizes, and carried an ass besides the merchandize; the animal was employed in conveying the vessel home by land when taken to pieces, as the downward force of the riyer's current prevented them from sailing up the stream. Major Rennel describes this vessel as being still in use in the lower parts of the river, under the name of Kufah, or round vessel. Very similar to this is the coracle, consisting of a large basket, over which was stretched a horse's hide. This was found among the ancient Britons when the Romans invaded the island, and is still seen in use on the Severn, and among the people of South Wales. The American Indians use wooden-ribbed vessels, covered with skins, which vessels, owing to their lightness, can be carried overland, when it is necessary to avoid the rapids and waterfalls, which are numerous in the country. The Greenlander's canoe is covered in at the top with a skin, so as to shut up the lower part of his body when he is sitting in the vessel; the water may thus be kept out in the roughest seas. The double canoe of the Society Islands is an ingenious contrivance for affording a safe platform, whereon the warriors may wage battle. Two canoes being placed alongside of each other, at a certain distance apart, planks are firmly fixed across, which make a stage safe from capsizing. The whole is so contrived, that the rowers may work *th this floor, while the soldiers engage in battle a DOWe.

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The proas of the Ladrone Islands present another form of the canoe, the peculiar quality of which, we are told, is swiftness to the extent of 20 miles an hour; this results from their construction. The lee side, or that which is away from the wind, is straight, while the other is bowed out as usual. This causes both ends of the vessel to be narrow, and thereby exceedingly sharp, so that it pierces through the water the more readily, and needs no turning round when the voyager wishes to come back. In a rough 'sea they have a contrivance on the windward side of the proa called an out-rigger, (see Vol. III., p. 181, of this work,) to preserve a steadw balance, and prevent its upsetting on the straight or lee side. The rapid motions of the swordfish would seem to have suggested the idea of forming these flying proas. The alder and poplar were used by the ancients for shipbuilding, as being hard and light woods, but oak and fir were chiefly sought after. The Greeks used chestnut and cedar, the latter of which they considered to be very durable. Cypress was valued for its not leaking, and elm was chiefly used for the parts of the vessel under water. Sometimes, in these days of nautical simplicity, a fleet of ships was formed within a month of the time when the timber spread out its leafy arms in the forest, haste, not skill, being used in their formation. When, however, time allowed, ship-timber was not always hastily felled, nor carelessly employed. The age of the moon, and the quarter from which the wind blew, were superstitiously heeded. Tacitus describes the Swedish boats, seen by the navigators of his time, as being like the Northern yawls of the present day, which are peaked at both ends. These boats were, in all probability, used for piracy, which in a barbarous condition of society, is the mode of gradually establishing commerce. A galley, the prow of which resembled the weapon of the sword-fish, was used by the ancient Greeks, as also in more modern times, for cruising against the pirates of the Mediterranean, whose vessels were of a similar sort. The materials with which the planks or other parts of these different vessels were put or fastened together, were various. Sometimes wooden pins were employed, and at other times they were connected together with thongs, made from the skins and sinews of animals; iron seldom, or never, coming within the reach of these primitive naval architects. The Icelanders and Esquimaux Indians were found to make their boats of long poles placed crosswise, tied together with whale-sinews, and covered with the skins of sea-dogs, sewed with sinews instead of thread. To stop leakage the ancients used lime and pounded shells, which being observed to waste away, pitch, resin, and wax were employed. Sometimes the crevices were first stopped up with flax, and then leather was employed for sheathing. We find sheet-lead used for the same purpose, and copper nails. For their tools they used flints and shells for cutting, while several of the bones of fishes served them to pierce, to saw, and to plane with. From these nature-suggested implements is derived, with improvements according to circumstances, a great portion of the tools with which the mechanic of modern days so skilfully performs his work.

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We arrive now at the general term of boat, by which we understand a combination of every peculiar excellence afforded by each sort of water-conveyance mentioned before, The method of making and finishing off a boat is to be sought for in the science of Naval Architecture; but we may merely mention that, from the lightest and most substantial material, strongly compacted into the form which will attain most speed, and admit of most room and convenience for the rowers, whether they be one, two, or more, is produced the most finished specimen of the first and original class of naval structures.

