or NAVAL ARCHITECTURE, is the art of constructing a ship so as to answer a particular purpose either of war or merchandise.

To whom the world is indebted for the invention of ships, is, like all other things of equal antiquity, uncertain.

A very small portion of art or contrivance was seen in the first ships: they were neither strong nor durable; but consisted only of a few planks laid together, without beauty or ornament, and just so compacted as to keep out the water. In some places they were only the hulks or stocks of trees hollowed, and then consisted only of one piece of timber. Nor was wood alone applied to this use; but any other buoyant materials, as the Egyptian reed papyrus; or leather, of which the primitive ships were frequently composed; the bottom and sides being extended on a frame of thin battens or scantlings, of flexible wood, or begirt with wickerwork, such as we have frequently beheld amongst the American savages. In this manner they were often navigated upon the rivers of Ethiopia, Egypt, and Sabaean Arabia, even in latter times. But in the first of them, we find no mention of any thing but leather or hides sewed together. In a vessel of this kind, Dardanus secured his retreat to the country afterwards called Troas, when he was compelled by a terrible deluge to forsake his former habitation of Samothrace. According to Virgil, Charon's infernal boat was of the same composition.

But as the other arts extended their influence, naval architecture likewise began to emerge from the gloom of ignorance and barbarism; and as the ships of those ages were increased in bulk, and better proportioned for commerce, the appearance of the floating citadels of unusual form, full of living men, flying with seemingly expanded wings over the surface of the untravelled ocean, struck the ignorant people with terror and astonishment: and hence, as we are told by Aristophanes, arose the fable of Perseus flying to the Gorgons, who was actually carried thither in a ship! Hence, in all probability, the famous story of Triptolemus riding on a winged dragon is deduced, only because he failed from Athens, in the time of great dearth, to a more plentiful country, to supply the necessities of his people. The fiction of the flying horse Pegasus may be joined with those, who, as several mythologists report, was nothing but a ship with sails, and thence said to be the offspring of Neptune the sovereign of the sea; nor does there appear any other foundation for the stories of griffins, or of ships transformed into birds and fishes, which we so often meet with in the ancient poets. So acceptable to the first ages of the world were inventions of this nature, that whoever made any improvements in navigation or naval architecture, building new ships better fitted for strength or swiftness than those used before, or rendered the old more commodious by additional contrivances, or discovered countries unknown to former travellers, were thought worthy of the greatest honours, and often associated into the number of their deified heroes. Hence we have in astronomy the signs of Aries and Taurus, which were no other than two ships; the former transported Phryxus from Greece to Colchos, and the latter Europa from Phenicia to Crete. Argos, Pegasus, and Perseus, were likewise new ships of a different sort from the former, which being greatly admired by the barbarous and uninstructed people of those times, were translated amongst the stars, in commemoration of their inventors, and metamorphosed into constellations by the poets of their own and of succeeding ages.

The chief parts, of which ships anciently consisted, were three, viz. the belly, the prow, and the stern: these were again composed of other smaller parts, which shall be briefly described in their order. In the description, we chiefly follow Scheffer, who has so copiously treated this subject, and with such industry and learning collected whatever is necessary to illustrate it, that very little room is left for enlargement by those who incline to pursue this investigation.

1. In the belly, or middle part of the ship, there was τροχις, carina, or the "keel," which was composed of wood: it was placed at the bottom of the ship, being designed to cut and glide through the waves, and therefore was not broad, but narrow and sharp; whence it may be perceived that not all ships, but only the μεγαλις, which ships of war were called, whose bellies were straight, and of a small circumference, were provided with keels, the rest having usually flat bottoms. Around the outside of the keel were fixed pieces of wood, to prevent it from being damaged when the ship was first launched into the water, or afterwards struck on any rocks; these were called κιλινματα, in Latin cunei.

Next to the keel was φακις, the "pump well, or well-room," within which was contained the αντλια, or "pump," through which water was conveyed out of the ship.

After this, there was δευτερον τροχις, or the "second keel," somewhat resembling what is now called kelson; it was placed beneath the pump, and called λεπτος, γαλαξις, κλινιματα; by some it is falsely supposed to be the same with φακις.

Above the pump was an hollow place, called by Herodotus καιλη των ναων, by Pollux, κυριας and γαλαξις, because large and capacious, after the form of a belly; by the Latins testudo. This was formed by crooked ribs, with which it was surrounded, which were pieces of wood rising from the keel upwards, and called by Hesychius and by others στεγαλίας, the belly of the ship being contained within them; in Latin coffe; and in English, timbers. Upon these were placed certain planks, which Aristophanes calls ἐπιστροφές, or ἐπιστροφαί.

The πλευρα, latera, or "fides" of the ship, encompassed all the former parts on both hands; these were composed of large rafters extended from prow to stern, and called ξυλίνης, and ξυλίνα, because by them the whole fabric was begirt or surrounded.

In these fides the rowers had their places, called τάξις and ἐπάλια, in Latin furi and tranflira, placed above one another; the lowest was called θαλάσσιος, and those that laboured therein ἐπαλασσιοι; the middle, ξυλίνη, and the men ξυλίναι; the uppermost θαλάσσιοι, whence the rowers were termed θαλάσσιοι. In these apartments were spaces through which the rowers put their oars: these were sometimes one continued vacuity from one end to the other, called τραχύς, but more usually distinct holes, each of which was designed for a single oar; these were styled τραχύς, τραχύτατα, as also οφθαλμοί, because not unlike the eyes of living creatures. All of them were by a more general name termed ημισκήνια, from containing the oars; but εμπρός seems to have been another thing, signifying the spaces between the banks of oars on each side, where the passengers appear to have been placed. On the top of all there was a passage or place to walk, called παράβας, and παραβάσιος, as joining to the θαλάσσιοι, or uppermost bank of oars.

2. Προς, the "prow," or "fore-deck," whence it is sometimes called μετωπος, and commonly distinguished by other metaphorical titles taken from human faces. In some ships there is mention of two prows, as also two sterns; such as Danaus's ship adorned by Minerva when he fled from Egypt. It was usual to beautify the prow with gold and various sorts of paint and colours; in the primitive times red was most in use; whence Homer's ships were generally dignified with the titles of μικτοπαρας, and φαινοπαρας, or "red faced;" the blue, likewise, or sky-colour, was frequently made use of, as bearing a strict resemblance to the colour of the sea; whence we find ships called by Homer κυανοπαρας, by Aristophanes κυανοπαρας. Several other colours were also made use of; nor were they barely varnished over with them, but very often annealed by wax melted in the fire, so that neither the sun, winds, nor water, were able to deface them. The art of doing this was called from the wax παραγραφα, from the fire σκαυσικα, which is described by Vitruvius, and mentioned in Ovid.

Pieta coloribus uscis Caruleam matrem concavae puppis habet.

The painted ship with melted wax anneal'd Had Tethys for its deity

In these colours the various forms of gods, animals, plants, &c. were usually drawn, which were likewise often added as ornaments to other parts of the ships, as plainly appears from the ancient monuments presented to the world by Bayfius.

The fides of the prow were termed ξυλίνη, or "wings," and ξυλίναι, according to Scheffer, or rather στεγαλίας; for since the prow is commonly compared to a human face, it will naturally follow that the fides should be called cheeks. These are now called bows by our mariners.

3. Περιστημη, "the hind-deck or poop," sometimes called οὐρα, the "tail," because the hindmost part of the ship; it was of a figure more inclining to round than the prow, the extremity of which was sharp, that it might cut the waters; it was also built higher than the prow, and was the place where the pilot sat to steer; the outer-bending part of it was called περιστημη, answering to our term quarter.

They had various ornaments of sculpture on the prow; as helmets, animals, triumphal wreaths, &c.—The stern was more particularly adorned with wings, shields, &c. Sometimes a little mast was erected wherever on to hang ribbands of divers colours, which served instead of a flag to distinguish the ship; and a weather-cock, to signify the part from whence the wind blew.

On the extremity of the prow was placed a round piece of wood, called the πλευρα, from its bending; and sometimes οφθαλμος, the "eye" of the ship, because fixed in the fore-deck; on this was inscribed the name of the ship, which was usually taken from the figure painted on the flag. Hence comes the frequent mention of ships called Pegasi, Scyllae, bulls, rams, tigers, &c. which the poets took the liberty to represent as living creatures that transported their riders from one country to another.

The whole fabric being completed, it was fortified with pitch, and sometimes a mixture of rosin, to secure the wood from the waters; whence it comes that Homer's ships are everywhere mentioned with the epithet of μικταλιας, or "black." Pitch was first used by the inhabitants of Phæcia, since called Corsica; sometimes wax was employed for the same purpose; whence Ovid,

Cerulea ceratas accipit unda rates.

The azure waves receive the waxed ships.

After all, the ship being bedecked with garlands and flowers, the mariners also adorned with crowns, she was launched into the sea with loud acclamations and other expressions of joy; and being purified by a priest with a lighted torch, an egg and brimstone, or after some other manner, was consecrated to the god whose image she bore.

The ships of war of the ancients were distinguished from other kinds of vessels by various turrets and accessions of building, some to defend their own soldiers, and others to annoy the enemy; and from one another, in latter ages, by several degrees or ranks of oars, the most usual number of which was four or five, which appear not to have been arranged, as some imagine, on the same level in different parts of the ship; nor yet, as others have supposed, directly above one another's heads; but their seats being placed one behind another, ascended, gradually, like flares. Ptolemy Philopater, urged by a vain-glorious desire of exceeding all the world besides in naval architecture, is said to have farther enlarged the number of banks to 40; and the ship being otherwise in equal proportion, this raised her to such an enormous bulk, that she appeared at a distance like a floating mountain or island; and, upon a nearer view, like a prodigious cattle on the ocean. She was 280 cubits long, 38 broad, and 48 high (each cubit being 1 English foot 5½ inches), and carried 400 rowers, 400 sailors, and 3000 soldiers. Another which the fame fame prince made to fail on the Nile, we are told, was half a stadium long. Yet these were nothing in comparison of Hiero's ship, built under the direction of Archimedes; on the structure of which Mochion wrote a whole volume. There was wood enough employed in it to make 50 galleys; it had all the variety of apartments of a palace; such as banqueting-rooms, galleries, gardens, fish-ponds, stables, mills, baths, and a temple to Venus. The floors of the middle apartment were all inlaid, and represented in various colours the stories of Homer's Iliad. The ceilings, windows, and all other parts, were finished with wonderful art, and embellished with all kinds of ornaments. In the uppermost apartment there was a spacious gymnasium, or place for exercise, and water was conveyed to the garden by pipes, some of hardened clay, and others of lead. The floors of the temple of Venus were inlaid with agates and other precious stones; the inside lined with cypres wood; the windows adorned with ivory paintings and small statues. There was likewise a library. This vessel was adorned on all sides with fine paintings. It had 20 benches of oars, and was encompassed with an iron rampart, eight towers, with walls and bulwarks, furnished with machines of war, particularly one which threw a stone of 300 pounds, or a dart 12 cubits long, the space of half a mile, with many other particulars related by Athenaeus. Caligula likewise built a vessel adorned with jewels in the poop, with sails of many colours, and furnished with large porticoes, bathings, and banquetting-rooms, besides rows of vines, and fruit-trees of various kinds. But these, and all such monstrous fabrics, served only for show and ostentation, being rendered by their vast bulk unwieldy and unfit for service. Athenaeus informs us, the common names they were known by, were Cyclades, or Aetna, i.e. "islands, or mountains," to which they seemed nearly equal in bigness; consisting, as some report, of as many materials as would have composed 50 triremes, or ships of three banks.

The vessels employed by the northern nations appear to have been still more imperfect than those of the Romans; for a law was enacted in the reign of the Emperor Honorius, 24th September, A.D. 418, inflicting capital punishment on any who should instruct the barbarians in the art of ship-building; a proof at once of the great estimation in which this science was then held, and of the ignorance of the barbarians with regard to it.

The fleet of Richard I. of England, when he weighed anchor for the holy war from Messina, in Sicily, where he had passed the winter, A.D. 1190-1, is said to have consisted of 150 great ships and 53 galleys, besides barks, tartans, &c. What kinds of ships these were is not mentioned. To the crusades, however pernicious in other respects, this science seems to owe some improvements; and to this particular one we are indebted for Richard's marine code, commonly called the Laws of Oleron, from the name of a small island on the coast of France, where he composed them, and which most of the nations in Europe have made the basis of their maritime regulations. Those ships, if they merited the name of ships, were probably very small, as we find that for long after as the time of Edward I. anno 1304, 40 men were deemed sufficient to man the best and largest vessels in England; and that Edward the Third, anno 1335, ordained the mayor and sheriffs' of London to "take up all ships in their port, and all other ports in the kingdom, of the burden of 40 tons and upwards, and to furnish the same with armed men and other necessaries of war, against the Scots his enemies, confederated with certain persons of foreign nations." Edward the Third's fleet before Calais, anno 1347, consisted of 738 English ships, carrying 14,956 mariners, being on an average but 20 men to each ship; 15 ships and 459 mariners, from Bayonne in Guienne, being 30 men to each ship; 7 ships and 184 men from Spain, which is 26 men to each ship; one from Ireland, carrying 25 men; 14 from Flanders, with 133 men, being scarcely 10 men to each ship; and one from Guelderland, with 24 mariners. Fifteen of these were called the king's own ships, manned with 419 mariners, being somewhat under 17 to each ship.

Historians represent the vessels of Venice and Genoa as the largest and the best about this time, but they were soon exceeded in size by the Spanish vessels called carricks, some of which carried cannon; and these again were exceeded by the vessels built by the northern people, particularly those belonging to the Hanse-towns.—In the 14th century, the Hanseatics were the sovereigns of the northern seas, as well without as within the Baltic; and their ships were so large, that foreign princes often hired them in their wars. According to Hakluyt, an English ship from Newcastle, of 200 tons burden, was seized in the Baltic by those of Wismar and Rottock, anno 1394; and another English vessel of the Federa, same burden was violently seized in the port of Lisbon, anno 1412.

Soon after ships of a much larger size were constructed. It is mentioned that a very large ship was built, anno 1449, by John Taverner of Hull; and in the year 1455, King Henry IV. at the request of Charles king of Sweden, granted a licence for a Swedish ship of the burden of a thousand tons or under, laden with merchandise, and having 120 persons on board, to come to the ports of England, there to dispose of their lading, and to relade back with English merchandise, paying the usual customs. The inscription on the ton of William Canning, an eminent merchant, who had been five times mayor of Bristol, in Ratcliff-church at Bristol, anno 1474, mentions his having forfeited the king's peace, for which he was condemned to pay 300 marks; in lieu of which sum, King Edward IV. took of him 2470 tons of shipping, amongst which there was one ship of 900 tons burden, another of 500 tons, and one of 400 tons, the rest being smaller.

In the year 1506, King James IV. of Scotland built the largest ship which had hitherto been seen, but which was lost in her way to France in the year 1512, owing probably to a defective construction, and the unskilfulness of the crew in managing so large a ship.—About this time a very large ship was likewise built in France. In the fleet fitted out by Henry VIII. anno 1512, there was one ship, the Regent, of 1000 tons burden, one of 500, and three of 400 each. A ship still larger than the Regent, was built soon after, called Henri Grace Dieu! In the year 1522 the first voyage round the globe was sailed.

The English naval historians think that ships carried cannon on their upper decks only, and had no gunports before the year 1545: and it is certain that many of the largest ships in former times were fitted out from harbours, where ships of a moderate size now would not have water enough to float them. In 1575, the whole of the royal navy did not exceed 24 ships, and the number of merchant-ships belonging to England amounted to no more than 135 vessels above 100 tons, and 656 between 40 and 100 tons.—At Queen Elizabeth's death, anno 1603, there were not above four merchant-ships in England of 400 tons burden each.—The largest of Queen Elizabeth's ships of war was 1000 tons burden, carrying but 340 men, and 40 guns, and the smallest 600 tons, carrying 150 men and 30 guns. Smaller vessels were occasionally hired by her from private owners.

In the memorable sea-fight of Lepanto between the Turks and Christians, anno 1571, no vessels were employed but galleys; and it would appear from the carcases of some of them, which are still preserved in the arsenal at Venice, that even these were not so large or so well constructed as those of our times. The Invincible Armada, as Spanish vanity styled it, once the terror and admiration of nations, in the pompous and exaggerated descriptions of which the Spanish authors of those times dwelt with so much apparent pleasure, consisted of 130 ships, near 100 of which were the state-ship that had yet been seen on the ocean. The largest of these, however, would be no more than a third rate vessel in our navy, and they were so ill constructed, that they would neither move easily, fail near the wind, nor be properly worked in tempestuous weather. The whole of the naval force collected by Queen Elizabeth to oppose this formidable fleet, including hired vessels, tenders, store-ships, &c. amounted to no more than 143.

Ship-building began now to make a considerable progress in Britain. Both war and trade required an increase of shipping; so that in the year 1670, the annual charge of the navy was reported to be 500,000l.; and in 1678 the navy consisted of 83 ships, of which 58 were of the line. At this time the exports amounted to ten millions per annum; and the balance of trade was two millions. In 1689 there were 173 ships, great and small, in the royal navy, and it has been constantly increasing; so that in 1761 the ships in the navy amounted to 372, of which 129 were of the line; and in the beginning of the year 1795, the total amount was above 430.

As ships of the common construction are found to be very defective in many particulars, various methods have therefore from time to time been proposed to remove some of the bad qualities they possessed. As it would be an endless task to enumerate the different inventions for this purpose, a few of them only will now be mentioned.

In 1663 Sir William Petty constructed a double ship, or rather a single ship with a double bottom, which was found to sail considerably faster than any of the ships with which it had an opportunity of being tried. Her first voyage was from Dublin to Holyhead; and in her return "she turned into that narrow harbour against wind and tide, among rocks and ships, with such dexterity as many ancient seamen confessed they had never seen the like." This vessel with 70 more was lost in a dreadful tempest.

The subject was again revived by Mr Gordon, in his Principles of Naval Architecture, printed at Aberdeen anno 1784; where, having delivered his sentiments on the construction of large masts, he says: "These experiments likewise point out to us methods by which two vessels may be laterally connected together, though at a considerable distance from each other, in a manner sufficiently strong, with very little increase of weight or expense of materials, and without exposing much surface to the action or influence of the wind or the waves, or obstructing their motion in any considerable degree, and consequently without being much opposed by them on that account under any circumstances; and if vessels are judiciously constructed with a view to such a junction, it would be no easy matter to enumerate all the advantages that may be obtained by this means." He then enumerates the advantages that double vessels would have over those of the common construction. And lately Soon after double ships were actually built by Mr Mil- ler of Dalwinton.

Another plan was proposed by Mr Gordon to make a ship fall fast, draw little water, and to keep a good wind. For this purpose, "the bottom (he says) should be formed quite flat, and the sides made to rise perpendicular from it, without any curvature; which would not only render her more steady, as being more opposed to the water in rolling, but likewise more convenient for piling water, &c. while the simplicity of the form would contribute greatly to the ease and expedition with which she might be fabricated. Though diminishing the draught of water is, cæteris paribus, undoubtedly the most effectual method of augmenting the velocity with which vessels go before the wind; yet, as it proportionally diminishes their hold of the water, it renders them extremely liable to be driven to leeward, and altogether incapable of keeping a good wind. This defect may, however, be remedied, in a simple and effectual manner, by proportionally augmenting the depth of keel, or, as so large a keel would be inconvenient on many accounts, proportionally increasing their number; as, in place of adding a keel eight feet deep to a vessel drawing fix feet water, to affix to different parts of her the num-flat bottom, which would be well adapted for receiving her of them, fix different keels of two feet deep each at equal distances from each other, with proper intervals between; which will be found equally effectual for preventing these pernicious effects. Four such, indeed, would have answered the purpose as well as the eight feet keel, were it not for the superior prelude or resistance of the lower water (A).

Thus

(a) This is frequently repeated on the authority of Mr Gordon and others. Theory says otherwise; and the experiments of Sir Isaac Newton show in the most unexceptionable manner, that the resistance of a ball descending through the water is the same at all depths; nay, the heaping up of the water on the bow, occasioning a hydro-statical prelude in addition to the real resistance, will make the whole opposition to an equal surface, but of greater horizontal dimensions, greater, because it bears a greater proportion to the resistance. Thus then it appears, that a vessel drawing eight feet water only, keels and all, may be made to keep as good a wind, or be as little liable to be driven to leeward, as the sharpest built vessel of the same length drawing 14, nay 20 or upwards, if a few more keels are added, at the same time that she would be little more resisted in moving in the line of the keels than a vessel drawing fix feet water only. These keels, besides, would strengthen the vessel considerably, would render her more steady, and less liable to be overset, and thereby enable her to carry more sail; and Mr Gordon then enumerates the several advantages that a ship of this construction will possess.

This plan has been put into execution by Captain Schank, with this difference only, that instead of the keels being fixed as proposed by Mr Gordon, Captain Schank constructed them so as to slide down to a certain depth below the bottom, or to be drawn up within the ship as occasion might require.

Captain Schank having communicated his plans to the Navy Board, two vessels were in consequence ordered to be built of 13 tons each, and similar in dimensions, one on the old construction, and the other flat-bottomed, with sliding keels. In 1790 a comparative trial in presence of the commissioners of the navy was made on the river Thames, each having the same quantity of sail; and although the vessel on the old construction had leeboards, a greater quantity of ballast, and two Thames pilots aboard, yet Captain Schank's vessel with three sliding keels beat the other vessel, to the astonishment of all present, one half of the whole distance failed; and no doubt he would have beat her much more had she been furnished with a Thames pilot.

This trial gave so much satisfaction, that a king's cutter of 120 tons was immediately ordered to be built on the same construction, and Captain Schank was requested to superintend its building. This vessel was launched at Plymouth in 1791, and named the Trial. The length of this vessel is 66 feet, breadth 21 feet, and depth of the hold seven feet: her bottom is quite flat, and draws only fix feet water, with all her guns, flores, &c. whereas all other vessels of her tonnage on the old construction draw 14 feet; so that she can go with safety into almost any harbour or creek. She has three sliding keels inclosed in a cafe or well; they are each 14 feet in length; the fore and the after keels are three feet broad each, and the middle keel is fix feet broad. The keels are moveable by means of a winch, and may be let down seven feet below the real keel; and they work equally well in a storm as in still water. Her hold is divided into several compartments, all water-tight, and so contrived, that should even a plank or two start at sea in different parts of the vessel, she may be navigated with the greatest security to any place. If she should be driven on shore in a gale of wind, she will not soon become a wreck, as her keels will be driven up into their cafes, and the ship being flat-bottomed, will not be easily overset; and being able to go into such shallow water, the crew may all be easily saved. By means of her sliding keel she is kept steady in the greatest gale; she is quite easy in a great sea, does not strain in the leaft, and never takes in water on her deck; and when at anchor, she rides more upright and even than any other ship can do: she falls very fast either before or upon a wind; no vessel she has ever been in company with, of equal size, has been able, upon many trials, to beat her in failing; and yet her fails seem too small.

It has also been proposed to construct vessels of other materials than wood; and a vessel was built whose bottom, instead of being plank, was copper.

Book I. Containing the Method of Delineating the several Sections of a Ship.

Chap. I. Of the Properties of Ships.

A ship ought to be constructed so as to answer the particular purpose for which she is intended. It would be an easy matter to determine the form of a ship intended to fail by means of oars; but, when sails are used, a ship is then acted upon by two elements, the wind and water; and therefore it is much more difficult than is commonly imagined to ascertain the form of a ship so as to answer in an unfavourable as well as a favourable wind; the ship at the same time having a cargo of a certain weight and magnitude.

Every ship ought to fail well, but particularly when the wind is upon the beam; for this purpose a considerable length in proportion to the breadth is necessary, must pof- and the plane of resistance should be the least possible. The main frame should also be placed in a proper situat- tion; but according to the experiments of Mr Chapman*, its plane is variable with the velocity of the ship: the mean place of the main frame has, however, la Confruc- tion des been generally estimated to be about one-twelfth of the length of the keel before the middle. Without a suffi- cient degree of stability a ship will not be able to car- ry a proa of fail; a great breadth in proportion to the length and low upper-works will augment the stability. The following particulars being attended to, the above property will be gained, and the ship will also steer well. The wing tranfom should be carried pretty high; the fashion pieces well formed, and not full below the load water-line: the lower part of the stem to be a portion of a circle, and to have a considerable rake: the sternpoft to be nearly perpendicular to the keel; and all the upper works kept as low as possible.

Many ships from construction are liable to make much To make a leeway. This may in a great measure be avoided by giv-ship keep ing the ship a long keel, little breadth, and a consider- a good able depth in the hold: whence the bow will meet with little resistance in comparison to the fide, and therefore the ship will not fall much to the leeward.

Another very great retardation to the velocity of a and to fail ship is her pitching. The principal remedy for this is to increase the length of the keel and floor, to diminish without the rising afore and abaft, and to construct the hull in hard. Such a manner that the contents of the fore-body may be duly proportioned to the contents of the after- body.

In a ship of war the lower tier of guns ought to be of a sufficient height above the water, otherwise it will war the be impossible to work the lee-guns when it blows hard, lower deck This property will be obtained by giving her a long floor-timber, little rifting, a full midship frame, light upper works, and the wing-tranfom not too high: And in every ship the extreme breadth ought always to be higher afore and abaft than at midships. A merchant ship, besides being a fast sailer, ought to carry a considerable cargo in proportion to its length, to fail with little ballast, and to be navigated with few hands.

That a ship may take in a considerable cargo, it should have a great breadth and depth in proportion to its length, a full bottom, and a long and flat floor. But a ship of this construction will neither fail fast, nor carry much fail.

If a ship be filled out much towards the line of floatation, together with low upper works, she will require little ballast; and that ship which is stiff from construction is much better adapted for failing fast than one which, in order to carry the same quantity of canvas, is obliged to be loaded with a much greater weight: for the resistance is as the quantity of water to be removed, or nearly as the area of a transverse section of the immersed part of the body at the midship frame; and a body that is broad and shallow is much stiffer than one of the same capacity that is narrow and deep.

"The advantages (says Mr Gordon) are numerous, important, and obvious. For it is evident, that by enlarging, perhaps doubling, the breadth of vessels, and forming their bottoms flat and well furnished with keels, they must, in the first place, become much steadier, roll little, if any, and be enabled to carry greatly more fail, and that in a better direction, at the same time that they would be in no danger of being dismasted or overlet, unless the masts were of a most extraordinary height indeed. Secondly, They would have little or no occasion for ballast, and if any was used, could incur less danger from its shifting. Thirdly, That there would be much more room upon deck, as well as accommodation below; the breadth being so much increased without any diminution of the height above the load-water line. Fourthly, That they would deviate much less from the intended course, and penetrate the water much easier in the proper direction; for doubling the breadth, without any increase of weight, would diminish the depth or draught of water one half; and though the extent of the directly oppoling surface would be the same as before, yet the vessel in moving would meet with half the former resistance only; for so great is the difference between the preface, force, or reaction, of the upper and the under water. Fifthly, That they would by this means be adapted for lying unsupported in docks and harbours when dry, be rendered capable of being navigated in shallow water, and of being benefited by all the advantages attending that very important circumstance: and it is particularly to be observed, that making vessels which may be navigated in shallow water, may, in many respects, justly be regarded as a matter of equal importance with increasing the number of harbours, and improving them, as having identically the same effects with regard to navigation; at the same time, that the benefits which would result from such circumstances are obtained by this means without either expence, trouble, or inconvenience: besides, it would not only enable vessels to enter many rivers, bays, and creeks, formerly inaccessible to ships of burden, but to proceed to such places as are most landlocked, where they can lie or ride most secure, and with least expence of men and ground tackle. As ships of war would carry their guns well by being fo steady, there could be but little occasion for a high topside, or much height of hull above water; and as little or no ballast would be required, there would be no necessity, as in other vessels, for increasing their weight on that account, and thereby pressing them deeper into the water. These are very important circumstances, and would contribute much to improve the failing of such vessels." From whence it appears, that there would be united, what hitherto been deemed irreconcilable, the greatest possible stability, which is nearly as the area of a transverse section of the immersed part of the body at the midship frame: and a body that is broad and shallow is much stiffer than one of the same capacity that is narrow and deep. A ship of this construction may take in a considerable cargo in proportion to her size; but if deeply loaded will not fail fast, for then the area of a section of the immersed part at the midship frame will be very considerable; and as the sails of such a ship must necessarily be large, more hands will therefore be required.

The lefs the breadth of a ship, the fewer hands will be necessary to work her; as in that case the quantity of sail will be lefs, and the anchors also of lefs weight. We shall gain much (says M. Bouguer) by making the extreme breadth no more than the fifth or sixth part of the length, if, at the same time, we diminish the depth proportionally; and likewise this most surprising circumstance, that by diminishing these two dimensions, or by increasing the length, a ship may be made to go sometimes as fast as the wind.

In order to obtain the preceding properties, very opposite rules must be followed; and hence it appears to be impossible to construct a ship so as to be possessed of them all. The body, however, must be so formed, that as many of these properties may be retained as possible, always observing to give the preference to those which are most required. If it is known what particular trade the ship is to be employed in, those qualities are then principally to be adhered to which are most essentially necessary for that employment.

It may easily be demonstrated that small ships will not have the same advantages as large ones of a similar inferior form, when employed in the same trade: for a large ship will not only fail faster than a small one of a similar form, but will also require fewer hands to work her. Hence, in order that a small ship may possess the same advantages as a large one, the corresponding dimensions will not be proportional to each other. The reader will see in Chapman's Architecture Navalis Mercatoria ample tables of the several dimensions of ships, of different classes and fizes, deduced from theory combined with experiment. Tables of the dimensions of the principal ships of the British navy, and of other ships, are contained in the Ship-builder's Repository, and in Murray's Treatise on Ship-building.

CHAP. II. Of the different Plans of a Ship.

When it is proposed to build a ship, the proportional size of every part of her is to be laid down; from whence the form and dimensions of the timbers, and of every particular piece of wood that enters into the construction, is to be found. As a ship has length, breadth, and depth, three different plans at least are necessary to exhibit

Different Plans of a Ship.

exhibit the form of the several parts of a ship; these are usually denominated the sheer plan, the half breadth and body plans.

The sheer plan or draught, otherwise called the plan of elevation, is that section of the ship which is made by a vertical plane passing through the keel. Upon this plan are laid down the length of the keel; the height and rake of the stem and sternpost; the situation and height of the midship and other frames; the place of the masts and channels; the projection of the head and quarter gallery, and their appendages; and in a ship of war the position and dimensions of the gun-ports. Several imaginary lines, namely, the upper and lower height of breadth lines, water lines, &c. are also drawn in this plane.

The half breadth, or floor plan, or, as it is frequently called the horizontal plane, contains the several half-breadths of every frame of timbers at different heights; ribbands, water lines, &c. are also described on this plane.

The body plan, or plane of projection, is a section of the ship at the midship frame or broadest place, perpendicular to the two former. The several breadths, and the particular form of every frame of timbers, are described on this plane. As the two sides of a ship are similar to each other, it is therefore unnecessary to lay down both; hence the frames contained between the main frame and the stem are described on one side of the middle line, commonly on the right hand side, and the after frames are described on the other side of that line.

Several lines are described on these planes, in order the more readily to assist in the formation of the timbers; the principal of which are the following:

The top-timber line, is a curve limiting the height of the ship at each timber.

The top-timber half breadth line, is a section of the ship at the height of the top-timber line, perpendicular to the plane of elevation.

The height of breadth lines, are two lines named the upper and lower heights of breadth. These lines are described on the plane of elevation to determine the height of the broadest part of the ship at each timber; and being described in the body plan, limit the height and breadth of each frame at its broadest part.

Main half breadth, is a section of the ship at the broadest part, perpendicular to the sheer plan, and represents the greatest breadth at the outside of every timber.

Water lines, are lines supposed to be described on the bottom of a ship when afloat by the surface of water; and the uppermost of these lines, or that described by the water on the ship's bottom when sufficiently loaded, is called the load water line. According as the ship is lightened, she will rise higher out of the water; and hence new water lines will be formed. If she be lightened in such a manner that the keel may preserve the same inclination to the surface of the water, these lines will be parallel to each other; and if they are parallel to the keel, they will be represented by straight lines parallel to each other in the body plan; otherwise by curves. In the half breadth plan, these lines are curves limiting the half breadth of the ship at the height of the corresponding lines in the sheer plan. In order to distinguish these lines, they are usually drawn in green.

Ribband liner, are curves on a ship's bottom by the intersection of a plane inclined to the plane of elevation; and are denominated diagonal or horizontal, according as they are measured upon the diagonal, or in a direction perpendicular to the plane of elevation. Both these answer to the same curve on the ship's bottom, but give very different curves when described on the half breadth plan.

Frames, are circular pieces of timber bolted together, and raised upon the keel at certain distances, and to which the planks are fastened. A frame is composed of one floor-timber, two or three futtocks, and a top-timber on each side: which being united together, form a circular inclosure, and that which incloses the greatest space is called the midhip or main frame. The arms of the floor-timber of this frame, form a very obtuse angle; but in the other frames this angle decreases with the distance of the frame from midships. Those floor-timbers which form very acute angles are called crutches. The length of the midhip floor-timber is in general about half the length of the main frame.

A frame of timbers is commonly formed by arches of sweeps of circles called sweeps. There are generally five sweeps: 1st, The floor sweep; which is limited by a line in the body plan perpendicular to the plane of elevation, a little above the keel; and the height of this line above the keel at the midhip frame is called the dead rising. The upper part of this arch forms the head of the floor timber. 2d, The lower breadth sweep; the centre of which is in the line representing the lower height of breadth. 3d, The reconciling sweep. This sweep joins the two former, without interfering either; and makes a fair curve from the lower height of breadth to the rising line. If a straight line is drawn from the upper edge of the keel to touch the back of the floor sweep, the form of the midhip frame below the lower height of breadth will be obtained. 4th, The upper breadth sweep; the centre of which is in the line representing the upper height of breadth of the timber. This sweep described upwards forms the lower part of the top timber. 5th, The top-timber sweep is that which forms the hollow of the top timber. This hollow is, however, very often formed by a mould, so placed as to touch the upper breadth sweep, and pass through the point limiting the half breadth of the top timber.

The main frame, or as it is usually called dead flat, is denoted by the character ⊕. The timbers before dead-flat are marked A, B, C, &c. in order; and those abaft dead-flat by the figures 1, 2, 3, &c. The timbers adjacent to dead-flat, and of the same dimensions nearly, are distinguished by the characters (A), (B), &c. and (1), (2), &c. That part of the ship abaft the main frame is called the after body; and that before it the fore body.

All timbers are perpendicular to the half breadth plan. Those timbers whose planes are perpendicular to the sheer plan, are called square timbers; and those whose planes are inclined to it are called canted timbers.

The rising line, is a curve drawn in the sheer plan, at the heights of the centres of the floor sweeps in the body plan. As, however, this line, if drawn in this manner, would extend beyond the upper line of the figure, it is therefore usually so drawn that its lower part may touch the upper edge of the keel. This is performed by taking the heights of each of the centres in the Different the body plan, from the height of the centre of the Plans of a sweep of dead-flat, and setting them off on the corresponding timbers in the sheer plan from the upper edge of the keel.

Half breadth of the rising, is a curve in the floor plan, which limits the distances of the centres of the floor sweeps from the middle line of the body plan.

The rising of the floor, is a curve drawn in the sheer plan, at the height of the ends of the floor timbers. It is limited at the main frame or dead flat by the dead rising, and in flat ships is nearly parallel to the keel for some timbers afore and abaft the midship frame; for which reason these timbers are called flats: but in sharp ships it rises gradually from the main frame, and ends on the stem and post.

Cutting-down line, is a curve drawn on the plane of elevation. It limits the depth of every floor timber at the middle line, and also the height of the upper part of the dead wood afore and abaft.

Timber and room, or room and space, is the distance between the moulding edges of two timbers, which must always contain the breadth of two timbers and an interval of about two or three inches between them. In forming the timbers, one would serve for two, the fore-side of the one being supposed to unite with the aftide of the other, and so make only one line, which is called the joint of the timbers.

In order to illustrate the above, and to explain more particularly the principal pieces that compose a ship, it will be necessary to give a description of them. These pieces are for the most part represented according to the order of their disposition in fig. 1.

A, Represents the pieces of the keel to be securely bolted together and clinched.

B, The sternpost, which is tenanted into the keel, and connected to it by the knee G.

E, The back of the post, which is also tenanted into the keel, and securely bolted to the post; the intention of it is to give sufficient breadth to the port, which seldom can be got broad enough in one piece. C is the false post, which is fayed (b) to the fore part of the sternpost.

C, The stem, in two pieces, to be scarfed together. The stem is joined to the fore foot, which makes a part of both.

H, The apron, in two pieces, to be scarfed together, and fayed on the inside of the stem, to support the scarf thereof; and therefore the scarf of the apron must be at some distance from that of the stem.

I, The stemson, in two pieces, to support the scarf of the apron.

D, The beams which support the decks; and F the knees by which the beams are fastened to the sides of the ship.

K, The wing transom: it is fayed across the sternpost, and bolted to the head of it, and its extremities are fastened to the fashion pieces. L, Is the deck transom, parallel to the wing transom. M, N, Two of the lower transoms: these are fastened to the sternpost and fashion pieces in the same manner as the wing transom.

Q, The knee which fastens the transom to the ship's side. And, O, The fashion piece, of which there is one on each side. The keel of the fashion piece is connected with the dead-wood, and the head is fastened to the wing transom.

R, S, Breast-hooks; these are fayed in the inside to the stem, and to the bow on each side of it, to which they are fastened with proper bolts. There are generally four or five in the hold, in the form of that marked R, and one in the form of that marked S, into which the lower deck planks are rabbeted: There is also one immediately under the hause holes, and another under the second deck.

T, The rudder, which is joined to the sternpost by the rudder irons, upon which it turns round in the goosings, fastened to the sternpost for that purpose. There is a mortise cut in the head of the rudder, into which a long bar is fitted called the tiller, and by which the rudder is turned.

U, A floor timber: it is laid across the keel, to which it is fastened by a bolt through the middle. V, V, V, V, The lower, the second, third, and fourth futtocks. W, W, The top timbers. These represent the length and scarf of the several timbers in the midship frame.

X, The pieces which compose the kelson. They are scarfed together in the same manner as the keel, and placed over the middle of the floor timbers, being scored about an inch and a half down upon each side of them, as represented in the figure.

Y, The several pieces of the knee of the head; the lower part of which is fayed to the stem, and its keel is scarfed to the head of the forecastle. It is fastened to the bow by two knees, called cheeks, in the form of that represented by Z; and to the stem, by a knee called a standard, in the form of that marked Θ.

a, The cathead, of which there is one on each side of the bow, projecting so far as to keep the anchor clear of the ship when it is hove up.

b, The bits, to which the cable is fastened when the ship is at anchor.

d, The side counter-timbers, which terminate the ship abaft within the quarter gallery.

e, e, Two pieces of dead wood, one afore and the other abaft, fayed on the keel.

Fig. 2. is a perspective representation of a ship framed and ready for the planking; in which A, A is the keel; B, the sternpost; C, the stem; K, L, M, the transoms; F, F, F, F, F, F, F, the ribbands.

CHAP. III. Containing Preliminary Problems, &c.

The general dimensions of a ship are the length, breadth, and depth.

To ascertain those dimensions that will best answer the intended purpose is, no doubt, a problem of considerable difficulty; and from theory it may be shewn that there are no determinate proportions subsisting between the length, breadth, and depth, by which these dimensions may be settled; yet, by combining theory and practice, the proportional dimensions may be approximated to pretty nearly.

(b) To fay, is to join two pieces of timber close-together. As ships are constructed for a variety of different purposes, their principal dimensions must therefore be altered accordingly, in order to adapt them as nearly as possible to the proposed intention; but since there is no fixed standard whereby to regulate these dimensions, the methods therefore introduced are numerous, and in a great measure depend upon custom and fancy.

With regard, however, to the proportional dimensions, they perhaps may be inferred from the circle. Thus, if the extreme breadth be made equal to the diameter, the length at the load water line, or the distance between the rabbets of the stem and post at that place, may be made equal to the circumference of the same circle; and the depth of the hold equal to the radius, the upper works being continued upwards according to circumstances. A ship formed from these dimensions, with a bottom more or less full according as may be judged necessary, will no doubt answer the proposed intention. Nevertheless, one or other of these dimensions may be varied in order to gain some essential property, which the trade that the vessel is intended for may require.

The following hints are given by Mr Hutchinson* towards fixing rules for the best construction of ships bottoms.

1. "I would recommend (says he), to prevent ships fore and after part of their keels deep enough, that the upper part may be made to admit a rabbet for the garboard streak, that the main body and bearing part of the ship's bottoms may be made to form an arch downwards in their length, suppose with the same sheer as their bends, at the rate of about 2 inches for every 30 feet of the extreme length of the keel towards the midship or main frame, which may be reckoned the crown of the arch; and the lower part of the keel to be made straight, but laid upon blocks so that it may form a regular convex curve downwards at the rate of an inch for every 30 feet of the extreme length of the keel, the lowest part exactly under the main frame; which curve, I reckon, is only a sufficient allowance for the keel to become straight below, after they are launched afloat, by the pressure of the water upward against their floors amidships, which causes their tendency to hog. And certainly a straight keel is a great advantage in sailing, as well as to support them when laid upon level ground or on straight blocks in a repairing dock, without taking damage.

