To a people whose power is essentially maritime it is not necessary to use any arguments in proof of the importance of ship-building. Without pausing to dwell on the various struggles by which England has maintained her position amongst nations, it must be seen by all who study her history, that it has been by keeping invaders from her shores, by means of her wooden bulwarks, that she has withstood the repeated attacks of the powerful nations of the continent. And whilst the navy must be looked upon as the proper means of defence to this sea-girt land, who can visit the docks of London, Liverpool, the Clyde, or any of her other commercial ports, and not feel that her very heart's strength lies in those forests of masts which bring wealth to her merchants and manufacturers, and the means of employment to her artizans, forming, at the same time, a nursery and a reserve of seamen, who will be ready in the hour of need to vindicate her claim to pre-eminence on the ocean? Who, it may also be asked, can look upon the changes effected by her instrumentality in all quarters of the globe, and not own that her winged messengers have, under God's blessing, been the means of spreading civilization and truth through a large portion of the world?

The love of a sailor's life, common to all ranks amongst her sons, owes perhaps its origin to their Norman forefathers; but, however begotten, and however fostered, England owes much to it, and to the spirit of adventure which it has engendered amongst them. Individual enterprise has led to national achievements, till the name and power of Great Britain have been so extended that the sun never sets upon her possessions.

In an age when science is lending its mighty aid to every peaceful and warlike art, when mighty armies may be suddenly concentrated by railroads, and a nation's fate may hang on the electric wire, England must not trust in the multitude alone of her ships. Every fresh struggle for wealth or power proves that it is the amount of mind and intellect put forth in that struggle, and the amount of energy, and of means used to effect the end desired, which, humanly speaking, ensure success; and, as knowledge is always increasing, nations or individuals must not rest upon what has been done, if they desire to keep pace with the world in its eager rush of advancement and improvement. With regard to ship-building, not only must ingenuity and skill be brought to bear to assist the artisan in the practical construction of the fabric, but men of science must lend their aid, and use their powers of investigation, to assist in designing a complete whole, adapted to meet the ever-increasing competition for mastership on that element on which not only the welfare of England but of the whole world seems to hang.

The limits of a treatise of this nature are such that a very general view only of the many branches of inquiry in...

History. volved in this important subject can be given. It could not, however, be considered complete without a short outline of the rise and progress of the art, or without some reference to the authors from whose works further information may be obtained. It is always interesting and instructive in every art to trace the various stages it has gone through before arriving at its existing state. The retrospect of the art of ship-building shows that there has been no standing still in its course without corresponding injury to the prosperity and power of the nation which has neglected it, and that there must be no relaxation of exertion to meet the demands of a commercial and warlike people.

RISE AND PROGRESS OF NAVAL ARCHITECTURE.

In tracing the progress of naval architecture among the nations of antiquity, in order to connect it with its advance in more modern times, the chronological divisions adopted by that indefatigable investigator, Charnock, in his valuable History of Marine Architecture, present a very succinct idea of the probable rise, progress, decline, and revival of the art, and therefore offer a valuable guide for investigation. It would not be consistent with the purpose of this article to enter into the detail that would be necessary to ascertain the state of naval architecture during the periods embraced in each of the sections he has assigned to this subject. Some few facts only will be collected from various authors in illustration of the probable size and nature of the shipping of the ancient world, with an outline of what little is known of the rude vessels which, during the darkness of the middle ages, bore the marauders of the northern nations on their predatory excursions. Charnock divides maritime history into seven sections. The first comprehends the time previous to the foundation of Rome, until which he considers that all history is founded on surmise. The second section comprises a period somewhat less obscure, in which the collateral testimony of various authors may be examined and compared; and therefore there certainly appears less difficulty in ascertaining facts. It extends from the foundation of Rome to the destruction of her rival, Carthage. The termination of the third is at the conversion of the Republic into an empire. The death of Charlemagne ends the fourth epoch. The fifth extends from this period to the discovery of the mariner's compass. The sixth ends with the discovery of cannon, and with their adaptation to naval warfare commences the seventh epoch.

The first vessel of which we have any description is the ark as built by Noah under the directions of the Almighty. Its proportions possess some interest, because, though not intended for a voyage, it may be inferred that it was constructed to float with as little motion as possible, considering that it "went upon the face of the waters" for about five months. It was no doubt exposed to the action of the winds and waves during that period, for before it rested "a wind was made to pass on the earth, and the waters asswaged." Assuming a cubit to be about 18 inches of our measure, its length was about 450 feet, its breadth about 75 feet, and its depth about 45 feet, with an arch or round-up of the upper deck of about 18 inches. Its draught of water must have varied greatly during the period of its occupation, as twelve months' provisions must have formed a very large proportion of the original weight, and these must have been gradually consumed. Its length is thus seen to have been six times its breadth, and it is perhaps curious that ship-builders should not sooner have given this, or a greater proportion of length to their vessels; seeing that these were intended for locomotion, with as much speed as possible, and consequently that an increase of length must have been proportionally advantageous to them, by giving them a finer form. The remembrance of this huge vessel, or floating house, would remain long on the minds of Noah's posterity; but it was not likely to influence them in the construction of petty floating vessels, to meet any of their limited requirements. Wickerwork frames of rushes, or reeds, or of the rind of the papyrus, smeared with mud or pitch, similar to the ark in which Moses was exposed, appear to have been at a very early age brought into use, and basketwork, covered with skin, has continued in constant use among many nations, even up to the present time. They are still in use in some parts of this and other countries under the name of coracles. Canoes, formed out of the trunk of a tree, require tools or implements for their construction, and were, therefore, no doubt of later introduction.

As early authentic records on the subject of ship-building, the paintings and sculptures of Upper and Lower Egypt may be referred to. These show regularly formed boats, constructed of sawn planks of timber, propelled by numerous rowers, and also by sails. Some are represented as formed with inclined planes, forward and aft in the same manner as the barges on the Thames, and in this respect are more correct in theory and in reality as to ease of propulsion than many canal-boats of the present day, constructed of a wedge-like form. The Hebrews in the time of Solomon must have possessed vessels of considerable size, as mention is made, in the sacred writings of that date, of "stately ships" and of voyages made to bring trees of considerable size to be used in the building of the temple. In addition to the trade in the Mediterranean from Joppa and Tarshish, it is also recorded that Solomon despatched a navy of ships from the Red Sea to fetch gold from Ophir, the position of which, though disputed, was probably on the east coast of Africa.

The Phoenicians were connected with the Hebrews in their maritime expeditions, and this people appear to have been the most enterprising in navigation of all the nations of antiquity. There can be no doubt from the accounts given by that most pains-taking and careful historian, Herodotus, that an expedition fitted out by this people sailed round the Cape of Good Hope. They started from the Red Sea, and after passing Ophir, if situated, as previously supposed, on the east coast of Africa, and to which they were in the habit of trading, they rounded the Cape, and keeping by the shore they entered the Mediterranean through the pillars of Hercules, or Straits of Gibraltar, and arrived in Egypt in the third year of their expedition. Vessels capable of performing such a voyage must have been of considerable size. The Phoenicians were also engaged, in concert with other nations, in wars with the Greeks; and it was from them that the latter nation learned in their wars what they knew of ships and of navigation. Amongst the Grecian states, the Corinthians appear to have most distinguished themselves by improving the forms of the galleys, and increasing their size. The people of Tuscany and the Carthaginians also became important maritime powers about this time.

The Romans in the earlier stage of their history paid little attention to navigation, until it was forced upon them by the necessity of competing with their great rivals the Carthaginians. The galleys of this period ranged from a single bark up to the quinquereme of five banks of oars. The oars in these large galleys being arranged in sets or banks, the number of these could be increased to any extent by giving additional length to the galley. The trireme, or three-banked galley, appears to have been generally open in the middle where the rowers sat, with decks or platforms at both ends for the soldiers; but this was not always the case, as in the representation of a trireme found at Pompeii, it is decked over for its whole length, and with a house or inclosed space at the stern. The galleys of greater size than the triremes appear to have been always decked-vessels, and the upper or fourth and fifth oars of

each bank were probably pulled from the deck, in the same manner as the long oars of the present day, called sweeps, while the three lower oars were pulled through port-holes by men seated below the deck.

The chief information on the vessels of this period is gathered from the accounts of naval expeditions and engagements as recorded in the histories of the Peloponnesian war by Thucydides; the wars of Alexander the Great, especially the siege of Tyre, by Curtius and Arrian; the battle between Demetrius and Ptolemy, by Diodorus Siculus; the first Punic war, by Polybius, in which a very minute account is given of the engagement between the Romans and the Carthaginians; and of the battle of Actium, by Dionysius Cassius. Cæsar, in his Commentaries, also gives an account of the vessels used in the invasion of Britain, which seem to have been of greater draught of water than common at that period, as he considers it worthy of recording, that the men on disembarking were breast-high in the water, and that at last the galleys were ordered in between these larger vessels and the shore, to protect the disembarkation.

The Roman ships were divided into three classes: the naves longae, or ships of war; the naves onerariae, or ships of burthen; and the naves liburnae, which were ships built expressly for great velocity, and may be supposed to have been used as despatch-boats, and for making passages with important personages. There is repeated evidence to prove that these vessels were invariably built of pine, cedar, or other light woods, excepting about the bows, which were of oak, strongly clamped and strengthened with iron or brass, in order to withstand the shock of opposing vessels; the tactics being comprised in the attempt to sink or damage the enemy's vessel, by violently propelling this armed bow against the weaker broadside of the enemy, or else endeavouring to break and cripple the oars. Oak was first applied to ship-building by the Veneti, on the testimony of Cæsar in his treatise De Bello Gallico, lib. iii. cap. 18. Copper or brass was introduced for fastenings, in consequence of the quick corrosion of the iron, about the time of Nero. This is stated on the authority of Vegetius, and also of Athenæus; and Pliny mentions that flax was used for the purpose of caulking the seams of the plank.

The following quotation is from Locke's History of Navigation:—"Sheathing of ships is a thing in appearance so absolutely new, that scarce any will doubt to assert it altogether a modern invention; yet how vain this notion is, will soon appear. Leo Baptisti Alberti, in his book of Architecture (lib. v. cap. 12), has these words: But Trajan's ship weighed out of the lake of Riccia at this time, while I was compiling this work, where it had lain, sunk and neglected, for above 1300 years; I observed that the pine and cypress of it had lasted most remarkably. On the outside it was built with double planks, daubed over with Greek pitch, caulked with linen rags; and over all a sheet of lead fastened on with little copper nails. Raphael Volaterranus, in his Geography, says this ship was weighed by the order of Cardinal Prospero Colonna. Here we have caulking and sheathing together above 1600 years ago; for I suppose no man can doubt that the sheet of lead nailed over the outside with copper nails was sheathing, and that in great perfection, the copper nails being used rather than iron, which, when once rusted in the water, with the working of the ship, soon lose their hold and drop out."

During the dark ages which followed the downfall of Rome, little progress was made in navigation, and but little is known of the vessels in which the northern hordes made their predatory and conquering excursions.

The investigations of the Royal Society of Northern Antiquarians at Copenhagen have thrown considerable light on the subject of this early navigation, and of the discoveries of the Scandinavians in the west; and it cannot be supposed that it was in coracles that frequent voyages were made to Newfoundland, and colonies established there, which it appears proved were in existence as early as the tenth century. But to recur to the description given by Cæsar of the ships of the Gaulish Veneti. "Their Gaulish bottoms were somewhat flatter than ours, their prows were very high and erect, as likewise their sterns, to bear the higness of the billows and the violence of the tempests. The body of the vessel was entirely of oak. The benches of the rowers were made of strong beams about a foot in breadth, and fastened with iron nails an inch thick. Instead of cables, they secured their anchors with chains of iron; and made use of skins and a sort of thin pliant leather, by way of sails, probably because they imagined that canvas sails were not so proper to bear the violence of tempests, the rage and fury of the winds, and to govern ships of that bulk and burthen. . . . . Neither could our ships injure them with their beaks, so great was their strength and firmness, nor could we easily throw our darts, because of their height above us, which also was the reason that we found it extremely difficult to grapple the enemy and bring him to close fight." And again, speaking of the manner in which these ships were eventually taken possession of: "They," the Romans, "had provided themselves with long poles, armed with long scythes; with these they laid hold of the enemies' tackle, and drawing off the galley by the extreme force of oars, cut asunder the ropes that fastened the sailyards to the masts; these giving way, the sailyards came down, insomuch that, as all the hopes and expectations of the Gauls depended entirely on their sails and rigging, by depriving them of this resource, we at the same time rendered their vessels wholly unserviceable."

The account proceeds to state, that many attempted to escape from this unforeseen means of aggression; but that the wind falling, and a perfect calm coming on, they were obliged to remain inactive on the water, and were taken possession of, one after the other, by the simultaneous attack of several Roman galleys. It would appear from this that they were vessels only intended for sailing, and that, since oars were used, from the mention made of seats for the rowers, they could have been as very partial accessories to the sails, or probably even only for steering. Another fact is mentioned by Cæsar, that the Veneti sailed from their port to meet the Roman fleet, and several of the vessels escaped to their port from the fleet. This, though not conclusive of the fact of sailing on a wind, is worthy of notice.

It is probable that it was ships such as these which brought Hengist Hengist and Horsa to England about the middle of the fifth century, since it is recorded that their force, which consisted of 1500 men, found accommodation in only three vessels. It is hardly to be imagined that the coracles, or skin-boats of the northern nations, were ever of sufficient dimensions to accommodate a force of 500 men, with arms and means of active aggression.

The earlier irruptions of the northern barbarians into the north of Italy had desolated the Roman province of Venetia, and Venice driven a remnant of its inhabitants to the refuge afforded by the small marshy islands at the extremity of the Adriatic. There they are described by Cassiodorus, who assimilates them to water-fowl, as subsisting on fish, and steeped in poverty, their only manufacture and their only commerce being salt. From such humble beginnings arose the state destined to connect the old world with the new, and to lead the van of modern commercial and maritime enterprise. The mercantile prosperity of Venice diffused its influence throughout the shores of the Mediterranean, which thus became once again the nursery of civilization. For many centuries Venice was the great school of the arts connected with navigation, and her shipwrights and seamen were long the most instructed in Europe. While the north- ern seas were navigated by the Scandinavian sea-kings, in their rude and frail boats, in quest of plunder or of a home, ships floated on the waters of the Mediterranean bearing the banner of St Mark, which, it is said, were, even as early as the tenth century, of the burthen of 1200 up to 2000 tons. The vessels, however, generally adopted by the Mediterranean states were either copies or modifications of the ancient galley.

It is a fact worth notice, that while the continuation of the use of this species of vessel in the comparatively tranquil waters of the Mediterranean fostered the arts of commerce and navigation, its introduction into the northern seas, to which it was ill adapted, appears to have checked, in a most remarkable degree, the maritime enterprise which had hitherto so characterized the population of their coasts. It is even probable that the barrier thus opposed to commerce entailed on the states of Northern and Western Europe centuries of comparative barbarism.

Alfred was the first ruler of England who clearly understood that the policy of Britain was rather to prevent than to resist invasion; and the bygone history of his country told him plainly that its military strength was not only insufficient to awe invaders from its shores, but that all the military resources at his command were inadequate to preserve the liberties of his people. He therefore turned the energies of his mighty mind to the task of creating a naval force, which should be more powerful than that of his uniting persecutors the Danes. In this he succeeded; and at length, under the protection of the fleets which his genius had created, he was enabled to establish that framework of internal policy and government, from the wisdom of which England has even to this day benefited. It is historically certain that Alfred himself superintended the formation of his fleet, and that he gave the design of vessels to be superior to those of the Danes.

These vessels were galleys, generally rowed with forty oars, some even with sixty, on each side; and they were twice as long, deeper, nimbler, and less "wavy" or rolling, than the ships of the Danes. The information on this subject is obtained by Selden from a Saxon chronicle of the time of Alfred, which is in the Cottonian Library.

It should be remembered, that when Alfred thus introduced the Mediterranean galley into these northern seas, his object was not so much to form a vessel adapted for the purpose of navigating those seas, as to obtain one which would afford space for a large force of fighting men. For this the galley was admirably qualified; and indeed it maintained its place as the appropriate ship for the purposes of war until the invention of cannon rendered other arrangements necessary.

The immunity which it insured from the attacks of the Danish marauders caused its general adoption along the coasts hitherto open to their incursions, on all of which it thus superseded the sailing vessels that have been already described; and voyages which, until its introduction, were boldly and successfully achieved, became of rare occurrence and of hazardous issue during the subsequent ages, until the galleys once again gave place to sailing vessels. It also gradually checked the enterprise of the Northmen, by the curb which it placed upon their successes.

It is not proposed to give more than a slight sketch of the naval history of Britain through the line of her Saxon princes; for little data can be found on which to base any speculation even, as to the progress of naval architecture during these ages. The galley of the Mediterranean continued to be used for the defence of the coasts; and the policy of Alfred appears to have been well understood by many of his successors—that England only enjoyed peace from invasion when her fleets were powerful enough to repel it from her shores. It is also to be inferred that the use of sailing vessels was not wholly abandoned; for in the reign of Athelstan, the third in descent from Alfred, as recorded by Hakluyt, it was decreed, that "if a merchant so thrived, that he passed thence over the wide seas of his owne crafte, he was thenceforth a Thein's right worthy."

This establishes two rather interesting facts: one is, that Mercantile at so early a period there were merchants of importance shipping enough to engage in such a traffic; and the other is, that from the richness of the reward held out to successful enterprise, the difficulty of the task assigned must have been estimated as great. It may be assumed that these long voyages were made in ships more adapted for the purpose than galleys; in fact, in the vessels which the galleys had been intended to supersede. But the spirit of maritime enterprise had, as before observed, evidently received a check, since one of the naval enterprises, the highest rewards in the power of the monarch to bestow was held out to the merchant as an incitement to an adventure, which the vague hope of plunder would alone have been sufficient to induce that merchant's progenitors to attempt and successfully perform. However, it is probable that at no time was the art of navigating vessels, which depended principally, although perhaps not wholly, upon their sails, lost in the northern seas. Gibbon says, that at the early crusades the vessels of the "Northmanni et Gothi" (the Norwegians and Danes) differed from those of the other powers, among all of whom the ships partook of the character of the Mediterranean galley. These northern crusaders are described by him as navigating "navibus rotundis—that is to say, ships infinitely shorter in proportion to their length than galleys." This was not later than the beginning of the twelfth century, and therefore not so far removed from the periods in question as to render the inference proposed to be deduced from it erroneous, particularly when referring to times of such slow improvement as the middle ages.

The "mighty" fleets maintained by Edgar afford no information on the subject of this article, excepting that the facts connected with that monarch's annual circumnavigation of his territories prove them to have consisted of row-galleys. They must, however, have formed comparatively a "mighty" fleet; for, from a grant of land made by Edgar to Worcester cathedral, it is found that he assumed to himself the title of "Supreme Lord and Governor of the Ocean lying round about Britain." That they were but of slight construction may be inferred from the low state of the navy so shortly after the death of Edgar as the reign of Ethelred, Ethelred, who, in order to re-establish it, instituted a regular tax for providing and maintaining a navy. It was enacted, according to Selden, that whoever possessed "310 hides of land was charged with the building of one ship or galley; and owners of more or less hides, or part of one hide, were rated proportionally"—the hide being, according to the best authorities, as much ground as a man could turn up with one plough in a year. But this tax appears to have been inadequate to the purpose of providing a sufficient fleet, for all the exertions of Ethelred could not preserve Britain from again being ravaged by the Danes, and, after the short reign of his son Edmund Ironsides, England was ruled by Danish monarchs. From the known talent of Canute, Canute, the first of these princes, and from the crowns of Denmark, Norway, and Britain being united in his person, it may be presumed that the naval affairs of England were not suffered to retrograde. There is, indeed, a record of their advance during this second Danish rule. It may also be inferred from the present which was made by Earl Godwin to Hardicanute, the third Danish sovereign, of a galley, sumptuously gilt, and rowed by fourscore men, each of whom wore on his arm a bracelet of gold weighing sixteen ounces; not that the mere gorgeousness of the gift would prove any advance in the art of ship-building, but it may be supposed, from its nature, that naval affairs found favour in the sight of this monarch. Of this there is also other historical evidence, as Hardicanute raised L11,048, in the first two years of his reign, for the purpose of building thirty-two ships; and the taxes he levied for the support of his navy were so grievous that, Florentius says, scarcely any man was able to pay them.

The marine of England seems to have been maintained on a comparatively powerful footing up to the period of the Norman conquest; and from the naval resources at the command of Harold the Saxon, in comparison with the insignificance of the shipping which brought William and his Normans across the channel, there can be no doubt that had Harold relied upon his naval strength, the conquest of England would never have been achieved; but, by some fatality, his fleet, which had been long stationed off the Isle of Wight, was dispersed, in consequence of a report that William had abandoned his enterprise.

The flotilla of William the Conqueror is variously stated; by some at 900, by others at 3000 vessels. Either number proves their insignificance, as the invading force consisted of about 60,000 troops, which would give in the one case about 66 men to each vessel, in the other 20 men only (figs. 1 and 2).

The conquest of England being completed, the shores on either side of the narrow seas between England and Normandy were under the same rule. William, therefore, claimed sovereignty over them, which right was maintained by his successors. There can be no doubt that the constant intercourse between the two portions of the empire, which continued throughout the Norman sway, and indeed for a period of upwards of three centuries, must have done much towards fostering a maritime spirit among the population of England, and accustomed it to consider that fame and fortune were the rewards of nautical adventure.

There is but slight evidence as to the state of naval architecture during the early period subsequent to the Conquest. There are a few facts scattered among the records of these times, from which some vague conclusions as to the probable size and nature of the vessels used may be drawn. When Prince William, son to Henry I., was drowned, by the loss of the vessel in which he was crossing from France to England, it is recorded that 300 souls perished with him. As of this number a large portion, historians say 140, were men of rank; and as there were many ladies, since the prince was accompanied by his sister, the vessel must have been of considerable burden. A similar event, namely, a shipwreck, that occurred during the reign of Henry II., by which nearly the same number of persons perished, tends to prove that such was about the extent of the accommodation afforded by the shipping of this period. Galleys still continued to be used for the purposes of war; but as commerce began to be extended, it became necessary to recur to the use of sails, and they were therefore gradually recovering their importance, and superseding oars. Indeed, it is difficult to conceive commerce to be profitably engaged in when attended with the immense expense of the crews necessary to propel the larger galleys. This must have had an important influence in the improvement of navigation and of naval architecture, for the commercial intercourse between the portions of the empire on either side of the channel must have been considerable. There is constant reference in the early chronicles to the great extent of the wine trade, and of the commerce in wool and woollen cloths.

The introduction of vessels propelled by sails for the purposes of commerce would necessarily cause a change in the constitution of the fleets assembled for the services of war; and this will be found to have been the case.

The expedition of Richard Coeur de Lion, in 1190, to join the crusade to the Holy Land, consisted of nine ships, Coeur de Lion, which are described as being of extraordinary size, 150 others of inferior dimensions, and only 38 galleys. After the reduction of Cyprus, and the addition of the vessels captured there, with others which he had hired at Marseilles and in Sicily, his armament consisted of 254 "tall shippes, and about three score galliots." The increase was, therefore, almost wholly in the ships. This, together with the recorded fact, that he captured a Saracenic vessel of such size as to be capable of containing 1500 Saracens, and a large quantity of military stores, destined for the relief of Acre, tends to prove that the progress of naval architecture, under the influence of the commercial powers of the Mediterranean, had been more rapid than in these northern seas, where the commerce was much more confined in its nature, and the nations bordering on which were in constant warfare with each other.

The Norman monarchs appear to have been very tenacious of their claim to the sovereignty of the narrow seas; and not only their claim, but their power to maintain their right, is admitted by the French historians. The Père Daniel sanctions the claim of Henry II. to this sovereignty.

In the reign of John the fleets of England were of such importance that the claim was extended; for it was then enacted, that if the masters of foreign ships should refuse to strike their colours, and thus pay homage to the English flag, such ships should be considered as lawful prizes. This monarch most carefully fostered the naval power of England; and it is in the records of the thirteenth year of this reign that mention is first made of any public naval establishment. There is in the close rolls, published by the Early Record Commission, an order, which is dated the 29th of May 1212, from the king to the sheriff of the county of Southampton, in which he is directed without delay to cause the king's docks at Portsmouth to be enclosed by a good and strong wall, in order to protect the king's galleys and ship's; and also to build storehouses against this wall, for the preservation of the fittings and equipment of the said vessels; all of which works are to be performed under the direction of William, archdeacon of Taunton, and the

The naval power of England appears to have continued sufficient to maintain the sovereignty assumed by John. For the occurrence of predatory excursions by some Genoese, during the reign of Edward I., caused all the nations of Europe, bordering on the sea, to appeal to the kings of England, whom they acknowledged to be in peaceable possession of the "Sovereign Lordship and Dominion of the Seas of England, and Islands of the same;" which proves that their claim was generally acknowledged. This document, Evelyn says, was still extant in his time, in the archives of the Tower. The right to the absolute sovereignty of the seas was maintained up to the reign of James I. Queen Elizabeth insisted on and maintained her power to refuse or grant passage through the narrow seas, according to her pleasure. In 1634 Charles I. asserted his right to their sovereignty; and in 1654 the Dutch were compelled, after a severe struggle, to submit to it, and consent to "strike their flags and lower their topsails on meeting any ship of the English navy on the British seas;" which homage the commanders of English men-of-war were instructed to exact from all foreign vessels until so lately as the close of the last war, when it was judiciously abandoned, for the following reasons, as given by Sir John Barrow. In his Life of Hose, with reference to Trafalgar, he says, "That battle, moreover, having so completely humbled the naval powers of France and Spain, suggested to the consideration of the Board of Admiralty, with the approbation of the government, the omission of that arbitrary and offensive article which required naval officers to demand the striking of the flag and lowering of the top-sail from every foreign ship they might fall in with. That invidious assumption of a right, though submitted to generally by foreigners for some centuries, could not probably have been maintained much longer, except at the cannon's mouth; and it was considered, therefore, that the proper time had come when it might, both morally and politically, be spontaneously abandoned."

It is generally supposed that ships intended only for sailing were first built by the Genoese, and that not until the beginning of the fourteenth century. It is perhaps more probable, that in the Mediterranean they date from an earlier period than this; and that although the general adoption of the galley in Western Europe had much checked the art of navigation by means of sails, it had never been wholly lost, but that sailing vessels, though probably very few in number, and imperfect in rig, had been constantly in use. To judge from the few hints handed down to us by history, they were probably luggers, and were adopted for mercantile purposes along the coast of the Channel and the Bay of Biscay. In the north of Europe sails had never been discontinued, although the more warlike galleys of England and France had gradually prevented the incursions of the northern nations into these more southern seas. The beginning of the fourteenth century is, however, decidedly an epoch in the histories both of navigation and of naval architecture, and from it may be dated the progress of navigation by means of sails. It is generally supposed that the "large ships" mentioned in the enumeration of the fleets of this period, were ships built only for sailing, and intended for those long voyages which the invention of the compass by Flavio Gioia, a Neapolitan, about the year 1300, had rendered of comparatively easy performance.

It has been surmised that the compass was brought to Europe from the East about forty years previous to this date, by Paulus Venetus. It is certain that the Portuguese found the knowledge of the magnetic needle generally and long diffused among the eastern navies. Evelyn says, that "it was, near eighty years after its discovery, unknown in Britain." This is not improbable, for there does not remain much record of maritime affairs in the interval between the reigns of John and Edward III. This monarch's reign was, after a most severe struggle with France for Edward supremacy on the seas, the era of a series of naval triumphs, and both navigation and naval architecture made most decided advances.

In an engagement which took place in 1340, the French Naval force amounted to 400 vessels, of which 120 were "large battle ships," these being principally Genoese mercenaries. Edward III. commanded the English fleet in person, which consisted of but 260 sail. The French are variously reported to have lost 20,000 and 30,000 men, and 200 vessels are said to have been captured. The loss to the English was only 4000 men. Two facts are elicited by the accounts of this engagement; one is, that there is no mention of galleys as forming any part of the fleets; the other is, that in the James of Dieppe, which was captured by the Earl of Huntingdon, 400 persons were found slain; consequently the size of the vessel must have been very considerable.

In 1344 Edward summoned commissioners from all the Royal ports, to meet in the metropolis, provided with the state of their "navies." The roll of this fleet is inserted in the first volume of Hackluyt, from a copy in the Cottonian Library. The total numbers were 710 ships, and 14,151 mariners; and there were 38 foreign ships, with 815 mariners. From this roll it will be seen that galleys had ceased to be used by England, either in her wars or in her commerce, as neither among the king's ships nor among those furnished by merchants is there any mention of them. This fleet was that engaged in the celebrated siege of Calais, and it Use of cannon was probably at this time that cannon were first employed by the English. Camden, in his Remains, says, "Certain it is, that King Edward III. used them at the siege of Calais in 1347."

Although from the fact of there being a royal dock-yard at Portsmouth so early as the reign of John, it is probable Edward's that the kings of England were possessed of a navy almost ships from the conquest; yet this roll of Edward's fleet contains the first enumeration of ships belonging to the sovereign, and employed in the service of the state, which occurs in English history; and consequently it is from the reign of Edward III. that the formation of a royal navy must be dated. The king's ships were 25 in number, and were manned by 419 mariners. It appears that the vessels belonging to the sovereign were inferior in force to many of those which were supplied by subjects; for the average number of the crews of the king's ships were 17 men to each vessel, while the average of the fleet was rather above 20. Of course these numbers only include the mariners employed in navigating the vessels, and not the soldiers to be afterwards embarked on board them. Considering the simplicity of the rig of these ships, in comparison to the wilderness of canvas and cordage covering the tall masts of a modern merchantman, there is more reason to be astonished at the large number of hands employed, than at the smallness of the averages, 17 and 20. There is good reason to suppose that the addition of the bowsprit to the rig of ships dates no farther back than late in the reign of Edward III., which is alone quite sufficient to prove the very imperfect state of the navigation at that period, and also to excite astonishment that, with such apparently inadequate means, so much was effected; for history would almost lead us to suppose that, for all the purposes of war and commerce, fleets as proudly as industriously ploughed the main then as now, "with all appliances and means to boot."

In the year 1381, the fourth of the reign of Richard II., Richard the first navigation act was passed in England, for the encouragement of the naval interest and the augmentation of our maritime power, by discountenancing the employment of foreign shipping. It enacted, "That for increasing the

History. shipping of England, of late much diminished, none of the king's subjects shall hereafter ship any kind of merchandise, either outward or homeward, but only in ships of the king's subjects, on forfeiture of ships and merchandise, in which ships also the greater part of the crews shall be of the king's subjects." This act was not, however, enforced, permission being given to hire foreign shipping when there were no English ships in readiness.

It has been remarked above, that the royal navy of England must date from the reign of Edward III. There is proof that it continued to be customary for the sovereign to possess ships; they were, however, used both for war and commerce. This practice, which does not at all militate against the existence of a royal navy, appears to have commenced when "large ships" were substituted for the galleys as vessels for war; and it long continued to be usual for merchants to hire shipping from the sovereign for commercial voyages. The proceedings of the privy council, which have been printed by the Record Commission, show that in June of the year 1400, Henry IV. ordered his "new ship," together with such others as were in the port of London, to proceed against the enemy. There is also a letter in the Cottonian Library, which has been printed in Ellis's Collection of Letters, from John Alcetre to King Henry V., concerning a ship building for that monarch at Bayonne. The letter is of the date of 1419; and as it contains more minute details than might be expected to have descended to us from such an early period, we give the following extract:—"At the making of this letter yet was in this estate, that ye, to wetting xxxvj. strakys in hyth y bordyd, on the webe strakys hyth y layde xj. bensys; the mast bene ys yn leyntye hyth y layde xj. comyn fete; and the bene of the hameron afore ys yn leyntye xxxix. fete, and the bene of the hameron by hynde is yn leyntye xxxiiiij. fete; fro the onemost ende of the stemme in to the post by hynde ys yn leyntye a hendryd iiij" and vj. fete; and the stemme ys in hithe iiiij" and xvij. fete; and the post xivij. fete; and the kele y yn leyntye a hendryd and xij. fete; but he is y rotyt, and must be chaungyd."

We have also evidence of the existence of ships which belonged to the monarch, in contradistinction to ships which belonged to the "commons," in the quaint rhymes of an anonymous author of the year 1433, which have been preserved by Hackluyt, termed The Prologue of the procees of the Libel of English policie, exhorting all England to kepe the sea, and namely, the narrowe sea, showing what profite commeth thereof, and also what worship and saluation to England, and to all Englisshmen.

"And if I should conclude all by the king Henrie the Fifth, what was his purposinge, Whan at Hampton he made the great dromons, Which passed other great ships of all the commons; The Trinitle, the Grace de Dieu, Holy Ghost, And other moe, which as nowe bee lost. What hope ye was the kings great intent Of thoo shippes, and what in mind he meant: It was not ellis; but that hee cast to be Lorde round about environ of the sea."

The term dromond is the corruption of a Levantine term, dromones, imported probably by the crusaders. The dromonds were long row-galleys, but the adopted term dromond was applied generally to all large ships.

There is a list of Henry's vessels in the fourth year of his reign preserved in the proceedings of the privy council. His navy then consisted of three "large ships," or "grands nies," three "carracks," eight barges, and ten balingers. In 1417 it was augmented to three "large ships," eight "carracks," six other ships, one barge, and nine balingers.

Again, in a letter preserved among the Cottonian manuscripts, and printed in Ellis's collection, it is stated that the Spaniards offered Henry V. two carracks for sale, one of which is described as of a tonnage equal to 1400, and the other to 1000 butts. So energetic was Henry V. in all things relating to his navy, and the consequent increase in the number of the royal ships during his reign was so great, as to have led to the error that before his time the sovereigns of England were not possessed of vessels, but relied wholly upon the aid to be gathered from the different ports of England, or to be hired from foreigners. This is evidently incorrect.

On the death of Henry V. a different line of policy appears to have been adopted; for in May 1423 the king's navy ships were all sold at Southampton, under a restriction that no foreigner could be a purchaser of them. But it appears that a long period did not elapse before the depressed state of the naval resources of the kingdom, consequent on this injudicious measure, attracted the attention of parliament. The following interesting quotation from the preface of the fifth volume of the Proceedings of the Privy Council, printed by the Record Commission, refers to this event:—"In 1443 the attention of parliament was directed to this important part of the national defence (the naval force), and a highly curious ordinance was made for the safeguard of the sea. From February to November eight ships with forecastles, or, as they were sometimes called then, as now, forecastles, armed with 150 men each, were to be constantly at sea. Every large ship was to be attended by a barge of 80 men, and a balinger of 40 men. There were also to be 'awaiting and attendant upon them' four 'spynes' or 'spinaces,' with 25 men each. The whole number of men in these 24 ships was 2240."

There is also in the same preface an account of the various kinds of ships which formed the navies of this period, a part of which we shall quote, and by the addition of some further information of the same nature, derived from Froissart, Monstrelet, and other sources, the reader will be enabled to form a tolerably correct opinion as to the state of naval architecture in England previous to and during the fifteenth century.

Ships. "The burthen of the largest ships at that period ships, probably did not exceed 600 tons, though some of them were certainly very large;" as, for instance, the vessel built at Bayonne for Henry V., already mentioned. "One which belonged to Hull was released from arrest" (she having been pressed into the king's service), "because she drew so much water that she could not approach within two miles of the coast of Guienne, where the Duke of Somerset's army intended to disembark;" and several notices occur of ships of 300 and 400 tons and upwards. Some had three and others only two masts, with short topmasts, and a "forestage" or "forecastle," consisting of a raised platform or stage, which obtained the name of castle from its containing soldiers, and probably from its having bulwarks. In this part of the ship it appears business was transacted; and in the reign of Edward III., if not afterwards, ships had sometimes one of these stages at each end, as ships "one chastel devant et derere" are then spoken of. Lydgate, describing the fleet with which King Henry V. went to France after the battle of Agincourt, says,

"Fifteen hundred ships ready there be found, With rich sails and high topeaste."

This is a confusion of terms. The "topcastles" were not the forecastles, but were castellated enclosures at the mastheads, in which the pages to the officers were stationed during an engagement, in order to annoy the enemy with darts and other missiles; as is frequently mentioned in Froissart, and is represented in the illuminations to his work.

Carracks were vessels of considerable burthen, and Carracks were next in size to great ships, in which class they indeed were sometimes included. Their tonnage may be estimated by their being in some instances capable of carrying 1400 butts; and the sail of one afforded Chaucer a strange simile expressive of magnitude, And now hath Satanas, saith he, a tayl Broder than of a carrike is the sayl."

Though occasionally armed and employed against the enemy, they were more generally used in foreign trade.

Charnock says that the first carrack which was built in England was built for a merchant, John Tavernier of Hull, who was consequently honoured by Henry VI. with distinguished favour; and she was licensed in 1449 with particular privileges to trade through the Straits of Morocco. The king also ordered her to be called the "Grace Dieu Carrack." The license states her to have been built "by the help of God and some of the king's subjects."

Barges were a smaller kind of vessel and of different construction from ships, though, like them, they sometimes had forecastles. Those appointed to protect the seas in 1415 were of 100 tons burthen, and contained forty mariners, ten men-at-arms, and ten archers; whilst the ships employed on the same occasion were of 120 tons, and had forty-eight mariners, twenty-six men at arms, and twenty-six archers each. Four large barges and two balingers were capable of holding 120 men-at-arms and 480 archers and sailors.

Balingers were still smaller than barges, had no forecastle, and sometimes contained about forty sailors, ten men-at-arms, and ten archers." Froissart makes frequent mention of "bailiers," "balleniers," which he describes "as drawing little water, and being sent in advance to seek adventures, in the same manner as knights and squires, mounted on the fleetest horses, are ordered to scour in front of an enemy, to see if there be any ambuscades." Monstrelet speaks of one vessel that was employed by Louis XI. to abduct the Count de Charolais, by the two names ballenier and balayer. It is not improbable that the name is derived from the French word baleine, and that its origin was similar to that of our English name whaler. The whale-fishery in Biscay was of a very early date.

Galleys are frequently mentioned at a very early period; and in the 5th Rich. II., 1381, the Commons complained that no measures had been taken to resist the enemy, who had attacked the English at sea with their barges, galleys, and other vessels. In 1405 Henry IV. directed his council to apply to the King of Portugal to lend him his galleys to assist the English navy against the French.

In Sir Grenville Temple's Travels in Greece and Turkey the following description of a Maltese galley, or, more correctly, galass, made from an old model preserved there, will be found:—"These galasses measured 169 feet 1 inch in length, and 39 feet 6 inches in breadth. They had three masts with lateen sails, and were propelled by forty-nine oars, each 44 feet 5 inches long. Their armament consisted of 1 thirty-six pounder, 2 of twenty-four, and 4 of six, all on the forecastle, which in those days had in reality some appearance of a castle. On each side of the vessel, aft of the forecastle, were 4 six-pounders." The total crew, including galley-slaves, consisted of 549 persons.

The Galass and the Galleon appear to have been successive improvements on the original galley, rendered necessary by the introduction of cannon into naval warfare. The artillery introduced on board the early galleys was placed either before or abaft the rowers, and to fire in the direction of the length. In the galleas, a description of vessel first used at the battle of Lepanto, guns were also placed between the rowers, to fire from the broadside. Evelyn describes the galleases he saw at Venice (1645) as being "vessels to rowe of almost 150 foote long and 30 wide, not counting prow or poop, and contain twenty-eight banks of oares, each seven men, and to carry 1300 men, with three masts." In the galleon the oars ceased to be the principal means of propulsion, and if used at all, were only so as occasional aids. The galley and galleas had overhanging topsides for the accommodation of the oars. In the galleon, on the contrary, the topsides "tumbled home" to so extraordinary an extent, that the breadth at the water was twice that at the topside, a fashion which has continued, but in a much less degree, to the present time.

Spynes or spynaces, "now called pinnaces, seem to have been large boats, capable of holding twenty-five men, and spynaces, were probably used for swiftness." To these must be added crayers, hulks, gabarres or gabbars, a kind of flat-bottomed boat, used in shallow rivers." The French still continue to apply the term "gabare" to store-ships.

Playtes, cogships, whence perhaps cogs and coggles are Playtes derived; farecrafts, passagers, which were perhaps boats and smaller used between England and France; and cock-boats, a small boat which attended upon all kinds of ships. The whole of these vessels were employed in conveying goods or passengers, and most of them on rivers or in the coasting trade. The ships, carracks, barges, balingers, and galleys, were employed equally for commerce or for war. When sent against the enemy, soldiers were put on board of them; and it is most likely they were at all times partly manned by soldiers. In foreign voyages they usually sailed in convoys; and it was a very ancient custom for the masters and sailors to elect their own admiral."

In Burchett's account of the unfortunate action in the Foists or Bay of Conquet, in 1513, in which the Lord High Admiral, foyst Sir Edward Howard, lost his life, four foists are mentioned as forming a part of the French force. They were probably vessels of a similar character with the galley, but smaller in size. About the beginning of the seventeenth century, "carracks," "galleons," and "tall shippes," appear to have become synonymous terms.

The term hulk originally was applied in a different sense Hulks, from that which is stated in the part of the foregoing remarks which we have quoted from the preface to the proceedings of the privy council. Frequent allusion is made to hulks in documents of the fifteenth and sixteenth centuries. In a letter from Sir Thomas Scymour to the privy council, dated the 13th of November 1544, when in command of the "shipes whyche was a poynete to kepe the Narrow Sees," vindicating himself for putting back on account of a storm, there is the following passage, from which it might almost be inferred that hulk was a general name synonymous with ships:—"Thre holkes that come after me colde nott gett syght thereof (the 'Eylle of Wyght') tyll they warre in a bay on the est syde of the Eylle, of the whyche Mr Strowd, Bramston, and Battersebe of the garde, God rest their sowles, was in on of them, whyche holke brake all her anekes and cabelles, and she brake all to peses on the shorr, and but 41 of 300 saved a lyve. The other two rode out the storme, whyche lasted all that nyght and the next day. My brother (Sir Hy Seymour) and John Roberts of the garde, tryde the sees all the first nyght, and the next day cam into Dartmouth haven, wharre my brothers holke stroke on a roke and brest all to peses; but God be praysede, all the men warre savede, savying thre; and a nother new holke that tryde the sees that nyght brake thre of her bemes, and with moche ado came into the Wyght."

Again, in a letter from Lord Viscount Lisle, Baron Malpas, the Lord High Admiral of England, to Henry VIII., there is an announcement, that "their is cum into the Downes 30 sayle of hulkes, whereof sum be tall shipes." And again, in a letter from the same to the Lord Chamberlain, Lord St John, he speaks of having detained "3 grate hulkes bound, as they say, for Lusselborne, the leste of y' 500 tunes." And again, from the same to the same, he speaks of his former letter and the "goodly hulkes," and says, "sithens that tyne I have stayed other too, which in beautye and well appoynting are beyond the others. That I have last stayd ys a shipe of 600 at the least, and hath The importance of the mercantile shipping of England during the fifteenth century must have been considerable. About the middle of it flourished the celebrated William Canyng, a merchant of Bristol, who built the church of St Mary's Redcliff in that city, in which church he was buried in 1474. This man appears to have been much in advance of the rude times in which he lived. His mercantile transactions were on so extensive a scale, and carried on in vessels of such large size, that they must have had an important influence in improving the navies of the period. The information which has descended to us respecting him is therefore not only a fact of much historical interest, but is one which is intimately connected with, and most materially affects, our subject. He was a great patron of the arts, a friend and protector of genius, and eminent for his virtue and piety. From an inscription upon his tomb, a tradition has become current, that Edward IV. took 2470 tons of shipping from him, he having "forfeited the king's peace;" and for the obtaining of which again, it is stated that Edward accepted these ships instead of a fine of 3000 marks.

The Itinerary of William of Worcester, preserved in the library of Bennett College, Cambridge, gives the names of Canyng's vessels, among which are the Mary and John of 900 tons, Mary Redcliff of 500 tons, and Mary Canyng of 400 tons. The same authority gives the names and tonnage of other large ships belonging to Bristol merchants, among which are the John of 511 tons, and the Mary Grace of 300 tons. If there be any truth in the tradition of the confiscation of the shipping, it is probable that the inscription on the tomb may refer to some act of Canyng's in favour of the house of Lancaster, as he appears to have enjoyed the favourable opinion of Henry VI. Another account, which, it is said, is authenticated by the original instrument in the Exchequer, states that this Canyng assisted Edward IV. with a loan, and received in return a license to have 2470 tons of shipping free of imposts. In Corry's History of Bristol it is said, "the commerce and manufactures of Bristol appear to have made considerable progress during the fifteenth century, about the middle of which flourished the celebrated Canyng." This extraordinary man employed 2853 tons of shipping, and 800 mariners, during eight years. Two recommendatory letters were written by Henry VI. in 1449, one to the master-general of Prussia, and the other to the magistrates of Danzig, in which the king styles Canyng his beloved eminent merchant of Bristol."

Some doubt must always remain as to the actual size of the shipping of this remote period, as we cannot ascertain the bulk that was then considered as equivalent to a ton. It is probable that the tonnage was estimated according to the number of butts of wine that a vessel could carry. For we find references to ships sometimes by tonnage, and sometimes by the "portage" of so many butts.

This, however, is only a question as to exactness of size. In whatever way measured, Canyng's ships must have been of very considerable dimensions. It is rather extraordinary, that at the unsettled period in question Bristol should have enjoyed such a state of commercial prosperity as the ownership of such shipping as that enumerated by William of Worcester necessarily involves. Bristol, for many centuries, was only second in mercantile importance to London; but the civil wars which distracted the kingdom during a great part of the fifteenth century must have much retarded the increase both of the military and the mercantile navy of England; and only when order was again re-established by the accession of Henry VII. to the throne, in 1485, could men's minds revert from the internal excitement of party strife to external affairs.

In this interval, in which England was torn by the wars of the houses of York and Lancaster, naval science had made more rapid strides than in any previous period of similar duration. The compass was not only known but progress was generally adopted. Navigators could take observations naval instruments called the astrolabe, invented by the use of an instrument called the astrolabe, invented by the Portuguese. The Spaniards and Portuguese were Compass sufficiently advanced in the art of navigation to sail on a Astrolabe wind, and their smaller vessels, at least, were adapted for this manoeuvre. New maritime states had started into existence. The Netherlands, until then scarcely known, Netherlands, under the Duke of Burgundy, the most formidable lands, naval power in the north of Europe. "His navy," says Philip de Commines, "was so mighty and strong, that no man durst stir in those narrow seas for fear of it, making war upon the king of France's subjects, and threatening them everywhere; his navy being stronger than that of France and the Earl of Warwick joined together." Venice, in 1420, according to Denina, in his Revolutions of Italy, supported 3000 merchant-ships, on board of which were 17,000 seamen. They employed 300 sail of superior force, manned by 8000 seamen; had forty-five carracks, with 11,000 men to navigate them; and her arsenals employed 16,000 carpenters. Portugal had pushed her discoveries round the Cape, and Spain had added America to the world.

The progress of discovery by the Portuguese to the south Portugal, east, and by the Spaniards to the west, in the voyages Spain. of Columbus, with the consequent rapid increase in the importance of these two powers, and the influence of their discoveries on the state of Europe, renders the fifteenth century probably the most important of modern history. In it was given the death-blow to the increase of the Saracenice power, and to that of the Mediterranean states. The Turk, the Venetian, and the Genoese, had hitherto been the monopolizers of the commerce of the east. The discovery of the passage round the Cape of Good Hope opened this trade to all nations. The commercial sceptre, and consequently the military sceptre, hitherto shared by the Turk, passed wholly from the infidel to the believer. The crescent sank before the cross.

There can be no doubt, also, that the "tormentas" of the "grão Cabo de boa Esperança," were a means of great improvement in naval architecture; for, in consequence of the representations of Bartholomew Diaz, John II., of Portugal ordered ships to be constructed for the special purpose of contending with the stormy seas of the Cape of Good Hope. The ships were built to form the squadron of Vasco de Gama, and were of small tonnage, from the very proper idea that small vessels were more adapted to prosecute researches in unknown seas than those of a large size, and consequent increased draught of water.

The squadron of Vasco de Gama consisted of three ships and a caravela. One of the ships was of the burthen of 200 tons, another 120, and the third 100; the caravela was of 50 tons. The largest of the ships was a victualler; the smallest was intended to prosecute discovery up creeks and shallows; and the other was for a display of force. As it is evident that it was not increase of dimensions which was to be the object in designing new vessels, the direction of improvement must have been towards perfecting their forms, strengthening their frames, and adding to the efficiency of their materiel. Portugal by these means became the most advanced state of Europe in knowledge of the art of shipbuilding; for it was long supposed that the passage to India required ships such as the Portuguese alone could build. Spain, in her career of discovery, conquest, and colonization across the mighty waters of the Atlantic, as if to assimilate the means to the vastness of her achievements, rapidly acquired the art of constructing ships of very large dimensions; and as long as she possessed a marine, her ships maintained this superiority. There is a curious instance of the light in which naval enterprises were considered in England at this time, notwithstanding the earnest desire of the monarch to re-establish his navy, which had necessarily suffered from the long civil war. A letter from Henry VII. to the Pope is preserved in the Cottonian Library, excusing himself from sending succour against the Turk, from which the following is a quotation:—“The Galees commyng from Venness o England be commonly vii. monethes sayllyng, and sometimes more;” and again, “it should be May or they should be ready to saill, and it shall be the last end of September or the said shippes shuld passe the Streits of Marrok; and grete difficulite to fynde any Maryners habile to take the rule and governance of the said shippes sayllyng into so jeopardous and ferre partes.”

There is a drawing extant in the Pepysian Library in Magdalen College, Cambridge, of the Henri Grace à Dieu, built by the order of Henry VII., which Charnock has engraved in his History of Marine Architecture, and argues as to the general authenticity of the representation. He says, “this vessel may be termed the parent of the British navy. This celebrated structure, the existence of which is recorded in many of the ancient chronicles, cost the king, by report, nearly 14,000 pounds.”

From this drawing may be traced the derivation of one or two names which have been preserved even to the present hour; as, for instance, the “yard-arm,” no doubt from the ends of the yards being armed with an iron hook. The castellated work from which has arisen the term “forecastle” is earlier than this; and the buckler-ports are most probably derived from a yet earlier period, when the bucklers of the knights were ranged along the sides of the ship, as they are represented in the illustrations of Froissart, and of the early chroniclers, and even in the Bayeux Tapestry.

“The masts were five in number, inclusive of the bowsprit, an usage which continued in the first-rates without alteration till nearly the end of the reign of King Charles I.; they were without division, in conformity with those which had been in unimproved use from the earliest ages. This inconvenience it was very soon found indispensably necessary to remedy, by the introduction of separate joints, or top-masts, which could be lowered in case of need.”

The drawing shows two tiers of ports. The introduction of port-holes is said to be an improvement due to a French ship-builder of Brest, named Descharges, in the reign of Louis XII., and about the year 1500. If the drawing be authentic, the correctness of this appropriation of the merit of the introduction of port-holes may be questionable.

Again, if the drawing be a correct representation of the vessel, she would have been in danger of upsetting, excepting in calm weather, and when her course was with the wind. In fact, as yet the large ships of war of England were not at all adapted to sail on a wind, and were very ill provided with such sails as would enable them to do so; they had therefore nothing to fear from the result of a measure which could not be put into execution. The fleets of war seldom ventured out of port excepting in the summer months, and then only when the wind was favourable to their intended course. But very shortly after the date of the building of the Henri Grace à Dieu, great improvement took place, and in the reign of Henry VIII. there is evidence to prove that sailing on a wind formed one of the qualities of the vessels composing his fleets. This fact appears to throw some doubt upon the correctness of the drawing, for it must have required ships widely different from any of which that would at all give an idea, to have performed the evolution of tacking or wearing; and as the Henri Grace à Dieu was in all probability the same ship that on the accession of Henry VIII. was called the Regent, she must have formed one in fleets which were capable of performing these manoeuvres. It is true that she may have been altered to adapt her to these new requirements of an improved system of seamanship; and it must also be said, that she was burned in an action with the French fleet, which occurred as early as the fourth year of the reign of Henry VIII.

Though it is out of the question that ships with the Henry enormous top-hamper which, on the evidence of all the VIII. drawings extant, still continued to be the fashion, could have made much progress in sailing on a wind, the letters of the time extant corroborate the statement made; for they begin to contain references to this improvement in navigation. In a letter from Sir Edward Howard, “Lord Admiral,” to King Henry VIII., upon the state of the fleet, A.D. 1513, preserved in the Cottonian Library, and published in Ellis’s collection, the following passage occurs:—“Ye commanded me to send your grace word how every shipp dyd saill; and this same was the best tryal that cowbe, for we went both slakying and by a bowlyn, and a cool acors and abouet in such wyse that few shippes lackyd no water in over the lee wales.” The Lord High Admiral Lisle, in one of his letters (1545), says the small vessels of his fleet could “lye best by a wynde;” and in 1567 we have conclusive proof that there were “fore and aft,” indeed “cutter-rigged” vessels on the British seas; as in a map of Ireland of that date, published in the state-papers, two such vessels are represented, for the purpose, apparently, of indicating regular packets from England to Ireland.

It has been very generally supposed, on the authority of Sir Walter Raleigh, that the “knowledge of the bowline” was a discovery in navigation made shortly before his time; but is is probable that there were, even from the time of the Northmen, craft so rigged as to be capable of sailing on a wind. Froissart mentions, in several instances, “a vessel called a Lin, which sails with all winds, and without danger;” and again, “a vessel called a Lin, which keeps nearer the wind than any other.” Boats with a rig adapted for this manoeuvre are also represented in engravings of a very early date. In the plates of Breydenbach’s Voyage to Palestine, which was published in 1483, boats and small vessels are represented with lateen sails; and in Braun’s Civitates Orbis Terrarum, published in 1572, sprit-sails are met with. It is quite certain, however, that sailing on a wind was by no means a general quality possessed by the ships of war, or to any extent even by the greater portion of the larger shipping, until about the reign of Henry VIII. One other instance may be adduced in the account of the loss of the Mari Rose, a ship of the “portage of 500 tons,” not so much to corroborate the fact of sailing on a wind, as to show that the two innovations, the introduction of port-holes and the “knowledge of the bowline,” were in advance of the qualities of the large ships of war of the time. Sir Walter Raleigh says that, “in King Henry VIII.’s time, at Portsmouth, the Mari Rose, by a little sway of the ship in casting about, her ports being within sixteen inches of the water, was overset and lost.”