THE SALL,

About 1230 years before the Christian era, as far as we are able to discern actual fact through the hazy and fabulous record of profane antiquity, the adoption of sails promoted the nautical art beyond former conception, and served as an era in history by the simultaneous wonder and admiration with which the discovery, and the authors of it, were hailed by their fellow-men, whose knowledge and comfort were, in process of time, so much promoted thereby. The statements of the early writers of the world seem to concur in describing Daedalus of Athens, the most skilful mechanician of his day, as the individual who first pressed the wind into the naval service of man. His genius, sharpened by fear, when seeking to escape the vengeance of Minos, king of Crete, put up in his own boat, and in that of his son, a cloth, or cloths, to catch the passing gale, thus using its force to hasten on their frail barks. The singers and bards of the time, whose avocation was with the multitude, and whose recitations pleased in proportion to the quantity of the marvellous they contained, being themselves, from the very nature of their pursuits, easily led off from matural principles to the sublime and mysterious, chanted before those, whom rumour had already prepossessed, the flight of Daedalus and the unfortunate death of Icarus, his son. Daedalus, say they, had carefully fitted to his own body, and to that of his son, wings, constructed with feathers and wax. Thus equipped, they took their flight through the air over that part of the sea which lay between Crete and Italy. Icarus, with the rashness and unsteadiness of youth, sought a higher flight than his sire, and getting, in consequence, too near the neighbourhood of the sun, the waxen cement of his wings was loosened, which, thus becoming powerless, he dropped into and was drowned, in that part of the AEgean Sea, or Archipelago, which bore for ages after the appellation of the Icarian Sea. The point in this relation which we are chiefly interested in clearing up, is the youth's mismanagement of his wings. The fact of the passage of one of these persons from Crete to Italy, and the drowning of the other, is undisputed; also that they went over the water and not over the land. As we know that it is incompatible with the human frame to be buoyed up by wings in the air, and unnatural that greater heat should be experienced in rising above the surface of the earth, balloons being at that time out of the question, and being aware of the stretch and license which the rude and unreflective imagination can take, we see easily that Daedalus and Icarus, by cutting their way through the waters with sails swelled out by the wind, seemed to have flown over it with wings; and this the more veritably to those who regarded only, or chiefly, the novelty of the proceeding, and received their accounts from the echo of rumour. The vessel of Icarus then, who seems not to have had his sail sufficiently under control, was capsized, and thus, as truly said in the fable, “he dropped into the sea, and was drowned."

Many other voyages, under circumstances so novel for the times, have received the utmost embellishment of the poetic art. When we consider the surprise of ignorant people, at beholding floating castles with expanded wings, making their unassisted way over the sea, we discern easily whence arose the fiction of the flight of Perseus to the Gorgons, who, we are told by Aristophanes, was carried thither in a ship. The story of Triptolemus, who was feigned to ride about the world on a winged dragon, doing good to the human race, is easily understood, when we remember that he was employed by his countrymen to procure in a ship corn from foreign shores, for the supply of their necessities. The winged horse, Pegasus, was a ship of that name, fabled to have been the offspring of Neptune, the god of the sea. In a word, we thus, account for the stories of griffins, or of ships transformed into fishes and birds, so frequently met with in the * poets.

58–2

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It is probable that some natural object, such as the wing of a bird, suggested the idea of the sail. By some it has been referred to the nautilus, or sailor-fish, which is seen in the Mediterranean Sea, the Indian Ocean, and the Polynesian waters of the Pacific. It is oftentimes observed in calm weather floating on the surface of the water, using its side-fins as oars, its hinder one for steering, while its dorsal-fin, which is formed from a peculiar membrane, serves as a sail. When wishing to go down all is drawn in, with a sufficient quantity of water to make it specifically heavier than its own bulk of water, it then sinks in an instant: when wishing to rise again it ejects the water. (See Vol. VI.,

. 149.) p The material of which the sail was usually composed was linen, or it depended upon the particular produce of the country which despatched a sailing vessel from its shores. A sail was, perhaps, at first most readily formed by the mariner's suspending his clothes upon a pole. In some countries they used leather, or skins of animals, for sails, as Julius Caesar observed the Gaulish Venetians to do. Thus Hercules is said to have sailed with the back of a lion, because he used no other sail than his garment, which was the skin of a lion. In other countries they used sails made from twisted flax or hemp, as the native West Indians are found, at the present time, to use in making a sail, a sort of silky grass, plaited to the length and breadth required.