2. "As square-terned ships, from experience, are found to answer all trades and purposes better than round or pink-terned ships, I would recommend the fore part of the sternpost, on account of drawing the water lines in the draught, only to have a few inches rake, that the after part may stand quite upright perpendicular to the keel: and for the rake of the stem I would propose the rabbet for the hudding ends for the entrance, and bows from the keel upwards, to form the same curve as the water line from the stem at the harpin towards the main breadth, and the bows at the harpin to be formed by a sweep of a circle of half the three-fourths of the main breadth; and the main transom to be three-fourths of the main breadth; and the buttocks, at the load or failing mark aft, to be formed, in the same manner as the bows at the harpin, with a sweep of a circle of half the three-fourths of the main breadth, to extend just as far from the stem and sternpost as to admit a regular convex curve to the main frame, and from these down to the keel to form regular convex water-lines, without any of those unnatural, hollow, concave ones, either in the entrance or run; which rules, in my opinion, will agree with the main body of the ship, whether she is designed to be built full for burden or sharp below for sailing.

3. "This rule for raking the stem will admit all the water lines in the ship's entrance to form convex curves all the way from the stem to the midship or main frame, which answers much better for sailing as well as making a ship more easy and lively in bad weather. And the bows should flange off, rounding in a circular form from the bends'up to the gunwale, in order to meet the main breadth the sooner, with a sweep of half the main breadth at the gunwale amidships; which will not only prevent them greatly from being plunged under water in bad weather, but spread the standing fore-rigging the more, to support these material masts and sails forward to much greater advantage than in those over sharp-bowed ships, as has been mentioned. And as the sailing trim of ships in general is more or less by the stem, this makes the water lines of the entrance in proportion the sharper to divide the particles of water the easier, so that the ship may pass through it with the least resistance.

4. "The run ought to be formed shorter or longer, fuller or sharper, in proportion to the entrance and main body, as the ship is designed for burden or sailing fast. The convex curves of the water lines should lessen gradually from the load or failing mark aft, as has been mentioned, downwards, till a fair straight taper is formed from the after part of the floor to the sternpost below, without any concavity in the water lines; which will not only add buoyancy and burden to the after-body and run of the ship, but, in my opinion, will help both her sailing and steering motions; for the pressure of the water, as it closes and rises upon it to come to its level again, and fill up that hollow which is made by the fore and main body being preffed forward with sail, will impinge, and act with more power to help the ship forward in her progressive motion, than upon those unnatural concave runs, which have so much more flat dead wood, that must, in proportion, be a hindrance to the stern being turned so easily by the power of the helm to steer the ship to the greatest advantage."

Many and various are the methods which are employed to describe the several parts of a ship. In the following problems, however, those methods only are given which appear to be most easily applied to practice, and which, at the same time, will answer any proposed purpose.

Problem I. To describe in the plane of elevation the sheer or curvature of the top timbers.

Let QR (fig. 3.) be the length of the ship between the wing transom and the rabbet of the stem. Then since it is generally agreed, especially by the French constructors, that the broadest part of the ship ought to be about one-twelfth of the length before the main of the frame or dead flat; therefore make R⊕ equal to five-twelfths of QR, and ⊕ will be the station of the main frame; space the other frames on the keel, and from these points let perpendiculars be drawn to the keel, middle of Let ⊕P be the height of the ship at the main frame, the ship. Preliminary VF the height at the aftermost frame, and RK the Problems height at the stem. Through P draw EPL parallel to the keel; describe the quadrants PGI, PMN, the radius being \( \oplus P \); make PH equal to EF, and PO equal KL, and draw the parallels GH, OM: Divide the top-timber line. GH similar to \( \oplus C \), and OM similar to \( \oplus R \). Through these points of division draw lines perpendicular to EL, and the several portions of these perpendiculars contained between EL and the arch will be the rifings of the top-timber line above EL. A curve drawn through these points will form the top-timber line.

This line is more easily drawn by means of a curved or bent ruler, so placed that it may touch the three points F, P, and K.

PROB. II. To describe the stem. Let K (fig. 3.) be the upper part of the stem, through which draw KS parallel to the keel, and equal to twice KR: Through the termination of the wales on the stem draw TW parallel to QR. Then from the centre S, with the distance SK, describe an arch: Take an extent equal to the nearest distance between the parallels WT, QR; and find the point W, such that one point of the compass being placed there, the other point will just touch the nearest part of the above arch; and from this point as a centre describe an arch until it meets the keel, and the stem will be formed.

PROB. III. To describe the sternpoft. Set off QV (fig. 3.) for the rake of the poft: draw VX perpendicular to the keel, and equal to the height of the wing transom, join QX, and it will represent the aft side of the poft.

PROB. IV. To describe the half breadth line. Let MN (fig. 4.) be the given length: Make N\( \oplus \) equal to five-twelfths of MN; draw the line \( \oplus P \) perpendicular to MN, and equal to the proposed extreme half breadth. Let ME be the round aft of the stern or wing transom; make EO perpendicular to MN, and equal to the given half breadth at the stern, which is generally between two-thirds and three-fourths of the main half breadth; and describe the arch MO, the centre of which is in the middle line. Space the frames (A), A, B, &c. and (1), 1, 2, &c. From the centre \( \oplus \), with the radius \( \oplus P \), describe the quadrant PRS; describe also the quadrant PCT. Through the point O draw ORU parallel to MN; divide the straight line RU similar to M\( \oplus \); and through these points of division draw lines perpendicular to MN, and meeting the arch. Transfer these lines to the correspondent frames each to each, and a curve drawn through the extremities will represent that part of the fide contained between the main frame and the stern. Again, through Q, the extremity of the foremost frame, draw QV parallel to MN. Or make PV a fourth or third part of PU, according as it is intended to make the ship more or less full towards the bow. Divide VC similar to \( \oplus C \); through these points draw lines perpendicular to MN, and terminating in the quadrantal arch: Transfer these lines to the corresponding timbers in the fore part, and a curve drawn through the extreme points will limit that part of the ship's fide contained between P and Q. Continue the curve to the next timber at X. From Q draw QZ perpendicular to QX; make the angle ZNO equal to ZQN, and the point Z will be the centre of the arch forming the bow. Remark, if it is proposed that the breadth of the ship at the frames adjacent to the main frame shall be equal to the breadth at the main frame; in this case, the centres of the quadrantal arches will be at the points of intersection of these frames with the line MN; namely, at (A) and (1). Also, if the height of the ship at the frames (A) and (1) is to be the same as at dead flat, the quadrantal arches in fig. 3. are to be described from the points of intersection of these frames with the line EL.

These rules, it is evident, are variable at pleasure; and any person acquainted with the first principles of mathematics may apply calculation to find the radii of the several sweeps.

PROB. V. To describe the main frame or dead flat. This frame is that which contains the greatest space, and the particular form of each of the other frames depends very much on it. If the ship is intended to carry a great burden in proportion to her principal dimensions, this frame is made very full; but if the is intended to fail fast, it is usually made sharp. Hence arises diversity of opinions respecting its form; each constructor using that which to him appears preferable. In order to save repetition, it is judged proper to explain certain operations which necessarily enter into all the different methods of constructing this frame.

In the plane of the upper side of the keel produced, draw the line AB (fig. 5.) equal to the proposed breadth precepts of the ship; bisect AB in C, and draw AD, CE, and describing BF, perpendicular to AB. Then, since the two sides fig. 5. of a ship are similar, it is therefore thought sufficient to describe the half of each frame between the main frame and the stern on one side of the middle line CE, and the half of each of those before the main frame on the other side of it. The first half is called the after-body, and the other the fore-body. The after-body is commonly described on the left side of the middle line; and the fore-body on the right side of it: hence the line AD is called the fide line of the after body, and BF the fide line of the fore body. Make AD and BF each equal to the height of the ship at the main frame. Make AG, BG, and AH, BH, equal to the lower and upper heights of breadth respectively, taken from the sheer plan. Let LI be the load water line, or line of floatation when the ship is loaded, and KK the height of the rising line of the floor at this frame. Make CN, CO, each equal to half the length of the floor timber, and N, O, will be the heads of the floor timber, through which draw perpendiculars to A.B. Make Cm, Em, each equal to half the thickness of the sternpoft, and En, En, equal to half the thickness of the stern, and join mm, nn.

Method I. Of describing a main frame.—From the centre a (fig. 5.), in the lower breadth line, describe the lower breadth sweep G e; make Nb equal to the proposed radius of the floor sweep, and from the centre b describe the floor sweep Nf. Let the radius of the reconciling sweep be Ag, equal to about the half of AC; then make Ah equal to Nb, and Am equal to Ga. Now from the centre a, with an extent equal to gm, describe an arch, and from the centre b2 with the extent gh, describe an arch intersecting the former in c, which will be the centre of the reconciling sweep ef. Join Nm by an inverted curve, the centre of which may be in the line b N produced downwards; or it may be joined by two curves, or by a straight line if there is little rising; and hence the lower part of the main frame will be described.

In order to form the top timber, make F k equal to such part of the half breadth, agreeable to the proposed round of the fide, as one-seventh; join H k, and make k i equal to about two-thirds of H k: make the angle H i l equal to i H l; and from the centre l at the distance l H describe the arch H i; and from the centre o, the intersection of l i, and k F produced, describe the arch i k; and the top timber will be formed.

II. To describe a main frame of an intermediate capacity, that is, neither too flat nor too sharp.—Divide the line AX (fig. 6.), which limits the head of the floor timber, into three equal parts; and make a b equal to one of them. Divide the line d B, the perpendicular distance between the load water line and the plane of the upper side of the keel, into seven equal parts; and set off one of these parts from d to c, and from c to m. Let GH be the lower deck, join G m, and produce it to g. Draw the straight line V a, bisect it in n, and from the points n, a, describe arches with the radius G q intersecting each other in P, which will be the centre of the arch n a. The centre of the arch V n is found by describing arches downwards with the same radius.

With an extent equal to once and a half of B e, describe arches from the points b, e, intersecting each other in A, and from this point as a centre describe the arch e b; make a t equal to d m, and join A m, A l. Then, in order to reconcile two arches so as to make a fair curve, the centres of these arches and of the points of contact must be in the same straight line. Hence the point k will be the centre of the arch d m, and o the centre of the arch a l. The arch l m is described from the centre A.

To form the top timber, set back the tenth part of the half breadth from K to S upon the line of the second deck; then with an extent equal to two-thirds of the whole breadth describe an arch through the points S and H, the upper height of breadth. Again, make MI equal to the fifth part of the half breadth; describe an arch of a circle through the points S and T, taking the diagonal GB for the radius. As this arch is inverted in respect of the arch d S, the centre will be without the figure. Hence one-half of the main frame is formed, and the other half is described by similar operations.

Remark. This frame may be made more or less full by altering the several radii.

III. To describe a main frame of a circular form.—Let the several lines be drawn as before: Then make O a (fig. 7.) equal to the half breadth G a, and from the centre a, with the radius G a, describe the arch b G c O. Let d be the head of the floor-timber, and d x the rising. Assume the point f in the arch, according to the proposed round of the second futtock, and describe the arch d f; the centre of which may be found as in the former method: from the centre a, with the distance a d, describe the arch d c O; make d c equal to one-third of d O, and the angle d c h equal to c d h, and from the centre h describe the arch d c. The inverted arch c O may described as before.

IV. To describe a very full main frame.—Let the vertical and horizontal lines be drawn as before: let b, fig. 8. be the floor-head, and b x the rising. Divide G c into two equal parts in the point a', and upon c d de-scribe the square d b a c, in which inscribe the quadrant d e a. Divide the line b d into any number of equal parts in the points O, N, M, L, and draw the lines L m, M e, N n, O b, perpendicular to d b. Divide the line G C, the depth of the hold, the rising being deducted, into the same number of equal parts in the points E, F, I, K, and make the lines E p, F q, I r, K s, in the frame, equal to the lines O b, N n, M e, L m, in the square, each to each respectively; and through the points G, p, q, r, s, b, describe a curve. The remaining part of the frame may be described by the preceding methods.

V. To describe the main frame of a ship intended to be a fast fader.—The principal lines being drawn as before, let the length of the floor-timber be equal to half the breadth of the ship, and the rising one-fifth or one-sixth of the whole length of the floor-timber, which lay off from x to E, fig. 9. Through the point E draw the Fig. 9. line T x perpendicular to G C, and d e perpendicular to AG. Join T d, which bisect in B, and draw BF perpendicular thereto, and meeting CG produced in F, from the centre F, at the distance FT, describe the semicircle T d D. Divide GT into any number of parts, VW, &c., and bisect the intervals DV, DW, &c. in the points X, Z, &c.; then, from the centre X, with the extent XV, describe the semicircle D b V, intersecting AG in b. Let VP be drawn perpendicular to GT, and b P perpendicular to AG, and the point of intersection P will be one point through which the curve is to pass. In like manner proceed for the others, and a curve drawn through all the points of intersection will be part of the curve of the main frame. The remaining part of the curve from E to Y will be composed of two arches, the one to reconcile with the former part of the curve at E, and the other to pass through the point Y, the centre of which may be found by any of the preceding methods. In order to find the centre of that which joins with the curve at E, make TR equal to the half of G D, and join ER, in which a proper centre for this arch may be easily found.

The portion G b E of the curve is a parabola, whose vertex is G and parameter G D.

For G D : G b :: G b : GV by construction.

Hence DG × GV = G b², which is the equation for a parabola.

VI. To describe a main frame of a middling capacity.—Let the length of the floor-timber be equal to one-half of the breadth of the ship. Make O d, fig. 10. equal to one-fourth of the length of the floor-timber, and divide it into two equal parts in the point e. Describe an arch through e, and the extremity a of the floor-timber, the radius being equal to the half breadth, or more or less according to the proposed round of the floor-head. Then with the radius O l, half the length of the floor-timber, describe the arch e Y.

Draw l m perpendicular to O A; bisect A n in p, and draw the perpendicular p q. From the middle of A p draw the perpendicular r s, and from the middle of A r draw the perpendicular t u. Make n z, p g, each equal to l n; make the distances p y, r b, each equal to a g; r F, t E, each equal to a b; and t x equal to a E. Then a curve drawn through the points a, z, y, F, x, T, will form the under part of the midship frame.

We shall finish these methods of describing the main Preliminary frame of a ship with the following remark from M. Vial Problems: du Clairbois*. "It seems (says he) that they have affected to avoid straight lines in naval architecture; yet, geometrically speaking, it appears that a main frame formed of straight lines will have both the advantage and simplicity over others." To illustrate this, draw the straight line MN (fig. 9.) in such a manner that the mixtilinear space M a l may be equal to the mixtilinear space DNY. Hence the capacity of the main frame formed by the straight lines MN, NY will be equal to that of the frame formed by the curve M a DY; and the frame formed by the straight lines will for the most part be always more susceptible of receiving a bow that will easily divide the fluid. It is also evident, that the cargo or ballast, being lower in the frame formed of straight lines than in the other, it will therefore be more advantageously placed, and will enable the ship to carry more sail (c); so that having a bow equally well or better formed, she will sail faster.

Fig. 11. Let AB (fig. 11.) be the middle line of the port, and let CD be drawn parallel thereto at a distance equal to half the thickness of the port. Make CE equal to the height of the lower part of the fashion-piece above the keel: make CT equal to the height of the extremity G of the transom above the plane of the keel produced, and CH equal to the height of the transom on the port, HT being equal to above one-ninth or one-tenth of GT, and describe the arch GH, the centre of which will be in BA produced: make EK equal to five-twelfths of ET: through K draw KL perpendicular to CD, and equal to EK; and with an extent equal to EL describe the arch EL. Make GI equal to the half of ET, and from the centre I describe the arch GM, and draw the reconciling curve ML.—Let the curve of the fashion-piece be produced upwards to the point representing the upper height of breadth as at O. Make ON equal to the height of the top-timber, and BN equal to the half breadth at that place, and join ON. Through N and the upper part of the counter, let arches be described parallel to GH. The taffrail, windows, and remaining part of the stern, may be finished agreeable to the fancy of the artist.

In fig. 12. the projection of the stern on the plane of elevation is laid down, the method of doing which is obvious from inspection.

If the transom is to round aft, then since the fashion-pieces are always fided straight, their planes will intersect the sheer and floor planes in a straight line. Let G g (fig. 14.) be the intersection of the plane of the fashion-piece with the floor plane. From the point g draw g W perpendicular to g M: make y k equal to the height of the tuck, and W k being joined will be the intersection of the plane of the fashion-piece with the sheer plane. Let the water lines in the sheer plane produced meet the line k W in the points a, s, h, and draw the perpendiculars aa, fs, hh. From the points a, s, h (fig. 14.) draw lines parallel to G g to intersect each corresponding water line in the floor plane in the points 3, 2, 1.

From the points G, 3, 2, 1, in the floor-plane draw Preliminary lines perpendicular to g M, intersecting the water lines Problems (fig. 13.) in the points G, 3, 2, 1/1; and through these points describe the curve G 3 2 1 k: and WG 3 2, 1 k will be the projection of the plane of the fashion-piece on the sheer plane. Through the points G, 3, 2, 1 (fig. 13.) draw the lines GF, 3 A, 2 S, 1 H, per-fig. 13., perpendicular to W k; and make the lines WF, a A, s S, h H, equal to the lines g G, a 3, s 2, h 1 (fig. 14.) respectively, and WFA SH k will be the true form of the plane of the aft side of the fashion-piece. When it is in its proper position, the line WF will be in the same plane with the sheer line; the line a A in the same plane with the water-line a 3 ; the line s S in the same plane with the water line r 2 ; and the line h H in the same plane with the water line h 1. If lines be drawn from the several points of intersection of the water lines with the rabbet of the port (fig. 13.), perpendicular to g M, and curved lines being drawn from these points to G, 3, 2, 1 (fig. 14.) respectively, will give the form Fig 14. and dimensions of the tuck at the several water lines.

Prob. VII. To bevel the fashion-piece of a square tuck by water-lines.

As the fashion-piece both rakes and cants, the planes of the water-lines will therefore intersect it higher on the aft than on the fore-fide; but before the heights on the fore-fide can be found, the breadth of the timber must be determined; which let be b n (fig. 15.). Then, as it cants, the breadth in the direction of the waterline will exceed the true breadth. In order to find the true breadth, form the aft-side of the fashion-piece as directed in the last problem.

Let t 5 (fig. 13.) be the aft side of the rabbet on the outside of the port, WM the common section of the plan of the fashion-piece and the sheer-plan. Before this last line can be determined, the several water-lines 1, 2, 3, 4, and 5, must be drawn parallel to the keel, which may represent so many transoms.—Let these water-lines be formed and ended at the aft-side of the rabbet, as in fig. 14. where the rounds aft of the several transoms are described, limiting the curves of the water-lines. Now the line WM must rake so as to leave room for half the thickness of the port, at the tuck : in order to which, produce W g to r; make r g half the thickness of the port; through r draw a line parallel to g M to intersect g G in b: then with the radius r b, from the point of the tuck as a centre, describe an arch, and draw the line WM just to touch the back of that arch.

The line WM being drawn, let any point k in it be assumed at pleasure: from k draw k y perpendicular to g M: through y draw y f (fig. 14.) parallel to g G, intersecting the line M f drawn perpendicular to g M in the point f. From M draw M i perpendicular to y f, and from y draw y n perpendicular to WM (fig. 13.). Make M n (fig. 15.) equal to M z (fig. 14.); then M l (fig. 15.) being equal to y k (fig. 13.), join n 1, and the angle t n M will be the beveling to the horizontal plane. Again, make M x, M f (fig. 15.) respectively equal to y n (fig. 13.) and M f (fig. 14.), and join x f;

(c) It is not a general rule, that lowering the cargo of a ship augments her stability. This is demonstrated by the Chevalier de Borda, in a work published by M. de Goimpy upon this subject. See also L'Architecture Navale par M. Vial du Clairbois, p. 23.

The bevelling being now found, draw the line a b (fig. 15.) parallel to z n, a z or b n being the scantling of the timber. Then n w will be the breadth of the timber on the horizontal plane, and z e its breadth on the sheer-plane, and a c what is within a square.

Now as the lines g G, a 3, s 2, h 1, y i, represent the aft-fide of the fashion-piece on the horizontal plane (fig. 14.), dotted lines may be drawn parallel to them to represent the fore-fide, making n x (fig. 15.) the perpendicular distance between the lines representing fore and aft sides of the fashion-piece. By these lines form the fore-fide of the fashion-piece in the same manner as the aft-fide was formed. The water-lines on the fore-fide of the plane of the fashion-piece must, however, be first drawn in fig. 13. thus: Draw the lines e b, c d parallel to WM, and whose perpendicular distances therefrom may be equal to a c and z e (fig. 15.), respectively. Draw a line parallel to a A through the point where the line c d intersects the fifth water-line. Draw a line parallel to a A through the point where the fourth water-line intersects the line c d, in like manner proceed with the other water-lines. The fore-fide of the fashion-piece is now to be described by means of these new water-lines, observing that the distances in the floor-plane must be set off from the line e b, and not from WM, as in the former case; and a curve described through the points 5, 3, 2, 1, where these distances reach to, will represent the fore-fide of the fashion-piece.

The nearest distance between the points 5, 3, 2, 1, and the aft-fide of the fashion-piece is what the bevelling is beyond the square when both stock and tongue of the bevel are perpendicular to the timber. Make M p (fig. 16.) equal to the breadth of the timber, and M 5 equal to the perpendicular distance of the point 5 (fig. 13.) from the aft-fide of the fashion-piece, and join 5 p. In like manner proceed with the others, and the bevellings at these parts will be obtained; but, in order to avoid confusion, the perpendiculars 4, 3, 2, (fig. 13.), instead of being laid off from M (fig. 16.), were set off from points as far below M as the other extremities of the lines drawn from these points are below the point p.

PROB. VIII. To describe the tranfoms of a round poop.

The tranfoms are fastened to the stern-post in the same manner that the floor-timbers are fastened to the keel, and have a rising called the flight similar to the rising of the floor-timbers. The upper tranform is called the wing tranform, the next the deck tranform, and the others the first, second, and third tranfoms in order. The wing tranform has a round aft and a round up: the round up of the deck tranform is the same as that of the beams.

The fashion-piece of a square tuck must be first described, together with the three adjacent frames, by the method to be explained. The part of the stern above the wing tranform is to be described in the same manner as before, and may therefore be omitted in this place. The part below the keel of the fashion-piece is also the same in both cases. Let fig. 17. represent the fashion-piece of a square tuck, and the three adjoining frames. Divide the interval AB into four equal parts in the points C, D, E, and draw the perpendiculars AF, CG, DH, EI, and BK: these will be portions of water-lines answering to the several tranfoms.

Let these water-lines be described on the floor-plan (fig. 18.), in which ABC represents the wing tranform. Describe the arch b C to reconcile the curves A b and CE. Let LFG be the water-line answering to the lower part of the fashion-piece, the distance between the points L and A being equal to the excess of the projection of the point A beyond that of B (fig. 20.). Draw CK (fig. 18.) perpendicular to AM, and make the angle KCM equal to about 25 degrees, and CN will be the projection of the fashion-piece on the floor-plane. Make AB (fig. 19.) equal to AB (fig. 17.). Divide it into four equal parts, and draw the perpendiculars AF, CH, DI, EK, and BG. Make AF equal to CM, and BG equal to MN, and draw the curve FHKG, having a less curvature than the fashion-piece of the square tuck r p g n. Make MO, MP, MQ, equal to CH, DI, and EK respectively. Divide AL (fig. 18.) into four equal parts, and to these points of division draw curves through the points O, P, Q, so as to partake partly of the curvature of A b CE and partly of that of LNF, but most of the curvature of that to which the proposed curve is nearest; and hence the form of the several tranfoms will be obtained.

In order to represent the curve of the fashion-piece on the plane of projection, make the lines AF, CG, DH, EI, and BK, (fig. 17.) respectively equal to the perpendicular distance of the points C, O, P, Q, and N. From the line AN (fig. 18.), and through the extremities of these lines, draw the curve FGHIK.

It remains to lay down the projection of the fashion-piece on the plane of elevation. In order to which, divide the line AB, fig. 20. (equal to AB fig. 17.) into four equal parts, and through the points of division draw the perpendiculars AF, CG, DH, EI, and BK; make AF (fig. 20.) equal to the perpendicular distance of the point C from the line BL (fig. 18.). In like manner make the lines CG, DH, EI, and BK (fig. 20.) respectively equal to the perpendicular distances of the points O, P, Q, and N, from the line BL (fig. 18.); and a curve drawn through these points will be the projection of the fashion-piece on the plane of elevation.

PROB. IX. To describe the intermediate frames in the after body.

For this purpose the midship and stern frames must be drawn in the plane of projection. As the main frame contains the greatest capacity, and the stern frame is that having the least, it hence follows that the form and dimensions of the intermediate frames will be between these; each frame, however, partaking most of the form of that to which it is nearest.

Let ACDE (fig. 21.) be the main frame on the plane of projection, and FGH the stern frame; and let there be any convenient number of intermediate frames, as nine. Draw the floor ribband CF, and the breadth ribband GD. Divide the curves CD, FG, each into the same number of equal parts, as three, in the points K, M; L, N; and draw the second and third ribbands KL, MN. In order to divide these ribbands so as to form fair curves in different sections, various methods have been proposed. One of the best of these, being that which is chiefly employed by the French construct- Preliminary tors, is by means of an equilateral triangle, which is constructed as follows.

Draw the line ME (fig. 22.), limited at M, but produced towards E: take MI equal to any convenient extent; make I, 2 equal to three that extent, 2, 3 equal to five times, and 3, 4 equal to seven times the above extent; and continue this division to E, always increasing by two, until there be as many points as there are frames, including the main and stern frames. Upon ME describe the equilateral triangle MSE, and draw lines from the vertex S to each point of division; then the line SM will be that answering to the main frame, and SE that corresponding to the post; and the other lines will be those answering to the intermediate frames in order.

Let fig. 23. be the projection of part of the stern on the plane of elevation, together with the eighth and ninth frames. From the points L, N, G, (fig. 21.) draw the lines LO, NP, GO perpendicular to the plane of the upper edge of the keel. Make AB (fig. 23.) equal to AF (fig. 21.), and draw the water line BCD. Draw the line BC (fig. 22.) so that it may be parallel to the base of the triangle, and equal to CD (fig. 23.), which produce indefinitely towards H. Make BD equal to BC (fig. 23.), and draw the dotted line SD (fig. 22.). The ribband FC (fig. 21.) is to be applied to the triangle, so that it may be parallel to the base, and contained between the line MS and the dotted line SD. Let ef represent this line; then transfer the several divisions from ef to the ribband CF (fig. 21.), and number them accordingly. Again, make EF (fig. 23.) equal to LO (fig. 21.), and draw the water line FGH; make BF (fig. 22.) equal to FG (fig. 23.), and draw the dotted line SF; apply the second ribband LK to the triangle, so that the extremity K may be on the line SM, and the other extremity L on the dotted line SF, and making with SM an angle of about 62½ degrees. Let k l be this line, and transfer the divisions from it to the ribband KL. In like manner make IK (fig. 23.) equal to NP (fig. 21.), and draw the water line KLM. Make BG (fig. 22.) equal to KL (fig. 23.), and draw the dotted line SG; then the ribband MN is to be applied to the triangle in such a manner that its extremities M and N may be upon the lines SM, SG respectively, and that it may make an angle of about 68 degrees with the line SM; and the divisions are to be transferred from it to the ribband MN. The same process is to be followed to divide the other ribbands, observing to apply the fourth ribband to the triangle, so that it may make an angle of 86 degrees with the line SM; the fifth ribband to make an angle of 65 degrees, and the sixth an angle of 60 degrees with the line SM.

The quantities of these angles are, however, far from being precisely fixed. Some constructors, in applying the ribbands to the triangle, make them all parallel to its base; and others vary the measures of these angles according to fancy. It may also be remarked, that a different method of dividing the base of the triangle is used by some. It is certainly proper to try different methods; and that is to be preferred which best answers the intended purpose.

Beside the frames already mentioned, there are other two laid down by some constructors in the several plans, called balance frames. The after balance frame is placed at one fourth of the length of the ship before the stempost; and the other, commonly called the loof frame, at one fourth of the ship's length aft of a perpendicular to the keel from the rabbet of the stem. Let the dotted line at X, between the fifth and sixth frames, (fig. 23.) be the place of the after balance frame in the plane of elevation. Then, in order to lay down this frame in the plane of projection, its representation must be previously drawn in the triangle. To accomplish this, draw the line SV (fig. 22.) so that the interval 5 V may have the same ratio to 5 6 (fig. 22.) that 5 X has to 5 6 (fig. 23.) (d). Then the several points in the ribbands in the plane of projection answering to this frame are to be found by means of the triangle in the same manner as before.

The loof frame is nearly of the same dimensions as the after balance frame, or rather of a little greater capacity, in order that the centre of gravity of that part of the ship may be nearly in the plane of the midship frame. Hence the loof frame may be easily drawn in the plane of projection, and hence also the other frames in the fore body may be readily described.

Prob. X. To describe the frames in the fore body.

Draw the middle line of the stem AB (fig. 24.); Fig. 24. make AC, BD each equal to half the thickness of the stem, and draw the line CD; describe also one half of the main frame CEFGHI. Let e E, f F, g G, h H, be water lines at the heights of the ribbands on the main frame; also let a be the termination of the floor ribband, and b that of the breadth ribband on the stem. Divide the interval a b into three equal parts in the points c, d, and draw the ribbands a E, c F, d G, and b H. Make e i, f k, g l, h m (fig. 24.) equal to e i, f k, g l, h m (fig. 21.) respectively, and draw the curve Ci k l m, which will be the projection of the loof frame. Or since it is necessary that the capacity of the loof frame should be a little greater than that of the after balance frame, each of the above lines may be increased by a proportional part of itself, as one tenth or one twentieth, as may be judged proper.

Construct the triangle (fig. 25.) in the same manner as fig. 22. only observing, that as there are fewer frames in the fore than in the after body, its base will therefore be divided into fewer parts. Let there be eight frames in the fore body, then there will be eight divisions in the base of the triangle beside the extremes.

Let fig. 26. represent the stem and part of the forebody in the plane of elevation, and let O be the place of the loof frame. Divide the interval 4, 5 (fig. 25.) so that 4, 5 may be to 4 Z as 4, 5 to 4, o (fig. 26.), and draw the dotted line SZ, which will be the line denoting the loof frame in the triangle.

Draw the lines AB, CD, EF, GH (fig. 26.) parallel to the keel, and whose perpendicular distances therefrom may be equal to C a, C c, C d, C b, (fig. 24.) the intersections

(d) It is evident, from the method used to divide the base of the triangle, that this proportion does not agree exactly with the construction: the difference, however, being small, is therefore neglected in practice. Preliminary intersections of these lines with the rabbet of the stem, Problems, namely, the points I, K, L, M will be the points of termination of the several ribbands on the stem in the plane of elevation. Divide 8 A (fig. 25.) so that 8 B, 8 C, 8 D, and 8 E, may be respectively equal to BI, DK, FL, and HM (fig. 26.), and draw the dotted lines SB, SC, SD, SE (fig. 25.). Apply the edge of a flip of card to the first ribband (fig. 24.), and mark thereon the extremities of the ribband a, E, and also the point of intersection of the loof frame. Then apply this flip of card to the triangle in such a manner that the point a may be on the dotted line SB, the point E on the line SM, and the point answering to the loof frame on the dotted line SZ; and mark upon the card the several points of intersection of the lines S 1, S 2, &c. Now apply the card to the ribband a E (fig. 24.) as before, and transfer the several points of division from it to the ribband. In like manner proceed with the other ribbands; and lines drawn through the corresponding points in the ribbands will be the projection of the lower part of the frames in the fore body. The projections of the top-timbers of the several frames may be taken from the half breadth plan; and hence each top-timber may be easily described.

In large ships, particularly in those of the French navy, a different method is employed to form the top-timbers in the fore body, which is as follows:

Let BI (fig. 27.) be one-fourth of the breadth of the ship, and draw IK parallel to AB. Take the height of the foremost frame from the plane of elevation, and lay it off from A to B: from the point B draw BH perpendicular to AB, and equal to half the length of the wing transom. Let E be the place of the breadth ribband on the main frame, and F its place on the stem at the height of the wing transom. With a radius equal to five-sixths of half the greatest breadth of the ship describe the quadrant EFG (fig. 28.); Make EH equal to FG (fig. 27.), the point F being at the height of the wing transom. Through H draw HO perpendicular to EH, and intersecting the circumference in O; then draw OL parallel to HE, and EL parallel to HO. Divide EL into as many equal parts as there are frames in the fore body, including the main frame, and from these points of division draw the perpendiculars 11, 22, &c. meeting the circumference as in the figure. Take the distance 11, and lay it off from G (fig. 27.) towards F to the point 1; and from the same point G lay off towards F the several perpendiculars contained between the straight line and the curve to the points 2, 3, &c. and through these points draw lines parallel to EG.

Take any line AB (fig. 29.) at pleasure: divide it equally in two in the point 8: divide 8 B in two parts in the point 7, and continue this method of division until there are as many points as there are frames in the fore body, including the main frame. Upon AB construct the equilateral triangle ACB, and draw the line C 8, C 7, &c. Place a flip of card on the parallel a K 8 (fig. 27.), and mark thereon the points opposite to a, K, and 8; and let them be denoted accordingly. Then apply this flip of card to the triangle, so that the point a, which is that answering to the rabbet of the stem, may be on the line AC; that the point answering to K may be on CS, and the extremity 8 on the line CB; and mark on the card the points of intersection of the lines C 7, C 6, &c. and number them accordingly. Now apply this flip of card to the seventh parallel (fig. 23.), the point a being on the line CD, and mark on this parallel the point of intersection 7; slide the card down to the sixth parallel, to which transfer the point N° 6. In like manner proceed with the other parallels.

The point K, at the intersection of the line IK with the eighth parallel, is one point through which the eighth frame passes. From this point upwards a curve is to be described so as to reconcile with the lower part of this frame already described, and the upper part, forming an inverted arch, which is to terminate at H. This top-timber may be formed by two sweeps, whose radii and centres are to be determined partly from circumstances and partly according to fancy. It however may be more readily formed by hand.

Let LM (fig. 27.) be the line of the second deck at the main frame, and let LN be the difference of the draught of water, if any. Make GN (fig. 28.) equal to LN; draw NM perpendicular to GN, meeting the circle in M; and through the points G and M draw the parallels GV and MV; divide GN as before, and from the several points of division draw perpendiculars terminating in the curve. Transfer these perpendiculars from L upwards (fig. 27.), and through the points thus found draw the lines 11, 22, &c. parallel to LM. Apply a flip of card to the eighth parallel, and mark upon it the point answering to the stem, the eighth and main frames: carry this to the triangle, and place it so that these points may be on the corresponding lines. Then the points of intersection of the lines C 7, C 6, &c. are to be marked on the card, which is now to be applied first to the eighth parallel (fig. 27.), then to the seventh, &c. transferring the several points of division in order as before.

Draw the line HO (fig. 27.); mark its length on a flip of card, and apply it to the triangle, so that it may be parallel to its base, and its extremities one on the eighth and the other on the main frame: mark on the card the points of intersection of the several intermediate lines as before; then apply the card to HO, and transfer the divisions.

There are now three points determined through which each top-timber must pass, namely, one in the breadth ribband, one in the fifth, and one in the upper ribband. Through these curves are to be described, so as to reconcile with the lower part of the frame, and partake partly of the curvature of the eighth frame, and partly of that of the main frame, but most of that of the frame to which it is nearest: and hence the plane of projection is so far finished, that it only remains to prove the several frames by water lines.

Another method of describing the frames in the body plan is by sweeps. In this method it is necessary, in the first place, to describe the height of the breadth lines, and the rifing of the floor, in the plane of elevation. The half breadth lines are next to be described in the floor plan. The main frame is then to be described by three or more sweeps, and giving it such a form as may be most suitable to the service the ship is designed for. The lower, upper, and top-timber heights of breadth, and the rifings of the floor, are to be set upon the middle line in the body plan, and the several half breadths are then to be laid off on lines drawn through Preliminary these points perpendicular to the middle line. A mould Problems. may then be made for the main frame, and laid upon the several risings, as in whole mouldings, explained in Chapter V. with this difference, that here an under breadth sweep is described to pass through the point which limits the half breadth of the timber, the centre of which will be in the breadth line of that timber. The proper eccentres for all the frames being found, and the arches described, the bend mould must be placed on the rising line of the floor that the back of it may touch the back of the under breadth sweep. But the general practice is, to describe all the floor sweeps with compasses, as well as the under breadth sweeps, and to reconcile these two by a mould which is an arch of a circle, its radius being the same with that of the reconciling sweep by which the midship frame was formed. It is usual for all the floor sweeps to be of the same radius; and in order to find their centres a line is formed on the floor plan for the half breadth of the floor. As this line cannot be described on the surface of a ship, it is therefore only an imaginary line. Instead of it some make use of a diagonal in the body plane to limit the half breadth of the floor upon every rising line, and to erect perpendiculars at the several intersections, in the same manner as for the midship frame.

After the sweeps are all described, recourse is had to moulds, or some such contrivance, to form the hollow of the timbers, much in the same manner as in whole moulding; and when all the timbers are formed, they must be proved by ribband and water lines, and altered, if necessary to make fair curves.

The preceding methods of describing the several planes or sections of a ship being well understood, it will be a very easy matter to construct draughts for any proposed ship: and as the above planes were described separately and independent of each other, it is therefore of little consequence which is first described. In the following application, however, the plane of elevation will be first drawn, then part of the floor plan, and lastly the body plan: and in connecting these plans the most rational and simple methods will be employed.

CHAP. IV. Application of the foregoing Rules to the Construction of Ships.

SECT. I. To construct a Ship intended to carry a considerable Burden in Proportion to her general Dimensions, and to draw little Water.

DIMENSIONS.

<table> <tr> <th>Length between the wing transom and a perpendicular from the rabbet of the stem at the height of breadth line</th> <th>F. In.</th> </tr> <tr> <td>Main half breadth moulded</td> <td>11 0</td> </tr> <tr> <td>Half breadth at the height of breadth line at the stern</td> <td>7 6</td> </tr> <tr> <td>Top-timber half breadth</td> <td>10 6</td> </tr> <tr> <td>Height of the stem above the upper edge of the keel</td> <td>17 0</td> </tr> <tr> <td>Height of the breadth line at the stem</td> <td>13 6</td> </tr> <tr> <td>Height of the breadth line at the stern</td> <td>12 3</td> </tr> <tr> <td>Upper height of breadth at the main frame</td> <td>7 4</td> </tr> <tr> <td>Lower height of breadth</td> <td>5 10</td> </tr> <tr> <td>Height of middle line of wales at the stem</td> <td>10 0</td> </tr> <tr> <td>Height of middle line of wales at the main frame</td> <td>6 10</td> </tr> <tr> <td>Height of middle line of wales at the stern</td> <td>10 6</td> </tr> <tr> <td>Breadth of the wales</td> <td>1 9</td> </tr> <tr> <td>Height of top-timber at midships</td> <td>14 0</td> </tr> <tr> <td>at stern</td> <td>18 0</td> </tr> </table>

Height of middle line of wales at the main frame Height of middle line of wales at the stern Breadth of the wales Height of top-timber at midships at stern

Draw the line ab (fig. 30.) equal to 80 feet, from a convenient scale: divide it into as many equal parts plus one as there are to be frames, which let be 16, and through each point of division draw perpendiculars. Make bc equal to 17 feet, the perpendicular height of the top of the stem above the upper edge of the keel, and describe the stem by Prob. II. Make ad equal to 10 1/2 feet, the height of the middle line of the wales at the stern, and ae equal to the proposed rake of the post, which may be about 2 feet: join de; and draw the line fg representing the aft-side of the post. Describe the counter and stern by Problem VI. and VII. Make eh equal to 14 feet, the top timber height at the main frame, and rk equal to 18 feet, the height at the stern; and through the three points c, h, k, describe the curve limiting the top-timbers by Problem I. Make bd equal to 10 feet, the height of the middle line of the wales at the stem, and H equal to 6 feet 10 inches, the height at the main frame; and the curve dHd being described will represent the middle line of the wales. At the distance of 10 1/2 inches on each side of this line draw two curves parallel thereto, and the wales will be completed in this plan. Make bl equal to 13 1/2 feet, the height of the breadth line at the stem; am equal to 12 1/2 feet, the height at the stern, and K ⊕ equal to 5 feet 10 inches and 7 feet 4 inches respectively; and draw the upper breadth line /K m and lower breadth line /I m. From the line a b lay downwards the breadth of the keel, which may be about one foot, and draw the line L t parallel to a b.

Let the line L r, which is the lower edge of the keel, represent also the middle line of the floor plan. Produce all the perpendiculars representing the frames; make ⊕ M (fig. 31.) equal to 11 feet, the main half breadth at midships; through m (fig. 30.) draw the line mn perpendicular to ab, and make p N equal to 7 1/2 feet, and draw the main half breadth line NM r by Problem IV. Describe also the top-timber half breadth line PO r, ⊕ O being equal to 10 1/2 feet, and form the projecting part of the item q r s t.