The loss of this ship has been the means of giving Loss of another interesting insight into the comparatively low state Mari Rose. of nautical skill in England at this period, namely, the middle of the sixteenth century. In a letter among the state-papers published under the direction of the Record Commission, addressed by the Duke of Suffolk to Sir William Pagett, “chief secretary to the kinge’s highnes,” dated the 23rd of July 1545, and containing a schedule of things necessary to be had for the raising of the Mari Rose, one item is “fifty Venzyan maryners and one Venzyan carpenter;” the next item is “sixty Englisshye maryners to attende upon them.” It would also appear that the attempt was to be made under the direction of an Italian, as the conclusion of the schedule is, “Item, Symond, petrone and master in the Foyst, doth aggrie that all thyngs must be had for the purpose aforesaid." The attempts, however, all failed; the wreck of the Mary Rose remains to this day at Spithead, and so lately as August 1836, several of her brass cannon, of most exquisite workmanship, were recovered from the sea by the enterprise and ability of an Englishman of the name of Deane.

Some idea of the detail of ship-building rather before this period may be obtained from an account of a vessel built by James IV. of Scotland, at the close of the fifteenth or the beginning of the sixteenth century. The extract is from Charnock, but he has not mentioned his authority. "The king of Scotland rigged a great ship, called the Great Michael, which was the largest and of superior strength to any that had sailed from England or France; for this ship was of so great stature, and took so much timber, that, except Falkland, she wasted all the woods in Fife which were oakwood, with all timber that was gotten out of Norway; for she was so strong, and of so great length and breadth, all the rights of Scotland, yea, and many other strangers, were at her device by the king's command, who wrought very busily in her; but it was a year and a day ere she was completed. To wit, she was twelve score feet of length, and thirty-six foot within the sides; she was ten foot thick in the wall and boards, on every side so slack and so thick that no cannon could go through her. This great ship cumbered Scotland to get her to sea. From that time that she was afloat, and her masts and sails complete, with anchors offering thereto, she was counted to the king to be thirty thousand pounds expense, by her artillery, which was very great and costly to the king, by all the rest of her orders. To wit, she bare many cannon, six on every side, with three great bassils, two behind in her dock and one before, with three hundred shot of small artillery, that is to say, myand and battered falcon, and quarter falcon, flings, pestilent serpents, and double dogs, with hagtor and culvering, corsbows and handbows. She had three hundred mariners to sail her, she had six score of gunners to use her artillery, and had a thousand men of war, by her captains, shippers, and quarter-masters."

Several of the writers of this period mention the fact of a Swedish ship of extraordinary dimensions being built in the middle of the sixteenth century, and which was burned in an action between the Swedes and Danes in 1564. Chapman has given an estimate of the dimensions of this vessel. She was called the Makalos (by Charnock, Megala). According to Chapman, she was 168 English feet in length and 43 English feet in breadth, an immense vessel for that period. Her armament was 173 guns, 67 only of which could be considered as cannon, the remainder being merely swivels.

Henry VIII. was deeply sensible of the necessity of a permanent and powerful naval force, and established the navy office, and also several dockyards for building and repairing the ships of the royal navy. Among these were Woolwich, Deptford, and Chatham. He also greatly added to and improved the dockyard at Portsmouth. He invited from foreign countries, particularly from Italy, the commercial cities of which were still in advance of the rest of Europe in the maritime arts, as many skilful foreigners as he could allure, either by the hope of gain or by the honours and distinguished countenance he paid to them. The following extract is from a report made to James I. in the year 1618, and published in the Archaeologia. It was made in answer to a commission issued by that monarch to the several master-builders.

The minority of Edward VI., and the civil and religious strife which distracted the kingdom during the reign of Mary, depressed the resources of the state, and evidently much checked the progress of its maritime strength. The report says, "In former times our kings have enlarged their dominions rather by land than sea forces, whereat even strangers have marvelled, considering the many advantages of a navy; but since the change of weapons and fight, Henry VIII., making use of Italian shipwrights, and encouraging his own people to build strong ships of war, to carry great ordnance, by that means established a puissant navy, which in the end of his reign consisted of 70 vessels, whereof 30 were ships of burthen, and contained in all 10,550 tons, and 2 galleys. The rest were small bargues and row-barges, from 80 tons downwards to 15 tons, which served in rivers and for landing of men. Edward VI., in the sixth year of his reign, had but 53 ships, containing in all 11,005 tons, with 7995 men, whereof only 28 vessels were above 80 tons each. Queen Mary had but 46 of all sorts."

There is one peculiarity about the fleets of this time, Defects of which exemplifies the defects of their design in a very remarkable feature. It is, that the ships built for the royal navy appear only to have been adapted for the lodgment of the soldiers and mariners, with their implements of war, and the necessary stores for navigation. The provisions were carried in an attendant vessel, called a "victualler," of which there was one attached to each of the large ships of war in the fleet, or to several of the smaller size. The hold appears to have been principally occupied by the "cook-room," the inconvenience of which arrangement, though much complained of, was general when Sir Walter Raleigh, in his Discourse on the Royal Navy and Sea Service, recommended that it should be removed to the forecastle; and even so lately as 1715, several men of war had "cook-rooms" in their holds. There is also no doubt that the enormous quantity of ballast which was rendered necessary by the immense top-hamper of these ships, and the space which it occupied, from being shingle, left but little room for the stowage of any quantity of provisions. In the ships built for commerce, this defect does not appear to have existed, as in fleets composed of the king's and of private shipping, those ships only which belonged to the royal navy had these attendant victuallers. The cook-rooms in the merchant shipping were under the forecastle; and they had less top-hamper, as less accommodation was required for officers.

Although the comparative inefficiency of the vessels may Epoch in be commented on, it will be apparent that that period in the naval architecture and of navigation has now been entered on in which, though still in their infancy, these arts may be considered as perfect in all but the maturity to be acquired by the experience of years. The mariner's compass was known; the theory of taking observations was understood, and the practice of it in the course of being perfected; and therefore the longest voyages could be undertaken with comparative certainty and safety. Besides this, the ships, though still imperfect, were becoming gradually manageable machines, and had ceased to be the cumbrous masses of the preceding ages, which, with few exceptions, were capable of little more than of being driven before the wind.

If the contents of the foregoing pages be considered, Three there will appear to be three epochs in the maritime history epochs in of England; the first commencing with the introduction of the marigalleys by Alfred, and ending with the reign of Edward III., before whose time these galleys and vessels, propelled England by oars, were the chief instruments of navigation; the second ending with the reign of Henry VIII., during which period, though sailing vessels were used for the purposes both of war and commerce, they were comparatively at the mercy of the winds, and, speaking generally, could sail only when they blew both fairly and gently; the third epoch has been already noticed.

From the extract of the report of the builders, the state of the navy during the reigns of Edward VI. and of Mary

It will be seen. It is known, therefore, that when Elizabeth ascended the throne, the marine of England, both military and mercantile, was in a very depressed state. The successful enterprise of Drake, and the fear of the Spanish Armada, aroused the energies of the country, and the force collected to resist the invasion amounted to 197 vessels of various descriptions, of the aggregate burthen of nearly 30,000 tons, 34 of which, measuring together 12,600 tons, composed the royal navy. It is true, that by far the larger portion were of small force. One only, the Triumph, was of 1100 tons; another, the White Bear, was of 1000 tons; two were of 800 tons, 3 of 600, six of 500, and five of 400; sixty-six were under 100 tons; and fifteen were victuallers, of which the tonnage is not mentioned. There are also seven other vessels included in the 197 which have no tonnage assigned them; but they must have been of small size, the number of mariners on board the whole seven being only 474. We have very conclusive means of comparing the Spanish with the English ships, and also of judging how very little naval arrangements were then understood, from their imperfect state even on board a fleet which had occupied the whole attention of the Spanish authorities for a space of three years, exemplified in the following anecdote. Burchett, in his account of the action of the 23rd of July 1588, says, "The great guns on both sides thundered with extraordinary fury, but the shot from the high-built Spanish ships flew over the heads of the English without doing any execution; one Mr Cock being the only Englishman who fell, while he was bravely fighting against the enemy in a small vessel of his own."

The Spaniards appear to have been the first to introduce a third tier of guns, the earliest mention of a three-decker being the Philip, a Spanish ship engaged in the action off the Azores in 1591, with the Revenge, commanded by Sir Richard Greenvil. The following armament of the Philip is extracted from a most spirit-stirring account of this tremendous action, which was written by Sir Walter Raleigh, and has been preserved by Hacktuyt. "The Philip carried three tier of ordnance on a side, and eleven pieces in euerie tire. She shot eight forth right out of her chase, besides those of her stern portes."

The English do not appear to have followed the example set by the Spaniards; for, during the long reign of Elizabeth, the ships of the royal navy were not much, if at all, increased in their dimensions, which was probably owing to the triumphant successes of her fleets, though they were composed of ships generally much smaller in size than those opposed to them. From the list of the royal navy at the time of her death, in 1603, given by Sir William Monson in his tracts, of 42 ships composing the navy, there were then only two ships of 1000 tons, three of 900, three of 800, two of 700, four of 600, four of 500, and there were eight under 100 tons burthen. Two of these ships, the Triumph and the White Bear, are rated in this list each at 100 tons less burthen than in the list of the fleet in the year 1588, already noticed.

The mercantile marine was also greatly improved and increased during the reign of Elizabeth. This wise monarch did all in her power to encourage foreign trade; and she honoured Drake by knighting him on board his own vessel at Deptford, after his return from circumnavigating the globe. The celebrated Sir Walter Raleigh, under a charter granted by her in 1584, commenced trading with America, and his successes, with those of others, in trade, as well as in the capture of richly laden Spanish merchantmen, prove the superiority of the English ships of this period. In 1600 the East India Company obtained their charter from Elizabeth, and merchant-ships, which proved the precursors of a fleet of the finest merchantmen, were immediately built by them for this distant traffic.

Shortly after the accession of James to the throne, several commissions were appointed to inquire into the state of the navy. From that of the year 1618 a very voluminous report emanated, of which the following is an extract, that James I. affords an example of the state of knowledge on naval architecture at that time:—"The next consideration is the manner of building, which in shippes of warre is of greatest importance, because therein consists both their sayling and force. The shippes that can saile best can take or leave (as they say), and use all advantages the winds and seas does afford; and their mould, in the judgment of men of best skill, both dead and alive, should have the length treble to the breadth, and breadth in like proportion to the depth, but not to draw above 16 foote water, because deeper shippes are seldom good saylers, and ever unsafe for our rivers, and for the shallow harbours, and all coasts of ours, or other seas. Besides, they must bee somewhat snugg built, without double gallarys, and too lofty upper workes, which overcharge many shippes, and make them coeme faire, but not worke well at sea.

"And for the strengthening the shippes, wee subscribe to the manner of building approved by the late worthy prince, the lord admiral, and the officers of the navy (as wee are informed), on those points.

"1. In makinge 3 orlopes, whereof the lowest being placed 2 foote under water, both strengtheneth the shipp, and though her sides bee shott through, keepeith it from bildeginge by shott, and giveth easier meanes to finde and stopp the leakes.

"2. In carrying their orlopes whole floored throughout from end to end, without fall or cutting off ye' wast, which only to make faire cabbins, hath decayed many shippes.

"3. In laying the second orlope at such convenient height that the portes may bearne out the whole fire of ordinance in all seas and weathers.

"4. In placinge the cooke roomes in the forecastle, as other war shippes doe, because beinge in the midships, and in the holds, the smoake and heate soe search every corner and seame, that they make the okam spew out, and the shippes leaky, and soone decay; besides, the best roome for stowage of victualising is thereby soe taken up, that transportors must be hyred for every voyage of any time; and, which is worst, when all the weight must bee cast before and abaf, and the shippes are left empty and light in the midst, it makes them apt to sway in the back, as the Guardland and divers others have done."

This commission was followed by several others during this and the succeeding reign, and from their reports arose many regulations tending much to the improvement of the navy, although the expenses incurred were, ostensibly at least, in part the means of causing the subsequent revolution.

In the early part of the reign of James I. the mercantile navy of England was reduced to a very low state, most of shipping of the commerce being carried on in foreign bottoms. The this pe- incitement offered by the advantageous trade which the Dutch had long engaged in to India at length aroused the nation, and the formation of the East India Company, which was the act of James, was followed by the building of the largest ship that had yet been constructed for the purposes of commerce, at least in England. The king dined on board Trade's Increase, and gave her the name of the Trade's Increase. She is reported to have been of the burthen of 1200 tons. The impetus once given, before the end of the reign of James an important mercantile navy was owned by British merchants.

Another interesting fact connected with this reign is the ship-founding of the Shipwrights' Company, in the year 1605, wrights' and which was incorporated by a charter granted to the Company, "Master, Warden, and Commonalty of the Art or Mystery of Shipwrights," in May 1612. Mr Phineas Pett was the first master. The draughts for the ships of the royal navy were subsequently ordered to be submitted to this company for approval previously to being built from. They also had jurisdiction over all builders, whether of the royal navy or of merchant-shipping.

In 1610 the Royal Prince was launched; she was the largest ship which at that time had been built in England, and was also a most decided improvement in naval architecture. The great projection of the prow, a remnant of the old galleys, was for the first time discontinued, and the stern and quarters assimilated more to those of a modern ship than to any which had preceded her. She is thus described in Stow's Chronicles—“A most godly ship for warre, the keel whereof was 114 feet in length, and the cross-beam was 44 feet in length; she will carry 64 pieces of ordnance, and is of the burthen of 1400 tons.” The great workmaster in building this ship was Master Phineas Pett, Gentleman, some time master of arts at Emanuel College, Cambridge.

The same gentleman, Mr Phineas Pett, continued the principal engineer of the navy during the reign of Charles. The family of the Petts were the great instruments in the improvement of the navy, and, if the term may be allowed, of modernizing it, by divesting the ships of much of the cumbrous top-hamper entailed on them from the castellated defences which had been necessary in, and which yet remained from, the hand-to-hand encounters of the middle ages; and it is probable that, but for the taste for gorgeous decoration which prevailed during the seventeenth century, this ingenious family would have been able to effect much more; as it was, they decidedly rendered England pre-eminently the school for naval architecture during the time they constructed its fleets. This family can be traced as principal engineers for the navy from about the middle of the fifteenth century to the end of the reign of William III.

Evelyn, in his Diary, relating a conversation, says, “Sir Anthony Deane mentioned what exceeding advantage we of this nation had by being the first who built frigates, the first of which ever built was that vessel which was afterwards called the Constant Warwick (built in 1646), and was the work of Pet of Chatham, for a trial of making a vessel that would sail swiftly. It was built with low decks, the guns lying near the water, and was so light and swift of sailing, that in a short time she had, ere the Dutch war was ended, taken as much money from privateers as would have laden her.” The dimensions of this vessel are given in Pepys’s Miscellanies as follows: length of the keel 85 feet, breadth 26 feet 5 inches, depth 13 feet 2 inches, and 315 tons burthen; her highest number of guns 32, and of crew 140.

Peter Pett, who built the Constant Warwick, was the son of Phineas Pett. He caused the fact of his being the inventor of the frigate to be recorded on his tomb. He was also the builder of the Sovereign of the Seas, in 1637, which was the first three-decker built in England. Her length over all is stated to have been 232 feet, her length of keel 128 feet, her main breadth 48 feet, and her tonnage 1637. Heywood describes her in the following terms:—“She hath three flush deckes and a forecastle, an halfe decke, a quarter decke, and a round-house. Her lower tyre hath thirty ports, which are to be furnished with demi-cannon and whole cannon throughout, being able to bear them. Her middle tyre hath also thirty ports for demi-culverin and whole culverin. Her third tyre hath twentie-sixe ports for other ordnance. Her forecastle hath twelve ports, and her halfe decke hath fourteen ports. She hath thirteen or foureteen ports more within board for murdering pieces, besides a great many loope-holes out of the cabins for musket shot. She carrieth, moreover, ten pieces of chase ordnance in her right forward, and ten right aft; that is, according to land service, in the front and the reare. She carrieth eleaven anchors, one of them weighing foure thou- Sweden have had good ships for these last fifty years. I say that the forenamed kings, especially the Spaniards and Portugalls, have ships of great bulke, but fitter for the merchant than the man of warre, for burthen then for battaille.

Although we have not at this time 135 ships belonging to the subjects of 500 tons each ship, as it is said we had in the 24th yeare of Queen Elizabeth, at which time also, upon a generall view and muster, there were found in England, of all men fit to beare arms, eleaven hundred and seventy-two thousand; yet are our merchants' ships now farre more warlike and better appointed than they were, and the royal navy double as strong as then it was. We have not, therefore, lese force than we had, the fashion and furnishing of our ships considered; for there are in England at this time 400 saile of merchants fit for the wars, which the Spaniards would call gallions; to which we may add 200 saile of crumsters or hoyes, of Newcastle, which each of them will beare six demi-culverins, and four sakers, needing no other addition of building than a slight spar-decke fore and aft, as the seamen call it, which is a slight decke throughout. The 200 which may be chosen out of 400, by reason of their ready staying and turning, by reason of their windwardnesse, and by reason of their drawing of little water, and they are of extreme vantage neere the shoare, and in all bayses and rivers to turn in and out; these, I say, alone, well manned and well conducted, would trouble the greatest prince in Europe to encounter in our seas; for they stay and turn so readily as, ordering them into small squadrons, three of them at once may give their broad-sides upon any one great ship, or upon any angle or side of an enemy's fleet. They shall be able to continue a perpetuall volleye of demi-culverins without intermission, and either sink or slaughter the men, or utterly disorder any fleete of crosse sailes with which they encounter.

I say, then, if a vanguard be ordained of these hoyes, who will easily recover the wind of any other ships, with a battalie of 400 other warlike ships, and a rearde of thirty of his majestie's ships to sustaine, relieue, and countenance the rest (if God beat them not); I know not what strength can be gathered in all Europe to beat them. And if it be objected that the states can furnish a farre greater number, I answer, that his majestie's forty ships, added to 600 before named, are of incomparable greater force than all that Holland and Zeeland can furnish for wars.

In the foregoing extract there is strong evidence that the ships of the royal navy were generally inferior to those employed by the merchant-service, in the essential qualifications of being weatherly. This is exactly the conclusion that might be arrived at from the consideration, that a private individual would dispense with all that superabundance of top-hamper which was entailed on the ships of the royal navy, by the accommodation required for the numerous officers and gentlemen generally embarked on board them, and also by the mania for gorgeous decorations. This mania is well exemplified by the fact, that of the Sovereign of the Seas it is stated, "She beareth five lanthornes, the biggest of which will hold ten persons to stand upright, and without shouldering one another."

Sir Walter Raleigh, in his Discoverie on the Royal Navy and Sea-Service, adverts to the same subject. He says, "We find by experience, that the greatest ships are lese serviceable, goe very deep to water, and of marvellous charge and fearefull cumber, our channells decaying every yeare. Besides, they are lese nimble, lese maincable, and very seldome employed. Grande navio, grande fatiea, saith the Spaniard; a ship of 600 tons will carry as good ordnance as a ship of 1200 tons; and though the greater have double the number, the lesser will turn her broad-sides twice before the greater can wend once; and so no advantage in that overplus of ordnance. And in the building of all ships, these six things are principally required:

1. First, that she be strong built; 2. Secondly, that she be swift; 3. Thirdly, that she be stout sided; 4. Fourthly, that she carry out her guns all weather; 5. Fifthly, that she hull and trye well, which we call a good sea ship; 6. Sixthly, that she stay well when bourding and turning on a wind is required.

"To make her strong, consisteth in the truth of the workeman and the care of the officers.

"To make her sayle well, is to give a long run forward, and so afterward done by art and just proportion. For, as in laying out of her bows before, and quarters behind, she neither sinck into nor hang in the water, but lye cleare off and above it; and that the shipwrights be not deceived herein (as for the most part they have ever been), they must be sure that the ship sinck no deeper into the water than they promise, for otherwise the bow and quarter will utterly spoile her sayling.

"That she be stout, the same is provided and performed by a long bearing floore, and by sharing off above water even from the lower edge of the ports.

"To carry out her ordnance all weather, this long bearing floore, and sharing off from above the ports, is a chiefe cause, provided always that your lowest tyre of ordnance must lye foure foot cleare above water when all loading is in, or else those your best pieces will be of small use at the same in any growne weather that makes the billoe to rise, for then you shall be enforced to take in all your lower-ports, or else hazard the ship.

"To make her a good sea ship, that is to hull and trye well, there are two things specially to be observed; the one that she have a good draught of water, the other that she be not overcharged, which commonly the king's ships are, and therefore in them we are forced to lye at trye with our maine course and misien, which, with a deep keel and standing streake, she will performe.

"The hinderance to stay well is the extreme length of a ship, especially if she be floaty and want sharpnesse of way forwards; and it is most true, that those over-long ships are fitter for our seas than for the ocean; but one hundred foot long, and five and thirty foot broad, is a good proportion for a great ship. It is a speciall observation, that all ships sharpe before, that want a long floore, will fall roughly into the sea, and take in water over head and ears.

"So will all narrow quartered ships sinck after the tayle. The high charging of ships is it that brings them all ill qualities, makes them extreme leeward, makes them sinck deep into the water, makes them labour, and makes them overset. Men may not expect the ease of many cabbins, and safety at once, in sea-service. Two decks and a half is sufficient to yield shelter and lodging for men and mariners, and no more charging at all higher, but only one low cabbin for the master. But our mariners will say, that a ship will beare more charging aloft for cabbins, and that is true, if none but ordinary marryners were to serve in them, who are able to endure, and are used to, the tumbling and rowling of ships from side to side when the sea is never so little growne; but men of better sort and better breeding would be glad to find more steadinesse and lese tottering cadge work. And albeit, the mariners doe covet store of cabbins, yet indeed they are but sluttish dens, that breed sickness in peace, serving to cover stealths, and in fight are dangerous to teare men with their splinters."

In Fuller's Worthies, there is also a short summary of fuller's the comparative qualities of the ships of different nations in Worthies, the middle of the seventeenth century. It is as follows:

"First, for the Portugal, his cavils and carriats, whereof few now remain (the charges of maintaining them far exceeding the profit they bring in); they were the veriest drones on the sea, the rather because formerly their seeling was dam'd up with a certain kind of mortar to dead the shot, a fashion now by them disused." "The French, however dexterous in land-battles, are left-handed in sea-fights, whose best ships are of Dutch building. The Dutch build their ships so floaty and buoyant, they have little hold in the water in comparison to ours, which keep the better wind, and so outsail them.

"The Spanish pride hath infected their ships with loftiness, which makes them but the fairer marke to our shot. Besides the wind hath so much power of them in bad weather, so that it drives them two leagues for one of ours to the leeward, which is very dangerous upon a lee-shore.

"Indeed the Turkish frigots, especially some thirty-six of Algier, formed and built much nearer the English mode, and manned by renegadoes, many of them English, being already too nimble heeld for the Dutch, may hereafter prove mischievous to us, if not seasonably prevented."

During the early part of the seventeenth century, the Dutch navy rapidly increased in importance. Their success in having wrested from the Portuguese a share of the commerce of the east, emboldened them, in the then depressed state of the Spanish marine, to make a similar attempt on the west, and endeavour to establish settlements in South America.

The wars with Spain, in which they were consequently engaged, had such an important effect in establishing their maritime power, that in 1650 their navy consisted of 120 vessels fitted for war, seventy of which had two tiers of guns; and their fleet was in all respects the most efficient in Europe.

Evelyn, in his tract on Navigation and Commerce, speaking of the fisheries, says "Holland and Zeeland alone should, from a few despicable boats, be able to set forth above 20,000 vessels of all sorts, fit for the rude seas, of which more than 7000 are yearly employed upon this occasion. 'Tis evident that by this particular trade they are able to breed above 40,000 fishermen and 116,000 mariners, as the census (1639) has been accurately calculated."

The tremendous struggle in which they were enabled by these means to engage with us shortly after this period, in consequence of the injurious operation of the navigation act on their commerce, had a most influential effect on the improvement of our navy, which at the commencement of the contest was very unequal to that of the Dutch; and it is probable that this war was the means of enabling us to contend triumphantly against the immense and unexpected attempts of Louis XIV. to wrest the sceptre of the seas from our grasp.

Charles I. The sovereigns of the house of Stuart, without exception, appear to have devoted much attention to the improvement of the navy. Charles I. may be almost said to have lost both crown and life in consequence of these efforts; nor would it be doing justice to Cromwell to omit mention of the energy with which he took advantage of the all but despotic power which he possessed to increase his naval force. For this purpose not only many ships were built during the protectorate, but numbers of merchant-vessels were bought for the service of the state.

After the Restoration, Charles II. paid great personal attention even to the minutiae of his navy, as shown by the following curious extract from a letter of his to Prince Rupert, preserved in the state-papers, and also by continual references to his naval predilections in Evelyn's and Pepys's memoirs and writings. The letter is dated 4th August 1678. It says, "I am very glad the Charles does so well; a gerdeling this winter when she comes in will make her the best ship in England; next summer, I believe, if you try the two sloops that were built at Woolidge that have my invention in them, they will outsail any of the French sloops. Sir Samuel Mooreland has now another fancy about weighing anchors; and the resident of Venice has made a model also to the same purpose. We have not yet consulted them with Mr Tippet nor Mr Deane; but hope when they are well considered, we may find one out of them that will be good."

In Pepys's Diary, 19th May 1666, there is the following notice relating to one of the gentlemen mentioned in the above letter:—"Mr Deane and I did discourse about his ship the Rupert, which succeeds so well, as he has got great honor by it, and I some by recommending him. The king, duke, and everybody, say it is the best ship that was ever built. And then he fell to explain to me his manner of casting the draught of water which a ship will draw before-hand, which is a secret the king and all admire in him; and he is the first that hath come to any certainty beforehand of foretelling the draught of water of a ship before she be first launched." This gentleman appears therefore to have been plication of the first who applied mathematical science to naval architecture in this country. Pepys also says, "another great step and improvement to our navy, put in practice by Sir Anthony Deane," was effected in the Warspight and Defiance, which were "to carry six months' provisions, and their guns to lie 4½ feet from the water." This was in 1665.

The foregoing extract probably indicates the date of the first practical application to a useful purpose in this country of the famous discovery of Archimedes. It is well known that he was called upon by his king to test the purity or the adulteration of the gold of the royal crown, and the displacement of the water of his bath by his own immersion therein suggested to his mind the means of solving the problem. He saw that a body immersed in water displaced its own bulk of water, and after this the knowledge followed that a body floating in a fluid displaced its own weight of that fluid. If the weight of the body, therefore, was known, the quantity of water which it would displace could immediately be calculated, and the depth to which it would sink be found.

In this historical sketch the probability that the merchant-shipping of England were superior in their sea-going qualities to those composing the royal navy, has been adverted to in a Discourse touching the Past and Present State of the Navy, by Sir Robert Slingsby, knight-baronet, and comptroller of the navy, dated 1669, there is the following interesting statement, which points to a reason why this superiority of the merchant-shipping may have existed. "But since these late distractions began at home" (the Commonwealth), "foreignage trade decayed, and merchants so discouraged from building, that there hath been navy scarce one good merchant-ship built these twenty years past, and of what were then in being, either by decays or accident, there are very few or none remaining. The merchants have found their private conveniences in being convoyed att the publick charge; they take noe care of making defence for themselves if a warr should happen." Yet he subsays, in the time of Charles I., "the merchants continued quent im- their trade during the wars with France and Spain, if there prove- could but two or three consort together, not caring who they met," they being little inferior in strength or burthen to the ships of the royal navy.

About 1684 Sir Richard Haddock, comptroller of the navy, adopted the recommendation of Mr, afterwards Sir Anthony Deane, at that time surveyor of the navy, and directed an inquiry to be made as to "the number of cube feet that are contained in the bodies of several draughts of their main water-line, when all materialis are on board royal navy, fitt for saileinge." The result of this inquiry was a very voluminous statement of the weights which made up the whole displacement of the fourth, fifth, and sixth rate ships, including minute details of their masts, yards, armament, &c., accompanied by perfect drawings of each ship. The following table contains the dimensions and displacements, &c., of each class: James II., from having so long and so gloriously filled the office of Lord High Admiral while Duke of York, was perfectly aware of the requirements of the navy; and during his short reign he paid great attention to increasing its efficiency. He also especially directed inquiries into the question of the durability of timber for the construction of it, and carefully accumulated both materials and stores for its maintenance. It is not a little curious that it was probably the attention which the monarchs of the line of Stuart had bestowed on the naval service, which enabled it so triumphantly to resist the persevering attempts of Louis XIV. to recover for them the throne of their ancestors.

Though England was at the Revolution possessed of an efficient fleet, manned by experienced seamen, who had all the confidence arising from a series of naval triumphs, it must be remembered that for a long period no opposition to her naval superiority had been anticipated from any other power than Holland; and consequently the fleets of England were composed of ships which had many of them been built to adapt them to this service, for which small dimensions and light draughts of water were essential qualifications, on account of the shoalness of the Dutch coast.

William was too cautious a monarch to have neglected so important a means of national defence as was the navy, when engaged with such an ambitious and energetic opponent as Louis XIV.; and we find that the naval force was considerably increased, both numerically and in dimensions, during his reign. But the triumphs of our armies under Marlborough having for a time diverted the attention of the nation from naval affairs, it fell into decay during the reign of his successor.

When Louis XIV. determined to dispute with England the sovereignty of the seas, he was not only without a navy, but without the means of forming one. The military and commercial marine of France had ceased to exist. The sanguine temperament of the monarch, and the wisdom of his minister Colbert, removed all obstacles; commerce began to flourish on the quays, merchant-vessels to crowd the ports; dockyards, harbours, and shipping appeared simultaneously to start into existence; and the nation, French which almost for centuries had been essentially military, felt constrained to turn its energies to commerce and to the sea. A navy which, in 1663, consisted of some four or five small vessels, in little more than ten years bearded and baffled the combined fleets of Holland and of Spain, and asserted the sovereignty of the Mediterranean. In 1681 her fleets consisted of 115 line-of-battle ships, manned by 36,440 men, with 179 smaller ships, the crews of which amounted to 3037 men; and in 1690 a fleet of eighty-four vessels of war, out of which three were of a hundred guns and upwards, and ten others were above eighty-four guns, with twenty-two fire ships, was cruising in the British seas. It is true that these mighty armaments failed in fulfilling the ambitious designs of Louis. But the severity of the struggle, which at length ended in the annihilation of his hopes, and in our triumphant assertion of our naval superiority, must always serve as an example of the danger we may incur by too great confidence in that superiority.

The following comparison between the French and British ships of about this period, is from an official contemporary paper, by a gentleman of the name of Gibson:

"Our guns being for the most part shorter, are made to carry more shot than a French gun of like weight, therefore the French guns reach further, and ours make a bigger hole. By this the French has the advantage to fight at a distance and we yard-arm to yard-arm. The like advantage we have over them in shipping; although they are broader and carry a better sail, our sides are thicker, and better able to receive their shot; by this they are more subject to be sunk by gunn shott than we."

The paper also complains much of the injudicious management of our shipping, by which it says, "many a fast sayling ship have come to loose that property, by being sent of over-masted, over-rigged, over-gunned (as the Constant royal navy, Warwick, from twenty-six gunns, and an incomparable sayler, to forty-six gunns and a slugg), over-manned (vide all the old shippes built in the parliament time now left),

History. over-built (vide the Ruby and Assurance), and having great taffellars, gallarys, &c., to the making many formerly a stiff, now a tender-sided ship, bringing thereby their head and tack to lie too low in the water, and by it taking away their former good property, in steering, saying, &c. The French by this defect of ours make war with the sword (by sending no small ships of war to sea, but clean), and wee, by cruising in fleetes, or single ships foul, with bare threats."

Lord Rodney. In a letter from Sir George (afterwards Lord) Rodney, dated the 31st May 1780, to Mr. Stephens, the secretary of the Admiralty, is a passage which goes to prove the truth of the above statement. "Nothing could induce them (the French fleet) to risk a general action, though it was in their power daily. They made, at different times, motions which indicated a desire of engaging, but their resolution failed them when they drew near; and as they sailed far better than his majesty's fleet, they with ease could gain what distance they pleased to windward."

Cause of inferiority of English ships. One great cause of the inferiority of our ships arose from the practice which prevailed during the first half of the eighteenth century, through a mistaken idea of economy, of "rebuilt" old ships, without reference to the opinions of practical men, so that the forms and dimensions of the previous century passed down, in many instances, into the succeeding one, and justice was not done to the shipbuilding knowledge of the surveyors.

The French system of improvement was followed by the French Spaniards, and the capture of the Princessa, in 1740, of system followed by 70 guns, 165 feet in length, and 49 feet 8 inches in breadth, when our ships of the same force then building were Spain. only 151 feet long and 48 feet 6 inches broad, caused an appeal to be made by the Admiralty to Admiral Sir John Norris. The surveyors of the navy of that date who had succeeded Sir A. Deane were men of no note, because no opportunity of showing their powers had been allowed them. In consequence of the inquiries then made, the several master-shipwrights of the dockyards were directed to send in proposals for the future established dimensions of the navy; and, in 1745, Sir Jacob Attwood being surveyor of the navy, the Admiralty issued a new establishment for the dimensions of the several ratings of ships. The following table, taken from Derrick's Memoirs of the Royal Navy, contains the various established alterations from time to time, from the reign of Charles II. to this of 1745, which was the last:

An Account showing the Dimensions established, or proposed to be established, at different times, for Building of Ships.

Extracted from Derrick's Memoirs of the Royal Navy.

| Establishment of | Proposed in | Establishment of | |------------------|-------------|------------------| | | | 1745. | | Ships of 100 Guns. | | | | Length on the gun-deck | Ft. In. | Ft. In. | Ft. In. | Ft. In. | Ft. In. | Ft. In. | | Length of the keel, for tonnage | 165 0 | 174 0 | 174 0 | 175 0 | 178 0 | 178 0 | | Breadth, extreme | 137 8 | 140 7 | 140 7 | 142 4 | 144 6 | 144 6 | | Depth in hold | 46 0 | 50 0 | 50 0 | 50 0 | 51 0 | 51 0 | | Burthen in tons | 19 2 | 20 0 | 20 0 | 21 0 | 21 6 | 21 6 | | | 1550 | 1869 | 1869 | 1892 | 2000 | 2000 | | Length on the gun-deck | 158 0 | 162 0 | 164 0 | 166 0 | 168 0 | 170 0 | | Length of the keel, for tonnage | 132 0 | 132 5 | 134 1 | 137 0 | 138 4 | 138 4 | | Breadth, extreme | 44 0 | 47 0 | 47 2 | 47 9 | 48 0 | 48 6 | | Depth in hold | 18 2 | 18 6 | 18 10 | 19 5 | 20 2 | 20 6 | | Burthen in tons | 1307 | 1551 | 1566 | 1623 | 1679 | 1730 | | Length on the gun-deck | 156 0 | 156 0 | 158 0 | 158 0 | 161 0 | 165 0 | | Length of the keel, for tonnage | 127 6 | 128 2 | 127 8 | 130 10 | 134 10 | 134 10 | | Breadth, extreme | 41 0 | 43 6 | 44 6 | 45 5 | 46 0 | 47 0 | | Depth in hold | 17 4 | 17 8 | 18 2 | 18 7 | 19 4 | 20 0 | | Burthen in tons | 1100 | 1283 | 1350 | 1400 | 1472 | 1585 | | Length on the gun-deck | 150 0 | 150 0 | 151 0 | 151 0 | 154 0 | 160 0 | | Length of the keel, for tonnage | 122 0 | 123 2 | 122 0 | 125 5 | 131 4 | 131 4 | | Breadth, extreme | 39 8 | 41 0 | 41 6 | 43 5 | 44 0 | 45 0 | | Depth in hold | 17 0 | 17 4 | 17 4 | 17 9 | 18 11 | 19 4 | | Burthen in tons | 1013 | 1069 | 1128 | 1224 | 1291 | 1414 | | Length on the gun-deck | 144 0 | 144 0 | 144 0 | 144 0 | 147 0 | 150 0 | | Length of the keel, for tonnage | 119 0 | 117 7 | 116 4 | 119 9 | 123 0 | 123 0 | | Breadth, extreme | 37 6 | 38 0 | 39 0 | 41 5 | 42 0 | 42 8 | | Depth in hold | 15 8 | 15 8 | 16 5 | 16 11 | 18 1 | 18 6 | | Burthen in tons | 900 | 914 | 951 | 1058 | 1123 | 1191 | | Length on the gun-deck | 130 0 | 134 0 | 134 0 | 140 0 | 144 0 | 144 0 | | Length of the keel, for tonnage | 108 0 | 109 8 | 108 3 | 113 9 | 117 8 | 117 8 | | Breadth, extreme | 35 0 | 36 0 | 38 6 | 40 0 | 41 0 | 41 0 | | Depth in hold | 14 0 | 15 2 | 15 9 | 17 2 | 17 8 | 17 8 | | Burthen in tons | 704 | 755 | 833 | 968 | 1052 | 1052 | | Length on the gun-deck | 118 0 | 124 0 | 124 0 | 126 0 | 133 0 | 133 0 | | Length of the keel, for tonnage | 97 6 | 101 8 | 100 3 | 102 6 | 108 10 | 108 10 | | Breadth, extreme | 32 0 | 33 2 | 35 8 | 36 0 | 37 6 | 37 6 | | Depth in hold | 13 6 | 14 0 | 14 6 | 15 54 | 16 0 | 16 0 | | Burthen in tons | 531 | 594 | 678 | 706 | 706 | 714 | | Length on the gun-deck | 106 0 | 106 0 | 112 0 | 113 0 | 113 0 | 113 0 | | Length of the keel, for tonnage | 87 9 | 85 8 | 91 6 | 93 4 | 93 4 | 93 4 | | Breadth, extreme | 28 4 | 30 6 | 32 0 | 32 0 | 32 0 | 32 0 | | Depth in hold | 9 2 | 9 5 | 11 0 | 11 0 | 11 0 | 11 0 | | Burthen in tons | 374 | 429 | 498 | 508 | 508 | 508 | The ships built after the establishment of 1745 are reported to have been stiff, and to have carried their guns well, but were still inferior to those of the French; and, consequently, about ten years afterwards an alteration was made in the draughts for the several ratings, and the dimensions were also slightly increased. It may not be uninteresting to remark, that the proportional breadths in the establishment of 1745 considerably exceeded those of more modern ships. Their length varied from 3'49 to 3'85 of their breadth; while the lengths of most of our line-of-battle ships, built shortly afterwards, are within the limits of 3'61 and 3'83 of their breadths.

The Royal George was the first ship built on the increased dimensions, which were the result of the before-mentioned inquiry. She was laid down in 1746, and launched in 1756; and rather more than ten years afterwards, that is, in 1758, Thomas Slade and William Bateley being the surveyors of the navy, the Triumph and Valiant of 74 guns were built on the lines of the Invincible, a French 74 gun-ship, captured in 1747.

The dimensions of these ships are given below, as they were manifestations of an improved system, which, however, was not persevered in; for, with the exception of occasionally building after a French or Spanish model, the English ships were scarcely altered from those built at the commencement of the century.

| Royal George | Triumph and Valiant | |--------------|---------------------| | Length on the gun-deck | 178 feet 0 inches | | Breadth, extreme | 51 feet 9 inches | | Depth in hold | 21 feet 5 inches | | Burthen in tons | 2047 tons |

There was still a very essential distinction between the navy of England and of either France or Spain, which was this, that until after 1763 neither of these nations had grand three-deckers in their fleets. Their largest armament appears to have been eighty-four guns on two decks, while we had third-rates which were three-deckers, as the Cambridege and Princess Amelia, launched in 1754 and 1757, and carrying only eighty-four guns, our naval officers of that period having advocated a high battery, and the naval architects having designed some very fine ships of this new class. The capture of the Foudroyant, a French eighty-four on two decks, in 1758, caused a change in this respect, by furnishing the English with a model for a very superior class of men-of-war, which was adopted. Derrick, in his Memoirs of the Royal Navy, says, that "no eighty-gun ship with three decks was built after the year 1757, no seventy-gun ship after 1766, nor any sixty-gun ship after 1759."

During the peace that preceded the war with America, French which commenced in the year 1768, the French had introduced three-deckers into their fleets, having found their deckers eighty-four on two decks to be no match for the more powerful of our three-deckers. Their first-rates were at this time generally of 110 guns on three decks. The Bretagne, one of these ships, was, according to Charnock, 196 feet 3 inches long on the water-line; and her moulded breadth was 53 feet 4 inches. Her displacement, it is stated in Sewell's Collection of Papers on Naval Architecture, was 4640 English tons.

In 1786 the establishment of the French fleet was fixed by an ordinance of the government, as according to the following table, which is extracted from Charnock, and some French very fine vessels of each class were built upon these dimensions:

| Ships of 120 Guns | Ships of 110 Guns | Ships of 100 Guns | Ships of 74 Guns | Ships of 64 Guns | |------------------|------------------|------------------|------------------|------------------| | Length from head to stern | 196 feet 6 inches | 186—185 feet | 184—180 feet | 170 feet 0 inches | | Breadth from outside to outside of the frame | 50 feet 9 inches | 49 feet 6 inches | 48 feet 0 inches | 44 feet 6 inches | | Depth in hold | 25 feet 0 inches | 24 feet 6 inches | 23 feet 9 inches | 22 feet 0 inches | | Draught of water abaft when light | 17 feet 6 inches | 17 feet 4 inches | 17 feet 0 inches | 15 feet 8 inches | | Draught of water forward when light | 14 feet 0 inches | 13 feet 8 inches | 12 feet 0 inches | 10 feet 10 inches | | Draught of water abaft when laden | 25 feet 0 inches | 24 feet 8 inches | 22 feet 6 inches | 21 feet 6 inches | | Draught of water forward when laden | 22 feet 8 inches | 22 feet 2 inches | 21 feet 0 inches | 19 feet 10 inches | | Total weight of the ship and stores when victualled and furnished for a six months' cruise | Tons. 5246 | Tons. 4910 | Tons. 3825 | Tons. 3548½ | | Weight of the hull and masts | 2500 tons | 2400 tons | 1804 tons | 1437 tons |

George III. The ships of England continued throughout the wars of the reign of George III. inferior to those of France and Spain. The skill of our commanders, and the indomitable courage of our seamen, eventually succeeded in these, as in all former contests, in annihilating opposition, and in triumphantly asserting our naval supremacy. It cannot be denied that their task would have been comparatively easy, accompanied with less loss of life and expenditure of treasure, had their ships been more upon a par with those of their opponents. The French officers, however, after the war, to save their vanity, attributed our successes at sea to the superiority of our ships, and they commenced building after our models.

Although so much attention appears to have been directed at various times to the improvement of the navy, not only by the servants of the crown officially connected with it, but by the sovereigns themselves, we have seen that the inferiority of our ships in sailing to those of our opponents has been repeatedly asserted on undoubted testimony. The reason that all the attention thus bestowed failed in producing a corresponding beneficial effect appears to have been that in England the speculative ideas of men, undoubtedly of sense and judgment, as may be seen from the quotations of their opinions which have been given, but men uninformed as to principles, were taken as the rules for guidance. In France, on the contrary, the aid of science was called in, and some of the greatest mathematicians of the time turned their attention to the improvement of the shipping of that country, and worked harmoniously with the naval officers who were to use the ships, as well as with the practical men who were to construct them, modifying their theories by the practice and experience of the others. Colbert employed an engineer of the name of Rénaud d'Étissagary, a protégé of the Count de Vermandois, whose first essay was in the adaptation of ships to carry bombs, to be used in the then projected armament against the piratical states of the Mediterranean. Under the enlightened direction of Colbert, the French ships which, by the ordinance of 1688, were much restricted in dimensions, were increased nearly one-fourth in size, and every means taken which the then state of knowledge could suggest to insure a proportionate improvement in their qualities; while a corresponding increase in size was not made in English ships till the commencement of the energetic surveyorship of Sir William Symonds in 1830. Rénaud was, we believe, the first French author who wrote on the theory of ships. He was followed by the Bernoullis, by Pére La Hoste, by Bouguer, Euler, Don Jorge Juan, Romme, and a host of others, the effects of whose writings may be traced in the progress of the improvements introduced into the navies of France and Spain, and which the navy of England was forced to imitate. The only English treatise of that period on ship-building that can lay any claim to a scientific character was published by Mungo Murray in 1754; and he, though his conduct was irreproachable, lived and died a working shipwright in Deptford dock-yard.

A palpable instance of the ignorance or neglect of all the principles of naval architecture among the authorities who were charged with designing our royal navy, even up to the close of the last century, may be quoted from an article in the Papers on Naval Architecture, as given by Mr Wilson then of the Admiralty.

Mr Wilson, speaking of the cutting down of the Anson, a sixty-four-gun ship, to a frigate of thirty-eight guns, says, "she was cut down in the year 1794; and although in all other maritime states the science of naval construction was well understood, yet so culpably ignorant were the English constructors, that this operation, so well calculated, when properly conducted, to produce a good ship, was a complete failure. Seven feet of the upper part of the top sides, together with a deck and guns, making about 160 tons, were removed, by which her stability was greatly increased; but, by a complete absurdity, the sails were reduced one-sixth in area. In her first voyage the rolling was so excessive that she sprung several sets of top-masts. To mitigate this evil, in 1795, her masts and yards were increased to their original size; but as there were no decrease of ballast, she was still a very uneasy ship, and, as a necessary result, her wear and tear were excessive.

"Other sixty-fours were cut down, masted, and ballasted in exactly the same manner, and, it need scarcely be added, experienced similar misfortunes; and although they were improved by enlarging their masts and yards, they were still bad ships. Had their transformations been scientifically conducted, a class of frigates would have been continued in the navy, capable, from their size, of coping with the large American frigates; and thus the disasters we experienced in the late war, from the superior force of that nation, would, without doubt, have been not merely avoided, but turned into occurrences of a quite opposite character."

The subject, however, of the improvement of ship-building was by no means lost sight of in this country at that period. The investigations and experiments which were made were, as usual in England in comparison with France and other continental nations, more of a practical than of a theoretical nature. Attwood's papers, read before the Royal Society in 1796 and 1798, form almost a solitary exception to this remark. In 1785, and subsequent years, Mr Miller of Dalswinton, in Dumfriesshire, made many experiments, expending as much as £1,30,000 of his own private fortune for the advancement of naval architecture. In 1788 he was induced, by a Mr Taylor, to allow Symington, a working-engineer, to place a steam-engine on board a pleasure-boat on his lake at Dalswinton, for the purpose of propelling it by a paddle-wheel, and he thus became the originator of steam-navigation.

In 1791, "a Society for the Improvement of Naval Beaufoy's Architecture" was instituted, mainly by the exertions of experiment Colonel Beaufoy. This society numbered amongst its members the then Duke of Clarence, afterwards William IV., and many noblemen and gentlemen of great influence. They conducted a most valuable series of experiments between 1793 and 1798, but a first report only of the results was ever published by the society. The funds at their disposal became exhausted, and the experiments were thus terminated, the interest of the public having flagged on account of the necessarily tedious nature of the proceedings. A detailed account of the whole of the experiments was subsequently published, in a most patriotic spirit, by Mr Henry Beaufoy, at his own private expense, and presented gratuitously to scientific societies and parties connected with naval architecture. Some valuable practical results were deduced from them, and these will be discussed hereafter, when treating of the resistances and other qualities of differently formed vessels.

At the commencement of the present century the merchant-shipping of this country had increased to such an extent as to be of great importance. From the returns prepared by the Registrar-General of the Board of Trade, the total number of British merchant-vessels in the year 1801 was 19,711, with an aggregate registered tonnage of 2,038,253 tons, employing 149,766 men. In 1811 the total number of merchant-vessels was 24,106, with an aggregate registered tonnage of 2,474,784 tons, employing 162,547 men.

In the Honourable East India Company's service there were at this period 67 ships, each carrying 30 to 38 guns, 31 ships of 20 to 28 guns, and 52 ships of 10 to 19 guns, thus forming a powerful addition to the warlike resources of the country. Additional attention was also attracted to the subject of ship-building in the early part of this century by the institution of the Royal Yacht Club. It was joined by many influential and wealthy noblemen and gentlemen, and they gave much encouragement to the production of superior fast-sailing yachts.

Another important effort to improve the scientific knowledge of naval architecture, was the establishment, in 1811, of a school for naval architecture in Her Majesty's Dockyard at Portsmouth. This school was the result of the statements and recommendations contained in the report of a commission of naval revision, appointed in 1806, to examine into the management of the dockyards. The commissioners found that the practice of permitting the master shipwrights and their assistants to take private apprentices, receiving high fees with them, had been at that time disallowed and discontinued. By this system young men of superior early education, and of superior standing to the ordinary shipwright apprentices, had been trained in the higher branches of the profession, and their further scientific and theoretical education had been attended to, while at the same time they had acquired a knowledge of practical shipbuilding by being employed amongst the workmen. The commissioners therefore considered it expedient that some means should be adopted to supply the future demand for such men to fill those higher civil situations in which scientific knowledge is indispensable for the due performance of the duties. The school was accordingly instituted, but upon so large a scale, and with so little consideration of the real requirements of the service, that in a very few years 42 students were educated there, while the whole number of places in the Admiralty service, requiring such education and training, did not exceed 25 or 26. The necessary result of this was, that they were put into inferior positions for which their previous standing and training had not adapted them, and the school was considered to have been a failure. Much increase, however, of sound scientific knowledge resulted from the labours of the principal of the school, the late Dr Inman, though it may be remarked that he confined his labours to too limited a sphere, and did not follow out the investigations of the French mathematicians. Many valuable papers on naval architecture have also been published by different members of the school, and the article Ship-building, in the previous edition of this work, and from which much of the present article is taken, was written by the late Mr Creuze, one of its most talented and distinguished members.

The following table, taken from the navy list of 1813, will show the force of the royal navy at that period, distinguishing the number of ships in each class:

**Extent and Disposition of the British Naval Force in 1813.**

| Stations | Lines | 50-44 | Frigates | Sloops & Yachts | Bombs, Fire Ships | Brigs | Cutters | Schooners, Gunvess., Lug, &c. | Total | |---------------------------|-------|-------|----------|-----------------|-------------------|------|---------|-------------------------------|-------| | Downs | 4 | 0 | 1 | 4 | 0 | 20 | 5 | | 40 | | North Sea and Baltic | 12 | 2 | 8 | 5 | 3 | 50 | 11 | | 100 | | English Channel and coast of France | 15 | 0 | 16 | 15 | 0 | 23 | 7 | | 89 | | Irish station | 0 | 0 | 5 | 3 | 0 | 5 | 1 | | 21 | | Jersey, Guernsey, &c. | 0 | 0 | 1 | 0 | 0 | 2 | 2 | | 7 | | Spain, Portugal, and Gibraltar | 15 | 0 | 11 | 6 | 2 | 14 | 4 | | 53 | | Mediterranean &c. | 27 | 5 | 33 | 19 | 2 | 26 | 1 | | 106 | | Coast of Africa | 0 | 0 | 0 | 1 | 0 | 0 | 0 | | 1 | | Halifax, Newfoundland, &c.| 9 | 2 | 23 | 13 | 0 | 23 | 1 | | 77 | | West Indies (Leeward Islands) | 2 | 1 | 10 | 8 | 0 | 6 | 2 | | 33 | | Jamaica and on passage | 5 | 1 | 11 | 7 | 0 | 8 | 0 | | 32 | | South America | 4 | 1 | 8 | 7 | 0 | 4 | 0 | | 24 | | Cape of Good Hope and southward | 1 | 0 | 3 | 3 | 0 | 2 | 0 | | 9 | | East Indies and on passage| 4 | 0 | 16 | 3 | 0 | 4 | 0 | | 27 | | Total at sea | 98 | 12 | 145 | 85 | 7 | 187 | 34 | | 619 | | In port and fitting | 24 | 9 | 24 | 21 | 0 | 25 | 9 | | 121 | | Guard-ships | 5 | 1 | 4 | 5 | 0 | 0 | 0 | | 15 | | Hospital ships, prison ships, &c. | 32 | 1 | 3 | 2 | 0 | 0 | 0 | | 38 | | Total in commission | 159 | 23 | 177 | 111 | 7 | 212 | 43 | | 793 | | Ordinary, and repairing for service | 72 | 11 | 50 | 37 | 4 | 12 | 1 | | 220 | | Building | 28 | 4 | 25 | 9 | 0 | 7 | 0 | | 73 | | Totals | 259 | 38 | 282 | 157 | 11 | 231 | 44 | | 1086 |

In 1832 the Navy Board was abolished, and it was determined to place the construction of ships under one head, continuing the name of surveyor of the navy, but altering the nature of the office by the appointment of a naval officer instead of a naval architect and ship-builder. Captain (afterwards Rear-Admiral Sir) William Symonds was the officer selected. He had early distinguished himself amongst his brother-officers by the attention he had paid to the sailing properties of boats and vessels. It was said of him that he could take any one of the boats in turn, of the vessel to which he was attached, and make her beat any of the others. His habit of observing the peculiarities of the different ships, whose properties he had an opportunity of witnessing, led him to draw certain conclusions respecting the forms of vessels; and, while holding a civil appointment in Malta, he built a yacht called the Nancy Dawson, in accordance with these preconceived views. The great speed of this yacht gained him notoriety, and procured for him the patronage and support of several influential and patriotic noblemen. Through their influence he obtained the sanction of the Board of Admiralty to build a corvette, the Columbine, and as this vessel was very favourably reported of, his character as a designer was proportionally raised. These successes led to his appointment as surveyor of the navy. It is not proposed here to discuss the propriety or otherwise of this office being filled by a naval officer, though in Sir William Symonds' case it led to important changes in the construction of the ships of the royal navy, and to much acrimony of feeling on the part of the shipwright officers of the service. One point is quite certain, that no man can be qualified to control the different forms of the various classes of ships, more especially of new classes that may be required in the navy, without long and careful study of the subject of naval architecture, both practically and theoretically. It is equally certain that a naval officer of experience is the most competent judge of the general proportions and qualities of the ships that will be most useful in the service, and that he is best able to point out the faults at sea of any ships that have been tested, so as to lead to the correction of these faults, and the improvement of future ships.