We do not find more than one sail used in the earliest ages, or more than one mast; their vessels had not even a deck. The sails were commonly white, which colour was esteemed more lucky, though sometimes they were of other colours. The vessels were painted red and sometimes blue,

which latter colour was intended to correspond with th, cerulean appearance of the sea, in climes where the blue sky overhangs the watery expanse, undimmed by clouds and vapour. When we read of the black ships of Homer, we must remember that they took this appearance from the pitch, with which they were externally covered to exclude the water. Sometimes other materials were used to produce the same effect, and hence a diversity in the colours of the ships. Such was the sort of vessels which conveyed the allied army to the plains of Troy. The size and number of the sails increased with the magnitude of the vessels and the length of their voyages, all which depended upon the importance of the nation, which, in the progress of time, by the searching spirit of commerce, or the desire of conquest, advanced the maritime arts. The form and disposition of the sails in the vessel have been found to be different in different countries. We are told that, in ancient Egypt, the sail was suspended on two upright poles, so that it could be used only before the wind, as is the case with many of the South Sea Islanders, whose sails are made of matting. The sails of the New Zealanders and Polynesians are found to be of a triangular form, the former having the base upwards and the latter downwards; and, in a general view of the case, the condition of the savage state in our times will be found very much upon a par with that of early antiquity, at least as far as art and science are concerned, which consideration must be kept in view, if any question should arise in the reader's mind, as to why we seem to treat of the naval pursuits of modern barbarians in conjunction with those of the people who lived before the Christian era

GALLEY, PROM A PAINTING AT HERCULANEUM.

THE RUDDER, ANCHOR, CABLEs, SBIP's NAME, &c.

Brfore proceeding to consider the more perfect condition of ancient Navigation with reference to its effects, we shall present a brief view of some of its appendages in detail. The rudder serves to regulate the course of the ship, as the tail of the fish guides the motions of its body. The principle is the same in both cases. When the rudder is in a right line with the central direction of the vessel, it is merely an enlargement of the keel. When drawn towards either side, it has to make way against a force of water, the resistance of which is in proportion to the angle formed by the rudder and the keel, and the rate of propulsion at which the vessel is urged along, or to the force of the surrounding current; , so that the stern or hinder part of the vessei is forced aside out of its place by the resisting water, and the prow, or forepart, consequently, assumes an opposite direction, according with the movement of the rudder. It seems that the original rudder was nothing more than one of the oars or paddles held sternwise by the person in the boat, which natural observation and practice taught him to steer the vessel by. This practice is even now far from obsolete. The ancient Greeks, we are told by Homer, used only one rudder; but as their vessels enlarged in size, they used two, one at the prow and the other at the stern: con

nected therewith by fastenings, termed rudder-bands, allu ded to in Acts xxvii. 40; so that these were called doublestern ships, and could be o either way, without turning. Tacitus relates that the Germans used vessels of this sort. The use of the rudder-bands was to fasten the helm up out of the water, when the ship was left to drive, or take its own course; but, if they were loosened, as St. Luke relates, the rudder dipped into the water for use. We read of four rudders being employed, but nothing definite seems to be known of ships of this sort; nor of ships, which are mentioned as having two prows and two sterns. It is a general feature in the maritime affairs of ancient nations, that their vessels in general could be conveniently carried overland, when so doing would tend to lessen distance; and for this purpose they were oftentimes so constructed, that they could be easily taken to pieces; as was often done, when they wished to pass over an isthmus. They were also drawn up out of the water, even for a single night. Hence, it is clear, that they were for a long time, at best, but sailing-boats; and that the anchor was not needed. The need or convenience of this grew with the size of the vessel. The Tuscans are said to have invented the anchor, while some ascribe it to Midas, whose anchor was long preserved in one of the temples of Jupiter. But, whatever means may have been originated by any party to

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