In order that the top-timber line may look fair on the bow, and to prevent the foremost top-timbers from being too short, it is necessary to lift or raise the sheer from the round of the bow to the stem. For this purpose the following method is usually employed: Produce the circular sheer before the item in the plane of elevation at pleasure; then place a batton to the round of the bow in the half breadth plan, and mark on it the stations of the square timbers and the side of the stem; apply the batton to the sheer plan, and place it to the sheer of the ship, keeping the stations of the timbers on the batton well with those on the sheer plan for several timbers before dead-flat, where they will not alter; then mark the other timbers and the stem on the sheer line produced; through these points draw lines parallel to the keel, to intersect their corresponding timbers and the stem in the sheer plan: then a curve described these last points will be the sheer of the ship round

Application the bow, lifted as required: and the heights of the fore-timbers thus lengthened are to be transferred to the body plan as before.

Draw the line AB (fig. 32.) equal to 22 feet, the whole breadth; from the middle of which draw the perpendicular CD: make CE equal to half the thickness of the post, and CF equal to half that of the stem, and from the points A, E, F, B, draw lines parallel to CD. Make AG, BG each equal to 14 feet, the height at the main frame, and draw the line GG parallel to AB. Make GH, GH each equal to half a foot, the difference between the main and top timber half-breadths. From A and B set up the heights of the lower and upper breadth lines to I and K, and draw the straight lines IK, IK. Let CL be the rising at the main frame, and ⊕, ⊕ the extremities of the floor timber. Hence, as there are now five points determined in each half of the main frame, it may be very easily described.

Make CM equal to L⊕, join M⊕, and draw the other ribbands NO, PQ. In order, however, to simplify this operation, the rectilineal distance ⊕I was triflected, and through the points of division the lines NO, PQ were drawn parallel to the floor ribband M⊕.

Take the distance bc (fig. 30.), and lay it off from F to (fig. 32.); also make Fb (fig. 32.) equal to Fa (fig. 30.); through b draw bc parallel to AB, and equal to FR (fig. 31.). In like manner take the heights of each top timber from fig. 30. and lay them off from C towards D (fig. 32.); through these points draw lines parallel to AB, and make them equal each to each, to the corresponding half breadth lines taken from the floor-plan: Then through the several points a, c, &c. thus found, draw a line a c H, which will be the projection of the top-timber line of the fore body in the body plan. Proceed in the same manner to find the top-timber line in the after body.

Transfer the height of the main-breadth line on the stem b l (fig. 30.), from F to d (fig. 32.). Transfer also the heights of the lower and upper breadth lines at timber F (fig. 30.), namely, FW, FX, from F to e and f (fig. 32.); through which draw the parallels eg, fh; make them equal to FS (fig. 31.), and draw the straight line g h. In this manner proceed to lay down the portions of the extreme breadth at each frame, both in the fore and in the after body in the body plan, and draw the upper and lower breadth lines d k, d e i in the fore body and K i, I i in the after body. Hence the portions of the several top-timbers contained between the top-timber and main breadth lines may be easily described. It was before remarked that their forms were partly arbitrary. The midship top-timber has generally a hollow, the form of which is left entirely to the artifit, though in some ships, especially small ones, it has none. It is the common practice to make a mould for this hollow, either by a sweep or some other contrivance, which is produced considerably above the top-timber line, in a straight line or very near one. The midship top-timber is formed by this mould, which is so placed that it breaks in four with the back of the upper breadth sweep. The other top-timbers are formed by the same mould, observing to place it so that the straight part of it may be parallel to the straight part of the midship timber, and moved up or down, still keeping it in that direction till it just touches the back of the upper breadth sweep.

Some constructors begin at the after timber, after the Application mould is made for the midship top-timber, because they think it easier to keep the straight part of the mould parallel to this than to the midship timber; and by this means the top side is kept from winding. Others, again, make a mark upon the mould where the breadth line of the midship timber crosses it, and with the same mould they form the after timber: this will occasion the mark that was made on the mould when at the main frame to fall below the breadth line of the after timber, and therefore another mark is made at the height of the breadth line at the after timber; the straight part of the mould is then laid obliquely across the breadth lines of the top-timbers in such a manner that it may intersect the breadth line of the midship timber at one of these marks, and the breadth line of the after timber at the other mark; then the several intersections of the breadth lines of the timbers are marked upon the mould; which must now be so placed in forming each timber, that the proper mark may be applied to its proper breadth, and it must be turned about fo as just to touch the upper breadth sweep. Any of these methods may make a fair side, and they may be easily proved by forming another intermediate half breadth line.

The remaining parts of the frames may be described by either of the methods laid down in Problems IX. and X. In order, however, to illustrate this still farther, it is thought proper to subjoin another method of forming the intermediate frames, the facility of which will recommend it.

Take FZ (fig. 30.), and lay it from F to k (fig. 32.); then describe the lower part of the foremost frame, making it more or less full according as proposed; and intersecting the ribbands in the points l, m, n. Describe also the aftermost frame o, p, q. Make αβ (fig. 30.) equal to FR (fig. 32.), and produce it to a (fig. 31.); also draw γδ and εζ (figs. 30.) equal to Er and Es (fig. 32.) respectively; and produce them to b and c: Make Fe, Ff, FR (fig. 31.) equal to M l, N m, P n (fig. 32.) each to each. Let also ⊕ h, ⊕ i, ⊕ k, and 9 l, 9 m, 9 n (fig. 31.) be made equal to M⊕, NO, PQ, and M o, N q, P p (fig. 32.); then through these points trace the curves a e n h l b, r f i m c, and r R k n p, and they will be the projections of the ribbands in the floor plane. Now transfer the several intervals of the frames contained between the middle line and the ribbands (fig. 31.) to the corresponding ribbands in the body plan (fig. 32.). Hence there will be five points given in each frame, namely, one at the lower breadth line, one at each ribband, and one at the keel; and consequently these frames may be easily described. In order to exemplify this, let it be required to lay down the frame E in the plane of projection. Take the interval E n (fig. 31.), and lay it from M to u (fig. 32.). Lay off also Ev, E e (fig. 31.) from N to v and from P to n (fig. 32.); then through the points F, u, v, n and the lower breadth line describe a curve, and it will be the representation of the frame E in the body plan. In like manner the other frames may be described.

The ribbands may now be transferred from the body plan to the plane of elevation, by taking the several heights of the intersection of each ribband with the frames, and laying them off on the corresponding frames in the floor plan; and if the line drawn through these points Application points make a fair curve, it is presumed that the curves of the fore of the frames are rightly laid down in the body plan, going Rule? Only one of these ribbands, namely, the first, is laid to the Construction of Ships. These curves may also be farther proved, by drawing water lines in the plane of elevation, and in the body plan, at equal distances from the upper edge of the keel. Then the distances between the middle line of the body plan, and the several points of intersection of these lines with the frames, are to be laid off from the middle line in the floor plan upon the corresponding frames; and if the line drawn through these points form a fair curve, the frames are truly drawn in the body plan.

In figs. 30. and 32. there are drawn four water lines at any equal distances from the keel, and from each other. These lines are then transferred from fig. 32. to fig. 31.; and the lines passing through these points make fair curves.

The transoms are described by Problem VIII. it is therefore unnecessary to repeat the process. A rifling line of the floor timbers is commonly drawn in the plane of elevation.

As this is intended only as an introductory example, several particulars have therefore been omitted; which, however, will be exemplified in the following section.

SECT. IV. To describe the several Plans of a Ship of War proposed to carry 80 Guns upon two Decks.

As it is proposed in this place to show the method of describing the plans of a ship of a very considerable size, it therefore seems proper to give the dimensions of every particular part necessary in the delineation of these plans. The several plans of this ship are contained in figs. 33. &c. Figs. 33. &c. and 34. But as it would very much confuse the figures to have a reference to every operation, and as the former example is deemed a sufficient illustration, the letters of reference are upon these accounts omitted in the figures.

PRINCIPAL DIMENSIONS.

Ship Build.: Lengths.—Length on the gun or lower deck from the aft part of the rabbit of the stem to the aft part of the rabbet of the port 182 0 Length from the foremost perpendicular to dead flat 63 11 1/2 Length from the foremost perpendicular to timber Y 4 0 Length from after perpendicular to timber 37 3 4 Room and space of the timbers 2 8 1/2 Length of the quarter-deck from the aft part of the stern 95 0 Length of the forecastle from the fore part of the beak-head 49 0 Length of round-house deck from the aft part of the stern 51 8

Heights.—Height of the gun or lower deck from the upper edge of the keel to the under side of the plank at dead flat 24 0 Height of the gun or lower deck from the upper edge of the keel to the under side of the plank at foremost perpendicular 26 Height of the gun or lower deck from the upper edge of the keel to the under side of the plank at after perpendicular 26 3 Height from the upper side of the gun-deck plank to the under side of the upper deck plank, all fore and aft 7 0 Height from the upper side of the upper deck plank to the under side of the greater deck plank afore and abaft 6 10 6 11 Height to the under side of forecastle plank, afore and abaft 6 6 Height from the upper side of the quarter-deck plank to the under side of the round-house plank afore and abaft 6 9 6 10 Height of the lower edge of the main wales at foremost perpendicular 24 6 Height of the lower edge of the main wales at dead flat 20 0 Height of the lower edge of the main wales at after perpendicular 26 6 Height of the lower edge of the channel wales at foremost perpendicular 32 6 Height of the lower edge of the channel wales at dead flat 29 0 Height of the lower edge of the channel wales at after perpendicular 34 0 Height of the upper side of the wing transom 28 4 Height of the touch of the lower counter at the middle line 33 5 Height of the touch of the upper counter at the middle line 36 2 Height of the top-timber line at the after part of the stern timber 44 7

Breadths.—Main wales in breadth from lower to upper edge 4 6 Channel wales in breadth from lower to upper edge 3 0 Waist rail in breadth 0 7 Distance between the upper edge of the channel wales and the under edge of the waist rail 2 9 Sheer rail in breadth 0 6 Distance between the sheer rail and the rail above from timber 13 to the stern 2 5 Distance between the sheer rail and the rail above from timber 7 to timber 11 1 4 Distance between the sheer rail and the rail above from timber C to the forepart of beak-head 1 2 And the said rail to be in breadth 0 6 Plank sheer to be in thickness 0 2 1/2

Centres of the masts.—From the foremost perpendicular to the centre of the mainmast on the gun-deck 103 2 From the foremost perpendicular to the centre of the foremast on the gun-deck 29 5 From the after perpendicular to the centre of the mizenmast on the gun-deck 28 6

Stem.—The centre of the sweep of the stem abaft timber P 0 4 Height of ditto from the upper edge of the keel 26 1 Stem moulded 1 3

Foremost part of the head afore the perpendicular - - - 2 4 Height of ditto from the upper edge of the keel - - - 38 3 Stern-porf.—Aft part of the rabbet afore the perpendicular on the upper edge of the keel - - - 3 4 Aft part of the port abaft the rabbet at the upper edge of the keel - - - 2 6 Aft part of the port abaft the rabbet at the wing transom - - - 1 1 Stern-port fore and aft on the keel - - - 3 1 Ditto square at the head - - - 2 0 1/2 Counters.—The touch of the lower counter at the middle line, abaft the aft part of the wing transom - - - 7 6 Round aft of the lower counter - - - 1 4 Round up of the lower counter - - - 0 9 The touch of the upper counter at the middle line, abaft the aft part of the wing transom - - - 9 9 Round aft of the upper counter - - - 1 3 1/2 Round up of the upper counter - - - 0 10 Aft part of the stern-timber at the middle line, at the height of the top-timber line, abaft the aft part of the wing transom 12 6

F. In. Round aft of the wing transom - - Round up of the wing transom - - Draught of water.—Load draught of water from the upper edge of the keel afore abaft 20 5 Channels.—Foremost end of the fore channel afore timber R - - - 1 0 The channel to be in length - - - 37 0 And in thickness at the outer edge - - - 0 4 1/2 The dead eyes to be 12 in number, and in diameter - - - 1 6 Foremost end of the main channel afore timber 9 - - - 0 10 The channel to be in length - - - 38 0 And in thickness at the outer edge - - - 0 4 1/2 The dead eyes to be 14 in number, and in diameter - - - 1 6 Foremost end of the mizen-channel abaft timber 27 - - - 2 4 The channel to be in length - - - 20 0 And in thickness at the outer edge - - - 0 4 The dead eyes to be 7 in number, and in diameter - - - 1 0

F. In. Application: of the foregoing Rules to the Construction of Ships.

DIMENSIONS of the several Parts of the Bodies.

<table> <tr> <th rowspan="2">Fore Body.</th> <th colspan="10">Timbers Names.</th> </tr> <tr> <th>⊕</th><th>C</th><th>G</th><th>L</th><th>P</th><th>T</th><th>W</th><th>Y</th><th>Outside</th> </tr> <tr> <td>Lower height of breadth</td> <td>22</td><td>6</td><td>22</td><td>6</td><td>22</td><td>7</td><td>23</td><td>0</td><td>23</td><td>11</td><td>25</td><td>7</td><td>26</td><td>10</td><td>28</td><td>8</td> </tr> <tr> <td>Upper height of breadth</td> <td>24</td><td>10</td><td>24</td><td>10</td><td>24</td><td>10</td><td>25</td><td>3</td><td>26</td><td>4</td><td>27</td><td>4 1/2</td><td>29</td><td>0</td><td></td><td></td> </tr> <tr> <td>Height of the top-timber line *</td> <td>37</td><td>5</td><td>37</td><td>7</td><td>38</td><td>0</td><td>38</td><td>5</td><td>39</td><td>1</td><td>39</td><td>10</td><td>40</td><td>4</td><td>40</td><td>9</td> </tr> <tr> <td>Height of the cutting down</td> <td>2</td><td>3 1/2</td><td>2</td><td>3 1/2</td><td>2</td><td>3 1/2</td><td>2</td><td>8</td><td>3</td><td>10</td><td>6</td><td>4</td><td></td><td></td><td></td><td></td> </tr> <tr> <td>Main half breadth</td> <td>24</td><td>5 1/2</td><td>24</td><td>5 1/2</td><td>24</td><td>4 1/2</td><td>24</td><td>0 1/2</td><td>23</td><td>2 1/2</td><td>20</td><td>2</td><td>17</td><td>0</td><td>11</td><td>0 1/2</td> </tr> <tr> <td>Top-timber half breadth</td> <td>20</td><td>11</td><td>20</td><td>10</td><td>20</td><td>9</td><td>20</td><td>6</td><td>20</td><td>0</td><td>18</td><td>9 1/2</td><td>17</td><td>10</td><td>16</td><td>6</td> </tr> <tr> <td>Half breadth of the rifing</td> <td>8</td><td>7</td><td>8</td><td>4</td><td>6</td><td>5 1/2</td><td>2</td><td>9</td><td>5</td><td>7</td><td></td><td></td><td></td><td></td><td></td><td></td> </tr> <tr> <td>Length of the lower breadth sweeps</td> <td>19</td><td>2</td><td>18</td><td>9</td><td>18</td><td>3</td><td>17</td><td>3</td><td>15</td><td>11</td><td>14</td><td>1</td><td>12</td><td>7</td><td>12</td><td>0</td> </tr> <tr> <td>First diagonal line</td> <td>7</td><td>9</td><td>7</td><td>8 1/2</td><td>7</td><td>7</td><td>7</td><td>1</td><td>6</td><td>3</td><td>3</td><td>8</td><td></td><td></td><td></td><td></td> </tr> <tr> <td>Second ditto</td> <td>13</td><td>9</td><td>13</td><td>8 1/2</td><td>13</td><td>4 1/2</td><td>12</td><td>1</td><td>10</td><td>3</td><td>7</td><td>1 1/2</td><td>4</td><td>6</td><td></td><td></td> </tr> <tr> <td>Third ditto</td> <td>20</td><td>0</td><td>19</td><td>11</td><td>19</td><td>2</td><td>17</td><td>7</td><td>15</td><td>1 1/2</td><td>1</td><td>8</td><td>3 1/2</td><td>3</td><td>4 1/2</td><td>0</td> </tr> <tr> <td>Fourth ditto</td> <td>23</td><td>4 1/2</td><td>23</td><td>4 1/2</td><td>23</td><td>0</td><td>21</td><td>8 1/2</td><td>18</td><td>11</td><td>14</td><td>8 1/2</td><td>11</td><td>5</td><td>6</td><td>0</td> </tr> <tr> <td>Fifth ditto</td> <td>24</td><td>8</td><td>24</td><td>8</td><td>24</td><td>4 1/2</td><td>23</td><td>5 1/2</td><td>21</td><td>2 1/2</td><td>17</td><td>1</td><td>13</td><td>8 1/2</td><td>7</td><td>11</td> </tr> <tr> <td>Sixth ditto</td> <td>24</td><td>1 1/2</td><td>24</td><td>1 1/2</td><td>24</td><td>0</td><td>23</td><td>9</td><td>22</td><td>10</td><td>20</td><td>10 1/2</td><td>18</td><td>6 1/2</td><td>14</td><td>7</td> </tr> </table>

* Rising height 11 feet 10 inches at dead flat, from which all the other risings must be set off. <table> <tr> <th rowspan="2">After Body.</th> <th colspan="13">Timbers Names.</th> </tr> <tr> <th>1</th><th>5</th><th>9</th><th>13</th><th>17</th><th>21</th><th>25</th><th>29</th><th>33</th><th>35</th><th>37</th> </tr> <tr> <td>Lower height of breadth</td><td>22</td><td>6</td><td>22</td><td>6</td><td>22</td><td>6</td><td>20</td><td>7 1/2</td><td>22</td><td>9</td><td>23</td><td>5 1/2</td><td>27</td><td>7 1/2</td><td>24</td><td>6</td><td>25</td><td>10 1/2</td><td>26</td><td>9 1/2</td><td>28</td><td>3</td> </tr> <tr> <td>Upper ditto</td><td>24</td><td>10</td><td>24</td><td>10</td><td>24</td><td>10</td><td>24</td><td>11</td><td>25</td><td>1</td><td>25</td><td>4 1/2</td><td>25</td><td>8</td><td>26</td><td>3</td><td>27</td><td>1</td><td>27</td><td>9</td><td>28</td><td>8</td> </tr> <tr> <td>Height of the top-timber line</td><td>37</td><td>5</td><td>37</td><td>5</td><td>37</td><td>5</td><td>37</td><td>10</td><td>38</td><td>3</td><td>38</td><td>11</td><td>39</td><td>8</td><td>40</td><td>6</td><td>41</td><td>5</td><td>42</td><td>0</td><td>42</td><td>6</td> </tr> <tr> <td>Height of the cutting down</td><td>2</td><td>3 1/2</td><td>2</td><td>3 1/2</td><td>2</td><td>3 1/2</td><td>2</td><td>3 1/2</td><td>2</td><td>4</td><td>2</td><td>7 1/2</td><td>3</td><td>5</td><td>2 1/2</td><td>8</td><td>7</td> </tr> <tr> <td>Height of the rifing</td><td>0</td><td>2 1/2</td><td>0</td><td>8 1/2</td><td>1</td><td>9</td><td>3</td><td>6 1/2</td><td>6</td><td>0</td><td>10</td><td>1</td><td>17</td><td>0</td> </tr> <tr> <td>Main half breadth</td><td>24</td><td>5 1/2</td><td>24</td><td>4 1/2</td><td>24</td><td>4 1/2</td><td>24</td><td>3 1/2</td><td>24</td><td>1</td><td>23</td><td>8 1/2</td><td>23</td><td>8 1/2</td><td>21</td><td>10</td> </tr> <tr> <td>Half breadth of the rifing</td><td>8</td><td>6</td><td>8</td><td>3</td><td>7</td><td>9</td><td>6</td><td>10 1/2</td><td>5</td><td>3 1/2</td><td>2</td><td>8</td><td>2</td><td>6</td><td>Outside</td> </tr> <tr> <td>Top-timber half breadth</td><td>25</td><td>11</td><td>20</td><td>10</td><td>20</td><td>9 1/2</td><td>20</td><td>9</td><td>20</td><td>7</td><td>20</td><td>3</td><td>19</td><td>5</td><td>18</td><td>2</td><td>16</td><td>8</td><td>15</td><td>10 1/2</td><td>15</td><td>0 1/2</td> </tr> <tr> <td>Topfides half breadth</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td> </tr> <tr> <td>Length of lower breadth sweeps</td><td>19</td><td>2</td><td>19</td><td>2</td><td>19</td><td>0</td><td>18</td><td>7</td><td>17</td><td>1</td><td>16</td><td>0</td><td>14</td><td>5</td><td>12</td><td>5</td><td>9 1/2</td><td>7 1/2</td><td>11</td><td>4</td><td>8</td> </tr> <tr> <td>Fifth diagonal</td><td>7</td><td>9</td><td>7</td><td>8 1/2</td><td>7</td><td>7</td><td>5 1/2</td><td>7</td><td>6</td><td>7</td><td>5</td><td>9</td><td>4</td><td>7</td><td>2</td><td>10</td><td>1</td><td>8 1/2</td><td>0</td><td>7</td> </tr> <tr> <td>Second ditto</td><td>13</td><td>9</td><td>13</td><td>8 1/2</td><td>13</td><td>6 1/2</td><td>12</td><td>6</td><td>11</td><td>2</td><td>9</td><td>7</td><td>7</td><td>4</td><td>8 1/2</td><td>3</td><td>1</td><td>0</td><td>11</td> </tr> <tr> <td>Third ditto</td><td>20</td><td>19</td><td>11 1/2</td><td>19</td><td>7 1/2</td><td>19</td><td>0</td><td>18</td><td>1 1/2</td><td>16</td><td>6</td><td>14</td><td>2</td><td>11</td><td>5 1/2</td><td>7</td><td>8 1/2</td><td>5 1/2</td><td>5</td><td>2</td><td>14</td> </tr> <tr> <td>Fourth ditto</td><td>23</td><td>4 1/2</td><td>23</td><td>3</td><td>23</td><td>1 1/2</td><td>22</td><td>6 1/2</td><td>21</td><td>11</td><td>20</td><td>3</td><td>18</td><td>0</td><td>15</td><td>3 1/2</td><td>11</td><td>4</td><td>8</td><td>7</td><td>4</td><td>6 1/2</td> </tr> <tr> <td>Fifth ditto</td><td>24</td><td>8</td><td>24</td><td>7</td><td>24</td><td>6</td><td>24</td><td>1 1/2</td><td>23</td><td>6 1/2</td><td>22</td><td>3</td><td>20</td><td>6 1/2</td><td>8</td><td>2</td><td>14</td><td>4</td><td>11</td><td>3</td><td>7</td><td>0</td> </tr> <tr> <td>Sixth ditto</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td> </tr> <tr> <td>Seventh ditto</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td> </tr> <tr> <td>23</td><td>9 1/2</td><td>23</td><td>0</td><td>21</td><td>8 1/2</td><td>20</td><td>0</td><td>18</td><td>11</td><td>17</td><td>8 1/2</td> </tr> </table>

Diagonal Lines for both the Fore and After Bodies.

<table> <tr> <th rowspan="2">Fore and After Bodies.</th> <th colspan="7">Names of the Diagonal Lines.</th> </tr> <tr> <th>1st</th><th>2d</th><th>3d</th><th>4th</th><th>5th</th><th>6th</th><th>7th</th> </tr> <tr> <td>Height up the middle line</td><td>6</td><td>11</td><td>11</td><td>4</td><td>16</td><td>5 1/2</td><td>20</td> </tr> <tr> <td>Distance from the middle line on the base line</td><td>4</td><td>8</td><td>9 1/2</td><td>1</td><td>15</td><td>6</td><td></td> </tr> <tr> <td>Height up the side line</td><td></td><td></td><td></td><td></td><td>0</td><td>9 1/2</td><td>6</td> </tr> <tr> <td></td><td></td><td></td><td></td><td></td><td>7</td><td>12</td><td>7 1/2</td> </tr> <tr> <td></td><td></td><td></td><td></td><td></td><td>3 1/2</td><td>32</td><td>8 1/2</td> </tr> </table>

I. Of the Sheer Draught or Plane of Elevation.

Draw a straight line (fig. 33.) to represent the upper edge of the keel, erect a perpendicular on that end to the right, and from thence fet off 182 feet, the length on the gun-deck, and there erect another perpendicular; that to the right is called the foremost perpendicular, and the other the after one : upon these two perpendiculars all the foremost and aftermost heights must be fet off, which are expressed in the dimensions.

Then fet off the distance of the main frame or dead flat from the foremost perpendicular, and at that place erect a third perpendicular, which must be distinguished by the character ⊕. From dead flat the room and space of all the timbers must be fet off ; but it will only be necessary to erect a perpendicular at every frame timber; which in the fore body are called dead flat, A, C, E, &c. and in the after body (2), 1, 3, 5, &c.: hence the distance between the frame perpendiculars will be double the room and space expressed in the dimensions. Then fet off the heights of the gun-deck afore at midship or dead flat, and abaft from the upper side of the keel ; and a curve described through these three points will be the upper side of the gun-deck. Set off the thickness of the gun-deck plank below that ; and another curve being drawn parallel to the former, the gun-deck will then be described at the middle line of the sheer plan.

The centre of the stem is then to be laid down by means of the table of dimensions ; from which centre, with an extent equal to the nearest distance of the upper edge of the keel, describe a circle upwards : describe also another circle as much without the former as the stem is moulded. Then fet off the height of the head of the stem, with the distance afore the perpendicular, and there make a point ; and within that fet off the moulding of the stem, and there make another point : from this last-mentioned point let a line pass downwards, intersecting the perpendicular at the height of the gun-deck, and breaking in fair with the inner circle, and the after part of the stem is drawn. Draw another line from the foremost point downwards, parallel to the former, and breaking in fair with the outer circle ; then the whole item will be formed, except the after or lower end, which cannot be determined till hereafter.

The stern-post must be next formed. Set off on the upper edge of the keel a spot for the aft part of the rabbet taken from the dimensions, and from that forward fet off another point at the distance of the thick- ness of the plank of the bottom, which is four inches and a half; and from this last-mentioned point draw a line upwards intersecting the perpendiculars at the height of the lower deck; then set up the perpendicular the height of the wing transom, and draw a level line, and where that line intersects, the line first drawn will be the aft side of the wing transom; on the upper part of the middle line set off from that place the distance of the aft side of the stern-post; set off also the distance of the after part from the rabbet on the upper edge of the keel, and a line drawn through these two points will be the aft side of the post. A line drawn parallel to the first drawn line at the distance of four inches and a half, the thickness of the plank on the bottom, will be the aft side of the rabbet: and hence the stern-post is described, except the head, which will be determined afterwards.

From the dimensions take the several heights of the upper deck above the gun-deck, afore, at midship, and abaft, and set them off accordingly; through these points describe a curve, which will be the under side of the upper deck; describe also another curve parallel thereto, at the distance of the thickness of the plank, and the upper deck will be then represented at the middle line of the ship.

Set off the height of the lower counter, at the middle line, from the upper edge of the keel, and draw a horizontal line with a pencil; then on the pencil line set off the distance the touch of the lower counter is abaft the aft side of the wing transom: from this point to that where the fore part of the rabbet of the stern-post intersects the line drawn for the upper part of the wing transom, draw a curve at pleasure, which curve will represent the lower counter, at the middle line. The height of the upper counter is then to be set off from the upper edge of the keel, and a horizontal line is to be drawn as before, setting off the distance the touch of the upper counter is abaft the aft side of the wing transom; and a curve described from thence to the touch of the lower counter will form the upper counter at the middle line.

Both counters being formed at the middle line, the upper part of the stern timber above the counters is to be described as follows: On the level line drawn for the upper side of the wing transom set off the distance of the aft side of the stern timber at the middle line from the aft side of the wing transom, at the height of the top-timber line, and erect a perpendicular: then upon this perpendicular, from the upper edge of the keel, set off the height at the middle line of the top timber line at the after side of the stern timber; through this point draw a straight line to the touch of the upper counter, and the upper part of the stern timber will be described.

As the stern rounds two ways, both up and aft, the stern timber at the fide will consequently alter from that at the middle line, and therefore remains to be represented. Take the round up of the upper counter from the dimensions, and set it below the touch at the middle, and with a pencil draw a level line; take also the round aft, and set it forward from the touch on the touch line, and square it down to the pencil line last drawn, and the point of intersection will be the touch of the upper counter at the fide. In the same manner find the touch of the lower counter; and a curve, similar to that at the middle line, being described from the one touch to the other, will form the upper counter of the fore-going Rules to the Construction of Ships.

Take the round up of the wing transom, and set it off below the line before drawn for the height of the wing transom, and draw another horizontal line in pencil: then take the round aft of the wing transom, and set it forward on the upper line from the point representing the aft side of the wing transom; square it down to the lower line, and the intersection will be the touch of the wing transom: then a curve, similar to that at the middle line, being drawn from the touch of the wing transom to the touch of the lower counter at the fide, will be the lower counter at the fide. Draw a line from the upper counter upwards, and the whole stern timber at the fide will be represented. But as the straight line drawn for the upper part of the fide timber should not be parallel to that at the middle line, its rake is therefore to be determined as follows.

Draw a line at pleasure, on which set off the breadth of the stern at the upper counter; at the middle of this line set off the round aft of the upper counter; then through this point and the extremities of the stern describe a curve. Now take the breadth of the stern at the top-timber line, and through the point where that breadth will intersect the curve for the round aft of the stern draw a line parallel to that first drawn, and the distance from the line last drawn to the curve at the middle of the line is the distance that the fide timber must be from the middle line at the height of the top-timber line.

The sheer is to be described, which is done by setting off the heights afore, at midships and abaft; and a curve described through these three points will be the sheer. But in order that the sheer may correspond exactly with the dimensions laid down, it will be necessary to proceed as follows: The perpendicular representing timber dead flat being already drawn, set off from that the distances of the other frame timbers, which is double the room and space, as the frames are only every other one; and erect perpendiculars, writing the name under each: then on each of these perpendiculars set off the corresponding heights of the top-timber line taken from the table of dimensions for constructing the bodies; and through these points a curve being described, will represent the sheer of the ship or top-timber line agreeable to the dimensions.

The quarter-deck and forecastle are next to be described, which may be done by taking their respective heights and lengths from the dimensions, and describing their curves. In the same manner also, the round-houfe may be drawn. The decks being described representing their heights at the middle, it is then necessary to represent them also at the fide. For this purpose take the round of the decks from the dimensions, and set them off below the lower line drawn for the middle; and a curve described both fore and aft, observing to let it be rather quicker than the former, will be the representation of the decks at the fide.

The ports come next under consideration. In the placing of them due attention must be paid, so as to preserve strength; or that they shall be so disposed as not to weaken the ship in the least, which is often done by cutting off principal timbers, placing them in too large openings, having too short timbers by the fide of them, Application them, &c. The frames represented by the lines all of the fore-ready drawn must be first consulted. Then with a going Rule, to the Con. pencil draw two curves, for the lower and upper parts of the lower deck posts, parallel to the line representing the lower deck; the distances of these lines from the deck are to be taken from the dimensions, observing, however, to add to these heights the thickness of the deck, as the deck line at the side represents the under part of the deck.

The foremost port is then to be described, observing to place it as far aft as to give sufficient room for the manger: the most convenient place will therefore be to put it between the frames R and T, and equally distant from each. It will then be placed in the most conspicuous point of strength, as it will have a long top-timber on the aft side and a long fourth futtock on the fore side of it. The second port may be placed in like manner between the next two frames, which will be equally well situated for strength as the former; and by proceeding in this manner, the ports on the gun deck may also be placed, taking care to have two frames between every two ports, all fore and aft.

The upper deck ports are then to be described; and in order to dispose of them in the strongest situation possible, they must be placed over the middle between the gun-deck ports, so that every frame in the ship will run up to the top of the side, by their coming between a gun and upper deck port; and every port will be between the frames, which will in a great measure contribute towards the strength of the ship. With regard to the ports on the quarter deck, it is not of such material consequence if they cut the head of the frame, as in placing them the situation of the dead eyes must be considered, placing a port where there is a vacancy between the dead eyes large enough to admit of one; observing always to place them as nearly as possible at equal distances from each other; and where it happens that they do not fall in the wake of a frame, then that frame must by all means be carried up to the top of the side.

The necessary length of the round-house being determined in the dimensions, it may be set off; observing, however, to let it be no longer than is just sufficient for the necessary accommodations, as the shorter the round-house the works abaft may be kept lower, and a low snug stern is always accounted the handsomest. Then set off the round of the deck at the foremost end, below the line drawn; the deck at the side may be described by another curve drawn quite aft. Now, from the point for the round of the deck to the stern-timber, draw a curve parallel to the top-timber line, and that will be the extreme height of the top of the side abaft, which height continues to range fair along to the foremost end of the round-house, and at that place may have a fall about 14 inches, which may be turned off with a drift scroll. At the fore part of the quarter-deck, the topside may have a rise of 14 inches, which may also be turned off with a scroll. But as the raising of the topside only 14 inches at that place will not be sufficient to unite with the heights abaft, it will therefore be necessary to raise 14 inches more upon that, and break it off with a scroll inverted on the first scroll, and continue these two lines, parallel to the top-timber line, to the distance of about seven feet aft. At the foremost end of the round-house there is a break of 14 inches already mentioned; and in order to make that part uniform with the breaks at the foremost end of the quarter-deck, there must be set down 14 inches more below the former; and at these two heights continue two curves parallel to the top-timber line, from the aft part of the stern to the ends of the two curves already drawn at the foremost end of the quarter-deck. If they should happen not to break in fair with them, they must be turned off with a round; but to make them appear more handsome, the lower line may be turned off with a scroll. These lines being drawn will represent the upper edges of the rails.

The height of the top side at the fore part of the ship must next be considered; which, in order to give proper height for the forecastle, must have a rise there of 14 inches, the break being at the after end of the forecastle, and turned off as before. But as this part of the ship is still considerably lower than the after part, it will be necessary to give another of eight inches upon the former, and turn it off with a scroll inverted. Hence this part of the ship will appear more uniform to the after part.

The finishing parts, namely the wales, stern, head, rails, &c. remain to be described. The wales may be first drawn; and as the strength of the ship depends very much on the right placing of them, great care must therefore be taken that they may be as little as possible wounded by the lower-deck ports, and so placed that the lower-deck bolts shall bolt in them, and also that they come as near as possible on the broadest part of the ship. In the first place, therefore, the height of breadth lines must be chosen for our guide. These heights of breadth are to be taken from the dimensions, and set off on the respective frames, and curves drawn through these points will be the upper and lower heights of breadth lines. The height of the wales may be now determined; which in general is in such a manner that the upper height of breadth line comes about fix inches below their upper edge, and the wales are then placed right upon the breadth lines. Take the heights and breadths of the wales afore, at midships, and abaft, from the table of dimensions; draw curves through the points thus found, and the wales will be represented.

The channel wales are then to be described. They are principally intended to strengthen the top side, and must be placed between the lower and upper deck ports; and the lower end of them at midships should be placed as low as possible, in order to prevent them from being cut by the upper deck ports afore and abaft. Take their heights and breadths from the dimensions; lay them off, and describe curves through the corresponding points, and the channel wales will be represented.

Lay off the dimensions of the waste rail found in the table; and through the points draw a line parallel to the top-timber line all fore and aft. This rail terminates the lower part of the paint work on the top side, as all the work above this rail is generally painted, and the work of the top side below it payed with a varnish, except the main wales, which are always payed with pitch.

Take the draught of water from the dimensions, and draw the load water-line, which is always done in green. Divide the distance between the load water-line and the upper edge of the keel into five equal parts, and through these points draw four more water-lines. Set off the centres of the masts on the gun-deck; their rake may likewise be taken from the dimensions. Set off also the centre of the bowsprit, letting it be four feet from the deck at the after part of the stem, which will give sufficient height for a light and airy figure.

Draw the knight-heads so as to be sufficiently high above the bowsprit to admit of a chock between them for the better security of the bowsprit. The timber heads may also be drawn above the forecastle, observing to place the most convenient for the timbers of the frame, being those which come over the upper deck ports, as they may be allowed long enough to form handsome heads. There should be one placed abaft the cat-head, to which the foremost block is to be bolted, and there may be two ports on the forecastle formed by them, and placed where it is most convenient to the dead eyes.

Describe the channels, taking their lengths and thicknesses from the dimensions, and place their upper edges well with the lower edge of the sheer rail. The dead eyes may then be drawn, observing to place them in such a manner that the chains may not interfere with the ports; and the preventer plates must all be placed on the channel wales, letting them be of such a length that the preventer bolt at each end may bolt on each edge of the channel wales. It must also be observed to give each of the chains and preventer plates a proper rake, that is, to let them lie in the direction of the throats, which may be done in the following manner: Produce the mast upwards, upon which set off the length of the mast to the lower part of the head; these straight lines drawn from that point through the centre of each dead eye will give the direction of the chains and preventer braces.

The fenders may be then drawn, observing to place them right abreast of the main hatchway, in order to prevent the ship's side from being hurt by whatever may be hoisted on board. The proper place for them will therefore be at timber 3; and the distance between them may be regulated by the distance between the ports. The cheft tree may also be drawn, which must be placed at a proper distance abaft the foremost, for the convenience of hauling home the fore tack. It may therefore be drawn at the aft side of timber C from the top of the side down to the upper edge of the channel wales; and the fenders may reach from the top of the side down to the upper edge of the main wales. As the fenders and cheft-tree are on the outside of the planks, wales, &c. the lines representing the wales, &c. should not be drawn through them.

Draw the steps on the side, which must be at the fore part of the main drift or break, making them as long as the distance between the upper and lower deck ports will admit of. They may be about fix inches alunder, and five inches deep, and continued from the top of the side down to the middle of the main wales.

In order to describe the head, the height of the beak-head must be first determined, which may be about two feet above the upper deck. At that place draw a horizontal line, upon which set off the length of the beak-head, which may be 7 1/2 feet abaft the fore part of the stem, and from thence square a line up to the forecastle deck; which line will represent the aft part of the beak-head, and will likewise terminate the foremost end of the forecastle. The length of the head may now be Application determined, which by the proportions will be found to of the fore- be 15 feet fix inches from the fore part of the item. Set going Rules to the Con- it off from the fore part of the item, and erect a per- struction of Ships. pendicular, which will be the utmost limits of the figure forward: then take the breadth of the figure from the proportions, which is four feet four inches, and set it off forward; and another perpendicular being drawn will show the utmost extent of the hair bracket forward, or aft part of the figure. Then draw the lower cheek, letting the upper edge be well with the upper edge of the main wales, and the after end ranging well with the beak-head line; set off the depth of it on the stem; which is about 11 inches, and let a curved line pass from the after end through the point on the stem, and to break in fair with the perpendicular first drawn for the length of the head, the fore part of the curve will then represent the position of the figure.

The upper cheek may next be drawn; but, in order to know the exact place of it on the stem, the place of the main rail must first be set off on the stem, the upper edge of which may be kept on a level with the beak-head; then setting off the depth of it below that, the place for the upper cheek may be determined, letting it be exactly in the middle between that and the lower cheek: then, by drawing curves for the upper and lower edges of the cheek from the after end parallel to the lower cheek, to break in fair with the perpendicular drawn for the back of the figure: then the upper cheek will be formed. The upper part may run in a ferpentine as high as where the shoulder of the figure is supposed to come, at which place it may be turned off with a scroll. The distance from the scroll to the heel of the figure is called the hair-bracket.

The head of the block may be formed by continuing the line at the breaf round to the top of the hair-bracket, observing to keep the top of it about fix inches clear of the under side of the bowsprit.

Having the distance set off on the stem for placing the main rail, it may next be described, keeping the bag of it as level as possible for the convenience of the gratings, and letting the foremost end rise gradually according to the rise of the upper cheek and hair bracket, and may turn off on the round of the scroll before drawn for the hair-bracket. To form the after end, set off the size of the head of the rail abaft the beak-head line, and erect a perpendicular; then describe the arch of a circle from that perpendicular, to break in fair with the lower side of the rail in the middle, and also another from the beak-head perpendicular, to break in fair with the upper side of the rail at the middle, observing to continue the head of it sufficiently high to range with the timber heads above the forecastle.

The head timbers are next to be drawn, placing the stem timber its own thickness abaft the stem, and the foremost must be so placed that the fore side may be up and down with the heel of the block or figure, which has not yet been set off. Take therefore the distance from the breast to the heel on a square which is seven feet, and erect a perpendicular from the lower part of the lower cheek to the lower part of the upper cheek; which perpendicular will terminate the foremost end of the lower cheek and the heel of the figure, and will also terminate the lower end of the hair-bracket: then, by continuing the same perpendicular from the upper part of

Application of the lower deck to the under part of the main rail, the fore side of the foremost head timber will be described; and by setting off its thickness aft, the other side may be drawn. The middle head timber may be spread between the two former ones; and there may also be one timber placed abaft the stem, at a distance from the stem, equal to that between the others, and the lower end of it may step on the upper edge of the lower rail.

To describe the middle and lower rails, divide the distance between the lower part of the main rail and the upper part of the upper cheek equally at every head timber; and curves being described through these points will form the middle and lower rails. The after end of the lower rail must terminate at the after edge of the after head timber.