Sir William Symonds was the first constructor of the English navy who was left unrestricted as to dimensions, and he was consequently enabled to introduce into the service ships which undoubtedly bear very high characters as men-of-war. He also practically demonstrated the possibility of ships of war obtaining sufficient stability without the aid of ballast—a very important advantage, and one which has been productive of much benefit. He was in error, however, as to the true principles on which the stability of floating bodies is dependent, in order to secure as great freedom from rolling and as great ease of motion as possible. His ships had great statical stability, and therefore great power of carrying sail, and hence were generally very successful in trials of speed in sailing. But this advantage was not obtained without, in many instances, incurring a compensating disadvantage from uneasiness of motion. This appears to have been a very general fault in ships of his construction, some of them being marked examples of the uneasiness attendant on a stability which depends almost wholly on breadth at the load-water section and above it, to the neglect of the form of the solids of The introduction of vessels propelled by steam for practical purposes dates its origin in the year 1812, when Henry Bell started the Comet steam-vessel on the Clyde, for the conveyance of passengers. In 1815 there were 10 steamers in existence, with an aggregate registered tonnage of 1633 tons. In 1825 this number had increased to 168, with an aggregate tonnage of 20,287 tons, and in 1835 the number was 538, with an aggregate tonnage of 80,520.

Some interesting and valuable experiments were made about 1832, by Mr Scott Russell, on the Forth and Clyde Canal, with a view to introduce steam on canals, and though not successful in their object, a peculiar class of very long and finely-formed boats for quick passenger traffic on canals resulted from them. These boats were drawn by two horses, and were expected to travel at the rate of 9 or 10 miles per hour, but it was found that if these were not at once put to this speed, but started sluggishly or gradually, a wave was formed in front of the boat and continued to precede it, washing over the banks of the canal and over the towing-path. Under these circumstances the horses were much distressed with the labour which they had to perform. If, on the other hand, they were urged into a speed of 9 or 10 miles an hour at once upon starting, no wave was formed, and the boat seemed to rise on the surface of the water and to be propelled with comparative ease so long as that speed was maintained; but if they flagged, and their rate of travelling fell to 6 or 7 miles an hour, the wave was formed, and it then became necessary to go slower, or walk them till it disappeared, and then to start them again at once into the higher speed. This peculiar result was no doubt mainly caused by the confined space of the canal, but no scientific investigation to account for it has yet been given. The lines of these boats were called wave-lines by Mr Scott Russell, and for ease of propulsion in smooth water they are undoubtedly beneficial. Lines of a similar character were also used about the same time by Mr Fearnall in fast-passenger steamers on the Thames. Their advantage was made very apparent by the construction of the Vesper in 1837, a passenger-boat from London Bridge to Gravesend. This boat went through the water at a speed of about 12 miles an hour, with scarcely any wave or even a ripple at her bows, while her competitors were carrying a heavy wave and swell before them. Other vessels with lines of a similar character were built subsequently by Messrs Fletcher and Fearnall, by Mr Ditchburn, who had been in their employment, and also by others.

Up to 1836 the mercantile marine had laboured under the disadvantage of a tonnage law for the charging of dues, which, by the mode of measurement enacted, held out a premium for the construction of inferior ships. In this year a new act was passed, and a better system introduced. By this act the internal capacity of a ship became the measure of her tonnage, and the serious objections to the former law were obviated.

It was about this period that iron began to be used to any great extent as a material for ship-building. Its merits for this purpose will be discussed hereafter, when treating of the practical construction of ships. Mr Manby, Mr Laird of Liverpool, and Mr Fairbairn of Manchester, were the first constructors of vessels of any size of this material. Mr Fairbairn, in 1833 and 1834, built two passenger-steamers of iron to ply on the Humber, between Selby and Hull, and in 1836 he commenced business in company with others as an iron-ship-builder at Millwall, on the Thames. In 1837 Mr Laird built an iron steam-vessel, the Rainbow, for the General Steam Navigation Company at Deptford, and from that time the use of iron has rapidly increased.

The next important step in the history of ship-building was the introduction of the screw-propeller. Many proposals had been made, and patents taken out, for propellers of this nature; but a small vessel fitted with a propeller, patented by Ericsson, was the first brought into practical use. A small experimental vessel called the F. B. Ogdon, was built in 1837, and fitted by Ericsson with one of his propellers, and the Lords Commissioners of the Admiralty, attended by their secretary, Sir William Symonds, took a trip in her in that year. They, however, failed to see the advantage of such an invention to men-of-war, and refused to entertain any proposal for its introduction into the navy. Mr P. P. Smith also built a small experimental vessel during this year, and fitted her with a screw propeller. Ericsson, on receiving no encouragement from the British government, took steps to bring his invention before the Americans, and a small vessel, the Robert F. Stockton, was built by him in 1838, in this country, with this view, and made the voyage safely to America. Mr Smith, in the meantime, induced a number of influential men to form a company to carry out his invention, and in 1839 the Archimedes was built by them, to test and demonstrate its value. The success of this vessel was such, and the advantages likely to accrue to men-of-war from the introduction of the screw were so apparent, that the Rattler was then ordered to be built in one of the government yards. This vessel was on the same lines as one of the Admiralty paddle-wheel steamers, but its stern was lengthened to fit it to receive the screw propeller. Her success was undeniable, but the progress of the screw in the navy was very slow for many years, owing to the opposition of Sir William Symonds and to the frequent changes of the Board of Admiralty. Some progress, however, was made in the introduction of screw-ships into the navy, several small vessels being built to the designs of Mr Fincham, the master shipwright of Portsmouth yard. This officer was in favour of its introduction, as were all the officers of the engineering department under the Board of Admiralty, and they were supported by the Hon. Mr Corry, the secretary of the Admiralty at that time. The Arrogant and Dauntless, two screw-frigates, were afterwards built by Mr Fincham; and, at the same time, the Ternagant, also a screw-frigate, was built by Mr White of Cowes. After this, the growing dissatisfaction with the excessive rolling of Sir William Symonds' ships, his obstinate adherence to his own forms of construction, together with his unwillingness to co-operate in the introduction of screw-steam ships into the navy, led the Board of Admiralty, of that date, to order that a committee of reference should be constituted, to whom all designs for ships should be submitted before they were laid down. This led to Sir William Symonds resigning his office, and Sir Baldwin Walker, the present surveyor, was appointed as his successor. It was understood that Sir Baldwin Walker had not given his attention to the study of naval architecture in all its branches, and the Board of Admiralty announced that they should not expect him to originate the lines of the vessels to be built, but that these should be designed by naval architects attached to his office. The construction of the ships of the royal navy was thus placed on a proper footing, and if this arrangement be carried out, and the naval architects have full power given to them, and be at the same time competent men, the country ought to reap the benefit of so judicious an arrangement.

With respect to the class of ships ordered to be built at this period in the dockyards no change in accordance with the advancing state of screw propulsion took place. The naval members of the Board of Admiralty were men who had long looked upon the noble line of battle-ships of the navy as not to be surpassed, and they could not apparently make up their minds to desecrate them, as they seemed to consider it, by the introduction of steam-power. The result of this somewhat romantic feeling was, that early in Sir Baldwin Walker's administration a number of sailing three-deckers were laid down in opposition to the expressed opinion of the leading civil professional officers attached to the admiralty. Not one of these vessels has been launched, or will be launched, as a sailing vessel. They have all been converted, or are under conversion, to screw-ships, by being lengthened in midships, at the bows, and also at the sterns. The greater proportion of the other sailing three-deckers are also being razed and converted into two-decked screw-ships, their sterns only being altered. These important changes on the last-mentioned vessels are being carried out, while two of the members of the late school of naval architecture are the assistant-surveyors; and a repetition of the errors committed at the end of the last century, on the occasion of a similar operation upon several ships, will no doubt be avoided. The errors committed at that time have been described by Mr Wilson, as previously quoted, and are ascribed by him to a want of sufficient scientific knowledge; but as this is not the case at the present time, the country may now expect a very fine class of vessels to be the result.

It may also be remarked, that the introduction of the system of distilling the necessary supply of fresh-water on board the ships, and thus obviating the necessity of carrying so great a weight of fresh-water, has materially facilitated the arrangements for these alterations.

The history of ship-building in the royal navy up to the present time (1859), cannot be closed without reference to the class of small gun-boats and of iron-cased floating batteries recently introduced into the service. The gun- boats are of three classes, varying slightly in size and horse-power. The greater proportion of them are 106 ft. long between the perpendiculars, 22 ft. beam and 8 ft. deep, and are fitted with high-pressure engines of sixty horse-power. They are of 233 tons burden, and their draught of water, when ready for sea, is about 6 ft. The importance of this class of vessels as a protection against invasion cannot be overrated. The introduction of steam as a mechanical agent for the propulsion of vessels, independent of wind and tide, brings back almost the same state of things as existed when hostile fleets were composed of rowing galleys. The supremacy on the ocean which this country has so long held by means of the experience of such a large proportion of her population as seamen, must now depend on other sources of strength, and it behoves the nation to make preparations suitable to meet the altered circumstances. If our fleet were to suffer any reverse, and thus leave the sea free to an enemy; or if an enemy came to a determination to try and evade our fleet, and land an army on our shores, that army might be embarked at many different points; and with steam as an agent, the different portions of it might, with almost perfect certainty, meet at any appointed time at any spot. When once upon our coasts, they could move along them with a rapidity far beyond that at which any troops on shore could follow them.

The importance, then, of keeping up a large and effective force of steam gun-boats, to lie, in the time of an expected invasion, in every bay and creek of our indented shores, is evident. For the construction of a fleet of such vessels, iron is fortunately the most valuable material, as the evils attending its use in large men-of-war will not militate against its use in these vessels. If they should be struck by shot, the men will be above the splinters, and by building these vessels with their frames very far apart, and with a strong inner and outer sheathing, both water-tight on every frame, they may be made almost unsinkable. The chief advantage, however, of iron for such vessels is its durability, if moderate care be taken to construct them in such a manner, that all the parts may be kept painted, and then that they be periodically cleaned and painted. Iron vessels so constructed and hauled up on shore, and so treated, might be considered as almost free from decay.

The floating batteries, coated with iron-plates 4 inches thick, appear at first sight to be most formidable vessels. Some of these have been built without any reference to speed, but with merely as much steam power as will give them the power of locomotion. Two others are now being built with great steam-power, and with finely-formed bodies, and these are therefore intended to have great speed. They are not protected at the bow and at the stern, but only in midships, and this part is separated from the ends by strong iron bulkheads, so that the centre portion is, as it were, a citadel into which the men may retire when attacked. Their cost is estimated at about L250,000 each; and this very large expenditure will necessarily prevent their number being greatly increased. It may be expected, therefore, that the nation which has the command of the sea, will send small vessels of superior speed, and armed with guns capable of penetrating the plates of these batteries, to watch them and prevent their being brought against the ordinary vessels composing the fleet. Whatever speed these batteries may attain, it cannot be doubted but that light vessels, unencumbered with such weight, may be built to surpass them as soon as their speed is known.

Table of the British Navy, extracted from the Navy List, October 1859.

| Class | Propelling power | Guns | In commission | In ordinary for service | Harbour vessels, building | Totals | |------------------------------|------------------|------|---------------|------------------------|--------------------------|-------| | Three-decked ships | Screw | 110 to 131 | 2 | 4 | 2 | 8 | | Do. do. | Sails | 117 to 134 | 2 | 4 | 2 | 8 | | Two-decked ships | Screw | 100 to 134 | 12 | 16 | 56 | | | Do. do. | Sails | 72 to 124 | 23 | 35 | | | | Frigates | Screw | 38 to 50 | 19 | 18 | 42 | | | Do. | Sails | 40 to 60 | 70 | 82 | | | | Corvettes and sloops | Screw | 4 to 21 | 29 | 11 | 50 | | | Do. do. | Sails | 14 to 20 | 45 | 45 | 66 | | | Frigates and sloops | Paddle | 3 to 22 | 46 | 18 | 64 | | | Transports | Screw | 3 | 7 | 3 | 10 | | | Despatch vessels | Screw | 2 to 4 | 16 | 4 | 22 | | | Gun and other vessels | Screw | 2 to 4 | 8 | 3 | 12 | | | Yachts, tugs, &c. | Paddle | 37 | 16 | 53 | | | | Do. and other vessels | Sails | 12 | 12 | 29 | | | | Floating batteries | Screw | 16 | 8 | 8 | | | | Grand total | | | | | | 547 | | Gun-boats | Screw | 2 | | | | 160 | | Frigates, iron-built, not yet in Navy-list-building | | | | | | |

By a return published during this year, it appears that the total number of ships of all classes belonging to the navies of other kingdoms is as follows:

| France | 448 | | Austria | 135 | | Russia | 164 | | Portugal | 37 | | Sweden—principally small vessels | 311 | | Sardinia | 28 | | Prussia | 55 | | Norway | 143 | | Greece | 26 | | Denmark | 120 | | Turkey | 49 | | United States | 79 | | Brazil | 27 | | Holland | 139 | | Peru | 15 | | Belgium | 7 | | Chili | 5 | | Spain | 82 | | Mexico | 9 | | The Two Sicilies | 121 |

In the merchant-service the screw for some time made but little progress. A company trading to Rotterdam, Messrs Lanning and Company, were amongst the first to adopt it; and the mercantile marine owes much to their enterprising spirit in this respect. Their vessels were very successful, and attracted much attention from the time of their first introduction; and doubtless much of their immediate success may be attributed to men of high stand-

Extract from Return of British Merchant-Shipping by the Registrar-General of the Board of Trade.

| Year | Number and Tonnage of New Vessels Built and Registered in the British Empire in each Year | Total Number of Registered Merchant-Vessels belonging to the British Empire in each Year | |------|---------------------------------------------------------------------------------|-------------------------------------------------------------------------------------| | | Sailing Vessels | Steamers | Sailing Vessels | Steamers | Total | | | Number | Tons | Number | Tons | Number | Tons | Number | Tons | Number | Tons | | 1840 | 1004 | 285,289 | 77 | 10,639 | 28,138 | 3,215,731 | 824 | 95,507 | 3,311,538 | 201,349 | | 1845 | 1183 | 154,783 | 73 | 11,950 | 50,805 | 3,582,859 | 1012 | 131,202 | 3,714,061 | 224,900 | | 1850 | 1381 | 229,603 | 81 | 15,527 | 32,938 | 4,045,331 | 1350 | 187,631 | 4,232,962 | 239,883 | | 1855 | 1319 | 305,113 | 269 | 84,862 | 33,782 | 4,842,223 | 1910 | 408,290 | 5,250,533 | 261,194 | History. Ing in their respective professions of ship-builders and engineers being employed in their construction, and being left unfettered to work out the end that was desired. From that time screw-vessels, constructed of iron, began rapidly to supersede paddle-wheel steamers and sailing vessels, especially for the conveyance of perishable merchandise, such as fruit and provisions; and the great capability of combining sailing and steaming which the screw affords, will no doubt tend to the continued increase of auxiliary steamers. The preceding table of the merchant-shipping of the country shows the extent to which the substitution of steamers for sailing vessels is taking place.

Reference has been previously made to the beneficial influence of the yacht clubs throughout the country. The English yachts were supposed to be unrivalled in speed; and in 1851 a challenge cup was given, open to the whole world for competition. A yacht from America, however, came over to this country, and carried off the prize. She soon showed such great superiority that the favourite English yachts at once gave up the contest, and it appeared likely that she would be allowed to walk over the course. To prevent this the late Mr Robert Stephenson entered his yacht, the Titania, built by Mr Scott Russell, to compete with her, and thus give her an opportunity of showing the extent of her superiority, and on what points that superiority was greatest. Representations of these two yachts are given in Plates V. and VI., and their relative performances and qualities will be examined hereafter. Though the introduction of steam has done much to lessen the interest taken in yachting, yet it is to be hoped that the valuable encouragement given to naval architects, and to the maritime predilections of the country by yachting clubs will be continued, and that many will follow the example already set by a few spirited men, of placing a small amount of auxiliary steam-power in their yachts with screw-propellers. This is done without impairing their beauty, and renders them certain in their movements when desired.

In connection with this subject, and as a means of forming a taste for it, the rowing and racing boats of the youths at public schools, and of the young men at the universities and elsewhere, may be mentioned. The following may be taken as the average performances of such boats at the present day. The drawings and the dimensions are from boats built by Messrs Searle and Sons of Lambeth, London:

| Description of Boat | Length | Breadth | Depth | Weight | Maximum speed per hour in still water | |---------------------|--------|---------|-------|--------|--------------------------------------| | **OUTRIGGER RACING BOATS** | | | | | | | Outrigger sculling boat | 32 | Ft. In. Ft. In. | 8½ in. | 30 to 40 | 6 | | " pair-cared" | 34 | 1 3 to 1 6 | 9 to 11 in. | 45 to 55 | 6½ to 7 | | " four-cared" | 42 to 45 | 1 10 to 2 3 | 1 foot. | 100 to 112 | 8½ to 9 | | " six-cared" | 50 to 54 | 2 2 to 2 4 | 1 " | 150 to 190 | 9 to 9½ | | " eight-cared" | 57 to 65 | 2 2 to 2 4 | 1 " | 280 to 330 | 9½ to 10 | | **RACING BOATS OF THE OLD STYLE** | | | | | | | Sculling boat | 30 | 3 4 to 3 6 | 1 0 to 1 2 | 55 to 60 | 6½ | | Randan wherry | 32 | 3 4 to 3 6 | 1 0 to 1 3 | 100 to 140 | 6 | | Four-cared cutter | 40 to 42 | 3 6 to 3 8 | 1 1 to 1 3 | 224 to 280 | 7½ to 8 | | Six-cared cutter | 45 to 50 | 3 6 to 3 8 | 1 1 to 1 3 | 336 to 376 | 8 | | Eight-cared cutter | 54 to 58 | 3 6 to 3 8 | 1 1 to 1 3 | 520 to 600 | 8½ to 9 | | **THE LARGER KIND OF PLEASURE BOATS** | | | | | | | Pair-cared gig | 23 to 25 | 3 6 to 3 8 | 1 foot 4 in. | 180 to 200 | 4 to 4½ | | Randan gig | 27 to 30 | 3 6 to 3 8 | 1 " | 200 to 224 | 5 | | Four-cared gig | 40 to 42 | 3 4 to 3 6 | 1 " | 250 to 300 | 6½ to 7 | | Six-cared gig | 55 to 48 | 3 4 to 3 6 | 1 " | 350 to 400 | 7 | | Eight-cared gig | 64 to 58 | 3 2 to 3 4 | 1 " | 500 to 620 | 7½ |

To pass from these diminutive but beautiful specimens of naval architecture, the last great work which requires to be noticed in this brief outline of the history of the rise and progress of ship-building is the construction of the Great Eastern, Plate VIII. The dimensions of this vessel, as given on the plate, are so far beyond those of ordinary vessels, that it is necessary to draw particular attention to them. At the period of writing this article she has not been to sea except for one or two trial trips. Her performances will be discussed hereafter, but the results predicted by science as to her speed, with a given amount of steam-power, appear to have been realized. How far mercantile enterprise will be benefited by the construction of vessels of her magnitude remains to be proved. DESCRIPTION OF THE MANNER OF PERFORMING THE CALCULATIONS INCIDENTAL TO DESIGNING A SHIP, WITH INVESTIGATIONS OF SOME OF THE PRINCIPAL ELEMENTS OF THE DESIGN.

The labours of the numerous men of science who have devoted either the whole or a portion of their attention to the various problems embraced in the theory of ships, have left but few of its abstract principles uninvestigated; most of the proportions of a ship have been examined, and the laws on which they depend clearly defined, either by the aid of mathematical demonstration, or by experimental induction. There are, however, some questions which, though sound in theory, still depend on the results of physical experiments for perfecting their practical application.

Many of the elements of naval construction are dependent on the known laws of nature; and it may now be said that the principal difficulties of these are surmounted, and are familiar to the instructed naval architect. These are of themselves sufficient to insure the attainment of a certain and considerable degree of excellency in a ship, to give it a preponderance of any given quality, to discover the causes of any bad quality, and to point out the means of providing a remedy for the faults discovered.

The forces which act upon a ship in motion, in a fluid, even though the fluid be at rest, are as yet but imperfectly defined by mathematicians; and the elements of naval construction dependent on the laws regulating them are, therefore, less known and less certain in their application. The form of a ship's body need not, however, remain imperfect, because the curve of the solid of least resistance is uncertain, since enough has resulted from the consideration of the nature of that solid to prove its inapplicability to vessels in general; and theoretic perfection of the science in this particular would, therefore, be of no practical utility.

A very unphilosophic mode of reasoning is frequently applied to the question of the application of the exact sciences to naval architecture. It has been argued, that because men without any great amount of scientific knowledge have produced good ships, therefore the exact sciences are not necessary for the advancement of naval architecture. In such instances the success has resulted in some cases from chance, in others from induction after a succession of failures, but more frequently from the results of observations on other good ships; and in all these cases, wherever the changes from a foregoing example have been of any moment, the result has been a matter of doubt until tested by trial after completion. It is true that the scientific naval architect cannot effect, by any mathematical process, the synthetical composition of a perfect ship, but he may, by the application of the principles fully established and known to him, produce one with a full confidence of its possessing a preponderance of those qualities which he has considered it desirable that it should possess. The mistake is in the assumption that men of science consider that the theory of naval architecture is already perfected, and is a definite science, whereas this is far from being the case; and it can only be advanced gradually to a greater degree of perfection by an analysis of the actual performances of ships at sea, collected and registered, and the abstract sciences then brought to bear upon them. In every science a perfect theory is the result of the perfection of the science. The time is gone by, when a theory was first formed, and facts were then warped or twisted to suit the pre-conceived theory.

It is now proposed to proceed to show, in as concise a manner as possible, the method of performing the calculations necessary to determine the essential elements of the design of a ship's body, and which are required in the course of preparing the original draught or drawing. The rules to find the areas of plane figures, bounded by straight lines and curves, will first be given; and afterwards those for finding the volumes of solids, bounded by planes and curvilinear spaces.

To find the area of a plane area, bounded by straight lines and a curve.

Art. I. If the area is symmetrical in regard to the line $A_1 A_n$, Simpson's that is, if a line $A_1 A_n$ can be found to divide the area into two rules for equal parts, as $A_1 a_1$ and $A_1 b_n$;

Divide this line (or axis) into a convenient number of equal parts, taking care to have an even number of such parts, then draw plane surfaces through the points $A_1, A_2, A_3, \ldots, A_n$, and meeting the curve in the points $a_1, a_2, a_3, \ldots, a_n$, these lines being called ordinates;

The second, $A_2 a_2$, fourth, $A_4 a_4$, &c., are called the even ordinates. The third, $A_3 a_3$, fifth, $A_5 a_5$, &c., are called the odd ordinates (the first and last being omitted).

Then, if these ordinates be measured on the same scale as the equal distances $A_1 A_2, A_2 A_3, \ldots$, the following rules will give the area of the figure:

Rule I.—To the sum of the first and last ordinates add four times the sum of all the even ordinates, and twice the sum of all the odd ordinates (omitting the first and last); multiply this final sum by the common distance between the ordinates, divide by 3, and the result will be the area (nearly).

Note 1.—The following is the usual demonstration given to this rule, which is due to Thomas Simpson, who was Professor of Mathematics at Woolwich, about the middle of the last century—

Referring to fig. 3,

Put $A_1 a_1 = a_1, A_2 a_2 = a_2, A_3 a_3 = a_3, \ldots, A_n a_n = a_n$,

$A_1 A_2 = A_2 A_3 = A_3 A_4, \ldots, A_{n-1} A_n = h$

We suppose a parabolic curve, the equation to which is

$$y = A + Bx + Cx^2$$

(1)

to pass through the three points $a_1, a_2, a_3$; for since (1) contains three arbitrary constants $A, B, C$, we can, as is well known, make the curve (1) pass through three given points. Now, since (1) passes through $a_1$, we know (if $A_1$ be taken as origin) that $y = a_1$ when $x = 0$; when $x = h$, $y = a_2 = A_2 a_2$, and $y = a_3 = A_3 a_3$ when $x = 2h$; hence we have the following equations:

$$a_1 = A \quad (2) \quad a_2 = a_1 + Bh + Ch^2 \quad (3) \quad a_3 = a_1 + 2Bh + 4Ch^2 \quad (4)$$

between (3) and (4) we readily determine $B$ and $C$, viz.:

$$B = \frac{4a_2 - a_1 - 3a_3}{2h} \quad (5)$$

$$C = \frac{a_3 - 2a_2 + a_1}{2h^2} \quad (6)$$

Introducing these values into (1), we obtain

$$y = a_1 + \frac{4a_2 - a_1 - 3a_3}{2h} x + \frac{a_3 - 2a_2 + a_1}{2h^2} x^2$$

But by the Integral Calculus we know that the area of a curve is represented by

$$\int y \, dx$$

taken between proper limits. In the present case these limits are $0$ and $2h$.

$$\therefore \text{area of } A_1 a_2, \text{ or } \int_0^{2h} y \, dx = 2a_1 h + \left(\frac{4a_2 - a_1 - 3a_3}{4h}\right) h^2$$

Calculations incidental to designing a Ship.

Again, by making a parabola of the same form as (1) pass through the three points \(a_2, a_3, a_4\), we obtain a result precisely similar to the above, that is,

\[ \text{area } A_2 = \frac{h}{3} (a_1 + a_2 + 4a_3), \quad \text{and} \]

\[ \text{area } A_3 = \frac{h}{3} (a_2 + a_3 + 4a_4), \]

\[ \text{area } A_4 = \frac{h}{3} (a_3 + a_4 + 4a_5). \]

Adding these areas we find

\[ (1) \quad \text{Area } A_1 a_4 = \frac{h}{3} \left( a_1 + a_2 + 4a_3 + a_4 + 4a_5 + 4a_6 + a_7 - 2 \right) \]

It ought to be observed that in the application of this, and the following rules, an odd number of ordinates are always to be taken, and the nearer the ordinates are taken, that is, the less the common interval, the more nearly will the final result approach the true area of the figure.

For those who are not familiar with the Integral Calculus, another demonstration may be obtained, as follows:

Through the point \(a_2\) draw a tangent to the parabola which passes through \(a_1, a_2, a_3\) and produce \(A_1 a_2, A_2 a_3\) to meet this tangent in the points \(c\) and \(d\); join \(a_1, a_2, a_3, a_4, a_5, a_6, a_7\), and \(d\) draw \(e\) and \(f\) parallel to \(A_1 A_4\); then it is shown in all works on Conic Sections that \(a_2\) is parallel to \(e f\). Hence by Eucl. I. 35—

Parallelogram \(a_1 d = \text{parallel } e f\), because they are on the same base and between the same parallels \(A_1, A_4\).

Now, \(A_2 b = \frac{A_1 a_1 + A_2 a_2}{2}\) and \(A_2 a_3 = a_2\)

\[ \therefore \text{area of parabola } ba_2a_3 = \frac{2}{3} \text{parallelogram } a_1 d = \frac{2}{3} \text{parallelogram } e f \]

Also area of trapezoid \(A_1 a_1 a_2 A_2 = \frac{(A_1 a_1 + A_2 a_2)}{2} A_1 A_2 = h(a_1 + a_2)\).

Adding these two areas, we obtain that of the whole figure

\[ A_1 a_1 a_2 a_3 = \frac{h}{3} \left( 3a_1 + 3a_2 + 4a_3 - 2a_4 - 2a_5 \right) \]

\[ = \frac{h}{3} \left( a_1 + 4a_2 + a_3 \right) \]

By repeating this process for the area of the figures \(A_2 a_2 a_3 a_4, A_3 a_3 a_4 a_5, \ldots\), and adding the results, we obtain for the whole area \(A_1 a_4\) the same result as before.

If \(a_2\) were less than \(a_1\), the parabola would be convex towards \(A_1 A_4\); but the same rule would still apply, for \(A_1 b\) would then be equal to \(\frac{a_1 + a_2}{2} - a_1\), and this introduced into the form for finding the area of the parabola, leads to the same result as that already obtained.

Another demonstration, on different principles, will be given in Note (3).

Rule II.—To the sum of the first and last ordinates, add three times the sum of the second, third, fifth, sixth, eighth, ninth, etc., ordinates, and twice the sum of the fourth, seventh, tenth, thirteenth, etc., ordinates (omitting the last ordinate); multiply this final sum by three times the common distance between the ordinates, divide the product by 8, and the result will give the area (nearly).

Note 2.—To obtain what naval architects call the "Second Rule," we suppose a parabola, the equation to which is

\[ y = A + Rx + Cx^2 + Dx^3 \]

to pass through the four points \(a_1, a_2, a_3, a_4\) (fig. 1), the four constants being determined by these conditions; that is, when \(x\) takes the successive values \(0, h, 2h, 3h\); \(y\) becomes \(a_1, a_2, a_3,\) and \(a_4\); hence the following equations:

\[ a_1 = A \quad (2) \quad \text{when } x = 0, y = a_1 \]

\[ a_2 = A + Ca + Da^2 \quad (3) \quad \text{when } x = h, y = a_2 \]

\[ a_3 = 2Rh + 4Ca^2 + 6Da^3 \quad (4) \quad \text{when } x = 2h, y = a_3 \]

\[ a_4 = 3Ra + 9Ca^2 + 27Da^3 \quad (5) \quad \text{when } x = 3h, y = a_4 \]

\((4)-(3) \times 2\) gives \(a_2 - 2a_1 + a_1 = 2Ca + 6Da^2 \quad (6)\)

\((5)-(3) \times 4\) gives \(a_3 - 2a_2 + a_2 = 2Ca + 12Da^3 \quad (7)\)

\((7)-(6)\) gives \(6Da^3 = a_3 - 3a_2 + 3a_1 - a_1 \quad (8)\)

From (6) and (8) \(2Ca^2 = a_1 + 4a_2 + 5a_3 + 2a_4 \quad (9)\)

From (3), (8) and (9) \(6Da^3 = 2a_1 - 9a_2 + 18a_3 - 11a_4 \quad (10)\)

But area, or \(\int_{a_1}^{a_4} y \, dx = \int_{a_1}^{a_4} \left( A + Rx + Cx^2 + Dx^3 \right) \, dx\)

(we write the limits of \(x, o, 3h\), because at \(A_1, x = 0\), and at \(A_4, x = 3h\)).

\[ \therefore \text{Area } A_1 a_4 = \frac{3h}{8} \left( 8A + 12Bh + 24Ca^2 + 54Da^3 \right) \]

Introducing the values of \(A, B, C, D\), given by the above equations, we find, after some obvious reductions,

\[ \text{Area } A_1 a_4 = \frac{3h}{8} \left( s_1 + s_2 + 3s_3 + 3s_4 \right) \quad (11) \]

In like manner, by making a curve similar to (1) pass through the points \(a_4, a_5, a_6, a_7\), we have

\[ \text{Area } A_4 a_7 = \frac{3h}{8} \left( s_2 + s_3 + 3s_4 + 3s_5 \right) \quad (12) \]

\[ \text{Area } A_7 a_8 = \frac{3h}{8} \left( s_3 + s_4 + 3s_5 + 3s_6 \right) \quad (13) \]

\[ \text{Area } A_8 a_9 = \frac{3h}{8} \left( s_4 + s_5 + 3s_6 + 3s_7 \right) \quad (N) \]

Adding equations (11), (12), (13), etc., (N), we get

\[ (II.) \quad \text{Area } A_1 a_9 = \frac{3h}{8} \left( s_1 + s_2 + 3(s_2 + s_3 + s_4 + s_5 + s_6 + s_7) + s_8 + s_9 \right) \]

It will be seen from the foregoing method that we may make a curve of the form

\[ y = A + Bx + Cx^2 + Dx^3 + Ex^4 + &c., N_{x+1} \]

pass through \(n\) points, taking care that the equation shall contain arbitrary constants, to be determined by the conditions that the curve may pass through \(a_1, a_2, a_3, a_4, \ldots, a_n\) (fig. 3, page 140), when \(x\) and \(y\) are respectively \(x = 0, x = h, x = 2h, \ldots, x = (n-1)h\),

\(y = a_1, y = a_2, y = a_3, \ldots, y = a_n\),

\(a_1, a_2, a_3, \ldots, a_n\), having the same interpretation as before; the ordinates being taken at equal distances apart, as on this hypothesis the calculation of the area is much simplified.

Rules obtained after this manner for any given number of ordinates will, in general, give us the area of the figure more correctly than if we employed the preceding rules, because in the latter case we suppose a continuous curve to pass through the given points, whereas, in the former case, instead of a series of curves passing through the given points, each the curvilinear boundary is itself supposed to be a continuous curve. Such rules (for many ordinates) give rise to a great deal of labour in obtaining them, and entail almost as much labour in their application. In the latter case, moreover, logarithms will assist us to some extent, and in the former,

---

1 The equation to a parabola being \(y^2 = 4ax\), or \(y = 2ax\),

\[ \text{Area, or } \int_{a_1}^{a_4} y \, dx = 2ah \int_{a_1}^{a_4} x \, dx = \frac{4a^2h^3}{3} = \frac{2xy}{3} \quad \text{by (1)} \]

\[ = \frac{2}{3} \text{ circumscribed parallelogram}. \] there are some remarkable properties of the natural numbers connected with the determination of the arbitrary constants, and on which perhaps more light may hereafter be thrown. We have remarked some curious properties of the squares, cubes, &c., of numbers connected with the elimination. There can be no doubt that many other cases of this simple kind may be obtained on the condition that any number of the constants may disappear from the general equation, which is equivalent to as many conditions.

Emerson, in his Arithmetic of Infinites, published by Nourse in the year 1767, gives the following formulae, obtained by the foregoing processes—from one up to nine ordinates.

\[ \text{Area} = \frac{h}{2} (a_1 + a_2) \quad \text{for one ordinate.} \]

\[ \begin{align*} (1) &= \frac{3}{8} \left(a_1 + a_2 + a_3\right) \\ (2) &= \frac{3}{8} \left(a_1 + a_2 + a_3 + a_4\right) \\ (3) &= \frac{5}{25} \left(7a_1 + 32a_2 + 12a_3\right) \\ (4) &= \frac{5}{288} \left(19a_1 + 75a_2 + 50a_3 + 12a_4\right) \\ (5) &= \frac{1}{140} \left(41a_1 + 216a_2 + 27a_3 + 27a_4\right) \\ (6) &= \frac{1}{17280} \left(751a_1 + 3577a_2 + 1323a_3 + 2989a_4\right) \\ (7) &= \frac{1}{14175} \left(989a_1 + 5883a_2 + 228a_3 + 10496a_4\right) \end{align*} \]

Where extreme accuracy is required, these may be combined such a way as to give the area. For instance, if there were fifteen ordinates in a figure, (6) and (7) may be combined, remembering that the last ordinate of (5) becomes the first in (7), &c., &c.

When seven ordinates are considered sufficient, the following elegant rule, due to the late Mr Thomas Weddle, of the Military College, Sandhurst, may be employed:

**Rule III.—When seven ordinates are employed.** To five times the sum of the even ordinates, add the fourth, or middle ordinate, and all the odd ordinates; multiply this sum by three times the common distance between the ordinates, divide by ten, and the result will give the area (nearly).

Note 3.—The Calculus of Finite Differences may be advantageously employed to approximate to the areas of surfaces, lengths of curves, volumes of solids, centres of gravity, moments of inertia, &c. For triple integrals may generally be reduced to integrals of the form

\[ \int_{x_1}^{x_2} u dx \]

where \(u\) represents a function of \(x\), or \(f(x)\), as it is usually written, and \(x_1, x_2\) represent the limits of the integral.

Now, if we suppose \(x\) to vary by the constant difference \(\Delta x\), we may suppose \(x = \frac{x}{\Delta x}\), and if \(a_1, a_2, a_3, \ldots, a_n\) be the values of \(u\) when \(x = 0, 1, 2, 3, \ldots, n\), we have, by Taylor's theorem,

\[ u = a_1 + \Delta a_1 + \frac{\Delta^2 a_1}{2!} + \frac{\Delta^3 a_1}{3!} + \ldots + \frac{\Delta^n a_1}{n!} \]

But by hypothesis \(\Delta x\) is constant, and according to the notation we have previously employed, we may suppose it \(= h\). Then \(x = \frac{x}{\Delta x} = \frac{x}{h}\), and

\[ \frac{dx}{h} = ds. \quad \text{Multiplying each side of (1) by these differentials, and integrating, we have} \]

\[ \int_{x_1}^{x_2} u dx = \frac{1}{h} \left[ a_1 + \frac{\Delta a_1}{2} + \frac{\Delta^2 a_1}{2!} + \frac{\Delta^3 a_1}{3!} + \ldots + \frac{\Delta^n a_1}{n!} \right] \]

The coefficients in each of these terms are readily obtained by multiplying \((p-1)(p-2)(p-3)(p-4)(p-5)\), &c., \((p-n)\) together.

If we take this integral between the limits \(x = 0\) and \(x = 2h\), after multiplying by \(h\),

\[ \int_{0}^{2h} u dx = \frac{1}{h} \left[ 2a_1 + 2\Delta a_1 + \frac{1}{3} \Delta^2 a_1 - \frac{1}{90} \Delta^4 a_1 + \frac{1}{90} \Delta^6 a_1 - \ldots \right] \]

But by the principles of the Calculus of Finite Differences:

\[ \Delta a_1 = a_2 - a_1 \]

\[ \Delta^2 a_1 = a_3 - 2a_2 + a_1 \]

\[ \Delta^3 a_1 = a_4 - 3a_3 + 3a_2 - a_1 \]

\[ \Delta^4 a_1 = a_5 - 4a_4 + 6a_3 - 4a_2 + a_1 \]

Now, if we add similar expressions for the area included between \(x = 2h\) and \(x = 4h\); \(x = 4h\) and \(x = 6h\), &c.; \(x = (n-2)\) and \(x = nh\) (\(n\) being an even number).

---

1 Seven, thirteen, nineteen, &c., ordinates, may be employed on the same hypothesis, as is mentioned hereafter.

2 The fourth ordinate is considered among the even ordinates. The first line corresponds to the Rule we have already obtained (I.) by supposing a parabola to pass through the extremities of the ordinates \(a_1, a_2, a_3\); and another through \(a_4, a_5, a_6, \ldots\).

The following terms are the correction of the first line; hence, when great accuracy is required, the following results may be taken into account.

To obtain Rule (III.), we only have to suppose the integral (1) taken between the limits \(x = 0\) and \(x = 6\), as was done by Mr Weddle in his demonstration, given in the Dublin and Cambridge Mathematical Journal for February 1856, which is similar to this:

\[ \int_0^6 u dx = h \left\{ \frac{a_1}{2} + 18 \Delta a_1 + 27 \Delta^2 a_1 + 24 \Delta^3 a_1 + \frac{123}{10} \Delta^4 a_1 + \frac{33}{10} \Delta^5 a_1 + \frac{41}{140} \Delta^6 a_1 + \ldots \right\} \]

And we may suppose sixth differences constant, and then all the terms after \(\Delta^6 a_1\) in (4) will vanish; but

\[ \frac{41}{140} \text{ differs from } \frac{42}{140} \text{ by the small fraction } \frac{1}{140} \]

hence, instead of \(\frac{41}{140}\) we may write \(\frac{42}{140}\) or \(\frac{3}{10}\) without material error. Replacing \(\Delta a_1\) by \(a_2 - a_1\), \(\Delta^2 a_1\) by \(a_3 - 2a_2 + a_1\), \(\Delta^3 a_1\) by \(a_4 - 3a_3 + 3a_2 - a_1\), etc., after some obvious reductions (4) becomes

\[ \int_0^6 u dx = \frac{3}{10} \left\{ a_1 + a_2 + a_3 + a_4 + a_5 + 5(a_2 + a_3) + 6a_4 \right\} \]

From the foregoing investigation, it is clear, that formula (5) gives the exact area, when fifth differences are constant, while it differs (in excess) from the true value by \(\frac{1}{140} \Delta^6 a_1\) when sixth, or even seventh, differences are constant. In other cases it will give the area very nearly, providing the differences, beginning at the sixth, are small.\(^1\)

As many rules as we please may be obtained by integrating (1.) from \(x = 0\) to \(x = 1\), \(x = 0\) to \(x = 2\), \(x = 0\) to \(x = 3\), \(x = 0\) to \(x = 4\), etc.; from \(x = 0\) to \(x = n\), and neglecting small quantities, as has been done by Mr Weddle, and by supposing the \((n-1)\)th order of differences constant.\(^2\)

Rule (II.) may be obtained by integrating equations (1.) from \(x = 0\) to \(x = 3\), which will be the same as supposing a series of parabolas to pass through the extremities of \(a_1, a_2, a_3, a_4; a_5, a_6, a_7, a_8, \ldots\), as was the case in formula (3).

In these rules, if the curve passes through \(A_1\) or \(A_n\) the first or last ordinate must be considered 0.

Some examples will now be given on the application of the preceding rules.

(1.) Find the area of a figure, bounded by right lines and a curve, the ordinates of which are taken at 3 feet apart, and measure 1, 2, 3, 4, 5, 4, 3, 2, and 1 feet respectively.

---

\(^1\) The Dub. and C. Math. Journal, Feb. 1854.

\(^2\) The coefficients of the various orders of differences have been extended, in order that the reader may obtain some of these rules for himself. Divide the radius \( A_1 \), \( A_2 \) into six equal parts (Fig. 5), and erect the ordinates \( A_2 a_2, A_3 a_3, \ldots \) observing that \( A_1 a_1 = 0 \).

\[ A_2 a_2 = \sqrt{(A_2 a_2)^2 - (A_2 a_2)^2} = \sqrt{6^2 - 5^2} = \sqrt{11} = 3.3163 \\ A_3 a_3 = \sqrt{(A_3 a_3)^2 - (A_3 a_3)^2} = \sqrt{6^2 - 4^2} = \sqrt{20} = 4.4721 \\ A_4 a_4 = \sqrt{6^2 - 3^2} = \sqrt{27} = 5.1961 \\ A_5 a_5 = \sqrt{6^2 - 2^2} = \sqrt{32} = 5.6568 \\ A_6 a_6 = \sqrt{6^2 - 1^2} = \sqrt{35} = 5.9160 \\ A_7 a_7 = 6 \]

The area found by Rule (I.) \( = 27.9901 \) feet.

\[ \text{II.} = 27.9285 \\ \text{III.} = 28.0401 \]

Apply formula (5.) given at the end of Note (I.)

\[ \text{Area} = \frac{A}{140} \left[ 41(s_1 + s_2) + 216(s_2 + s_3) + 27(s_3 + s_4) + 272s_4 \right] \]

Where \( A = 6, s_1 = 0, s_2 = 3.3163, s_3 = 4.4721, \ldots \)

And area \( = 28.05 \) feet.

But true area of quadrant \( = \frac{6^2 \times 3.1416}{4} = 28.2744 \), so that

Rule (III.) and formula (5.), in the present case, give the area almost accurately.

(4.) The ordinates of a curve taken 6 feet apart are, 20, 22, 24, 25; 24, 23, and 21 feet, respectively: find the area of the figure.

By Rule (I.) Area \( = \frac{6}{3} \left[ 20 + 21 + 4(22 + 25 + 23) + 2(24 + 21) \right] = 834 \) feet.

By Rule (II.) Area \( = \frac{3 \times 6}{8} \left[ 20 + 21 + 3(22 + 24 + 24 + 23) + 2 \times 25 \right] = 832.5 \) feet.

By Rule (III.) Area \( = \frac{3 \times 6}{10} \left[ 20 + 24 + 25 + 21 + 5(22 + 25 + 23) \right] = 835.2 \) feet.

By formula (5.) Area \( = \frac{6}{140} \left[ 20 + 21 + 216(22 + 23) + 27(24 + 24) + 272 \times 25 \right] = 835.5 \) feet.

(5.) Find the area, when the ordinates, taken 4 feet apart measure 0, 2.275, 3.476, 4.567, 5.673, 6.451, 5.341, 4.236, 3.254, 3.055, 2.784, 1.876, and 0, respectively.

By Rule (I.) Area \( = 174.6293 \).

(6.) Find the area by Rules (II.) and (III.) when the ordinates, taken 1 foot apart, measure, 0, 1.7684, 2.3457, 3.4567, 3.214, 2.97654, and 2.8543 feet, respectively.

By Rule (II.) Area \( = 15.2556, \ldots \)

By Rule (III.) Area \( = 15.86367 \).

Art. 2. Def.—By the Displacement of a ship is meant the volume of water which the ship displaces when floating on its surface.

Now, by the principles of hydrostatics, it is well known that the weight of a body floating in water, or any other fluid, is equal to the weight of the water or fluid displaced. Hence, after obtaining the displacement of a body, it is only necessary to multiply the volume (say in cubic feet) of the displaced fluid, by the weight of a cubic foot of the fluid, in order to obtain the weight of the floating body.

Def.—By a plane of flotation is meant that section of the vessel, in any position, made by the surface of the water.

Several general rules have been given to determine the displacement of ships, which can be but approximations to the true results, since the outlines of ships differ so widely, and it is therefore not considered necessary to give them.

In order to find the displacement, the ship is supposed to be divided by any number of equidistant horizontal planes, that is, planes taken parallel to the load-water line, and also by any convenient number of equidistant vertical planes, intersecting, of course, the former series of horizontal planes at right angles. These planes are generally projected by the draughtsman on the three plans of the vessel, viz., the body plan, the sheer plan, and half-breadth plan. (See Plate I.)

As is seen in the half-breadth plan, the ship is divided into two equal portions by a vertical plane, running from stem to stern; and the perpendicular distances measured on each horizontal plane, from their intersection with this plane to the ship's side, are considered as ordinates.

Thus in the half-breadth plan (Plate I.), \( F \) is the projection of the vertical plane which divides the ship into two equal parts, and \( F' \) \( E \) are the ordinates in the horizontal plane, \( F \), \( E \); any number of these horizontal planes may be taken, and for the purposes of calculation they may be numbered 1, 2, 3, 4, &c.; and \( A, B, C, \ldots \)

The small portions, fore and aft, are usually calculated separately, the horizontal and vertical planes being taken much nearer to each other in consequence of the greater curvature of the vessel at these parts.

The calculation of the displacement may be proceeded with in two ways:

1st. By finding the areas of all the horizontal sections, and employing these as ordinates in Rule (I.) or (II.)

2nd. By finding the areas of all the vertical sections, and using these as ordinates in the same rules.

These two results ought to agree.

Or, the rule may be enunciated as follows, ordinates on the half-breadth plan being understood:

**Rule IV.** To the sum of the first and last horizontal sectional areas, add your times the sum of all the even horizontal areas, and twice the sum of all the odd horizontal areas; multiply this final sum by one-third the common distance between these horizontal planes, and this result gives one-half the displacement.

We could not, from what has already been done, a priori, conclude that " Simpson's Rule " would enable us to find the volume of a solid, bounded by planes and a curvilinear surface. The following demonstration, however, proves that it holds true.

Note 4.—Let \( A_1 e_1 \) represent a portion of such a body, bounded by the planes \( A_1, C_1, C_2, A_2, A_3, A_4, C_3, C_4, A_5, A_6, C_5, C_6, A_7, A_8, C_7, C_8, A_9, A_{10}, C_9, C_{10} \), and by the surface \( a_1, e_1 \), we take the planes \( A_1, a_1, A_2, e_1, \ldots \), and \( A_9, a_9 \), as the three planes of reference, viz., \( (x, y), (y, z), \) and \( (z, x) \), respectively.


Bisect \( A_1, A_2, A_3, C_1, C_2, A_4, C_3, A_5, C_4, A_6, C_5, A_7, C_6, A_8, C_7, A_9, C_8, A_{10}, C_9, A_{11}, C_{10} \) in the points \( A_{11}, B_1, C_{11}, \ldots \), and \( B_{11} \), respectively; join \( A_1, C_{11} \) and \( B_1, B_{11} \); through these right lines let planes \( A_2, e_2, B_2, b_2 \), be drawn at right angles to the plane \( A_1, C_{11} \), then

Assume \( A_2 = A_2, A_3 = B_3, B_2 = B_2, C_2 = C_2, C_3 = h \)

\( A_1, B_1 = B_1, C_1 = A_2, B_2 = B_2, C_2 = A_3, B_3 = B_3, C_3 = k \)

\( A_1, a_1 = a_1, B_1, b_1 = b_1, C_1, c_1 = y_1 \)

\( A_2, a_2 = a_2, B_2, b_2 = b_2, C_2, c_2 = y_2 \)

\( A_3, a_3 = a_3, B_3, b_3 = b_3, C_3, c_3 = y_3 \)

We may then imagine a surface of the form (I.) to pass through the nine points, \( a_1, a_2, a_3, b_1, b_2, b_3, c_1, c_2, c_3 \),

\[ s = A + Bx + Cx^2 + B_1y + C_1y^2 + Dxy + Ex^2y + Ey^2 + Cx^2y^2 \]

(I.) Since it contains nine arbitrary constants, A, B, C, D, E, F, G, H, I, &c., observing that the x's are measured along A, A', A", A"' the y's along A, A', A", A"', and the z's are A, A', A", A"', A", A"', A", A"', &c. Hence we have the following equations:

1. \(a_1 = A\), when \(x = 0, y = 0, z = a_1\) by (I) 2. \(a_2 - a_1 = Ba + Ca^2\), when \(x = k, y = 0, z = a_2, a_3 = a_2\) 3. \(a_3 - a_2 = 2Ba + 4Ca^2\), when \(x = 2k, y = 0, z = a_3, a_4 = a_3\) 4. \(a_4 - a_3 = Ba + Ca^2\), when \(x = 0, y = k, z = a_4, b_1 = b_1\) 5. \(a_5 - a_4 = 2Ba + 4Ca^2\), when \(x = 0, y = 2k, z = a_5, c_1 = c_1\) 6. \(b_2 = a_2 - b_1 = a_1 = Da + Ea^2 + Fa^3 + Ga^4\), by (2) and (4) 7. \(b_3 = a_3 - b_2 = a_2 = 2Da + 4Ea^2 + Fa^3 + Ga^4\), by (3) and (4) 8. \(c_2 = a_4 - c_1 = a_3 = 2Da + 4Ea^2 + Fa^3 + Ga^4\), by (2) and (5) 9. \(c_3 = a_5 - c_2 = a_4 = 2Da + 4Ea^2 + Fa^3 + Ga^4\), by (3) and (5)

Now, B, C, D, E, F, and G are readily determined from equations (2), (3), (4), and (5), and D, E, F, and G, from equations (6), (7), (8), and (9); their values are:

\[A = a_1\] \[B = \frac{4a_2 - 3a_1}{24}\] \[C = \frac{a_3 - 2a_2 + a_1}{24}\] \[D = \frac{4a_4 - 3a_3 - a_2}{24}\] \[E = \frac{a_5 - 2a_4 + a_3}{24}\] \[F = \frac{4a_6 - 3a_5 - a_4}{24}\] \[G = \frac{a_7 - 2a_6 + a_5}{24}\]

In order to find the volume of a solid, we must integrate the equation \(f(x)dx\), as shown in most works on the Differential and Integral Calculus, or, what amounts to the same thing, \(f(x)dx\), where \(x\) is given by the equation to the surface, and the integrations in regard to \(x\) and \(y\) are to be determined by the conditions of the question. It is evident that, in the present case, the limiting values of \(x\) are 0 and 2k, those of \(y\) being 0 and 2k. Hence

\[\int_{0}^{2k} \int_{0}^{2k} z \, dx \, dy = \int_{0}^{2k} \int_{0}^{2k} (A + Bx + Cx^2 + Dx^3 + Ex^4 + Fx^5 + Gx^6)\, dx \, dy\]

Introducing the values of A, B, C, D, E, F, G already found, we get, after obvious reductions, volume \(A_1c_1 = \frac{h^3}{9} \left( a_1 + 4a_2 + a_3 + 4(b_1 + 4b_2 + b_3) + c_1 + 4c_2 + c_3 \right)\) (II).

On examining the equations, we perceive that \(\frac{h^3}{9} \left( a_1 + 4b_1 + b_2 \right)\) represents the area of the section \(A_1c_1\) (Vide Equation I, p. 141), and \(\frac{h^3}{9} \left( b_1 + 4b_2 + b_3 \right)\) represents the area \(B_1c_2\); also, \(\frac{h^3}{9} \left( c_1 + 4c_2 + c_3 \right)\) that of \(C_1c_2\). Writing for the area of \(A_1c_2\), for that of \(B_1c_2\), for \(C_1c_2\), \(A_1c_2\) (Equation II.) becomes

Volume \(A_1c_2 = \frac{h^3}{9} \left( A_1 + 4A_2 + A_3 \right)\) (III.)

By making similar paraboloidal surfaces pass through \(c_1, c_2, c_3\), and six other points, &c., we have

Volume \(A_2c_3\) next portion \(= \frac{k}{3} \left( A_3 + 4A_4 + A_5 \right)\),

Adding these—

Total volume \(= \frac{k}{3} \left\{ A_1 + A_2 + 4(A_3 + A_4 + A_5 + &c. + A_n - 1 + 2(A_3 + A_4 + &c. + A_n - 2) \right\}\) (IV.)

We might have regarded \(\frac{k}{3} \left( a_1 + 4b_1 + c_1 \right)\) as the area of the section \(A_1c_1\), or \(B_1c_2\), as we shall denote it, \(\frac{h^3}{9} \left( a_1 + 4b_1 + c_1 \right)\) that of \(A_2c_3\), &c., or \(B_2c_4\), &c., and then

Volume \(= \frac{k}{3} \left\{ B_1 + B_2 + 4(B_3 + B_4 + &c. + B_n - 1) + 2(B_3 + B_4 + &c. + B_n - 2) \right\}\). Multiplying these volumes by 2, we get the total displacement of the ship.

A Rule similar to that of (II.) Note (2) may be found by making a surface, the equation to which is of the form \(z = A + Bx + Cx^2 + Dx^3 + Ex^4 + Fx^5 + Gx^6 + Hx^7 + Ix^8 + Jx^9 + Kx^{10} + Lx^{11} + Mx^{12} + Nx^{13}\) pass through sixteen points, since the equation contains this number of arbitrary constants, which are determined as before, and the integrations are taken from \(x = 0\) to \(x = 2k\), and \(y = 0\) to \(y = 2k\). We shall leave this work for the student, and proceed at once to

Observe that vertical areas may be employed in the place of horizontal areas, and care must be taken to omit the first and last areas from the odd ones in each case.

Rule (II.) might have been employed; but the following is the neatest, most concise, and at the same time sufficiently accurate, that has yet been given. It is by the Rev. Joseph Woolley, M.A., LL.D., Her Majesty's Inspector of Schools, to whom naval architects are under great obligations for the attention he has given to this branch of science:

**Rule V.**

1. Add together all the even ordinates in the first and last horizontal planes. 2. Add together all the even ordinates in the 3rd, 5th, 7th, &c., sections, omitting the first and last, and multiply the sum by 2. 3. Add together all the first and last ordinates of all the even horizontal planes. 4. Take twice the sum of all the ordinates, omitting the first and last of all the even horizontal planes.

Then, add together the results of (1), (2), (3), (4), and multiply this final sum by two-thirds of the product of the common distances between the horizontal and vertical planes, and this result gives the displacement.

Note 6.—Not having seen the demonstration by Dr Woolley to this rule, the editors beg to offer the following, which must be somewhat similar in principle.

Dr Woolley supposes fig. 4 to be divided into two portions by a plane passing through \(C_1B_2A_3A_4C_1\), and the equation to the surface passing through \(a_1, b_1, c_1, d_1, e_1\) may be assumed as

\[z = A + Bx + Cx^2 + Dx^3 + Ex^4 + Fx^5 + Gx^6 + Hx^7 + Ix^8 + Jx^9 + Kx^{10} + Lx^{11} + Mx^{12} + Nx^{13}\] (I.)

And the limits are \(x = 0\) and \(x = 2k\), and since, \(A_1C_1 = 2k\), at any point \(y\), we must have \(y = \frac{(2k-x)}{h}\).

\[\int_{0}^{2k} \int_{0}^{2k} z \, dx \, dy = \int_{0}^{2k} \int_{0}^{2k} (A + Bx + Cx^2 + Dx^3 + Ex^4 + Fx^5 + Gx^6 + Hx^7 + Ix^8 + Jx^9 + Kx^{10} + Lx^{11} + Mx^{12} + Nx^{13}) \, dx \, dy.\] Calculations incidental to designing a Ship.

\[ \int_{0}^{2h} dx \left( A \left( \frac{2h-x}{h} \right) + Bx \left( \frac{2h-x}{h} \right) + Cx^2 \left( \frac{2h-x}{h} \right) \right) \]

\[ = \frac{2Ah}{3} + \frac{4Bh^2}{3} + \frac{4Ck^3}{3} + \frac{4Dk^3}{3} + \frac{2Dk^3}{3} \] (II)

Now, since the surface (L) passes through the six points already mentioned, we readily determine \( A, B, C_1, \ldots \), as in the last note. Their values are

\[ A = a_1 \] \[ 2Bh = 4a_2 - a_3 - 3a_1 \] \[ 2Ca^2 = a_1 - 2a_2 + a_3 \] \[ 2Bk = 4b_1 - b_2 - 3b_1 \] \[ 2Ck^2 = a_1 - 2b_2 + b_1 \] \[ Dk = a_1 + b_1 - a_2 - b_1 \]

Writing these values in (II), it reduces to

\[ \text{Volume} = \frac{2Ah}{3} \left( a_1 + b_1 + a_2 + b_2 \right) \]

In the same way, we find the volume of the figure \( C_1, b_2, a_2, C_3 \)

\[ = \frac{2Ah}{3} \left( a_1 + b_1 + a_2 + b_2 \right) \]

Adding these results, we find for the whole volume \( A_1C_3 \)

\[ \frac{2Ah}{3} \left( a_1 + b_1 + 2a_2 + b_2 + b_3 + b_4 + \ldots \right) \]

With similar expressions for the other portions of the ship.

\[ \therefore \text{Whole volume} = \frac{2Ah}{3} \left( a_1 + b_1 + 2(a_2 + b_2 + b_3 + b_4 + \ldots) \right) \]

To find the Centres of Gravity of Bodies.

Art. 3. As a knowledge of the centres of gravity of bodies is of so much importance in the calculation of stability, it has been thought advisable to introduce the subject here at some length.

Various definitions have been given of the centre of gravity of a body. It is shown in almost every work on statics, that there is a point in (sometimes without) every body such, that if the particles of the body be acted on by parallel forces, and the point already mentioned be fixed or supported, the body will remain in equilibrium, no matter in what position it is placed; and when the forces herein mentioned are replaced by the weights of the elementary portions of the body, or bodies, this point is known as the centre of gravity of the body or bodies.

Gravity, or the force which attracts all bodies towards the earth's centre, is supposed to act on every particle of the body in parallel and vertical directions. This force is supposed to be constant at the earth's surface, and therefore attracts all bodies with an equal intensity. The reader will readily perceive that this hypothesis cannot differ materially from the truth when he compares the earth's radius with the dimensions of all bodies at its surface, and remembers that this attractive force varies inversely as the square of the distance. Under these circumstances, then, the centres of gravity of bodies are calculated. This point cannot be obtained, however, without the aid of the integral calculus, except in the case of a few plane surfaces and solids. We shall premise that when bodies are homogeneous, or of the same density throughout their parts,—that is, having equal weights, comprised under equal volumes,—we may then replace weights by masses, and conversely. Thus if \( M \) represent the mass of a body, \( d \) the density of a unit of the body, \( V \) the volume, \( W \) the weight, then

\[ M = d \times V \] (1) \[ W = g \times d \times V = gM \] (2)

When a body is not homogeneous throughout its parts, the determination of the centre of gravity becomes somewhat more difficult.

To find the Centre of Gravity of an Area similar to fig. 1.

Art. 4.—Rule VI. Multiply the ordinates, beginning Centre of at the first by 0, 1, 2, 3, 4, &c., respectively, and employ gravity, these as ordinates in Rule (I); multiply the result thus obtained by one-third of the common interval squared, divide by the area of the curve, and the result gives the distance we are to measure along \( A_1A_n \)—i.e., \( A_1g \).

Having obtained the distance \( A_1g \), we may obtain the length of the perpendicular \( Gg \) (\( G \) being the centre of gravity of the figure, and \( g \) the point where the perpendicular drawn from \( G \) intersects \( A_1A_n \)) by

Rule VII. To the sum of the squares of the first and last ordinates, add four times the sum of the squares of all the even ordinates, twice the sum of the squares of all the odd ordinates; multiply by one-third the common interval, and divide this result by twice the area, the quotient gives the perpendicular height of the centre of gravity above the axis \( A_1A_n \).

Similar rules apply for finding the centres of gravity of the displacement of a ship.

Art. 5. To find the centre of gravity of the displacement of a ship floating in the water, and in a state of equilibrium—

The horizontal sections are taken at equal distances apart and parallel to the plane of flotation. The vertical sections are also taken at equal distances apart and parallel to the midship section. The ship is then cut into two equal portions by a plane running fore and aft, and at right angles to the two planes just mentioned. In the following rules, half areas and half volumes are to be understood.

Rule VIII. Find the areas of all the horizontal sections (such as those shown in the half-breadth plan) and multiply these, beginning from the first, or plane of flotation, by the consecutive numbers 0, 1, 2, 3, 4, &c., respectively; introduce these products as ordinates into "Simpson's Rule"; multiply this result by one-third of the square of common distance between the sections, divide by the volume, and the quotient gives the distance of the centre of gravity below the plane of flotation.

Rule IX. Find the areas of all the vertical sections, multiply these, beginning from the first, by the consecutive numbers 0, 1, 2, 3, 4, &c., respectively, and work as in the last rule; the result thus obtained gives the distance of the centre of gravity from the first vertical plane.

---

1 Pratt's Mechanical Philosophy, 2d edit., pp. 18 and 19. 2 The centre of gravity has also been defined as that point within or without the body, from which, if the body be conceived to be suspended, it will remain in equilibrium in any position. 3 "g, or the accelerating force of gravity, is uniform, and is the same for all substances, and in the latitude of London = 32-18 feet." 4 Care must be taken not to multiply by one-third of the common distance, as is mentioned in Rule I. 5 The last ordinate must not be reckoned among the odd ordinates in these and the following rules. 6 Either the first vertical section of the main body nearest the bow or stern may be taken as the first. These two distances fix the position of the centre of gravity of the main body. Since a ship is symmetrical in regard to the plane which divides it, fore and aft, into two equal parts, we know that the centre of gravity must lie in this plane.

No account is here taken of the small portions at the stem, stern, and that between the keel and last horizontal section. These are usually calculated separately, and in the same way as the main body. Having obtained the centres of gravity of all these portions, we readily obtain the centre of gravity of the total displacement by the rule which follows, observing, that if we consider the first vertical plane to be that about the bow, the volume of the small portion forward multiplied by the distance from the centre of gravity from the plane just mentioned must be subtracted. Or, in other words, if we consider all horizontal distances, measured in the opposite direction (from the first vertical plane) to the centre of gravity of the main body as negative, and all distances measured in the same direction as positive, we have then only to add the products algebraically, and this is to be understood in the following rule (one product being always negative in Rule XI). All results will be positive in finding the distance of the centre of gravity below the plane of flotation.

**Rule X.** Multiply each of the volumes by the perpendicular distance of its centre of gravity from the plane of flotation, and add the products; divide this result by the sum of all the volumes, and the quotient is the distance of the centre of gravity of the total displacement below the plane of flotation. Also,

**Rule XI.** Multiply each of the volumes by the perpendicular distance of its centre of gravity from the first vertical plane, and add algebraically (observing that one result will be negative), divide this result by the sum of all the volumes, and the quotient is the distance of the centre of gravity of the total displacement from the first vertical plane.

One of the properties of Guldinus is also of great use in finding centres of gravity when the necessary data are supplied.

**Rule XII.** Any solid of revolution is equal to the area of the surface which generates this solid, multiplied by the circumference, which is described by the centre of gravity of the latter.

Without attempting to demonstrate formulae (1.) of this article, since a demonstration may be found in almost every work on statics, we proceed to lay before the mathematical reader the principles on which the centres of gravity are calculated.

*Note 6.—If we consider, in the first place, a system of material points having weight, and connected in an invariable manner, the weights of these points may be considered as so many vertical forces acting in parallel directions. If, moreover, we take three fixed planes, mutually at right angles to each other, their point of intersection being the origin (as is done in Geometry of three dimensions) let $w_1$ be the weight of the first material point, and its co-ordinates $x_1$, $y_1$, $z_1$, measured along the three co-ordinate axes; $w_2$, $y_2$, $z_2$, the weight and co-ordinates of the second point, &c. &c.; also, let $x$, $y$, $z$ represent the co-ordinates of the centre of gravity of the system of weights measured along the same axes, then we have

$$\begin{align*} x &= \frac{w_1 x_1 + w_2 x_2 + \ldots}{w_1 + w_2 + \ldots} \\ y &= \frac{w_1 y_1 + w_2 y_2 + \ldots}{w_1 + w_2 + \ldots} \\ z &= \frac{w_1 z_1 + w_2 z_2 + \ldots}{w_1 + w_2 + \ldots} \end{align*}$$

Remark.—These formulae would be equally true if we suppose $w_1$, $w_2$, $w_3$, &c., to represent the weights of any bodies whatever, and connected in an invariable manner, providing we suppose these weights to act at their respective centres of gravity, and $x_1$, $y_1$, $z_1$, &c., to be the co-ordinates of these centres of gravity. Next, if we suppose the density of the weights to be uniform throughout, we can replace the weights by their respective volumes $v_1$, $v_2$, $v_3$, &c., since $w \times d$ appears both in numerator and denominator. The proposition is also true for areas. Therefore, if $A_1$, $A_2$, $A_3$, &c. represent areas

$$\begin{align*} x &= \frac{A_1 x_1 + A_2 x_2 + \ldots}{A_1 + A_2 + \ldots} \\ y &= \frac{A_1 y_1 + A_2 y_2 + \ldots}{A_1 + A_2 + \ldots} \\ z &= \frac{A_1 z_1 + A_2 z_2 + \ldots}{A_1 + A_2 + \ldots} \end{align*}$$

If the centres of gravity of the weights, volumes, or areas, as the case may be, range in a right line, the first equation gives the distance of their common centre of gravity from the origin. If the weights, or areas, &c., are in the same plane, the four former equations are all that are necessary to determine the centre of gravity.

Premising that the centre of gravity of a ball, or sphere, is at the centre of the body, we shall proceed to give two or three examples on these formulae.

(1.) Four cannon-balls have their centres in the same right line at 2, 3, and 4 feet, respectively, apart, and weigh 68, 32, 12, and 8 lbs. respectively; that is, the "68" is 2 feet from the "68," the "12" is 3 feet from the "32," &c. Find the distance of the common centre of gravity from the centre of the "68" (supposing their centres to be in the same horizontal line).

Taking the origin at the centre of the "68," we have $x_1 = 0$, $x_2 = 2$, $x_3 = 2 + 3 = 5$, $x_4 = 2 + 3 + 4 = 9$ feet.

$$\begin{align*} x &= \frac{68 \times 0 + 32 \times 2 + 12 \times 5 + 8 \times 9}{68 + 32 + 12 + 8} = 1.63 \text{ feet.} \end{align*}$$

That is, if the balls were connected by an indefinitely fine rigid rod, without weight, passing through the centres of the balls, the whole might be suspended, and remain in equilibrium, at a point distant 1.63 feet from the centre of the "68."

(2.) Five cannon-balls, whose weights are 2, 8, 12, 32, and 68 lbs., lie on the floor of a room, at the respective perpendicular distances 3, 4, 5, 6, and 7 feet from the side, and 1, 2, 3, 4, and 5 feet from one end of the room; find their common centre of gravity from that corner of the room where the side and end (from which these distances are measured) intersect, supposing the centres of the balls to lie in the plane of the floor.

Here $x = \frac{2 \times 3 + 8 \times 4 + 12 \times 5 + 32 \times 6 + 68 \times 7}{2 + 8 + 12 + 32 + 68} = 6.28$ feet nearly.

$$\begin{align*} y &= \frac{2 \times 1 + 8 \times 2 + 12 \times 3 + 32 \times 4 \times 68 \times 5}{2 + 8 + 12 + 32 + 68} = 4.28 \text{ feet nearly.} \end{align*}$$

But distance from corner $= \sqrt{x^2 + y^2} = \sqrt{(6.28)^2 + (4.28)^2} = 7.6$ feet nearly.

(3.) Four cannon-balls, whose weights are 1, 8, 32, and 68 lbs., are suspended in a room (of the form of a parallelopipedon), their vertical heights from the floor being 2, 4, 6, and 5 feet, respectively, and their perpendicular distances, from an end and side of the room, are 2, 4, 5, 6 feet, and 3, 5, 6, 7 feet, respectively; find the distance of the centre of gravity of the balls, from that corner of the room where the side and end, herein mentioned, intersect. Here the side, end, and floor of the rooms are the planes of reference, and the origin at the corner, mentioned in the question, the line where the side intersects the floor may be taken as the axis of \( x \), and the intersection of the end and floor as the axis of \( y \), or vice versa, the intersections of the end and side being the axis of \( z \).

\[ \begin{align*} x &= \frac{1 \times 2 + 8 \times 4 + 5 \times 32 + 6 \times 68}{1 + 8 + 32 + 68} = 5.523 \text{ ft. nearly}, \\ y &= \frac{1 \times 3 + 8 \times 5 + 32 \times 6 + 68 \times 7}{1 + 8 + 32 + 68} = 6.623 \\ z &= \frac{1 \times 2 + 8 \times 4 + 32 \times 6 + 68 \times 5}{1 + 8 + 32 + 68} = 5.192 \end{align*} \]

Again, it is easily shown that the distance of a point \( x, y, z \) from the origin is

\[ d = \sqrt{x^2 + y^2 + z^2} = \sqrt{(5.523)^2 + (6.623)^2 + (5.192)^2} = 10 \text{ feet nearly}. \]

For if XOY be the plane of the floor, XOZ the side, and YOZ the end of the room, G the centre of gravity. Draw GZ \( \perp \) to the plane XOY; and from Z draw ZX and ZY respectively, \( \perp \) to OX and OY; then \( OX = x, OY = y, GZ = z \). In the above equations, and since the triangles OXZ, OZG are right-angled,

\[ OG^2 = OZ^2 + GZ^2 = OX^2 + XZ^2 + GZ^2, \quad \text{and} \quad XZ^2 = OY^2 \]

\[ OG = \sqrt{OX^2 + OY^2 + GZ^2} \]

We might have determined the centre of gravity of any system of material points, or balls, not situated in the same line, or plane, and rigidly connected in the following manner: \( W_1, W_2, W_3, \ldots \) representing these material points and their positions, join \( W_1, W_2, \ldots \) and let \( G_1 \) be their common centre of gravity, then these two points will act in the same manner as if their weights were collected at the point \( G_1 \). Join \( G_1, W_3 \), and let \( G_2 \) be the centre of gravity of \( W_1, W_2 \), acting at \( G_1 \), and of \( W_3 \); then \( W_1, W_2, W_3 \) may be conceived to act at \( G_2 \). Join \( G_2, W_3, \ldots \) etc.

Note 7.—The principles made use of in equations (1.) may readily be extended to any body, or system of bodies; for, suppose the body referred to three co-ordinate planes mutually at right angles to each other, their common point of intersection being the origin, and \( x_1, y_1, z_1 \), the co-ordinates of any point in the body; then it is shown, in most works on the "Calculus," that the volume of an infinitesimal parallelopipedon, at that point, is represented by \( \Delta x \times \Delta y \times \Delta z \). Also, if \( \rho \) represents the density of a unit of volume at that point, its mass is the particle \( \rho \Delta x \Delta y \Delta z \), and its weight is \( \rho g \Delta x \Delta y \Delta z \). But as it is convenient to follow that we may either employ the weights or masses of the body in finding its centre of gravity, and

\[ M = \int (\Delta x_1 \Delta y_1 \Delta z_1 + \Delta x_2 \Delta y_2 \Delta z_2 + \ldots + \Delta x_n \Delta y_n \Delta z_n + \ldots) \]

\[ \bar{x} = \frac{\int (\Delta x_1 \Delta y_1 \Delta z_1 + \Delta x_2 \Delta y_2 \Delta z_2 + \ldots + \Delta x_n \Delta y_n \Delta z_n + \ldots)}{M} \]

\[ \bar{y} = \frac{\int (\Delta x_1 \Delta y_1 \Delta z_1 + \Delta x_2 \Delta y_2 \Delta z_2 + \ldots + \Delta x_n \Delta y_n \Delta z_n + \ldots)}{M} \]

\[ \bar{z} = \frac{\int (\Delta x_1 \Delta y_1 \Delta z_1 + \Delta x_2 \Delta y_2 \Delta z_2 + \ldots + \Delta x_n \Delta y_n \Delta z_n + \ldots)}{M} \]

But at the limit \( \Delta x_1, \Delta y_1, \Delta z_1 \) become \( dx_1, dy_1, dz_1 \), and dropping the suffixes, and extending the summation, or rather integration, to all the elements of the body, we obtain

\[ (1.) \quad M = \int \int \int dx \, dy \, dz \cdot \bar{z} \]

Where \( \bar{z} \) is given by an equation of the form \( \bar{z} = f(x, y, z) \).

Hence \( \bar{x} = \frac{\int \int \int x \, dx \, dy \, dz}{M}, \quad \bar{y} = \frac{\int \int \int y \, dx \, dy \, dz}{M}, \quad \bar{z} = \frac{\int \int \int z \, dx \, dy \, dz}{M} \]

These equations are to be taken between proper limits, and if the body is homogeneous, \( \bar{z} \) will appear in both numerators and denominators, and the equations may then be written:

\[ (2.) \quad \bar{x} = \frac{\int \int \int x \, dx \, dy \, dz}{V}, \quad \bar{y} = \frac{\int \int \int y \, dx \, dy \, dz}{V}, \quad \bar{z} = \frac{\int \int \int z \, dx \, dy \, dz}{V} \]

We may obtain a clearer idea of these integrals from the following considerations. Let us take the first of the latter set of equations, and integrate, first, in regard to \( x \), and next in regard to \( y \), observing that in these integrations \( z \) is constant, we may then write

\[ \bar{x} = \int \left[ \frac{\int \int y \, dx \, dz}{V} \right] \, dx \]

Where the quantity within the brackets represents the product of \( x \) by the area, \( A \), of a plane section of the figure, perpendicular to the axis of \( x \), and at a distance \( x \) from the plane of \( yz \).

\[ \bar{x} = \frac{\int A \, dx}{V}, \quad \text{and similar expressions may be obtained for } \bar{y} \]

If it be required to find the centre of gravity of any area, &c., we have only to suppose it to lie in the plane of \( xy \) and formulae (2) reduce to

\[ (3.) \quad \bar{x} = \frac{\int \int x \, dy \, dz}{A}, \quad \bar{y} = \frac{\int \int y \, dx \, dz}{A}, \quad \bar{z} = \frac{\int \int z \, dx \, dy}{A} \]

Remark.—In many cases it is convenient to employ polar co-ordinates to find centres of gravity, and we have for the transformation

\[ x = r \sin \theta \cos \phi, \quad y = r \sin \theta \sin \phi, \quad z = r \cos \theta \]

Formulae (2.) become

\[ \begin{align*} \bar{x} &= \frac{\int \int \int r^3 \sin^2 \theta \cos \phi \, dr \, d\theta \, d\phi}{\int \int \int r^2 \sin^2 \theta \, dr \, d\theta \, d\phi}, \\ \bar{y} &= \frac{\int \int \int r^3 \sin^2 \theta \sin \phi \, dr \, d\theta \, d\phi}{\int \int \int r^2 \sin^2 \theta \, dr \, d\theta \, d\phi}, \\ \bar{z} &= \frac{\int \int \int r^3 \cos \theta \, dr \, d\theta \, d\phi}{\int \int \int r^2 \sin^2 \theta \, dr \, d\theta \, d\phi}, \end{align*} \]

where \( \int \int \int r^2 \sin^2 \theta \, dr \, d\theta \, d\phi \) between proper limits gives the volume.

We shall at once proceed to show by formulae (3.) how to find the centre of gravity of an area, similar to the horizontal or vertical sections of a ship, premising that the notation is the same as that employed above (p. 140).

Note 8.—To find the centre of gravity of the portion \( A_1 \), the equation to the parabola passing through \( a_1, a_2, a_3 \) being \( b \) the common interval),

\[ y = A + Bx + Cx^2, \quad \text{denoting } A_1 y_1 \text{ and } A_1 y_1. \]

\[ \bar{x}_1 = \frac{\int \int xy \, dx \, dy}{\int \int y \, dx \, dy} = \frac{\int \int x(A + Bx + Cx^2) \, dx}{\int \int (A + Bx + Cx^2) \, dx} \]

\[ \bar{y}_1 = \frac{A^2}{3} \left\{ \frac{6A + 8BA + 12CA^2}{6A + 6BA + 8CA^2} \right\} = \frac{6A + 8BA + 12CA^2}{6A + 6BA + 8CA^2} \]

But by Note (1.), formulae (2., 5, and 6) \( A = a_1, B = \frac{a_2 - a_3}{2h}, \quad \text{and} \quad C = \frac{a_3 - 2a_2 + a_1}{2h^2} \).

Writing these in the above, we get

\[ \bar{x}_1 = \frac{2h(2a_2 + a_3)}{a_1 + a_2 + 4a_3} \]

In the same way, the centre of gravity of \( A_2 \), along the line \( A_1 A_3 \) is found to be

\[ A_2 y_2 = \frac{2h(2a_4 + a_5)}{a_2 + a_3 + 4a_4} \]

\[ \bar{y}_2 = A_1 A_3 + A_3 y_2 = 2h + \ldots \]

\( \Delta x_1, \Delta y_1, \Delta z_1 \) represent the respective increments of \( x_1, y_1, z_1 \).

Calculations incidental to designing a Ship.

\[ \frac{2}{a_1 + a_2 + a_3} \text{ or } \bar{x}_1 = A_1, \bar{x}_2 = A_2, \text{ etc.} \]

\[ \bar{x}_2 = 2h + \frac{2a_2 + a_3 + a_4}{a_2 + a_3 + a_4} = \frac{2b(a_2 + a_3 + a_4)}{a_2 + a_3 + a_4}. \]

\[ \bar{x}_3 = 4h + \frac{2(2a_2 + a_3)}{a_2 + a_3 + a_4} = \frac{2(2a_2 + a_3)}{a_2 + a_3 + a_4}. \]

And if \( g \) be the distance along the line \( A_1A_2 \) of the centre of gravity of the whole figure, we have by formula (2), since the areas may be supposed to be collected at their respective centres of gravity, \( G_1, G_2, G_3, \text{ etc.} \)

\[ A_g = \frac{\text{Area } A_1a_2 \times A_2g_1 + \text{Area } A_2a_3 \times A_3g_2 + \text{Area } A_3a_4 \times A_4g_3 + \text{Area } A_4a_5 \times A_5g_4 + \text{Area } A_5a_6 \times A_6g_5 + \text{etc.}}{\text{Area } A_1a_2 + \text{Area } A_2a_3 + \text{Area } A_3a_4 + \text{Area } A_4a_5 + \text{etc.}}. \]

Introducing the values of \( A_1, A_2, A_3, \text{ etc.}, \bar{x}_1, \bar{x}_2, \bar{x}_3, \text{ etc.} \) already found, this reduces to

\[ \bar{x} = \frac{1}{n} \left\{ \frac{(n-1)a_1 + 4(a_2 + a_3 + a_4 + a_5 + \text{etc.})}{a_1 + a_2 + a_3 + a_4 + a_5 + \text{etc.}} \right\}. \]

Next, to find \( G_y \) or \( \bar{y} \), we have

\[ \bar{y} = \frac{\int y^2 dx}{\int y dx}. \]

But \( y^2 = (\Lambda + Bx + Cx^2)^2 \); and this integration, added to the work connected with the substitution into the form

\[ \bar{y} = \frac{A_1y_1 + A_2y_2 + \text{etc.}}{A_1 + A_2 + \text{etc.}}. \]

would lead to an immense amount of labour, which may be avoided by observing that the integral \( \int y^2 dx \) may be taken to represent the area of a curve, the ordinates of which are the squares of those at given points of the curve, as \( a_1, a_2, a_3, \text{ etc.} \). With this understanding, we readily find, by employing "Simpson's Rule,"

\[ \bar{y} = \frac{1}{2} \left\{ \frac{a_1^2 + a_2^2 + a_3^2 + a_4^2 + \text{etc.}}{a_1 + a_2 + a_3 + a_4 + \text{etc.}} \right\}. \]

whence the centre of gravity of the curve is completely determined.

Note 9.—We next proceed to show how the centre of gravity of the volume of a figure similar to fig. 4, page 144, may be found, its equation being

\[ z = \Lambda + Bz + Cz^2 + B_1y + C_1y^2 + Dzy + Ez^2y + Fzy^2 + Gz^2y^2. \]

By formula 2 if we integrate in regard to \( z \),

\[ \bar{z} = \frac{\int zdxdy}{\int dxdy}. \]

\[ \int \frac{2h}{2k} \int \frac{2k}{2k} \int zdxdy(A + Bx + Cx^2 + By + Cy^2 + Dzy + Ez^2y + Fzy^2 + Gz^2y^2) \]

\[ = \frac{36Ah + 36Bh^2 + 72Ch^3 + 36B_1kh + 48C_1kh^2 + 48Dkh^3 + 64Ekh^4 + 48Fkh^5 + 64Gkh^6}{36Ah + 36Bh^2 + 48Ch^3 + 36B_1kh + 48C_1kh^2 + 48Dkh^3 + 64Ekh^4 + 48Fkh^5 + 64Gkh^6}. \]

Hence the centre of gravity of the displacement is determined; for we know that it will lie somewhere in the plane which cuts the vessel into two equal parts, and the value of \( \bar{z} \) gives its distance below the load-water plane, \( y \) gives its distance from the origin. which may be taken for convenience at the point of intersection of the load-water plane, the plane just mentioned, and the first vertical plane next the bow, or stern (as the calculator pleases). We will suppose the former, and that the centres of gravity of the small portions, fore and aft, and below the last horizontal plane, are not taken into account. Let \( V_f, V_m, V_b \) be their volumes, \( x_f, x_m, x_b \), \( y_f, y_m, y_b \), the distances of their centres of gravity from the origin.

Therefore, for the whole ship, \( V \) representing the volume between the first and last vertical sections,

\[ \bar{x} = \frac{V_f + V_m + V_b - V_f}{V + V_m + V_b} \]

\[ \bar{y} = \frac{V_f + V_m + V_b - V_f}{V + V_m + V_b} \]

Observe that \( \bar{x}, \bar{y} \) has a negative sign because it is in the opposite side of the origin to the other quantities, that is, \( \bar{x} \) is negative.

Note 10.—The mathematical reader will at once perceive that these are not the only rules which might be obtained to calculate the centre of gravity of a vessel. As has been remarked before, the Calculus of Finite Difference again comes to our aid; and, by neglecting small orders of differences, we may obtain any number of rules we please. As an instance, let us take the case given by Mr Weddle for a curve passing through seven points, and suppose sixth differences constant. We have for \( x \), using the same notation as in Note 3,

\[ x = \int_{a}^{b} y \, dx \text{ taken between proper limits; and } y = a + z + \Delta z + \Delta^2 z + \Delta^3 z + \Delta^4 z + \Delta^5 z + \Delta^6 z \]

Multiplying this by \( \Delta x = \frac{\Delta x}{\Delta x} \), we have

\[ \bar{x} = \frac{1}{\Delta x} \int_{a}^{b} y \, dx = \int_{a}^{b} \left[ a + z + \Delta z + \Delta^2 z + \Delta^3 z + \Delta^4 z + \Delta^5 z + \Delta^6 z \right] \, dx \]

Taking this integral from \( x = 0 \) to \( x = 6 \), or \( x = 0 \) to \( x = 6 \),

and multiplying by \( \Delta x \), we find, after considerable reductions,

\[ \bar{x} = \frac{1}{\Delta x} \left[ 18a + 72a + 126a + 606a + 657a + 639a + 123a + 78a \right] \]

We might obtain a tenth rule by neglecting small quantities; but we shall simply write down the total result, leaving the reader to obtain any other rules he may think proper.

\[ \bar{x} = a_1 + a_2 + a_3 + a_4 + a_5 + a_6 + a_7 + a_8 + a_9 + a_{10} \]

Introducing these values, and reducing

\[ \bar{x} = \frac{1}{\Delta x} \left[ 36a_1 + 9a_2 + 136a_3 + 18a_4 + 180a_5 + 61a_6 \right] \]

\[ = \frac{9a^2}{70} \left[ \frac{28a_1 + 5a_2}{9} + 4(a_2 + 3a_3 + 5a_4) + (a_3 + 2a_4 + 4a_5) \right] \]

which will give a result much more accurate than that obtained by "Simpson's Rule." The result for \( \bar{y} \) may be obtained by "Simpson's Rule," or by squaring the value of \( y \), given above, and neglecting the squares and products of higher order of differences.

Note 11.—The reader will have no difficulty in obtaining for Property of any plane surface

\[ \bar{y} = \int_{a}^{b} y \, dx \, dy \]

or \( \bar{y} \times A = \frac{1}{2} \int_{a}^{b} (Y_1^2 - Y_2^2) \, dx \); if \( A \) represent the area of the surface, and \( Y_1, Y_2 \) denote the limits of \( y \). Multiply both sides by \( 2\pi \).

\[ \therefore A \times 2\pi \bar{y} = \pi \int_{a}^{b} Y_1^2 \, dx - \pi \int_{a}^{b} Y_2^2 \, dx \]

The left hand side is the area of the surface multiplied by the circumference described by its centre of gravity, and the right hand side denotes the difference of the volumes of revolution described by the plane surfaces comprised between the axis of \( x \), the extreme ordinates, and the two curves which terminate the generating surface.

(1.) Find the centre of gravity of an area, similar to fig. Examples (1.) page 140, the equidistant ordinates measuring 2-5, 3, 3-5, 4, 5, 6, 5-5, 5, 4, 3, 2, 1-5 and 1 feet, respectively, the common interval being 2 feet.

1st. To find the Area by "Simpson's Rule."

| Ordinates | Ordinates | Ordinates | |-----------|-----------|-----------| | 2-5 first ordinate | 3 second ord. | 3-5 third ordinate | | 1-0 last | 4 fourth | 5-0 fifth | | 6 sixth | 6-5 seventh | | | 5 eighth | 4-0 ninth | | | 3 tenth | 2-5 eleventh | | | 1-5 twelfth | | | | 20 sum of odd ord. | | | | 22-5 sum of | | | | 4 | | | | 40 twice sum of ord. | | | | 90-0 four times sum of ordinate. | | | | 400 twice sum of odd | | | | 3-5 sum of first and last | | | | 133-5 | | | | 2 common interval. | | | | 3/267 | | | | 89 = area. | | |

2d. To find the Distance of the Centre of Gravity from \( A \).

| 1st, 2-5 x 0 = 0 | ordinates multiplied by 0, 1, 2, 3, &c. | |------------------|----------------------------------------| | 2d, 3 x 1 = 3 | | | 3d, 3-5 x 2 = 7 | | | 4th, 4 x 3 = 12 | | | 5th, 4 x 4 = 20 | | | 6th, 6 x 5 = 30 | | | 7th, 5-5 x 6 = 33| | | 8th, 5 x 7 = 35 | | | 9th, 4 x 8 = 32 | | | 10th, 3 x 9 = 27 | | | 11th, 2 x 10 = 20| | | 12th, 1-5 x 11 = 16-5| | | 13th, 1 x 12 = 12 | |

Calculations incidental to designing a Ship.

By "Simpson's Rule."

Results. 0 first result. 12 last 12 sum of

Remains. 3 second result. 12 fourth 30 sixth 34 eighth 27 tenth 16-5 twelfth

Results. 7 third result. 29 fifth 33 seventh 32 ninth 20 eleventh

112 sum of odd results.

123-5 sum of even results.

494 four times 224 two times 12 first and last

730 2 common interval.

31460

486-66 2 common interval.

973-3

Distance of centre of gravity from $A_1 = \frac{973-3}{89} = 12-4344$.

$(2-5)^2 = 6-25$ $3^2 = 9-00$ $3^2 = 9-00$ $4^2 = 16-00$ $5^2 = 25-00$ $6^2 = 36-00$ $(6-5)^2 = 30-25$ $5^2 = 25-00$ $4^2 = 16-00$ $3^2 = 9-00$ $2^2 = 4-00$ $(1-5)^2 = 2-25$ $1^2 = 1$

$7-25$ sum of first and last ordinates squared.

$389-00$ $175-00$

$571-25$

By last process, we have

$\therefore$ Perpendicular $Gy = \frac{571-25 \times 1}{207 \times 4} = 2-139$, &c.

2. Find the centre of gravity of a figure similar to the above, when the ordinates are taken 3 feet apart, and measure 1-25, 2-35, 4-56, 7-87, 8-97, 9-65, 10-54, 9-97, 8-65, 7-54, 6-34, 7-43, 5-42, 4-53, 4-23 feet, respectively.

Distance along the axis from $A_1 = 20-82$. Distance above the axis at the above point = 3-945.

(3.) Find the same, as in the last example, when the equidistant ordinates measure 20, 20-5, 21, 22, 22-5, 23, 24-5, 25, 26; 25, 24, 23; 23, 22-5, 21, 20; 19, 18, and 17 feet, respectively, and are taken at 6 feet apart.

Distance along the axis $A_1 A_n$ from $A_1 = 52-42$. Perpendicular distance above ditto at the above point = 11-18.

(4.) Find the same, as in the former examples, when the ordinates are 0, 2, 3, 3-5, 4-5, 5, 6, 7-5, 8, 8-5, 9, 8, 7, 6, 5-5, 4-5, 4, 3-5, 3, 2-5, and 2 feet, and their distance apart is 2 feet.

Distance along $A_1 A_n$ from $A_1 = 20$ feet nearly. Distance above $A_1 A_n$ at the above point = 3-0506.

(5.) Find the same when the equidistant ordinates measure 17, 18, 18-5, 19, 19-5, 20, 20-5, 21, 22, 22, 22, 21-5, 20, 19, and 18 feet, their distance apart being 4 feet apart.

Distance along $A_1 A_n$ from $A_1 = 28-605$. Distance above $A_1 A_n$ at the above point = 10-134.

Examples on the Calculation of the Centre of Gravity of Displacement.

Half-Horizontal Areas, square feet.

| Half-Areas multiplied by | 0, 1, 2, 3, &c. | |--------------------------|---------------| | 250-25 x 0 | 000-00 | | 300-05 x 1 | 300-05 | | 325-00 x 2 | 650-00 | | 400-25 x 3 | 1200-75 | | 405-25 x 4 | 1621-00 | | 450-65 x 5 | 2253-25 | | 470-75 x 6 | 2824-50 | | 490-00 x 7 | 3430-00 | | 495-25 x 8 | 3962-00 | | 500-00 x 9 | 4500-00 | | 487-65 x 10 | 4870-50 | | 470-55 x 11 | 5176-05 | | 460-25 x 12 | 5527-80 | | 450-75 x 13 | 5859-75 | | 435-25 x 14 | 6093-50 | | 400-15 x 15 | 6002-25 | | 390-00 x 16 | 6240-00 | | 375-25 x 17 | 6379-25 | | 350-00 x 18 | 6300-00 |

$7643-23 =$ volume by Simpson's Rule.

Half-vertical Areas in square feet.

| Half-Areas multiplied by | 0, 1, 2, &c., respectively. | |--------------------------|-----------------------------| | 4975 x 0 | 000-00 | | 49-95 x 1 | 49-95 | | 52-00 x 2 | 104-00 | | 54-25 x 3 | 162-75 | | 56-45 x 4 | 225-80 | | 78-43 x 5 | 392-15 | | 60-00 x 6 | 360-00 | | 55-25 x 7 | 388-75 | | 48-65 x 8 | 389-20 | | 47-00 x 9 | 423-00 | | 45-75 x 10 | 457-50 | | 43-50 x 11 | 478-50 | | 42-23 x 12 | 506-75 | | 40-22 x 13 | 522-85 | | 38-21 x 14 | 534-94 |

Volume by Simpson's Rule = 7643-23 nearly.

1st. Beginning with the results in the right hand column of the horizontal section,

| Results. | Results. | |----------|----------| | 0000-000 | 300-05 | | 6300-000 | 1200-75 | | | 2253-25 | | | 3430-00 | | | 4500-00 | | | 5176-05 | | | 5859-75 | | | 6002-25 | | | 6379-25 | | | [results.] | | | 31795-30 | | | sum of odd | | | 2 | | | 35101-35 | | | sum of even | | | 4 | | | 63590-6 | | | twice do. | | | 63590-6 | | | twice sum of odd | | | do. | | | 6300-0 | | | sum of first and last do. | | | 210296 | | | 1 common interval. | | | 3210296 |

70098-6 result obtained by "Simpson's Rule."

---

1 The calculator will always have a check on his work by observing the length of the axis $A_1 A_n$ and observing also whether or not the ordinates near the beginning differ widely from those at the end. If the ordinates do not differ widely in this sense, the centre of gravity will be determined by a line perpendicular to the axis near its middle point. If the ordinates are greater near the beginning than at the end, the centre of gravity determined along $A_1 A_n$ will be nearer the first ordinate than the last, and vice versa. Therefore, distance of centre of gravity of main body below the plane of flotation = \(\frac{70098}{\text{volume}} = 7643-23 = 9-17\) feet.

24. Taking the results in the right hand column of the vertical section,

| Results | Results | Results | |---------|---------|---------| | 000-00 first result | 49-05 | 104-00 | | 534-94 last do. | 162-75 | 222-80 | | 392-15 | 360-00 | | 534-94 sum of do. | 386-75 | 389-20 | | 423-00 | 467-50 | | 478-50 | 506-76 | | 622-86 | [results. 2043-26 sum of odd] | | 2415-96 sum of even | 2 | | 4 | 4086-52 twice do. | | 9683-84 four times do. | | | 4086-52 twice sum of odd do. | | | 534-94 sum of first and last. | |

10-56 common distance.

| 14285-30 | | 857118 | | 714255 | | 1423530 | | 3)150852768 |

[Rule.]

50284-256 result obtained by "Simpson's"

10-56 common distance.

| 301705535 | | 251421280 | | 502842560 | | 531601-74336 |

Distance of centre of gravity from first vertical section \(= \frac{531601-74}{7643-23} = 69-47\) feet.

We shall suppose the first vertical section 49-75 to be that nearest the bow, and

234-25 cubic feet, to be the volume of the portion below the last horizontal section, or the portion just above the keel.

22-5 feet, the distance of its centre of gravity below the plane of flotation.

70° from the first vertical plane.

324-75 cubic feet, the volume of the portion before the first vertical plane, or between this plane and the bow.

10 and 7 feet, the respective distances of the centre of gravity from the same planes as above.

576-00 cubic feet, the volume of the portion aft of the last vertical plane, or lying between this plane and the stern.

8 and 150 feet, the respective distances of the centre of gravity from the planes already mentioned.

Then, if \(d_f, d_v\) be the distances of the centre of gravity of the total displacement from the planes of flotation and first vertical, we have

\[d_f = \frac{7643-23 \times 9-17 + 234-25 \times 22-5 + 324-75 \times 10 + 576 \times 8}{7643-23 + 234-25 + 324-75 + 576} = 9-48 \text{ feet below the plane of flotation.}\]

\[d_v = \frac{7643-23 \times 69-47 + 234-25 \times 70 + 576 \times 160 - 324-75 \times 7}{7643-23 + 234-25 + 576 + 324-75} = 71-8 \text{ nearly.}\]

The reader will perceive that all the quantities are added in obtaining the former result, and that the last one is subtracted in the latter case. The reason for this is, that, in the latter case, the portion forward lies on the opposite side of the first vertical plane to all the rest, or is measured, what we have called, backwards. Now, if we had considered the first vertical section, 49-75, as being taken at the stern, then 324-75 \times 7 would have been added, and 576 \times 160 subtracted, in consequence of the portion aft lying, in this case, on the opposite side of the first vertical plane to the other portions. In the first result, all the portions lie below the plane of flotation. We also perceive that the centre of gravity lies between the sixth and seventh vertical sections, inasmuch as their common distance is 10-56, and 10-56 \times 6 = 63-36; also, 10-56 \times 7 = 73-92; therefore 71-8 - 63-36 = 8-44 feet abaft the sixth section.

STABILITY OF FLOATING BODIES.

Art. 6.—Various definitions have been given of the Theory: stability of floating bodies. The reader will probably comprehend the term from the explanation and definitions principles which follow.

Euler, in his Theory of the Construction of Vessels, &c., as translated by Colonel Watson, observes, that "As soon as a vessel becomes ever so little inclined, or displaced from its state of equilibrium, three consequences may happen:—1st. Either the vessel remains in the inclined state; or, 2ndly, It re-establishes itself in its preceding situation, when its equilibrium will be permanent, or rather, it will be endowed with a stability which may be great or little according to circumstances; or, 3rdly, The vessel after this inclination will be completely overturned. This equilibrium is called unstable, or ready to fall. We can see, evidently, that neither this last case nor the first can have place in vessels; and, with respect to the second case, a sufficient stability is absolutely necessary."

The last remarks here made are not altogether true when a vessel is inclined through considerable angles by impulsive forces. We shall therefore proceed to investigate the different kinds of stability.

Def. (I)—Statical Stability is defined to be the movement of force (or effort), by which a floating body endeavours to regain its upright or vertical position, after having been deflected from that position.

Def. (II)—Dynamical Stability is defined to be the amount of work done on any body, in order to deflect it through any angle from its upright position.

As has already been stated, it is shown in books on Hydrosstatics, that when a body floats in equilibrium, the following conditions must be fulfilled:

1st. \(\rho g V_d = M\), or simply \(V_d = M\),

where \(M\) represents the mass of the floating body, \(V_d\) the volume of water displaced, \(\rho\) the density of a cubic unit (say a cubic foot) of water, and \(g\) the accelerating force of gravity.

2nd. The centres of gravity of the body, and of the water which it displaces, must lie in the same vertical line—that is, in a line at right angles to the plane of flotation.

From the first condition, namely \(V_d = M\), it is at once manifest, that in many bodies, such as some of the solids of revolution, this will furnish us with an infinite number of positions of equilibrium, for all of which the second condition will be fulfilled.

When a body is inclined through any angle from its upright position, the point of stability will differ in position from the plane of flotation in the former case; and for every plane of flotation the centres of gravity of the vessel and its displacement will,

1 Vide chap. iv., sect. 22, of the work here mentioned.

2 By the amount of work, here alluded to, is meant the weight of the body, in pounds avoirdupois, multiplied by the vertical height, in feet, of the sum or difference of displacements of the centres of gravity of the body and of the water which it displaces. Stability in general, have different positions. If we suppose the vessel to be floating roll and pitch uniformly through any finite angles, the centre of gravity of displacement \( G_d \) or centre of buoyancy, as this point is sometimes called, will describe a portion of a surface in the interior of the vessel.

It will readily be comprehended by the reader, that a vessel may possess a great amount of both kinds of stability specified in the definitions up to a certain point, that is, through a given angle from its upright position, and then instantaneously become unstable. Sufficient attention has not been paid to this fact, inasmuch as writers on stability, as applied to ships, generally neglect to discuss the case of unstable equilibrium. It is a well-known fact, that ships have been capsized through unforeseen impulsive forces, as in the case of the Royal George. When the vessel has been inclined through an angle, it has been always customary to assume that the centre of the section which is immersed is equal to that which is emerged. This is not accurately true on account of the inertia of the vessel and the water, as well as on account of the effect of the wind in the sails, which may tend to increase the total displacement.

**Art. 7. Theorem I.—The line joining the centres of gravity of the displacement of the body in any two positions is parallel to the line joining the centres of gravity of the immersed and emerged portions due to these positions.**

For, let \( FKL' \) represent a transverse section of the body, made by the plane of the paper, and \( G_d, G'_d \) the projections of the centre of gravity of displacement in the two positions, \( g_d, g'_d \) the projections of the centres of gravity of the emerged and immersed volumes due to the two positions.

Then the immersed portion of the body in the two positions will have the common part \( V_d - v \) (the section of which is shown by \( F'PLK \)), where \( v \) represents the volume of the part emerged or immersed.

Let \( O' \) be the projection of the centre of gravity of the volume \( V_d - v \) on the plane of the paper, then by the principles which have been already enunciated (Art. 4, p. 147, &c.), the centre of gravity \( G_d \) is determined from

\[ G_d g_d x = G_d O' \times (V_d - v) \]

and the centre of gravity \( G'_d \) in like manner from

\[ g'_d G'_d x = G'_d O' \times (V_d - v) \]

By (1) and (2)

\[ g_d G_d x = G_d O' \times (V_d - v) \]

or,

\[ g_d G_d : G_d O' :: g'_d G'_d : G'_d O' \]

hence \( G_d G'_d \) is parallel to \( g_d g'_d \). (Euclid, vi. 2.)

Next, if we consider the volumes immersed and emerged to be infinitely small, or, in other words, the two planes of flotation, of which \( ML, F'L' \) are the projections, to be indefinitely near, the centres of gravity of these two volumes may be considered situated in the plane of flotation (\( FL \)). In this case \( G_d G'_d \) becomes parallel to \( FL \), that is, \( G_d G'_d \) becomes a tangent at \( G_d \) to the curve traced out by the latter point in the plane of the paper. This is rigorously true at the limit, no matter in which direction we suppose the body to revolve (through an infinitely small angle); it follows, therefore, that all the tangents drawn through \( G_d \) are parallel to the plane of flotation; hence

**Theorem II.—The tangent plane, drawn through the centre of gravity of displacement in position to the surface traced out by this point during the rolling and pitching of the vessel, is parallel to the plane of flotation corresponding to that position.**

**Art. 8.—If \( G \) (fig. 7) denote the centre of gravity of the floating body, and \( G_d \) that of the water displaced, then in positions of equilibrium \( G_d G \) is a normal to the surface described by the latter points. For, by the second condition of equilibrium, given in Art. 14, \( G_d G \) is necessarily perpendicular to the plane of flotation, and, therefore, perpendicular to the tangent-plane at the point \( G_d \), since the latter plane is parallel to the former. Let us suppose the surface traced out by \( G_d \) to be actually described, then if from \( G \), the centre of gravity of the body, we draw all the normals which it is possible to do from this point to the surface, we shall determine as many positions of \( G_d \) as there are normals, and consequently as many planes of flotation, for all of which there will be equilibrium of one kind or the other—that is, stable or unstable.

A rolling motion will be sufficient to establish the following principles:

Let us suppose the plane of the paper to be that transverse vertical section of the vessel which contains the centre of gravity of the vessel and its displacement when floating at rest. Next let the body be made to roll through any angle, and the point \( G_d \) will describe a curve in the same plane, which is represented by \( AGB \).

Let \( G_d, G'_d \) (fig. 7) be two consecutive positions of the centre of gravity of displacement (that is, two positions indefinitely near to each other); draw normals through these two points to the curve \( AGB \), and let them intersect in \( M \), the latter point in geometry and analysis receives the name of the centre of curvature; but in regard to the floating body it was named by Bouguer the meta-centre, and the circle described through \( G_d \) with radius \( MG_d \) is called the circle of curvature, or sometimes the oscillating circle.

The curve described by the centre of gravity of displacement (centre of buoyancy) has been named the metacentric curve. Mr Read, late master-shipwright of H.M. Dockyard, Sheerness, pro-

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1 By a rolling motion is understood a motion about a longitudinal axis, or from stem to stern. By a pitching motion is to be understood the motion of the vessel about an axis at right angles to the former axis, or about an axis which lies in a transverse vertical section. During a rolling motion only, the centre of gravity of the vessel will remain in the same transverse section; and during a pitching motion only, the centre of gravity will remain in a vertical section at right angles to the former. When the motion is due to rolling and pitching combined, the vessel will revolve about an instantaneous axis, which may be determined.

2 And in all probability many other vessels.

3 By a tangent-plane is here meant a plane which touches the surface described by \( G_d \) at a given point, and which, if produced, does not intersect this surface. For the general definition of a tangent-plane and its properties, see Hymers's and Gregory and Walton's Geometry of Three Dimensions.

4 By a normal to a surface at a given point is meant the line drawn at right angles to the tangent-plane at that point. Stability posed to call it the metacentric formula, and the curve described by floating M with the metacentric formula, which terms are strictly in accordance with mathematical theory.

It will be seen hereafter that the position of the metacentre is of the greatest importance in the determination of the stability and times of oscillation of vessels. Its height above the centre of gravity of displacement may be determined as follows—

Art. 9.—The notation and figure remaining the same as in the previous article; the ordinates measured on the half-breadth plan at the load-water line being employed.

Rule XIV.—Cube the ordinates measured on the half-breadth plan, introduce these cubes as ordinates in Rule I., p. 140, and proceed as therein stated; divide the result thus obtained by the volume of water displaced, and two-thirds of the quotient gives the distance of the metacentre from the centre of gravity of displacement.

Let the vessel be slightly inclined from its upright position, we may consider the areas FPF' and LPL' to be two equal sectors of the same circle; then \( g_1 \) \( g_2 \), the line joining their centres of gravity, will bisect this angle. Draw \( g_1 P_1 \) \( g_2 q_1 \) perpendicular to FF', and \( G_d R \) perpendicular to MG'.

Let \( r = FP = F'P = LP = L'P \), and it is well known that the centres of gravity are determined by

\[ P_g = P_g = \frac{2}{3} r \text{ chord } FF' = \frac{2}{3} r \text{ chord } LL' \]

\[ = 4r \sin \frac{\phi}{2}, \quad \phi \text{ being } < FPP' \]

But area of sector FPF' or LPL' \( = \frac{r^2 \phi}{2} \). And

\[ P_p = P_q = P_g \cos \frac{\phi}{2} = P_g \cos \frac{\phi}{2} = \frac{4}{3} r \sin \frac{\phi}{2} \]

Also moment of sector FPF', or sector LPL', \( = \text{area } FPF' \times P_p \)

\[ = \text{area } LPL' \times P_q = \frac{r^2 \phi}{2} \times 2 \sin \frac{\phi}{2} \]

\[ = \frac{r^2 \sin \phi}{3} \quad \ldots \quad (I) \]

Now, since the solids emerged and immersed are supposed to be equal, and that these solids may be conceived to be collected at their respective centres of gravity, it is clear that the centre of gravity of the volume of water emerged has been moved from \( p_1 \) to \( q_1 \) in the direction \( F'L' \), while the total volume of water displaced by the vessel has been transferred from \( G_d \) to \( R \) in a parallel direction. Hence taking moments, we have, by elementary mechanical principles,

\[ G_d R \times \text{Vd} = P_1 q_1 \times v \quad \ldots \quad (II) \]

Or, \( G_d R \cdot Vd = P_1 q_1 \cdot v \).

But the angle FPP' = angle \( G_d MG' \) between two consecutive normals

\[ MG_d \sin \phi = G_d R \]

From (II) \( MG_d = \frac{P_1 q_1 \cdot v}{Vd \sin \phi} \quad \ldots \quad (III) \]

Now, if we imagine a plane drawn parallel to the plane of the paper, or to the section shown in the figure, and at the infinitesimal distance \( \Delta x \), the moments of the volumes of the solids emerged and immersed will be represented by

\[ \frac{\sin \phi}{3} \times r^2 \Delta x, \text{ from (I)}, \text{ or } \frac{\sin \phi}{3} \int r^2 dx; \]

by employing the notation of the Integral Calculus, observing that the integral here given must be taken from stem to stern.

\[ MG_d = \frac{2 \sin \phi}{3} \int \frac{1}{Vd \sin \phi} r^2 dx \quad \ldots \quad \text{from (III)} \]

\[ = \frac{2}{3} Vd \int r^2 dx \quad \ldots \quad (IV) \]

The integral, \( \int r^2 dx \) is sometimes named the moment of inertia of floating the load-water section \( FL \), about a horizontal axis through the centre of gravity.

It ought to be observed that, though we have here obtained the position of the metacentre of the vessel when in a vertical position, this point may in like manner be obtained, by employing the same rule, when the vessel is inclined through any angle, provided we substitute the ordinates of the inclined load-water section for those of the load-water section of the vessel when in an upright position.

Art. 10.—Having obtained the position of the metacentre, we are now in a position to determine the nature of the equilibrium when a vessel is in any position; for, if we call the lengths of the lines drawn from \( G \), perpendicular to the curve described by \( G_d \) normals, then

**Theorem III.**—Positions of stable equilibrium correspond to minimum normals, and positions of unstable equilibrium correspond to maximum normals; also these normals will have alternately maximum and minimum values.