The cat-head ought to be represented in such a manner as to come against the aft side of the head of the main rail, to rake forward four inches in a foot, and to sleeve up 5/8 inches in a foot, and about one foot six inches square. The lower part of it comes on the plank of the deck at the side, and the supporter under it must form a fair curve to break in with the after end of the middle rail.

The hawse holes must come between the cheeks, which is the most convenient place for them; but their place fore and aft cannot be exactly determined until they are laid down in the half-breadth plan.

The knee of the head is to project from the breast of the figure about two inches; and particular care must be taken that in forming it downwards it be not too full, as it is then liable to rub the cable very much: it may therefore have no more substance under the lower cheek at the heel of the figure than is just sufficient to admit of the bobstay holes, and may be 3 1/2 feet distant from the stem at the load-water line, making it run in an agreeable serpentine line from the breast down to the third water line, where it may be 1 1/2 feet from the stem. By continuing the same line downwards, keeping it more distant from the stem as it comes down, the gripe will be formed. The lower part of it must break in fair with the under part of the false keel; and the breadth of the gripe at the broadest place will be found by the proportions to be 4 1/2 feet. As the aft part of the gripe is terminated by the fore foot, or foremost end of the keel, it will now be proper to finish that part as follows: From the line representing the upper edge of the keel set down the depth of the keel, through which draw a line parallel to the former, and it will be the lower edge of the keel. From that point, where the aft side of the stem is distant from the upper edge of the keel by a quantity equal to the breadth of the keel at midships, erect a perpendicular, which will limit the foremost end of the keel; and the after or lower end of the stem may be represented by setting off the length of the scarf from the foremost end of the keel, which may be six feet. Set down from the line representing the lower edge of the keel the thickness of the false keel, which is seven inches; and a line drawn through that point parallel to the lower edge of the keel will be the under edge of the false keel, the foremost end of which may be three inches afore the foremost end of the main keel.

The head being now finished, proceed next to the stern, the side and middle timbers of which are already drawn. From the side timber set off forward 14 feet, the length of gallery, and draw a pencil line parallel to the side timber; draw also a line to intersect the touch of the upper counter at the side, producing it forwards parallel to the sheer as far as the pencil line first drawn, and this line will represent the upper edge of the gallery rim. From which set down eight inches, the breadth of the gallery rail, and draw the lower edge of the rail. At the distance of eight inches from the fore side of the side timber draw a line parallel thereto; and from the point of intersection of this line with the upper edge of the gallery rim, draw a curve to the middle timber parallel to the touches of the upper counter, which line will represent the upper edge of the upper counter rail as it appears on the sheer draught. The lower edge of this rail may be formed by setting off its depth from the upper edge. In the same manner the lower counter rail may be described: then take the distance between that and the upper counter rail, and set it off below the rim rail; and hence the rail that comes to the lower stool may be drawn, keeping it parallel to the rim rail. Underneath that, the lower finishing may be formed, making it as light and agreeable as possible.

Set off from the middle timber on the end of the quarter-deck the projection of the balcony, which may be about two feet, and draw a line with a pencil parallel to the middle timber. On this line set off a point 1 1/2 inches below the under side of the quarter-deck, from which draw a curve to the side timber parallel to the upper counter rail, which curve will represent the lower side of the foot space rail of the balcony as it appears in the sheer draught.

Take the distance between the point of intersection of the upper edge of the upper counter with the middle line, and the point of intersection of the under side of the foot space rail with the middle line, which set up on a perpendicular from the upper edge of the rim rail at the foremost end. Through this point draw a line parallel to the rim rail to intersect the lower part of the foot space rail, and this line will represent the lower edge of the rail that comes to the middle stool, and will answer to the foot space rail. Then between this line and the rim rail three lights or sashes may be drawn, having a muntin or pillar between each light of about 1 1/4 inches broad, and the lower gallery will be finished. Set off the depth of the middle stool rail above the line already drawn for the lower edge, and the upper edge may be drawn. Then set off the same depth above the curve drawn for the lower edge of the foot space rail, and the upper edge of that rail may then be drawn.

The quarter-piece must be next described, the heel of which must step on the after end of the middle stool. Draw a line with a pencil parallel to the middle timber, and at a distance therefrom, equal to the projection of the balcony. Upon this line set up from the round-house deck the height of the upper part of the stern or taff rail, which may be four feet above the deck. At that height draw with a pencil a horizontal line, and from its intersection with the line first drawn describe a curve to the middle stool rail, observing to make the lower part of this curve run nearly parallel to the side timber, and the lower part about three inches abaft the side timber; and this curve will represent the aft side of the quarter-piece at the outside. There let off the thick- application nefs of the quarter-piece, which is one foot six inches, the fore-afare the curve already drawn; and another curve being described parallel to it from the lower part to the top of the sheer, and the quarter-piece at the outside will be represented. On the horizontal line drawn for the upper part of the taff-rail set off forward the thickness of the taff-rail, which is one foot; then draw a curve down to the head of the quarter-piece parallel to the first, and that part of the taff-rail will be described. Instead of a fair curve, it is customary to form the upper part of the taff-rail with one or two breaks, and their curves inverted. Either way may, however, be used according to fancy.

Set off the depth of the taff-rail, which may be about 3 1/2 feet, on the line drawn for the projection; from the upper part, and from this point, describe a curve as low as the heel of the quarter-piece, and about five inches abaft it at that place; observing to make it run nearly parallel to the after edge of the quarter-piece; and the after part of the quarter-piece, which comes nearest to the side, will be represented.

Set up on the line drawn for the projection of the balcony the height of the upper part of the balcony or breast rail, which is 3 1/2 feet from the deck; set off the thickness of the rail below that, and describe the balcony, keeping it parallel to the foot space rail, and terminating it at the line drawn for the after part of the quarter-piece nearest the side; and the whole balcony will then be represented.

The upper gallery is then to be described. In order to this, its length must be determined, which may be 11 feet. Set off this distance from the side timber forward with the sheer; and at this point draw a line parallel to the side timber, which line will represent the fore part of the gallery. Then take the distance between the upper part of the foot space rail and the upper part of the breast rail on a perpendicular, and set it off on a perpendicular from the upper part of the middle stool rail on the line drawn for the fore part of the gallery, from which to the fore part of the quarter-piece draw a straight line parallel to the rail below, which line will be the upper edge of the upper rim rail; and its thickness being set off, the lower edge may also be drawn. From the upper edge of that rail set up an extent equal to the distance between the lower rim rail and middle stool rail, and describe the upper stool rail, the after end of which will be determined by the quarter-piece, and the fore end by the line for the length of the gallery. There may be three fathoms drawn between these two rails as before; and hence the upper gallery will be formed.

The upper finishing should be next drawn, the length of which may be 1 1/2 foot less than the upper gallery. Draw a line parallel to the rake of the stern for the fore end of it, and let the upper part of the top side be the upper part of the upper rail, from which set down three inches for the thickness of the rail, and describe it. Describe also another rail of the same length and thickness as the former; and eight inches below; from the end of which a serpentine line may be drawn down to the upper stool rail, and the upper finishing will be completed.

The stern being now finished, the rudder only remains to be drawn. The breadth of the rudder at the lower part is to be determined from the proportions, and set off from the line representing the aft part of the Application stern-post; which line also represents the fore part of the rudder. Then determine on the lower hance, letting it be no higher than is just sufficient, which may be about one foot above the load water-line, and set off its breadth at that place taken from the proportions. Then a line drawn from thence to the breadth set off at the lower part will be the aft side of the rudder below the lower hance. There may also be another hance about the height of the lower deck. The use of these breaks or hances is to reduce the breadth as it rises toward the head. The aft part may be drawn above the lower hance, the break at the lower hance being about ten inches, and the break at the upper hance fix inches.—The back may be then drawn. It is of elm, about four inches thick on the aft part. That thickness being set off, and a line drawn from the lower hance to the lower end, will represent the back. The head of the rudder should be as high as to receive a tiller above the upper deck. Therefore set off the size of the head above the upper deck, and draw a line from thence to the break of the upper hance, and the aft part of the rudder will be represented all the way up. The bearding should be drawn, by setting off the breadth of it at the keel from the fore side of the rudder, which may be nine inches. Set off also the breadth at the head of the wing-tranfom, which may be a foot. Then a line being drawn through these two points, from the lower part of the rudder to about a foot above the wing-tranfom, and the bearding will be represented. As the bearding is a very nice point, and the working of the rudder depending very much upon it, it should always be very particularly considered. It has been customary to beard the rudder to a sharp edge at the middle line, by which the main piece is reduced more than necessary. The rudder should, however, be bearded from the side of the pintles, and the fore side made to the form of the pintles.

The pintles and braces may next be drawn. In order to which determine the place of the upper one, which must be so disposed that the straps shall come round the head of the standard, which is against the head of the stern-post on the gun-deck, and meet at the middle line. By this means there is double security both to the brace and standard. To obtain those advantages, it must therefore be placed about four inches above the wing-tranfom: the second must be placed just below the gun-deck so as to bolt in the middle of the deck-tranfom, and the rest may be spaced equally between the lower one, which may be about fix inches above the upper edge of the keel. The number of them is generally seven pair upon this class of ships; but the number may be regulated by the distance between the second and upper one, making the distance between the rest nearly the same. The length of all the braces will be found by setting off the length of the lower one, which may be eight feet afore the back of the stern-post, and also the length of the third, which is four feet and a half afore the back of the stern-post; and a line drawn from the one extremity to the other will limit the intermediate ones, as will appear on the thee draught. The braces will seem to diminish in length very much as they go up; but when measured or viewed on the shape of the body, they will be nearly of an equal length. The length of the straps of the pintles which come Application come upon the rudder may all be within four inches of the fore of the aft side of the rudder; and the rudder being a flat surface, they will all appear of the proper lengths.

II. Of the half-breadth and body plans.—The half-breadth plan must be first drawn. Then produce the lower edge of the keel both ways, and let it also represent the middle line of the half-breadth plan. Produce all the frames downwards, and also the fore and after perpendiculars. Then from the place in the sheer-plan, where the height of breadth-lines intersect the stem, square down to the middle line the fore and aft part of the rabbet and the fore part of the stem. Take from the dimensions what the stem is fided at that place, and set off half of it from the middle line in the half-breadth plan, through which draw a line parallel to the middle line through the three lines squared down, and the half breadth of the stem will be represented in the half-breadth plan. Take the thickness of the plank of the bottom which is 4\(\frac{1}{2}\) inches, and describe the rabbet of the stem in the half-breadth plan.

From the points of intersection of the height of breadth lines with the counter timber at the side, and with the counter timber at the middle line, draw lines perpendicular to the middle line of the half-breadth plan, from which set off the half breadth of the counter on the line first drawn; and from this point to the intersection of the line last drawn, with the middle line draw a curve, and the half breadth of the counter will be represented at the height of breadth, which will be the broadest part of the stern.

Take the main half breadth of timber dead flat from the dimensions, and lay it off from the middle line on dead flat in the half-breadth plan. Take also from the dimensions the main half-breadth of every timber, and set off each from the middle line on the corresponding timbers in the half-breadth plan. Then a curve drawn from the end of the line representing the half-breadth of the counter through all the points, set off on the timbers, and terminating at the aft part of the stern, will be the main half-breadth line. Take from the dimensions the top timber half-breadth, and describe the top-timber half-breadth line in the half-breadth plan, in the same manner as the main half-breadth line.

Take from the dimensions the half-breadth of the rising, and set it off from the middle line on the corresponding timbers, in the half-breadth plan, observing, where the word outside is expressed in the tables, the half-breadth for that timber must be set off above or on the outside of the middle line. Then a curve drawn through these points will be the half-breadth of rising in the half-breadth plan.

It will now be necessary to proceed to the body plan. Draw a horizontal line (fig. 35.), which is called the base line, from the right hand extremity of which erect a perpendicular. Then set off on the base line the main half-breadth at dead flat, and erect another perpendicular, and from that set off the main half-breadth again, and erect a third perpendicular. The first perpendicular, as already observed, is called the side line of the fore body; the second the middle line; and the third the side line of the after body.

Take from the dimensions the heights of the diagonals up the middle line, and set them from the base up the middle line in the body plan. Take also their distances from the middle line on the base, and set them off. Set off also their heights up the side lines, and draw the diagonals. Then take from the sheer plan the heights of the lower height of breadth-line, and set them off upon the middle line in the body plan; through these points lines are to be drawn parallel to the bale, and terminating at the side lines. In like manner proceed with the upper height of breadth line.

The rising is next to be set off on the body plan; it must, however, be first described in the sheer plan: Take, therefore, the heights from the dimensions, and set them off on the corresponding timbers in the sheer plan, and a curve described through these points will be the rising line in the sheer plan. Then take from the dimensions the rising heights of dead flat. Set it off in the body plan, and draw a horizontal line. Now take all the rising heights from the sheer plan, and set them off in the body plan from the line drawn for the rising height of dead flat, and draw horizontal lines through these points. Take from the half-breadth plan the half breadths of the rising, and set them off from the middle line in the body plan, and the centres of the floor sweeps of the corresponding timbers will be obtained.

From the half-breadth plan take the main half-breadth lines, and set them off from the middle line in the body plan on the corresponding lines before drawn for the lower height of breadth; and from the extremities of these lines set off towards the middle line the lengths of the lower breadth sweeps respectively.

Take from the dimensions the distance of each frame from the middle line on the diagonals, and set them off from the middle line on their respective diagonal lines. Now these distances being set off, and the lower breadth and floor sweeps described, the shape of the frames below the breadth line may easily be drawn as follows: Place one point of a compass in the distance set off for the length of the lower breadth sweep, and extend the other to the point which terminates the breadth, and describe an arch of a circle downwards, which will intersect the points set off on the upper diagonal lines, letting it pass as low as convenient. Then fix one point of the compasses in the centre of the floor sweep, and extend the other to the point set off on the fourth diagonal, which is the floor head; and describe a circle to intersect as many of the points set off on the diagonals as it will. Then draw a curve from the back of the lower breadth sweep, through the points on the diagonals, to the back of the floor sweep. Describe also another curve from the back of the floor sweep through the points on the lower diagonals, and terminating at the upper part of the rabbet of the keel, and that part of the frame below the breadth will be formed. In like manner describe the other frames.

Through the extremities of the frames at the lower height of breadth draw lines parallel to the middle line, and terminating at the upper height of breadth line, and from thence set off the upper breadth sweeps; now fix one point of the compass in the centres of the upper breadth sweeps successively, and the other point to the extremities of the frames, and describe circles upwards. Then from the sheer plan take off the heights of the top-timber lines, and set them off in the body plan, drawing horizontal lines; upon which set off the top-timber half-breadths taken from the corresponding tim- application bet in the half-breadth plan; and by describing curves from the back of the upper breadth sweeps through the points let off on the seventh or upper diagonal; and in- tersecting the top-timber half-breadths, the timbers will then be formed from the keel to the top of the side.

The upper end of the timbers may be determined by taking the several heights of the upper part of the top side above the top-timber line on the corresponding timbers in the body plan. The lower parts of the timbers are ended at the rabbet of the keel as follows: With an extent of four inches and a half, the thickness of the bottom, and one leg of the compasses at the place where the line for the thickness of the keel intersects the base line; with the other leg describe an arch to intersect the keel line and the base. Then fix one point at the intersection of the arch and keel, and from the point of intersection of the keel and base describe another arch to intersect the former. Then from the intersection of these arches draw one straight line to the intersection of the keel and base, and another to the intersection of the lower arch and the keel, and the rabbet of the keel will be described at the main frame. All the timbers in the middle part of the ship which have no rising terminate at the intersection of the upper edge of the rabbet with the base line; but the lower part of the timbers, having a rising, end in the centre of the rabbet, that is, where the two circles intersect. Those timbers which are near the after end of the keel must be ended by setting off the half breadth of the keel at the port in the half breadth plan, and describe the tapering of the keel. Then at the corresponding timbers take off the half breadth of the keel; set it off in the body plan, and describe the rabbet as before, letting every timber end where the two circles for its respective rabbet intersect.

To describe the side counter or stern timber, take the height of the wing transom, the lower counter, upper counter, and top-timber line at the side; from the sheer plan transfer them to the body plan, and through these points draw horizontal lines. Divide the distance between the wing transom and lower counter into three equal parts, and through the two points of division draw two horizontal lines. Draw also a horizontal line equidistant from the upper counter and the top-timber line in the sheer plan, and transfer them to the body plan.

Now, from the point of intersection of the aft side of the stern timber at the side, with the wing transom at the side in the sheer plan, draw a line perpendicular to the middle line in the half breadth plan. Draw also perpendicular lines from the points where the upper and lower transoms touch the stern-pot; from the points of intersection of the stern-timber with the two horizontal lines drawn between, and from the intersection of the stern-timber with the horizontal line drawn between the upper counter and top-timber line. Then curves must be formed in the half breadth plan for the shape of the body at each of these heights. In order to which, begin with the horizontal or level line representing the height of the wing transom in the body plan. Lay a slip of paper to that line, and mark on it the middle line and the timbers 37, 35, 33, and 29; transfer the slip to the half-breadth plan, placing the point marked on it for the middle line exactly on the middle in the half breadth plan, and set off the half breadths on the corresponding timbers 37, 35, 33, and 29, and describe of the fore... a curve through these points, and to intersect the per- perpendicular drawn from the sheer plan. In like manner proceed with the horizontal lines at the heights of the counters, between the lower counter and wing transom, above the upper counter and top-timber line; and from the intersections of the curve drawn in the half breadth plan, with the perpendicular lines drawn from the sheer plan, take the distances to the middle line, and set them off on the corresponding lines in the body plan; then a curve described through the several points thus set off will be the representative of the stern-timber.

The round-up of the wing transom, upper and lower counter, may be taken from the sheer draught, and set off at the middle line above their respective level lines in the body plan, by which the round-up of each may be drawn. The round-af of the wing transom may also be taken from the sheer plan, and set off at the middle line, abait the perpendicular for the wing transom in the half breadth plan, whence the round-af of the wing transom may be described.

The after body being now finished, it remains to form the fore body; but as the operation is nearly the same in both, a repetition is therefore unnecessary, except in those parts which require a different process.

The foremost timbers end on the stem, and consequently the method of describing the ending of them differs from that used for the timbers used in the after body. Draw a line in the body plan parallel to the middle line, at a distance equal to the half of what the stem is fidded. In the sheer plan take the height of the point of intersection of the lower part of the rabbet of the stem with the timber which is required to be ended, and set it off on the line before drawn in the body plan. Then take the extent between the points of intersection of the timber with the lower and upper parts of the rabbet, and with one leg of the compasses at the extremity of the distance laid off in the body plan describe a circle, and the timbers may then pass over the back of this circle. Now, by applying a small square to the timber, and letting the back of it intersect the point set off for the lower part of the rabbet, the lower part of the rabbet and the ending of the timbers will be described.

The foremost timbers differ also very much at the head from those in the after body: For since the ship carries her breadth so far forward at the top-timber line, it therefore occasions the two foremost frames to fall out at the head beyond the breadth, whence they are called knuckle timbers. They are thus described: The height of the top-timber line being set off in the body plan, set off on it the top half breadth taken from the half breadth plan, and at that place draw a perpendicular; then from the sheer plan take the height of the top of the side, and set it off on the perpendicular in the body plan: Take also the breadth of the rail at the top-timber line in the sheer plan, and set it off below the top-timber line at the perpendicular line in the body plan, and the straight part of the knuckle timber to be drawn will be determined. Then from the last-mentioned point set off describe a curve through the points set off for the timber down to the upper breadth, and the whole knuckle timber will be formed. It will hence be seen that those timbers forward will fall out of the fore beyond the main breadth with a hollow, contrary to the going rules to the construction of the top side, which falls within the main breadth of with a hollow.

Ships. The fore and after bodies being now formed, the water lines must next be described in the half-breadth plan, in order to prove the fairness of the bodies. In this draught the water lines are all represented parallel to the keel; their heights may, therefore, be taken from the sheer plan, and transferred to the body plan, drawing horizontal lines, and the water lines will be represented in the body plan. In ships that draw more water abaft than afore, the water lines will not be parallel to the keel; in this case, the heights must be taken at every timber in the sheer plan, and set off on their corresponding timbers in the body plan; and curves being described through the several points, will represent the water lines in the body plan.

Take the distances from the middle line to the points where the water lines intersect the different timbers in the body plan, and set them off on their corresponding timbers in the half-breadth plan. From the points where the water lines in the sheer plan intersect the aft part of the rabbet of the sternpost draw perpendiculars to the middle line of the half-breadth plan, and upon these perpendiculars set off from the middle line the half thickness of the sternpost at its corresponding water line; which may be taken from the body plan, by setting off the size of the post at the head and the keel, and drawing a line for the tapering of it; and where the line so drawn intersects the water lines, that will be the half thickness required: then take an extent in the compasses equal to the thickness of the plank, and fix one point where the half thickness of the post intersects the perpendicular, and with the other describe a circle, from the back of which the water lines may pass through their respective points set off, and end at the fore part of the half-breadth plan, proceeding in the same manner as with the after part. A line drawn from the water line to the point set off for the half thickness of the post will represent the aft part of the rabbet of the post; and in like manner the rabbet of the stem may be represented. The water lines being all described, it will be seen if the body is fair; and if the timbers require any alteration, it should be complied with.

The cant-timbers of the after body may next be described in the half-breadth plan; in order to which the cant of the fashion-piece must first be represented. Having therefore the round aft of the wing tranfom represented in the half-breadth plan, and also the shape of a level line at the height of the wing tranfom; then set off the breadth of the wing tranfom at the end, which is one foot four inches; and that will be the place where the head of the fashion-piece will come: now to determine the cant of it, the shape of the body must be considered; as it must be canted in such a manner as to preserve as great a straightness as is possible for the shape of the timber, by which means the timber will be much stronger than if it were crooked; the cant must also be considered, in order to let the timber have as little bevelling as possible. Let, therefore, the heel of the timber be set off on the middle line, two feet afore timber 35; and then drawing a line from thence to the point set off on the level line for the wing tranfom, the cant of the fashion-piece will be described, and will be found situated in the best manner possible to answer the before-mentioned purposes.

The cant of the fashion-piece being represented, the cant of the other timbers may now be easily determined. Let timber 29 be the foremost cant timber in the after body, and with a pencil draw timber 28; then observe how many frames there are between timber 28 and the fashion-piece, which will be found to be nine, namely, 29, 30, 31, 32, 33, 34, 35, 36, and 37. Now divide the distance between timber 28 and the fashion-piece on the middle line into 10 equal parts: Divide also the corresponding portion of the main half-breadth lines into the same number of equal parts; and straight lines joining the corresponding points at the middle line with those in the half-breadth line will represent the cant timbers in the after body.

The line drawn for the cant of the fashion-piece represents the aft side of it, which comes to the end of the transoms; but in order to help the conversion with regard to the lower transoms, there may be two more fashion-pieces abaft the former; therefore the foremost fashion piece, or that which is already described in the half-breadth plan, may only take the ends of the three upper transoms, which are, the wing, filling, and deck: the middle fashion-piece may take the four next, and the after fashion-piece the lower ones: therefore set off in the half-breadth plan the fiding of the middle and after fashion-piece, which may be 13 inches each; then by drawing lines parallel to the foremost fashion-piece, at the aforesaid distance from each other, the middle and after fashion-piece will be represented in the half-breadth plan.

The fashion-piece and transoms yet remain to be represented in the sheer plan; in order to which, let the number of transoms be determined, which, for so large a buttock, may be seven below the deck tranfom: draw them with a pencil, beginning with the wing, the upper side of which is represented by a level line at its height; set off its fiding below that, and draw a level line for the lower edge. The filling tranfom follows; which is merely for the purpose of filling the vacancy between the under edge of the wing and the upper part of the deck plank: it may therefore be represented by drawing two level lines for the upper and lower edge, leaving about two inches between the upper edge and lower edge of the wing tranfom, and four inches between the lower edge of the gun-deck plank; then the deck tranfom must be governed by the gun-deck, letting the under side of the gun-deck plank represent the upper side of it, and setting off its fiding below that; the under edge may also be drawn: the tranfoms below the deck may all be fided equally, which may be 11 inches; they must also have a sufficient distance between to admit the circulation of the air to preserve them, which may be about three inches.

The tranfoms being now drawn with a pencil, the fashion-piece must next be described in the sheer plan, by which the length of the tranfoms as they appear in that plan will be determined. As the foremost fashion-piece reaches above the upper tranfom, it may therefore be first described: in order to which, draw a sufficient number of level lines in the sheer plan; or, as the water lines are level, draw therefore one line between the upper water line and the wing tranfom, and one above the

Application the wing transom at the intended height of the head of the fashion-piece, which may be about five feet: then take the height of these two level lines, and transfer them to the body plan; and take off two or three timbers and run them in the half-breadth plan, in the same manner as the water lines were done; then from the point where the line drawn for the cant of the fashion-piece, in the half-breadth plan, intersects the level line drawn for the head of the fashion-piece, draw up a perpendicular to the said line in the sheer plan, making a point. Again, from the intersection of the cant line, with the level line for the wing transom in the half-breadth plan, draw a perpendicular to the wing transom in the sheer plan. Also draw perpendiculars from the points where the cant line in the half-breadth plan intersects the level line below the wing transom, and also the water lines to the corresponding lines in the sheer plan; then a curve described through these points will be the representation of the foremost fashion-piece in the sheer-plan. In the same manner the middle and after fashion-pieces may be described; observing to let the middle one run up no higher than the under part of the deck transom, and the after to the under side of the fourth transom under the deck. The transoms may now be drawn with ink, as their lengths are limited by the fashion-pieces.

Neither the head nor the foreside of the sternpost are yet described; take, therefore, from the dimensions, the breadth of the post on the keel, and set it off on the upper edge of the keel from the aft side of post. The head of the post must next be determined, which must just be high enough to admit of the helm-post transom and the tiller coming between it and the upper deck beam; the height therefore that is necessary will be one foot nine inches above the wing transom. Now draw a level line at that height, upon which set off the breadth of the sternpost at that place, taken from the dimensions, and a line drawn from thence to the point set off on the keel will be the foreside of the sternpost; observing, however, not to draw the line through the transoms, as it will only appear between them. The inner post may be drawn, by setting off its thickens forward from the sternpost, and drawing a straight line as before, continuing it no higher than the under side of the wing transom.

The cant timbers in the after body being described, together with the parts dependent on them, those in the fore body may be next formed; in order to which, the foremost and aftermost cant timbers must be first determined, and also the cant of the foremost ones. The foremost cant timber will extend so far forward as to be named \( \psi \); the cant on the middle line may be one foot four inches afore square timber W, and on the main half breadth line one foot nine inches afore timber Y; in which situation the line may be drawn for the cant; the aftermost may be timber Q. The cant timbers may now be described in the same manner as those in the after body, namely, by spacing them equally between the cant timber \( \psi \) and the square timber P, both on the main half-breadth, and middle lines, and drawing straight lines between the corresponding points, observing to let them run out to the top-timber half-breadth line, where it comes without the main half-breadth line.

The hawse pieces must next be laid down in the half-breadth plan; the sides of which must look fore and aft with the ship upon account of the round of the bow. Take the siding of the apron, which may be about four inches more than the item, and set off half of it from the middle line, drawing a line from the main half breadth to the foremost cant timber, which will represent the foremost edge of the knight-head; then from that set off the siding of the knight-head, which may be one foot four inches, and draw the aft side of it. The hawse pieces may then be drawn, which are four in number, by setting off their sidings, namely, one foot fix inches parallel from the knight-head and from each other; and straight lines being drawn from the main half-breadth line to the foremost cant timber will represent them.

The hawse holes should be described in such a manner as to wound the hawse pieces as little as possible; they may therefore be placed so that the joint of the hawse pieces shall be in the centre of the holes, whence they will only cut half the hawse pieces. Take the dimensions of the hawse holes, which is one foot fix inches, and set off the foremost one, or that next the middle line, on the joint between the first and second hawse piece; then set off the other on the joint between the third and fourth hawse piece; and small lines being drawn across the main half-breadth at their respective places will represent the hawse holes in the half-breadth plan.

The hawse holes should next be represented in the sheer plan. In this clas of ships they are always placed in the middle between the cheeks; therefore set off their diameter, namely, one foot fix inches, between the cheeks, and draw lines parallel to the cheeks for their upper and lower part. Then to determine their situation agreeable to the half-breadth plan, which is the fore and aft way, draw perpendiculars from their intersections with the main half-breadth line to the lines drawn between the cheeks, and their true situations, the fore and aft way, will be obtained; and, by describing them round or circular, according to the points set off, they will be represented as they appear in the sheer plan.

The apron may be drawn in the sheer plan, setting off its bigness from the stem, and letting it come so low that the scarf may be about two feet higher than the foremost end of the fore foot; by which it will give slip to the scarfs of the stem. It may run up to the head of the stem.

The cutting down should next be drawn. Take therefore from the tables of dimensions the different heights there expressed, and set them off from the upper edge of the keel on the corresponding timbers in the sheer plan: then a curve described through the points set off, from the inner post aft to the apron forward, will be the cutting down. Next set off from the cutting down the thickens of the timber strake, which is eight inches and a half, and a curve described parallel to the former will represent the timber strake, from which the depth of the hold is always measured.

The kelson is drawn, by taking its depth from the dimensions, and set it off above the cutting down line; and a curve described parallel to the cutting down will represent the kelson.

The cutting down line being described, the knee of the dead wood abait timber 27, being the after floor timber, may then be represented. Set off the siding of the floor abait it, and erect a perpendicular in the sheer plan, which will terminate the foremost end of Application of the dead wood: then the fore and aft arm of the knee of the foregoing Rules may be half the length of the whole dead wood, and the up and down arm may reach to the under part of the lower transom; and the whole knee may be placed in such a manner that the upper piece of the dead wood shall bolt over it, and be of as much substance as the knee itself; therefore the knee must consequently be placed its whole thickness below the cutting down line representing the upper part of the dead wood.

The steer draught, the body, and half-breadth plan are now finished, from whence the ship may be laid down in the mould loft, and also the whole frame erected. As, however, the use of the diagonal lines in the body plan has not been sufficiently explained, it is therefore thought proper to subjoin the following illustration of them.

The diagonal lines in the body plan are mentioned in the tables of dimensions merely for the purpose of forming the body therefrom; but after the body is formed, they are of very principal use, as at their stations the ribbands and harpins which keep the body of the ship together while in her frames are all described, and the heads of the different timbers in the frame likewise determined.

The lowermost diagonal, or No. 1. which is named the lower firmark, at which place the bevellings are taken for the hollow of the floors; its situation is generally in the middle between the keel and the floor firmark.

Second diagonal is placed in the midships, about 18 inches below the floor head, and is the station where the floor ribband is placed in midships, and likewise the floor harpin forward; there is also a bevelling taken at this diagonal all the way fore and aft, from which it is termed the floor firmark.

Third diagonal, terminates the length of the floors, and is therefore called the floor head. There are likewise bevellings taken at this diagonal as far forward and aft as the floor extends. The placing of this diagonal is of the utmost consequence to the strength of the ship, it being so near to that part of the bulge which takes the ground, and of consequence is always liable to the greatest strain; it should therefore be placed as much above the bearing of the body in midships as could be conveniently allowed by conversion of the timber; but afore and abait it is not of so much consequence.

Fourth diagonal is placed in the middle between the floor head and the fifth diagonal, at which place a ribband and harpin are stationed for the security of the first or lower futtock, from whence it is named the first futtock firmark. There are also bevellings taken at this diagonal all afore and aft, which being part of the body where the timbers most vary, occasions them to be the greatest bevellings in the whole body.

Fifth diagonal terminates the heads of the first futtocks, and is therefore called the first futtock head. It should be placed at a convenient distance above the floor head, in order to give a sufficient scarf to the lower part of the second futtocks. There are likewise bevellings for the timbers taken at this diagonal, all fore and aft.

Sixth diagonal should be placed in the middle between the first futtock head and the seventh diagonal; at which place the ribband and harpin are stationed for the support of the second futtocks. Bevellings are taken at this diagonal all fore and aft. It is named the second futtock firmark.

Seventh diagonal terminates the second futtock heads from the fore to the aftermost floors, and afore and abait them it terminates the double futtock heads in the fore and aft cant bodies. It should be placed in midships, as much above the first futtock head as the first futtock is above the floor head: by which it gives the same scarf to the lower part of the third futtock as the first futtock does to the second. There are bevellings taken all fore and aft at this diagonal. It is named the second futtock head.

Eighth diagonal is the station for the ribband and harpin which supports the third futtocks, and is therefore placed between the second futtock head and ninth diagonal. It is also a bevelling place, and is named the third futtock firmark.

Ninth and last diagonal is placed the same distance above the second futtock head as that is above the first, and terminates all the heads of the third futtocks which are in the frames, as they come between the ports; but such as are between the frames, and come under the lower deck ports, must run up to the under part of the ports, as no short timbers should by any means be admitted under the ports, which require the greatest possible strength. This diagonal is likewise a bevelling place for the heads of the third futtocks, and is there-called the third futtock head.

The fourth futtock heads are terminated by the under part of the upper deck ports all fore and aft, and a ribband is placed fore and aft at the height of the upper breadth line, another between the lower and upper deck ports, and one at the top-timber line; which, with the ribbands and harpins before mentioned, keep the whole body of the ship together, and likewise in its proper form and shape.

It must be observed, that the diagonal lines laid down in the dimensions will not correspond to what has been said above upon diagonals, as they were drawn differently upon the body for the purpose of giving the true dimensions of it. Therefore, when the body is drawn in fair, the first diagonals (which should only be in pencil) are to be rubbed out, and the proper diagonals drawn with red ink, strictly adhering to what has been said above.

Sect. III. Of the Inboard Works of the Ship described in the preceding Section.

Draughts of the outboard works being now constructed, in which every part is described that is necessary to enable the artist to put the ship in her frames, we must now proceed to form another draught of the cavity of the ship or inboard works, which must be so contrived that every thing within the ship may be arranged in the most commodious manner and to the best advantage.

It is usual to draw the inboard works in the sheer-draught; but as this generally occasions much confusion, it is therefore the best and easiest method to appropriate a draught to this particular purpose.

Take from the sheer-draught the stem, stern-post, counter timbers, and keel, and describe them on another paper; draw in also the cutting down, kelson, apron, transoms, fashion-pieces, and decks, and the upper line of the sheer all fore and aft, also pass the timbers and ports. The beams come first under consideration, and should be so disposed as to come one under and one between each port, or as near as can be to answer other works of the ship; but where it happens that a beam cannot possibly be placed under the port, then a beam arm should be introduced to make good the deficiency. Every beam, and also the beam arms, should be kneed at each end with one lodging and one hanging knee; and in those parts of the ship which require the knees to be very acute, such as the after beams of the gun-deck, and in some ships, whose bodies are very sharp, the foremost beams of the gun-deck, there should be knees of iron. Care should be taken always to let the upper side of the knees be below the surface of the beams, in large ships one inch and a half, and in small ships an inch, by which means the air will have a free passage between the knees and under part of the deck.

In the conversion of the beams the side next the lodging knee should be left as broad at the end of the beam as can possibly be allowed by the timber, the beam retaining its proper scantling at the end of the lodging knee: by so doing the lodging knees will be more without a square, which consequently makes them the more easy to be provided.

In ships where the beams can be got in one piece, they should be so disposed as to have every other one with the butt end the same way; for this reason, that the butts will decay before the tops. In large ships the beams are made in two or three pieces, and are therefore allowed to be stronger than those that are in one piece. The beams in two pieces may have the scarf one-third of the length, and those in three pieces should have the middle piece half the length of the whole beam. The customary way of putting them together is to table them; and the length of the tablings should be one-half more than the depth of the beam. It is very common to divide the tablings in the middle of the beam, and that part which is taken out at the upper side to be left at the lower side, and then kersey or flannel is put into the scarf: but in this case the water is liable to lie in the scarf, and must be the means of rotting the beams. If, however, the beams were tailed together in dovetails, and taken through from side to side, putting tar only between them, which hardens the wood; then the water occasioned by the leaking of the decks would have a free passage, and the beam would dry again; and this method would not be found inferior in point of strength to the other. The length of the fore and aft arm of the lodging knee should extend to the side of the hanging knee next to it; but there is no necessity for that arm to be longer than the other. In fastening the knees, care would be taken to let one bolt pass exactly through the middle of the throat, one foot fix inches from each end, and the rest divided equally between; observing always to have the holes bored square from the knee. The bolts for the thwartship arms of both hanging and lodging knees may go through the arms of each knee, and drive every one the other way.

In order to draw the beams in the draught, take the moulding of the lower deck beams, and set it off below the line representing the deck at the side, and draw a line in pencil parallel thereto, which will represent the under side of the beams. In like manner represent the under side of the beams for the upper deck, quarter deck, forecastle, and roundhouse. Then take the fiding of the fore of the lower-deck beams, and place one under and one between each port, all fore and aft, drawing them in pencil. Determine the dimensions of the well fore and aft, which is ten feet, and set it off abaft the beam under the eighth port, placing the beam under the ninth port at that distance: those two beams may then be drawn in ink, and will terminate the extent of the well the fore and aft way; and as a beam cannot go across the ship at that place upon account of its being the well and mast room, there must therefore be a beam arm between these two beams.

The main hatchway should then be determined, letting the beam that forms the fore part of the well form the aft part of it, and the beam under the next part may form the fore side of it, which beam may also be now drawn in ink: there should also be another beam arm introduced in the wake of the main hatchway.

The fore hatchway may be next determined; the fore side of which should range well up and down with the after end of the forecastle, and it may be fore and aft about four-fevenths of the main hatchway. At the fore side of the fore hatchway there must be a ladderway down to the orlop, which may be as much fore and aft as the beams will allow. The rest of the beams afore the fore hatchway may remain as first placed, there being nothing in the way to alter the ship. Then determine on the after hatchway, the foreside of which comes to the aft side of the mainmast room.

There should also be a hatchway, the foreside of which may be formed by the aft side of the beam under the twelfth port; which is for the convenience of the spirit and fish rooms: and there should be a ladderway abaft it to lead down to the cockpit. There may be also another hatchway, the foreside of it to be formed by the aft side of the beam under the eleventh port. The size of the ladder and hatchways must be governed by the beams, as when there is a good shift of beams they should not be altered for ladder and hatchways, unless it is the three principal hatchways, which must always be of a proper size, according to the size of the ship.

The after captain must be placed between the two-hatchways last described, and the beams abaft may stand as they are already shifted, observing only the mizenmast. There should be a small scuttle placed afore the second beam from aft, for the convenience of the bread room: it must be on one side of the middle lines, as there is a carling at the middle under the four or five after beams to receive the pillars for the support thereof.

The bits may be placed, letting the foreside of the after ones come against the aft side of the beam abaft the third port, and the foreside of the foremost ones against the next beam but one forward; then at the foreside of each bit there should be drawn a small scuttle for the convenience of handing up the powder from the magazine. The breast hook should also be drawn, which may be three feet the moulding away, and fided nine-tenths of the beams of the lower deck.

The gun-deck, beams, knees, &c. being described; in which, as well as all the decks having ports, the same precautions are to be used as in the gun-deck; and observing Application serving to keep the beams upon one deck as nearly as possible over the beams of the other, for the convenience of pillaring, as they will then support each other.

Ships. The hatchways are to be placed exactly over those on the lower deck, each over each; and therefore, where there is a beam arm in the lower deck there must also be one above it in the upper deck, and the same in the middle deck in three-deck ships. It commonly happens in ships of the line that there cannot be a whole beam between the deck breast hook and the beam that supports the step of the bowprit, because the bowsprit passes through that place: in this case, there must be a beam arm placed, letting the end come equally between the beam and the breast hook: but in ships that the bowprit will allow of a whole beam, then the ports and the rest of the beams must be consulted in order to space it; and when it so happens that the foremast comes in the wake of a port, then a beam arm must be necessarily introduced.

Having placed the beams according to the disposition of the other beams below, the ladderways should be contrived: there should be one next abait the fore hatchway, which is a single ladderway; and one next afore the main hatch, which is a double ladderway; the ladders standing the fore and aft way. There should also be another next abait the after hatch, and one over the cockpit corresponding with that on the lower deck.

The captains are next to be considered; the after one is already placed on the lower deck, the barrel of which must pass through the upper deck to receive the whelps and drumhead there, it being a double captain. In ships having three decks, the upper part of each captain is in the middle deck; but in ships with one deck there is only this one captain, the upper part of which is placed on the quarter deck. The foremost captain should be placed in the most convenient spot, to admit of its being lowered down to the orlop out of the way of the long boat: it may therefore be placed between the main and fore hatchways; the beam under the fifth port of the lower deck may form the aft side of its room, and the beams on each side of it should be placed exactly over or under the beams on the other decks, and they should be at a distance from each other sufficient to let the drumsheads pass between them. The centre of the captain should then be placed in the middle between the beams which compose its room; and the partners should be fitted in such a manner as to shift occasionally when wanted, which is by letting them be in two pieces fitted together. The partners on the lower deck, wherein the captain steps, must be supported by a pillar on the orlop deck, the lower part of which may be fitted in an oak chock; so that when the pillar is taken away, and the captain lowered down, that chock serves as a step for the captain. Those two beams on the orlop, by having the pillar and chock upon them, have therefore the whole weight of the captain pressing downwards: for the support of them, there should be a carling placed underneath the fore and aft way, with three pillars, one under each beam, and one between; all of them being flept in the kelson, by which the orlop deck will be well supported in the wake of the captain, and the other decks will feel no strain from it.