Various demonstrations of this theorem have been given in books on Hydrostatics, and the reader will find the subject discussed in the Mechanic's Magazine, a periodical which contains many valuable papers on shipbuilding. The following exposition of the principle may be found sufficient for the mathematical reader.

If (fig. 7) \( M \) be the centre of curvature corresponding to \( G_d \), and situated at first above \( G \), the osculating circle at \( G_d \) will lie both within and without the curve \( AG_d B \) in the immediate neighbourhood of \( G_d \), and the circle described from \( G \) as a centre, with radius \( GG_d \), will lie entirely within the curve in the vicinity of \( G_d \), and the normal \( GG_d \) will be a minimum normal for all those drawn from \( G \) to the points of the curve in the neighborhood of \( G_d \); that is, \( GG_d \) will be less than \( GG_d \) and \( GG_d \). If \( M \) lie below \( G \), we learn by the same reasoning that \( GG_d \) is greater than \( GG_d \) and \( GG_d \), since the circle described from \( G \) with radius \( GG_d \) lies entirely without the curve \( AG_d B \); that is, the contact is of the third order.

These normals are alternately maxima and minima, since between two maximum values there is a minimum, and a maximum between two minima. There are as many maximums as minimum values; hence the number of positions of equilibrium, neglecting the kind, is even. Moreover,

**Theorem IV.**—When the metacentre lies above the centre of gravity of the vessel, the equilibrium is stable.

For, if we incline the vessel in such a manner that \( G_d \) shall be at \( G_d \), indefinitely near to \( G_d \), the normal at \( G_d \) will pass through \( M \) (since the latter point is the intersection of two consecutive normals); then the weight of the water displaced applied at \( G_d \) will be parallel to \( MG_d \), and will act upwards, whilst the weight of the body at \( G \) will act downwards in the direction parallel to \( MG_d \), and it is evident that the effect of these two forces will be to bring the points \( M \) and \( G_d \) into their original position.

**Theorem V.**—When the metacentre lies below the centre of gravity of the vessel, the equilibrium is unstable.

For, inclining the vessel as before, through an indefinitely small angle, the effect of the two forces just mentioned will be to bring \( G_d \) and \( M \) into a vertical position; and since \( G \) is above \( M \), the vessel will be capsized.

**Theorem VI.**—When the metacentre coincides with the centre of gravity, the equilibrium is said to be indifferent or neutral; that is, the vessel will rest in the position in which it is then placed.

Art. 11.—Having obtained the kind of stability, we may

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1 The metacentric curve is that made by any plane (a transverse vertical one in the present case) with the metacentric surface. 2 It is not necessary to consider the sectors as equal, providing we bisect the angle FPP'; and with centre \( P \) and radii \( PC, PC' \), we describe arcs of circles intersecting the two planes of flotation (the projections of which are \( FL \) and \( F'L' \)), the same result as is obtained below may be shown to hold true. 3 Because \( 2 \sin \frac{\phi}{2} \cos \frac{\phi}{2} = \sin \phi \). 4 Maximum and minimum values mean greatest and least values. 5 See Hall's Calculus, p. 200. Stability at once obtain the analytical condition for the natural stability of floating bodies after having proved the following:

**Theorem VII.**—The centre of gravity of a plane of flotation lies on the line of its intersection with a plane of flotation indefinitely near to the former plane.

Let \( PQ \) represent the intersection of the two planes here mentioned, \( g, g' \), the centres of gravity of the areas \( EPQ \) and \( LIPQ \), the areas being denoted by \( A \) and \( A' \). Now, the centre of gravity of \( PFLQ \) is obtained by dividing \( g, g' \) into two parts reciprocally proportional to those areas. Let, then, \( l \) be the infinitely small angle between the two planes of flotation, \( l \) and \( r \) the perpendicular distances of \( g, g' \) from \( PQ \). As the wedge-like portions emerged and immersed are exceedingly small, we may apply the principle of Guldinus, given at page 147, viz.:—

Volume \( F'FPQ = Al\phi \), and volume \( LL'PQ = Al'\phi \); and since these volumes are equal

\[ \begin{align*} Al\phi &= Al'\phi \\ \text{that is, } l : l' : : A : A' \\ \end{align*} \]

From the similar triangles \( ghO \) and \( g'O \), we have

\[ l : l' : : gO : g'O \]

hence by (1) and (2),

\[ gO : g'O : : A : A' \]

that is, \( O \) is the centre of gravity of the plane of flotation.

It is clear that the point \( O \) will trace out a curve in the plane of the paper, provided the body be made to revolve through a finite angle in this direction, and \( F'L' \) is a tangent at \( O \) to this curve. Moreover, the vessel might be made to revolve in any direction, and the point \( O \) would then trace out what is called the surface of flotation. From the manner in which we have obtained the result just given, we arrive at Euler's theorem, viz.—

The point of contact of the plane of flotation with the surface of flotation is the centre of gravity of that plane.

Moreover, if we conceive \( (\Delta A) \) to represent an elemental portion of the plane \( FPQ \), and \( r_1 \) the distance of this element from \( PQ \), then \( \phi (\Delta A) r_1 \) will represent the corresponding volume of the portion \( FPQ \), assuming it to be a solid of revolution, and the total volume is got from

\[ v = \phi \left[ (\Delta A_1) r_1 + (\Delta A_2) r_2 + (\Delta A_3) r_3 + \ldots \right] = \phi \int (\Delta A) r \]

We know from the formula for determining the centre of gravity of bodies (p. 146), that

\[ gO = \frac{\phi}{\int (\Delta A) r^2} \int (\Delta A) r^2 \]

By employing the notation of the Integral Calculus, and bearing in mind that these integrals are to be taken between proper limits:—

Now, \( \int (\Delta A) r^2 \) is called the moment of inertia of the plane \( PQF \) in regard to the axis \( PQ \), the density being unity.

\[ gO = \frac{\phi k}{v}, \quad k_1 \text{ representing this moment of inertia; also, } g'O = \frac{\phi k}{v}, \quad k_2 \text{ represents the moment of inertia of the plane } LPQ, \text{ in regard to the same axis. } \]

But \( gO + g'O = \frac{\phi (k_1 + k_2)}{v} = \frac{\phi k}{v} \), being the moment of inertia of the plane \( PFLQ \) in regard to \( PQ \). Returning again to fig. 7, where \( g_e, g_i \) represent the centres of gravity of the infinitely small volumes emerged and immersed, we have shown that \( g_e g_i \) is parallel to \( GdG'd \).

\[ \begin{align*} GdG'd &= \frac{V_d}{v} = \frac{\phi k}{V_d} \\ \end{align*} \]

and \( \phi \) being the angle between two consecutive normals, then

\[ MG_d = \frac{GdG'd}{\sin \phi} = \frac{GdG'd}{\phi}, \quad \text{since } \phi \text{ is exceedingly small, and the sine may be taken equal to the arc, and } g_e g_i \text{ is the same as the value of } g'g \text{ (given above) at the limit; hence } MG_d = \frac{k}{V_d} = \frac{\phi k}{W} \quad \text{(I)} \]

We have seen that the condition of stable equilibrium is \( MG_d > GG_d \); so that if \( h \) denote the distance \( GG_d \), the condition is

\[ \frac{k}{V_d} > h, \quad \text{or } \frac{\phi k}{W} > h \quad \text{(II)} \]

**Theorem VIII.**—The moment of inertia of the plane of flotation must be greater than the product of the volume of water displaced, and the distance between the centres of gravity of the body and its displacement.

The value of \( k \) may be found from Equation IV., Art. 9.

From (I) \( G_dM = GG_d + GM = \frac{\phi k}{W} \)

\[ GM = \frac{\phi k}{W} - GG_d \quad \text{(III)} \]

**Art. 12.**—To determine the line of intersection of the plane of flotation of the vessel, when in a vertical position with the plane of flotation, when the vessel has been inclined through any angle; or to determine the point \( P \) (fig. 7) of the intersection of \( FL \) and \( F'L' \).

Through \( O \) (fig. 7), the middle point of \( FL \), draw \( f't \), making the angle \( FOF' = LOI = \) given angle \( \phi \). Let the volumes, of which \( FO \) and \( LOI \) are sections, be represented by \( V_1 \) and \( V_2 \), respectively; also, let \( v_1 \) and \( v_2 \) represent the volumes of which \( EPQ \) and \( LPQ \) are sections, and \( v \) volume emerged or immersed; then

\[ V_2 = v + v_2 \\ V_1 = v - v_1 \\ V_2 - V_1 = v_1 + v_2 \]

area plane \( f't \times OE \) (nearly) where \( OE \) is drawn perpendicular to \( F'L' \).

But \( OE = OP \sin \phi \)

\[ OP = \frac{V_2 - V_1}{\text{area plane } f't \sin \phi} \quad \text{(I)} \]

Various methods have been recommended for the calculation of the solids \( V_2 \) and \( V_1 \) as well as for the volume \( v \), all three of which are obtained in the same way. The following plan will guide the reader to find them.

1st. Join \( PP' \) and \( LL' \), and the areas of the triangles \( PPP' \) or \( LPL' = \frac{PP' \times L'L' \sin \phi}{2} \) or \( \frac{LP' \times L'L' \sin \phi}{2} \).

2nd. The curves \( FCF' \) and \( LC'L' \) may be considered as parabolas, and the areas lying between \( F'L' \) or \( LL' \) and the curves are equal to \( \frac{2PP' \times \text{perpendicular height of segment } FCF'}{3} \), and \( \frac{2LL' \times \text{perpendicular height of segment } LC'L'}{3} \); or we may employ instead of 2nd to find the areas of the segments just mentioned.

3rd. When \( \phi \) is very large, ordinates may be measured at right angles to \( F'L' \) and \( LL' \) (seven will always be sufficient), and at equal distances apart, and the area found by Rule (III), Art. I. (or by Rule L)

4th. Having found the areas \( FPF' \) and \( LPL' \) made by each vertical section, introduce these as ordinates in Rule (I.), and proceed as therein stated.

Remark.—Several writers have proposed to draw the ordinates, mentioned in (3), parallel to the plane of flotation. There is, however, little labour saved by such a plan.

For a very large number of vessels, which are full below the load-water plane, the following method may be applied, and will, it is believed, be found almost as accurate as those just recommended. Bisect the angle \( FPF' \) by the line \( CC' \), and with radii \( PC, PC' \), describe the arcs \( HCH' \) and \( NCN' \); then the sectors will, in general, be very nearly equal in area to the portions \( FPF' \) and \( LPL' \). If \( CP = r \), and \( CP' = r \), then the area of the sector \( HCH' = \frac{r^2 \phi}{2} \), and area \( NPN' = \frac{r^2 \phi}{2} \). Summing these areas (by Rule

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1 We here suppose that the volumes emerged and immersed are solids of revolution, that is, solids described by the revolution of the planes \( FPQ \) and \( LPQ \) round \( PQ \). This assumption will be accurate enough when the angle \( \phi \) is very small, as we have assumed it to be. Stability L) from stem to stern, and writing \( r_1, r_2, r_3, \ldots \) for the 1st, 2d, 3d, etc., of Floating &c., radius, with similar expressions for \( r, s, t, \ldots \), we have

\[ \text{Volume emerged} = \frac{h^2}{6} \left[ r_1^2 + r_2^2 + \cdots + (r_1^2 + r_2^2 + \cdots) + 2(r_1^2 + r_2^2 + \cdots) \right] \]

\[ \text{Volume immersed} = \frac{h^2}{6} \left[ r_1^2 + r_2^2 + \cdots + (r_1^2 + r_2^2 + \cdots) + 2(r_1^2 + r_2^2 + \cdots) \right] \]

Calling the lines CP, C'P', measured on each vertical section, ordinates, we have the following approximate rule to find the volumes of the solids emerged or immersed:

**Rule XV.**—To the sum of the squares of first and last ordinates add four times the sum of the squares of all the even ordinates, and twice the sum of the squares of all the odd ordinates; multiply this result by the common distance and by the angle through which the ship has rolled—divide by 6, and we obtain the volume required (nearly).

**Art. 13.**—Returning to Art. 7, and referring to fig. 7,

Draw GT parallel to MG and GG' parallel to G'dL.

Then, \( G'dR \cdot e \cdot V_d = p_1q_1 \cdot e \cdot w \);

And \( GG' = G'dR - G'dT \)

\[ = \frac{p_1q_1 \cdot e \cdot w}{eV_d} = GG_d \sin \phi. \]

Or, \( W \cdot GG' = (p_1q_1 \cdot w - GG_d \cdot W \sin \phi) \)

as representing the weight of water emerged or immersed; Formula (L) measures the statical stability, Def. (L) of a vessel as given by Atwood in his paper published in the Transactions of the Royal Society for the year 1796.

**Art. 14.**—The rule most frequently used by naval architects to determine the centre of gravity of a vessel, when fully equipped for sea, is due to Chapman, and is as follows:

Suppose any weight (or weights) \( W_1 \), either on the upper deck or elsewhere, is moved from its position at \( W_1 \) (fig. 7) to another position \( W'_1 \), and that by this change of position the ship has been inclined through the angle \( \phi \). From \( W_1 \) (the centre of gravity of the weights or weights) draw \( W'_1E \) parallel to \( F'L' \), and \( W_1E \) perpendicular to \( W'_1E \); then \( W'_1E = W_1W'_1 \cos \phi = e \cos \phi \); if \( W_1W'_1 = c \).

So long as the disturbing weight \( W_1 \) remains in its new position \( W'_1 \), the vessel will remain in equilibrium, and therefore its centre of gravity must lie in the line \( G'A'M \) by the second condition of equilibrium. Hence it has been transferred a distance \( GG' \) parallel to the plane of flotation \( F'L' \), while \( W_1 \) has been moved through a distance \( W'_1E \) in a parallel direction. Taking moments, we have

\[ W \cdot GG' = W_1 \cdot e \cos \phi. \]

From Equation L of last article—

\[ GG' = \frac{p_1q_1 \cdot W \cdot GG_d \cdot W_1 \sin \phi}{W} \]

Writing this latter value of \( GG' \) in the former equation, we get

\[ GG_d = \frac{p_1q_1 \cdot w - eW_1 \cos \phi}{W \sin \phi} \]

which determines the centre of gravity of the ship, when the centre of gravity of displacement has been determined.

Mr. Abethell, master-shipwright of H.M. Dockyard, Portsmouth, proposed the following method, in the second volume of the Papers on Naval Architecture:

"It is applicable whenever a ship is taken into dock with the under side of her keel deviating from parallelism with the upper surface of the blocks. This is almost always the case; and it also not unfrequently occurs that ships are docked 'all standing,' and with so large a portion of their armament and stores on board, that the correction necessary to be made to the result which would be obtained by the experiment and investigation about to be described, in order to make that result agree with the circumstances of any additional armament and equipment, would be comparatively easy.

We will now quote from the article in question.

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1 See Moseley's paper, p. 619. which represents the height through which the centre of gravity of the floating displacement has been raised.

Then there will be two cases: 1st, When the centres move in the same direction; 2d, When they move in opposite directions. In the first case, we shall have to subtract (L) and (M); in the second case, add these results. Performing these operations, we have for the sum, or difference of the vertical displacements of the centre of gravity of the body, and that of the fluid which it displaces,

\[ G'dR = (Gd \text{ vers } \phi + Xs) + (GO \text{ vers } \phi + Xs); \]

Or, \( G'dR = GGd \text{ vers } \phi \)

by taking the upper sign.

The dynamical stability is readily obtained by multiplying this result by the weight of the vessel; that is—

\[ \text{Dynamical stability} = W(G'dR + GGd \text{ vers } \phi). \]

Canon Moseley makes the following remarks at page 634 of his paper:

"The force of the winds and waves, to the action of which a vessel is liable, may be supposed to vary as the surface she opposes to them; that is to the area of her sails and the superficial dimensions of the hull. If vessels geometrically similar, these vary as the squares of any of their linear dimensions; their lengths, for instance. On the other hand, the weights of such vessels, supposed to be similarly loaded, varying as the cubes of their lengths; and the depths of their centres of gravity, and of the centres of gravity of their immersed parts varying as their lengths, their dynamical stabilities, with reference to a given inclination, vary as the fourth powers of their lengths. Since then, in reference to vessels thus geometrically similar, the disturbing forces, to the action of which they are subject, vary as the squares of their lengths, and their stabilities as the fourth powers, it follows that their actual steadiness in the water will vary as the square of their lengths, the greater vessel being more steady than the less in this proportion."

**Time of Performing an Oscillation.**

ART. 16.—There is much difficulty attending the investigation of the times of rolling and pitching of vessels through large angles, insomuch as the axis about which the motion takes place is instantaneous. This axis can, however, be determined at any instant, providing the direction in which the ship is rolling or pitching be given. All methods hitherto given are incomplete, yet all tend to show, that no matter what may be the amplitudes (the angles through which the vessel revolves, providing the position of the ballast, cargo, and other weights retain their original positions), the time of performing a complete oscillation, in smooth waters, is the same.

Writers on Hydrostatics, in investigating the time of an oscillation, have usually considered the plane of flotation as constant throughout the motion. The Rev. Canon Moseley, in his paper already quoted, endeavoured to obtain new results for the time of performing an oscillation, as well as for the dynamical stability of the vessel. Notwithstanding that several corrections have been made in the paper, as published in his second edition of *The Mechanical Principles of Engineering and Architecture*, the results are still open to the same objection, since they are made to depend upon the moment of inertia of the plane of flotation, which is itself a variable quantity throughout the motion.

It would seem that the Calculus of Variations might be advantageously applied to the question, or, at all events, Canon Moseley's paper might be made available, providing we were to calculate the amount of probable error in assuming the plane of flotation constant within given limits.

As the question stands, we do not know that a better Stability of Floating Bodies and more simple method can be brought before the practical man than the following, which is due to the Rev. Dr Woolley:

"Suppose \( Gd \) to be an arc described by the centre of gravity of displacement, corresponding to the half-angle through which the vessel rolls, and let \( M, M' \) be the limits within which the normals to the curve \( GdM \), the former corresponding to the upright position of the vessel, \( G \) the centre of gravity of the vessel, then the time of rolling, supposing \( M \) to be fixed during the motion, is too great; and if \( M' \) were the point of suspension, the time would be too small; but taking intermediate points, and calculating the time for each, supposed fixed, let \( T \) be the true time, \( s_1, s_2, s_3, \ldots \) the errors, \( t_1, t_2, t_3, \ldots \) the calculated times, then

\[ T + s_1 = t_1 \\ T + s_2 = t_2 \\ T + s_3 = t_3 \\ \vdots \\ T + s_n = t_n \]

Now, since some of these errors are negative and some positive, we may make this result as small as we please, by taking sufficiently great.

\[ T = \frac{t_1 + t_2 + t_3 + \ldots + t_n}{n}, \quad \text{very nearly.} \]

When the distance between \( M \) and \( M' \) is very small, as is the case in most vessels for a moderate amplitude, then the question is reduced to the case of a simple pendulum, the length of which is \( GM \). Therefore \( K \) being the radius of gyration of the ship round a longitudinal axis through its centre of gravity,

\[ T = \frac{\pi K}{\sqrt{gGM}} \quad \text{(L)} \]

\( K \) is obtained by multiplying each of the elementary weights of the vessel by the square of its distance from the horizontal axis through the centre of gravity, and extending the summation throughout the whole ship. Divide this result by the total weight of the ship when ready for sea, and extract the square root of the quotient, which gives \( K \).

We see from (L), that the time of a natural oscillation varies directly as the radius of gyration, and inversely as the square root of the distance between the centre of gravity of the vessel and its metacentre. Hence, by increasing \( K \), which may be done by moving the weights on board further from the axis about which the ship revolves, the time of oscillation is increased; also \( K \) remaining constant, if \( GM \) be diminished, \( T \) is also increased, and vice versa.

Canon Moseley gives the following approximate result for the time of performing an oscillation:

\[ T = \frac{\pi K}{\sqrt{g(GGd + \frac{k}{W})}} \quad \text{For } \frac{k}{W} = MGd. \]

Art. 11, formula (L), where \( k \) represents the moment of inertia of the plane of flotation about one of its principal axes.

The Forces which act upon a Ship in motion, as they influence her general dimensions, form, and qualities.

The methods by which the displacement of a ship are found, and those by which the positions of her centres of gravity are determined, having been described, and the principles on which her stability depends having been

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1 The reader who is desirous of learning more on this subject may consult the paper just cited, or Fincham's *Outlines of Ship-Building*, 3rd ed. 2 See Moseley's paper. 3 It would be a very easy matter to compare the time of a vessel's rolling through an angle with a pendulum whose length varies between the limits \( GM \) and \( GM' \). For we have only to conceive a fine string suspended from \( A \), and carrying a bob at \( Gd \), and passing through an exceedingly fine aperture in a rod \( GM' \), the latter rod making a vertical motion \( MM' \) in the same time that \( Gd \) completes the arc \( GGd \); that is, moved on the same plan as the motion of the slide-valve of a steam-engine. Indeed, it would not be difficult to make the point \( M \) describe the exact curve traced out by this point during the motion of the ship, providing that curve be calculated; we should then be in a position to learn accurately what error is made by assuming \( M \) to be the point of suspension. 4 See Barnshaw's *Dynamics*, p. 229; Poisson's *Mechanics*, vol. II., chap. III., art. 2 (Dr Harte's translation); or, Pratt's *Mechanical Philosophy*, chap. vii. 5 From a paper by the Rev. Dr Woolley. pointed out, it is now proposed to consider the forces which affect her speed through the water.

It was at a very early period pointed out by mathematicians, that the velocity with which water will run out through a hole in the bottom of a vessel is the same as that acquired by a body falling from a height equal to the depth from the surface of the water to the hole. The truth of this has been at various times tested by many experiments, and has been confirmed by all that have been made. Euler, in his work, *Theorie Complette de la Construction des Vaissoux*, took this as the basis of his investigations of the theory of the resistances which solid bodies moving in a fluid have to overcome. A passage in the English translation of his work is given thus:—

"We know, both from theory and experience, that the water contained in a vessel, whose height is \( h \), will run out through a hole in the bottom with the same velocity that a body falling from the same height, \( h \), would acquire. And if the letter \( g \) denotes the height through which a body falls in one second, we also know the velocity will be such that it would run through a distance \( = 2g^2 \) in the same time. Since, therefore, this velocity is supposed \( = c \), or \( 2g^2 = c^2 \); and, by taking the square, \( 4g^2 = c^2 \); hence we have the height sought, \( h = \frac{c^2}{4g} \); consequently, the force of the resistance which a supposed plane surface \( = f \), will experience by moving in water, with the velocity \( c \), will be \( = \frac{c^2f}{4g} \); and by this force the surface will be acted on, in a direction contrary to its motion. Hence, we see that this resistance is always proportional to the square of the velocity, and also proportional to the area of the surface itself, so that by this means the resistance is perfectly determined."

If the direct resistance to the motion of a vessel through the water were not lessened by her form, it would, by this rule, be ascertained by finding the weights of a column of water, whose base is equal to her midship section, and whose height is equal to that from which a body must fall to acquire the velocity at which she is propelled, and the resistances of similar vessels when moved with the same velocity, would be proportional to their midship sections. The direct resistance, however, to any plane surface will be diminished by placing a triangular, or other form of body, before and behind it; and many experiments have been made on the form to be added, with a view to discover the law of the diminution of this resistance, and thus to be able to approximate to the form of least resistance. All attempts to reconcile the theory of the resistances on the oblique surfaces thus presented to the fluid with the observations by experiment, have as yet failed. Bossut gives the theoretical resolution of the resistance on the sides of a wedge-shaped body as follows, and then shows that this is found by experiment not to be true with respect to bodies with sharp ends moving in water:

Let \( ADB \) (fig.12) be an isosceles triangle, moving in a fluid of infinite extent in the direction of its height \( QD \). The face \( AD \) is subject, according to theory, to a resistance in the direction \( PB \) perpendicular to itself, such that in calling \( w \) the perpendicular and direct resistance experienced by the half-base \( AQ \). When moved with the same velocity as the triangle, we have force

\[ FE = \pi \times \frac{AD \times (\sin \angle ADQ)^2}{AD \times ADQ^2} \]

\[ = \pi \times \frac{AQ \times ADQ^2}{AD \times ADQ^2} \]

\[ = \pi \times \frac{AQ}{AD} \]

and in a similar manner we have, for the other force \( BD \), force \( f_e = \pi \times \frac{BQ}{BD} \).

Resolving each of the two equal forces \( PE \) and \( f_e \) into the two others, \( PH \), \( FK \), and \( f_k \), the one perpendicular, and the other parallel to the base \( AD \) of the triangle, it is evident that the two forces equal, and directly opposed to each other, \( FK \) and \( f_k \), destroy each other, and that the triangle is simply acted on in the direction \( QD \) by one force \( = PH + f_k = 2 FH = 2 PE \times \frac{AQ}{AD} \) on oblique surfaces.

Hence, if we call this force \( 2 FH = p \), and call the perpendicular and direct force which acts upon the base \( AB \), when moved with the same velocity as the triangle \( = P \), we have

\[ p = P \times \frac{AQ^2}{AD^2} \]

Comparing this formula with his experiments, Bossut found the following results in four instances of experiments with different models:

| Distinguishing No. of Model Experimented upon | Angle of Incidence | Value of \( p \) in Mares | |-----------------------------------------------|-------------------|--------------------------| | | | by Experiment. | | | | by Theory. | | 9 | 45° | 12-96 nearly | | 10 | 33° 41' | 10-80 | | 11 | 26° 34' | 8-39 | | 12 | 21° 49' | 8-32 |

From the above it is seen that the results of theory differ further and further from those of experiment, the smaller the angle of incidence or the finer the angle of entrance of a ship is made. Further experiments have been made with a view to discover the law of this branch of the theory of resistances, but as yet without any results such as will enable any calculation to be made to determine beforehand, with any accuracy, the extent to which the resistance of a body of any given form will be diminished from that due to the base or midship section of the body. Even if a law were discovered for different angles of incidence, the difficulty of the investigation would still be great, when it is considered how constantly this angle varies in the form of the fore-body of a ship.

Theory, therefore, fails to give any rule by which to ascertain, by any abstract calculation, the resistance of a vessel of any given form, and consequently to ascertain the velocity that she will obtain by the exertion of any given ties, and amount of power to propel her; and the naval architect is properly driven to ascertain these points by comparison with those of the results obtained from vessels of known form and power.

It has already been shown in the extract from Euler, that the resistances experienced by the same body, when moved at different velocities, vary as the squares of the velocities, and that the resistances of similar vessels, moved at the same velocity, are proportional to their surfaces or the areas of their midship sections. Many experiments have been made to test the accordance or otherwise of these theoretical deductions with the actual results obtained in practice. M. Bossut reported, as the result of the experiments conducted for the Royal Academy of Sciences at Paris in the year 1776, that the resistances of the same surface, moved with different velocities through a fluid infinite in extent, follow nearly the proportion of the squares of the velocities, and also that the perpendicular and direct resistances of several plane surfaces, moved with the same velocity, are very nearly proportional to the areas of the surfaces; and, consequently, that experiment and theory may be said to agree on these points. The experiments made in 1796 and 1798 in this country by the Society for the Improvement of Naval Architecture, and conducted by Colonel Beaufort, lead to the same conclusion. These experiments were made with bodies of various forms, and at velocities varying from 1 to 8 nautical miles per hour. The relative proportion or degree in which the resistances and velocities varied in the bodies of different forms differed comparatively slightly, being in some cases above the square or second power, and in other cases below it; in one instance it reached as high as the power of $2^2 = 4$, and in another instance as low as $1^2 = 1$, but the average of the results obtained from these experiments may safely be taken as corroborative of the theory.

Exception has been taken by some to the results of these experiments, because the bodies were entirely submerged, but the reasons for so conducting them appear to be stronger than those for conducting a series of experiments on bodies only partially submerged, and then subject to other influences than the action of the water through which they are passing. Deductions based upon the grounds thus established, as furnishing correct data on the subject of resistances, are of great practical value to the naval architect.

The resistances, whatever they may be, of the same body, having been shown to be as the squares of the velocities, it follows necessarily that the horse-powers exerted to produce the different velocities will vary as the cubes of the velocities. This is evident, because the power is the product of the distance passed over, multiplied into the force exerted, while the distances vary directly as the velocities and the forces vary in the proportion of the squares. The origin and the truth of the formula in common use

$$V^3 \times \text{Mid. Sec.}$$

equal to a co-efficient C is therefore apparent; the resistances being in proportion to the areas of the midship sections, and L.H.P. being put to represent the indicated horse-power.

It is sometimes preferred to use a ratio of the displacement instead of the midship section, and as the ratio of the midship section of similar bodies is also expressed by the ratio of the cube root of the square of their cubical contents, this may be substituted in lieu of the midship section in the foregoing formula. It will then become

$$\frac{V^3 D}{L.H.P.} = C,$$

and hence V, or any one unknown element in the formula may be found, all the others being known. A ready means of comparison between different ships is thus obtained. If the vessels are different in size, but mathematically similar, that is, if one is a type of the other, and the whole particulars of one are known, the velocity of the other, for any supposed amount of power, or the necessary amount of power to produce any proposed velocity, will be obtained.

The practical application of these principles to the propulsion of vessels by steam-power, which is always applied in the direction of the keel, would be easily carried out if the amount of power which is actually effective in propelling the vessel could be accurately ascertained separately from the power expended in working the parts of the engine itself, and in the friction. The total horse-power generated or exerted by the steam, is measured by the indicator, and is called the indicated horse-power; but engineers have as yet failed to discover any satisfactory method by which the effective can be separated from the gross horse-power. It is usual, therefore, to assume that, for every indicated horse-power, a given amount of effective power is exerted, and the gross power is argued upon as a measure of the effective power. In many cases this assumption is no doubt correct, but in many others it is open to great question, and results thus obtained must not be argued upon as by any means definite, or anything more than an approximation sufficiently accurate for most practical purposes.

The form of the engines and boilers to be used in the propulsion of a vessel is generally left by the naval architect to be determined by the engineers; but at the same time, the amount of power to be placed in the vessel, the weight and the positions of the centres of gravity, both vertically and longitudinally, of the machinery, must be duly considered and determined in concert with the naval architect. The form of the vessel at the place where the paddle-wheels, or where the screw are to act, also require special consideration on the part of the naval architect, otherwise the power exerted by the engine may be wasted, as it formerly was in churning the water when the paddle-wheels were boxed up in spindles.

The arrangements for the propulsion of vessels by the agency of the wind come within the province of the naval architect, and much consideration has been given to the subject in many works.

When the ship is under sail, there are two forces acting on it—the one, the force of the wind on the sails, to propel the ship; and the other, the resistance of the water to oppose her motion. These forces, immediately the ship under sail has acquired the velocity due to the strength of the wind, are equal, and, as is the case with all forces, may each be reasoned on as if acting only on one point of the surface over which its effect is diffused. This point is that in which, and centres if the whole force were to be concentrated, its effect would be the same as when dispersed over the whole area: it is usual to call these, "resultants of forces," and the points on which they are supposed to act, "centres of effort."

From what has been before said, the resultant of the force of the wind on the sails, and the resultant of the force of the water on the hull, are equal; the one acting on the sails, and weather-side of the ship, in the direction into which the force of the wind resolves itself, and the other opposed to it, acting on the lee-side, in the direction into which the force of the water resolves itself; and their effect is necessarily in proportion to their distance from the centre of gravity. If they are equally distant, they will destroy each other, and the ship will remain at rest with respect to the line of its course; if the resultant of the resistance of the water passes before the resultant of the wind, the ship will turn to the wind; but if the resultant of the wind passes before that of the water, the effect will be the contrary, and the ship will fall off from the wind. In either case it will be necessary to equalize the forces, by the action of the water on the rudder, on its lee-side, to bring the resultant of the water more aft, and on its weather-side to destroy a part of the effect of the wind. This is the principle of the action of the wind on the sails, and of that of the water on the hull, with respect to the course of the ship through the water; and it is on these considerations only that the various alterations can be regulated, which it may from time to time be necessary to make in the trim either of the sails or of the ship; and hence the accurate determination of the positions and directions of these two forces is a point of great importance in naval architecture. The position of the centre of effort of the wind on the sails may be found under certain reservations; and that being known, enough is determined to lead to correct conclusions on the other circumstances attendant on the subject.

In order to find the distance of the centre of effort of the wind on the sails before the centre of gravity of the ship, the moment of each sail is calculated by multiplying its area by the horizontal distance of its centre of gravity from that of the ship; the sum of the negative moments, or those abaft the centre of gravity of the ship, is then subtracted from the sum of the positive moments, or those before the centre of gravity of the ship; the remainder is then divided by the total area of the sails, and the result gives the required distance of the centre of effort of the wind on the sails before the centre of gravity of the ship.

The situation of this point with respect to the length of the vessel must determine in a considerable degree the positions of the masts; for experience has proved that it is among the most essentially requisite good qualities of a ship, that she shall carry a weather-helm.

With respect to ships carrying a weather-helm, it may be assumed that the particles of water have a motion at the position of stern of the vessel, the direction of which forms an acute angle with the middle line of the ship produced aft, which angle will evidently be dependent on the fulness or the fineness of the after-part of the body, and on the angle which the line of the ship's course, or that of the lee-way, makes with the middle line of the ship; consequently, the inactive position of the rudder will be when it forms this angle with the middle line of the ship, that is, when the rudder is to leeward, and consequently, the helm a-weather. And this position should be the theoretic limit of the degree of weather-helm a ship should carry, as in any other position there must be a force acting on the rudder, which must increase the resistance the ship experiences in her passage through the water. A practical confirmation of the correctness of this principle, and of the fact that this generally advantageous position of the rudder is a-lee of the middle line of the ship, may be drawn from the common observation, that when a ship is in good trim, the helm, being a-weather, has a very perceptible tremulous motion, which must arise from the rudder being in a position in which it is not acted upon on either side by any constant force. This method of considering the direction of the flow of the water to the rudder considerably diminishes the estimate of the excess of its effect on the lee-side of the rudder over that on the weather. But there are several other considerations which operate in increasing the effect of the weather-helm. From the direction in which the water flows past the ship, there will be a much greater reduction of pressure on the weather-side of the rudder when the helm is to windward, and therefore a greater positive pressure on its lee-side to turn the ship, than will occur under the opposite circumstances, or when the helm is a-lee. Also, the broken and disturbed state of the water on the after-part of the weather-side of the ship, and the consequent various degrees of resistance it opposes, must lessen its effect when the helm is a-lee.

It has been said to be proved by practice, that ships which carry lee-helms cannot be weatherly; that is, will fall faster to leeward than those which carry weather-helms. But though the fact is correct, the reason assigned is in some degree mistaking the effect for the cause. It has before been said, that a part of the force of the wind acts in driving a ship bodily to leeward; of course its effect will be greater or less in proportion to the lateral resistance opposed to it, and the ship which opposes less lateral and greater longitudinal resistance to the water than another, will in the same period of time have fallen farther to leeward, and the line of her course will have made a larger angle with her middle line, by which the effect of the water on the after-part of the lee-side is increased, while that on the fore-part, both of the lee and weather sides, is diminished, and the helm must consequently be kept less a-weather. A practical proof of the correctness of this reasoning may be drawn from the practice of the older class of merchant vessels, which are generally, from form, more leewardly than men-of-war. They have their fore-mast placed much nearer the centre of the ship than is usual in sharper and finer formed bodies. This has evidently arisen from the operation of the cause above mentioned, which has shown that they require the resultant of the effort of the wind on the sails to be proportionately farther aft to insure their carrying a weather-helm. From this reasoning it is evident that, under some circumstances, it may be the leewardliness of the ship which causes her to carry a lee-helm; and that when such is the case, the defect might be remedied, not only by the usual methods of placing the masts farther aft, and altering the draught of water, but by increasing the lateral resistance by the addition of false keel, or by greater depth in the water.

There is another disadvantage arising from a ship's carrying a lee-helm, which is, that the action of the water on the weather-side of the rudder acts in conjunction with the force of the wind in forcing the ship bodily to leeward; while, on the contrary, when the helm is a-weather, the action of the water on the rudder is in opposition to the force of the wind. The ardency of a ship, which is her tendency to fly to the wind, depends on the relative positions of the resultant of the effort of the wind on the sails, and the resultant of the resistance of the water on the hull, acting on a Ship in motion. The position of the centre of effort of the wind on the sails is calculated under the supposition that the sails are plane surfaces, and equally disposed with regard to the longitudinal axis of the ship; but when a ship is on a wind, as the force of the wind acts in a direction oblique to the surface of the sails, a greater proportion of the sail is carried to leeward of this axis, and the whole sail assumes a curved surface, the curvature of which increases from the weather to the lee side. From these circumstances, the centre of effort is in fact carried gradually farther aft as the action of the wind takes place on the sails. Also, as the force of the wind inclines the ship, the centre of effort of the wind on their curves is carried, by this inclination, over to the lee-side, where, by which, as also by the effect produced on the resultant of the water, which has been before mentioned, the distance between them is farther increased. It therefore appears Of increase that, the quantity and disposition of the sail set remaining of wind, the same, the ardency will increase as the force of the wind increases, and diminish as that force diminishes. The defect of a vessel carrying a lee-helm may be lessened by those means of trimming either the sails or the ship, which will tend to increase the distance of the resultant of the water before the centre of effort of the wind. Great caution is necessary before altering the position of the masts with a view to remedy this defect, because her working quickly depends on the proportion of sail before and abaft the axis of rotation, and not on the position of the centre of effort of the whole surface of the sails. The limits of this article will not permit the subjects of masting, or rigging, or sail-making to be gone into. Much valuable information on the subject of the effect of the wind upon the sails, the angle of lee-way, the position of the centre of effort, and other points, will be found in the article Seamanship.

The motion of pitching and scending is, generally the Pitching most violent action to which a ship is subjected, and the most injurious, both to the connection between the parts ing. of her structure and the velocity of her sailing. It is the longitudinal motion caused by the variable support afforded to the body by the waves as the vessel meets and passes over them; pitching being dipping of the bows into the water, and scending, the dipping of the stern. To obtain ease of motion in this respect, Mr Henwood advocated, in a paper published in the Papers on Naval Architecture, that the after-part of the ship, or that part abaft the centre of gravity, should be constructed so as to have precisely the same cubic contents as the fore-body, and that its centre of gravity should be at the same distance from the centre of gravity of the ship as that of the fore-body. The disposition of the weights, and especially of the masts, influences this motion in a powerful degree; because, though the weights in the fore and after bodies may balance each other while at rest, a greater weight, perhaps at a less distance, balancing a less weight at a greater distance; yet, when the ship is set in motion the balance will no longer hold, because the moments of the weights in motion will be according to the squares of their distances from the common centre of gravity. If a vessel pitches heavily, the moments of the weights forward are too great, and the contrary if she scends heavily abaft. An uneasy motion in pitching is much more common than in scending, and this no doubt arises from the generally very forward position of the fore-mast, especially in men-of-war. The importance of a little attention to this subject on the part of naval men will be at once apparent, when it is considered that the effect of moving or placing 5 tons at a distance of 120 feet from the centre of gravity of the ship is represented by the number $72,000 = 120^2 \times 5$, while it would be necessary to move 720 tons to a distance of 10 feet on the opposite side. of the centre of gravity to produce the same effect on the pitching and scending motions of a ship.

The rolling motion of a ship is caused more by the undulations of the waves than by the shock of a wave striking the side of a ship. The principles on which the rolling of a vessel depends have been already investigated, and a few practical remarks will only be added here. The remark is common, and it is true, that the crank ship is the easy ship—that is, the more readily a vessel rolls, the easier will be the rolling motion. Mr Wilson, late of the Admiralty Office, in an able article in the Papers on Naval Architecture, says, "If stability is too great, the most efficacious way of diminishing the rolling is to bring up the ballast, because it raises the centre of gravity, and it increases the distance of the centre of oscillation from the axis of rotation. The ballast removed from near the keelson to the wings, even if placed as high as the deck, is as far from the metacentre as when it was in the hold, and consequently its weight multiplied into the square of that distance is the same as before; the rollings, therefore, will be slower." The cables, shot, stores, &c., in any ship, if placed near the side, while this will not affect the stability, will increase the distance between them and the axis of rotation, and will consequently lengthen the time of vibration. Mr Wilson proceeds to say, that it is by no means a difficult task to reduce a ship of extraordinary stability, which is always an uneasy one, to a state of easy rolling by increasing the masts and yards, and increasing the weights above and putting them in the wings, and removing some ballast, if she has any on board.

Fincham, in his History of Ship-Building, gives a remarkable instance of the extent to which the qualities of a ship may be influenced by other circumstances than her form. "The Mutine, an experimental brig, built to compete with others, was beaten on the first experimental cruise, but she afterwards beat the others, alterations having been made in the trim of her sails and in her stowage. After the alterations, instead of rolling the shot out of the racks and the wind out of the sails, as before, she rolled little, and neither deep nor quick. At first her weights were carried too low down."

The motions of a vessel are much affected by the proportions which the general dimensions bear to each other. An increase of length gives an increase of displacement, or if this is not desired, it allows of finer lines forward and aft, and it also increases the stability and the resistance to lee-way. The power of turning, tacking, wearing, or making any other change in her course, is lessened by an increase of length; but this effect may be much modified by diminishing the amount of fore-foot, or of dead-wood forward, which will alter the position of the resultant of the action of the water, and will consequently also require a corresponding alteration in the amount or position of the forward and aft sails. A vessel need not necessarily pitch more heavily on account of any increase of length, but it is necessary in long vessels to take greater care that the weights of the fore and aft bodies are properly balanced in regard to their moments. It will be evident that the moments of small weights when placed well forward or aft, become very much greater in long vessels, when it is considered that all weights are multiplied by the squares of their distances from the centre of gravity of the ship for their moments.

The friction upon the sides of a vessel, from any additional length of parallel body amidships, appears to be very trifling, if we may judge from the results of cases where vessels have been cut in midships and lengthened, without any other alteration in their form having been made. The following is a statement of the results obtained by lengthening the Candia, a vessel belonging to the Peninsular and Oriental Company, by putting 35 feet into her amidships:

| Draft forward | 18 ft. 6 in. | 18 ft. 2 in. | 18 ft. 2½ in. | |---------------|-------------|-------------|--------------| | " aft" | 18 ft. 6 in. | 19 ft. 5 in. | 19 ft. 7 in. | | Mean | 18 ft. 6 in. | 18 ft. 9½ in.| 18 ft. 11 in.| | Area of ship section | 536 feet | 551 feet | 556 feet | | Displacement | 450 tons | 450 tons | 450 tons | | Nominal horse-power | 1,415 | 1,250 | about 1,400 | | Indicated horse-power | 341 to 37 | 31 | 33 | | Revolutions | 22 lb. | 16 lb. | 20 lbs. | | Pressure | 26½ | 26 | 26½ | | Vacuum | 12,651 | 11,675 | 12,443 | | Speed | 20 feet | 21 feet | 21 feet | | Pitch of screw | 15 ft. 6 in.| 15 ft. 6 in.| 15 ft. 6 in.| | Diameter of ditto | 3 | 3 | 3 |

By increasing the breadth amidships, as well as the breadth, average breadth throughout the whole length of the vessel, while the length and depth are kept the same as before, the stability, which varies as the cube of the breadth, is increased. As the angular momenta of the weights, estimated from the axis of rotation, vary as the squares of their distances from that axis, and the momentum of the action of a wave is increased in the same proportion, therefore the increase of stability is accompanied by increased violence in the motions, and consequent increased strain on the combinations and materials of the structure, especially danger to the masts, by which the safety of the vessel may be compromised. The stability of a ship of war, being the quality on which the efficiency of her armament is essentially dependent, and which also, by enabling her to carry a press of sail in circumstances of danger, as a lee-shore, or an enemy of superior force, is essential to her safety; the only limit to its increase is involved in the consideration of easiness of motion. But if this consideration be neglected, and the breadth be such that the moment of stability in proportion to the moment of sail is so large, or of such sudden increase, that the masts are endangered or the combinations of the structure prematurely destroyed, the object for which a large moment of stability was desirable is frustrated. The breadth, therefore, is limited by easiness of motion. The best mode of insuring stability is to give a large area and great fulness and similarity of form immediately above and below the average water-line, as by this means the centre of gravity of the displacement will be kept at as short a distance as possible below the surface of the water.

The depth of a ship, or her draught of water, may vary according to local circumstances or the objects for which she is to be employed, or by a judicious arrangement of her other proportions and of her form, and the positions of the centre of gravity. Good ships may be produced varying considerably in the proportions of their depth to their breadth.

An important consideration connected with the forming of the design of a ship is involved in the gradual alteration of seat in the vessel's seat in the water from the consumption of water from stores. It is not only essential that a ship should be possessed of stability combined with easiness of motion, be stores, weatherly and quick in manoeuvring when she is stored and completed for foreign service as a ship of war, or fully laden as a merchant-ship, but it is equally essential that she should be possessed of these qualities towards the expiration of her cruise, or on her return light from her voyage.

The loss of stability which results from the diminution of draught of water cannot be compensated by a proportionate arrangement of sail, without incurring other evil consequences. If the quantity of sail, which at all times is comparatively small in a merchant-ship, be lessened, the wind... on the increased hull might so counterbalance its effect that she would be utterly unable to beat off a lee-shore, or make any way on a wind.

A ship is not only subject to a loss in stability when lightened, but becomes laboursome, on account of top-lumper; her rolling motion is more violent as her diminished depth in the water decreases the resistance which is opposed to the inclination, and she also generally becomes more leewardly, owing to the difference made in the resultant of the resistance, the diminution of the lateral resistance, and of her power of carrying sail.

It is almost a universal custom in all vessels to give a greater draught of water abaft than forward. Occasional attempts have been made to discontinue this practice, as involving a supposed unnecessary increase in the water required for floating a ship; but the increased draught of water for the after-body has been reverted to as essentially requisite in practice.

There are several minor advantages which result from this arrangement; such as the more easy and unchecked flow of the water to the rudder, and its consequent increased effect in governing the motions of the ship; also the diminution of the negative resistance which the vessel would otherwise experience from the greater difficulty with which the flow of water would fill the vacancy caused by the passage of the vessel, if the fulness of the after-body were such as would be required to preserve an even draught of water; and again, the adjustment of the resultant of the resistance of the water to that position of the masts which experience has determined to be requisite for the facility of manoeuvring the sails. But the principal reason for the inequality in the draught of water appears to be the advantage which results from it to the more easy regulation of the motions of the vessel by an adjustment of the resultant of the resistance of the water on the lee-side when on a wind.

The considerations which lead to a settlement of the general dimensions of a vessel, and which must vary greatly according to the purpose for which she is intended, having been touched upon, it is proposed to give an outline of the course pursued in designing the form, or making the constructive drawing, as it is termed, of any vessel. Three plans are required in all designs of vessels—the body-plan, the sheer-plan, and the half-breadth plan (see Plate III.). The form of the midship section, or a vertical cross-section at the point of greatest breadth, is generally the first portion of a ship that is designed; the outline of the sheer-plan may then be delineated, and after that the half-breadth plan may be begun. The vessel is supposed to be divided into a certain number of horizontal sections, and these are represented by the lines on the sheer-plan, marked 1st, 2d, 3d, 4th, and 5th water-line. The sheer-plan is either a vertical longitudinal section, or a side-plan of the ship, and on it may be delineated any points in her length or height. On the half-breadth plan are delineated the outlines of the horizontal sections previously referred to, and marked water-lines. These horizontal sections may either be parallel to the keel or to the intended water-line of the vessel if she is intended to draw more water abaft than forward. When parallel with the keel, they are sometimes called level-lines. The midship section is not necessarily in the middle of the length; it is called dead-flat, and is always marked as shown on the plate. The length of the vessel is divided into any desired number of sections, and these sections are marked forward and aft from dead-flat with distinguishing letters and figures. The water-lines being also drawn upon the midship section or body-plan, the form of the body at each section in the half-breadth plan is obtained by finding the distance from the centre-line at each water-line, and transferring it to the body-plan, showing the sections of the fore-body and of the after-body on different sides of the middle-line. In addition to these lines, the vessel is supposed to be cut into various longitudinal sections, at given distances from the centre-line; these lines of sections are shown on the half-breadth and body plans; and the form of the body where these cut the exterior surface of the ship are shown on the sheer-plan; they are marked 1v, 2v, 3v, in all the plans. The sections represented in all these plans must be fair and of easy curvature, and many little alterations will probably require to be made by the draughtsman, to get them to coincide.

The constructor or designer is now in a position to test his work by making the necessary calculations. These will be comprised in ascertaining the area of the midship section, the area of the load-water section, the displacement, the positions of the centres of gravity of these two sections, and also the position of the centre of gravity of the displacement.

The areas of the two sections, and the positions of their respective centres of gravity, are required to be determined, on account of the influence of these areas and their positions on the content of the displacement, and the position of its centre of gravity, and also in consequence of their influence on the stability of the ship. If the results of these calculations do not accord with the intentions of the constructor, or are inadequate to the development of his design, he must make such alterations in his curves or in his dimensions as he may consider necessary, before proceeding further with his design; and if he shall have sufficiently informed himself on the theory of ships, he will be enabled to do so with considerable confidence at this stage of his progress, as to the final result of his work.

These calculations are no doubt laborious, but there is no difficulty in them, and any moderately educated subordinate may soon be taught to assist greatly in working them out. Space will not permit an example to be given here; but the labour will be greatly facilitated by tabular forms, and examples will be found in Mr Peake's work on Ship-building, and in one of a series of articles on Shipbuilding in the London Mechanic's Magazine for 1859.

Before the design can be considered complete, it is necessary to ascertain the weight of the hull and of the whole of the proposed contents of the ship, and compare these with the calculated displacement. It is seldom that these weights can be obtained with perfect accuracy, and it is therefore scarcely necessary in practice to go to any undue labour to bring out results to fractions.

It is usual to delineate the results of the calculations of scale of the displacement in the form shown in Plate IV. The curved displacement line representing the displacement of the ship at any draught.

As a guide in commencing a design, it is also usual, and proportion very useful, to know what proportion the circumscribing of circum-parallelipipedon will bear to the body of the ship—that is, parallelogram of the ship together, and deduct such portion as will leave a body of a form of any desired fineness. The amount to be deducted, or the decimal fraction by which the parallelo-pipedon is to be multiplied, varies, of course, for every class of ship.

The form of the midship section, and of the other sections influence near it and therefore influenced by it, affect the question of form of rolling, by affecting the position of the centres of gravity rolling, of the displacement and of the ship and her weights; but there is no doubt but that if it were possible to keep these centres of gravity relatively in the same position with different forms of bodies, the rapidity and extent of rolling would still be influenced by the form, and be different. No rules can be laid down definitely on this subject; but ships with a form of midship-section approaching a semicircle have a bad reputation for rolling; as also those with a very rising floor, if accompanied with great beam, or such beam that the half-breadth exceeds the draught of water by more than 1 or 2 feet. A flat floor is also injurious, as tending Form and to keep the centre of gravity of the displacement too low.

Tonnage of Some good midship-sections of ships of various classes will be found in Fincham's Outlines of Ship-Building; but the great length now given to the fore and after bodies of ships renders the effect of the form of the midship-section much less influential on the general properties of a vessel than formerly, when the proportion of length was so much less.

For the water-lines of vessels no definite instructions have been attempted to be laid down that have been of any practical value. A few general remarks may be made, to the effect that certain degrees of sharpness seem suited for different degrees of speed—the faster the vessel, the finer are the lines required; and if a moderate amount of power only be applied to a vessel, so that her speed cannot be great, it will be of little avail to give her finer lines than those suited to her actual speed. Hollow water-lines below the surface of the water seem to be beneficial for high velocities, but not at the water-line or above it, as the waves seem then to dash into the hollow and obstruct the vessel's way, by their being confined and not passing freely away.

In all the plates given with this article, vertical lines are shown. The form of vessels, in respect of the sections shown by these lines, would appear to have been too much neglected by naval architects. It is considered that the form of vessels at the bows or at the stern, may be looked upon as made up of lines representing a wedge with its face vertical, and dividing the water sideways, combined with other lines representing an inclined plane, as in the Thames barges. Bodies of a wedge form were experimented upon by Colonel Beaufoy, as also others, with an inclined plane forward and aft to compare with them, and the results were decidedly in favour of the inclined plane; the inclined plane in the after-body having been proved decidedly superior. The bodies which gave these results were those designated m, b, m, and p, b, p, and the experiments were conducted at the surface, and not with the bodies totally submerged.

The tonnage of a ship is her assumed capacity for carrying cargo of any description. The capacity or space required for a ton of iron being very different from that required for a ton of light goods, a certain number of cubic feet are necessarily taken as the measure of a vessel's tonnage. An empirical rule, founded upon obsolete proportions of a vessel's dimensions, continued in use for many years, serving as a measurement, not only of builders' tonnage, but also of the register tonnage for regulating the dues payable by the ship. This rule is still continued by builders as the measure by which ships are bought and sold; but as the price per ton may be varied in the same proportion as the dimensions, and are known at the time of purchase or sale, no evil results arise from this adherence to the old rule, however far the measurement may be from the truth.

This rule for old or builders' measurement was established by act of Parliament in the reign of George III. It enacted, that "the length shall be taken in a straight line along the rabbet of the keel of the ship, from the back of the main stern-post to a perpendicular line from the fore-parts of the main-stem under the bowsprit. The breadth also shall be taken from the outside of the outside plank, in the broadest part of the ship, either above or below the main wales, exclusive of all manner of doubling planks that may be wrought upon the sides of the ship." If the ship be afloat, the directions are, "to drop a plumb-line over the stern of the ship, and measure the distance between such line and the after-part of the stern-post, at the load-water mark; then measure from the top of the said plumb-line, in a parallel direction with the water, to a perpendicular point immediately over the load-water mark at the fore-part of the main-stem; subtracting from such adjustment the above distance, the remainder will be the ship's extreme length, from which is to be deducted 3 inches for every foot of the load draft of water for the rake abaft; from the length, taken in either of the ways above-mentioned, subtract 2/5ths of the breadth taken as above, the remainder is esteemed the just length of the keel to find the tonnage; then multiply this length by the breadth, and that product by half the breadth, and dividing by 94, the quotient is deemed the true contents of the lading."