The fire hearth is next to be disposed; which is placed differently according to the size of the ship. In three-deckers it is found most convenient to place it on the middle deck; whence there is much more room under the forecastle than there would have been had it been placed there. In all two-deck ships it is placed under the forecastle, because on the deck underneath the bits are in the way. It is also under the forecastle in one-deck ships, though confined between the bits: in this case it should be kept as near as possible to the after bits, that there may be more room between it and the foremost bits to make a good galley.

The positions of the main-topfall-sheet bits are next to be determined; the foremost of which must be so placed as to let its foreside come against the aft side of the beam abait the main hatchway, and to pass down to the lower deck, and there step in the beams: admitting it to be a straight piece, it would come at the aft side of the lower deck beam the same as it does at the upper deck beam, in consequence of those two beams ranging well up and down with each other: it must therefore have a cast under the upper deck beam, by which the lower part may be brought forward sufficient to stop in the lower deck beam. The aftermost must be placed against the foreside of the beam abait the mast, and step on the beam below; but there is no necessity to provide a crooked piece as before, for the beam of the upper deck may be moved a little farther aft, till it admit of the bit flopping on the lower deck beam, unless the beam comes under a port, as in that case it must not by any means be moved. The cross pieces to the bits should be on the foreside, and in height from the upper deck about one third of the height between it and the quarter deck. With regard to the heads of the bits, the length of the ship's waste should be considered; and if there is length enough from the forecastle to the foremost bits to admit of the spare gear being flowed thereon without reaching farther aft, the quarter deck may then run so far forward that the head of the foremost bits shall tenon in the foremost beam; this gives the mainmast another deck, and admits of the quarter deck being all that the longer: but if there is not the room before mentioned, then the quarter deck must run no further forward than the after bits, which will then tenon in the foremost beam; and the foremost bits must have a crook piece let on their heads, which is termed a horse, and will be for the purpose of receiving the ends of the spare gear.

The length of the quarter deck being now determined, the beams are then to be placed. For this purpose the several contrivances in the quarter deck must be previously consulted. It is necessary to observe, that there are neither carlings nor lodges, the carlings of the hatches excepted, in the quarter deck, round-houfe, and forecastle; as they would weaken instead of strengthening the beams, which should be as small as the size of the ship will permit, in order that the upper works may be as light as possible. Hence, as there are to be neither carlings nor lodges, the deck will require a greater number of beams, and a good round up, as on the contrary the deck will be apt to bend with its own weight. The most approved rule is therefore to have double the number of beams in the quarter deck as there are in a space of the same length in the upper deck.

Then proceed to shift the beams to the best advantage, tage, consulting the hatchways, ladder-ways, masts, bits, wheel, &c. With respect to the ladder-ways on the quarter decks of all ships, there should be one near the fore part of the great cabin for the officers, and another near the forecast end of the quarter deck, consisting of double ladders for the conveyance of the men up from the other decks in cases of emergency; and likewise one on each side of the fore part of the quarter deck from the gangway: and in every ship of the line all the beams from the forecast ladder-way to the after one should be open with gratings, both for the admission of air, and for the greater expedition of conveying different articles in the time of action.

Two scuttles are to be disposed one on each side of the mainmast, if it happens to come through the quarter deck, for the top tackles to pass through, to hook to the eye bolts drove in the upper deck for that purpose.

The steering wheel should be placed under the forepart of the roundhouse, and the two beams of the quarter deck, which come under it, should be placed conformable to the two uprights, so that they may tenon in them. The quarter deck beams should be kned at each end with one hanging and one lodging knee; which adds greatly to the strength of the side. The hanging knees which come in the great cabin may be of iron; their vertical arms to be two-thirds of the length of that of wood, and to reach the spirketing. It should be observed, that the beam abaft, which comes under the screen bulkhead, should round aft agreeable to the round of the bulkhead, for the support of the same.

The forecastle beams should be placed according as the works of the deck will admit. The hatchways are therefore to be considered first. There should be one for the funnel of the fire hearth to pass through, and one for the copper to admit of vent for the steam; and also one or two over the galley as the forecastle will admit of. The fore-topail-sheet bits should be so disposed as to come one pair on the fore and one on the aft side of the mast, to let into the side of the forecastle beams, and step on the upper deck beams below: there should also be a ladder-way at the fore part of the forecastle for the convenience of the fore part of the ship.

The beams may now be placed agreeable thereto, their number being four more than there are in a space in the upper deck equal in length to the forecastle; and where there happens to be a wide opening between the beams, as in the case of a hatchway, mast room, &c. then half a beam of fir may be introduced to make good the deficiency. The foremost beam should be of a breadth sufficient to take the aft side of the inboard arms of the catheads, as they are secured upon this beam by being bolted thereto. Every beam of the forecastle should be kned at each end with one hanging and one lodging knee: the vertical arms of the hanging knees should reach the spirketing, and the knees well bolted and carefully clenched.

Proceed to the roundhouse; the same things being observed with respect to the beams as in the quarter deck: for as the roundhouse beams are fided very small, it hence follows that they must be near to each other. Let therefore the number of beams on the roundhouse be four more than in the same length of the quarter deck; every other beam being of fir for lightness, and Application every oak beam may be kned at each end with one of the fore-hanging and one lodging knee; the hanging knees abaft may be of iron, their vertical arms to be in length two thirds of those of wood. The roundhouse should always have a great round up, both for strength and convenience. There must be on the roundhouse a small pair of knec-bits on each side of the mizenmast, turned round and scarfed over each other, and bolted through the mast carlings. There must also be a companion on the round-house placed over the middle of the coach, in order to give light thereto.

With regard to placing the roundhouse beams, the uprights of the steering wheel and the mizenmast are to be observed; as when the beams which interfere with those parts are properly spaced, the rest may be disposed of at discretion, or at an equal distance from each other, and letting the beam over the screen bulkhead have a proper round aft, agreeable to the quarter deck beam underneath.

The upper parts of the inboard works being now described, proceed next to the lower parts, or to those which come below the lower deck. Draw in the orlop, by taking the heights afore, at midships, and abaft, between that and the gun-deck, from the dimensions, and a curve described through these points will represent the upper part of the deck. Set off the thickness of the plank below, and the under side of the plank will be represented. As this deck does not run quite forward and aft as the other decks, the length of it must be therefore determined; for this purpose let the after beam be placed at a sufficient distance from aft to admit of the broad rooms being of a proper size for the ship, which will be under that beam of the gun-deck that comes at the second part from aft. The after beam being drawn in, proceed to space the other beams, placing them exactly under those of the gun-deck; and that which comes under the foremost beam of the gun-deck may terminate the fore part of the orlop. Draw the limber strake, by setting off its thickness above the cutting down line, and a line drawn parallel thereto will represent the limber strake. That part of the orlop which is over the after magazine, spirit room, and fifth room, and also that which is over the fore magazine, is laid with thicker planks than the rest of the deck; which is for the better security of those places, the planks being laid over the beams; but in the midships, from the fore part of the spirit room to the aft part of the fore magazine, the beams are laid level with the surface of the deck, and the planks are rabbeded in from one beam to the other.

In order to represent the orlop as just described, the dimensions of the different apartments above mentioned must be determined: Let the aft side of the after beam be the aft side of the after magazine, and from thence draw the bulkhead down to the limber strake; and the foreside of the third beam may be the foreside of the after magazine, drawing that bulkhead likewise, which will also form the aft side of the fifth room; the foreside of the fifth room may be drawn from the aft side of the fifth beam, which will also represent the aft side of the spirit room; then the foreside of the spirit room may be drawn from the foreside of the fifth beam. Hence from the foreside of the fifth beam quite aft the deck Application will be represented by the two lines already drawn, and of the fore; the upper side of the beams will be represented by the going Rules to the Construction of Ships.

Proceed next to the fore part of the orlop, letting the foreface of the after bits be the aft part of the forecastle magazine, drawing the bulkhead thereof, which will come to the aft side of the sixth beam; therefore, from the sixth beam to the forecastle end of the orlop, the plank and beams will be represented just in the same manner as before mentioned for the after part of the orlop; then the midship part of the deck will be represented by letting the upper line be the upper side of the plank, and likewise the upper side of the beams; and the lower line will represent the lower edge of the plank, only drawing it from beam to beam, and observing not to let it pass through them.

The hatchways, &c. may now be represented on the orlop, letting the main, fore, and after hatchway, be exactly under those of the gun deck; there must be one over the fish room, and one over the spirit room. There must be two scuttles over the after magazine for the passage to the magazine and light room. There should also be one afore the fourth beam from forward for the passage to the fore magazine, and one abaft the second beam for the passage to the light room.

The bulkheads for the fore and after parts of the well may be drawn from the lower deck beams to the orlop, and from thence to the limber frake in the hold. The shot lockers may also be represented, having one afore and one abaft the well: there should also be one abaft the forecastle magazine, the ends of which may be formed by the after bits. The steps of the masts may be drawn in by continuing their centres down to the limber frake; and likewise two crutches abaft the mizen step divided equally between that and the after part of the cutting down: the braft hooks may also be drawn, letting them be five in number below the lower deck hook, and all equally divided between that and the forestep. Hence every part of the inboard is described as far as necessary.

CHAP. V. Of the Method of Whole-moulding.

HAVING now finished the methods of laying down the several plans of a ship, any farther addition on this subject might appear unnecessary. We cannot, however, with propriety, omit to describe the method called whole-moulding, used by the ancients, and which still continues in use among those unacquainted with the more proper methods already explained. This method will be illustrated by laying down the several plans of a long-boat; the length of the keel being 29 feet, and breadth moulded nine feet.

Draw the straight line PO (fig. 37.) equal to 29 feet, the extreme length of the boat, and also to represent the upper edge of the keel. Let ⊕ be the station of the midship frame. From the points, P, ⊕, and O, draw the lines PT, ⊕M, and OS, perpendicular to PO. Make ⊕M, ⊕N, equal to the upper and lower heights of breadth respectively at the main frame, PT the height of breadth at the transom, and OS the height at the item. Describe the curve TMS to represent the sheer or extreme height of the side, which in a ship would be called the upper height of breadth line, or upper edge of the wale. Through the point N draw a curve parallel to TMS, to represent the breadth of the upper frake of a boat, or lower edge of the wale if in a flip. The dotted line TNS may also be drawn to represent the lower height of breadth.

Set off the rake of the port from P to p, and draw the line pt to represent the aft side of the port; then Tt will represent the round-up of the transom. Set off the breadth of the port from p to r, and from T to s, and draw the line rs to represent the foreside of the port, which may either be a curve or a straight line at pleasure. Set up the height of the tuck from p to k. Let k X be the thickness of the transom, and draw the line ZX to represent the foreside of the transom.

There is given the point S, the height of the sheer on the foreside of the item; now that side of the item is to be formed either by sweeps or some other contrivance. Set off the breadth of the item, and form the aft side of it.

Set up the dead-rising from ⊕ to d, and form the rising line r i s. Draw the line KL parallel to PO to represent the lower edge of the keel, and another to represent the thickness of the plank or the rabbet. The rabbet on the port and item may also be represented; and the stations of the timbers assigned, as ⊕, (1), 1, 2, 3, 4, 5, 6, 7, 8, 9; and ⊕, (A), A, B, C, D, E, F, G, H; and the sheer plan will be completed.

The half-breadth plan is to be formed next; for this purpose the perpendiculars TP, 9, 8, &c. must be produced. Upon M⊕ produced let off the half breadth from the line KL to R (fig. 38.); set off also the half breadth at the transom from K to b, and describe the extreme half breadth line b RX, making the forepart of the curve agreeable to the proposed round of the transom.

We may next proceed to form the timbers in the body plan. Let AB (fig. 39.) be the breadth moulded at ⊕. Erect the perpendicular CD in the middle of the line AB; draw the line mn distant therefrom the half thickness of the port, and xy the half thickness of the stern. Then take off the several portions of the perpendiculars ⊕, 1, 2, &c. intercepted between the upper edge of the keel and the rising line in the sheer plan, and set them up from C upon the line CD; through these points draw lines parallel to AC; take off also the several lower heights of breadth at ⊕, 1, 2, &c. from the sheer plan; and set them up from C upon the middle line in the body plan; and draw lines parallel to AC through these points: Then take off the several half breadths corresponding to each from the floor plan: and set them off on their proper half-breadth lines from the middle line in the body plan.

Construct the midship frame by Problem V. the form of which will in some measure determine the form of the rest. For if a mould be made on any side of the middle line to fit the curve part of it, and the rising line, or that marked bend mould (fig. 40.) and laid in such a manner that the lower part of it, which is straight, may be set upon the several rising lines, and the upper part just touch the point of the half breadth in the breadth line corresponding to that rising upon which the mould is placed, a curve may then be drawn by the mould to the rising line. In this manner we may proceed so far as the rising line is parallel to the lower height of the breadth line. Then a hollow mould must be made, the upper end of which is left straight, as that marked hollow mould (fig. 40.). This is applied in such a manner, that some part of the hollow may touch the side of the keel, and the straight part touch the back of the curve before described by the bend mould; and, beginning abaft, the straight part will always come lower on every timber, till we come to the midship timber, when it comes to the side of the keel. Having thus formed the timbers, so far as the whole mouldings will serve, the timbers abaft them are next formed. Their half breadths are determined by the sheer and floor plans, which are the only fixed points through which the curves of these timbers must pass. Some form these after timbers before the whole is moulded, and then make the hollow mould, which will be straighter than the hollow of either of these timbers. It is indifferent which are first formed, or what methods are used; for after the timbers are all formed, though every timber may appear very fair when considered by itself, it is uncertain what the form of the side will be. In order to find which, we must form several ribband and water lines; and if these do not make fair curves, they must be rectified, and the timbers formed from these ribband and water lines. In using the hollow mould, when it is applied to the curve of each timber, if the straight part is produced to the middle line, we shall have as many points of intersection as there are timbers; and if the heights above the base be transferred to the corresponding timbers in the sheer plan, a curve passing through these points is what is called a rising strait. This may be formed by fixing a point for the aftermost timber that is whole moulded, and transferring that height to the sheer plan. The curve must pass through this point, and fall in with the rising line somewhere abaft dead flat; and if the several heights of this line be transferred from the sheer to the middle line in the body plan, these points will regulate what is called the hauling down of the hollow mould.

The timbers in the after body being all formed, those in the fore body are formed, in the same manner, by transferring the several heights of the rising and breadth lines from the sheer to the body plans; the half breadths corresponding to each height must also be transferred from the floor to the body plan. The same hollow mould will serve both for the fore and after body; and the level lines, by which the water lines to prove the after body were formed, may be produced into the fore body, and by them the water lines to prove the fore body may be described.

Another method of proving the body is by ribband lines, which are formed by sections of planes inclined to the sheer plan, and intersecting the body plan diagonally, as before observed, of which there may be as many as may be judged necessary. As this has been already explained, we shall therefore lay down only one, represented in the body plan by the lines marked d i a. These are drawn in such a manner as to be perpendicular to as many timbers as conveniently may be. After they are drawn in the body plan, the several portions of the diagonal intercepted between the middle line and each timber must be transferred to the floor plan. Thus, fix one foot of the compasses in the point where the diagonal intersects the middle line in the body plan; extend the other foot to the point where the diagonal intersects the timber; for example, timber 9: Set off the same extent upon the perpendicular representing the plane of timber 9 from the point where it intersects the line K.L' on the floor plan; in like manner proceed with all the other timbers both in the fore and after body; and these shall have the points through which the curve must pass. If this should not prove a fair curve, it must be altered, observing to conform to the points as nearly as the nature of the curve will admit: so it may be carried within one point, and without another, according as we find the timbers will allow. For after all the ribband lines are formed, the timbers must, if needful, be altered by the ribband lines: this is only the reverse of forming the ribband lines; for taking the portions of the several perpendiculars intercepted between the line K.L and the curve of the ribband line in the floor plan, and setting them off upon the diagonal from the point where it intersects the middle line, we shall have the points in the diagonal through which the curves of the timbers must pass. Thus the distance between the line K.L and the ribband at timber 3 on the floor plan, when transferred to the body plan, will extend on the diagonal from the middle line to the point where the curve of timber 3 intersects that diagonal. The like may be laid off all the other timbers; and if several ribband lines be formed, they may be so contrived that their diagonals in the body plan shall be at such distances, that a point for every timber being given in each diagonal, will be sufficient to determine the form of all the timbers.

In stationing the timbers upon the keel for a boat, there must be room for two futtocks in the space before or abaft \( \oplus \); for which reason, the distance between these two timbers will be as much more than that between the other as the timber is broad. Here it is between \( \oplus \) and (A); which contains the distances between \( \oplus \) and (1), and the breadth of the timber besides.

The timbers being now formed, and proved by ribband and water lines, proceed then to form the transom, fashion-pieces, &c. by Problem VI.

This method of whole-moulding will not answer for the long timbers afore and abaft. They are generally canted in the same manner as those for a ship. In order to render this method more complete, we shall here describe the manner of moulding the timbers after they are laid down in the mould loft, by a rising square, bend, and hollow mould.

It was shewn before how to form the timbers by the bend and hollow moulds on the draught. The same method must be used in the loft; but the moulds must be made to their proper cantlings in real feet and inches. Now when they are set, as before directed, for moulding each timber, let the middle line in the body plan be drawn across the bend mould, and draw a line across the hollow mould at the point where it touches the upper edge of the keel; and let them be marked with the proper name of the timber, as in fig. 40. The graduations of the bend mould will therefore be exactly the same as the narrowing of the breadth. Thus, the distance between \( \oplus \) and \( \gamma \) on the bend mould is equal to the difference between the half breadth of timber 7 and that of \( \oplus \). The height of the head of each timber is likewise marked on the bend mould, and also the floor and breadth firmarks. The floor firmark is in that point where a straight edged batten touches the Method back of the bend mould, the batten being so placed as to touch the lower edge of the keel at the same time. The several risings of the floor and heights of the cutting down line are marked on the rising square, and the half breadth of the keel is set off from the side of it.

The moulds being thus prepared, we shall apply them to mould timber 7. The timber being first properly sided to its breadth, lay the bend mould upon it, so as may best answer the round according to the grain of the wood; then lay the rising square to the bottom of the bend mould, so that the line drawn across the bend mould at timber 7 may coincide with the line representing the middle of the keel upon the rising square; and draw a line upon the timber by the side of the square, or let the line be scored or cut by a tool made for that purpose, called a raising knife (E); this line so raised will be the side of the keel. Then the square must be moved till the side of it comes to 7 on the bend mould, and another line must be raised in by the side of it to represent the middle of the keel. The other side of the keel must likewise be raised after the same manner, and the point 7 on the rising square be marked on each side of the keel, and a line raised across at these points to represent the upper edge of the keel. From this line the height of the cutting-down line at 7 must be set up, and then the rising square may be taken away, and the timber may be raised by the bend mould, both inside and outside, from the head to the floor firmark, or it may be carried lower if necessary. After the firmarks and head of the timbers are marked, the bend mould may likewise be taken away, and then the hollow mould applied to the back of the sweep in such a manner that the point 7 upon it may intersect the upper side of the keel, before set off by the rising square; and when in this position the timber may be raised by it, which will complete the outside of the timbers. The inside of the timbers may likewise be formed by the hollow mould. The scantling at the keel is given by the cutting down before set off. The mould must be so placed as to touch the sweep of the inside of the timber formed before by the bend mould, and pass through the cutting down point.

The use of the firmarks is to find the true places of the futtocks; for as they are cut off three or four inches short of the keel, they must be so placed that the futtock and floor firmarks may be compared and coincide. Notwithstanding which, if the timbers are not very carefully trimmed, the head of the futtock may be either within or without its proper half breadth; to prevent which a half breadth staff is made use of.

The half breadth staff may be one inch square, and of any convenient length. Upon one side of it are set off from one end the several half-breadths of all the timbers in the after body, and those of the fore body upon the opposite side. On the other two sides are set off the several heights of the sheer, the after body on one side, and the fore body on its opposite. Two sides of the staff are marked half breadths, and the other two sides heights of the sheer.

The staff being thus prepared, and the floor timbers fastened on the keel, and levelled across, the futtocks must next be fastened to the floor timbers; but they must be set first to their proper half breadth and height. The half breadth staff, with the assistance of the ram-line*, serves to set them to the half breadth; for as* see next the keel of a boat is generally perpendicular to the horizon, therefore the line at which the plummet is suspended, and which is moveable on the ram line, will be perpendicular to the keel. Whence we may by it set the timbers perpendicular to the keel, and then set them to their proper half breadths by the staff: and when the two firmarks coincide, the futtock will be at its proper height, and may be nailed to the floor timbers and also to the breadth ribband, which may be set to the height of the sheer by a level laid across, taking the height of the sheer by the staff from the upper side of the keel; by which means we shall discover if the ribband is exactly the height of the sheer; and if not, the true height may be set off by a pair of compasses from the level, and marked on the timbers.

CHAP. VI. Of the Practice of Ship-Building.

The elevation, projection, and half-breadth plans, of a proposed ship being laid down on paper, we must next proceed to lay down these several plans on the mould loft of the real dimensions of the ship proposed to be built, and from which moulds for each separate part are to be made. The method of laying down these plans, from what has been already said, will, it is presumed, be no very difficult task to accomplish, as it is no more than enlarging the dimensions of the original draughts; and with respect to the moulds, they are very easily formed agreeable to the figure of the several parts of the ship laid down in the mould loft.

Blocks of wood are now to be prepared upon which the keel is to be laid. These blocks are to be placed at nearly equal distances, as of five or fix feet, and in such a manner that their upper surfaces may be exactly in the same plane, and their middle in the same straight line. This last is easily done by means of a line stretched a little more than the proposed length of the keel; and the upper planes of these blocks may be verified by a long and straight rule; and the utmost care and precaution must be taken to have these blocks properly bedded. Each block may be about fix or eight inches longer than the keel is in thickness; their breadth from 12 to 14 inches, and their depth from a foot to a foot and half.

The dimensions of the keel are to be taken from the mould loft, and the keel is to be prepared accordingly. As, however, it is seldom possible to procure a piece of wood of sufficient length for a keel, especially if for a large ship, it is, therefore, for the most part necessary to compose it of several pieces, and these pieces are to be scarfed together, and securely bolted, so as to make one entire piece. It must, however, be observed, that the pieces which compose the keel ought to be of such lengths, that a scarf may not be opposite to the step of any of the masts. Rabbets are to be formed on each side of the keel to receive the edge of the planks next

*(E) The term raising is used when any line is drawn by such an instrument instead of a pencil.

to it, or garboard strake, and the keel is to be laid on the blocks (r).

The stem, and the post, and the several transoms belonging to it, are to be prepared from the moulds, and rabbeted in like manner as the keel, to receive the ends of the plank. The transoms are to be bolted to the post at their middle, each at its respective height, taken from the elevation in the mould loft, and the extremities of the transoms are to be firmly connected with the fashion-pieces. Both stem and post are then to be erected, each at its respective extremity of the keel. The tenons at the heel of each being let into mortises prepared to receive them, and being let to their proper rakes or angles with the keel, are to be supported by props or shores. Pieces of wood called dead wood are to be laid upon and fixed to the upper side of the keel towards the fore and aft parts of it; the depth of the dead wood increasing with its distance from the middle, agreeable to the proposed form of the cutting-down line.

A line is to be stretched from the middle of the head of the stem to that of the post, called the ram line, upon which is a moveable line with a plummet affixed to it. The midship and other frames are to be erected upon the keel at their proper stations. The extremities of each frame are set at equal distances from the vertical longitudinal section of the ship, by moving the frame in its own plane until the plumb-line coincides with a mark at the middle between the arms of each frame; and although the keel is inclined to the horizon, yet the frames may also be set perpendicular to the keel by means of the plumb-line. The shores which are supporting the frames are now to be securely fixed, that the position of the frames may not be altered. The ribbands are now to be nailed to the frames at their proper places, the more effectually to secure them; and the intermediate vacancies between the frames filled up with filling timbers. For a perspective view of a ship framed, see fig. 2.

The frames being now stationed, proceed next to fix on the planks, of which the wales are the principal, being much thicker and stronger than the rest. The harpins, which may be considered as a continuation of the wales at their fore ends, are fixed across the hawse pieces, and surround the fore part of the ship. The planks that inclose the ship's sides are then brought about the timbers; and the clamps, which are of equal thickness with the wales, fixed opposite to the wales within the ship. These are used to support the ends of the beams, and accordingly stretch from one end of the ship to the other. The thick stuff or strong planks of the bottom within board are then placed opposite to the several scarsf of the timbers, to reinforce them throughout the ship's length. The planks employed to line the ship, called the ceiling or foot-waling, is next fixed in the intervals between the thick stuff of the hold. The beams are afterwards laid across the ship to support the decks, and are connected to the side by lodging and hanging knees: the former of which are exhibited at F, Plate CLXIX. See also the article Deck; and the hanging knees, together with the breadth, thickness, and position of the keel, floor timbers, futtocks, top-timbers, wales, clamps, thick stuff, planks within and without, beams, decks, &c.

The cable bits being next erected, the carlings and ledges, represented in Plate CLXIX, are disposed between the beams to strengthen the deck. The waterways are then laid on the ends of the beams throughout the ship's length, and the spirketing fixed close above them.—The upper deck is then planked, and the spring placed under the gunnel, or plankeer, in the waist.

Then proceed next to plank the quarter-deck and forecastle, and to fix the partners of the masts and capsterns with the coamings of the hatches. The breafhooks are then bolted across the stem and bow withinboard, the step of the foremast placed on the kelson, and the riders fayed to the inside of the timbers, to reinforce the sides in different parts of the ship's length. The pointers, if any, are afterwards fixed across the hold diagonally to support the beams; and the crotches stationed in the after hold to unite the half timbers. The flaps of the mainmast and capsterns are next placed; the planks of the lower decks and orlop laid; the navel-hoods fayed to the hawse holes; and the knees of the head, or cut-water, connected to the stern. The figure of the head is then erected, and the trail-board and cheeks fixed on the side of the knee.

The taffarel and quarter piece, which terminate the ship abaft, the former above and the latter on each side, are then disposed, and the stern and quarter galleries framed and supported by their brackets. The pumps, with their well, are next fixed in the hold; the timber boards laid on each side of the kelson, and the garboard strake fixed on the ship's bottom next to the heel without.

The hull being thus fabricated, proceed to separate the apartments by bulkheads or partitions, to frame the port-lids, to fix the catheads and ches-trees; to form the hatchways and scuttles, and fit them with proper covers or gratings. Next fix the ladders at the different hatchways, and build the manger on the lower deck, to carry off the water that runs in at the hawse-holes when the ship rides at anchor in a sea. The bread-room and magazines are then lined; and the gunnel, rails, and gangways fixed on the upper part of the ship. The cleats, kevels, and ranges, by which the ropes are fastened, are afterwards bolted or nailed to the sides in different places.

The rudder, being fitted with its irons, is next hung to the stern-post, and the tiller or bar, by which it is managed, let into a mortise at its upper end. The jeypers, or leaden tubes, that carry the water off from the decks, are then placed in holes cut through the ship's sides; and the standards bolted to the beams and sides above the decks to which they belong. The poop lanterns are laid fixed upon their cranes over the stern, and the bilge-ways or cradles placed under the bottom to conduct the ship steadily into the water whilst launching.

(v) In ships of war, which are a long while in building, it has been found that the keel is often apt to rot before they are finished. Upon this account, therefore, some builders have begun with the floor timbers, and added the keel afterwards. As the various pieces which have been mentioned above are explained at large in their proper places, it is therefore superfluous to enter into a more particular description of them here.

CHAP. VII. Of Improvements in the Masts and Rudder.

An account of a method for restoring masts of ships when wounded, or otherwise injured, in an easy, cheap, and expeditious manner, by Captain Edward Pakenham of the royal navy, has been published in the tenth volume of the Transactions of the Society for the Encouragement of Arts, &c. Captain Pakenham introduces his invention with the following observations:

"Among the various accidents which' ships are liable to at sea, none call more for the attention and exertion of the officer than the speedy refitting of the masts; and having observed, in the course of last war, the very great destruction made among the lower masts of our ship's from the enemy's mode of fighting, as well as the very great expense and delay in refitting a fleet after an action, particularly across the Atlantic—a very simple expedient has suggested itself to me as a resource in part; which appears so very speedy and secure, that the capacity of the meanest sailor will at once conceive it. I therefore think it my duty to state my ideas of the advantages likely to result from it; and I shall feel myself exceedingly happy should they in any wise contribute to remedy the evil.

"My plan, therefore, is, to have the heels of all lower masts so formed as to become the heads: but it is not the intention of the above plan to have the smallest alteration made in the heels of the present lower masts; for as all line-of-battle ships masts are nine inches in diameter larger at the heel than at the head, it will follow, that by letting in the trefoil-trees to their proper depth, the mast will form its own cheeks or hounds; and I flatter myself the following advantages will result from the above alteration.

"First, I must beg to observe, that all line-of-battle ships bury one-third of their lower masts, particularly three-deckers; it therefore follows, that if the wounds are in the upper third, by turning the mast so as to make the heel the head, it will be as good as new; for, in eight actions I was present in last war, I made the following observations:

"That in the said actions fifty-eight lower masts were wounded, and obliged to be shifted, thirty-two of which had their wounds in the upper third, and of course the ships detained until new masts were made. And when it is considered that a lower mast for a 90 or 74 stands government in a sum not less, I am informed, than 2000l. or 2300l. the advantages across the Atlantic resulting from the aforesaid plan will be particularly obvious; not to mention the probability of there being no fit spars in the country, which was the case in the instances of the Isis and Prince of Royal; and as I was one of the lieutenants of the Isis at that time, I am more particular in the circumstance of that ship. The Isis had both her lower masts wounded above the cathar pins in her action with the Caesar, a French 74; and as there were no spars at New York, the Isis was detained five weeks at that place.—Now, if her masts had been fitted on the plan I have proposed, I am confident she would have been ready for sea in 48 hours; and as a further proof, I beg leave to add, that the whole fleet, on the glorious 12th of April, had not the least accident of any consequence except what befel their lower masts, which detained them between eight and ten weeks at Jamaica.

"The delay of a ship while a new mast is making, and probably the fleet being detained for want of that ship, which frequently occurred in the course of last war, the taking of shipwrights from other work, with a variety of inconveniences not necessary to mention here, must be obvious to every officer that has made the smallest observations on sea-actions.

"You will further observe, that this substitute is formed on the most simple principle, fitted to the meanest capacity, and calculated to benefit all ships, from a first-rate down to the smallest merchantman, in cases of an accident by shot, a sprung, a rottenness, particularly as these accidents generally happen in the upper third of the mast and above the cheeks.

"It might probably be objected, that a difficulty and some danger might arise from the wounded part of the mast being below; but this will at once be obviated, when it is remembered, that as the wounded part is below the wedges, it may with ease be both fitted, caled, and secured, to any size or degree you please, with the addition of its being wedged on each deck."

Fig. 41. represents a mast of a first-rate in its proper state, the figures representing its thickness at the different divisions.

Fig. 42. the same mast inverted, the heel forming the head, and the trefoil-trees let into their proper depth, the additional thickness of the mast forming its own cheeks.

Fig. 43. the proposed mast, the figures representing the thickness of the mast in the proposed alterations; a, the heel made square; b, the letting in of the trefoil-trees; c, the third proportion of thickness continued up to where the fourth is in the present mast, or at least some little distance above the lower part of the cheeks, which is always looked upon as the weakest part of the mast; and by its being so proportioned, the mast, when turned, will be nearly as strong in the partners as before.

As the expense of a mast is much greater than is generally imagined, it is therefore thought proper to subjoin the following statement of the several articles used in making a 74 gun ship's mainmast.

<table> <tr> <th>Fishes for a spindle, 21 inches, 2 nails of two masts,</th> <th>Value.</th> </tr> <tr> <td></td> <td>L. 101 3 11</td> </tr> <tr> <th>Two side fishes, 22 inches, 2 ditto,</th> <td>133 10 9</td> </tr> <tr> <th>Fore and aft fishes, 22 inches, 2 nails of one mast,</th> <td>66 13 10</td> </tr> <tr> <th>Filh 21 1/2 inches, 1 nail of half a mast,</th> <td>29 8 5</td> </tr> <tr> <th>On the fore part</th> <td></td> </tr> <tr> <th>Iron 3 qrs. 19 lbs.</th> <td>1 5 9</td> </tr> <tr> <th>Aries load balk, 2 loads 22 feet,</th> <td>12 2 5</td> </tr> <tr> <th>Broadthing 2 loads 7 feet,</th> <td>11 1 7</td> </tr> <tr> <th>Dantzic fir timber.</th> <td></td> </tr> <tr> <th>Checks 4 loads 2 feet,</th> <td>20 18 4</td> </tr> <tr> <th>Iron, 5 ewt. 2 qrs. 24 lb.</th> <td>8 0 0</td> </tr> <tr> <th>Knees, elm timber, 13 feet,</th> <td>0 15 2</td> </tr> <tr> <th>Iron, 2 qrs. 14 lb.</th> <td>0 17 6</td> </tr> </table>

Carried over L. 385 17 8

<table> <tr> <th></th> <th>Value.</th> </tr> <tr> <td>Hoops and bolts on the body, 13 cwt.</td> <td>L. 385 17 8</td> </tr> <tr> <td>1 qr. 16 lb.</td> <td>18 15 0</td> </tr> <tr> <td>Treble-trees, straight oak timber, second sort, 2 loads 12 feet,</td> <td>10 2 4</td> </tr> <tr> <td>Iron, 3 qrs. 10 lb.</td> <td>1 3 6</td> </tr> <tr> <td>Crofts trees, straight oak timber, second sort, 1 load 12 feet,</td> <td>5 14 0</td> </tr> <tr> <td>Iron, 2 qrs. 2 lb.</td> <td>0 14 6</td> </tr> <tr> <td>Cap, elm timber, 1 load 24 feet,</td> <td>4 6 0</td> </tr> <tr> <td>Iron, 2 cwt. 14 lb.</td> <td>2 19 6</td> </tr> <tr> <td>Fullings, bolsters, bollins, and Dantzic fir, 1 load 2 feet,</td> <td>5 7 8</td> </tr> <tr> <td>Workmanship,</td> <td>78 6 0</td> </tr> <tr> <td>Main-topmast of a 74 gun ship,</td> <td>L. 513 6 2</td> </tr> <tr> <td>Main-top-gallant-mast,</td> <td>50 16 3</td> </tr> <tr> <td></td> <td>8 11 0</td> </tr> </table>

In order to lessen the enormous expense of masts, a propol was made some years ago to construct them hollow; and the author having premised several experiments which he had made, proceeds as follows:

"Galileo taught us, that the resistance or strength of a hollow cylinder is to that of a full cylinder, containing the same quantity of matter, as the total diameter of the hollow one is to the diameter of the full one; and these experiments show us, that the strength or resistance of two or more pieces of wood, fastened together at each end, and connected by a pillar, pillars, or framing, increases, at least to a certain degree, exeteris paribus, as the distance between them and number of pillars, provided the force is applied in the line or direction of the pillars.

"It is surprising that this discovery of Galileo has not been made subservient to more useful purposes. It is particularly applicable to the construction of masts, as not requiring that the hollow cylinder should be made of one solid piece of wood (G).

"However, the foregoing experiments teach us, that the same advantages may be obtained by other forms besides that of a cylinder; and that perhaps not only in a superior degree, but likewise with greater facility of execution; as by adopting a square figure, but more particularly by constructing them of separate pieces of wood, placed at proper distances from each other, in the following, or any other manner that may be found most convenient. Fig. 44, 45, and 46. exhibit each the transverse section of a mast, in which the small circles represent the trees or upright pieces of wood, and the lines the beams or framing of wood, which are employed at proper places and at proper distances from each other, for connecting them together. Perhaps solid frames of wood, placed at proper distances from each other, and filling up the whole dotted space, would answer better; in which event, the mast could be strongly hoop'd with iron at those places, and the uprights formed square, or of any other convenient form.

"It will be evident to those acquainted with this subject, that such masts would be greatly stronger than common ones containing the same quantity of materials. It is likewise evident that they would be less apt to spring, as being supported on a more extended base, and affording many conveniences for being better secured; and that they might be constructed of such wood as at present would be deemed altogether improper for masts: a circumstance of importance to Britain at all times, but more particularly now, when there is such difficulty in procuring wood proper for the kind of masts in common use."

An improvement in the rudder has lately taken place in several ships, particularly in some of those in the service of the East India Company. It will, however, be necessary previously to describe the usual form of the rudder, in order to show the advantages it possesses when constructed agreeable to the improved method.

No. 1. (fig. 47.) represents the rudder according to the common method of construction; in which A B is the axis of rotation. It is hence evident that a space considerably greater than the transverse section of the rudder at the counter must be left in the counter for the rudder to revolve in. Thus, let C A B (No. 2.) be the section of the rudder at the counter; then there must be a space similar to C D E in the counter, in order that the rudder may be moveable as required. Hence, to prevent the water from walking up the rudder case, a rubber coat, that is, a piece of tarred canvas, is nailed in such a manner to the rudder and counter as to cover the intermediate space: but the canvas being continually washed by the sea, soon becomes brittle, and unable to yield to the various turns of the rudder without breaking; in which case the ship is of course left pervious to the waves, even of three or four feet high; in fact, there are few men bred to the sea who have not been witnesses to the bad effects of such a space being left so ill guarded against the stroke of the waves; and many ships have, with great probability, been supposed to founder at sea from the quantity of water shipped between the rudder and counter.

It was to remedy this defect that the alteration above alluded to took place; which consists in making the upper part A F G (fig. 48. No. 1.) of the rudder A B D Fig. 48. cylindrical, and giving that part at the same time a cast forward, so that the axis of rotation may by that means be the line A D, passing as usual from E to D, through the centres of the braces which attach the rudder to the stern-post, and from E to A through the axis of the cylinder A F G, in order that the transverse section K H (No. 2.) at the counter may be a circle revolving upon its centre; in which case the space of half an inch is more than sufficient between the rudder and the counter, and consequently the necessity of a rudder coat entirely done away. But as it was foreseen, that if the rudder

(c) The strength of these cylinders would be still further augmented by having solid pieces of wood placed within them at proper distances, and securely fastened to them, in the same manner, and on the same principles, that nature has furnished reeds with joints; and for answering, in some respects, the same purpose as the pillars in the experiments alluded to. Load-water Line and Ship's Capacity.

Rudder by an accident was unshipped, this alteration might endanger the tearing away of the counter, the hole is made much larger than the transverse section of the cylindric part of the rudder, and the space between filled up with pieces of wood so fitted to the counter as to be capable of withstanding the shock of the sea, but to be easily carried away with the rudder, leaving the counter under such circumstances, in as safe a state as it would be agreeable in the present form of making rudders in the navy.

CHAP. VIII. Upon the Position of the Load-water Line, and the Capacity of a Ship.

The weight of the quantity of water displaced by the bottom of a ship is equal to the weight of the ship with its rigging, provisions, and every thing on board. If, therefore, the exact weight of the ship when ready for sea be calculated, and also the number of cubic feet in the ship's bottom below the load-water line, and hence the weight of the water she displaces; it will be known if the load-water line is properly placed in the draught.

The position of the ship in the draught may be either on an even keel, or to draw most water abaft; but an even keel is judged to be the best position in point of velocity, when the ship is constructed suitable thereto, that is, when her natural position is such. For when a ship is constructed to swim by the stern, and when brought down to her load-water made to swim on an even keel (as is the case with most ships that are thus built), her velocity is by that means greatly retarded, and also her strength greatly diminished: for the forepart being brought down lower than it should be, and the middle of the ship maintaining its proper depth in the water, the after part is by that means lifted, and the ship is then upon an even keel: but in consequence of her being out of her natural position, the after part is always placed downwards with a considerable strain, which will continue till the ship's sheer is entirely broken, and in time would fall into its natural position again: for which reason we see so many ships with broken backs, that is, with their sheers altered in such a manner that the sheer rounds up, and the highest part is in the midships.

Such are the disadvantages arising from not paying a due attention to those points in the construction of a draught; therefore, when the load-water line is found to be so situated at a proper height on the draught, according to the weight given for such a ship, and also drawn parallel to the keel, as supposing that to be the best failing trim, the next thing is to examine whether the body is constructed suitable thereto, in order to avoid the above-mentioned ill consequences.

In the first place, therefore, we must divide the ship equally in two lengthwise between the fore and after perpendiculars; and the exact number of cubic feet in the whole bottom beneath the load-water line being known, we must find whether the number of cubic feet in each part so divided is the same; and if they are found to be equal, the body of the ship may then be said to be constructed in all respects suitable to her swimming on an even keel, let the shape of the body be whatever it will; and which will be found to be her natural position at the load-water line. But if either of the parts should contain a greater number of cubic feet than the other, that part which contains the greatest will swim the most out of the water, and consequently the other will swim deepest, supposing the ship in her natural position for that construction. In order, therefore, to render the ship suitably constructed to the load-water line in the draught, which is parallel to the keel, the number of cubic feet in the left part must be subtracted from the number contained in the greater part, and that part of the body is to be filled out till it has increased half the difference of their quantities, and the other part is to be drawn in as much: hence the two parts will be equal, that is, each will contain the same number of cubic feet, and the ship's body will be constructed in a manner suitable to her swimming on an even keel.