The existing act for ascertaining the tonnage is a great improvement upon the above, and its directions are as follows:—Divide the length of the upper-deck, between the after-part of the stem and the foremost part of the stern-post, into six equal parts. Depth,—at the foremost, middle, and aftermost of these points of division, measure in feet, and decimal parts of a foot, the depths from the under-side of the upper-deck to the ceiling at the limber-stake. In case of a break in the upper-deck, the depths are to be measured from a line stretched in a continuation of the deck. Breadths,—divide each of these three depths into five equal parts, and measure the inside breadths at the following points: viz., at 1/6th and at 5/6ths from the upper-deck of the foremost and aftermost depths, and at 1/3rd and 2/3rds from the upper-deck of the midship depth. Length,—at half the midship depth, measure the length of the vessel from the after-part of the stem to the foremost part of the stern-post; then to twice the midship depth add the foremost and aftermost depths for the sum of the depth; add together the upper and lower breadths, at the foremost division, three times the upper breadths and the lower breadth at the midship division, and the upper and twice the lower breadth at the after-division, for the sum of breadths; then multiply the sum of the breadths by the sum of the depths, and this product by the length, and divide the final product by 3500, which will give the number of tons for register. If the vessel have a poop, or half-deck, or a break in the upper-deck, measure the inside mean length, breadth, and height of such part thereof as may be included within the bulkhead. Multiply these three measurements together, and dividing the product by 92·4, the quotient will be the number of tons to be added to the result as above found. In order to ascertain the tonnage of open vessels, the depths are to be measured from the upper edge of the upper strake. In vessels propelled by steam, the tonnage due to the cubical contents of the engine-room is to be deducted from the gross tonnage thus found. It is enacted that the tonnage due to the cubical contents of the engine-room shall be determined in the following manner; that is to say, measure the inside length of the engine-room in feet, and decimal parts of a foot, from the foremost to the aftermost bulkhead, then multiply the said length by the depth of the ship or vessel at the midship division aforesaid, and the product by the inside breadth at the same division, at two-fifths of the depth from the deck, taken as aforesaid, and divide the last product by 92·4, and the quotient will be deemed the tonnage due to the cubical contents of the engine-room.

Among the plates will be found vessels of the highest character of the present day. The Pera of the Peninsular and Oriental Company's fleet is a well-known vessel, and one whose results are looked upon as of the highest character; and if the form of her body, as shown by the vertical lines on the sheer-plan, be examined and compared with those of any of the other vessels, it will be seen that she excels in this particular. The kindness of the different owners and builders in permitting the lines of their different vessels to be published has been great, and it is to

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3 Beaufoy's Nautical and Hydraulic Experiments, Introduction, p. 43. he hoped that so much public spirit as is now manifested in this respect may be rewarded by still further improvements upon the forms of vessels.

The clipper sailing-ship Schomberg, represented in Plate III., is a specimen of a first-class Aberdeen clipper, built by Messrs Hall of Aberdeen.

The Lord of the Isles is a very fine iron vessel, built by Messrs Jn. Scott and Company of Cartyske, near Greenock. Although a sharp ship, she carries a good cargo of weight and measurement goods combined. On her first voyage from Clyde to Sydney she had 1300 tons of weight and measurement cargo on board, and made the passage in 70 days—a passage which, it is believed, has not yet been surpassed. Her register tonnage is 691 tons; and her tonnage, by builders' measurement, is 770 tons. She also made a passage from Shanghai to London in 87 days, with 1030 tons of tea on board. On one voyage she averaged 320 nautical miles for five consecutive days; and on her last voyage to China, in crossing the N.E. trades, her average way was over 12 knots.

Plates V. and VI. represent the rival yachts Titania and America, when the prize was carried off from all England by the latter. The sections of the vertical lines are shown upon the drawings of both of these yachts; and if the vertical lines on the sheer-plan of the one are traced and laid upon those of the other, a marked difference in favour of the America will be apparent.

Plate VII. is a representation of a paddle-steamer, the Delta. The engines in this vessel were taken out of a vessel of 500 tons, and put into the Delta, of nearly four times this tonnage, and the result is a specimen of what may be achieved by fine lines with a judicious application of power; the larger vessel having nearly a knot more speed.

Plates VIII. and IX. represent the Great Eastern, and from the fineness of her lines there can be no doubt of her success, if the engines do their duty.

Plate X. is a representation of the Bremen, a vessel whose performances have been such as to attract special attention, and to lead the Committee appointed by the British Association for the Advancement of Science to make the following report concerning her:

"This Committee are assured, on authority which they believe to be unquestionable, that a certain vessel, the Bremen, of 3440 tons displacement at the time of trial, propelled by engines working up to 1624 indicated horse-power, attained the speed of 13-15 nautical miles per hour. Now, if we estimate the dynamic duty thus performed by the formula

\[ \text{Ind. h.p.} = C \times \frac{V^2}{D} \]

we shall have the co-efficient,

\[ C = \frac{(13-15)^2 \times (3440)}{1624} = \frac{2274 \times 2278}{1624} = 319, \]

and this co-efficient of dynamic duty, resulting from the mutual relation of displacement, speed, and power, appears, from the statements which have been communicated to this Committee, nearly 50 per cent. higher than that realised by the average performance of the steamships of the present day. The following are the co-efficients of dynamic duty deduced by the foregoing rule from the performances of merchant steamers of high reputation, which the trial data have been communicated to this committee, viz. 325, 294, 291, 283, 250, 248, 231, 230, and 204, and many others below 200.

This Committee, therefore, regard the Bremen as being a felicitous exemplification of naval architecture as respects type of form adapted for steam propulsion; and as we conceive that the prolongation of some of the constructive elements of this vessel may be of public importance, we are happy in being authorised and enabled by Messrs Caird and Company, of Greenock, the constructors of the ship and of the engines, to communicate to the British Association the following statistical data as to the elements of construction of the Bremen:

Length between perpendiculars of stem and rudderpost: 318 feet. Breadth of beam: 40 feet.

Depth of hold: 26 feet. Mean draught of water at the time of trial: 18 ft. 6 in. Displacement (D) at trial draught: 3440 tons. Area of maximum immersed section (A) at the trial draught: 606 sq. ft. Distance of maximum section (A) measuring from the stem: 159 feet. Constructors' load draught: forward: 18 feet. Displacement at constructors' load draught: aft: 19 feet. Rate of ships' displacement at constructors' load draught: 3440 tons. Rate of ships' displacement at constructors' load draught: 25 tons per inch.

Areas of immersed vertical section at the distance of \( \frac{1}{2} \) length measuring from the stem: Do. \( \frac{1}{2} \) do. do. 486 sq. ft. Do. \( \frac{1}{2} \) do. do. 605 sq. ft. Do. \( \frac{1}{2} \) do. do. 489 sq. ft. Do. \( \frac{1}{2} \) do. do. 253-5 sq. ft.

Displacement at draught of 4' 7\(\frac{1}{2}\)" being \( \frac{1}{4} \) load draught: 300 tons. Displacement at draught of 9' 3" being \( \frac{1}{2} \) load draught: 1165 tons. Displacement at draught of 13' 10\(\frac{1}{2}\)" being \( \frac{3}{4} \) load draught: 2210 tons. Displacement at draught of 18' 6" or load draught: 3440 tons.

"The foregoing data afford all the particulars required for the construction of Peake's curve of vertical sections, whence may be deduced the position of the vertical line passing through the centre of gravity of displacement, and also the positions of the centre of gravity of the fore and aft bodies respectively.

"It will be observed, from the foregoing data of the constructive elements of the Bremen, that the maximum immersed section is at the middle of the length, and that the vertical sections are in such ratio to each other, with reference to their respective positions that the curve of vertical sections will be a close approximation to a parabola.

"The ratios deducible from the foregoing particulars of constructive data, combining Peake's curve of immersed vertical sections with the curve of displacement, will give a close approximation to the type of form of the immersed hull.

"The engines of the Bremen consist of two direct-acting inverted cylinders, 90 inches diameter and 3 feet 6 inches stroke, fitted with expansion-valves capable of working expansively to a high degree. All parts of the engines are felted and lagged with wool wherever practicable, the lower 16 feet of the funnel being surrounded by a casing forming a superheating chamber, the steam entering at the lower end, and passing off at the top into the steam-pipes leading to the cylinders.

"On the important question as to the extent to which the ordinary smooth-water trial of a steamer affords a criterion of the greatest average performance that may be expected of the vessel at sea, this Committee has not been able to obtain such an extent of returns of the comparative smooth-water trials and sea performances of the same ships as enable them fully to respond to this part of the inquiry, and they refrain from expressing any speculative opinion, because they have adopted the principle which they desire to recommend to the notice of the British Association, that shipping improvement is to be discovered by statistical records and analysis of the constructive elements of ships that have practically shown themselves to possess good sea properties, rather than by assuming the mere theories of optimistic speculation from whatever source such opinions may emanate; in short, that experience of actual performances at sea, statistically recorded and utilized by being made the basis of comparison, is the most reliable base on which to construct an inductive system of progressive improvement in naval architecture and marine-engine construction. This Committee, however, have much satisfaction in being enabled to commence this inquiry by recording the sea performance of the before-mentioned vessel Bremen, on a passage from Bremen Haven to New York and back, during the months of June and July last, during the whole of which passages indicator-cards were frequently taken, and the indicated working power of the engines ascertained. On the outward passage the mean displacement was 2578 tons, the mean indicated horse-power was 1078, and the mean speed 12-28 knots per hour, giving a coefficient by the formula referred to as 204; but on the return-passage the mean displacement was 2900, the mean indicated horse-power 1010 and the mean speed at the rate of 11-92 knots per hour, giving a co-efficient = 348. Hence, the mean co-efficient of the out and home passage = 276, being about 13 per cent. below the co-efficient (319) obtained on the smooth-water test-trial of the ship. The state of the weather and the sea was also recorded daily; it appears to have been adverse on the out passage, but favourable on the homeward passage. The committee are therefore of opinion, that by following up this course of statistical record of the smooth-water trial and subsequent sea performances of ships respectively, a tabular statement might be compiled, showing the probable ratios of the coefficients of smooth-water and sea performance, corresponding to the various rates of speed for which steamers may be respectively powered, whence the smooth-water test-trials of ships may be made available as approximately indicative of the sea service capabilities of ships as respects their dynamic properties.

Such are the statistical data of the constructive elements and dynamic capabilities of the Bremen; and if all steam-vessels engaged in the mercantile transport service of Britain were equally effective as respects the mutual relations of displacement, speed, and power, that is capable of producing a coefficient of dynamic capability = 319, by the formula referred to, it is probable that the prime cost expenses of steamship transport per ton weight of cargo conveyed on long passages would, on the aggregate of the foreign trade of Britain, be reduced not less than 25 per cent. as compared with the prime cost expenses incurred by steam-vessels of the average dynamic capability in present use.*

Tabulated results of the performances of many vessels will be found in the article Steam Navigation; but the following results of the trials in smooth water of four of the vessels, whose lines and dimensions are given in the plates, may be quoted here:

| Name of Ship | Draught of Water | Indicated Horse-power | Speed in Knots | |--------------|------------------|-----------------------|---------------| | Delta | | | | | Ceylon | | | | | Pera | | | | | Nubia | | | |

Plates XI., XII., XIII., and XIV. are specimens of very fine vessels in the fleet of the Peninsular and Oriental Company. The Pera is especially celebrated for her performances, as also the Ceylon. The following table is interesting as showing the performances of the Nubia on her actual voyages at sea:

### S.S. NUBIA.—Calcutta to Suez.

| Voyage | Sandheads to Madras, 663 Miles | Madras to Point de Galle, 243 Miles | Point de Galle to Aden, 2154 Miles | Aden to Suez, 1308 Miles | |--------|---------------------------------|-------------------------------------|-----------------------------------|-------------------------| | Time | Speed | Time | Speed | Time | | No. | H. M. | E. F. | H. M. | E. F. | | 4 | 52 25 | 12 5 | 43 8 | 12 5 | | 5 | 66 55 | 9 7 | 52 30 | 10 3 | | 6 | 66 55 | 9 7 | 52 30 | 10 3 | | 7 | 54 55 | 12 4 | 43 30 | 11 6 | | 8 | 56 0 | 11 6 | 43 30 | 11 6 | | 9 | 59 40 | 11 1 | 47 20 | 9 4 |

Under weigh, 27,900 miles Under steam, 28,542 miles

Total: 2525 6 2751 0 Average: 420 51 458 30

### Suez to Calcutta.

| Voyage | Suez to Aden, 1308 Miles | Aden to Point de Galle, 2154 Miles | Point de Galle to Madras, 545 Miles | Madras to Sandheads, 663 Miles | |--------|--------------------------|------------------------------------|-------------------------------------|-------------------------------| | Time | Speed | Time | Speed | Time | | No. | H. M. | E. F. | H. M. | E. F. | | 4 | 112 16 | 11 5 | 178 0 | 12 0 | | 5 | 108 16 | 12 1 | 174 40 | 12 2 | | 6 | 112 0 | 11 5 | 190 55 | 11 1 | | 7 | 122 10 | 10 5 | 206 30 | 10 3 | | 8 | 129 40 | 10 1 | 194 15 | 11 0 | | 9 | 118 15 | 11 0 | 192 10 | 11 1 |

Under weigh, 27,900 miles Under steam, 28,542 miles

Total: 2458 50 2673 0 Average: 409 52 445 30

Distance in calculating speed taken from Sandheads; but, in calculating consumption of coal, the whole distance to Calcutta is taken.—Coal account not available for other distances.

* Instead of Voyage 4, on which iron shaft was broken. SHIP-BUILDING.

MATERIALS USED IN SHIP-BUILDING.

Nothing can be more important to the naval architect than a thorough knowledge of the properties of the materials with which he has to deal. He requires this to enable him to dispose them to the greatest advantage, and with the least possible expenditure; and thus to produce a well-proportioned structure of great and uniform strength. The introduction of iron as a material for ship-building has enlarged this field of inquiry, and has led to much discussion as to its merits in comparison with those of timber.

The properties of timber will be first considered. A lengthened examination into the nature and qualities of the different varieties used in ship-building cannot, however, be attempted here, as the space which can be allotted to the subject will not admit of more than a few practical observations. Deterioration and decay, in timber-built ships, may result either from the decay to which timber itself is subject, in common with all organic matter, and which may be hastened or retarded according as destructive or preservative influences are brought into action; or they may be the consequences of an injudicious combination of destructive agents with the inorganic compounds of the timber, thus inducing not only premature but unnatural decay. All large masses of timber in close contact are subject to deteriorating influences, such as a high degree of temperature, an increase of moisture, or a want of free circulation of air. These and other agencies, by promoting fermentation, lead to the first stage of decomposition, whereas the reverse of these conditions would in like manner retard its progress. Moisture as well as heat is necessary to produce fermentation, but when heat and the other agencies are at work, moisture will generally be found to exist, either left in the timber itself, or absorbed by it from the atmosphere.

Decay of timber, when accompanied by the growth of fungi upon its surface, has received the name of dry-rot. This term was probably applied to it in consequence of the peculiarity, that wood so decomposed becomes a dry friable mass without fibrous tenacity, the parasitical fungi robbing the timber of its substance to support their own growth. In general, decay, when it takes place in this particular form, may be traced to imperfectly seasoned material, and the inference may be drawn with a considerable degree of probability, that the natural juices of the timber are necessary to the growth of fungi, and consequently that if these juices could be entirely abstracted or destroyed, this species of decay might be prevented. It does not follow that the presence of any of these juices will necessarily produce dry-rot, should the circumstances in which the timber is placed be such as to tend to their dispersion, or to their remaining in a dormant state. But as they do undoubtedly remain in much timber that is considered seasoned, any alteration of circumstances to prevent a free circulation of air, to lead to a deposition of additional moisture, and at the same time to an increased temperature, will in all probability induce the growth of fungi, and cause the destruction of the timber.

In ships, the frequent presence of these injurious elements must necessarily tend to produce fermentation. But though these facts are perfectly well known, it is remarkable how little attention has been paid to the necessity of a free circulation of air upon the timber of such parts of a ship as are below the surface of the water. This may be effected in various ways, though it is doubtful whether in all cases the current of air produced by natural causes would induce a sufficiently rapid circulation. This subject was forcibly brought before the Admiralty by Mr Creuze in 1827, but was not taken up or acted upon. In the navy, the decrease of expense which would be occasioned by any increase of durability in ships, laid up in ordinary, would be great; and in reality, with proper care and arrangements, there is no reason why the timbers of a ship so situated should not be almost as durable as the same wood employed in houses and other structures. The expense caused by decay is even greater in ships than in houses, yet the attention paid to the subject has been in an inverse ratio. The same facilities for the prevention of decay are not available for ships in commission, and if their timbers should have been unseasoned, or have had much of the natural sap left in them, dry-rot must almost necessarily ensue. It may be especially looked for in ships sent to a warm climate immediately after their construction, and exposed to a high temperature, and of its attacking these, many instances have occurred even within the last few years.

The same evils exist to a greater degree in merchant vessels. Private ship-builders are unable to keep their capital locked up in a large stock of the different classes of timber fit for the different ships they may be called upon to build, and as the purchaser ordinarily requires a speedy execution of his order, the use of unseasoned timber is the necessary consequence. No better arrangements for the prevention of decay seem to be made on board of merchantmen, after they are built, than on board of men-of-war. Lloyd's register of shipping may be said to have an injurious influence on this question. The register is kept by a joint-stock company, and a committee of their body composed of ship-owners, merchants, and underwriters, with a staff of professional surveyors, have laid down a code of rules for the construction of ships as a guide to their classification on survey. By these rules, a ship built of the very best species of timber, thoroughly seasoned, can be classed as a first-class ship for twelve years only; a renewal for eight years may be obtained, but not without much trouble and expense; and further extension again of four years involves another expensive survey. Sufficient inducements are apparently, therefore, not held out for increasing the durability of ships. Many teak-built ships have lasted longer than these assigned limits, and yet no attempts have been made to rival them, thus leading to the belief that Lloyd's rules have had the effect of rendering builders and owners satisfied with existing results. It has been argued that, to season a ship after she is built, by a free circulation of air, will cause shrinkage, and thus injure the good fitting and the strength of the fabric, and that it will strain the fastenings, and admit damp, and thus cause the decay it was intended to obviate. In reply to this it may be urged, that shrinkage could never be produced to this extent on the timbers of a ship by the circulation of air, had they not been in such an unseasoned state as to be totally unfit for use; and that even in such a case, it would be far better to take the chance of less certain mischief, than to leave the ship to inevitable destruction by dry-rot. These remarks show the importance of well-seasoned timber for ship-building, and have been insisted upon here, not from any supposed want of general knowledge of the fact, but to show the importance of applying the means which exist to remedy the evil.

It must be evident that when timber is to be closely jointed to other timber, to form a compact mass, the whole should not be wet with rain, or water-soaked when put in place. The importance of this is recognised by Lloyd's rules allowing one year to be added to the prescribed period of durability of any ship built under a roof. All vessels laid down in royal dockyards have this advantage.

Different species of timber are possessed of very different qualities, both as regards their durability and their strength; qualities. Oaks and other hard close-grained woods, being the most different durable, are chiefly used for the frames of ships. The species of juices of the oak are of an acid nature, and besides the woods, ligneous, which it has in common with other woods, it contains the Gallic acid peculiar to itself. Oak when used in

Materials in an unseasoned state is extremely liable to dry-rot, which in some cases has been found to destroy it in the space of a few months. Teak is a very valuable timber for shipbuilding, but like other woods it varies much in quality according to the soil in which it is grown, and consequently requires great care in its selection. Morning sail, green heart, morra, and iron-hawk, are also valuable woods. Like teak they are extremely durable, and are more oily and resinous in their nature than oak. The whole of the foregoing are classed together by Lloyd's committee as superior woods, and are admitted for the construction of ships classed for a durability of twelve years. The general classification of woods by this committee is as follows:

Mahogany of hard texture, Cuba Sibon, and pencil cedar, Adriatic, Spanish, and French oak ........... 10 years. Red cedar, Angelica, and Venetian; other continental white oaks, Spanish chestnut, stringy bark, and blue gum ........... 9 North American white oak, and American sweet chestnut ........... 8 Larch, hackmatack, tamarack and juniper, pitch pine and English ash ........... 7 Coward, American rock elm ........... 6 Baltic and American red pine, European and American grey elm, black birch, spruce fir, English beech ........... 5 Hemlock ........... 4

There are some slight variations in the durability assigned to these when used for other parts of the ship than the ribs or frames. Elm, which decays very rapidly when alternately wet and dry, is very durable if kept constantly submerged in water. On this account, as well as for its qualities of strength and toughness, it is well adapted for the keels of vessels. Other woods will be mentioned hereafter when the sources of the supply of timber for shipbuilding are considered.

The difficulty of obtaining properly seasoned timber whenever it may be wanted, and the great expense attending the early decay of unseasoned timber, have led to various means being proposed for its preservation. Saturation of the timber with various chemical compounds, has been the method generally suggested for its accomplishment. In India, Machenochie, by steaming his timber, and then condensing the steam in the tank, and producing a partial vacuum, endeavoured to dissolve and carry off the juices of the timber, and he then submerged it in an oil obtained from the chips and sawdust of teak. Steaming or stoving timber has always been considered advantageous for wood used in a green state. Exposing it to the action of water has been advocated with the same view, and this certainly tends to shorten the time required for weather seasoning thereafter. About 40 years ago the timber used in the royal dockyards was ordered to be submerged in salt water for some time, and then stamped with the word "salt." Pieces of sound timber with this mark are found in men-of-war up to the present day. Mr Kyan patented a process for preserving timber, by saturating it with corrosive sublimate; and Sir W. Burnett, late Medical Director-General of the Navy, patented the use of chloride of zinc, but with neither of these processes is the effect in all cases certain. Creozote appears to preserve timber with greater certainty than any other chemical material yet used. The timber is put into a close tank, the air is abstracted, and the vacuum is kept up for two or three hours by continued pumping, to allow the air to escape from the pores of the wood. The creozote is then introduced, and is forced into the tank, until a pressure of about 150 lb. to a square inch is obtained. This pressure is kept up by continued pumping during successive days for forty-eight hours, or for as long as may be required to make the timber absorb the requisite amount. This process is chiefly used for pine timber. Yellow pine should absorb about 11 lb. to the cubic foot, and Riga pine about 8 lb. The timber is weighed before it is put into the tank, and again after it is taken out, to ascertain the amount absorbed. Should this prove less than the amount required, it is returned to the tank for a repetition of the process.

Creozote timber has hitherto been chiefly used by civil engineers in land and sea works. The objections to its use in ship-building are its offensive smell and its great inflammability. Its power of protecting timber from natural decay, and of resisting the teredo navalis, or any of the other worms to whose ravages ship's timber is subject, if it be not thoroughly covered with copper sheathing, appear to render it peculiarly fit for such a purpose as doubling upon a ship. If found to answer, it might be used in thin boards as a sheathing instead of copper.

Another process which is applicable to the preservation of Dr Boucherie's certain descriptions of straight-grained and porous timber, cherries has been patented by Dr Boucherie, a French chemist of process note, and been brought forward in this country by a company formed for the maintenance of the permanent way of railways. They have published the following information respecting it. Instead of using great pressure, as before explained, to impregnate the tree, a moderate pressure only is applied to one end of it; the effect is to expel the sap, and fill the tubes or pores of the timber with the preserving liquor. The tubular structure of trees has been long known, and Dr Boucherie's process shows that no connection exists between the tubes laterally. Colouring liquid applied in the form of a letter or word at one end of the tree appears in the same shape at the other. The fluid used by Dr Boucherie is a solution composed of one part of sulphate of copper to one hundred parts of water by weight. The specific gravity of the solution, when of proper strength, at 60° Fahr., is 1-005, or nearly so. A water-tight cap is placed on one end of the tree which is to be saturated, and the solution is introduced within it by a flexible tube. The pressure required not being more than from 15 to 20 lb. on the square inch, it may be obtained in a very simple way, by raising the tank which contains the solution 30 or 40 feet from the ground. When the pressure is applied the sap runs in a stream from the opposite end of the tree; and a ready means exists of discovering when it is exhausted and the whole length of the tree penetrated, by rubbing the end with a piece of prussiate of potash, which will leave a deep brown mark when brought into contact with the copper of the solution. The sap and surplus solution, should any pass through the tree, may be pumped back into the reservoir, the sap being a better solvent of the sulphate of copper than water, if it should happen to be impregnated with lime or other impurities. There are certain kinds of timber which are impenetrable by the solution applied in the manner described. It answers best with trees that are the least costly, as beech, birch, larch, Scotch fir, alder, elm, poplar, &c. Trees felled any time between November and May may be prepared in the latter month. But when they are cut down in May or any month between then and November, they should be prepared within three weeks of the time of felling. It has been found, in the preparation by this system of vast quantities of timber for the French navy and railways, that the time necessary for the operation depends both on the length of the tree and on the description of timber. Trees of 40 feet in length, prepared at Fontainbleau for the French navy, required from eight to ten days to become sufficiently impregnated; whereas for lengths of 9 feet only, the process was accomplished in twenty-four hours. A summary of experiments made in Derby with this process is given in the following table. It will be observed from the facts there stated, that the pores of the poplar are more pervious than those of other woods; and the rapid and large absorption of the fluid by the memel timber shows, that the pores of fir timber, when the natural juices are dried up, still afford a continuous channel for its flow:— One great advantage attending this method, and which is likely to render its application very general, is the inexpensive nature of the apparatus required.

Seasoning timber, by exposing it for a lengthened period without subjecting it to any other process, has received much attention, and much controversy has arisen upon the best mode of carrying it into effect. It may perhaps be stated as the general opinion, that rough timber may be improved in this country by stacking it off the ground, that it may not be injured by damp. Sided timber, thick stuff, and plank, should always be stowed under sheds, and these must be airy and well ventilated, without partial draught which could affect the ends or any one portion of the timber more than another. Two or three years are required to season these descriptions of timber to a moderate degree only. Mast spars are best protected when submerged under water, and if buried in mud they are still more effectually preserved. Boards of mahogany or fir are well seasoned by being stacked on end in the open air without covering, but raised a little from the ground to avoid damp. In the royal yards it was formerly the custom to allow ships to stand in frames for various periods before they were planked, but the necessity of building ships rapidly has of late years precluded the possibility of doing this; and the evil effects have been too apparent. The following tables show the results of weather seasoning, as collected by Mr Fincham, and published in his work on the Outlines of Ship-Building:

### A Table of the Shrinkage and Loss of Weight in Seasoning, of the principal Timbers used in Ship-building: the period of seasoning was ten years.

| Species of Timber | Green | Seasoned | Relative shrinkage and loss of weight | Weight of a cubic foot | |------------------|-------|----------|-------------------------------------|-----------------------| | | Dimens. | Weight. | Dimensions. | Weight. | Dimens. | Weight. | Green | Seasoned | | English Oak | butt... | 6 by 6 | 7 8 | 6 by 5 1/2 | 6 7 | 1 000 | 1 000 | 60 | 51 1/2 | | | top... | 7 10 | 5 1/2 | 5 1/2 | 6 6 | 1 010 | 1 176 | 61 | 51 | | African Oak | butt... | 8 0 | 5 1/2 | 5 1/2 | 6 5 | 1 010 | 1 588 | 64 | 50 1/2 | | | top... | 7 4 | 5 1/2 | 5 1/2 | 6 0 | 1 000 | 1 176 | 68 | 48 | | | butt... | 9 2 | 5 1/2 | 5 1/2 | 6 0 | 1 068 | 1 069 | 73 | 64 | | | top... | 8 6 | 5 1/2 | 5 1/2 | 7 2 | 1 066 | 1 176 | 67 | 57 | | Italian Larch | butt... | 7 12 | 5 1/2 | 5 1/2 | 7 2 | 1 033 | 0 588 | 62 | 57 | | | top... | 7 4 | 5 1/2 | 5 1/2 | 6 10 | 1 010 | 0 588 | 68 | 53 | | Scotch Larch | butt... | 4 15 | 5 1/2 | 4 8 | 1 000 | 0 411 | 39 | 36 | | | top... | 4 15 | 5 1/2 | 4 8 | 1 021 | 0 333 | 36 | 36 | | Cuba Cedar | butt... | 5 0 | 5 1/2 | 4 9 | 1 021 | 0 334 | 40 | 36 | | | top... | 5 1 | 5 1/2 | 4 9 | 1 021 | 0 354 | 40 | 27 | | | butt... | 4 8 | 5 1/2 | 4 9 | 1 021 | 0 323 | 34 | 23 | | | top... | 4 10 | 5 1/2 | 4 1 | 1 000 | 0 530 | 37 | 22 | | New South Wales Cedar | butt... | 4 5 | 5 1/2 | 4 0 | 1 010 | 0 300 | 34 | 22 | | | top... | 3 12 | 5 1/2 | 3 7 | 1 021 | 0 300 | 30 | 27 1/2 | | | butt... | 4 0 | 5 1/2 | 3 12 | 1 000 | 0 235 | 32 | 30 | | | top... | 4 3 | 5 1/2 | 3 12 | 1 010 | 0 411 | 33 | 30 | | | butt... | 3 14 | 6 | 3 0 | 0 979 | 0 833 | 31 | 24 | | | top... | 3 10 | 5 1/2 | 3 5 | 0 989 | 0 830 | 29 | 26 | | | butt... | 4 0 | 5 1/2 | 3 10 | 1 010 | 0 382 | 32 | 29 | | | top... | 3 12 | 5 1/2 | 3 6 | 1 000 | 0 323 | 30 | 27 1/2 | | | butt... | 4 5 | 5 1/2 | 3 8 | 1 000 | 0 823 | 35 | 28 | | | top... | 4 5 | 5 1/2 | 3 9 | 1 021 | 0 706 | 34 | 28 |

### A Table of the Transverse Shrinkage in Seasoning of Board, 12 inches square and half-an-inch thick: the period of seasoning was thirteen years.

| Species of Timber | Shrunken in Seasoning | |------------------|-----------------------| | English Oak | butt... | 1/4 the breadth | | | top... | 1/4 " | | African Oak | butt... | 1/4 " | | | top... | 1/4 " | | Elga Fir | butt... | 1/4 " | | | top... | 1/4 " | | Dantle Fir | butt... | 1/4 " | | | top... | 1/4 " | | Virginia Pine | butt... | 1/4 " | | | top... | 1/4 " | | Yellow Pine | butt... | 1/4 " | | | top... | 1/4 " | | Larch | butt... | 1/4 " | | | top... | 1/4 " | | English Elm | butt... | 1/4 " | | | top... | 1/4 " | | Canada Elm | butt... | 1/4 " | | | top... | 1/4 " | | Cowdie | butt... | 1/4 " | | | top... | 1/4 " | Seasoning timber by exposing it to a current of heated air at a higher velocity than is engendered by natural causes, was introduced by Mr Davison. The desiccating process, as he terms it, and as explained by him to the institution of civil engineers in 1853, consists in impelling rapid currents of air through a chamber or chambers containing the wood; spaces being left between the ranges or tiers of timber for the heated air to act uniformly upon all its sides. The moisture, as soon as it is cooled, passes instantly away through an opening in the roof of the chamber, and this appears to be a distinguishing and essential feature in the process. The wood remains in the chamber until by weighing a sample from time to time, the whole aqueous matter had been expelled from its pores. Charring wood in a sand-bath was practised in the beginning of the last century, and apparently with some success; but the heat must have been much greater than that employed by Davison, and the process probably was much more rapid. In carrying out the desiccating system, attention must be paid to the following points:—Different woods and different thicknesses of wood, require different degrees of heat; hard woods and thick logs of wood require a moderate degree of heat, from 90° to 100° Fahr. The softer woods, such as pine, may be safely exposed to 120°, or even to a still higher temperature; and when cut extremely thin and well clamped, 180° or 200° have been found rather to harden the fibre and to increase its strength. Honduras mahogany in boards of one inch in thickness may be exposed with advantage as regards colour, beauty, and strength, to a heat as great as 280° or 300° Fahr. A slab of Honduras mahogany 1½ inch thick, cut fresh from the log, was wholly deprived of its moisture, amounting to 36 per cent. by exposure to the temperature of 300° for fifty consecutive hours. In practice, however, it is found that from 115° to 120° of temperature brings almost every kind of timber in slabs or boards of moderate thickness, safely and steadily towards complete desiccation in a comparatively short space of time. For boards up to 4 inches thick, one week is sufficient for every inch of thickness, thus one week for 1 inch thick, and four weeks for 4 inches thick, but beyond this thickness the proportions require to be increased. For 6 inches thick, seven weeks should be allowed; for 8 inches ten weeks, and so on. These periods are fixed on the supposition, that the rapid forced current of heated air will be kept up only during the day of twelve hours, and that the chamber will then be closed till the following morning, that being the customary mode of working.

English oak requires more than ordinary care when thus prepared. It should never be exposed under any circumstances for any length of time to a higher temperature than 105°; more intense heat has been found to act upon the Gallic acid, or on the fibres in some peculiar way, so as to produce internal fissures. Mr Davison also stated, that still heat like that of an oven had an effect upon wood totally different from that produced by a current of heated air. In the one case the fibre is rendered short, brittle, and weak; in the other, all that is valueless is driven away, and the albumen becomes solidified or coagulated into a hard compact substance, and the fibres gain a great increase of strength and rigidity. Seasoning under ordinary degrees of temperature has a completely different effect on the albumen, which, if not previously dissolved or washed out by any of the processes previously referred to, remains, when dried, in a soft spongy state, ready to become an absorbent of moisture.

It has been found by experience that 100 feet per second is the best velocity for the current of heated air, and with a proportionate area of inlet-pipe, a sufficient quantity should be delivered into the chamber to cause a complete displacement of the air and moisture in three minutes. If a desiccating chamber contains 30,000 cubic feet of air, 10,000 cubic feet ought therefore to be propelled into it per minute, care being at the same time taken that the area of the outlet or outlets for the escape of the moisture exceed the area of the inlet-pipe, and that they be so arranged as to avoid a direct current between them.

The Board of Ordnance adopted this system for gun-stocks in 1840. Previous to its introduction, about 400,000 stocks were undergoing regularly a course of seasoning, each requiring to be turned once or twice every year to avoid the ravages of worms or decay. In a report from Mr Lovell, then her Majesty's inspector of firearms, he states respecting some gun-stocks subjected to the process:—"One half of the number were quite fresh cut and green wood, the other mostly, had been about twelve months in store; the total weight before the process, 536 lb. 9 oz., and after sixteen days' exposure to a current of air heated to 110°, or 114° Fahr., that weight was reduced to 413 lb. 14½ oz.; that is to say, 122 lb. 10½ oz. of moisture had been driven off. Some of the stocks had been purposely selected with seen cracks in the butts and other faults, for I expected that those cracks and faults would be exaggerated by the heat of the chamber. But the result was not so; on the contrary, they were closed considerably behind the marks that had been stamped upon the ends of them before they were put in, and the whole number of stocks came out in good condition, and fit for immediate use." He proceeds to say:—

"The wood is better seasoned than when dried in the open air; 1st, Because the albumen being dried on the pores and in the capillary tubes, renders the fibre stronger and less liable to absorb moisture; 2d, The wood is stronger, tougher, and, of course, more capable of withstanding the effects of violent vibration from the lateral adhesion of the fibre being better preserved; 3d, It works smoother and more waxy under the chisel, and has less tendency to speel and crumble away, which is generally the great fault of steam-dried timber. I have now worked nearly 30,000 desiccated stocks, none of which had been under the process more than twenty-one days; and my opinion is very decided, that the wood is more thoroughly seasoned, and with much greater certainty, than if it had been merely exposed to the open air in the usual way for three or four years. The desiccating chamber created in the royal manufactory at Enfield continues in full activity. The heat is kept down to a medium degree, between 90° and 100°; and at this temperature it delivers the stocks perfectly seasoned in fourteen to sixteen days, according to the quality of wood, whether of sap or heart; and I propose to subject the whole of the stocks to it in future, whether they have been air-dried previously or not, in order to make sure that the whole shall have been equally seasoned."

Some bearers of Riga pine and American elm, after they had been in use for about six years, and exposed for that length of time to a temperature of 115° or 120° of heat, at which the chamber invariably stood, were examined, and were found to be perfectly sound and in excellent condition; thus proving that the process, even though continued for so long a period, did not injure in the slightest degree the fibre or the strength of the wood.

It is difficult to understand how the timber subjected to this process can be rendered more capable of sustaining a tensile strain, if this be the case, but it is natural that the albumen, when hardened in the pores, should render it more incompressible, and therefore more capable of resisting any strain when the strength depends on this property. For hard woods, to which Dr Boucherie's process is not applicable, desiccation seems to be admirably adapted," Mr Lovell's experience with the walnut-tree gun-stocks appearing conclusive.

The following table is interesting, giving the results of experiments made by Mr Davison:— ### General Results of Desiccation

| Description | Yellow Pine | Mahogany | Riga Pine | English Oak | |-------------|-------------|----------|-----------|-------------| | **Dimensions** | **Average Percentage lost** | **Average No. of Days desiccating** | **Ratio of time in which equal degrees of desiccation were effected by the natural and artificial processes** | **Average Percentage lost** | **Average No. of Days desiccating** | **Ratio of time in which equal degrees of desiccation were effected by the natural and artificial processes** | **Average Percentage lost** | **Average No. of Days desiccating** | **Ratio of time in which equal degrees of desiccation were effected by the natural and artificial processes** | | Board | | | | | | | | | | | Inch | 20-76 | 21 | 25-8 | 26 | 6:1 | 17-63 | 24-3 | 36:1 | 24-9 | 31-5 | 11:1 | | Plank | 35 | 42 | 6:1 | 21-2 | 37 | 15:1 | 14-61 | 34-3 | 62:1 | 32-36 | 47 | 20:1 | | Mean results | 20-44 | 52-8 | 7:4:1 | 18-55 | 45-2 | 29-4:1 | 16-11 | 45-79 | 43-4:1 | 29-19 | 55-8 | 29-6:1 | | Sq. Inch | 17-19 | 7 | 28:1 | 13-97 | 7 | 71:1 | 13-46 | 7 | 71:1 | 22-72 | 12 | 16:1 | | Mean results | 18-27 | 10 | 36:1 | 14-95 | 10½ | 71:1 | 24-38 | 7 | 71:1 | 23-04 | 16-5 | 13:1 | | Scantling | 37-19 | 23 | 6:1 | 17-56 | 23 | 71:1 | 12-05 | 12-33 | 71:1 | 29-38 | 37 | 20:1 | | Mean results | 26-2 | 9:1 | 15-7 | 34-6 | 46:1 | 12-64 | 32-11 | 65:1 | 22-57 | 55-8 | 20-4:1 |

### Comparative Strength and Deflection of Desiccated Specimens and their Duplicates

| Description | Yellow Pine | Mahogany | Riga Pine | English Oak | |-------------|-------------|----------|-----------|-------------| | Dimensions | Sq. Inch | In. | Sq. Inch | In. | Sq. Inch | In. | Sq. Inch | In. | | Broke with | Deflection | Broke with | Deflection | Broke with | Deflection | Broke with | Deflection | | Desiccated specimens | 1 | 45½ | 6 | 1 | 70½ | 9½ | 1 | 46 | 8½ | 1 | 64½ | 9½ | | Woolwich | 1 | 40½ | 11 | 1 | 62½ | 8½ | 1 | 48½ | 8½ | 1 | 84½ | 11½ | | Desiccated | 1½ | 138 | 6½ | 1½ | 182½ | 6½ | 1½ | 100 | 4½ | 1½ | 128½ | 7 | | Woolwich | 1½ | 107 | 4 | 1½ | 156 | 4½ | 1½ | 127 | 5½ | 1½ | 135½ | 4 | | Desiccated | 2 | 237 | 4 | 2 | 436 | 6½ | 2 | 346 | 4½ | 2 | 335 | 4 | | Woolwich | 2 | 282 | 3½ | 2 | 304 | 4½ | 2 | 363 | 4½ | 2 | 327 | 4 | | Desiccated | 3 | 884 | 3½ | 3 | 1514 | 4½ | 3 | 996 | 3½ | 3 | 996 | 3½ | | Woolwich | 3 | 716 | 4½ | ... | 1318 | 5½ | 3 | 793 | 4½ | ... | 3 | 793 | 4½ | | Desiccated | 4 | Were not broken | 1½ | ... | ... | ... | 4 | Were not broken | 1½ | ... | 4 | Were not broken | 1½ |

The weights were applied at one end of the piece, at a distance of 3 feet from the fulcrums.

The slow progress made in the introduction of this process has doubtless arisen partly from a fear that so speedy a method of drying or seasoning is likely to warp and rend the timber. Though this result does ensue from exposing it to draughts in covered sheds, yet as the evil in this case arises from the partial action of the currents of air on the log or piece of timber, it need not be feared where the temperature and the current are equally diffused, as in the desiccating chamber. The expense of the apparatus is, however, a serious drawback to its introduction, except in works where a very large quantity of timber is used.

The best season for felling timber has been a subject of some discussion; but the evidence that has been collected felling seems to be in favour of that which is winter-felled. Its timber-specific gravity is less than if summer-felled; and it is natural to suppose that the less amount of sap in the tree will render it more readily and easily seasoned.

The relative value of the various woods must also de-

Materials used in Ship-Building.

The cohesive strength per square-inch, or power of resisting a tensile strain to tear the particles asunder, varies in different species. Professor Barlow, in his work on the strength and stress of timber, gives it as under for the following kinds of wood:

| Species of Timber | Cohesive strength per square inch | |-------------------|----------------------------------| | Ash | 17,600 | | Teak | 15,000 | | Fir | 12,000 | | Beech | 11,500 | | Oak | 10,000 | | Pear | 9,800 | | Mahogany | 8,000 |

These being the breaking weights, it will not be safe in practice to expose timber to more than about one-half of them.

Professor Hodgkinson has investigated the powers of different species of timber to resist a direct crushing force, and the results which he obtained show that this power varied greatly according to the state of seasoning. He found that timber, when in a wet and unseasoned state, could be crushed by a force less than one-half of that which would be required to crush it when properly seasoned, the moisture acting as a lubricating medium to allow the particles to slide upon each other more easily.

The following, however, may be taken as the crushing weights of the different species named, in an ordinary state as regards their degree of seasoning:

| Specific Gravity of Specimen | Species of Timber | Resistance per square inch in lbs. | |------------------------------|------------------|------------------------------------| | 560 | Yellow Pine | 5376 | | 540 | Cedar | 6674 | | 580 | Red deal | 5748 | | 640 | Birch | 6402 | | 660 | Sycamore | 7082 | | 753 | Spanish mahogany | 8198 | | 780 | Ash | 8883 | | 700 | Dry English oak | 9509 | | 980 | Box | 9771 |

No satisfactory rules have yet been promulgated to determine the weights which may be placed with safety upon wooden columns of different diameters and different lengths. It is not unusual in practice to confine the load to 500 lb. per square inch of section on a column of oak, and when required to carry this load per sq. inch, the length is generally limited to fifteen times the diameter. But, however short the column may be, it should never be loaded to a greater degree than one-third of the weights in the foregoing table, and the length should never exceed twenty, or at the utmost twenty-five, times the diameter without a great diminution of the load proposed above.

The strength of similar columns varies inversely as the squares of their lengths. Thus, if the weight which a column of oak of 5 inches diameter and 6 feet long will support with safety be taken at 9800 lbs., a column of oak of 5 inches diameter, and 10 feet long, will support only 2450 lbs., with an equal degree of safety, because by the proportion mentioned above

\[ \frac{10^2}{5^2} : 9800 : 2450. \]

The annexed table of data is given by Professor Barlow, in his work, for determining the weights which the different woods enumerated will respectively carry, when exposed to a transverse strain, and the rules which follow for its practical application are also taken from the same authority:

| Species of Timber | Tabular Value | |-------------------|---------------| | Teak | 2462 | | English Oak | 1672 | | Canadian, ditto | 1768 | | Danzic, ditto | 1457 | | Adriatic, ditto | 1383 | | Ash | 2026 | | Beech | 1556 | | Elm | 1013 | | Pitch Pine | 1632 | | Red Pine | 1341 | | New England FIR | 1102 | | Riga Fir | 1108 | | Mar Forest FIR | 1262 | | Larch | 1197 |

To find the ultimate strength of any rectangular piece of timber fixed at one end and loaded at the other:

**Rule:** Multiply the value given in the table of data by the breadth and square of the depth, both in inches, and divide the product by the length, also in inches; the quotient will be the breaking weights in pounds.

**Example 1.** What weights will a beam of English oak sustain before it breaks, when the breadth is 8 inches, the depth 12 inches, and the length 10 feet from the point of support?

The relative strength of English oak, as given in the table, is 1672.

Then \( \frac{1672 \times 8 \times 12^2}{120} = 16,051 \) lbs., or 7.255 tons.

**Example 2.** What weight will a beam of larch sustain before it breaks, when the breadth is 4 inches, the depth 6 inches, and the length 5 feet from the point of support?

Answer—2704 lbs.

To find the ultimate transverse strength of any rectangular beam, when supported at both ends and loaded in the centre:

**Rule:** Multiply the value given in the table of data by four times the breadth and square of the depth in inches, and divide that product by the length, also in inches, for the weight.

**Example 1.** What weight will be necessary to break a beam of teak, the breadth being 10 inches, the depth 14 inches, supported at each end, and the distance between the faces of the supports being 20 feet, the beam being loaded in the middle?

For teak, the value given in the table is 2462.

Then \( \frac{2462 \times 4 \times 10 \times 14^2}{240} = 80,425 \) lbs., or 35.904 tons.

**Example 2.** What weight will a beam of English oak carry before it breaks, the breadth being 8, the depth 12 inches; the beam being loaded in the middle, and supported at each end, and the distance between the faces of the supports being 15 feet? Answer—42,803 lbs., or 19.153 tons.

If the dimensions of a beam be required so as to support a given weight, the following rule must be used:

**Rule:** Multiply the weight in pounds by the length in inches; and this product, divided by the tabular value, will give the product of four times the breadth and square of the depth; then the breadth being known, we can find the depth; or the depth being known, we can find the breadth.

**Example 1.** What must be the dimensions of a beam of English oak to carry a weight of 5 tons in the middle, where the distance between the supports is 20 feet?

The tabular value for English oak is 1672,

\[ \frac{11200 \times 240}{1672} = 1607, \] which is the square of the depth multiplied by four times the breadth.

Let the breadth be 6 inches; then \( 6 \times 4 = 24, \) or four times the breadth.

Then \( \frac{1607}{24} = 66.96 = \) the square of the depth,

and \( \sqrt{66.96} = 8.18 \) inches, or 8\(\frac{1}{4}\) inches nearly.

Or, if we take the depth at 8 inches, then

\[ 8^2 = 64 \text{ and } \frac{1607}{64} = 25.1, \] and \( \frac{25}{4} = 6.25 \), or a little more than 6\(\frac{1}{4}\) inches—the breadth.

**Example 2.**—What must be the dimensions of a beam of red pine to carry a weight of 15 tons in the middle, when the distance between the supports is 30 feet? Answer—10 inches in breadth by 15 inches deep nearly.

If a beam be supported at both ends, and the load be equally distributed over its length, it will carry twice the weight; that is, the result obtained by the foregoing rule must be doubled.

If the beam be firmly fixed at both ends, so as to prevent the ends from rising, when the weight is applied in the middle, the result will be increased by its half; that is, a weight of 10 tons may be increased to 15 tons.

If the beam be fixed at both ends and loaded uniformly throughout its length, the result must be multiplied by 3; that is, a beam which will carry 10 tons in the middle when it is laid loosely upon its supports, will carry 30 tons when fixed at both ends, and the load distributed uniformly over its length.

It must always be remembered, in applying these rules to practice, that the weights found by them are the breaking weights. The proportion of the breaking weight with which it is considered safe to load a beam in actual use varies according to the nature of the material. In the case of cast-iron, which breaks without giving any warning, it is not considered safe to place more than one-third of the breaking weight upon it. In wrought iron and timber, which both show symptoms of being overstrained before they break, by becoming crippled, or by an amount of flexure so great as to be very observable to the eye, the load in practice may be one-half of the breaking weight, as found by the rules.

Experiments on the strength of materials are always valuable to practical men, as adding to the store of knowledge, and acting as a check on any rules which may be in use. A series of experiments on timber were made by Colonel Fowke, of the Royal Engineers, at Paris, during the universal exhibition held there in 1855, and the results were published at great length in the report upon that exhibition.

Mr Fincham made some experiments, with great care, on the transverse strength of timber, and the following table, showing the results, is extracted from his work on ship-building:

**A Table of a Series of Experiments on the Strength of the Undermentioned Species of Timber.** In each case the piece was three inches square and four feet long between the supports, and the weights were placed in the middle.

| Species of Timber and No. of Experiments | Specific Gravity | Weight at which piece broke | |-----------------------------------------|-----------------|----------------------------| | English oak, the mean of 8 experiments...| .791 | 32,973 | | Italian oak, the mean of 4 experiments...| 1.077 | 38,792 | | Danish oak, the mean of 4 experiments... | .704 | 39,732 | | African oak, the mean of 4 experiments...| 1.021 | 59,897 | | Maltese teak, the mean of 4 experiments...| .724 | 43,723 | | Moulmein teak, the mean of 4 experiments...| .909 | 34,292 | | Riga fir, the mean of 4 experiments... | .576 | 35,558 | | Diantaic fir, the mean of 4 experiments...| .708 | 36,718 | | Italian larch, the mean of 4 experiments...| .645 | 40,047 | | Scotch larch, the mean of 4 experiments...| .561 | 27,750 | | Hackmatack larch, the mean of 4 experiments...| .708 | 37,886 | | Cowdie, the mean of 4 experiments... | .614 | 39,317 | | Bermuda cedar... | .932 | 36,776 | | Cuba cedar, the mean of 4 experiments... | .524 | 24,948 | | Van Dieman's Land cedar... | .616 | 18,303 | | Mahogany, the mean of 4 experiments... | .636 | 30,093 | | New South Wales mahogany, the mean of 4 experiments...| 1.382 | 36,777 |

Rigidity, or the opposite of elasticity, is the power of resisting deflection or bending, when a weight is placed upon a beam, or when a side pressure is brought to bear against it. This power is increased in a much more rapid ratio than the power to sustain loads without fracture; thus, in order that a beam may bear 10 tons with the same degree of deflection as one bearing 5 tons, much less increase of dimensions will be required than will be necessary for a beam whose breaking weight is to be 10 tons, in comparison with one whose breaking weight is 5 tons. The possession of rigidity in a lateral direction is necessary to every beam to a certain extent, to prevent its bending side-wise and becoming crippled, and hence beams must not be too much reduced in their breadth relatively to their depth. In practice, the proportions of 2 for the breadth to 3 for the depth, and also of 3 for the breadth to 5 for the depth, are very common; but in joists of floors, and in other situations, where side props, or supports to prevent flexure, can be introduced, the depth is often made in a greater proportion, with the advantage of a saving of material, to carry the same weight.

The supply of timber for ship-building purposes is a subject of great importance, and has attracted much attention, both as regards the species grown in this country and those which are imported from abroad.

Some valuable remarks on foreign woods were lately made by Mr Leonard Wray, in a paper read before the Society of Arts, and published in their journal of 6th May 1859. He called attention to the fact, that before forests of the finest timber can be brought into beneficial use, a population is required to fell and trim the trees, as well as a good shipping port, and the cheapest possible means of bringing the timber from its native forests to the port of shipment. Honduras has long had its organised bands of woodcutters, and has long been one of the most important timber-exporting countries. It now exports about 25,000 tons of mahogany and 6000 tons of logwood annually, and the woodsmen in pursuit of these two staple products continually pass and repass other species of the finest quality of timber in the world. Amongst many other fine trees found there, Mr Wray specially enumerated the following:—The green heart, the live oak (Bignonia), and other oaks; the mahoe, the bullet-tree, the Neesberry bullet-tree, the ironwood, the locust, used for ships' planking and trenails; the dogwood, the red pine, the pitch pine (much superior to that of Carolina and the other southern states of America); the cedar (Cedrela odorata), a light and durable wood, not liable to dry-rot, nor subject to the attack of insects, and of which the trunk is 70 or 80 feet long, with a diameter of from 4 to 7 feet.

The morra is described by Mr Wray as a most valuable timber, the trees often attaining a height of from 100 to 150 feet, the lowest branches being 60 feet from the ground. The wood is extremely tough, close, and cross-grained, so that it is difficult to split, and not liable to splinter, which renders it particularly adapted for ship-building, more especially in the royal navy. The trunk makes admirable keels, timbers, and beams; and the branches having a natural crookedness of growth, are unsurpassed as knees.

Sir R. Schomburgk, referring to this tree, states that it grows abundantly in Guiana, on the banks of the river Berima, which is navigable for vessels drawing 12 feet of water, so that they might load close to the spot where the trees are cut down.

Mr Wray also mentions many other fine timber trees as the growth of Guiana, and Assam, Tenassarim, and the provinces and settlements in the neighbourhood of the Straits of Malacca. He states that a quantity of teak has for many years been exported from Moulmein, and other parts along the coast, but that the field which this healthy and most pleasant country still presents is so inexhaustible.

Materials that he considers it to stand unrivalled as a timber-producing country. Hitherto teak alone has been exported, but there are others which are considered quite equal, and even superior to it. He gives the following list of some of the best timber woods, which will serve to give an idea of the capabilities of these neglected provinces:

- **Aman**.—One of the hardest and most compact woods known. - **Adams**.—Strong and very durable; used in ship-building. - **Koan-las (Rottlera)**.—Excellent for rudders. - **Kot-wat-sai (Cedrela).**—Large timber, 40 to 70 feet long; used for ship-building. - **Eu-nyang-kwong-Ehong**.—For ship-builders; contains an aromatic oil, and is not attacked by insects. - **Kyee-go**.—Similar to teak. - **Kud-doss-alais**.—A large tree; used in ship-building. - **Kumazos**.—A very large tree; very hard and durable timber. - **May-Mayix**.—Used in ship-building. - **May-rang**.—Said to be very durable. - **May-tobol**.—Used for the bottoms of ships, considered preferable to teak. - **Mayan**.—An indestructible, strong, heavy, dark-red wood. - **Padaw**.—A beautiful, compact, and hard wood, sometimes called rosewood. - **Pengadok**.—Strong and durable. - **Pen-makes**.—Yields very strong knee-timber. - **Pyau-pau-dans**.—Hard, dense, and durable; called iron-wood. - **Sowndra**.—A very tough, elastic wood; said to be the strongest of all the Indian woods. - **Thal-bon**.—Fine solid timber, sometimes 70 feet long; used for boats. - **Tham-kya**.—A species of wood similar to Saul. - **Tha-nei**.—A kind of grey teak. - **Tha-nei**.—More resembling Saul. - **Tham-That**.—A kind of wood like Saul. - **Thet-yu-bon**.—A species of teak; close grained. - **Thuy-yau (Hopea odorata).**—An enormous tree of the Saul tribe; yields a strong, compact, and excellent timber, considered superior to teak; also a quantity of good dammar or resin. Insects never attack this wood, nor is it liable to rot. - **Tirbae (Quercus Ameritana).**—An oak; large tree; used in boat-building. - **Thomassupa**.—A large tree; used in boat-building. - **Thongy kyaus**.—Close grained, strong, heavy wood; used in ship-building. - **Thulboe (Mimusops).**—Used in ship-building. - **Thubor (Uvaria).**—A large tree; used in boat-building. - **Tongy-bong**.—A kind of red Saul. - **Thym-tree**.—A good, strong, durable wood; used in boat-building.