If it is proposed that the ship laid down on the draught shall not swim on an even keel, but draw more water abaft than afore, then the fore and after parts of the ship's body below the load-water line are to be compared; and if these parts are unequal, that part which is least is to be filled out by half the difference, and the other part drawn in as much as before.

It will be necessary, in the first place, to calculate the weight of a ship ready equipped for sea, from the knowledge of the weight of every separate thing in her and belonging to her, as the exact weight of all the timber, iron, lead, masts, sails, rigging, and in short all the materials, men, provisions, and every thing else on board of her, from which we shall be able afterwards to judge of the truth of the calculation, and whether the load-water line in the draught be placed agreeable thereto. This is indeed a very laborious task, upon account of the several pieces of timber, &c. being of so many different figures, and the specific gravity of some of the timber entering the construction not being precisely determined.

In order to ascertain the weight of the hull, the timber is the first thing which comes under consideration: the number of cubic feet of timber contained in the whole fabric must be found; which we shall be able to do by help of the draught and the principal dimensions and scantlings; observing to distinguish the different kinds of timber from each other, as they differ considerably in weight; then the number of cubic feet contained in the different sorts of timber being reduced into pounds, and added, will be the weight of the timber. In like manner proceed to find the weight of the iron, lead, paint, &c. and the true weight of the whole will be found.

In reducing quantity to weight, it may be observed that a cubic foot of oak is equal to 66 pounds, and the specific gravity of the other materials is as follows:

<table> <tr> <th>Water being</th> <th>1000</th> <th>Oak is</th> <th>891.89</th> </tr> <tr> <th>Lead is</th> <th>11345</th> <th>Dry elm</th> <th>702.70</th> </tr> <tr> <th>Iron</th> <th>7643</th> <th>Dry fir</th> <th>648.64</th> </tr> </table>

An Estimate of the Weight of the Eighty Gun Ship in Plates CCCXC. and CCCCCXI. as fitted for Sea, with Six Months Provisions.

Weight of the Hull.

<table> <tr> <th></th> <th>N° of Ft.</th> <th>N° of lbs.</th> <th>Tons.</th> <th>Lbs.</th> </tr> <tr> <td>Oak timber at 66 lb. to the cubic foot</td> <td>48497</td> <td>3200802</td> <td>1428</td> <td>2082</td> </tr> <tr> <td>Fir timber at 48 lb. to the cubic foot</td> <td>4457</td> <td>213936</td> <td>95</td> <td>1136</td> </tr> <tr> <td>Elm timber at 52 lb. to the cubic foot</td> <td>520</td> <td>27040</td> <td>12</td> <td>160</td> </tr> <tr> <td>Carve work and lead work</td> <td></td> <td>4651</td> <td>2</td> <td>171</td> </tr> <tr> <td>Iron work, rudder irons, chain-plates, nails, &c.</td> <td></td> <td>88254</td> <td>39</td> <td>894</td> </tr> <tr> <td>Pitch, tar, oakum, and paint</td> <td></td> <td>17920</td> <td>8</td> <td></td> </tr> <tr> <td>Cook-room fitted with fire hearth</td> <td></td> <td>16123</td> <td>7</td> <td>443</td> </tr> <tr> <th>Sum</th> <th></th> <th>3568726</th> <th>1593</th> <th>406</th> </tr> </table>

Weight of the Furniture.

<table> <tr> <th></th> <th>N° of lbs.</th> <th>Tons.</th> <th>Lbs.</th> </tr> <tr> <td>Complete set of masts and yards, with the spare geer</td> <td>161000</td> <td>71</td> <td>1960</td> </tr> <tr> <td>Anchors with their stocks, and master's stores</td> <td>39996</td> <td>17</td> <td>1916</td> </tr> <tr> <td>Rigging</td> <td>69128</td> <td>30</td> <td>1928</td> </tr> <tr> <td>Sails, complete set, and spare</td> <td>32008</td> <td>14</td> <td>648</td> </tr> <tr> <td>Cables and hawfers</td> <td>73332</td> <td>32</td> <td>1652</td> </tr> <tr> <td>Blocks, pumps, and boats</td> <td>62030</td> <td>27</td> <td>1576</td> </tr> <tr> <th>Sum</th> <th></th> <th>437520</th> <th>195</th> <th>720</th> </tr> </table>

Weight of the Guns and Ammunition.

<table> <tr> <th></th> <th></th> <th></th> <th></th> </tr> <tr> <td>Guns with their carriages</td> <td>377934</td> <td>168</td> <td>714</td> </tr> <tr> <td>Powder and shot, powder barrels, &c.</td> <td>116320</td> <td>51</td> <td>2080</td> </tr> <tr> <td>Implement for the powder</td> <td>6500</td> <td>2</td> <td>2020</td> </tr> <tr> <td>Ditto for guns, crows, handspikes, &c.</td> <td>21573</td> <td>9</td> <td>1413</td> </tr> <tr> <th>Sum</th> <th></th> <th>521427</th> <th>232</th> <th>1747</th> </tr> </table>

Weight of the Officers Stores, &c.

<table> <tr> <th></th> <th></th> <th></th> <th></th> </tr> <tr> <td>Carpenter's stores</td> <td>20187</td> <td>9</td> <td>27</td> </tr> <tr> <td>Boatwain's stores</td> <td>21112</td> <td>9</td> <td>952</td> </tr> <tr> <td>Gunner's stores</td> <td>8964</td> <td>4</td> <td>4</td> </tr> <tr> <td>Caulker's stores</td> <td>5200</td> <td>2</td> <td>720</td> </tr> <tr> <td>Surgeon and chaplain's effects</td> <td>11096</td> <td>4</td> <td>2136</td> </tr> <tr> <th>Sum</th> <th></th> <th>66559</th> <th>29</th> <th>1599</th> </tr> </table>

Weight of the Provisions.

<table> <tr> <th></th> <th></th> <th></th> <th></th> </tr> <tr> <td>Provisions for six months for 700 men, with all their equipage</td> <td>858970</td> <td>383</td> <td>1050</td> </tr> <tr> <td>Water, casks, and captain's table</td> <td>933900</td> <td>416</td> <td>2060</td> </tr> <tr> <th>Sum</th> <th></th> <th>1792870</th> <th>800</th> <th>870</th> </tr> </table>

Weight of the Men, &c.

<table> <tr> <th></th> <th>N° of lbs.</th> <th>Tons.</th> <th>Lbs.</th> </tr> <tr> <td>Seven hundred men with their effects, including the officers and their effects</td> <td>316961</td> <td>141</td> <td>1121</td> </tr> <tr> <td>Ballast</td> <td>1478400</td> <td>660</td> <td></td> </tr> <tr> <th>Sum</th> <th></th> <th>1795361</th> <th>801</th> <th>1121</th> </tr> </table>

RECAPITULATION.

<table> <tr> <th></th> <th></th> <th></th> <th></th> </tr> <tr> <td>The hull</td> <td></td> <td>3568726</td> <td>1593</td> <td>406</td> </tr> <tr> <td>The furniture</td> <td></td> <td>437520</td> <td>195</td> <td>720</td> </tr> <tr> <td>Guns and ammunition</td> <td></td> <td>521427</td> <td>232</td> <td>1747</td> </tr> <tr> <td>Officers stores</td> <td></td> <td>66559</td> <td>29</td> <td>1599</td> </tr> <tr> <td>Provisions</td> <td></td> <td>1792870</td> <td>800</td> <td>870</td> </tr> <tr> <td>Weight of the men and ballast</td> <td></td> <td>1795361</td> <td>801</td> <td>1121</td> </tr> <tr> <th>Sum</th> <th></th> <th>8182463</th> <th>3652</th> <th>1983</th> </tr> </table>

Agreeable to the above estimate, we find that the eighty gun ship, with every thing on board and fit for sea, when brought down to the load-water line, weighs 8,182,463 pounds, or nearly 3653 tons. It may now be known if the load-water line in the draught be properly placed, by reducing the immered part of the body into cubic feet. For if the eighty gun ship, when brought down to the load-water line, weighs 3653 tons, the quantity of water displaced must also be 3653 tons: now a cubic foot of salt water being supposed to weigh 74 pounds, if therefore 8182463 be divided by 74, the quotient is 110573, the number of cubical feet which the must displace agreeable to her weight.

It is now necessary to find the number of cubic feet contained in the ship's bottom below the load-water line by calculation. If the bottom was a regular solid, this might be very easily done; but as it is otherwise, we must be satisfied with the following method by approximation, first given by M. Bouguer.

Take the lengths of every other of the lines that represent the frames in the horizontal plane upon the up-calculating per water line; then find the sum of these together, the contents with half the foremost and aftermost frames. Now multiply that sum by the distance between the frames, and the product is the area of the water line contained between the foremost and aftermost frames: then find the area of that part abait the after frame, which forms a trapezium, and also the port and rudder; find also the area of that part afore the foremost frame, and also of the stem and grip; then these areas being added to that first found, and the sum doubled, will be the area of the surface of the whole water line. The reason of this rule will be obvious to those acquainted with the first principles of mathematics.

The areas of the other water line may be found in the same manner: then the sum of all these areas, except that of the uppermost and lowermost, of which only one half of each must be taken, being multiplied by the distance between the water lines (these lines in the plane of elevation being equidistant from each other), and the product will be the solid content of the space contained between the lower and load-water lines. Add the area of the lower water line to the area of the upper side of the keel; multiply half that sum by the distance between them, the product will be the solid content of that part between the lower water line and upper edge of the keel, supposing them parallel to each other. But if the lower water line is not parallel to the keel, the above half sum is to be multiplied by the distance between them at the middle of the ship.

The solid contents of the keel must be next found, by multiplying its length by its depth, and that product by the breadth. Then the sum of these solid contents will be the number of cubic feet contained in the immersed part of the ship's bottom, or that part below the load-water line.

Determination of the number of Cubic Feet contained in the Bottom of the Eighty-Gun Ship. See Plates CCCCXC. and CCCCXCII.

The fore body is divided into five, and the after body into ten, equal parts in the horizontal plane; besides the parts contained between the foremost timber and the stem, and the aftermost timber and the poft. The plane of elevation is also divided into five equal parts by water lines drawn parallel to the keel. These water lines are also described upon the horizontal plane.

It is to be observed that there must be five inches added to each line that represents a frame in the horizontal plane for the thickness of the plank, that being nearly a mean between the thickness of the plank next the water and that on the lower part of the bottom.

Upper Water Line abaft Dead Flat.

<table> <tr> <th>The breadth at</th> <th>Ft.</th> <th>In.</th> </tr> <tr> <td>frame dead flat is 24 feet 10 inches, one-half of which is</td> <td>12</td> <td>5</td> </tr> <tr> <td>frame (4)</td> <td>24</td> <td>10</td> </tr> <tr> <td>frame 3</td> <td>24</td> <td>10</td> </tr> <tr> <td>frame 7</td> <td>24</td> <td>10</td> </tr> <tr> <td>frame 11</td> <td>24</td> <td>10</td> </tr> <tr> <td>frame 15</td> <td>24</td> <td>9½</td> </tr> <tr> <td>frame 19</td> <td>24</td> <td>5</td> </tr> <tr> <td>frame 23</td> <td>23</td> <td>10</td> </tr> <tr> <td>frame 27</td> <td>22</td> <td>9</td> </tr> <tr> <td>frame 31</td> <td>20</td> <td>11</td> </tr> <tr> <td>frame 35 is 16 feet 3 inches, the half of which is</td> <td>8</td> <td>1½</td> </tr> <tr> <td>Sum</td> <td>236</td> <td>7</td> </tr> <tr> <td>Distance between the frames</td> <td>10</td> <td>11</td> </tr> <tr> <td>Product</td> <td colspan="2">2582 8½</td> </tr> <tr> <td>Area of that part abaft frame 35</td> <td>78</td> <td>0</td> </tr> <tr> <td>rudder and poft</td> <td>5</td> <td>6</td> </tr> <tr> <td>Sum</td> <td>2666</td> <td>2½</td> </tr> <tr> <td>Area of the load water line from dead flat aft</td> <td colspan="2">5332 5</td> </tr> </table>

Second Water Line abaft Dead Flat.

<table> <tr> <th>The breadth at</th> <th>Ft.</th> <th>In.</th> </tr> <tr> <td>frame dead flat is 23 feet 10½ inches, the half of which is</td> <td>11</td> <td>11½</td> </tr> <tr> <td>frame (4)</td> <td>23</td> <td>10½</td> </tr> <tr> <td>frame 3</td> <td>23</td> <td>10½</td> </tr> <tr> <td>frame 7</td> <td>23</td> <td>10½</td> </tr> <tr> <td>frame 11</td> <td>23</td> <td>10½</td> </tr> <tr> <td>frame 15</td> <td>23</td> <td>8½</td> </tr> <tr> <td>frame 19</td> <td>23</td> <td>3½</td> </tr> <tr> <td>frame 23</td> <td>22</td> <td>5</td> </tr> <tr> <td>frame 27</td> <td>20</td> <td>10</td> </tr> <tr> <td>frame 31</td> <td>17</td> <td>8</td> </tr> <tr> <td>frame 35 is 8 feet 6 inches, the half of which is</td> <td>4</td> <td>3</td> </tr> <tr> <td>Sum</td> <td>219</td> <td>7½</td> </tr> <tr> <td>Distance between the frames</td> <td>10</td> <td>11</td> </tr> <tr> <td>Product</td> <td colspan="2">2397 4</td> </tr> <tr> <td>Area of that part abaft frame 35</td> <td>31</td> <td>7</td> </tr> <tr> <td>rudder and poft</td> <td>5</td> <td>5</td> </tr> <tr> <td>Sum</td> <td>2434</td> <td>4</td> </tr> <tr> <td>Area of the 2d water line from dead flat aft</td> <td colspan="2">4868 8</td> </tr> </table>

Third Water Line abaft Dead Flat.

<table> <tr> <th>The breadth at</th> <th>Ft.</th> <th>In.</th> </tr> <tr> <td>frame dead flat is 22 feet 1½ inches—half</td> <td>11</td> <td>0½</td> </tr> <tr> <td>frame (4)</td> <td>22</td> <td>1½</td> </tr> <tr> <td>frame 3</td> <td>22</td> <td>1½</td> </tr> <tr> <td>frame 7</td> <td>22</td> <td>1½</td> </tr> <tr> <td>frame 11</td> <td>22</td> <td>1</td> </tr> <tr> <td>frame 15</td> <td>21</td> <td>5</td> </tr> <tr> <td>frame 19</td> <td>20</td> <td>8½</td> </tr> <tr> <td>frame 23</td> <td>19</td> <td>3½</td> </tr> <tr> <td>frame 27</td> <td>16</td> <td>5</td> </tr> <tr> <td>frame 31</td> <td>11</td> <td>2½</td> </tr> <tr> <td>frame 35 is 4 feet 3 inches—half</td> <td>2</td> <td>1½</td> </tr> <tr> <td>Sum</td> <td>190</td> <td>8½</td> </tr> <tr> <td>Distance between the frames</td> <td>10</td> <td>11</td> </tr> <tr> <td>Area of that part abaft frame 35</td> <td>2081</td> <td>8</td> </tr> <tr> <td>rudder and poft</td> <td>14</td> <td>5½</td> </tr> <tr> <td>Sum</td> <td>2101</td> <td>7½</td> </tr> <tr> <td>Area of the 3d water line from dead flat aft</td> <td colspan="2">4203 3</td> </tr> </table>

Fourth Water Line abaft Dead Flat.

<table> <tr> <th>The breadth at</th> <th>Ft.</th> <th>In.</th> </tr> <tr> <td>frame dead flat is 20 feet 1 inch—half</td> <td>10</td> <td>0½</td> </tr> <tr> <td>frame (4)</td> <td>20</td> <td>1</td> </tr> <tr> <td>frame 3</td> <td>20</td> <td>1</td> </tr> <tr> <td>frame 7</td> <td>19</td> <td>11</td> </tr> <tr> <td>frame 11</td> <td>19</td> <td>7½</td> </tr> <tr> <td>frame 15</td> <td>19</td> <td>0</td> </tr> <tr> <td>Carry over</td> <td>108</td> <td>9</td> </tr> <tr> <td>Brought</td> <td colspan="2"></td> </tr> </table>

Brought over - - 108 9 frame 19 - - 17 7 1/2 frame 23 - - 14 10 frame 27 - - 10 11 frame 31 - - 5 11 frame 35 is 1 foot 11 1/2 inches—half 0 11 1/2 159 0 10 11

Area of that part abaft frame 35 1735 9 rudder and post - 9 9 - 5 0 1750 6

Area of the 4th water line from dead flat aft 3501 0

Fifth or Lower Water Line abaft Dead Flat.

The breadth at frame dead flat is 17 feet 2 inches—half 8 7 frame (4) - - 17 2 frame 3 - - 17 2 frame 7 - - 17 1 frame 11 - - 16 4 frame 15 - - 15 4 frame 19 - - 13 1 frame 23 - - 8 9 frame 27 - - 4 10 frame 31 - - 2 11 frame 35 is 1 foot 2 1/2 inches—half 0 7 1/2 121 10 1/2 10 11

Area of that part abaft frame 35 1330 2 rudder and post - 4 8 1/2 - 4 6 1/2 1339 5 2

Area of the 5th or lower water line from dead flat aft 2678 10 Half the area of the load water line 2666 2 1/2 Area of the second water line 4868 8 Area of the third water line 4203 3 Area of the fourth water line 3501 0 Half the area of the lower water line 1339 5 Sum - - 16578 6 1/2 Distance between the water lines - 4 1 Content in cubic feet between the lower and load-water lines - 67695 8 1/2 Area of the lower water line 2678 10 Area of the upper side of the keel 206 4 Sum - - 2885 2 Half - - 1442 7 Distance between the lower water line and the keel - 4 1 Cub. feet contained between lower water line and the keel 5890 6 1/2 5890 6 1/2 Content of the keel, lower part of rudder, and false keel - - 464 3 Cubic feet abaft the midship frame under water when loaded - - 74050 6

Upper or Load Water Line afore Dead Flat.

The breadth at frame dead flat is 24 feet 10 inches—half 12 5 frame E - - 24 10 frame I - - 24 8 1/2 frame N - - 24 0 frame Q - - 21 10 1/2 frame W is 15 feet 1 inch—half 7 6 1/2 Sum - - 115 4 1/2 Distance between the frames - 10 11 Product - - 1259 6 Area of the part afore frame W - 80 3 stem and knee - - 4 0 Sum - - 1343 9 Multiply by - - 2

Area of the load water line from dead flat forward - - 2687 6

Second Water Line afore Dead Flat.

The breadth at frame dead flat is 23 feet 10 1/2 inches—half 11 11 1/2 frame E - - 23 10 frame I - - 23 5 frame N - - 22 5 frame Q - - 19 11 frame W is 11 feet 11 inches—half 5 11 1/2 Sum - - 107 5 1/2 Distance between the frames - 10 11 Product - - 1173 9 Area of the part afore frame W, with the stem and knee - - 43 9 Sum - - 1217 6 Area of the second water line from dead flat forward - - 2435 0

Third Water Line afore Dead Flat.

The breadth at frame dead flat is 22 feet 1 1/2 inch—half 11 0 1/2 frame E - - 22 1 frame I - - 21 8 frame N - - 20 1 frame Q - - 16 1 1/2 frame W is 7 feet—half - 3 6 Sum - - 94 6 1/2 Distance between the frames - 10 11 Product - - 1031 10 Area of the part afore W, with the stem and gripe - - 25 10 Sum - - 1057 8 2 Area of the third water line from dead flat forward - - 2115 4 Fourth Water Line afore Dead Flat.

The breadth at frame dead flat is 20 feet 1 inch—half 10 0 1/2 frame E 20 0 1/2 frame I 19 3 frame N 16 5 frame Q 11 2 frame W is 2 feet nine inches—half 1 4 1/2

Sum 78 3 1/2 Distance between the frames 10 1 1/2

Product 854 8 Area of part before W, with the stem and gripe 8 10 1/2

Sum 863 6 1/2

Area of fourth water line from dead flat forward 1727 1 1/2

Fifth Water Line afore Dead Flat.

Breadth at frame dead flat is 17 feet 2 inches—half 8 7 frame E 16 9 frame I 14 10 frame N 10 9 1/2 frame Q is 5 feet—half 2 6

Sum 53 5 1/2 Distance between the frame 10 1 1/2

Product 583 7 Area of part afore Q 26 2 1/2 stem and knee 5 1 1/2

Sum 61 5 9 1/2

Area of the fifth or lower water line from dead flat forward 1231 6 Area of the upper side of the keel 87 4

Sum 1318 10 Half 659 5 Distance between the lower water line and keel 4 1

Content of the part contained between the lower water line and the keel in cub. feet 2692 7 1/2

Half of the area of the load water line 1343 9 Area of the second water line 2435 0 third water line 2115 4 fourth water line 1727 1 1/2 Half the area of the fifth or lower water line 615 9

Sum 8236 11 1/2 Distance between the water lines 4 1

Cubic feet contained between the lower and load water lines 33634 2 1/2 Cubic feet contained between lower water line and keel 2692 7 1/2 Content of the keel and false keel 196 6 Content afore midship frame under water when loaded 36523 4 Content abaf midship frame 74050 6 Content under water 110573 10 Weight of a cubic foot of salt water 74 lbs. Weight of the whole ship with every thing on board 8182463.8 lbs.

As the weight of the ship, with every thing on board, found by this calculation, is equal to that found by estimate; it hence appears that the water line is properly placed in the draught. It now only remains to find whether the body is constructed suitably thereto, that is, whether the ship will be in her natural position when brought down to that line. For this purpose a perpendicular must be erected 27 feet 1/2 inch. abaft dead flat, which will be the middle between the two perpendiculars and the place where the centre of gravity should fall, that the ship may swim on an even keel. The solidity of that part of the bottom contained between the said perpendicular and dead flat is then to be calculated, which will be found to be 25846 feet 7 inches.

Solidity of the bottom afore dead flat 36523 f. 4 in. between the middle and dead flat 25846 7

Solid content of the fore part of the bottom 62369 11 Solidity of the bottom abaft dead flat 74050 6 between the middle and dead flat 25846 7

Solid content of the aft. part of the bot. 48203 11 fore part of the bottom 62369 11

Difference 14166 Half 7083

Hence the after part of the ship's bottom is too lean by 7083 cubic feet, and the fore part as much too full. The after part must therefore be filled out until it has received an addition of 7083 feet, and the fore part must be drawn in till it has lost the same quantity, and the bottom will then be constructed suitable to the ship's swimming on an even keel.

CHAP. IX. Of the Tonnage of a Ship.

This is a question of equal importance and difficulty. By the tonnage of a ship is meant the weight of every thing that can with safety and expediency be taken on board that ship for the purpose of conveyance; it is also called the ship's burthen; and it is totally different from the weight of the whole as she floats in the water. It is perhaps best expressed by calling it the weight of the cargo. It is of importance, because it is by this that the merchant or freighter judges of the fitness of

Tonnage of the ship for his purpose. By this government judge a ship, of the ships requisite for transport service, and by this are all revenue charges on the ship computed. It is no less difficult to answer this question by any general rule which shall be very exact, because it depends not only on the cubical dimensions of the ship's bottom, but also on the scantling of her whole frame, and in short on the weight of every thing which properly makes part of a ship ready to receive on board her cargo. The weight of timber is variable; the scantling of the frame is no less so. We must therefore be contented with an average value which is not very remote from the truth; and this average is to be obtained, not by any mathematical discussion, but by observation of the burthen or cargo actually received, in a great variety of cases. But some sort of rule of calculation must be made out. This is and must be done by persons not mathematicians. We may therefore expect to find it incapable of being reduced to any principle, and that every builder will have a different rule. Accordingly the rules given for this purpose are in general very whimsical, measures being used and combined in a way that seems quite unconnected with stereometry or the measurement of solids. The rules for calculation are even affected by the interests of the two parties oppositely concerned in the result. The calculation for the tonnage by which the customs are to be exacted by government are quite different from the rule by which the tonnage of a transport hired by government is computed; and the same ship hired as a transport will be computed near one half bigger than when paying importation duties.

Yet the whole of this might be made a very simple business and very exact. When the ship is launched, let her light water line be marked, and this with the cubical contents of the immersed part be noted down, and be ingrossed in the deed by which the property of the ship is conveyed from hand to hand. The weight of her masts, sails, rigging, and sea-flores, is most easily obtained; and every builder can compute the cubical contents of the body when immered to the load water line. The difference of these is unquestionably the burthen of the ship.

It is evident from what has been already said in the last chapter, that if the number of cubic feet of water which the ship displaces when light, or, which is the same, the number of cubic feet below the light water line, found by the preceding method of calculation, be subtracted from the number of cubic feet contained in the bottom below the load water line, and the remainder reduced to tons by multiplying by 74, the number of pounds in a cubic foot of sea water, and divided by 2240, the number of pounds in a ton, the quotient will be the tonnage.

But as this method is very troublesome, the following rule for this purpose is that which is used in the king's and merchants service.

Let fall a perpendicular from the foreside of the stem at the height of the hawse holes (H), and another perpendicular from the back of the main post at the height of the wing transom. From the length between these two perpendiculares deduct three-fifths of the extreme breadth (r), and also as many times 2\frac{1}{2} inches as there are feet in the height of the wing transom above the upper edge of the keel; the remainder is the length of the keel for tonnage. Now multiply this length by the extreme breadth, and the product by half the extreme breadth, and this last product divided by 94 is the tonnage required.

Or, multiply the length of the keel for tonnage by the square of the extreme breadth, and the product divided by 188 will give the tonnage.

Calculation of the Tonnage of an Eighty Gun Ship.

I. According to the true method.

<table> <tr> <th></th> <th>Tons.</th> <th>lbs</th> <th>Calculation</th> </tr> <tr> <td>The weight of the ship at her launching draught of water</td> <td>1593</td> <td>406</td> <td>of the tonnage of the eighty gun ship.</td> </tr> <tr> <td>The weight of the furniture</td> <td>195</td> <td>720</td> <td></td> </tr> <tr> <td>The weight of the ship at her light water mark</td> <td>1788</td> <td>1126</td> <td></td> </tr> <tr> <td>The weight of the ship at the load water mark</td> <td>3652</td> <td>1983</td> <td></td> </tr> <tr> <td>Real burthen</td> <td>1864</td> <td>857</td> <td></td> </tr> </table>

II. By the common rule.

<table> <tr> <th></th> <th>Ft.</th> <th>Inch.</th> </tr> <tr> <td>Length from the foreside of the stem at the height of the hawse holes, to the aft side of the main post, at the height of the wing transom</td> <td>185</td> <td>10</td> </tr> <tr> <td>Three-fifths of the extreme breadth is</td> <td>29 f. 9\frac{1}{2} in.</td> <td></td> </tr> <tr> <td>Height of the wing transom is 28 f. 4 in. which multiplied by 2\frac{1}{2} inches is</td> <td>6</td> <td>8\frac{1}{2}</td> </tr> <tr> <td>Sum</td> <td>36</td> <td>6</td> </tr> <tr> <td>Length of the keel for tonnage</td> <td>149</td> <td>4</td> </tr> <tr> <td>Extreme breadth</td> <td>49</td> <td>8</td> </tr> <tr> <td>Product</td> <td>7416</td> <td>10\frac{1}{2}</td> </tr> <tr> <td>Half the extreme breadth</td> <td>24</td> <td>10</td> </tr> <tr> <td></td> <td>94)</td> <td>184185</td> <td>8\frac{1}{2}</td> </tr> <tr> <td>Burthen according to the common rule</td> <td>1959</td> <td>929</td> <td></td> </tr> <tr> <td>Real burthen</td> <td>1864</td> <td>857</td> <td></td> </tr> <tr> <td>Difference</td> <td></td> <td>95</td> <td>72</td> </tr> </table>

Hence an eighty gun ship will not carry the tonnage she is rated at by about 95 tons. As the body of this ship is fuller than in ships of war in general, there is therefore a nearer agreement between the tonnages found by the two different methods. It may be observed that greater ships of war carry less tonnage than they are rated at by the common rule, and that most merchant ships carry less, than the truth.

Common rule.

(1) In the merchant service this perpendicular is let fall from the fore side of the stem at the height of the wing transom, by reason of the hawse-holes being generally so very high in merchant ships, and their stems also having a great rake forward.

(1) The breadth understood in this place is the breadth from outside to outside of the plank.

Tonnage of a great deal more. In confirmation of this, it is thought proper to subjoin the dimensions of several ships, with the tonnage calculated therefrom.

1. Audacious of seventy-four guns.

Length on the gun deck - 168 f. o in. Length of the keel for tonnage - 138 0 Extreme breadth - 46 9 Depth of the hold - 19 9 Launching draught of water { afore 12 0 { abaft 17 4 Load draught of water { afore 20 6 { abaft 21 6 The weight of the ship at her launching draught of water - 1509 t. 678lbs. The weight of the furniture - 120 1500 Weight of the ship at her light water mark - 1629 2178 Weight of the ship at her load water mark - 2776 498 Real burthen - 1146 560

By the common rule. Length of the keel for tonnage - 138 f. o in. Extreme breadth - 46 9 Product - 6451 6 Half the extreme breadth - 23 4½ 94)150803

Tonnage according to the common rule 1604 643 Real burthen - 1146 560 Difference - 458 83

2. An East Indiaman.

Length between the perpendiculars forward and aft - 132 f. 8 in. Length of the keel for tonnage - 105 0 Extreme breadth - 38 0 Depth in hold - 16 0 Launching draught of water { afore 7 10 { abaft 11 10 Load draught of water { afore 19 8 { abaft 20 8 The weight of the ship at her launching draught of water - 602 t. 2116lbs. The weight of the furniture - 50 124 Weight of the ship at her light water mark - 653 Weight of the ship at her load water mark - 1637 1670 Real burthen - 984 1670

By the common rule. Keel for tonnage - 105 f. Extreme breadth - 38 Product - 3999 Half extreme breadth - 19 94)75819

Tonnage - 806 1096 Tonnage of a Ship. Real tonnage - 984 1670 Difference - 178 574

3. A Cutter.

Length of the keel for tonnage - 58 f. oin. Extreme breadth - 29 0 Launching draught of water { afore 5 10 { abaft 9 8 Load draught of water { afore 9 0 { abaft 12 0 The weight of the cutter at her launching - 147 t. 640lbs. Weight of the furniture - 9 199 Weight of the cutter at her light water mark - 156 839 Weight of the cutter at her load water mark - 266 1970 Real burthen - 110 1131

By the common rule. Keel for tonnage - 58 f. Extreme breadth - 29 Product - 1682 Half extreme breadth - 14½ 94)24389

Tonnage by the common rule - 259 1024 Real tonnage - 110 1131 Difference - 148 2133

The impropriety of the common rule is hence manifest, as there can be no dependence on it for ascertaining the tonnage of vessels.

We shall now subjoin the following experimental method of finding the tonnage of a ship.

Construct a model agreeable to the draught of the proposed ship, to a scale of about one-fourth of an inch to a foot, and let the light and load water lines be of determined on it. Then put the model in water, and load it until the surface of the water is exactly at the light water line; and let it be suspended until the water drains off, and then weighed. Now since the weights of similar bodies are in the triplicate ratio of their homologous dimensions, the weight of the ship when light is, therefore, equal to the product of the cube of the number of times the ship exceeds the model by the weight of the model, which is to be reduced to tons. Hence, if the model is constructed to a quarter of an inch scale, and its weight expressed in ounces; then to the constant logarithm 0.4893556, add the logarithm of the weight of the model in ounces, and the sum will be the logarithm of the weight of the ship in tons.

Again, the model is to be loaded until the surface of the water coincides with the load water line. Now the model being weighed, the weight of the ship is to be found by the preceding rule: then the difference between the weights of the ship when light and loaded is the tonnage required. It will also be worth while to add the following exact rule of Mr Parkins, who was many years foreman of the shipwrights in Chatham dockyard.

1. For Men of War.

Take the length of the gun-deck from the rabbet of the stem to the rabbet of the stern post. \( \frac{2}{3} \) of this is to be assumed as the length for tonnage, = L.

Take the extreme breadth from outside to outside of the plank; add this to the length, and take \( \frac{1}{3} \) of the sum; call this the depth for tonnage, = D.

Set up this height from the limber strake, and at that height take a breadth also from outside to outside of plank in the timber when the extreme breadth is found, and another breadth in the middle between that and the limber strake; add together the extreme breadth and these two breadths, and take \( \frac{1}{3} \) of the sum for the breadth for tonnage, = D.

Multiply L, D, and B together, and divide by 49. The quotient is the burthen in tons.

The following proof may be given of the accuracy of this rule. Column 1. is the tonnage or burthen by the king's measurement; col. 2. is the tonnage by this rule; and, col. 3. is the weight actually received on board these ships at Blackstakes:

<table> <tr> <th></th> <th>Victory</th> <th>London</th> <th>Arrogant</th> <th>Diadem</th> <th>Adamant</th> <th>Dolphin</th> <th>Amphion</th> <th>Daphne</th> </tr> <tr> <th></th> <th>100 guns.</th> <th>96</th> <th>74</th> <th>64</th> <th>50</th> <th>44</th> <th>32</th> <th>20</th> </tr> <tr> <th></th> <th>2162</th> <th>1845</th> <th>1614</th> <th>1369</th> <th>1044</th> <th>879</th> <th>667</th> <th>429</th> </tr> <tr> <th></th> <th>1839</th> <th>1575</th> <th>1308</th> <th>1141</th> <th>870</th> <th>737</th> <th>554</th> <th>349</th> </tr> <tr> <th></th> <th>1840</th> <th>1677</th> <th>1314</th> <th>965</th> <th>886</th> <th>758</th> <th>549</th> <th>374</th> </tr> </table>

2. For Ships of Burthen.

Take the length of the lower deck from the rabbet of the stem to the rabbet of the stern-post; then \( \frac{1}{3} \) of this is the length for tonnage, = L.

Add the length of the lower deck to the extreme breadth from outside to outside of plank; and take \( \frac{1}{3} \) of the sum for the depth for tonnage, = D.

Set up that depth from the limber strake, and at this height take a breadth from outside to outside. Take another at \( \frac{2}{3} \) of this height, and another at \( \frac{1}{3} \) of the height. Add the extreme breadth and these three breadths, and take the 4th of the sum for the breadth for tonnage, = B.

Multiply L, D, and B, and divide by 36\( \frac{1}{2} \). The quotient is the burthen in tons.

This rule rests on the authority of many such trials, as the following:

<table> <tr> <th></th> <th>King's Meas.</th> <th>Rule.</th> <th>reed. on bd.</th> </tr> <tr> <th></th> <th></th> <th></th> <th></th> </tr> <tr> <td>Northington Indiaman</td> <td>676</td> <td>1053</td> <td>1064</td> </tr> <tr> <td>Granby Indiaman</td> <td>786</td> <td>1179</td> <td>1179</td> </tr> <tr> <td>Union coallier</td> <td>193</td> <td>266</td> <td>289</td> </tr> <tr> <td>Another coallier</td> <td>182</td> <td>254</td> <td>277</td> </tr> </table>

CHAP. X. Of the Scale of Solidity.

By this scale the quantity of water displaced by the bottom of the ship, for which it is constructed, answering to a given draught of water, is easily obtained; and also the additional weight necessary to bring her down to the load water line.

In order to construct this scale for a given ship, it is necessary to calculate the quantity of water displaced by the keel, and by that part of the bottom below each water line in the draught. Since the areas of the several water lines are already computed for the eighty-gun ship laid down in Plates CCCCXCI. and CCCCXCI., the contents of these parts may hence be easily found for that ship, and are as follow.

<table> <tr> <th rowspan="2">Draught of Water.</th> <th colspan="2">Water displaced in</th> </tr> <tr> <th>Cubic feet.</th> <th>tons. lbs.</th> </tr> <tr> <td>Keeland false keel</td> <td>2 f. 3 in.</td> <td>660.9</td> <td>21 1855</td> </tr> <tr> <td>Diff. bet. keel and 5th w. line</td> <td>4 1</td> <td>8583.1\frac{1}{2}</td> <td>283 1233</td> </tr> <tr> <td>Sum</td> <td>6 4</td> <td>9243.10\frac{1}{2}</td> <td>305 848</td> </tr> <tr> <td>Diff. 5th and 4th w. line</td> <td>4 1</td> <td>18657.8\frac{1}{2}</td> <td>616 828</td> </tr> <tr> <td>Sum</td> <td>10 5</td> <td>27901.7\frac{1}{2}</td> <td>921 1676</td> </tr> <tr> <td>Dist. 4th and 3d w. line</td> <td>4 1</td> <td>23574.6\frac{1}{2}</td> <td>778 1795</td> </tr> <tr> <td>Sum</td> <td>14 6</td> <td>51476.2\frac{1}{2}</td> <td>1700 1231</td> </tr> <tr> <td>Dist. 3d and 2d w. line</td> <td>4 1</td> <td>27812.1\frac{1}{2}</td> <td>918 1775</td> </tr> <tr> <td>Sum</td> <td>18 7</td> <td>79288.3\frac{1}{2}</td> <td>2619 796</td> </tr> <tr> <td>Dist. 2d and 1st w. line</td> <td>4 1</td> <td>31285.7\frac{1}{2}</td> <td>1033 1218</td> </tr> <tr> <td>Sum</td> <td>22 8</td> <td>110573.11\frac{1}{2}</td> <td>3652 1984</td> </tr> </table>

Construct any convenient scale of equal parts to represent tons, as scale No. 1. and another to represent feet as No. 2.

Draw the line AB (fig. 36.) limited at A, but produced indefinitely towards B. Make AC equal to the depth of the keel, 2 feet 3 inches from scale No. 2. and through C draw a line parallel to AB, which will represent the upper edge of the keel; upon which set off for C c equal to 21 tons 18 5 lbs. taken from scale No. 1, the ship of eighty guns. Again, make AD equal to the distance between the lower edge of the keel and the fifth water line, namely, 6 feet 4 inches, and a line drawn through D parallel to AB will be the representation of the lower water line; and make DB equal to 305 tons 848 lbs. the corresponding tonnage. In like manner draw the other water lines, and lay off the corresponding tonnages accordingly: then through the points A, c, b, e, f, g, h, draw the curve Ac b e f g h. Through h draw hB perpendicular to AB, and it will be the greatest limit of the quantity of water expressed in tons displaced by the bottom of the ship, or that when she is brought down to the load water line. And since the ship displaces 1788 tons at her light water-mark, take therefore that quantity from the scale No. 1. which being laid upon AB from A to K, and KL drawn perpendicular to AB, will be the representation of the light water Scale of water line for tonnage. Hence the scale will be completed.

Let it now be required to find the number of cubic feet displaced when the draught of water is 17 feet, and above scale the number of additional tons necessary to bring her down to the load water mark.

Take the given draught of water 17 feet from the scale No 2, which laid from it will reach to I; through which draw the line IMN parallel to AB, and intersecting the curve in AC; then the distance IM applied to the scale No 1, will measure about 2248 tons, the displacement answerable to that draught of water; and MN applied to the same scale will measure about 1405 tons, the additional weight necessary to bring her down to the load water mark. Also the nearest distance between M and the line KL will measure about 460 tons, the weight already on board.

It will conduce very much to facilitate this operation to divide KB into a scale of tons taken from the scale No 1, beginning at B, and also h L, beginning at h. Then when the draught of water is taken from the scale No 2, and laid from it to I, as in the former example, and IMN drawn parallel to AB, and intersecting the curve in M. Now through M draw a line perpendicular to AB, and it will meet KB in a point representing the number of tons aboard, and also h L in a point denoting the additional weight necessary to load her.

Again, if the weight on board be given, the corresponding draught of water is obtained as follows.

Find the given number of tons in the scale KB, through which draw a line perpendicular to AB; then through the point of intersection of this line with the curve draw another line parallel to AB. Now the distance between A and the point where the parallel intersected AH being applied to the scale No 2, will give the draught of water required.

Any other case to which this scale may be applied will be obvious.

Book II. Containing the Properties of Ships, &c.

Chap. I. Of the Equilibrium of Ships.

Since the pressure of fluids is equal in every direction, the bottom of a ship is therefore acted upon by the fluid in which it is immersed; which pressure, for any given portion of surface, is equal to the product of that portion by the depth and density of the fluid: or it is equal to the weight of a column of the fluid whose base is the given surface, and the altitude equal to the distance between the surface of the fluid and the centre of gravity of the surface pressed. Hence a floating body is in equilibrium between two forces, namely, its gravity and the vertical pressure of the fluid; the horizontal pressure being destroyed.