Of the Malacca woods Mr Wray gives a long list, and of these he describes the following from his own experience while resident in the straits:

- **Marboue**.—Very strong, hard, and heavy; used in shipping; not attacked by insects; will last 100 years. - **Bialangoe**.—Valuable wood for ship-building, especially for planks, mast, spars, &c. It grows in great abundance, especially near Singapore, and is largely exported to Mauritius, California, &c. - **Veserlant**.—Hard, tough, and very durable. - **Gibon**.—A pale yellow wood, close grained, hard, elastic, very durable, and generally used in boat-building. - **Tongmou**.—Used for house-building; hard, and exceedingly durable. - **Tongmou**.—House beams; considered very durable. - **Gibon**.—Hard, tough, elastic; used in boats. - **Moromate**.—Very large; light resinous wood, much used for planking, and in building boats.

Australia is the next country to which he directed attention; and though distant, it may yet become an important timber-exporting country, the timber being brought here as a home freight in return for our large exports. The trees of this country which are mentioned are the iron-bark, the tuart, the jarrah blue-gum, and morrell.

The tuart is especially mentioned as adapted for ship-building, as it is most difficult to split, and not liable to splinter.

The jarrah, whose stems average 65 feet long, nearly parallel, and without a branch or knot, is also a most important tree of this colony. It is not attacked by insects of any kind, nor has it any tendency to dry-rot.

There are forests of this wood, almost unmixed with other trees, in Western Australia, of more than 4 miles in depth, and which are known to extend for a length of 150 miles. Planks may be obtained from it 10 feet wide if desired. It is not only valuable as a ship-building timber, but also for furniture, being found of various shades of colour, and of almost every variety of grain.

A ship may therefore be loaded very advantageously with this timber after proper sawing-machinery has been erected in the country, as it may be converted into scantling and other pieces for furniture, which may be stowed along with the bulk timber of any size that may be desired.

Some very fine specimens of pine have likewise been imported lately from Vancouver's Island, of immense size, of great strength, and very durable.

Specimens of foreign woods may be found in the collections at Kew; at the Kensington Museum; East India House; Somerset House, Admiralty branch; and at the Crystal Palace.

Since the publication of this paper, containing so much valuable information, and so liberally contributed by Mr Wray to the Transactions of the Society of Arts, and from which the foregoing extracts have been so copiously taken, contracts have been made by the government for green-heart Tuart and Jarrah timber. It is to be hoped that this is a prelude to timber from our own colonies being hereafter used in the royal dockyards in larger quantities.

The importance of ship-building timber for the merchant service is undoubtedly decreasing, on account of the increasing use of iron; and it therefore behoves the government to make its own arrangements to originate and foster this trade in those districts pointed out by Mr Wray.

Though insignificant in comparison with these magnificent trees of foreign growth, the increasing quantity of larch now grown in this country deserves attention.

The larch (Pinus Larix) now so much grown in England as well as in Scotland, is frequently called Scotch fir, thus being mistaken for the "Scotch fir" as so called in Scotland (Pinus sylvestris), which has a dark-coloured foliage. The latter is considered superior for the purposes of architecture, but larch is better adapted for ship-building purposes whenever its size is sufficient. Like most other woods, it varies extremely, according to the soil on which it is grown, and care must therefore be taken in its selection and use. It stands exposure to wet and dry better than most timber, and is hence much used for pit-props in coal mines. The late Duke of Atholl induced the government to build a vessel of larch from his forest. She was called the Atholl; and though her durability has been very great, no further attention appears to have been as yet paid to the subject by the authorities.

A knowledge of the weight of the different species of Weight of timber is necessary to the naval architect, to enable him to compute or estimate the weight of the hull of the vessel which he is designing or constructing. Mr Edye, the late assistant-surveyor of Somerset House, published an elaborate work containing tables of the weights and the displacements of the different classes of men-of-war of his day, but now rendered comparatively valueless by the introduction of steam-vessels and the great changes in the proportion of ships. The following table, containing the weight of a cubic foot of timber in a green and seasoned state, is extracted from this work; and if the weights of the different timbers be compared with their strengths as previously given, it will be seen that the heavier timbers may be used without increasing the weight of the vessel, as their scantling may be reduced, and the same strength be retained, and with advantage, also, as to durability: Special care is required in the selection of materials to be used in combination with timber, in order that no chemical or other action, which may tend to premature decay, may take place between them and the timber. Great care is required in the use of iron for fastenings on account of the great affinity which exists between this metal and oxygen. The oxidation of the iron not only destroys the fastening itself, but has an injurious effect upon the timber surrounding it. If the nature of the wood be such that a supply of oxygen from the atmosphere can be kept up through its pores, the oxidation and destruction of the iron will be very rapid. The use of iron in combination with oak is particularly objectionable on account of the acid nature of this wood, and the quantity of oxygen which it contains. In oily and resinous woods the surface of the bolt, when driven, receives a coating of this matter, and is thus rendered less liable to oxidation. Such woods are also more impervious to the passage of a continued supply of oxygen. Iron fastenings, under copper sheathing, are also liable to be destroyed by the galvanic action which takes place between these metals. Many attempts have been made to prevent this action by driving the bolt so far into the wood that a cement of some kind could be put over the head of it, so as to break the connection between the metals, but no important results of any system of this kind are as yet known to have obtained.

Copper is therefore used largely for the fastenings of ships. This metal is liable to a very slight oxidation only upon its surface, and when this has taken place, all further oxidation ceases, and the metal is not destroyed, as is the case with iron. Copper, however, is not possessed of the same strength as iron, and is soft and ductile in comparison with it. It is therefore far from being so good a fastening, especially when driven through iron-knees and iron-riders. It is liable to be bent and crushed, or crippled at the neck, by the iron through which it has passed, if the ship be severely strained and work in any degree.

Some valuable experiments were made on the tensile strength of bolts of dockyard copper, Grenfell's copper, and Muntz's yellow metal, by Mr Jn. Kingston, of Woolwich dockyard.

The results are shown in the following table:

| Description of bolt | Tensile strength per square inch | |---------------------|----------------------------------| | Dockyard copper, average of 12 experiments | 49,480 lb., or 23 tons nearly | | Grenfell's copper, average of 11 experiments | 46,592 lb., or 23½ tons nearly | | Muntz's yellow metal, average of 11 experiments | 49,945 lb., or 24½ tons nearly |

Copper, from its ductile nature, is quite unfit to be used for any purpose where a cross-strain has to be resisted.

A late invention, by which a coating of copper is put upon iron, in the same manner that iron-plates are coated with tin, promises to be very valuable. Fastenings of this kind will then combine all the good qualities of both metals, and will tend materially to strengthen the general fabric of the ship.

Treenails of timber, equal in quality to that through which they are to be driven, make excellent fastenings, but their strength and their power of holding are not such that they can be used to the entire exclusion of metal fastenings.

The materials used for the sheathing of ships to protect them from fouling, and from the attacks of the teredo navalis, and other destructive worms, are chiefly copper and Muntz's metal. These metals are kept clean by the sea-water acting slightly upon them as a solvent, or by oxidation; and a gradual waste is therefore taking place continuously from their surface, thus preventing the adherence of any animal or vegetable matter. With a view to obviate this gradual wearing away, Sir H. Davy proposed to induce a galvanic action upon the sheathing by attaching protectors of iron on its surface. He succeeded to some extent; but in proportion as the iron was eaten away and the copper preserved, it became foul with sea-weed and shell-fish, so that his proposal was abandoned.

Iron for Ship-building.

The use of iron having now become common in the construction of ships instead of timber, a thorough knowledge of its properties is thus rendered necessary to the naval architect. The properties of wrought or malleable iron, as a material for the construction of the component parts of ships, will first be considered in a general point of view.

The strength of rolled iron varies with its quality; the Cohesive results given will be those due to an average quality, such strength as ought to be used in ship-building. The cohesive strength of bar-iron, or its power to resist a tensile strain, may be Bar-iron, safely taken at 25 tons, or 56,000 lb. per square inch of section. Messrs Robert Napier and Sons of Glasgow have made some valuable experiments on the cohesive strength of wrought-iron, and steel bars and plates, which have been published in the Transactions of the Institution of Engineers in Scotland, vol. ii., 1859, and the results, along with others, by Mr Fairbairn of Manchester, on iron-plates, are given here by their kind permission.

Table of the average Strength of Steel-bars, as found by Messrs Napier and Sons.

| Steel-bars | Strength per sq. inch of section | |------------|---------------------------------| | Cast-steel for rivets | 106,950 lb. | | Homogeneous metal for rivets | 90,647 " | | Puddled steel-forged bars | 71,488 " | | " rolled bars | 70,166 " |

The average cohesive strength of rolled bars of Yorkshire iron was found by Messrs Napier to be 61,505 lb. per square-inch, this being the mean of twenty experiments on bars varying from ¼ inch diameter, up to 1 inch square. And the average strength of bars manufactured by nine different makers in different parts of the country, and purchased promiscuously in the market, was 59,276 lb.; this being the mean of 110 experiments on bars varying from ¼ inch up to 1 inch diameter, and it is most satisfactory to find that the experiments showed a remarkable uniformity of results.

Mr Fairbairn of Manchester directed his attention, at a very early date, to the subject of iron for ship-building; plates by commencing his operations by the construction of various small vessels for canal navigation. In 1830 and 1831 he built three iron steam-vessels for the Forth and Clyde Canal Company, and to be employed as coasting traders to Grangemouth. These vessels made the voyage from Liverpool to Glasgow, and showed such symptoms of strength as to induce Mr Fairbairn to enter more largely into the business. Within the next four years he constructed a vessel for the Lake of Zurich, and two river-steamers of about 170 tons for the navigation of the Humber; and in 1836 he commenced the building of iron-ships at Millwall, on the Thames, in company with others. With a view to the introduction of correct principles into what was then a new line of manufacture, he made some valuable experiments at Manchester in 1838, to test the strength of iron-plates and of riveted joints. The results were communicated to the Philosophical Society of that town, and have since been republished by him. The results which he obtained were as follow:

| Species of Iron | Mean breaking weight in tons per sq. inch | |-----------------|------------------------------------------| | Yorkshire plates | 25.770 | | Derbyshire plates | 21.680 | | Shropshire plates | 22.926 | | Staffordshire plates | 19.563 |

The plates experimented upon were as nearly \(\frac{1}{4}\) inch thick as could be obtained; due allowance being made, in calculating the results, for any excess or deficiency in thickness in the different specimens.

The section through AB was 2 inches wide. The plate having been made narrower there to ensure its breaking at that part. Plates were riveted on each side of the ends to stiffen them. The holes O (fig. 14) were bored through the ends at right angles to the plates, with their centres in a direct line along the centre line of the part AB; and the apparatus for tearing the plates asunder was attached by bolts passing through these holes.

Iron-plates are supposed to be fibrous lengthwise, or in the direction in which they are rolled; but their cohesive strength ought to be nearly equal, whether the strain be applied with the fibres or across it. This uniformity of strength is attained by the shingles, or piles from which the plates are rolled, being composed of layers of bars carefully selected and laid at right angles to each other. When plates are very inferior in this respect, they may be supposed to have been manufactured from masses or blooms made up of irons or ores of different qualities, and these not sufficiently worked to amalgamate them properly. In testing iron-plates, it is therefore important to test their strength in both directions.

The very extensive series of experiments on the strength of iron-plates by Messrs Napier have fully corroborated the results previously obtained by Mr Fairbairn. The strengths per square inch of sections were as follow:

**Yorkshire Plates.**

| Lengthwise | Crosswise | Mean strength | |------------|-----------|--------------| | 55,433 lb. | 50,462 lb. | 52,947 lb. |

This result being obtained from 45 experiments upon plates varying in thickness from \(\frac{1}{4}\) inch up to \(\frac{3}{4}\) inch.

**Ordinary best, and best best boiler-plates,** as manufactured by ten different makers in different parts of the country, and purchased promiscuously in the market—

| Lengthwise | Crosswise | Mean strength | |------------|-----------|--------------| | 50,242 lb. | 45,986 lb. | 48,114 lb. |

This result being obtained from ninety-three experiments upon plates varying in thickness from \(\frac{1}{4}\) inch up to \(\frac{3}{4}\) inch.

**Glasgow Ship Plates.**

| Lengthwise | Crosswise | Mean strength | |------------|-----------|--------------| | 47,773 lb. | 44,355 lb. | 46,064 lb. |

This result being obtained from twelve experiments on plates, varying in thickness from \(\frac{1}{4}\) inch up to \(\frac{3}{4}\) inch.

Messrs Napier made some experiments upon steel-plates also, with a view to test their value for the construction of light boats for river navigation, or for any portion of iron-ships generally. The results were as follow:

**The Mersey Company's Steel-plates, for Ships.**

| Per sq. in. of section | Lengthwise | Crosswise | Mean strength | |------------------------|------------|-----------|--------------| | | 101,450 lb.| 84,968 lb.| 93,209 lb. |

**Steel-plates for Ships—Puddled Steel—"Mild"—by the same makers.**

| Per sq. in. of section | Lengthwise | Crosswise | |------------------------|------------|-----------| | | 71,532 lb. | not recorded |

**Blochairn Boiler-plates—Puddled Steel.**

| Per sq. in. of section | Lengthwise | Crosswise | Mean strength | |------------------------|------------|-----------|--------------| | | 96,320 lb. | 73,898 lb.| 85,010 lb. |

**Homogeneous Metal.**

| Per sq. in. of section | Lengthwise | Crosswise | Mean strength | |------------------------|------------|-----------|--------------| | | 96,280 lb. | 97,150 lb.| 96,715 lb. |

**Same Metal—Second Quality.**

| Per sq. in. of section | Lengthwise | Crosswise | Mean strength | |------------------------|------------|-----------|--------------| | | 72,408 lb. | 73,680 lb.| 72,994 lb. |

The portions of the plates tested by Messrs Napier and Sons were made of a similar form to those tested by Mr Fairbairn. As the result of these experiments, it may fairly be assumed, that iron-plates of good average quality should stand a strain of 56,000 lb., or 21 tons, as their breaking weight per square inch of section.

The results from the Yorkshire plates have been kept separate, because their quality and their price are such as to preclude their general use in ship-building. In boiler-making they are only used for furnaces, and those parts which require especial care.

The strength of rivets and of riveted joints, to connect plates in various ways, was also made the subject of experiment by Mr Fairbairn in 1838; and as no subsequent experiments appear to have thrown any further light upon the subject in its bearing upon ship-building, the results obtained at that time will be given.

The experiments were conducted in the same manner as those to test the strength of plates.

---

1 Useful Information for Engineers, London, Longman & Co., 1856. In lap-joints with a single line of rivets, the edges are made to lap over each other, thus—

When the strain is applied to a joint of this kind, the edges of the plates turn up, and the plates themselves bend till they take the direct line of the strain, as indicated by the dotted line, \(a b\).

Plates may also be united by bringing their edges together to make a flush or butt-joint, putting an extra piece of plate behind the joint to which both plates are riveted by single lines of rivets, thus—

This joint also gives way by the plates bending and taking the line of strain; and no material difference of strength was found between this and the preceding joint.

Tredgold has shown that when the line of strain is not in the axis or centre of the material, the strength decreases with the divergence in a much more rapid ratio than the direct distance of the divergence. It is therefore evident that this evil is greatest in thick plates, and that the strength of thick plates will not be proportioned to that of thin plates, though the sections of each through the rivet-holes may bear the same relative proportion to the sections through the solid plates.

Double-riveted lap-joints are those in which a second line of rivets is introduced. The edges are overlapped as in single riveting, but to a greater breadth, thus—

The line of rivets nearest the edge keeps it from rising. In this joint the strength is much increased, but the plates bend as before, and take the line of tension when a direct tensile strain is brought upon them.

The edges may also be brought together flush, with a broader piece of plate behind the joints, and a double line of rivets, thus—

In this joint, also, the plates bend before they give way, and the strength is similar to that of the preceding double-riveted joint.

The relative strength of these joints, in comparison with the strength of the body of the plate, was found to be as follow:

| Thickness of Plates in Inches | Diameter of Rivets in Inches | Length of Rivets from Head in Inches | Distance of Rivets from Centre to Centre in Inches | Quantity of Lap in Single Riveted Joints in Inches | Quantity of Lap in Double-riveted Joints in Inches | |-----------------------------|-----------------------------|------------------------------------|-------------------------------------------------|-------------------------------------------------|-------------------------------------------------| | 19 = 38 | 38 | 125 | 6 | 125 | For the double-riveted joint and 3ds of the depth of the single lap. |

This subject has also been ably investigated in a pamphlet and report on W. Bertram's patent welding process, by Mr Renton, C.E.

Materials used in Ship-Building.

The figures 2, 15, 45, 6, 5, &c., in the preceding table, are multipliers for the diameter, length, and distance of rivets, also for the quantity of lap allowed for the single and double joints. These multipliers may be considered as proportional of the thicknesses of plates to the diameter, length, distance of rivets, &c. For example, suppose we take 3 plates, and require the proportionate parts of the strongest form of joint, it will be:

\[ \frac{3}{75} \times 2 = \frac{750}{75} \text{ diameter of rivet, } \frac{1}{2} \text{ inch.} \] \[ \frac{3}{75} \times 4 = \frac{1688}{75} \text{ length of rivets, } \frac{1}{2} \text{ inch.} \] \[ \frac{3}{75} \times 5 = \frac{1875}{75} \text{ distance between rivets, } \frac{1}{2} \text{ inches.} \] \[ \frac{3}{75} \times 6 = \frac{2063}{75} \text{ quantity of lap, } \frac{2}{3} \text{ inches.} \] \[ \frac{3}{75} \times 8 = \frac{3438}{75} \text{ quantity of lap, for double joints, } \frac{3}{2} \text{ inch.} \]

In practice plates and rivets of certain thicknesses and diameters only are obtainable in the market, and for these the table would stand thus:

| Thickness of Plates in Inches | Diameter of Rivets in Inches | Length of Rivets from the Head in Inches | Distance of Rivets from Centre to Centre in Inches | Quantity of Lap in Single Joint in Inches | Quantity of Lap in Double Riveted Joints in Inches | |-------------------------------|-----------------------------|------------------------------------------|-------------------------------------------------|------------------------------------------|-------------------------------------------------| | \( \frac{1}{2} \) | \( \frac{1}{2} \) | \( \frac{1}{2} \) | \( \frac{1}{2} \) | \( \frac{1}{2} \) | \( \frac{1}{2} \) | | \( \frac{3}{4} \) | \( \frac{1}{2} \) | \( \frac{1}{2} \) | \( \frac{1}{2} \) | \( \frac{1}{2} \) | \( \frac{1}{2} \) | | \( \frac{1}{2} \) | \( \frac{1}{2} \) | \( \frac{1}{2} \) | \( \frac{1}{2} \) | \( \frac{1}{2} \) | \( \frac{1}{2} \) | | \( \frac{3}{4} \) | \( \frac{1}{2} \) | \( \frac{1}{2} \) | \( \frac{1}{2} \) | \( \frac{1}{2} \) | \( \frac{1}{2} \) | | \( \frac{1}{2} \) | \( \frac{1}{2} \) | \( \frac{1}{2} \) | \( \frac{1}{2} \) | \( \frac{1}{2} \) | \( \frac{1}{2} \) |

By using these proportions, it will be found that the rivets will not be sheared in two by the plates when a strain is brought on them, and that efficient joints will be made for all vessels which require to be steam or water tight. When this is not required, some additional strength may be obtained by enlarging the rivets and increasing the distance between them.

In forming the hull of a ship, the riveting is at present entirely performed by manual labour; but in the construction of beams, or any such separate parts, considerable advantage, both as regards strength and economy, will be obtained by riveting them by machine. The rivet by the latter process is more compressed, and thus made to fill the hole; and the operation being completed while the rivet is still hot, its shrinkage in cooling draws the plates together. This adds to the strength of the joint by causing friction, when a strain is applied to pull it asunder. The extent, however, of the advantage so obtained is necessarily very variable, depending on the amount of compression by the machine in forming the head of the rivet, and on the temperature of the rivet when closed, Mr Fairbairn does not attach much importance to it, and as it certainly does not exist to any important extent in hand-riveted work, it is safest to disregard it when any calculations of strength are being made.

The liability of plate to yield by flexure depends upon its thickness, and upon the amount of lateral support given to it, compared with the area of its surface. To give different plates an equal capability to resist flexure, the unsupported lengths should vary as the thickness.

The transverse strength of iron equally requires the attention of the iron ship-builder. It is necessary to bear constantly in mind, that in supporting a load, or resisting a transverse strain, the upper portion of a beam, which is supported at both ends, is subjected to compression, while the lower portion is in a state of tension. The line between the particles exposed to these opposite forces is called the neutral axis; but its position and direction, whether straight or curved, has not yet been definitely or mathematically determined. If the material of which a beam is composed be better able to resist compression than extension, it is evident that there may be less material in the upper than in the lower portion of the beam. The power to resist fracture is therefore looked upon as mainly concentrated in these portions; and while the duty of the centre portion, called the plate or the web of the beam, has not yet been brought clearly under the rigid laws of mathematics, its chief duty may be said to be to keep the top and bottom flanges separate from each other, and in their relative positions.

The power of iron to resist compression is generally taken at 31\(\frac{1}{2}\) tons, or 70,000 lb. per square inch.

It is one of the advantages of iron over wood that it can be made of any form, and that we can thus bring the foregoing principles, in as far as we are acquainted with them, into action.

The accompanying sections may be taken as representing the sections of the beams in general use at the present day.

The proper proportions of iron-beams, and the consequent rules for their strengths, have been much discussed.

Box-girders were used for the paddle beams of vessels built at Millwall by Messrs Fairbairn and Co. as early as 1840. They are stronger than any of the forms of plate-beams given above; and for long spans on board ship, plate-beams should not be used on account of their want of lateral stiffness, unless they are supported by trimmers or fore and aft carlines.

The ordinary rule for the strength of iron-beams, as given by Mr Fairbairn, is applicable to all the foregoing forms, the number 80 being used as the constant to represent the strength of the box-beam, and 75 that of the plate-beam.

Let W represent the breaking weight in tons, a the area of the bottom flanche, d the depth of the beam, and l the length of the beam, C representing the constant as usual. Then the area of the bottom flanche multiplied by the depth of the beam, and by 80 for a box-beam, and 75 for a plate-beam, and the product divided by the length of the beam (all these dimensions being

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1 See Proceedings C.E. Inst., vol. xv., p. 176; and the subject will be found further investigated, vols. xi., xiv., and xvi. Materials taken in inches), will give the breaking weight in tons— or \( W = \frac{ade}{l} \).

It will be observed that the top flange is not an element in this formula. Its correctness, therefore, is dependent upon the maintenance of certain relative and definite proportions in the parts, and it is not applicable to beams of indefinite forms or proportions. For beams of the ordinary length used in ships, the top and bottom flanges may be made of equal sectional area, and the greater the length of the beam the greater should be the comparative sectional area given to the top flange, to prevent its buckling or bending.

It has been argued that one-half the area of the centre web or plate should be added to the sectional areas of the top and bottom flanges, so as to include its strength as one of the elements of the formula, and a new formula be then deduced, but the rule, as given, is more simple, and may be relied upon.

From the nature of the material it is considered that wrought-iron beams may be loaded up to one-half of their breaking weight, though with cast-iron this limit is not permitted to exceed one-third.

The following are given as examples of the rule:

1. What is the breaking weight of a box-beam 60 feet long, between the supports 18 inches deep, and the area of the section of the bottom flange being 16 inches?

\[ W = \frac{16 \times 18 \times 80}{720} = 32 \text{ tons}. \]

2. What is the breaking weight of a plate-beam 30 feet long, between the supports 10 inches deep, and the area of the section of the bottom flange being 5 inches?

\[ W = \frac{5 \times 10 \times 75}{360} = 10.41 \text{ tons}. \]

The crushing force which malleable iron is capable of sustaining has been stated to be 70,000 lb. per square inch, but it could only sustain this great load when the force applied is so truly in the axis of the material, and when the specimen under pressure is so short that no deflection is produced. Wrought-iron, however, is very liable from its nature to give way by bending or buckling when the length bears too great a proportion to the area of the cross-section. This was previously mentioned when the relative sections of the area of the top flanges of beams which are exposed to a crushing force were recommended to be increased.

It has been found by experiment that wrought-iron is crippled, and its power of resistance destroyed by a weight of 30,000 to 40,000 lb. per square inch, whenever the length is such as to permit of its bending. The load, therefore, which it may be considered safe to put upon it in practice may be assumed at 6000 to 8000 lb. per square inch for columns of ordinary proportions. With this load the length of the column should not exceed ten times its diameter, and however short the column may be made, the load should never exceed 10,000 lb. per square inch of section.

The strength of similar columns of wrought-iron, as before stated to be the case with wooden columns, also varies as the squares of their lengths inversely. In all columns it is most important that the pressure should be applied in the line of the axis of the material.

By Hodgkinson's valuable experiments on the subject of columns, it was found that the strength of a column rounded at both ends, in comparison with one whose ends were flat, was as one to three. This result no doubt arose mainly from the strain not being correctly conveyed and kept in the axis of the material. If the strain on a column be in any degree greater on one side than on the other, this side will be unduly compressed, while the other side will be extended, and fracture or crippling will take place with a very small proportion of the load which the column ought otherwise to have sustained.

Dr Young was the first to investigate this subject properly, and his work may still be consulted with advantage by any one who is desirous of following up this inquiry. When treating of the strength of riveted joints, the importance of attending to the line of the strain, when the material was exposed to a tensile force, was dwelt upon; and it is evident, from what has now been said, that this is equally important when it is exposed to a crushing force. In the latter case, if the column be in the least degree curved, the strain increases the deflection, whereas in the former any curvature will be diminished, the tendency being to pull the material into a straight line. Hence, it is of the greatest importance to place columns directly under the weight which they have to support, and by all means to avoid unequal strains on the sides, whether the columns be round or square. With wrought-iron it is also very evident, that by using a hollow column much greater strength is obtained from the same quantity of metal, great stiffness being obtained by the increased dimensions. Hollow wrought-iron tubes, such as those used by engineers in boiler-making, may therefore be used with great advantage. They may be rolled to almost any diameter and length likely to be required in shipbuilding. No experiments appear yet to have been made on the power of such tubes to resist a direct crushing force, but the following experiments were lately made at Portsmouth Dockyard, by Mr Lynn of that yard, to test their power of resistance when used at an angle, as a pair of sheer-legs, to raise screw-propellers on board ships. The tubes were \( \frac{3}{4} \) inch thick, 4 inches external diameter, and 12 feet long. They were fitted with wrought-iron ends, the lower ends being prepared to rest on a step on the deck, and the upper ends had a double and single eye to fit into each other, and receive a pin for the shackle to carry the weight. The length was thus increased, from step to eye, to 12 feet 5 inches. At 9 feet spread at the base, one of the tubes which had been annealed in the fire for the purpose of straightening it, as it was slightly curved when received from the maker, deflected \( \frac{3}{4} \) inch when the weight reached 26 tons. On removal of the weight it returned \( \frac{3}{4} \) inch, leaving a permanent set of \( \frac{3}{4} \) inch. At 7 feet spread at the base, the same tube yielded when the weight reached 29½ tons, the other tube remaining uninjured.

The durability of iron is entirely dependent upon the state in which its surface is kept. Under ordinary circumstances there is probably no better preservative than good paint; but in the interior of iron-vessels it tends materially to their preservation, if the surface be coated with asphaltic, or cement sufficiently thickly to cover the heads of the rivets. In some cases it is even desirable, especially in the sharp run of a ship fore and aft, in the position of the dead-wood in a wooden vessel, to fill up the entire spaces between the frames, and form a flush surface. The exterior also of an iron-vessel is easily maintained in good condition by frequent painting. Below the water-line, where the surfaces cannot be reached by heeling the ship to a moderate degree, the iron is not apt to corrode. There is no chemical action by sea-water upon malleable iron, and there is not sufficient oxygen present below the surface to induce oxidation. In every instance in which an iron-vessel has been rapidly destroyed, it has been by corrosion on the interior surface. Great injury has in some cases resulted from acids leaking from certain cargoes, such as sugar, and also in parts where the leakage of brine from provision casks has been allowed to lie upon the plates.

For gun-boats or vessels, which it may be desired to lay up or preserve for any lengthened time, iron is peculiarly adapted, as, under such circumstances, the whole of the surfaces can always be attended to both externally and internally.

Malleable-iron, when submerged in salt-water, rapidly becomes foul by sea-weed and shell-fish adhering to its surface; but these do not cause decay; they may rather be said to form a coating to protect the iron from decay of any kind as long as it is submerged.

The decay of iron externally on ships' bottoms has, however, been observed to take place in the neighbourhood of copper-pipes. This is caused by a galvanic action which takes place between the copper and the iron, tending to the preservation of the former and the destruction of the latter, on the same principle as that proposed to be brought into action by the use of Sir Humphrey Davy's protectors for the preservation of copper sheathing. A layer of zinc at the point of junction, to separate the copper from the iron, will protect the iron, but as the zinc will then be rapidly eaten away, care must be taken that it is not used in such a manner that a leak would ensue in consequence.

The ready fouling of iron in sea-water is still a great drawback to its use. Many applications for this purpose have been proposed, but none seem yet to have been so thoroughly successful as to require any special mention as deserving of any decided preference.

The weight of a cubic foot of wrought-iron is 480 lb. The weight of a square foot of plate 4th inch thick, is therefore 10 lb., and this gives a ready and easily remembered standard for calculating the weight of any surfaces of iron of different thicknesses.

PRACTICAL BUILDING.

There is, perhaps, no structure exposed to a greater variety of strains than a ship, and none in which greater risks of life and property are incurred.

A consideration of the disturbing forces in action, either to injure or destroy the several combinations embraced in its structure, is therefore most important. And a thorough knowledge of their action is necessary to a practical builder to enable him to guard against them, in whatever form they may present themselves, and to dispose and arrange the materials at his command, accordingly, in the most judicious manner. Some of these forces are always in action whether the ship be at rest or in motion. She may be at rest floating in still water, or she may be cast on shore; and when there she may be resting on her keel as a continuous bearing, with a support from a portion of her side; she may be supported in the middle only, with both ends for a greater or less length of her body left wholly unsupported; or she may be resting on the ends with the middle unsupported: or under any other modification of these circumstances, and under all these the strains will vary in their direction and in their intensity.

If the ship be in motion, the same disturbing forces may still be in action, with others in addition, which are produced by, and belong only to, a state of motion. When a ship is at rest in still water, it has been before explained, that the upward pressure of the water upon its body is equal to the total weight of the ship, but it does not necessarily follow that the weight of every portion of the vessel will be equal to the upward pressure of that portion of the water directly beneath it, and acting upon it; on the contrary, the shape of the body is such that their weights and pressures are very unequal.

If the vessel be supposed to be divided into a number of laminae of equal thickness, and all perpendicular to the vertical longitudinal section, it is evident that the after laminae comprised in the overhanging stern above water, and the fore laminae comprised in the projecting head also above water, cannot be supported by any upward pressure from the fluid, but their weight must be wholly sustained by their connection with the supported parts of the ship.

The laminae towards each extremity immediately contiguous to these can evidently derive only a very small portion of their support from the water, whilst toward the middle of the ship's length a greater proportionate bulk is immersed, and the upward pressure of the water is increased.

At some certain station from the middle of the length in each body, fore and aft, the upward pressure will therefore be equal to the weight of the superincumbent laminae, and all the laminae composing that portion of the body between these two stations will be subjected to an excess of pressure above their weight, tending to force them upward; which upward pressure will be the greatest at the laminae having the greatest transverse area of section. Now, as the total pressure upward is equal to the total weight of the vessel, this excess of upward pressure to which the midship part of the body is subjected, must be equal to the excess of weight over the upward pressure in the parts of the vessel before and abaft those laminae at which the pressure and weight have been supposed to be in equilibrium.

A ship, when at sea, is subjected to severer strains than when floating at rest, and if cast on shore it may be subjected to still greater strains. Its strength, therefore, as a fabric, should be considered with reference to the severest trial of strength which may be required of it under any circumstances.

A ship floating at rest under the view just taken of the relative displacement of different portions of the body, if the weights on board are not distributed so that the different laminae may be supported by the upward pressure beneath them as equally as possible, may be supposed to be in the position of a beam supported at two points in its length at some distance from the centre, and with an excess of weight at each extremity.

At sea it would be exposed to the same strain; and if supported on two waves, whose crests were so far apart that they left the centre and ends comparatively unsupported, the degree of this strain would be much increased. The strain would be still more severe if the vessel got aground, and rested on two isolated points situated in the supposed positions in her length.

Under these circumstances, however, the strain would depend upon whether the weights in the middle or in the ends preponderated. The latter is the usual case; and then the whole of the upper portion of the vessel will be subjected to a tensile strain from the tendency of the ends to droop.

The more these two points of support approach each other, or if they come so near each other that the vessel may be looked upon as supported on one wave, or on one point only in the middle of her length, the greater will be the tensile strain on the upper portion, and the crushing strain on the lower portion of the fabric of the ship.

The importance, therefore, of so forming the deck and the upperworks that they may afford an efficient tie is apparent; and it is to be feared that this has been too much neglected, especially in many iron-ships.

If a vessel be weak in this respect, and touch the ground in the middle of her length, the consequences will necessarily be most disastrous, as she will open at perhaps more than one place, and her sides will tear down instantaneously after the tie of the deck and upperworks is gone. These results appear to accord with the accounts given of the manner in which several iron-vessels have broken up on their being cast ashore.

A vessel whose weights and displacements are so disposed as to render her subject to a strain of this kind beyond what the strength of her upperworks will enable her to bear, will assume a curved form.

The centre is curved upwards by the excess of the pressure beneath it, and the ends drop, producing what is called The main remedy for these evils, as before stated, is in the strength of the deck and upperworks, and their power to resist a tensile strain. There is seldom a want of sufficient strength in the lower parts of the vessel to resist the crushing or compressing force to which it is subjected. The decks of vessels should not, therefore, be too much cut up by broad hatchways; and care should be taken to preserve entire as many strakes of the deck as possible. The tensile strength of iron can be brought to bear most beneficially in this respect, and some continuous strakes of it laid upon the tops of the beams and below the deck-plank would add materially to the strength of all ships.

Deck-planking has been sometimes laid diagonally at an angle across a ship, but it will be evident, from these remarks, that the value of the longitudinal tie is thereby much lessened, and there is no sufficient corresponding benefit of any other kind to justify the whole deck being laid in this manner.

Great sheer, or rising of the deck, fore and aft, is objectionable, from its lessening the strength of the longitudinal tie, though it is much practised, as it gives a lively appearance to a ship, and hides the defects of hogging if it should occur.

In the whole of the upper parts of a ship, as well as in the deck, every means should be taken to increase the power of resisting tension. In a wooden ship the upper part of the frame should be chain-boiled wherever the continuous range of bolts can be placed so as not to interfere with the in and out fastenings; and the shifts of the different wales, and other parts, which act as longitudinal ties, should be carefully attended to. The waterway-planks and shelf-pieces are also most important, and their continuity should be maintained throughout the length of the vessel, with as little diminution of strength as possible, at the junction of the different lengths.

In iron-vessels the parts corresponding to these are particularly important, as the plating exposes a very weak edge at the top, and is liable to be torn down if this edge be not well guarded and supported. To enable the lower part of the ship to resist the compression to which it is subject, the spaces between the frames in the best built wooden vessels are filled in solid, so as to make, as far as possible, an incompressible mass. The various abutments of this part of the body should be as closely fayed or fitted as possible. In iron-vessels, as the spaces between the frames cannot be filled in solid, the keelsons should be of great strength. The power of wrought-iron to resist compression, when it is prevented from buckling, is here of great value, as the fastening of the keelson to every frame as it passes gives stiffness and rigidity to it, and consequently great power to resist compression.

Though these are the strains to which a ship is most likely to be exposed, it by no means follows that there are no circumstances under which strains of the directly opposite tendency by recoil, when pitching and tossing, or otherwise, may be brought to act upon the parts. The weights themselves in the centre of the ship may be so great that they may have a tendency to give a hollow curvature to the form, and it is therefore equally necessary to guard against this evil. When this occurs, the vessel is technically said to be "sagged," in distinction to the contrary or opposite change of form by being hogged. The weight of machinery in a steam-vessel, or the weight or undue setting up of the main-mast, will sometimes produce sagging. The introduction of additional keelsons tended to lessen this evil, by giving great additional strength to the bottom, enabling it to resist extension, to which, under such circumstances, it became liable; and as the strain upon the deck and upperworks becomes changed at the same time, they are then called upon to resist compression.

In iron-vessels, the waterway-planks and shelf-pieces are again, in this case, very important to aid in resisting this strain. The deck-planks may become shortened by the deck assuming a curved form in the middle of the length of the ship, the beams yielding and working with them; and a crushing strain is then brought to bear upon the plating of the topsides, which they are not calculated to sustain. Some light flat-bottomed river-steamer of iron with very full lines forward and aft, have given way from this cause. The best practical lesson upon the subject, and the most direct proof of the want of strength of iron-vessels at the topsides, if constructed without additional strengthening there, was given by the Nemesis when her topsides opened, as so well described by Captain Hall in his account of her voyage to India, and when he so judiciously strengthened her by attaching balks of timber longitudinally to the two sides.

A corresponding action to that described as hogging takes place in relation to the breadth of the vessel, but more particularly in the case of men-of-war, on account of the weight of the ordnance concentrated along the sides. The central portion of the body is subjected to an undue upward pressure, while the outer portions are strongly acted upon by the weight there tending to depress and immerse them. The effects of this action may be greatly modified by the form of the vessel; longitudinally, it produces the upward curvature previously referred to; and transversely, it tends to separation of the sides, except in three-decked or very lofty ships, in which, if the tumbling home be very great, the tendency is to produce a separation at the main breadth and below it, and a collapsing of the sides above it.

Another force tending to alter the form of a vessel arises from the horizontal pressure of the water on the sides of the vessel. The sides are compressed or forced together, and the tendency produced is to add to the curvature of the deck amidships, and increase the hogging both longitudinally and transversely.

When a ship is in motion, if the surface of the sea be very uneven, so that her passage will be over the waves, which affect the supports become very variable, and the opposing forces of upward pressure and gravitation will have a tendency to produce corresponding changes in the form of the body; and if the motion of the ship be violent, and thus produce any sudden shock or jerk, the strain upon the materials and upon the fastenings will become immeasurably increased.

When the ship is on a wind, the lee-side is subjected to a series of shocks from the waves, the violence of which may be imagined from the effects they sometimes produce in destroying the bulwarks, tearing away the channels, &c. The lee-side is also subjected to an excess of hydrostatic pressure over that upon the weather side, resulting from the accumulation of the waves as they rise against the obstruction offered by it to their free passage. These forces tend in part to produce lateral curvature. When in this inclined position, the forces which tend to produce hogging when she is upright also contributes to produce this lateral curvature. By experiments made on her Majesty's ship Genoa, in 1823, by Mr. Moorsom, a member of the late school of naval architecture, he ascertained that this lateral curvature amounted to $1\frac{1}{2}$ inch on each tack, making an alteration of form to the extent of 3 inches from being on one tack to being on the other.

The strain from the tension of the rigging on the weather side when the ship is much inclined is so great as to frequently cause working in the topsides, and sometimes even to break the timbers on which the channels are placed. Additional strength ought therefore to be given to the sides of the ship at this place; and in order to keep them apart, the beams ought to be increased in strength in comparison with the beams at any other part of the ship.

It has been proposed to introduce tie-rods from the channels to the step of the mast, so as to render each mast and its supports a combination of struts and ties with the strains self-contained. This may be explained by the annexed figure.

Let AB represent the deck-beam, or beams of the ship at marks, that the disturbing influences which cause "hoggling," commence their action at the moment of launching the ship, and are thenceforward in constant operation. As this curvature can only take place by the compression of the materials composing the lower parts of the ship, and the extension of those composing the upper parts as more particularly explained when treating of the strength of beams, the importance of preparing these separate parts with an especial view to withstand the forces to which they are each to be subjected cannot be overrated by the practical builder. The side of a ship is, however, in a somewhat different position from the plate or web of an ordinary plate-beam, or the sides of a box-beam, on account of the horizontal pressure of the water against it; and because in deep ships, with one or more intermediate decks, some of the strain is brought upon it in the middle of its depth.

The position of the neutral axis or line between those particles exposed to a crushing and those exposed to a tensile strain, is therefore very difficult to determine; but from a consideration of the circumstances just mentioned, it must be higher in a ship than theory would place it if the ship were considered in the light of an ordinary beam exposed to strains brought upon it in the ordinary way.

The importance of the system of diagonal trussing and diagonal bracing in ship-building appears to have been first fully appreciated by Sir Robert Seppings, and the principle on which it should be introduced to have been first explained by him. It is obvious that if four pieces of timber be put together, so as to form a square, or a rectangular parallelogram, with their ends connected by a round pin only at each corner, they may assume the form of any other parallelogram whose sides are of the same length, but that in so doing the length of the two diagonal lines will be altered; thus—

In both of the annexed figures, the sides are of the same length, but AC of fig. 29 is shortened into ac in fig. 30, and BD of fig. 29 is lengthened into bd in fig. 30. The introduction, therefore, of diagonals of a fixed or unalterable length into any piece of frame-work will tend to prevent alteration of form, and it will be perceived that the duty required of the two diagonals in resisting any change is different, the one being required to resist extension, and the other to resist compression. One diagonal only is sometimes considered sufficient, but in this case care must be taken that the material of which it is composed, and the manner in which it is applied, be such that it may be fit to resist either extension or compression, if the frame-work is liable to be alternately strained in either direction. In any piece of frame-work, however large, a straight wrought-iron bar is excellent as a tie, but as a strut it would be nearly useless on account of its liability to bend. Wrought-iron, however, is the material chiefly used in diagonal bracing; and it may be used with propriety for both diagonals, wherever on account of liability to a strain in both directions two are used, because each in its turn will resist extension, and that diagonal which is exposed to compression will be protected from injury by the resistance of the other to extension. The sides of a ship may be supposed to be divided into a number of pieces of frame-work of imaginary outlines or dimensions. Those embraced in the midship body may be supposed liable to be strained in both directions; but the upper portions of those composing

Practical Building.

The fore and after bodies will be inclined to fall forward and aft respectively; and if this tendency only is to be guarded against, the ties must be placed in different directions in the two bodies sloping up from below amidships forward and aft in parallel lines, extension being the force which they will be called upon to resist. The system is not so much required in the bottom of a ship. In the decks diagonal trussing, placed diagonally across a ship, is advantageous as tending to prevent the ship working, by one side advancing or receding alternately with the other, and here the diagonals should be made to cross each other and lie in both directions.

Diagonal trussing, as used by Sir Robert Seppings, was introduced into some ships as part of frame-work along the centre of the ship, from pillar to pillar, from the keelson to the decks, and he arranged these on the principle of depending upon struts and not upon ties. Wrought-iron was then much less used than in the present day, and timber forms an excellent material for a strut, weight for weight, in comparison with solid iron-bars, on account of its dimensions giving it stiffness. Struts are also convenient because they require comparatively little attention to the fastening of their ends. They abut against a surface, or into a corner, and their ends are easily prevented from shifting. With ties this is very different; their ends must be made sufficiently secure to resist a strain equal to their whole strength.

Before the introduction of this system, it was no uncommon thing to find ships hogged to the extent of from two to three feet. An instance is quoted in Portsmouth dockyard of an old ship, whose keel was curved upwards to the extent of two feet or more, and which was grounded in drydock on a set of blocks laid level. She straightened as she settled upon them, and diagonal trussing being then introduced, it was found to support her in a remarkable degree, when she was again floated. In this case the trussing was applied chiefly in midships, from pillar to pillar, from the keelson to the deck-beams.

In iron-ships diagonals are not so much required on the sides of the ship, because the plating being a connected surface of equal or nearly equal strength in all directions, it is incapable of motion in its parts, and the line of any supposed diagonal is incapable of extension otherwise than by a force sufficient to tear the plating asunder.

A general consideration of all the strains to which ships are subjected naturally leads to the question of selecting the material which is best adapted to resist them. In treating of the materials used in ship-building, especial reference was had to the various qualities possessed by each, which rendered them more or less valuable individually or collectively. It may perhaps be expected, that before leaving this part of the subject a more direct comparison should be drawn than has yet been done between the relative merits of wood and iron vessels, and that the points in their structure, in which they chiefly differ in strength and safety, should be pointed out. The advocates of either system will, no doubt, discover many errors and omissions in the remarks on this subject, which have been made, or which may now be made; but they are given as the results of close observation and experience for a period of upwards of twenty-five years of practical connection with both classes of vessels. It may at the same time be stated with respect to this treatise, that while the increase of steam-vessels, and the great alterations in the forms of ships since the publication of the previous edition of the Encyclopedia Britannica, had to be considered, much of the alteration from the previous very able article on this subject, by the late Mr Cruze, is caused by the necessity of now treating of iron-ships equally with those of wood. An endeavour has been made to introduce as much information respecting iron-vessels, in addition to as full information respecting wooden vessels, as the assigned limits would permit; and the substance of the article by Mr Cruze has been retained in many points, and free use has been made of it wherever desired, so as to form, as far as may be, a concise and consecutive treatise.

If strength alone were to be assumed as the basis of comparison, without reference to weight or cost, it would probably be conceded that a stronger vessel could be built of iron than it would be possible to construct by any combination of wood. It will, however, be more practically useful to compare vessels of about equal weight, or equal cost or strength.

An individual frame in an iron-vessel is formed with greater continuity of strength throughout its length, than is the case in a wooden vessel, and greater opportunity is given of obtaining strength, no matter what may be the form of the body. By the variety of form into which iron can be rolled by the manufacturer, opportunity is also given to obtain the desired strength with less useless material.

In the sheathing, whether internal or external, much greater difference exists. In wooden vessels the planks are laid side by side, and with few exceptions are not fastened or connected with each other; indeed they are forced asunder by the caulking required to make the joints between them water-tight. Their only connection therefore is by means of the fastenings which unite them to the frames. The plating of an iron-vessel, on the contrary, is made into one completely connected surface, and even if all the frames were removed, it would remain in shape, and would still form a vessel of great strength and stiffness. The fastenings, also, to the frames will not bear comparison, the power of iron to resist shearing across being so much greater than that of trenails or copper-bolts.

The power of iron-plates to resist a force similar to that to which they would be subjected if an iron-vessel took to the ground on a hard bottom, with some projecting points force of rock or stones, was also experimented on by Mr Fairbairn. The plates were placed upon a frame, leaving a space of 1 foot square, unsupported, and on the centre of this a bar of iron, 3 inches diameter, with its end rounded, was brought to bear. Plate \(\frac{1}{4}\) inch thick was burst with a force of 16,779 lb., and a plate \(\frac{1}{2}\) inch thick, bore a strain of 37,723. The plate of double the thickness, therefore, bears more than double the pressure. The power of timber to bear a similar strain was tested at the same time. Oak planks, 3 inches thick, were burst with a force of 17,933 lb., or only a little more than was required to burst the same surface of a plate \(\frac{1}{4}\) inch thick. Oak planks, of \(1\frac{1}{2}\) inch thick, were burst with 4406 lb. A plank of double the thickness, therefore, bore much more than double the pressure, the proportion being as the squares nearly.

Beams of iron are applicable to both classes of vessels, and their superiority is now becoming so generally acknowledged, that they are being largely used in wooden vessels in the merchant-service and in the French navy. It is, however, to the results of the combination of these materials as a whole that consideration must chiefly be given. Unfortunately there are no want of instances of both species of vessels going to pieces suddenly when cast on shore on rocks; and until iron-vessels are double-plated with an interior water-tight sheathing, wooden vessels, with solid bottoms of floors and futtocks, will probably give greater security in such a position for a short period of time if the sea be rough, and for a greater period if it be smooth; on a flat beach, however, iron-vessels seem undoubtedly to have the advantage. The Great Britain, lying for a whole winter on the coast of Ireland, and the Vanguard, lying ashore for several days on a rocky beach, are two notable instances of iron-vessels having come off comparatively uninjured, after having been exposed to strains which it is believed no wooden vessels could have undergone. There are, at least, no such instances on record with regard to them. As another direct comparison, the Demerara may be mentioned as a wooden vessel which, after being launched, grounded in the river at Bristol while being brought down, and she was so much injured that she was condemned; whereas the Australia, an iron-vessel, on first coming down the Clyde grounded in a similar manner, lying right across the river in one of its narrowest parts, but she came off quite uninjured. Another instance of strength, such as no wooden vessel has ever exhibited, may be quoted in the case of an iron-vessel which, on the occasion of her being launched, stuck on the ways which were upon a high wharf above the water, and more than one-third of the whole length of the vessel was left totally unsupported, overhanging the wharf, and yet she did not break or receive any damage.

The same elements of strength which enabled these vessels, especially the Great Britain and the Vanguard, to withstand the strain to which they were exposed, will also be efficacious in preventing a vessel straining at sea in a heavy sea-way, so as to become leaky and founder at sea from this cause. From a consideration of such facts as the foregoing, the general opinion appears to be, that iron-vessels, as a whole, are not only stronger than wooden vessels, generally speaking, but that they may be made of greater or equal strength, with considerably less weight of hull. The extent to which this saving of weight may be carried, without impairing the strength to an improper or unsafe degree, will always be a subject of inquiry to the iron shipbuilder; but if he err in judgment and produce too weak a ship, the error must be attributed to him, and the material must not be considered to be in fault.

The power of fitting water-tight bulkheads to iron-vessels is also a great advantage, and will be a source of much greater security hereafter, when vessels are better built than they have hitherto been. Their importance, and the great additional safety which they impart, are evident, and the principle may be carried out to any extent, and this longitudinally as well as athwartship. In the after part of screwships, the passage alongside of the shaft to the propeller may be made water-tight, and communication with the engine-room may be cut off, if it be desired, and if proper arrangements be made for this purpose. These bulkheads also form a good protection against the very rapid spreading of fire, and in the case of any vessels particularly liable to this danger they might be made double, and water be admitted between them.

The durability of iron-ships has been already referred to, as far as regards ordinary tear and wear; but their superiority in the event of injury by collision, or by being on shore, is still more marked. If a few frames or floors are broken in a wooden vessel, the amount of work required to be entered into to replace them is very great, a large portion of the plank in the neighbourhood requiring to be ripped off. In an iron-vessel, on the contrary, a new piece of frame can be put in to replace the injured part, and the whole made as strong as before, by lapping pieces. And in the sheathing, an injured plate, or a piece of a plate, can be cut out and replaced without disturbing any of the other work.

For purposes of war iron-vessels have been pronounced by some as unfit, the reasons given being, that the iron when struck flies into innumerable small pieces, which would be most destructive to the men on board; and that in the event of a shot passing through the ship and striking the further side, the plates being no longer supported by the frames, but depending upon the rivets only, are apt to be torn off in large pieces. In some experiments made at the Royal Arsenal at Woolwich, in 1844, by the late General Dundas of the Royal Artillery, it was found that the splinters resulted equally whether the plates fired at were of the best Lownmoor iron or of common boiler-plate. A thickness of 12 to 15 inches of wood was found to stop almost the whole of the small splinters; and a less thickness of a material composed of a mixture of saw-dust and India-rubber effected the same object. With a shot fired with no greater velocity than would just enable it to penetrate the plates, the splinters were fewer; and at the edges of the hole through which the shot had passed, the plate was bent back with ragged edges. In some experiments in Portsmouth harbour, an iron target was fired at, with a screen of canvas behind it to show the splinters, and the same results were obtained. In both cases the plates were \(\frac{3}{4}\)-inch and \(\frac{3}{4}\)-inch thick. In iron-vessels, therefore, constructed for the purposes of war, if composed of plates of ordinary thickness, it would be judicious to line them with wood to prevent the men being exposed to the risk of such splinters. In ordinary gun-boats, or corvettes, where the men are above the hull of the ship when fighting the guns, this danger is obviated, and a portion of the ship might also be protected to any extent that might be considered desirable. The present changing state of the science of projectiles renders it difficult to provide against all contingencies; but plates of only ordinary thickness will stop all ordinary shells. This is a most important difference, as these, in their various forms, are now the most dangerous to a ship, and iron-vessels may therefore, on this account, lay claim to great consideration as adapted for warlike purposes. If the iron-vessel, then, be so constructed that it can be penetrated by solid shot only, it would become a question of a wooden vessel being burnt or destroyed by shells, or of an iron-vessel being sunk; and it is believed that many would prefer the latter risk. A shell bursting on board, or in the side of a wooden vessel, would cause greater injury and loss of life than the splinters from the shot in an iron-vessel, and these, as has been said, might be lessened in a large vessel, and avoided in the smaller vessels. It was the opinion of many naval officers respecting the effects shown by the experiments at Portsmouth, that if the same number of shots had been fired at targets of wood, the canvas screen would have been swept bodily away, and that such parts of the targets themselves as remained would have been reduced to a mass of fibres, without strength to sustain themselves or resist any strain or pressure whatever. If iron-vessels hereafter show such great superiority in strength and safety at sea, or when cast on shore, or in durability, as to make their introduction into the royal navy important on these accounts, it may then become a question whether a system may not be introduced of constructing the whole of the lower part of the vessel of iron, up to the neighbourhood of the water-line, and that the portion of the vessel above this, where the men would be exposed to the splinters, should be of wood. The iron-frames could be continued up for some distance alongside of the wooden frames, and there are no practical difficulties in such a system that could not be overcome.