Let ABC (fig. 49.) be any body immersed in a fluid whose line of floatation is GH: hence the pressure of the fluid is exerted on every portion of the surface of the immersed part AFCH. Let EF, CD be any two small portions contained between the lines ED, FC, parallel to each other, and to the line of floatation GH: then the pressure exerted upon EF is expressed by EF × IK, IK being the depth of EF or CD; the density of the fluid being supposed equal to 1. In like manner the pressure upon CD is equal to CD × IK. Now since the pressure is in a direction perpendicular to the surface, draw therefore the line EL perpendicular to EF, and DM perpendicular to DC, and make each equal to the depth IK, below the surface. Now the effort or pressure of the fluid upon EF will be expressed by EF × EL, and that upon CD by CD × DM. Complete the parallelograms ON, QS, and the pressure in the direction EL is resolved into EN, EO, the first in a horizontal, and the second in a vertical direction. In like manner, the pressure in the direction DM is resolved into the pressures DS, DQ. Hence the joint effect of the pressures in the horizontal and vertical directions, namely, EF × EN, and EF × EO, will be equal to EF × EL: For the same reason, CD × DP + CD × DQ = CD × DM. But the parts of the pressures in a horizontal direction EF × EN, and CD × DP, are equal. For, because of the similar triangles ENL, ERF, and DPM, DSC, we have \( \frac{EL}{EN} = \frac{EF}{FR} \) and \( \frac{DM}{DP} = \frac{DC}{CS} \). Hence DM × CS = DP × DC, and EL × FR = EN × EF. Now since EL = DM, and FR = CS, therefore EL × FR = DM × CS = DP × DC = EN × EF. Hence since EF × EN = DP × CD, the effects of the pressures in a horizontal direction are therefore equal and contrary, and consequently destroy each other.

The pressure in a vertical direction is represented by EO × EF, DQ × DC, &c. which, because of the similar triangles EOL, ERF, and DLM, DSC, become EL × ER, DM × DS, &c. or IK × ER, IK × DS, &c. By applying the same reasoning to every other portion of the surface of the immersed part of the body, it is hence evident that the sum of the vertical pressures is equal to the sum of the corresponding displaced columns of the fluid.

Hence a floating body is pressed upwards by a force equal to the weight of the quantity of water displaced; of a ship and since there is an equilibrium between this force and equal to the weight of the body, therefore the weight of a floating body is equal to the weight of the displaced fluid (k). Hence also the centre of gravity of the body and the centre of gravity of the displaced fluid are in the same vertical, otherwise the body would not be at rest.

Chap. II. Upon the Efforts of the Water to bend a Vessel.

When it is said that the pressure of the water upon the immersed part of a vessel counterbalances its weight, complete, it is supposed that the different parts of the vessel are closely connected together, that the forces which act upon its surface are not capable of producing any change. For we may easily conceive, if the connection of the parts were not sufficiently strong, the vessel would run the risk either of being broken in pieces, or of suffering some alteration in its figure.

The vessel is in a situation similar to that of a rod

(k) Upon this principle the weight and tonnage of the 80 gun ship laid down were calculated. AB (fig. 50.), which being acted upon by the forces A a, C c, D d, B b, may be maintained in equilibrium, provided it has a sufficient degree of stiffness: but as soon as it begins to give way, it is evident it must bend in a convex manner, since its middle would obey the forces C c and D d, while its extremities would be actually drawn downwards by the forces A a and B b.

The vessel is generally found in such a situation; and since similar efforts continually act, whilst the vessel is immerfered in the water, it happens but too often that the keel experiences the bad effect of a strain. It is therefore very important to inquire into the true cause of this accident.

For this purpose, let us conceive the vessel to be divided into two parts by a transverse section through the vertical axis of the vessel, in which both the centre of gravity G (fig. 51.) of the whole vessel and that of the immersed part are situated: so that one of them will represent the head part, and the other that of the stern, each of which will be considered separately. Let g be the centre of gravity of the entire weight of the first, and o that of the immersed part corresponding. In like manner, let γ be the centre of gravity of the whole after part, and ω that of its immediate portion.

Now it is plain, that the head will be acted upon by the two forces g m and o n, of which the first will press it down, and the latter push it up. In the same manner, the stern will be pressed down by the force γ μ, and pushed by the force ω ν. But these four forces will maintain themselves in equilibrium, as well as the total forces reunited in the points G and O, which are equivalent to them; but whilst neither the forces before nor those behind fall in the same direction, the vessel will evidently sustain efforts tending to bend the keel upwards, if the two points o and ω are nearer the middle than the two other forces g m and γ μ. A contrary effect would happen if the points s and w were more distant from the middle than the points g and γ.

But the first of these two causes usually takes place almost in all vessels, since they have a greater breadth towards the middle, and become more and more narrow towards the extremities; whilst the weight of the vessel is in proportion much more considerable towards the extremities than at the middle. From whence we see, that the greater this difference becomes, the more also will the vessel be subject to the forces which tend to bend its keel upwards. It is therefore from thence that we must judge how much strength it is necessary to give to this part of the vessel, in order to avoid such a consequence.

If other circumstances would permit either to load the vessel more in the middle, or to give to the part immersed a greater capacity towards the head and stern, such an effect would no longer be apprehended. But the definition of most vessels is entirely opposite to such an arrangement: by which means we are obliged to strengthen the kneel as much as may be necessary, in order to avoid such a disaster.

We shall conclude this chapter with the following practical observations on the hogging and fagging of ships by Mr Hutchinson of Liverpool:

"When ships with long floors happen to be laid adry upon mud or fand, which makes a solid resistance against the long straight floors amidships, in comparison with the two sharp ends, the entrance and run meet with little support, but are pressed down lower than the flat of the floor, and in proportion hogs the ship amidships; which is too well known from experience to occasion many total losses, or do so much damage by hogging them, as to require a vast deal of trouble and expense to save and repair them, fo as to get the hog taken out and brought to their proper thee again: and to do this the more effectually, the owners have often been induced to go to the expence of lengthening them; and by the common method, in proportion as they add to the burden of these ships, by lengthening their too long straight floors in their main bodies amidships, so much do they add to their general weakness to bear hardships either on the ground or afloat; for the scantling of their old timber and plank is not proportionable to bear the additional burden that is added to them.

"But defects of this kind are best proved from real and incontrovertible facts in common practice. At the very time I was writing upon this subject, I was called upon for my advice by the commander of one of those strong, long, straight floored ships, who was in much trouble and distraction of mind for the damage his ship had taken by the pilot laying her on a hard, gentle sloping fand, at the outside of our docks at Liverpool, where it is common for ships that will take the ground to lie for a tide, when it proves too late to get into our wet docks. After recommending a proper ship carpenter, I went to the ship, which lay with only a small keel, yet was greatly hogged, and the butts of her upper works strained greatly on the lee side; and the seams of her bottom, at the lower futtock heads, vastly opened on the weather fide: all which strained parts were agreed upon not to be caulked, but filled with tallow, putty, or chay, &c. with raw bullocks hides, or canvas, nailed with battons on her bottom, which prevented her sinking with the flow of the tide, without hindering the prelude of water from righting and closing the seams again as she floated, so as to enable them to keep her free with pumping. This vessel, like many other instances of ships of this construction that I have known, was faved and repaired at a very great expence in our dry repairing docks. And that their bottoms not only hog upwards, but fag (or curve) downwards, to dangerous and fatal degrees, according to the strain or pressure that prevails upon them, will be proved from the following facts:

"It has been long known from experience, that when ships load deep with very heavy cargoes or materials that are flowed too low, it makes them to very labourome at sea, when the waves run high, as to roll away their masts; and after that misfortune causes them to labour and roll the more, so as to endanger their working and straining themselves to pieces: to prevent which, it has been long a common practice to leave a great part of their fore and after holds empty, and to flow them as high as possible in the main body at midships, which causes the bottoms of these long straight-floored ships to fag downwards, in proportion as the weight of the cargo flowed there exceeds the prelude of the water upwards, so much as to make them dangerously and fatally leaky.

"I have known many instances of those strong ships of 500 or 600 tons burdens built with long straight-floors, on the east coast of England, for the coal and timber trade, come loaded with timber from the Baltic to Liverpool, where they commonly load deep with rock salt, which is too heavy to fill their holds, so that for the above reasons they flowed it high amidships, and left large empty spaces in their fore and after holds, which caused their long straight floors to sag downwards, so much as to make their hold stanchions amidships, at the main hatchway, settle from the beams three or four inches, and their mainmasts settle so much as to oblige them to set up the main rigging when rolling hard at sea, to prevent the masts being rolled away; and they were rendered so leaky as to be obliged to return to Liverpool to get their leaks stopped at great expense. And in order to save the time and expense in discharging them, endeavours were made to find out and stop their leaks, by laying them ashore dry on a level land; but without effect: for though their bottoms were thus fagged down by their cargoes when afloat, yet when they came a-dry upon the land, some of their bottoms hogged upwards so much as to raise their mainmasts and pumps so high as to tear their coats from their decks; so that they have been obliged to discharge their cargoes, and give them a repair in the repairing dock, and in some to double their bottoms, to enable them to carry their cargoes with safety, flowed in this manner. From this cause I have known one of these strong ships to founder.

"Among the many instances of ships that have been distressed by carrying cargoes of lead, one failed from hence bound to Marseilles, which was soon obliged to put back again in great distress, having had four feet water in the hold, by the commander's account, owing to the ship's bottom fagging down to such a degree as made the hold stanchions settle fix inches from the lower deck beams amidships; yet it is common with these long straight floored ships, when these heavy cargoes are discharged that make their bottoms sag down, then to hog upwards: so that when they are put into a dry repairing dock, with empty holds, upon straight blocks, they commonly either split the blocks close fore and aft, or damage their keels there, by the whole weight of the ship lying upon them, when none lies upon the blocks under the flat of their floors amidships, that being hogged upwards; which was the case of this ship's bottom; though fagged downwards fix inches by her cargo, it was now found hogged so much that her keel did not touch the blocks amidships, which occasioned so much damage to the after part of the keel, as to oblige them to repair it; which is commonly the case with these ships, and therefore deserving particular notice."

In order to prevent these defects in ships, "they should all be built with their floors or bottoms lengthwise, to form an arch with the projecting part downwards, which will naturally not only contribute greatly to prevent their taking damage by their bottoms hogging and straining upwards, either aground or afloat, as has been mentioned, but will, among other advantages, be a help to their failing, steering, staying, and waring."

CHAP. III. Of the Stability of Ships.

When a vessel receives an impulse or pressure in a horizontal direction, so as to be inclined in a small degree, the vessel will then either regain its former position as the pressure is taken off, and is in this case said to be possessed of stability; or it will continue in its inclined state; or, lastly, the inclination will increase until the vessel is overturned. With regard to the first case, it is evident that a sufficient degree of stability is necessary in order to sustain the efforts of the wind; but neither of the other two cases must be permitted to have place in vessels.

Let CED (fig. 52.) be the section of a ship passing Fig. 51. through its centre of gravity, and perpendicular to the sheer and floor plans; which let be in equilibrium in a fluid; AB being the water line, G the centre of gravity of the whole body, and g that of the immersed part AEB. Let the body receive now a very small inclination, so that a E b becomes the immersed part, and γ its centre of gravity. From γ draw γ M perpendicular to a b, and meeting g G, produced, if necessary, in M. If, then, the point M thus found is higher than G the centre of gravity of the whole body, the body will, in this case, return to its former position, the prelude being taken off. If the point M coincides with G, the vessel will remain in its inclined state; but if M be below G, the inclination of the vessel will continually increase until it is entirely over-set.

The point of intersection M is called the metacenter, and is the limit of the altitude of the centre of gravity of the whole vessel. Whence it is evident, from what has already been said, that the stability of the vessel increases with the altitude of the metacenter above the centre of gravity; But when the metacenter coincides with the centre of gravity, the vessel has no tendency whatever to move out of the situation into which it may be put. Thus, if the vessel be inclined either to the right or left side, it will remain in that position until a new force is impressed upon it: in this case, therefore, the vessel would not be able to carry sail, and is hence unfit for the purposes of navigation. If the metacenter is below the common centre of gravity, the vessel will instantly overset.

As the determination of the metacenter is of the utmost importance in the construction of ships, it is therefore thought necessary to illustrate this subject more particularly.

Let AEB (fig. 52.) be a section of a ship perpendicular to the keel, and also to the plane of elevation, and passing through the centre of gravity of the ship, and also through the centre of gravity of the immersed part, which let be g.

Now let the ship be supposed to receive a very small inclination, so that the line of floatation is a, b, and γ the centre of gravity of the immersed part a E b. From γ draw γ M perpendicular to a b, and intersecting GM in M, the metacenter, as before. Hence the prelude of the water will be in the direction γ M.

In order to determine the point M, the metacenter, the position of γ with respect to the lines AB and g G, must be previously ascertained. For this purpose, let the ship be supposed to be divided into a great number of sections by planes perpendicular to the keel, and parallel to each other, and to that formerly drawn, these planes being supposed equidistant. Let AEB (fig. 53.) Fig. 53: be one of these sections, g the centre of gravity of the immersed part before inclination, and γ the centre of gravity of the immersed part when the ship is in its inclined state; the distance g γ between the two centres of stability of gravity in each section is to be found. Let AB be the line of floatation of the ship when in an upright state, and ab the water line when inclined. Then, because the weight of the ship remains the same, the quantity of water displaced will also be the same in both cases, and therefore AEB = aEb, each sustaining the same part of the whole weight of the ship. From each of these take the part AEb, which is common to both, and the remainders AOa, BOb will be equal; and which, because the inclination is supposed very small, may be considered as rectilineal triangles, and the point O the middle of AB.

Now, let H, I, K, be the centres of gravity of the spaces AOa, AEb, and BOb, respectively. From these points draw the lines Hh, Ii, and Kk, perpendicular to AB, and let IL be drawn perpendicular to EO. Now to ascertain the distance γq of the centre of gravity γ of the part aEb from the line AB, the momentum of aEb with respect to this line must be put equal to the difference of the momentums of the parts AEb, AOa, which are upon different sides of AB.* Hence aEb × γq, or AEB × γq = AEb × Ii - AOa × Hh. But since g is the common centre of gravity of the two parts AEB, BOB, we have therefore AEB × gO = AEB × Ii + BOB × Kk. Hence by expunging the term AEB × Ii from each of these equations, and comparing them, we obtain AEB × γq = AEB × gO - BOB × Kk - AOa × Hh.

Now, since the triangles AOa, BOb, are supposed infinitely small, their momentums or products, by the infinitely little lines Hh, Kk, will also be infinitely small with respect to AEB × gO; which therefore being rejected, the former equation becomes AB × γq = AEB × gO, and hence γq = gO. Whence the centres of gravity γ, g, being at equal distances below AB, the infinitely little line γq is therefore perpendicular to EO. For the same reason gγ, fig. 52, may be considered as an arch of a circle whose centre is M.

To determine the value of γq, the momentum of aEb with respect to EO must be taken, for the same reason as before, and put equal to the momentums of the two parts AOa, AEb; and we shall then have aEb × γq, or AEB × γq = AEB × IL + AOa × Oh. But since g is the common centre of gravity of the two spaces AEb, BOB, we shall have AEb × IL - BOB × Ok = 0, or AEB × IL = BOB × Ok. Hence AEB × γq = BOB × Ok + AOa × Oh = 2BOB × Ok; because the two triangles AOa, BOB are equal, and that the distances Ok, Oh, are also evidently equal.

Let w be the thickness of the section represented by ABC. Then the momentum of this section will be 2BOB × w × Ok, which equation will also serve for each particular section.

Now let / represent the sum of the momentums of all the sections. Hence /, AEB × x × gγ = /, 2BOB × w × Ok. Now the first member being the sum of the momentums of each section, in proportion to a plane passing through the keel, ought therefore to be equal to the sum of all the sections, or to the volume of the immersed part of the bottom multiplied by the distance γq. Hence V representing the volume, we shall have V × gγ = /, 2BOB × w × Ok.

In order to determine the value of the second member of this equation, it may be remarked, that when the ship is inclined, the original plane of floatation CBPQ (fig. 54.) becomes CbpQ. Now the triangles NI n, Stability of BO b, being the same as those in figures 52. and 53.; and as each of these triangles has one angle equal, they may, upon account of their infinite finalinefs, be considered as similar; and hence BO b : NI n : : OB1 : IN12; whence BO b = \( \frac{OB^3}{IN^2} \) × NI n. Moreover, we have (fig. 53.) O k = \( \frac{3}{2} OB \), for the points K and k may be considered as equidistant from the point O:

whence BO b × O k = \( \frac{3}{2} \frac{OB^3}{IN^2} \) × NI n.

Hence V × gγ = \( \frac{3}{2} \frac{OB^3}{IN^2} \) × x × NI n. From this equation the value of gγ is obtained.

To find the altitude gM (fig. 55.) of the meta-center above the centre of gravity of the immersed part of the bottom, let the arc NS be described from the centre I with theradius IN; then NI n = \( \frac{IN \times NS}{2} \). Now since the two straight lines γM, gM are perpendicular to an and AN respectively, the angles M and NI n are therefore equal: and the infinitely little portion gγ, which is perpendicular to gM, may be considered as an arch described from the centre M. Hence the two sectors NIS, gMγ are similar; and therefore gM : gγ : : IN : NS. Hence NS = \( \frac{IN \times g\gamma}{gM} \); and consequently

NI n = \( \frac{IN^2 \times g\gamma}{2gM} \). Now this being substituted in the former equation, and reduced, we have V × gγ = \( \frac{3}{2} \frac{OB^3}{IN^2} \times x \times g\gamma \). But since gM and gγ are the fame, whatever section may be under consideration, the equation may therefore be exprefed thus, V × gγ = \( \frac{3}{2} \frac{g\gamma}{gM} \times f_1 \frac{OB^3}{IN^2} \times x \). Hence gM = \( \frac{3}{2} \frac{f_1 OB^3}{V} \times x \). Let y = OB, and the equation becomes gM = \( \frac{3}{2} \frac{f_1 y^3}{V} \times x \).

Whence to have the altitude of the metacenter above the centre of gravity of the immersed part of the bottom, the length of the section at the water-line must be divided by lines perpendicular to the middle line of this section into a great number of equal parts, so that the portion of the curve contained between any two adjacent perpendiculars may be considered as a straight line. Then the sum of the cubes of the half perpendiculars or ordinates is to be multiplied by the distance between the perpendiculars, and two-thirds of the product is to be divided by the volume of the immersed part of the bottom of the ship.

It is hence evident, that while the sector at the water line is the same, and the volume of the immersed part of the bottom remains also the same, the altitude of the metacenter will remain the same, whatever may be the figure of the bottom.

CHAP. IV. Of the Centre of Gravity of the immersed Part of the Bottom of a Ship.

The centre of gravity * of a ship, supposed homogeneous, and in an upright position in the water, is in a chancis. vertical section passing through the keel, and dividing the ship into two equal and similar parts, at a certain distance from the stern, and altitude above the heel.

In order to determine the centre of gravity of the immersed part of a ship's bottom, we must begin with determining the centre of gravity of a section of the ship parallel to the keel, as ANDFPB (fig. 56.), bounded by the parallel lines AB, DF, and by the equal and similar curves AND, BPF.

If the equation of this curve were known, its centre of gravity would be easily found; but as this is not the case, let therefore the line CE be drawn through the middle C, E, of the lines AB, DF, and let this line CE be divided into so great a number of equal parts by the perpendiculars TH, KM, &c. that the arches of the curves contained between the extremities of any two adjacent perpendiculars may be considered as straight lines. The momentums of the trapeziums DTHF, TKMH, &c. relative to the point E, are then to be found, and the sum of these momentums is to be divided by the sum of the trapeziums, that is, by the surface ANDFPB.

The distance of the centre of gravity of the trapezium THFD from the point E is \( \frac{\frac{1}{2}IE \times (DF+2TH)}{DF+TH} \).

For the same reason, and because of the equality of the lines IE, IL, the distance of the centre of gravity of the trapezium TKMH from the same point E will be \( \frac{\frac{1}{2}IE \times (TH+2KM)}{TH+KM} + IE \), or \( \frac{\frac{1}{2}IE \times (4TH+5KM)}{TH+KM} \).

In like manner, the distance of the centre of gravity of the trapezium NKMP from the point E will be \( \frac{\frac{1}{2}IE \times (KM+2NP)}{KM+NP} + 2IE \), or \( \frac{\frac{1}{2}IE \times (7KM+8NP)}{KM+NP} \)

&c.

Now, if each distance be multiplied by the surface of the corresponding trapezium, that is, by the product of half the sum of the two opposite sides of the trapezium into the common altitude IE, we shall have the momentums of the trapeziums, namely, \( \frac{1}{2}IE^2 \times (DF+2TH) \), \( \frac{1}{2}IE^2 \times (4TH+5KM) \), \( \frac{1}{2}IE^2 \times (7KM+8NP) \), &c. Hence the sum of these momentums will be \( \frac{1}{2}IE^2 \times (DF+6TH+12KM+18NP+24QS+14AB) \). Whence it may be remarked, that if the line CE be divided into a great number of equal parts, the factor or coefficient of the last term, which is here 14, will be \( 2+3(n-2) \) or \( 3n-4 \), n being the number of perpendiculars. Thus the general expression of the sum of the momentums is reduced to \( IE^2 \times (\frac{3}{2}DF+TH+2KM+3NP+4QS+...+\frac{3n-4}{6}AB) \).

The area of the figure ANDFPB is equal to \( IE \times (\frac{1}{2}DF+TH+KM+NP+...+\frac{1}{2}AB) \); hence the distance EG of the centre of gravity G from one of the extreme ordinates DF is equal to

\[ IE \times (\frac{1}{2}DF+TH+2KM+3NP+...+\frac{3n-4}{6}AB) \]

\[ = \frac{1}{2}DF+TH+KM+NP+...+\frac{1}{2}AB \]

Whence the following rule to find the distance of the centre of gravity G from one of the extreme ordinates DF. To the fifth of the first ordinate add the sixth of the last ordinate multiplied by three times the number of ordinates minus four; then the second ordinate, twice the third, three times the fourth, &c. the sum will be a first term. Then to half the sum of the extreme ordinates add all the intermediate ones, and the sum will be a second term. Now the first term divided by the second, and the quotient multiplied by the interval between two adjacent perpendiculars, will be the distance sought.

Thus, let there be seven perpendiculars, whose values are 18, 23, 28, 30, 30, 21, 0, feet respectively, and the common interval between the perpendiculars 20 feet. Now the fifth of the first term 18 is 3 ; and as the last term is 0, therefore to 3 add 23, twice 28 or 56, thrice 30 or 90, four times 30 or 120, five times 21 or 105 ; and the sum is 397. Then to the half of 18+0, or 9, add the intermediate ordinates, and the sum will be 141. Now \( \frac{397 \times 20}{141} \), or \( \frac{7940}{141} = 59 \) feet four inches nearly, the distance of the centre of gravity from the first ordinate.

Now, when the centre of gravity of any section is determined, it is easy from thence to find the centre of gravity of the solid, and consequently that of the bottom of a ship.

The next step is to find the height of the centre of gravity of the bottom above the keel. For this purpose the bottom must be imagined to be divided into gravity sections by planes parallel to the keel or water-line, (figs. 57., 58.). Then the solidity of each portion contained between two parallel planes will be equal to half the sum of the two opposed surfaces multiplied by the distance between them; and its centre of gravity will be at the same altitude as that of the trapezium abcd, (fig. 58.), which is in the vertical section passing through the keel. It is hence obvious, that the same rule as before is to be applied to find the altitude of the centre of gravity, with this difference only, that the word perpendicular or ordinate is to be changed into section. Hence the rule is, to the fifth part of the lowest section add the product of the sixth part of the uppermost section by three times the number of sections minus four; the second section in ascending twice the third, three times the fourth, &c. the sum will be a first term. To half the sum of upper and lower sections add the intermediate ones, the sum will be a second term. Divide the first term by the second, and the quotient multiplied by the distance between the sections will give the altitude of the centre of gravity above the keel.

With regard to the centre of gravity of a ship, whether it is considered as loaded or light, the operation becomes more difficult. The momentum of every different part of the ship and cargo must be found separately with respect to a horizontal and also a vertical plane. Now the sums of these two momentums being divided by the weight of the ship, will give the altitude of the centre of gravity, and its distance from the vertical plane; and as this centre is in a vertical plane passing through the axis of the keel, its place is therefore determined. In the calculation of the momentums, it must be observed to multiply the weight, and not the magnitude of each piece, by the distance of its centre of gravity.

A more easy method of finding the centre of gravity of a ship is by a mechanical operation, as follows: Construct a block of as light wood as possible, exactly similar to the parts of the proposed draught or ship, by a scale of about one-fourth of an inch to a foot. The block is then to be suspended by a silk-thread or very fine line, placed in different situations until it is found to be in a state of equilibrium, and the centre of gravity will be pointed out. The block may be proved by fastening the line which suspends it to any point in the line joining the middles of the stem and post, and weights are to be suspended from the extremities of this middle line at the stem and post. If, then, the block be properly constructed, a plane passing through the line of suspension, and the other two lines, will also pass through the keel, stem, and post. Now, the block being suspended in this manner from any point in the middle line, a line is to be drawn on the block parallel to the line of suspension, so that the plane passing through these two lines may be perpendicular to the vertical plane of the ship in the direction of the keel. The line by which the block is suspended is then to be removed to some other convenient point in the middle line; and another line is to be drawn on the block parallel to the line suspending it, as before. Then the point of intersection of this line with the former will give the position of the centre of gravity on the block, which may now be laid down in the draught.

CHAP. V. Application of the preceding Rules to the Determination of the Centre of Gravity and the Height of the Metacentre above the Centre of Gravity of a Ship of 74 Guns.

In fig. 59. are laid down the several sections in a horizontal direction, by planes parallel to the keel, and at equal distances from each other, each distance being 10 feet or inches 4 parts.

I. Determination of the Centre of Gravity of the Upper Horizontal Section.

To find the distance of the centre of gravity of the plane 8 g o G from the first ordinate 8 g.

<table> <tr> <th>Ordinates.</th> <th>Double Ord.</th> <th>1st Factors.</th> <th>1st Products.</th> <th>2d Factors.</th> <th>2d Products.</th> </tr> <tr> <td>Fect. In. Pts.</td> <td>Fect. In. Pts.</td> <td></td> <td>Fect. In. Pts.</td> <td>Fect. In. Pts.</td> <td></td> </tr> <tr> <td>14 9 0</td> <td>29 6 0</td> <td>0 2</td> <td>4 11 0</td> <td>0 2</td> <td>14 9 0</td> </tr> <tr> <td>17 1 6</td> <td>34 3 0</td> <td>1</td> <td>34 3 0</td> <td>1</td> <td>34 3 0</td> </tr> <tr> <td>18 9 0</td> <td>37 6 0</td> <td>2</td> <td>75 0 0</td> <td>1</td> <td>37 6 0</td> </tr> <tr> <td>19 10 0</td> <td>39 8 0</td> <td>3</td> <td>119 0 0</td> <td>1</td> <td>39 8 0</td> </tr> <tr> <td>20 7 6</td> <td>41 4 3</td> <td>4</td> <td>165 0 0</td> <td>1</td> <td>41 4 3</td> </tr> <tr> <td>21 1 9</td> <td>42 3 6</td> <td>5</td> <td>211 5 6</td> <td>1</td> <td>42 3 6</td> </tr> <tr> <td>21 6 3</td> <td>43 0 6</td> <td>6</td> <td>258 3 0</td> <td>1</td> <td>43 0 6</td> </tr> <tr> <td>21 7 9</td> <td>43 3 6</td> <td>7</td> <td>303 0 6</td> <td>1</td> <td>43 3 6</td> </tr> <tr> <td>21 7 6</td> <td>43 3 0</td> <td>8</td> <td>346 4 0</td> <td>1</td> <td>43 3 6</td> </tr> <tr> <td>21 4 0</td> <td>42 8 0</td> <td>9</td> <td>389 3 0</td> <td>1</td> <td>43 3 0</td> </tr> <tr> <td>20 10 6</td> <td>41 9 0</td> <td>10</td> <td>426 8 0</td> <td>1</td> <td>42 8 0</td> </tr> <tr> <td>19 9 0</td> <td>39 6 0</td> <td>11</td> <td>459 3 0</td> <td>1</td> <td>41 9 0</td> </tr> <tr> <td>17 4 6</td> <td>34 9 0</td> <td>12</td> <td>474 0 0</td> <td>1</td> <td>39 6 0</td> </tr> <tr> <td>13 1 3</td> <td>26 2 6</td> <td>(3×15)-4</td> <td>179 1 1</td> <td>0 2</td> <td>13 1 3</td> </tr> <tr> <td>291 1 3</td> <td>582 2 6</td> <td></td> <td>3897 3 1</td> <td></td> <td>554 4 3</td> </tr> </table>

Now \( \frac{3897}{554} = \frac{3}{4} \times 10 = 4 \)

\( 3897 \cdot 25 \times 10.03 = 70.5 \).

Hence the distance of the centre of gravity of double the plane 8 g o G from the first ordinate, 8 g, is

<table> <tr> <th>Fect.</th> <th>70.5</th> </tr> <tr> <th>Distance of this ordinate from the aft side of stern-post,</th> <th>13.5</th> </tr> <tr> <th>Distance of the centre of gravity from the aft side of post,</th> <th>8.40</th> </tr> <tr> <th>Distance of the centre of gravity of double the trapezium AR g 8 from its ordinate AR,</th> <th>8.42</th> </tr> <tr> <th>Distance of this ordinate from the aft side of the stern-post,</th> <th>0.58</th> </tr> <tr> <th>Distance of the centre of gravity of this plane from the aft-side of the stern-post,</th> <th>9.0</th> </tr> <tr> <th>Distance of the centre of gravity of double the trapezium G o γ γ from its ordinate G o,</th> <th>5.44</th> </tr> <tr> <th>Distance of this ordinate from the aft-side of the post,</th> <th>153.78</th> </tr> <tr> <th>Distance of the centre of gravity of this trapezium from the aft-side of the post,</th> <th>159.22</th> </tr> <tr> <th>Distance of the centre of gravity of the section of the stern-post from the aft part of the post,</th> <th>0.29</th> </tr> <tr> <th>Distance of the centre of gravity of the section of the stern from the aft-side of the post,</th> <th>169.76</th> </tr> </table>

The areas of these several planes, calculated by the common method, will be as follow:

5558.90 for that of the plane, and its momentum 5558.9 × 84 = 466947.6000 199.13 for that of double the trapezium ARf 8, and its momentum 199.13 × 9 = 1792.1700 214.59 for that of double the trapezium G o γγ, and its momentum 214.59 × 159.22 = 34167.0236 0.77 for that of the section of the stern-post, and its momentum 0.77 × 0.29 = 0.2233 0.77 for that of the section of the stem, and its momentum 0.77 × 169.76 = 130.7152

5974.16 Sum - - - - - - 503037.7321

Now \( \frac{503037.7321}{5974.16} = 84.2 \), the distance of the centre of gravity of the whole section from the aft side of the stern-post.

II. Determination of the Centre of Gravity of the Second Horizontal Section.

To find the distance of the centre of gravity of double the plane 8fnG from its first ordinate 8f.

<table> <tr> <th>Ordinates.</th> <th>Double Ord.</th> <th>1. Factors.</th> <th>1. Products.</th> <th>2. Factors.</th> <th>2. Products.</th> </tr> <tr> <th>Feet. In. Pts.</th> <th>Feet. In. Pts.</th> <th></th> <th>Feet. In. Pts.</th> <th></th> <th>Feet. In. Pts.</th> </tr> <tr> <td>11 2 3</td> <td>22 4 6</td> <td>0.5</td> <td>3 8 9</td> <td>0.5</td> <td>11 2 3</td> </tr> <tr> <td>15 3 0</td> <td>30 6 0</td> <td>1</td> <td>30 6 0</td> <td>1</td> <td>30 6 0</td> </tr> <tr> <td>17 5 0</td> <td>34 10 0</td> <td>2</td> <td>69 8 0</td> <td>1</td> <td>34 10 0</td> </tr> <tr> <td>18 10 3</td> <td>37 8 6</td> <td>3</td> <td>113 1 6</td> <td>1</td> <td>37 8 6</td> </tr> <tr> <td>19 10 6</td> <td>39 9 0</td> <td>4</td> <td>159 0 0</td> <td>1</td> <td>39 9 0</td> </tr> <tr> <td>20 7 0</td> <td>41 2 0</td> <td>5</td> <td>205 10 0</td> <td>1</td> <td>41 2 0</td> </tr> <tr> <td>21 0 3</td> <td>42 0 6</td> <td>6</td> <td>252 3 0</td> <td>1</td> <td>42 0 6</td> </tr> <tr> <td>21 2 0</td> <td>42 4 0</td> <td>7</td> <td>296 4 0</td> <td>1</td> <td>42 4 0</td> </tr> <tr> <td>21 0 6</td> <td>42 1 0</td> <td>8</td> <td>336 8 0</td> <td>1</td> <td>42 1 0</td> </tr> <tr> <td>20 10 9</td> <td>41 9 6</td> <td>9</td> <td>376 1 6</td> <td>1</td> <td>41 9 6</td> </tr> <tr> <td>20 6 6</td> <td>41 1 0</td> <td>10</td> <td>410 10 0</td> <td>1</td> <td>41 1 0</td> </tr> <tr> <td>19 10 0</td> <td>39 8 0</td> <td>11</td> <td>436 4 0</td> <td>1</td> <td>39 8 0</td> </tr> <tr> <td>18 6 0</td> <td>37 0 0</td> <td>12</td> <td>444 0 0</td> <td>1</td> <td>37 0 0</td> </tr> <tr> <td>15 9 6</td> <td>31 7 0</td> <td>13</td> <td>410 7 0</td> <td>1</td> <td>31 7 0</td> </tr> <tr> <td>11 2 9</td> <td>22 5 6</td> <td>(3×15)-4</td> <td>153 5 6</td> <td>0.5</td> <td>11 2 9</td> </tr> <tr> <td>273 2 3</td> <td>546 4 6</td> <td></td> <td>3698 5 3</td> <td></td> <td>523 11 6</td> </tr> </table>

Hence the distance of the centre of gravity of double the plane 8fnG from its first ordinate 8n is: \[ \frac{3698.43}{523.95} \times 10.04 = 70.79 \] Distance of this ordinate from the aft side of the stern-post = 13.5

Distance of the centre of gravity of the above plane from the aft side of post = 84.29

Distance of the centre of gravity of double the trapezium ARf8 from its ordinate AR = 8.38 Distance of this ordinate from aft side of stern-post = 0.57

Distance of the centre of gravity of the trapezium from the aft side of the post = 8.95

Distance of the centre of gravity of the trapezium before the ordinate Gn from that ordinate = 5.74 Distance of that ordinate from the aft side of the post = 153.78

Distance of the centre of gravity of the trapezium from the aft side of the post = 159.52

Distance of the centre of gravity of the section of the stern-post from the aft side of the post = 0.29 Distance of the centre of gravity of the section of the stem from the aft side of the post = 169.76.

The areas of these several planes being calculated, will be as follow:

5255.22 for that of the plane 8 fn G, and its momentum 5255.22 × 84.29 = 442962.4938 153.11 for that of double the trapezium AR f 8, and its momentum 153.11 × 8.95 = 1370.3345 182.40 the area of the trapezium before, and its momentum 182.40 × 159.52 = 29096.4480 0.77 the area of the section of the sternpost, and its momentum 0.77 × 0.29 = 0.2233 0.77 the area of the section of the stem, and its momentum 0.77 × 169.76 = 130.7152

5592.27 Sum - - - - - - 473560.2148

Now \( \frac{473560.2148}{5592.27} = 84.68 \), the distance of the centre of gravity of the whole section from the aft-side of the stern-post.

III. Determination of the Centre of Gravity of the Third Horizontal Section.

Distance of the centre of gravity of double the plane 8 em G from its first ordinate 8 e.

<table> <tr> <th>Ordinates.</th> <th>Double Ord.</th> <th>1st Factors.</th> <th>1st Products.</th> <th>2d Fact.</th> <th>2d Products.</th> </tr> <tr> <th>Feet. In. Pts.</th> <th>Feet. In. Pts.</th> <th></th> <th>Feet. In. Pts.</th> <th>Feet. In. Pts.</th> <th></th> </tr> <tr> <td>6 7 6</td> <td>13 3 0</td> <td>0.5</td> <td>2 2 6</td> <td>0.5</td> <td>6 7 6</td> </tr> <tr> <td>11 7 6</td> <td>23 3 0</td> <td>1</td> <td>23 3 0</td> <td>1</td> <td>23 3 0</td> </tr> <tr> <td>15 1 0</td> <td>30 2 0</td> <td>2</td> <td>60 4 0</td> <td>1</td> <td>30 2 0</td> </tr> <tr> <td>17 1 3</td> <td>34 2 6</td> <td>3</td> <td>102 7 6</td> <td>1</td> <td>34 2 6</td> </tr> <tr> <td>18 3 0</td> <td>36 6 0</td> <td>4</td> <td>146 0 0</td> <td>1</td> <td>36 6 0</td> </tr> <tr> <td>19 3 0</td> <td>38 6 0</td> <td>5</td> <td>192 6 0</td> <td>1</td> <td>38 6 0</td> </tr> <tr> <td>19 9 0</td> <td>39 6 0</td> <td>6</td> <td>237 0 0</td> <td>1</td> <td>39 6 0</td> </tr> <tr> <td>20 0 0</td> <td>40 0 0</td> <td>7</td> <td>280 0 0</td> <td>1</td> <td>40 0 0</td> </tr> <tr> <td>20 0 0</td> <td>40 0 0</td> <td>8</td> <td>320 0 0</td> <td>1</td> <td>40 0 0</td> </tr> <tr> <td>19 8 3</td> <td>39 4 6</td> <td>9</td> <td>354 4 6</td> <td>1</td> <td>39 4 6</td> </tr> <tr> <td>19 1 3</td> <td>38 2 6</td> <td>10</td> <td>382 1 0</td> <td>1</td> <td>38 2 6</td> </tr> <tr> <td>18 1 0</td> <td>36 2 0</td> <td>11</td> <td>397 1 0</td> <td>1</td> <td>36 2 0</td> </tr> <tr> <td>16 3 9</td> <td>32 7 6</td> <td>12</td> <td>391 6 0</td> <td>1</td> <td>32 7 6</td> </tr> <tr> <td>13 2 3</td> <td>26 4 6</td> <td>13</td> <td>342 10 6</td> <td>1</td> <td>26 4 6</td> </tr> <tr> <td>8 4 6</td> <td>16 9 0</td> <td>(3×15)-4</td> <td>114 5 6</td> <td>0.5</td> <td>8 4 6</td> </tr> <tr> <td>242 5 3</td> <td>484 10 6</td> <td></td> <td>3347 0 6</td> <td></td> <td>469 10 6</td> </tr> </table>

Hence the distance of the centre of gravity of double the plane 8 em G from its first ordinate 8 e is: \( \frac{4347 \times 6}{469 \times 10} \times 10 = 3347.04 \times 10.03 = 33470.4 \times 10.03 = 71.44 \) Distance of this ordinate from the aft side of the post - - - - - - 13.5

Hence the distance of the centre of gravity of this plane from the aft side of the post is 84.94

Distance of the centre of gravity of double the trapezium AR e 8, from its ordinate AR 8.03 Distance of this ordinate from the aft side of the post 0.58

Distance of the centre of gravity of this trapezium from the aft side of the post 8.61

Distance of the centre of gravity of the foremost trapezium from its ordinate G m 5.19 Distance of this ordinate from the aft side of the post 153.78

Distance of the centre of gravity of this trapezium from the aft side of the post 158.97

Distance of the centre of gravity of the section of the post from the aft side of the post 0.29 Distance of the centre of gravity of the section of the stem from the aft side of the post 169.76

The areas of these several planes will be found to be as follow:

4712.7961 for that of double the plane 8emG, and its momentum 4712.7961 × 84.94 = 400304.9007 93.84 the area of double the trapezium AR 3e 88, and its momentum 93.84 × 8.61 = 807.9624 131.1 for the area of foremost trapezium, and its momentum 131.1 × 158.97 = 20840.907 0.77 the area of the section of the post, and its momentum 0.77 × 0.29 = 0.2233 0.77 the area of the section of the stem, and its momentum 0.77 × 169.76 = 130.7152

4939.2761 Sum - - - - - - 422084.7706

Now \( \frac{422084.7706}{4939.2761} = 85.45 \), the distance of the centre of gravity of the whole section from the aft side of the post.

IV. Determination of the Centre of Gravity of the Fourth Horizontal Section.

Distance of the centre of gravity of double the plane 8 d / G from its first ordinate 8 J.

<table> <tr> <th>Ordinates.</th> <th>Double Ord.</th> <th>1. Factors.</th> <th>1. Products.</th> <th>2. Fact.</th> <th>2. Products.</th> </tr> <tr> <th>Feet. In. Pts.</th> <th>Feet. In. Pts.</th> <th></th> <th>Feet. In. Pts.</th> <th></th> <th>Feet. In. Pts.</th> </tr> <tr> <td>3</td> <td>3 6</td> <td>6 7 0</td> <td>0 6</td> <td>1</td> <td>15 6 0</td> <td>0 6</td> <td>3 3 6</td> </tr> <tr> <td>7</td> <td>9 0</td> <td>15 6 0</td> <td>1</td> <td>47 8 0</td> <td>1</td> <td>23 10 0</td> </tr> <tr> <td>11</td> <td>11 0</td> <td>23 10 0</td> <td>2</td> <td>88 4 6</td> <td>1</td> <td>29 5 6</td> </tr> <tr> <td>14</td> <td>8 9</td> <td>29 5 6</td> <td>3</td> <td>130 0 0</td> <td>1</td> <td>32 6 0</td> </tr> <tr> <td>16</td> <td>3 0</td> <td>32 6 0</td> <td>4</td> <td>173 II 5</td> <td>1</td> <td>34 9 6</td> </tr> <tr> <td>17</td> <td>4 9</td> <td>34 9 6</td> <td>5</td> <td>217 9 0</td> <td>1</td> <td>36 3 6</td> </tr> <tr> <td>18</td> <td>1 9</td> <td>36 3 6</td> <td>6</td> <td>257 10 0</td> <td>1</td> <td>36 10 0</td> </tr> <tr> <td>18</td> <td>5 0</td> <td>36 10 0</td> <td>7</td> <td>292 0 0</td> <td>1</td> <td>36 6 0</td> </tr> <tr> <td>18</td> <td>3 0</td> <td>36 6 0</td> <td>8</td> <td>322 1 6</td> <td>1</td> <td>35 9 6</td> </tr> <tr> <td>17</td> <td>10 9</td> <td>35 9 6</td> <td>9</td> <td>340 10 0</td> <td>1</td> <td>34 5 0</td> </tr> <tr> <td>17</td> <td>2 6</td> <td>34 5 0</td> <td>10</td> <td>348 9 6</td> <td>1</td> <td>31 8 6</td> </tr> <tr> <td>15</td> <td>10 3</td> <td>31 8 6</td> <td>11</td> <td>324 0 0</td> <td>1</td> <td>27 0 0</td> </tr> <tr> <td>13</td> <td>6 0</td> <td>27 0 0</td> <td>12</td> <td>250 3 0</td> <td>1</td> <td>19 3 0</td> </tr> <tr> <td>9</td> <td>7 6</td> <td>19 3 0</td> <td>13</td> <td></td> <td></td> <td></td> </tr> <tr> <td>5</td> <td>4 9</td> <td>10 9 6</td> <td>\((3 \times 15) - 4\)</td> <td>\(\times \frac{7}{6}\)</td> <td>73 8 11</td> <td>0 2</td> <td>5 4 9</td> </tr> <tr> <td colspan="4">205 7 6</td> <td>411 3 0</td> <td>2883 11 0</td> <td>492 6 9</td> </tr> </table>

Hence the distance of the centre of gravity of double the plane 8 d / G from its first ordinate 8 d is \( \frac{2883 11 0}{492 6 9} \times 10 0 = \frac{2883.916}{402.56} \times 10.03 = 71.85 \)

Distance of this ordinate from the aft side of the post - - - - - 13.5

Distance of the centre of gravity of the plane from the aft side of the post - - - - - 85.35

Distance of the centre of gravity of double the trapezium AR d 8 from its ordinate AR - 7.89 Distance of this ordinate from the aft side of the post - - - - - 0.58

Distance of the centre of gravity of the trapezium from the aft side of the post - - - - - 8.47

Distance of the centre of gravity of the foremost trapezium from its ordinate G / - - - - - 4.83 Distance of this ordinate from aft side of the post - - - - - 153.78

Distance of the centre of gravity of the trapezium from the aft side of the post - - - - - 158.61

Distance of the centre of gravity of the section of the post from its aft side - - - - - 0.29 Distance of the centre of gravity of the section of the stem from the aft side of the post - - - - - 169.76

The areas of these several planes being calculated, will be as follow:

4937.6768 for that of double the plane 8 d/G, and its momentum 4937.6768 × 85.35 = 4169.4968 51.12 the area of double the trapezium AR d/8, and its momentum 51.12 × 8.47 = 79.16 the area of the foremost trapezium, and its momentum 79.16 × 158.61 = 0.77 the area of the section of the post, and its momentum 0.77 × 0.29 = 0.77 the area of the section of the stem, and its momentum 0.77 × 169.76 =

4169.4968 Sum - - - - - - - - 357735.2074

Then \( \frac{357735.2074}{4169.4968} = 85.80 \), the distance of the fourth horizontal section from the aft side of the stern-post.

V. Determination of the Centre of Gravity of the Fifth Horizontal Section.

Distance of the centre of gravity of double the plane 8 c k G from its first ordinate 8 c.

<table> <tr> <th>Ordinates.</th> <th>Double Ord.</th> <th>1. Factors.</th> <th>1. Products.</th> <th>2. Faet.</th> <th>2. Products.</th> </tr> <tr> <td>Feet. In. L.</td> <td>Feet. In. L.</td> <td></td> <td>Feet. In. L.</td> <td>Feet. In. L.</td> <td></td> </tr> <tr> <td>1 9 0</td> <td>3 6 0</td> <td>0.5</td> <td>0 7 0</td> <td>0.5</td> <td>1 9 0</td> </tr> <tr> <td>4 6 0</td> <td>9 0 0</td> <td>1</td> <td>9 0 0</td> <td>1</td> <td>9 0 0</td> </tr> <tr> <td>8 3 0</td> <td>16 6 0</td> <td>2</td> <td>33 0 0</td> <td>1</td> <td>16 6 0</td> </tr> <tr> <td>11 8 3</td> <td>23 4 6</td> <td>3</td> <td>70 1 6</td> <td>1</td> <td>23 4 6</td> </tr> <tr> <td>13 10 3</td> <td>27 8 6</td> <td>4</td> <td>110 10 0</td> <td>1</td> <td>27 8 6</td> </tr> <tr> <td>15 3 0</td> <td>30 6 0</td> <td>5</td> <td>152 6 0</td> <td>1</td> <td>30 6 0</td> </tr> <tr> <td>16 0 3</td> <td>32 0 6</td> <td>6</td> <td>192 3 0</td> <td>1</td> <td>32 0 6</td> </tr> <tr> <td>16 5 0</td> <td>32 10 0</td> <td>7</td> <td>229 10 0</td> <td>1</td> <td>32 10 0</td> </tr> <tr> <td>16 3 0</td> <td>32 6 0</td> <td>8</td> <td>260 0 0</td> <td>1</td> <td>32 6 0</td> </tr> <tr> <td>15 9 0</td> <td>31 6 0</td> <td>9</td> <td>283 6 0</td> <td>1</td> <td>31 6 0</td> </tr> <tr> <td>14 10 0</td> <td>29 8 0</td> <td>10</td> <td>296 8 0</td> <td>1</td> <td>29 8 0</td> </tr> <tr> <td>12 10 3</td> <td>25 8 6</td> <td>11</td> <td>282 9 6</td> <td>1</td> <td>25 8 6</td> </tr> <tr> <td>9 8 9</td> <td>19 5 6</td> <td>12</td> <td>233 6 0</td> <td>1</td> <td>19 5 6</td> </tr> <tr> <td>6 1 6</td> <td>12 3 0</td> <td>13</td> <td>159 3 0</td> <td>1</td> <td>12 3 0</td> </tr> <tr> <td>3 3 0</td> <td>6 6 0</td> <td>(\( (3 \times 15) - 4 \)) × \( \frac{1}{8} \)</td> <td>44 5 0</td> <td>0.5</td> <td>3 3 0</td> </tr> <tr> <td>166 6 3</td> <td>333 0 7</td> <td></td> <td>2358 3 0</td> <td></td> <td>328 0 6</td> </tr> </table>

Hence the distance of the centre of gravity of double the plane 8 c k G from its first ordinate is \( \frac{2358}{328} \times \frac{3}{6} \)

\( \times 10 \times 4 = \frac{2358.25}{328.04} \times 10.03 = 72.10 \)

Distance of this ordinate from the aft side of the post - - - - - - 13.50

Distance of the centre of gravity of the plane from the aft side of the post - - - - - - 85.60

Distance of the centre of gravity of double the trapezium AR c 8 from its ordinate AR - - - - 7.42

Distance of this ordinate from the aft side of post - - - - - - 0.58

Distance of centre of gravity of trapezium from aft side of the post - - - - - - 8.00

Distance of the centre of gravity of the foremost trapezium from its ordinate G k - - - - 4.22

Distance of this ordinate from the aft side of post - - - - - - 153.78

Distance of the centre of gravity of the foremost trapezium from the aft side of the post - - - - 158.00

Distance of the centre of gravity of the section of the post from the aft side of post - - - - 0.29

Distance of the centre of gravity of the section of the stem from the aft side of post - - - - 169.76

The areas of these several planes being calculated, will be as follow:

3290.2412 for the area of double the plane 8 c k G, and its momentum 3290.2412 × 85.6 = 281644.6467 31.21 the area of double the trapezium AR c 8, and its momentum 31.21 × 8 = 249.68 42.43 the area of the foremost trapezium, and its momentum 42.43 × 158 = 6703.94 0.77 the area of the section of the post, and its momentum 0.77 × 0.29 = 0.2233 0.77 the area of the section of the item, and its momentum 0.77 × 169.76 = 130.7152

3365.4212 Sum - - - - - - - - 288729.2052

Now \( \frac{288729.2052}{3365.4212} = 85.79 \), the distance of the centre of gravity of the whole section from the aft side of the stern.

VI. Determination of the Centre of Gravity of the Sixth Horizontal Section.

Distance of the centre of gravity of double the plane 8 b i G from its first ordinate 8 b.

<table> <tr> <th>Ordinates.</th> <th>Double Ord.</th> <th>1. Factors.</th> <th>1. Products.</th> <th>2. Fact.</th> <th>2. Products.</th> </tr> <tr> <td>Feet. In. L.</td> <td>Feet. In. L.</td> <td></td> <td>Feet. In. L.</td> <td>Feet. In. L.</td> <td></td> </tr> <tr> <td>1 0 0</td> <td>2 0 0</td> <td>0 5</td> <td>0 4 0</td> <td>0 5</td> <td>1 0 0</td> </tr> <tr> <td>2 5 0</td> <td>4 10 0</td> <td>1</td> <td>4 10 0</td> <td>1</td> <td>4 10 0</td> </tr> <tr> <td>4 5 0</td> <td>8 10 0</td> <td>2</td> <td>17 8 0</td> <td>1</td> <td>8 10 0</td> </tr> <tr> <td>7 3 6</td> <td>14 7 0</td> <td>3</td> <td>43 9 0</td> <td>1</td> <td>14 7 0</td> </tr> <tr> <td>10 1 9</td> <td>20 3 6</td> <td>4</td> <td>81 2 0</td> <td>1</td> <td>20 3 6</td> </tr> <tr> <td>12 1 3</td> <td>24 2 6</td> <td>5</td> <td>121 0 6</td> <td>1</td> <td>24 2 6</td> </tr> <tr> <td>13 3 0</td> <td>26 6 0</td> <td>6</td> <td>159 0 0</td> <td>1</td> <td>26 6 0</td> </tr> <tr> <td>13 9 9</td> <td>27 7 6</td> <td>7</td> <td>193 4 6</td> <td>1</td> <td>27 7 6</td> </tr> <tr> <td>13 7 0</td> <td>27 2 0</td> <td>8</td> <td>217 4 0</td> <td>1</td> <td>27 2 0</td> </tr> <tr> <td>12 8 0</td> <td>25 4 0</td> <td>9</td> <td>228 0 0</td> <td>1</td> <td>25 4 0</td> </tr> <tr> <td>10 6 6</td> <td>21 1 0</td> <td>10</td> <td>210 10 0</td> <td>1</td> <td>21 1 0</td> </tr> <tr> <td>7 1 0</td> <td>14 2 0</td> <td>11</td> <td>155 10 0</td> <td>1</td> <td>14 2 0</td> </tr> <tr> <td>4 7 3</td> <td>9 2 6</td> <td>12</td> <td>110 6 0</td> <td>1</td> <td>9 2 6</td> </tr> <tr> <td>2 10 6</td> <td>5 9 0</td> <td>13</td> <td>74 9 0</td> <td>1</td> <td>5 9 0</td> </tr> <tr> <td>x 6 9</td> <td>3 1</td> <td>6 × ((3 × 15) - 4) × \( \frac{1}{8} \)</td> <td>21 4 3</td> <td>c\( \frac{3}{8} \)</td> <td>1 6 9</td> </tr> <tr> <td>117 4 3</td> <td>234 8 6</td> <td></td> <td>1639 9 3</td> <td></td> <td>232 1 9</td> </tr> </table>

Hence the distance of the centre of gravity of double the plane 8 b v G from its first ordinate 8 b is

\[ \frac{1639.93 \times 10}{232.14} \times 10.03 = 70.84 \]

Distance of this ordinate from aft side of post - - - - - - - - 13.30

Hence the distance of the centre of gravity of the plane from the aft side of the post is - - - - - - - - 84.34

Distance of the centre of gravity of the trapezium AR b 8 from its ordinate AR - - - - - - - - 6.88 Distance of this ordinate from the aft side of the post - - - - - - - - 0.58

Distance of the centre of gravity of the trapezium from the aft side of the post - - - - - - - - 7.46

Distance of the centre of gravity of the foremost trapezium from the ordinate G i - - - - - - - - 2.92 Distance of this ordinate from the aft side of the post - - - - - - - - 153.78

Distance of the centre of gravity of this trapezium from the aft side of the post - - - - - - - - 156.70

Distance of the centre of gravity of the section of the post from its aft side - - - - - - - - 0.29 Distance of the centre of gravity of the section of the item from the aft side of the post - - - - - - - - 169.76

The areas of these planes will be found to be as follow:

2328.3642 for that of double the plane 8 b i G, and its momentum 2328.3642 + 84.34 = 196374.2366 21.52 for the area of double the trapezium AR b 8, and its momentum 21.52 × 7.46 = 160.5392 15.04 the area of the foremost trapezium, and its momentum 15.04 × 156.7 = 2356.7680 0.77 the area of the section of the post, and its momentum 0.77 × 0.29 = 0.2233 0.77 the area of the section of the item, and its momentum 0.77 × 169.76 = 130.7152

2366.4642 Sum - - - - - - - - 199022.4823 Now VII. Determination of the Centre of Gravity of the Seventh Horizontal Section.

Distance of the centre of gravity of double the plane 8 a h G from its first ordinate 8 a.

<table> <tr> <th>Ordinates.</th> <th>Double Ord.</th> <th colspan="2">1. Factors.</th> <th colspan="2">1. Products.</th> <th colspan="2">2. Fact.</th> <th colspan="2">2. Products.</th> </tr> <tr> <th>Feet. In. Lin.</th> <th>Feet. In. Lin.</th> <th>Feet. In. Lin.</th> <th>Feet. In. Lin.</th> <th>Feet. In. Lin.</th> <th>Feet. In. Lin.</th> </tr> <tr> <td>0 8 0</td> <td>1 4 0</td> <td>0 2</td> <td>0 2 8</td> <td>0 2</td> <td>0 8 0</td> </tr> <tr> <td>1 1 6</td> <td>2 3 0</td> <td>1</td> <td>2 3 0</td> <td>1</td> <td>2 3 0</td> </tr> <tr> <td>1 7 6</td> <td>3 3 0</td> <td>2</td> <td>6 6 0</td> <td>1</td> <td>3 3 0</td> </tr> <tr> <td>1 10 9</td> <td>3 9 6</td> <td>3</td> <td>11 4 6</td> <td>1</td> <td>3 9 6</td> </tr> <tr> <td>2 1 3</td> <td>4 2 6</td> <td>4</td> <td>16 10 0</td> <td>1</td> <td>4 2 6</td> </tr> <tr> <td>2 1 0</td> <td>4 2 0</td> <td>5</td> <td>20 10 0</td> <td>1</td> <td>4 2 0</td> </tr> <tr> <td>1 10 9</td> <td>2 9 6</td> <td>6</td> <td>22 9 0</td> <td>1</td> <td>3 9 6</td> </tr> <tr> <td>1 8 0</td> <td>3 4 0</td> <td>7</td> <td>23 4 0</td> <td>1</td> <td>3 4 0</td> </tr> <tr> <td>1 1 0</td> <td>2 2 0</td> <td>8</td> <td>17 4 0</td> <td>1</td> <td>2 2 0</td> </tr> <tr> <td>0 9 0</td> <td>1 6 0</td> <td>9</td> <td>13 6 0</td> <td>1</td> <td>1 6 0</td> </tr> <tr> <td>0 8 0</td> <td>1 4 0</td> <td>10</td> <td>13 4 0</td> <td>1</td> <td>1 4 0</td> </tr> <tr> <td>0 8 0</td> <td>1 4 0</td> <td>11</td> <td>14 8 0</td> <td>1</td> <td>1 4 0</td> </tr> <tr> <td>0 8 0</td> <td>1 4 0</td> <td>12</td> <td>16 0 0</td> <td>1</td> <td>1 4 0</td> </tr> <tr> <td>0 8 0</td> <td>1 4 0</td> <td>13</td> <td>17 4 0</td> <td>1</td> <td>1 4 0</td> </tr> <tr> <td>0 8 0</td> <td>1 4 0</td> <td>(3 × 15) - 4</td> <td>9 1 4</td> <td>0 2</td> <td>0 8 0</td> </tr> </table>

18 2 9 36 5 6

Hence the distance of the centre of gravity of double this plane from its first ordinate is \( \frac{205\ 4\ 6}{35\ 1\ 6} \times 10\ 0\ 4 = 58.65 \)

The distance of this ordinate from aft side of post = 13.50

Hence the distance of the centre of gravity of this plane from the aft side of the post is 72.15

Distance of the centre of gravity of double the rectangle AR a 8 from its ordinate AR = 6.45

Distance of this ordinate from the aft side of the post = 0.58

Distance of the centre of gravity of this rectangle from the aft side of the post = 7.03

Distance of the centre of gravity of the foremost rectangle from its ordinate '7 e' = 1.25

Distance of this ordinate from the aft side of the post = 153.78

Distance of the centre of gravity of this rectangle from the aft side of the post = 155.03

Distance of the centre of gravity of the section of the post from its aft side = 0.29

Distance of the centre of gravity of the section of the item from the aft side of the post = 169.76

Now, the areas of these several plans being calculated will be as follows.

352.2536, the area of double the plan 8 a h G, and its momentum 352.2536 × 72.15 = 25415 9 2

17.1570, the area of double the rectangle AR a 8, and its momentum 17.1570 × 7.03 = 120.6137

3.3250, the area of the foremost rectangle, and its momentum 3.3250 × 155.03 = 515.4747

0.77, the area of the section of the post, and its momentum 0.77 × 0.29 = 0.2233

0.77, the area of the section of the stem and its momentum 0.77 × 166.76 = 130.7152

374.2756 Sum 26182.1242

Then \( \frac{26182.1242}{374.2756} = 69.95 \), the distance of the centre of gravity of the whole section from the aft side of the post.

VIII. Determination of the Centre of Gravity of the Eighth Plane.

This plane is equal in length to the seventh horizontal plane, and its breadth is equal to that of the keel. The distance between the seventh and eighth planes is three feet, but which is here taken equal to 2 feet 1 1/3 inches. Distance between the aft side of the poft and the first ordinate 13.5 Fourteen intervals between the fifteen ordinates, each interval being 10.03 feet 140.42 Distance of the last ordinate from the fore foot 2.2 Hence the length of the eighth plane is 156.12 Which multiplied by the breadth 1.33 The product is the area of this plane 208. The distance of its centre of gravity from the aft side of the poft, being equal to half its length, is 78.06

The centres of gravity of these eight planes being found, the distance of the centre of gravity of the bottom of the ship from the aft side of the poft, and also its altitude, may from thence be easily determined.

From the principles already explained, the distance of the centre of gravity of the bottom from the aft side of the poft, is equal to the sum of the momentums of an infinite number of horizontal planes, divided by the sum of these planes, or, which is the same, by the solidity of the bottom. As, however, we have no more than eight planes, we must therefore conceive their momentums as the ordinates of a curve, whose distances may be the same as that of the horizontal planes. Now the sum of these ordinates minus half the sum of the extreme ordinates being multiplied by their distance, gives the surface of the curve; of which any ordinate whatever represents the momentum of the horizontal plane at the same altitude as these ordinates; and the whole surface will represent the sum of the momentums of all the horizontal planes.

<table> <tr> <th>Hor. Planes.</th> <th>FaCt.</th> <th>Products</th> <th>Momentums</th> <th>FaCt.</th> <th>Products</th> </tr> <tr> <td>5974.16</td> <td>0.5</td> <td>2987.08</td> <td>50307.73</td> <td>0.5</td> <td>25151.80</td> </tr> <tr> <td>5592.27</td> <td>1</td> <td>5592.27</td> <td>473560.21</td> <td>1</td> <td>473560.21</td> </tr> <tr> <td>4939.27</td> <td>1</td> <td>4939.27</td> <td>422084.77</td> <td>1</td> <td>422084.77</td> </tr> <tr> <td>4169.50</td> <td>1</td> <td>4169.50</td> <td>357735.21</td> <td>1</td> <td>357735.21</td> </tr> <tr> <td>3365.42</td> <td>1</td> <td>3365.42</td> <td>288729.20</td> <td>1</td> <td>288729.20</td> </tr> <tr> <td>2366.46</td> <td>1</td> <td>2366.46</td> <td>199222.48</td> <td>1</td> <td>199222.48</td> </tr> <tr> <td>374.27</td> <td>1</td> <td>374.27</td> <td>21682.12</td> <td>1</td> <td>21682.12</td> </tr> <tr> <td>208.00</td> <td>0.5</td> <td>104.00</td> <td>16236.48</td> <td>0.5</td> <td>8118.24</td> </tr> <tr> <td colspan="3">23898.27</td> <td colspan="3">2022451.09</td> </tr> </table>

Now \( \frac{2022451.09}{23898.27} = 84.63 \), the distance of the centre of gravity of the bottom of the ship from the aft side of the poft.

The height of the centre of gravity of the bottom above the lower edge of the keel may be determined by the same principles. Thus,

To one-sixth of the lowermost horizontal section add the product of one-sixth of the uppermost section by three times the number of sections minus four the second section in ascending, twice the third, three times the fourth, &c.; and to half the sum of the extreme planes add all the intermediate ones. Now the first of these sums, multiplied by the distance between the planes or sections, and divided by the second sum, gives the altitude of the centre of gravity of the bottom of the ship above the lower edge of the keel as required.

Hor. Planes. FaCt. 1st FaCt. 1st Products. 2d FaCt. 2d Products. Centre of Gravity. 374.27 1 374.27 1 374.27 1 374.27 2366.46 2 4732.92 1 2366.46 3365.42 3 10906.26 1 3365.42 4169.50 4 16678.00 1 4169.50 4939.27 5 24696.35 1 4939.27 5592.27 6 33553.62 1 5592.27 \( 5974.16((3\times8)-4)\times\frac{1}{2} 19913.87 \) \( \frac{1}{2} 2987.08 \)

Now \( \frac{110079.96}{23898.27} \times 2.95 = 13.588 \), the height of the centre of gravity of the bottom of the ship above the lower edge of the keel.

We have now found the distance of the centre of gravity of the bottom of the ship from the aft side of the poft, and its altitude above the lower edge of the keel. Hence the ship being supposed in an upright position, this centre of gravity will necessarily be in the vertical longitudinal section which divides the ship into two equal and similar parts; the position of this centre is therefore determined.

It now remains to find the height of the metacentre above the centre of gravity; the expression for this altitude, as found in Chap. III., is \( \frac{\frac{2}{3}f^3x}{V} \); which we shall now apply to determine the metacentre of the ship of above the 74 guns, whose centre of gravity we have already found.

<table> <tr> <th>Feet. Inches.</th> <th>Feet and dec. of Foot.</th> <th>Cub. of Ordinates.</th> </tr> <tr> <td>14 9 0</td> <td>14.7</td> <td>3209.046</td> </tr> <tr> <td>17 1 6</td> <td>17.1</td> <td>5000.211</td> </tr> <tr> <td>18 9 0</td> <td>18.7</td> <td>6591.797</td> </tr> <tr> <td>19 10 0</td> <td>19.8</td> <td>7762.392</td> </tr> <tr> <td>20 7 6</td> <td>20.6</td> <td>8741.816</td> </tr> <tr> <td>21 1 9</td> <td>21.2</td> <td>9595.703</td> </tr> <tr> <td>21 6 3</td> <td>21.5</td> <td>9938.375</td> </tr> <tr> <td>21 7 9</td> <td>21.7</td> <td>10280.109</td> </tr> <tr> <td>21 7 6</td> <td>21.7</td> <td>10280.109</td> </tr> <tr> <td>21 4 0</td> <td>21.3</td> <td>9663.597</td> </tr> <tr> <td>20 10 6</td> <td>20.9</td> <td>9129.329</td> </tr> <tr> <td>19 9 0</td> <td>19.7</td> <td>7703.734</td> </tr> <tr> <td>17 4 6</td> <td>17.4</td> <td>5268.024</td> </tr> <tr> <td>13 1 3</td> <td>13.1</td> <td>2248.091</td> </tr> <tr> <td>291 1 3</td> <td>291.1</td> <td>115719.442</td> </tr> </table>

Ordinate at 10.03 feet abaft the ordinate 8, \( g_5 = 4 \), of which the cube is 64, and \( 64 \times \frac{1}{2} = 32 \). Ordinate at 10.03 feet afore the ordinate \( G_0 = 6 \), cube of which is 216 and \( 216 \times \frac{1}{2} = 108 \).

Sum 115859.442 Distance between the ordinates 10.03 Product 1162070.20326 Product centre of Product - - - 1162070.20326 Gravity. Half the cube of the aftermost ordinate 32. Half the cube of the thickness of the item 0.14 Sum - - - 32.14 Distance between the ordinates 3.0

Product - - - 96.42 Half the cube of the foremost ordinate 108. Half the cube of the thickness of the item .14 Sum - - - 108.14 Distance between the ordinates 5.5

Product - - - 594.77 \( \int y^3 x \) - - - 1162761.39326 \( 2 \int y^3 x \) - - - 2325522.78652 \( \frac{2}{3} \int y^3 x \) - - - 775174.26217

The solidity of the bottom is \( 2527\frac{1}{3} \) tons = 70018.67 cubic feet; hence \( \frac{\frac{2}{3} \int y^3 x}{V} = \frac{77517.26}{70018.67} = 11.07 \) feet, the altitude of the metacentre above the centre of gravity of the bottom of the ship.

APPENDIX.

When a ship is built, the masts be fitted with masts, yards, sails, ropes, and blocks, or, in other words, she must be rigged before she can go to sea. To complete this article, it may therefore be thought necessary to treat of the art of rigging vessels; but we have elsewhere (see Mast-Rigging, Rope-Making, and Sail) shown how the several parts of a ship's rigging are made; and the art of putting them properly together, so as to make the ship best answer the purpose for which she is intended, depends upon a just knowledge of the impulse and resistance of fluids, and of the theory and practice of seamanship. See Resistance of Fluids and Seamanship). Nothing, therefore, of the subject is left to us here, except we were to state in few words the progressive method of rigging ships; but there is no one undeviating mode which is pursued, as the nature of the operation is such that all the parts of it may be advancing at the same time. We shall therefore take our leave of ships and ship-building with a few general observations on sail-making, and refer our readers for farther information to the very elegant work on the Elements and Practice of Rigging and Seaman/bip in two volumes quarto.

Sails are made of canvas, of different textures, and are extended on or between the masts, to receive the wind that forces the vessel through the water. They are quadrilateral or triangular, as has been elsewhere described, and are cut out of the canvas cloth by cloth. The width is governed by the length of the yard, gaff, boom, or stay; the depth by the height of the mast.

In the valuable work to which we have just referred, Appendix the following directions are given for cutting sails.

"The width and depth being given, find the number of cloths the width requires, allowing for seams, tabling on the leeches, and slack cloth; and, in the depth, allow for tabling on the head and foot. For sails cut square on the head and foot, with gores only on the leeches, as some topsails, &c., the cloths on the head, between the leeches, are cut square to the depth; and the gores on the leeches are found by dividing the depth of the sail by the number of cloths gored, which gives the length of each gore. The gore is set down from a square with the opposite selvage; and the canvas being cut diagonally, the longest gored side of one cloth makes the shortest side of the next; consequently, the first gore being known, the rest are cut by it. In the leeches of topsails cut hollow, the upper gores are longer than the lower ones; and in sails cut with a reach leech, the lower gores are longer than the upper ones. This must be regulated by judgment, and care taken that the whole of the gores do not exceed the depth of the leech. Or, by drawing on paper the gored side of the sail, and delineating the breadth of every cloth by a convenient scale of equal parts of an inch to a foot, the length of every gore may be found with precision. Sails, gored with a sweep on the head or the foot, or on both, have the depth of their gores marked on the selvage, from the square of the given depth on each cloth, and are cut as above; the longest selvage of one serving to measure the shortest selvage of the next, beginning with the first gored cloth next the middle in some sails, and the first cloth next to the mast leech in others. For those gores that are irregular no strict rule can be given; they can only be determined by the judgement of the sail-maker, or by a drawing.

"In the royal navy, mizen topsails are cut with Elements three quarters of a yard hollow in the foot; but, in the merchant service, top and topgallant sails are cut, with more or less hollow in the foot. Flying jibs are cut and Sailing with a reach curve on the stay, and a three-inch gore man/ship, in each cloth, shortening from the tack to the clue, vol. i. p. 91. Lower studding-falls are cut with square leeches, and topmast and topgallant-mast studding falls with goring leeches.

"The length of reef and middle bands is governed by the width of the sail at their respective places; the leech-linings, buntline-cloths, top-linings, mast-cloths, and corner-pieces, are cut agreeably to the depth of the sail; each cloth and every article should be properly marked with chareoal, to prevent confusion or mistake. Sails that have bonnets are cut out the whole depth of the sail and bonnet included, allowing enough for the tablings on the foot of the sail and head and foot of the bonnet. The bonnet is cut off after the sail is sewed together. If a drabler is required, it is allowed for in the cutting out the fame as the bonnet.

When the cloth is thus properly cut, the different pieces are to be joined-together in the form of a sail; and for doing this properly we have the following directions in the work already quoted. "Sails have a double flat stem, and should be sewed with the best English made twine of three threads, spun 360 fathoms to the pound, and have from one hundred and eight to one hundred and fifteen stitches in every yard in length. The twine for large sails, in the royal navy, is waxed by hand, with genuine bees wax, mixed with one sixth part of clear turpentine; and, for small sails, in a mixture made with bees wax 4 lb., hogs lard 5 lb. and clearturpentine 1 lb. In the merchant service, the twine is dipped in tar (L), softened with a proper proportion of oil.

"It is the erroneous practice of some sailmakers not to sew the seams any farther than where the edge is creased down for the tabling; but all sails should be sewed quite home to the end, and, when finished, should be well rubbed down with a rubber. In the merchant service seams are sometimes made broader at the foot than at the head, being stronger. Broad seams are not allowed to be made on courses, in the royal navy, but goring leeches are adopted in lieu of them. Boom-mainails and the fails of floops generally have the seams broader at the foot than at the head. The seams of courses and topfails are stuck or stitched up, in the middle of the seams, along the whole length, with double fleming twine; and have from 68 to 72 stitches in a yard. In the merchant service it is common to stick the seams with two rows of stitches, when the fail is half worn, as they will then last till the fail is worn out.

"The breadth of the seams of courses, topfails, and other fails, in the royal navy, to be as follow, viz. courses and topfails, for 50 gun ships and upwards, one inch and a half, and for 44 gun ships and under, one inch and a quarter, at head and foot; all other fails, one inch at head and foot.

"The tablings of all fails are to be of a proportionable breadth to the size of the fail, and sewed at the edge, with 68 to 72 stitches in a yard. Those for the heads of main and fore courses to be four to fix inches wide; for sprit courses and mizens, drivers, and other boom fails, 3 to 4 inches wide; for topfails, 3 inches to 4 inches and a half; topgallant and sprit topfails, 3 inches; royal fails, 2 inches and a half; jib and other staysails, 3 inches to 4 inches and a half, on the stay or hoist; and for studding fails, 3 inches to 4 inches on the head. Tablings on the foot and leeches of main and fore courses to be 3 inches to 5 inches broad; sprit course and topfails, 3 inches; topgallant and sprit topfails, 2 inches and a half; royals, 2 inches; fore leeches of mizen, driver, and other boomfails, 3 inches and a half to 4 inches; after leech, 3 inches; and on the foot 2 or 3 inches. Tablings on the after leech of jibs and other staysails to be from 2 to 3 inches broad; and, on the foot, 2 to 2 inches and a half: on studding fail leeches one inch and a half to two inches and a half; and on the foot, from one to two inches.

"Main and fore courses are lined on the leeches, from clue to earing, with one cloth feamed on and stuck or stitched in the middle, and have a middle band half way between the lower reef band and the foot, also four buntline cloths, at equal distances between the leeches, the upper ends of which are carried under the middle band, that the lower side of the band may be tabled upon or sewed over the end of the buntline pieces. They have likewise two reef bands; each in breadth one third of the breadth of the canvas; the upper one is one sixth of the depth of the fail from the head, and the lower band is at the same distance from the upper one; the ends go four inches under the leech linings, which are feamed over the reef bands. All linings are feamed on, and are stuck with 68 to 72 stitches in a yard.

"Main, fore, and mizen topfails have leech linings, mast and top-linings, buntline cloths, middle bands, and reef bands. The leech linings are made of one breadth of cloth, so cut and sewed as to be half a cloth broad at the head, and a cloth and a half broad at the foot; the piece cut out being half the breadth of the cloth at one end, and tapering to a point at the other. The middle bands are put on half way between the lower reef and foot, the buntline cloths join the top-linings, and the buntline cloths and top-linings are carried up to the lower side of the middle band, which is tabled on them. The mast lining is of two cloths, and extends from the foot of the fail to the lower reef, to receive the beat or chase of the mast. The middle band is made of one breadth of canvas, of the same number as the top-lining. It is first folded and rubbed down, to make a crease at one third of the breadth; then tabled on the felvage, and stuck along the crease; then turned down, and tabled and stuck through both the double and single parts, with 68 to 72 stitches in a yard. It is the opinion of many, that middle bands should not be put on until the fail is half worn.

"Main and fore topfails have three and sometimes four reef bands from leech to leech, over the leech linings; the upper one is one eighth of the depth of the fail from the head, and they are the same distance aunder in the royal navy, but more in the merchant service. The reef bands are each of half a breadth of canvas put on double; the first side is stuck twice, and the last turned over, so that the reef holes may be worked upon the double part of the band, which is also stuck with 68 to 72 stitches in a yard.

"The top-lining of topfails is of canvas, No 6 or 7. The other linings of this, and all the linings of other fails, should be of the same quality as the fails to which they belong.

"Top-linings and mast cloths are put on the aft side, and all other linings on the fore-side, of fails. Mizens are lined with one breadth of cloth from the clue five yards up the leech, and have a reef band sewed on, in the same manner as on other fails, at one fifth the depth of the fail from the foot; they have also a nock-piece and a peek-piece, one cut out of the other, so that each contains one yard. Mizen topfails of 50 gun ships and upwards have three reefs, the upper one is one eighth of the depth of the fail from the head, and the reefs are at the same distance aunder. Mizen topfails of ships of 44 guns and under have two reefs one seventh part of the depth of the fail aunder, the upper one being at the same distance from the head. Main and main top studding fails have each one reef, at one eighth of the depth of the fail from the head. Reef bands should not be put on until the fail is sewed up, a contrary practice being very erroneous. Lower staysails,

(L) The dipping of the twine in tar, we are persuaded, is a very bad practice, for the reason assigned in Rope-Making. See that article, No 32.

PLATE CCCCLXXXIV.

Fig. 1. PIECES of the HULL.

Fig. 2. FRAMES of a SHIP.

E. Mitchell sculp't

PLATE CCCCLXXXV.

Fig. 3.

Fig. 4.

Fig. 5.

Fig. 6.

E. Mitchell sculp!

PLATE CCCCLXXXVI.

Fig. 7. Fig. 8. Fig. 9. Fig. 10. Fig. 11. Fig. 12.

R. Train Sculp. SHIP BUILDING. PLATE CCCCLXXVII.

Fig.13.

Fig.14.

Fig.15.

Fig.16.

W. Train Sculpt

PLATE CCCCLXXXVIII.

Fig. 17. Fig. 18. Fig. 19. Fig. 20.

Fig. 21. Fig. 22. Fig. 23.

Fig. 24. Fig. 25. Fig. 26.

W. Train Sculp't.

PLATE CCCCLXXXX.

Fig. 27. Fig. 28. Fig. 29. Fig. 32. Fig. 30.

4th Wat.L. 3rd Wat.L. 2nd Wat.L. 1st Wat.L. 1st Ribband.

First Water Line. First Ribband. Second Water Line. Second Ribband. Third Water Line. Third Ribband.

Scale of Feet to Fig. 30, 31 & 32.

W. Archibald sculp't Fig. 35.

Fig. 34.

Scale of Feet.

PLATE CCCXCII.

Fig. 35.


Fig. 36.


PLATE CCCCXCIII.

Fig. 37.

Fig. 38.

Fig. 39.

Fig. 40.

Fig. 41.

Fig. 42.

Fig. 43.

W. Evans Sculpt.

PLATE CCCCXCIV.

Fig. 44. Fig. 45. Fig. 46. Fig. 47. N. 1. N. 2. Fig. 48. N. 1. N. 2. Fig. 49. Fig. 50.

BOSWELL'S improved CAPSTAN.

PLATE CCCCXCV.

Fig. 51. Fig. 52. Fig. 53. Fig. 54. Fig. 55. Fig. 56. Fig. 57. Fig. 58. Fig. 59.

E. Mitchell sculp.

Appendix. fails, fore top and main top stayfails, and flying jibs, have clue-pieces two yards long. Square tack stayfails, have half a breadth of cloth at the fore part, with a clue-piece containing two yards, and a peek-piece, containing one yard.

"Sails have two holes in each cloth, at the heads and reefs of courses, topfails, and other square sails; one hole in every yard in the stay of flying jibs, and one in every three quarters of a yard in the stays of square tack and other stayfails. These are made by an instrument called a pegging awl, or a stabber, and are fenced round by stitching the edge to a small grommet, made with log or other line; when finished, they should be well stretched or rounded up by a pricker or a marline spike. Reef and head holes of large fails have grommets of twelve-thread line, worked round with 18 to 21 stitches; smaller fails have grommets of nine-thread line, with 16 to 18 stitches, or as many as shall cover the line, and smaller holes in proportion. The holes for marling the clues of fails and the top-brims of topfails have grommets of log-line, and should have from 9 to 11 stitches; twelve holes are worked in each cloth. Main courses have marling holes from the clue to the lower bow line cringle up the leech, and from the clue to the first buntline cringle on the foot. Fore courses have marling holes one-eighth of the depth of the sail up the leech, and from the clue to the first buntline cringle at the foot. Main and fore topfails have marling holes three feet each way from the clue and at the top-brims. Spritfails, mizen topfails, lower stayfails, main and fore top stayfails, and jibs, have marling holes two feet each way from the clues. All other fails are sewed home to the clues. Marling holes of courses are at three-fourths of the depth of the tablings at the clues from the rope, and those of topfails are at half the depth of the tablings at the clues and top brim from the rope."

The rope, which is sewed on the edges of fails to prevent their rending, and which is called bolt-rope, should be well made of fine yarn, spun from the best Riga rhine hemp well topt, and sewed on with good English made twine of three threads, spun 200 fathom to the pound; the twine in the royal navy is dipped in a composition made with bees-wax 4 lbs. hogs lard Appendix-5 lbs. and clear turpentine one pound; and in the merchant service, in tar softened with oil. They should be stoved in a stove by the heat of a flue, and not in a baker's oven or a stove tub; and tarred in the best Stockholm tar. The flexibility of them should be always considered, in taking in the flack, which must rest on the judgment of the failmaker.

"Bolt ropes of courses, topfails, and all other fails, should be neatly sewed on through every buntline of the rope; and, to avoid stretching, the rope must be kept tightly twisted while sewing on, and care taken that neither too much nor too little flack is taken in; they are to be cros stitched at the leeches every twelve inches in length; at every seam, and in the middle of every cloth at the foot, with three cros-stitches: four cros-stitches should be taken at all beginnings and fallenings off; the first stitch given twice, and the last three times. Small fails have two cros stitches at every seam, and three at every fallening off.

"On main and fore courses two inches flack cloth should be allowed in the head and foot, and one inch and a half in the leeches, in every yard in length. Topfails are allowed 3 inches flack in every cloth in the foot, one inch and a half in every yard in the leech, and two inches in every cloth left open in the top-brim. Mizzen courses have two inches flack in every yard in the foremost leech, but none in the after leech or foot. Spritfail courses have no flack cloth. Jibs have four inches flack in every yard in the stay, one inch in every cloth in the foot, and none in the leech. Stayfails have three inches flack in every yard in the stay, one inch in every cloth in the foot, but none in the leech. Toggallant fails have two inches flack in every cloth in the foot, and one inch in every yard in the leech. Studding fails have an inch and a half flack in every yard in going leeches, but no flack in square leeches, and one inch in every cloth in the head and foot."

These directions for failmaking, we trust may be useful. They are indeed very general, but the failmaker will find every instruction that he can want in the Elements of Rigging and Seamanship, a work which we therefore recommend to his attention.