**PRACTICAL OPERATIONS.**

After the cursory view which has been taken of the Commencements to which ships are liable, and the general remarks of which have been made on the points to be attended to in their construction, it is now proposed to give a short outline of the proceedings in the actual building of the vessel.

The term "laying off" is applied to the operation of Laying off, transferring to the mould loft-floor those designs and general proportions of a ship which have been drawn on paper, and which have been previously referred to, and from which all the preliminary calculations have been made and the form decided. The lines of the ship, and exact representations of many of the parts of which it is to be composed, are to be delineated there to their full size, or the actual or real dimensions, in order that moulds or skeleton outlines may be made from them for the guidance of the workmen. These working drawings are made by projection, and are not views of the parts as they appear to the eye. In a projected drawing the eye is supposed to move and be directly opposite to each line, as it, in its turn, is represented by the draughtsman. Separate drawings must, therefore, be made for the different faces of any object which are at right angles to each other.

The delineation in this manner of solids of a complicated form is of itself a science, and one which is now attracting much more attention than formerly. It is very ably treated by the Rev. Dr Woolley in a work entitled Descriptive Geometry. Before the publication of this work the efforts in this direction in this country had been chiefly made by practical men, each showing the mode of delineating the more difficult objects in his own art. Architectural works showed the mode of delineating the mouldings and details of the columns of the seven orders of architecture. Books on carpentry showed the mode of working and laying off a geometrical or winding staircase, and works on ship-building included, at great length, the modes of laying off complicated and irregularly formed parts. To show the mode of delineating not only the frames, but all the pieces of varying form which are required in the bows or sterns of ships, would be far beyond the limits of this treatise. It is impossible to include either a complete treatise on drawing or a complete set of delineations of the modes of combining the whole of the various minute parts of which all classes of vessels of wood and of iron are composed.

A proper knowledge of the minute of construction and of workmanship can only be obtained by practical experience upon the work itself; and the form and combination of the parts will continually vary with the variations in the form and outline of the bodies and of the heads and sterns of the ships.

The principal plans of a ship are the sheer plan, the body plan, and the half-breadth plan, and these have been already fully discussed, and their uses explained. In addition to these plans it is customary to furnish the architect with a profile of the inboard works, showing the disposition or distance apart, and the appearance of the timbers which constitute the frame, also the length or the heads and heels, and general arrangement of the floors and futtocks, the midship section, on which is described the moulding or athwartship size of the timbers, the thickness of the exterior and interior planking, the connection of the beams to the side, the dimensions of the waterways and shell-pieces, and the forms and fastenings of the knees, &c. These, with a scheme of scantlings containing the dimensions and other particulars of the principal pieces which enter into the construction of the fabric, constitute all the preparatory information required by the builder. In private contracts very full information on all these points is generally included in the specification.

A ship is generally spoken of as divided into fore and after bodies, and these combined constitute the whole of the ship; they are supposed to be separated by an imaginary athwartship section at the widest part of the ship, called the midship section or dead-flat.

The midship body is a term applied to an indefinite length of the middle part of a ship longitudinally, including a portion of the fore-body and of the after-body. It is not necessarily parallel or of the same form for its whole length.

Those portions of a ship which are termed the square and cant bodies may be considered as subdivisions of the fore and aft bodies. There is a square fore-body and a square after-body towards the middle of the ship, and a cant fore-body and a cant after-body at the two ends. In the square body the sides of the frames are square to the line of the keel, and are athwartship, vertical planes. In the cant bodies the sides of the frames are not square to the line of the keel, but are inclined aft in the fore-body, and forward in the after-body. The reasons for the frames in these portions of a wooden ship being canted, is that, in these parts of the ship, the timber would be too much cut away on account of the fineness of the angle formed between an athwart ship plane and the outline or water-lines of the ship. The timber is therefore turned partially round till the outside face coincides nearly with the desired outline, and it is by this movement that the side of a frame in the cant fore-body is made to point aft, and in the cant aft-body to point forward. This will be best understood by the annexed figure, showing an exaggerated horizontal section of a frame in the fore cant-body, the dotted line representing the extent to which the timber would have been cut away if it had been placed square to the line of keel, and if the side \(ab\) had not been "canted" aft, turning on the point or edge \(a\).

In wooden ships the term "timbers" is sometimes applied to the frames only, but more generally to all large pieces of timber used in the construction. Timbers, when combined together to form an athwartship outline of the body of a ship, are technically called frames, and sometimes ribs. In iron-ships the frames are composed of iron-bars of various forms.

The terms moulding and siding are nearly synonymous with thickness and breadth, observing that the moulding of a piece of timber is the dimension of the side on which the mould is applied for determining its shape or curvature. For instance, the moulding of a beam is its length and thickness; its siding is its fore-and aft dimension or breadth.

Room and space is a certain distance determined by the Room and fore and aft dimensions, or the siding of two adjacent timbers, together with the opening between them. It is generally defined as the distance from centre to centre of the frames, or from centre to centre of the spaces between them. The centre line between two adjacent frames is called the joint.

Shift in its general sense is applied to a certain arrangement among the component parts of a ship. Thus a shift of deadwood, or a shift of plank, means the disposition of the butts of the timber or plank with reference to the longitudinal distance of one joint from another, and this with respect both to strength and economy.

The bevelling of a timber is the angle contained between two of its adjacent sides. Bevellings are either acute angles, right angles, or obtuse angles. These three separate cases are denominated under bevellings, square bevellings, and standing bevellings.

Sirmarks are certain points or stations marked on the Sirmark mould of the timbers, at which the bevellings are applied, in order to cut the timber to the bevelling required at that spot. These sirmarks are determined, and their positions denoted in the body plan, by the various diagonal lines.

Water-lines in the sheer plan, are lines drawn parallel Water- to the surface of the water (Plate III.). Level-lines are lines similar to water-lines, except that they are drawn parallel level-line to the keel instead of to the water (Plates V. and VI.). In the half-breadth plans, the water-lines or level-lines show the outline of the form of the ship at sections at the corresponding heights in the sheer and body plans.

Diagonal lines, as shown in the body plan and half Diagonal breadth plan (Plate III.), and marked 1 D, 2 D, 3 D, lines.

show the boundaries of various sections which are oblique to the vertical longitudinal plane, and which intersect that plane in straight lines parallel to the keel. In wooden ships, the position of the diagonal lines drawn in the body plan is not arbitrary, because it has reference to the different timbers of which the frame is composed, and also to the station of the ribs and harps. The number of diagonals is increased in the deeper class of vessels. They are drawn to show the lengths of the floors and futtocks, together with the heights of their heads and heels above the keel, and are marked floor-head, &c. Diagonals, marked as 1st sirmark, 2d sirmark, 3d sirmark, &c., or 1 D, 2 D, 3 D, on the body plan (Plate III.), show the heights and situation of the harps and ribs which are used to give support to the ship whilst in frame. In wooden ships they are always placed between the heads of the respective timbers.

The following is the mode of setting off the diagonals in the sheer plan:—Take the perpendicular heights in the body plan, that is, the heights square to the upper edge of the keel of the intersection of the diagonal with each of the transverse sections, and transfer these heights to the corresponding section in the sheer plan. Through the points thus obtained draw a curve, which will be the line required.

To transfer the diagonals to the half-breadth plan: observe the point of intersection of the diagonal on the body plan with each transverse section, and take the horizontal distance of each of these points from the middle line, and transfer it to the corresponding section in the half-breadth plan. Through the points thus obtained draw a curved line, which will represent the horizontal line of the diagonal. After these lines have been added to the sheer, body, and half-breadth plans on paper, the transference to the floor, where the ship is to be delineated to the full size, is easy.

It is the duty of the draughtsman in the mould-loft floor to fair the body, if any of the curves shown by the lines previously drawn on the paper do not appear of easy and good forms, when represented of their full size.

On the mould-loft floor it is necessary, in iron-ships, to draw out every frame, so as to be able to give the particulars to the workmen; and it is not only necessary to give them the outline of the frame, but also the beveling or the angle which the outer surface makes with the side at each spot or sirmark. This is obtained from the half-breadth plan at the various points where the different level lines or diagonal lines cross each frame. A variety of modes are practised by different builders of iron-ships to convey this information from the mould-loft to the workmen, instead of using moulds, as almost universally practised by builders of wooden ships. Great accuracy in this respect is required in iron-ships, as in them no dubbing off or pairing the body by the adze is practicable.

Expanding the body so as to represent the whole of the planking or outer skin or surface of a ship, is another process connected with laying off; and it is particularly important to the iron ship-builder, as it enables him to obtain the necessary iron-plates from the rolling-mills of the exact widths and lengths that will be required. This is done by drawing a line, to represent the line where the plates meet the keel and stern-posts. On this line the station of any number of frames that may be necessary to give the desired degree of accuracy must be set off, and at these stations lines must be drawn of a length equal to the girt or outline of the frame at that station; this length will be obtained from the body plan. The number of strakes to be used in planking or sheathing the ship must next be determined and be set off accordingly, on the lines representing the different frames; and great art is necessary in this operation, as upon these lines much of the beauty of a ship depends to please the eye of a connoisseur. The shift or the distances between the ends of the different plates may also be determined and marked in this plan, and thus the length, width, and breadth of every plate may be accurately ascertained.

The circumference of the bottom being much larger at the midship part than toward the extremities—that is, at the bow and buttock—the lines for the strakes taper as they recede from midships. They also acquire an upward curve, called "Sny," which renders it difficult to work the plank. "Sny." When the sny becomes too great, a strake is ended short of the others, and this is termed a "stealer," as it diminishes the sny for the succeeding strakes. Under the buttock it is often necessary to work some of the after-plank wider at the after-end, and this has the same effect of diminishing the sny of the following strakes. "Hang" is the exact reverse of "sny." It mostly occurs in working plank on the inner surface of the timbers, and outside above the main breadth.

With regard to the practical operations in building a ship, nothing more can be attempted here than a few general observations on the principal parts of a ship, and the mode of putting them together, to resist the various strains to which each part will be subjected. The practice in her Majesty's yard will be found very fully explained in Fincham's outlines of shipbuilding, and in a very excellent treatise by Mr Peake, now master-shipwright at Devonport. Some details of wooden ships of the ordinary system of construction will be first described.

The keel of a ship built in this country is generally composed of elm, on account of its toughness, and from its not being liable to split if the ship should take the ground, though pierced in all directions by the numerous fastenings passing through it. It is generally composed of as long pieces as can be obtained, united to each other by horizontal scarphs. These scarphs are made sloping up from the bottom to the upper surface, on which the floors rest. But the strain to which a keel is subjected has a tendency to curve it up or down, and not sideways. These scarphs should, therefore, be made vertical, in the same manner as scarphs of the beams, as there can be no doubt that the vertical scarph will give the greatest strength to resist a strain in this direction.

The rabbet of the keel is an angular recess cut into the Rabbet of side to receive the edge of the planks on each side of it, the keel. In the government service this rabbet is made of greater breadth vertically, so that the plank to fill it is required to be of such great thickness that it altogether loses the character of a plank, and becomes a stout massive piece of timber. This arrangement was introduced by Mr Lang, and has been denominated Lang's safety keel. It gives great additional strength to the bottom of a ship, and great lateral support to the keel, when the ship takes the ground and rests on the edge, as the leverage to displace it sideways is thus reduced.

In the merchant service the rabbet is seldom carried so low down on the side, and the garboard strake or strakes are not so thick. The keel forward is connected to the stem by a scarph, sometimes called the boxing scarph, and aft to the stern-post, by mortice and tenon. The apron is fayed or fitted to the after-side of the stem, and is intended to give shift to its scarphs, the lower end scarphs to the deadwood. The keelson is an internal line of timbers fayed upon the inside of the floors directly over the keel, the floors being thus confined between it and the keel. Its use is to secure the frames and to give shift to the scarphs of the keel, and thus give strength to the ship to resist extension lengthways, and to prevent her hogging or sagging. The foremost end of the keelson scarphs to the stentons, which is intended to give shift to the scarphs connecting the stem and keel. The frames or ribs are composed of the strongest and most durable timber obtainable. By Lloyd's rules a durability of twelve years is assigned to frames composed of English, African, and live oak; East India teak; Morning Saut greenheart, morris or iron-bark; of ten years to mahogany of hard texture; Cuba, sabicu, and pencil cedar; of ten years for floors and first futtock, and nine years for second and third futtocks and top timbers, to Adriatic, Spanish, and French oak; of nine years to red cedar, angelly and Venatici; of nine years for floors and first futtocks, and seven years to second and third futtocks and top timbers of other continental white oaks, Spanish chestnut, stringy bark, and blue gum; of eight years and seven years respectively, as before, for North American white oak and American sweet chestnut; of seven years for larch, hack-matac, tamarack and juniper, and pitch-pines.

The floors in the government service are carried across the keel with a short and long arm on either side alternately, so as to break joint, and between the frames the space is filled in solid.

Longitudinal pieces of timber are worked round the interior of a ship for the purpose of receiving the ends of the beams of the several decks; they are called shelves, and are of the greatest importance, not only for this purpose, but also as longitudinal ties and struts. In any system of diagonal bracing, properly carried out, they should form one side of the parallelogram or of the triangle, and those other timbers, or iron-bars, which form the diagonals or the other sides of the parallelogram or triangle ought to be firmly secured to them. A thick strake of plank used formerly to be worked between the shelf and the timbers or frames, but now it is generally worked home upon them. The shelf is generally supported by some thick strakes of plank worked immediately under it, and formerly it was also sometimes supported by chocks or triangular pieces, like brackets on the ship's side, brought out to be flush with the inner edge of the shelf, and on the face of this an iron-knee. This chock is now generally dispensed with, and the lower side of the shelf is bevelled off towards the ship's side, and the iron-knee is forged to fit under it accordingly. These fastenings will be referred to when treating of the means of securing the ends of the beams. The other fastenings of shelf-pieces are by numerous through-bolts. Timbers which are fayed to the inside of the frame, or upon the inside of the plank, longitudinally or diagonally, solely for the purpose of supporting the frame, are called riders.

The beams. The beams of a ship prevent the sides from collapsing, and at the same time carry the decks. The beams are spaced, and their scantling settled upon, according to the strength required to be given to the decks, and to suit the positions of the masts and hatchways, and other arrangements connected with the economy of the ship. All beams have a curve upwards towards the middle of the ship called the round up. This is for the purpose of strength, and for the convenience of the run of the water to the scuppers. Wooden beams are single piece, two, three, or four piece beams according to the number of pieces of timber of which they are composed. The several pieces are scarphed together, and doweled and bolted, the scarps being always vertical. A scarf now very generally adopted was introduced by Mr Edge, late master-shipwright of Devonport dockyard, and is represented in the annexed figure. The beams of ships being supported at both ends, and one of the strains to which they are chiefly subjected being a downward pressure, the upper part of the beams will then be compressed, and the lower parts extended. It is therefore desirable that the lower part of the beams should not be wounded so as to cut the fibres across in that part. An incision above the line of the vertical axis is of less moment, and if an incision be made there for the purpose of introducing a carling, for instance, and if this be well fitted, and be of as hard wood as the beam, the strength of the beam will not be impaired, but may even be increased.

The connection of the ends of the beams to the sides of the ship have been made in various ways. The points to be considered, with reference to this connection, are, that the beam is required to act as a shore or strut, to prevent the sides of the ship from collapsing, and also as a tie to prevent their falling apart; that the beam shall not rise from its seat, and that it shall not work in a fore and aft direction; that the beam may be an effective shore, nothing more is necessary than that the abutment of the end against the ship's side may be perfect.

In order that it may act as a tie between the two sides, it is generally doweled to the upper surface of the shelf on which it rests; and the under surface of the water-way plank which lies upon it is sometimes doweled into it. These dowels, therefore, connect it with the shelf and the waterway, and through this means it is thus connected with the sides of the ship. There is, also, in the ships of the royal navy, a plank called a side-binding strake, scored down over and into the beam-ends at some distance from the side, and bolted through the side between the beams. The scoring into the beams connects the in and out fastenings of this strake with the longitudinal tie of the beams, but the advantage does not seem to be commensurate with the labour.

The beams are also supported by knees below them. Knees to Wooden knees are chiefly used in America; and it is argued that they give a better support to the beam from their greater surface, and from their stiffness in the throat, or angle of the knee. The iron-knees used in the royal navy vary in form; they are made not only to support the beam from below, but sometimes with horns to clasp it sideways at a short distance from the side of the ship. The lower arms of these knees are so formed as to fit round the shelf; or sometimes, with a view to prevent the necessity of working the iron into this form, and at the same time afford additional support to the shelf, a chock is fitted under the shelf to receive the face of the knee. While the knee is instrumental in supporting the beam, it is also upon it that dependence is mainly placed to prevent the beam rising, or working in an upward direction. In these fastenings there appears a want of any very efficient means to prevent the beam straining in a fore and aft direction, or working upon the end as upon a pivot.

From the short outline previously given of the disturbing forces acting on a ship, it will be seen that the strain which acts on the ends of the beams to destroy their connection with the side and loosen the fastenings, must be very great when the ship is under sail, either on a wind or before it—that is, either inclined or rolling. The principal action of these forces is to alter the vertical angle made by the beam and the ship's side—that is, to raise or depress the beam, and so alter the angle between it and the side of the ship above or below it. On the lee-side the weight of the weather side of the ship and all connected with it, and of the decks and everything upon it, as well as the upward pressure of the water, all tend to diminish the angle made by the beam and the ship's side below it, and consequently increase the angle made between them above it. The contrary effect is produced on the weather side, where the tendency is to close the angle above the beam and open that below it. If the beam when subjected to these strains, be considered as a lever, it will be evident that the fastenings to prevent its rising ought to be as far from the side as is consistent with the convenience or accommodation of the ship; and that while the support should also be extended inwards, the fastening to keep down the beam-end should be as close to the end of the beam, and consequently to the ship-side, as it can be placed. The annexed section of the side of a three-decked ship of the royal navy shows some of the modes that have been adopted for securing the ends of the beams.

Beams which do not extend from one side of the ship to the other are called half-beams. They are introduced whenever the hatches or openings in the middle of the ship are such as to require the whole or unbroken beams to be so wide apart that the deck requires support between them. Their ends, towards the midships, are received by fore and aft pieces called carlings, which go from beam to beam; and any intermediate athwartship pieces between the carlings are called ledges.

The two sides of the ship at the bows are connected by hooks, which are either of timber or of iron. It is important to remember that the hooks above, and those below the surface of the water, are subjected to an opposite strain. The tendency of the pressure of the water on the bow is to make the sides collapse, and therefore the hooks below the water's surface should not only act as ties to the bow while the ship is grounded—as, for instance, when in dock—but should be formed more especially to resist the pressure of the water when she is afloat. Those hooks which are above the surface of the water act principally as ties, the rake of the bow and the weight of its parts tending to separate the two sides of the ship.

The plank, or skin, or sheathing of a ship, both external planking, and internal, is of various thicknesses. A strake of planking is a range of planks abutting against each other, and generally extending the whole length of the ship. A thick strake, or a combination of several thick strakes are worked wherever it is supposed that the frame requires particular support—for instance, internally over the heads and heels of the timbers; both externally and internally in men-of-war vessels between the ranges of ports; and internally to support the connection of the beams with the sides, and at the same time form a longitudinal tie. The upper strakes of plank, or assemblages of external planks, are called the sheer-strakes. The strakes between the several ranges of ports, beginning from under the upper-deck ports of a three-decked ship in the royal navy, are called the channel wale, the middle wale, and the main wale. The strake immediately above the main wale is called the black strake. The strakes below the main wale diminish from the thickness of the main wale to the thickness of the plank of the bottom, and are therefore called the diminishing strakes. The lowest strake of the plank of the bottom, and whose edge fits into the rabbet of the keel, is called the garboard strake.

Plank is either worked in parallel strakes, when it is called "straight edged," or in combination of two strakes, so that every alternate seam is parallel. There are two methods of working these combinations, one of which is called "anchor stock," and the other "top and butt." The difference will be best shown by the annexed figure. The difference in the intention is, that in the method of working two strakes anchor-stock fashion, the narrowest part of one strake always occurs opposite to the widest part of the other strake, and consequently the least possible sudden interruption of longitudinal fibre, arising from the abutment, is obtained. This description, therefore, of planking is used where strength is especially desirable. In top and butt strakes the intention is, by having a wide end and a narrow end in each plank, to approximate to the growth of the tree, and to diminish the difficulty of procuring the planks. When the planking is looked upon as a longitudinal tie, the advantage of these edges being, as it were, imbedded into each other is apparent, all elongation by one edge sliding upon the other being thus prevented. The shift of plank is the manner of arranging the butts of the several strakes. In the ships of the royal navy the butts are not allowed to occur in the same vertical line, or on the same timber, without the intervention of three whole strakes between them.

Of the internal planking the lowest strake, or combination of strakes, in the hold, is called the limber-strake. A strake-limber is a passage for water, of which there is one throughout the length of the ship, on each side of the keelson, in order that any leakage may find its way to the pumps.

The whole of the plank in the hold is called the ceiling. Ceiling and Those strakes which come over the heads and heels of the internal timbers are worked thicker than the general thickness of planking, the ceiling, and are distinguished as the thick strakes over the several heads. The strakes under the ends of the beams Practical of the different decks in a man-of-war, and down to the ports of the deck below, if there be any ports, are called the clamps of the particular decks, to the beams of which they are the support, as the gun-deck clamps, the middle-deck clamps, &c. The strakes which work up to the sills of the ports of the several decks are called the spirketting of those decks—as gun-deck spirketting, upper-deck spirketting, &c.

The fastening of the plank is either "single," by which is meant one fastening only in each strake, as it passes each timber or frame; or it may be "double," that is, with two fastenings into each frame which it crosses; or, again, the fastenings may be "double and single," meaning that the fastenings are double and single alternately in the frames as they cross them. The fastenings of planks consist generally either of nails or treenails, excepting at the butts, which are secured by bolts. Several other bolts ought to be driven in each shift of plank as additional security. Bolts which are required to pass through the timbers as securities to the shelf, water-way, knees, &c., should be taken advantage of to supply the place of the regular fastening of the plank, not only for the sake of economy, but also for the sake of avoiding unnecessarily wounding the timbers.

The planking in the royal yards is not usually fastened permanently till some time after it is trimmed and brought on to the bottom of a ship. It is thus allowed to season and shrink; and one strake in eight or ten is left out for the purpose of allowing ventilation, and to make good the shrinkage, and also to allow the strakes to be refayed. Without the latter provision there would be such an alteration of edge as would throw the holes made for the temporary securities out of the range of the strakes; but with this precaution it is very seldom that the alteration of edge is such as to require new holes, especially as the iron screw-eye bolts used for this temporary fastening are of much smaller diameter than the permanent treenail fastening, and therefore the holes for them through the plank can still be made good holes for the treenails. This method of securing the planks by a first or temporary fastening, to be afterwards substituted by a treenail, is also of advantage in enabling them to be brought into close contact with the timbers, in the saving of bolt fastenings, and in causing a good and regular seam to be given for the caulking.

The advantages and disadvantages of iron as a fastening for planking have been already discussed. The strength of treenails to resist a cross-sheering strain, as found by Mr Parsons, late of H.M. Dockyard Service, is shown in the following table:

| Diameter of the Treenails | Number of the Experiment | Thickness of the Plank | |---------------------------|--------------------------|-----------------------| | | | 1 Inch. | 1\(\frac{1}{2}\) Inch. | 1\(\frac{3}{4}\) Inch. | 1\(\frac{5}{8}\) Inch. | | 1 In. | | 1 | 2 | 3 | 4 | | 2 In. | | 1 | 2 | 3 | 4 | | 3 In. | | 1 | 2 | 3 | 4 | | 4 In. | | 1 | 2 | 3 | 4 | | 5 In. | | 1 | 2 | 3 | 4 | | 6 In. | | 1 | 2 | 3 | 4 | | 7 In. | | 1 | 2 | 3 | 4 | | 8 In. | | 1 | 2 | 3 | 4 | | 9 In. | | 1 | 2 | 3 | 4 | | 10 In. | | 1 | 2 | 3 | 4 | | 11 In. | | 1 | 2 | 3 | 4 | | 12 In. | | 1 | 2 | 3 | 4 | | 13 In. | | 1 | 2 | 3 | 4 |

Average: 1\(\frac{1}{11}\), 1\(\frac{1}{13}\), 2\(\frac{6}{16}\), 2\(\frac{6}{16}\), 3\(\frac{10}{16}\), 4\(\frac{6}{16}\)

"In all these experiments on treenails, when the treenails were evidently good, they gave way gradually. In some of the rejected experiments, however, the treenails certainly did break off suddenly, but then they were evidently, on examination, either of bad or over-seasoned material. It has been asserted that the treenails made from the Sussex oak are much stronger than those made from the New Forest timber, or any other English oak. To ascertain the truth of this assertion, some experiments were made with Sussex and New Forest treenails of all sizes; and the result was, that there was not the least difference in them, the New Forest were, on experiment, quite as strong as the Sussex. In the experiments on treenails, the plank generally moved about half an inch previous to the fracture of the treenail."

The following useful tables were also drawn up by Mr Parsons from a series of valuable experiments carefully made by him, and show the longitudinal holding power of treenails. The first of these tables exhibits the adhesion of iron and copper bolts, driven into sound oak, with the usual drift, not clenched, and subject to a direct tensile strain. By drift is meant the allowance made to insure sufficient tightness in a fastening; it is therefore the quantity by which the diameter of a fastening exceeds the diameter of the hole bored for its reception.

"Table of the Adhesion of Iron and Copper Bolts driven into sound Oak with the usual Drift, not clenched, and subjected to a direct Tensile Strain."

| Diameter of the Bolt | Length of the Bolt driven into the Wood | |----------------------|----------------------------------------| | | Iron | | | Copper | | | Length of the Bolt driven into the Wood | | | Four Inches | Six Inches | Four Inches | Six Inches | | 1 In. | 1 | 1 | 1 | 1 | | 2 In. | 2 | 2 | 2 | 2 | | 3 In. | 3 | 3 | 3 | 3 | | 4 In. | 4 | 4 | 4 | 4 | | 5 In. | 5 | 5 | 5 | 5 | | 6 In. | 6 | 6 | 6 | 6 | | 7 In. | 7 | 7 | 7 | 7 | | 8 In. | 8 | 8 | 8 | 8 | | 9 In. | 9 | 9 | 9 | 9 | | 10 In. | 10 | 10 | 10 | 10 | | 11 In. | 11 | 11 | 11 | 11 | | 12 In. | 12 | 12 | 12 | 12 | | 13 In. | 13 | 13 | 13 | 13 |

"In Riga fir the adhesion was, on an average, about one-third of that in oak, and in good sound Canada elm it was about three-fourths of that in oak.

The following table exhibits the strength of clenches and of forelocks as securities to iron and copper bolts, driven six inches, without drift, into sound oak, either clenched or forelocked on rings, and subjected to a direct tensile strain. It gives the diameter of the bolt on which the experiment was made, as well as the number of the experiment:..." Table of the Strength of Clenches and of Forelocks, as securities to Iron and Copper Bolts, driven six inches without Drift, into sound Oak, either clenched or forelocked on Rings, and subjected to a direct Tensile Strain.

| Diameter of the Bolt | Number of the Experiment | Iron | Copper | |---------------------|--------------------------|------|--------| | | | Clench | Forelock | Clench | Forelock | | Inch | | Tons. Cwt. | Tons. Cwt. | Tons. Cwt. | Tons. Cwt. | | 1 | | 1 16 | 0 16 | 1 0 | 0 8 | | 2 | | 1 13 | 0 14 | 1 0 | 0 7 | | 3 | | 1 9 | 0 12 | 1 0 | 0 6 | | 4 | | 1 9 | 0 18 | 1 0 | 0 7 | | 5 | | 1 3 | 0 15 | 2 10 | 1 4 | | 6 | | 2 0 | 0 18 | 2 10 | 1 4 | | 7 | | 2 16 | 1 9 | 2 5 | 1 2 | | 8 | | 2 15 | 1 4 | 2 9 | 1 4 | | 9 | | 2 15 | 1 4 | 3 10 | 1 8 | | 10 | | 2 10 | 2 15 | 3 15 | 1 8 | | 11 | | 2 10 | 2 15 | 4 0 | 2 4 | | 12 | | 2 12 | 2 12 | 4 10 | 1 16 | | 13 | | 2 18 | 3 15 | 6 0 | 2 13 | | 14 | | 2 18 | 3 15 | 6 0 | 2 13 | | 15 | | 2 18 | 3 15 | 6 0 | 2 13 | | 16 | | 2 18 | 3 15 | 6 0 | 2 13 |

"In the experiments on the clenches, the clenches always gave way; but with the forelocks it as frequently occurred that the forelock was cut off as that the bolt broke; and in the cases of the bolt breaking, it was invariably across the forelock hole. According to the tables, the security of a forelock is about half that of a clench.

"It appears an anomaly that the strength of a clench on copper should be equal to that of one on iron. But, in consequence of the greater ductility of copper, a better clench is formed on it than on iron. Generally the thickness of the fractured clench in the copper was double that in the iron. With rings of the usual width for the clenches, the wood will break away under the ring, and the ring be imbedded for two or more inches before the clench will give way.

"With the inch copper-bolts, all the rings under the clenches turned up into the shape of the frustum of a cone, and allowed the clench to slip through at the weights specified.

"Experiments with ring-bolts were made to ascertain the strength of the rings in comparison with the clenches. The rings were of the usual size, viz., the iron of the ring one-eighth inch less in diameter than that of the bolt. It was found that the rings always carried away the clenches, but that they were drawn into the form of a link with perfectly straight sides. The rings bore, before any change of form took place, not quite one-half the weight which tore off the clenches. It appears that the rings are well proportioned to the strength of the clenches."

From these tables it will be seen how much the strength of a clenched or fore-locked bolt falls short of the strength due to the full diameter of the bolt where a tensile strain only is applied to it; and when exposed to a cross strain, it is also well known how much the strength is diminished when the ends are not fastened and held securely in position. An increased use of screw-bolts with nuts and larger plates or rings under the heads and under the nuts would therefore give great additional strength; and if a sufficient length of the bolt were screwed at the end to allow of as much as an inch being cut off when too long, the supply of sizes necessary to be kept in store would not be large. Economy also would be likely to result from the greater accuracy in the length required to be given for the bolt about to be drawn from the store for use.

Screw-treenails of the annexed form have lately been introduced by Messrs Hall, the well known builders of the Aberdeen clipper-ships, and whose modes of construction will be more particularly referred to hereafter. The increased holding power of such treenails to prevent planks from starting needs no demonstration.

The decks of a ship, as has before been stated, must not be considered merely as platforms, but must be regarded as performing an important part towards the general strength of the whole fabric. They are generally laid in a longitudinal direction only, and are then useful as a tie to resist extension, or as a strut to resist compression. The outer strakes of decks at the sides of the ship are generally hard wood, and of greater thickness than the deck itself; they are called the water-way planks, and are sometimes dowelled to the upper surface of each beam. Their rigidity and strength is of great importance, and great attention should be paid to them, and care taken that their scarps are well secured by through bolts, and that there is a proper shift between their scarps and the scarps of the shelf.

When the decks are considered as a tie, the importance of keeping as many strakes as possible entire for the whole length of the ship must be evident; and it has already been stated that a continuous stroke of wrought-iron plates beneath the decks is of great value in this respect. The straighter the deck, or the less the sheer or upward curvature at the ends that may be given to it, the less liable will it be to any alteration of length, and the stronger will it be. The ends of the different planks forming one strake are made to butt on one beam, and as the fastenings are then driven close to the ends, they do not possess much strength to resist being torn out. The shifts of the butts, therefore, of the different strakes require great attention, because the transference of the longitudinal strength of the deck from one plank to another is thus made by means of the fastenings to the beams, the strakes not being united to each other sideways.

These fastenings have also to withstand the strain during the process of caulking, which has a tendency to force the planks sideways from the seam; and as the edges of planks of hard wood will be less crushed or compressed than those of soft wood when acted on by the caulking-iron, the strain to open the seam between them to receive the caulking will be greater than with planks of softer wood, and will require more secure fastenings to resist it. It may also be remarked that the quantity of fastenings should increase with the thickness of the plank which is to be secured, for the set of the oakum in caulking will have the greater mechanical effect the thicker the edge.

A deck, laid in a diagonal direction only, involves a great loss of strength longitudinally, and the advantages are not laid decks, such as to compensate for this loss, and for the other inconveniences as to wear and tear, which result from such a system. Mackonochie proposed to lay decks in three layers, one diagonally from starboard to port, another from port to starboard, and an upper layer fore and aft. He also proposed a somewhat similar system for the outside planking, and vessels have been built on different modifications of this plan both in this country and in America. At the two ends of a ship it is important that the strength of the tie of the deck should be maintained there, and while the continuation and connection of the shelf-pieces and waterway-planks are duly attended to, with any necessary hooks and crutches, additional strength to sustain the projecting bows and raking sterns may be obtained by a judicious connection of several beams to the extreme ends. This may be done by long bolts passed through the beams and secured by nuts and screws at their ends, or by pieces of timber fore and aft, underneath the beams, and bolted to them. These beams should have several ranges of carlings let down between them to diffuse the strain.

In all such connections of wood with wood, dowelling is much to be preferred to scoring down. The latter is objectionable on account of its wounding and weakening the parts in a greater degree, and the joint is subject to become loose or open by the shrinkage of the materials, and it also requires much more care and skill on the part of the workman for its perfect execution. It should therefore be discontinued wherever practicable.

The frame-work of timbers which is formed round the mast-holes in each deck is called the mast partners. "Partners" generally are the principal timbers in a framing formed for the support of anything passing through a deck, as the masts and capstans.

The pieces of timber to receive the heels of the several masts are called steps, as the main, fore, or mizen steps.

Coamings are pieces generally faying on carlings, and rising higher than the flat of the deck, to form the fore and aft sides or boundaries of openings, such as hatch or ladder-ways; head ledges forming the athwartship boundaries to the same openings.

When the planks are fastened, the seams or the intervals between the edges of the strakes are filled with oakum, and this is beaten in or caulked with such care and force that the oakum, while undisturbed, is almost as hard as the plank itself. If the openings of the seam were of equal widths throughout their depth between the planks, it would be impossible to make the caulking sufficiently compact to resist the water. At the bottom edges of the seams the planks should be in contact throughout their length, and from this contact they should gradually open upwards, so that, at the outer edge of a plank 10 inches thick, the space should be about \( \frac{4}{9} \)th of an inch, that is, about \( \frac{1}{2} \)th of an inch open for every inch of thickness. It will hence be seen that if the edges of the planks are so prepared that when laid they fit closely for their whole thickness, the force required to compress the outer edge by driving the caulking-iron into the seams, to open them sufficiently, must be very great, and the fastenings of the planks must be such as to be able to resist it. Bad caulking is very injurious in every way, as leading to leakage and to the rotting of the planks themselves at their edges. It frequently happens, however, that the caulking is blamed when the leakage and the attendant evils have been caused by the edges of the planks sliding upon each other through the working of the deck or of the ship.

Instead of pitch for closing the seams above the oakum, Mr Jeffery introduced a mixture of shellac and caoutchouc, combined with naptha. This is at first more expensive, but its decided superiority and greater durability, preventing the necessity of so frequently re-caulking, will counterbalance this in due time, so as to be to the advantage of the ship-owner, though this will not make it economical to the ship-builder who builds and completes a vessel by contract. It is insoluble in water, and impervious to it; it is also elastic, and yet of sufficient solidity to fill up the joint and give strength; and it is also powerfully adhesive, so as to connect the planks together at their edges.

The mode of applying diagonal trussing to strengthen the side of a ship constructed in accordance with the foregoing outline, will next be considered.

In the system of building which was superseded by that termed the diagonal system, the whole of the interior surface of the frame was planked, and a second series of internal trusses was worked upon this planking, agreeing in direction with the timbers of the ship. Riders were also introduced in various parts, but not diagonally, and those in the hold were no doubt necessary when it was the custom to "ground" ships on a beach for repair; a large quantity of timber was thus massed together, having the appearance of great strength; but, in fact, from its weight, injudicious combination, disposition and fastening, much of it was, if not injurious, at least useless. The idea of diagonal trussing was not an entire novelty at the time when Sir Robert Seppings introduced it as a system. There is evidence, in the representation of a vessel under repair in the fifteenth century, of some pieces of timber having been used diagonally in her construction, as also in some other isolated instances. The credit, however, of calling the attention of ship-builders to the principles on which the advantages of diagonal trussing depend, is entirely due to Sir Robert Seppings, and no ship is now ever built without the principle being brought into action in a greater or less degree.

He described his system in a paper communicated by him to the Royal Society, and which is printed in their Transactions for the year 1814. In that paper, after supposing the frames for a two-decked 74 gun-ship to be in place, and the spaces between the frames filled-in solid, he proceeds as follows:

"In this state the diagonal timbers are introduced, intersecting the timbers of the frame at about the angle of 45°, and so disposed as that the direction in the fore is contrary to that in the after part of the ship, and their distance asunder from 6 to 7 feet or more; their upper ends abutting against the horizontal hoop or shelf-piece of the gun-deck beams, and the lower ends against the limber strakes, except in the midships, where they come against two pieces of timber placed on each side of the keelson (called additional keelsons), for the purpose of taking off the partial pressure of the main-mast, which always causes a sagging down of the keel, and sometimes to an alarming degree. These pieces of timber are nearly as square as the keelson, and fixed at such a distance from it that the main step may rest upon them. They may be of oak or pitch-pine, and as long as can be conveniently procured. Pieces of timber are next placed in a fore and aft direction over the joints of the frame-timbers, at the floor and first futtock-heads; their ends in close contact with, and coaked or doweled to, the sides of the diagonal timbers. In this state the frame-work in the hold presents various compartments, each representing the figure of a rhomboid.

"A truss-timber is then introduced into each rhomboid, with an inclination opposite to that of the diagonal timbers, thereby dividing it into two parts. The truss-pieces so introduced into the rhomboid are to the diagonal frame what the key-stone is to the arch; for no weight or pressure on the fabric can alter its position in a longitudinal direction, till compression takes place at the abutments, and extension of the various ties.

"This arch-like property of the diagonal frame not only opposes an alteration of position in a longitudinal direction, but also resists external pressure on the bottom, either from grounding or any other cause, because no impression can be made in its figure in these directions without forcing the several parts of which it is composed into a shorter space."

The trussing here proposed for the hold of the ship was undoubtedly with the intention of introducing the principle of the inverted arch or dome; and it must be remembered, that the general form of the vessels to which Sir Robert Seppings was accustomed approached that of a hemisphere at their midship section, and was very different from the comparatively flat or plain surfaces now common. Any lower ranges of riders and trusses brought on the floors and first futtocks could have little effect in preventing arching beyond that which arises from the additional resistance they offer to deflexion by their rigidity. In men-of-war with several decks above the lower deck, the object aimed at seems to have been to obtain a firm base on which to ground a new and upper series of diagonal ties and struts. It will be evident from these remarks, that it is not considered that the bottom of a ship, if filled-in solid, and made as little compressible as possible by this means, and by the introduction of additional or sister keelsons, requires any great expenditure of material or labour, in order to adapt a system of diagonal trussing to it. The position for its most beneficial application is undoubtedly the sides of the vessel, but whether struts or ties be used, there must be a proper starting point for their ends. In wooden vessels of ordinary construction, this would, perhaps, be found to be in the sister keelson, nearest the wing; or in the thick strakes or riders brought on at the head and heels of the floors and first futtocks. The importance of these last in resisting any strain, if the ship takes the ground and rests on her bilge, is also evident; and it would therefore be advantageous to increase their strength with this view, even if there existed no other reason. Having determined a base or starting point for the lower ends of the diagonals, the next point to be attended to is to determine a strong line of work to which to attach their upper ends. Where intermediate decks occur the diagonals must either be carried past them in one continued line, or a new system be commenced and carried on from that line. In this case the strain on the parts may become such that the direction of the ties and struts may require to be changed. While diagonals are useful as a means of firmly connecting the adjacent pieces of timber, it must be remembered that this is a small portion of their value, and that full advantage will not be ensured from them without due consideration being given to keep up an unbroken system of sides and of diagonals, with their ends firmly united. It is immaterial whether parallelograms or triangles be used, if the last side of the one be always made the first side of the next. A triangle is a valuable form in structures of this kind, because it is a figure which admits of no alteration in its form; its angles are invariable as long as the sides remain the same, that is, as long as they are neither elongated nor shortened.

These principles are becoming more and more appreciated every day, and the strength of ships is consequently becoming much increased.

In the government service the diagonals, which extend over the surface of the side of the ship, are of iron-bars, varying according to the size of the ship, and also of wood. The annexed wood-cuts represent and show portions of the vessels. In other vessels the iron-bars are laid upon, and sunk into, the frames in one direction, while a series of wooden diagonal riders are placed upon the surface of the internal sheathing, crossing them in the other direction. In the fabric, as a whole, there appears a want, to the eye of an engineer, of a due consideration to the fact, that the strength of a box-girder, or tubular bridge, to which the mind naturally reverts as the simplest form of a long body to sustain without the top and bottom bars uniting the lattice or trellis works. If a weight is to be supported by ties, there must be something to carry their upper ends without yielding; and if it is to be supported by struts, there must be a sound and unyielding foundation for them to rest upon, and from which they may rise.

Messrs Hall and Co., of Aberdeen, carry out the principle to a great extent in the vessels built by them.

The following is a general description of the Schomberg (Plate III.), as built by them, in 1854, for James Baines and Co., of Liverpool, and many valuable hints may be gained from the practice of these eminent builders. She was expressly designed for an Australian passenger-ship, and every attention was paid to render her ventilation complete:

Her register measurement was 2400 tons; her frames were of British oak, 4 feet from centre to centre, close-jointed and bolted, and her sheathing consisted of four thicknesses of 2½ inch Scotch larch, first two courses worked diagonally at an angle of 45° passing under the bottom of inside keel, and up the opposite side; the third course also passed under the keel, and was laid on transversely, same as the frames; there was a similar course worked inside between the frames, each course having a layer of felt, and a coat of Archangel tar, between them. The outside longitudinal planking averaged 6 inches in thickness, and the whole mass was combined by screw trenails of African oak, 1½ inches diameter, put through the whole, there being one trenail at every foot in each stake of plank.

She had three tiers of malleable iron-beams, there being one attached to each frame on each side of the three decks, as shown in the transverse section (Pl. III.) These beams were laid on pitch pine stringers, which were in two depths, and were attached to the sides by iron staple knees, a piece of plate-iron passing betwixt the beam end and the frame, and these plates being connected with the knees by the throat-bolts passing through them, and thus forming a lodgment for the iron beam ends. There was also a malleable iron-plate, 16 x ½ inches, riveted to the top angle-irons on the beams; to this plate the water-ways were secured, besides being bolted horizontally. The sizes of the beams were:

- Upper deck, 7x½ width, 21x2½ inches in single iron. - Middle deck, 8x¾ 3 inches angle iron. - Lower deck, do. do. do.

The beams were in one length; the lower edge with a bulb, and upper edge with angle-irons, back to back. They were supported by three tiers of iron stanchions, riveted to the beams, and bolted to the keelson and sister-keelsons.

For ventilation, the spaces, 3 feet wide, between the frames, were boarded up, and formed excellent ventilators from the various decks and hold, leading up to a space immediately under the main rail, which was fitted all round with venetians. She was also fitted with large funnels, and with a fanner for forcing the air down to the keel, besides scuttles on every six feet on the middle deck. The saloon was on the upper deck, and was fitted with a double roof for causing a current of air, with orifices all round under the cornice outside.

The vessel having a great rise of floor, it was levelled off inside to the 5 feet water-line, by having a fourth deck laid from end to end, and under this deck tanks were fitted to hold 300 tons of fresh water. Along the upper deck, from saloon forward, there was a range of houses for live stock, cook-house, and accommodation for the crew. This vessel sailed from Liverpool for Australia in 1854, drawing 21' 6" forward and 24' 6" aft, and on the eighty-fourth day was lost on Cape Otway, on a fine moonlight night. No favourable opportunity occurred during the passage to test her speed for any continued length of time; but she attained, on one occasion, a speed of sixteen knots for a few hours.

This ship, complete, cost L.45,000.

The annexed figures are further illustrations of the details of construction adopted by the same builders.

A section of a clipper ship, of 700 tons burthen, The Vision, of Liverpool, built in 1854, is given in fig. 39. The larboard side represents the bolting in the frames,

Practical which are 4½ feet asunder from centre to centre. The Balling starboard side shows the application of the screw-treenails in connecting the various layers of plank, which consist of Practical two thicknesses of 2-inch larch worked diagonally, as shown Building.

In figs. 38a and 38b, one thickness of larch worked vertically, and one outside, of an average thickness of 4½ inches, worked longitudinally, the sheer-strakes of East India teak, top sides Dantzig red pine, Wales, and to light water-line of

Dantzig imported plank, from thence to the keel-strakes between the planks, which are all coated with vegetable, of Dantzig red pine, with two complete layers of hair felt tar. Fig. 38 a represents an outside longitudinal section of the side planking fastened with screw-treenails; and fig. 38 b represents a vertical section of the same, with the felt between and the metal bolting in the frames.

Fig. 40 represents the mode of laying the diagonal planking of the deck under the longitudinal upper-deck planks.

A cursory view will now be taken of a few of the leading features in the construction of iron-ships, and of the mode of forming and uniting some of the principal parts; and the specifications, in full, to which two first-class steamships have been built, will then be given.

The keel is sometimes formed of a single bar, with the floors crossing above it, and united to the floors by being riveted to the garboard strake. It is more frequently formed of a plate, sufficiently deep to form both the keel and the centre plate of the keelson, or of a box form. Specimens of these forms of keel will be found in the engravings. A box-keel may also be made thus (fig. 41):


The points, in addition to general strength, which require attention, are, that if the keel be injured by the vessel taking the ground, it shall cause as little damage as possible to the vessel itself. A keel should also be capable of being varied in strength, so that it may be made stronger at the heel of the stern-post, where the bottom of the rudder is attached to it. It will be observed that this latter point is particularly attended to in the vessel for the Peninsular and Oriental Company.

In the keel, according to the sketch shown above, it will be observed that the plating is carried right across it, so that it might be very much injured, and probably even torn away in parts, without causing any leak into the ship, its edge being made purposely weaker than the bottom plate to which it is attached. Cross-plates with flanges, or with angle-iron, may be riveted across it, at any distance that may be desired, so as to stiffen it; and the plates can be made thicker, or additional strengthening plates may be added inside or outside the side-plates, at the stern-post, or at the forefoot.

The keelson is generally formed in one or other of the manners shown on the sections; and the floors may be carried across the bottom of the vessel, and the keelson be placed upon the top of the floors, following the same arrangement as in wooden vessels. In the latter case the side-plates of the keelson should be the whole depth of the floors, in addition to the height of the keelson above them, a space for each frame being cut out of the lower part of the plate to allow it to pass down between the frames, and be attached to the bottom by short pieces of angle-iron, as specified for the side keelsons of the Australasian, and shown in the section of that vessel at HH.

There does not appear to be any particular advantage gained by the floor being made continuous across the bottom of the vessel; and as additional height is occupied by placing the keelson above them, there does not appear to be sufficient grounds for adopting this system in preference to the other.

With any side or sister-keelsons this is different, as it would be inconvenient to break the floors or frames again. In cases where such sister-keelsons are to be used as engine or boiler bearers, it would much improve their strength, and they would be better fitted to receive any such weights to be bedded upon them, if the plates were double, and they were brought up above the top of the floors, and formed into a box-keelson, thus (fig. 42). The angle-irons of the keelson lying on the floors, and attached to them as they pass, stiffen them, and will tend to prevent their buckling or bending sideways when a great strain from the outside is brought upon them.

Where the floors abut on each side of the centre keelson, there is no reason why they should be the same height as the top of the keelson; and if the top or covering plate of the keelson be put on with external angle-iron (as shown in the above sketch) for a sister-keelson, great facilities are given for taking off the plate at any time for repair, or to renew any of the rivets. Indeed, there is no reason why different lengths of the covering plate should not be put on with screw-bolts, care being taken that the bolts fill the holes correctly.

The floors are generally composed of an angle-iron, to which the external plating is attached, and a plate of any depth that may be desired, with single or double angle-iron on the inner edge of this plate. For the frames two angle-irons riveted back to back are generally sufficient. A T-shaped iron is also sometimes used, and if made with the centre web very deep, so as to be similar to the bulb-iron used for deck beams, it would be suitable for vessels of great strength, and, in some cases, for the floors with a single or double angle-iron on its inner edge.

Some of the forms of beams have already been described. Beams formed of bulb-iron, with two angle-irons, are decidedly the most convenient, as there is no difficulty in welding them up in a common smith's fire to any length that may be required; and the top edge may be cut so as to vary the depth, and this even in the same beam if desired. By doing this the lower edge of the beam might be made straight, so as not to follow the round-up of the deck and of the upper edge; and thus any slight elongation of the beam, when brought down or straightened by any weight or strain, and the pressure to force out the sides of a ship consequent upon this, as dreaded by some, would be obviated.

The forms of bulb-iron, as generally rolled, do not give nearly so large a proportion of iron in the bulb as would be desirable. It is not consistent with the proper proportion of the flanches of beams, in reference to their depths, as laid down by Mr Fairbairn and other authorities on the subject. breaking weights of these beams, at the distances of 10 feet, 15 feet, 20 feet, and 30 feet between the supports, are respectively 10, 15½, 21, and 22 tons. The thickness of the webs may be considered by many to be too thin, but a beam of the annexed figure (fig. 47) is given by Mr Fairbairn as one much used by him, with a distance of 30 feet between the supports, and it may therefore be taken as a standard pattern. Where a saving of depth is a great object, the proportions may be varied. The relative strengths and weights of such beams, in comparison with ordinary wood beams, may be easily obtained by the rules which have been given.

Of the desirability of introducing iron-beams into wooden vessels there can be no doubt. Their durability alone ought to be a sufficient inducement.

Beams are now being welded up to any lengths by a process patented by Mr Bertram, late of Woolwich dockyard. The edges to be welded are brought together, and two jets of gas are made to play upon both sides at the same time till the iron is brought to a welding heat, when it is united in a most perfect and satisfactory manner.

An increase of thickness in the plates of iron-vessels adds to the safety and general strength of the vessel in a much more important degree than putting the additional weight into the frames to strengthen them. A large surface of unequal strength in different parts is objectionable; it will be sure to yield at the line where the weak and the strong parts meet, and probably a rupture may take place along that line; but if the surface be all of nearly equal strength, and a pressure be then applied, as may be the case on the exterior of a vessel, it may yield, and the indentation may be extensive without any rupture.

The subject of riveting has already been fully treated, when giving the details of Mr Fairbairn's experiments on the strength of riveted joints. Mr Bertram's process, as adapted for the welding of beams, and by which one or more experimental boilers have already been constructed, is also proposed for the purpose of uniting the plates of iron-ships, and there do not appear to be any reasons to prevent it from becoming available after more experience in its use has been obtained. The same remarks, with regard to decks, apply to iron-ships as to wooden ships; but iron has been more used as diagonal and longitudinal stringers under the deck-planks in the former than in the latter class of vessels.

In the accompanying sections of a vessel constructed to the design of Mr Bowman of London (fig. 48), the iron-plating below the deck-planks is shown, and it is laid complete over the whole surface beneath the deck-planks. The water-ways, or pieces for forming the run of the water at the sides to the scuppers, it will also be observed, are of iron, which is not usual, but it is an important improvement, and a step in the right direction of greater deck-strength. At the risk of its being considered a repetition, reference is again made here to the importance of this point, as the strength of an iron-vessel may be compared more easily than that of a wooden one, with the strength of iron tubular bridges. As has been before observed, the severest strain to which a vessel is likely to be exposed is when it is supported in the middle, and the two ends are left unsupported. As a familiar illustration of the mode of dealing with this subject, a vessel in this position may be looked upon as a beam supported at the middle, and weighted at the two ends, or, which is the same thing, as a beam pushed up in the middle and prevented from rising by the weights, or by being fixed at the two ends. And if this beam be now supposed to be turned upside down, or reversed, and then to be subjected to the same strains upon it as before, it becomes equivalent to a beam supported at the two ends and weighted at the middle, and all the calculations for beams or tubular bridges so weighted immediately become applicable. It will thus be seen that the bottom of the ship has to bear a strain of compression due to the top, or top flanche of the tubular bridge, and the deck has to bear a strain of extension as due to the bottom or bottom flanche. The keel and keelsons, and the internal and external plates of the bottom, supported, or rather stiffened and kept in the direct line of the strain, by being attached at such short intervals to the floors, duly meet the case of the top flanche, and give the requisite strength; and the deck of the ship, and the strengthening pieces connected with it, must be made equal to meet the strain of extension, to which the bottom flanche of the beam is subjected. Let a vessel be supposed to be of the length of 300 feet, with a depth of 30 feet, and the weight of fittings, machinery, and everything which she has to carry to be 1500 tons, which may be assumed to be nearly correct for a passenger screw steam-ship of this length,—and let it be Practical further supposed that the weights are equally distributed over her length, then the strain would require to be the same as for a tubular bridge, or girder, to carry a weight of 750 tons at the middle. Now, if the ordinary rules be applied, it will be found that the sectional area of the bottom flange of a box-girder of these dimensions, and whose breaking weight is 750 tons, would be 94 square inches; and doubling this for the excess of strength necessary in practice, will give an area of 188, or say 200 square inches of iron. The strength of the deck, therefore, at the middle, should be equal to the strength of iron-bars or plates of this sectional area, and towards the ends it may be diminished to about two-thirds of this strength, on the same principle and in the same manner as the flanges of a beam may be diminished.

An explanation of the theory of the strength of girders is not within the province of this article. It will be found very fully treated in the works of Tredgold, Hodgkinson, Barlow, Fairbairn, Latham and others, as also in some papers in the Transactions of the Institution of Civil Engineers, and in a paper in the Transactions of the Royal Society, by Mr Barlow, "On the position of the Neutral Axis."

While the advantages of iron water-tight bulkheads are unquestionable, nothing can be worse than that the sheathing should be weakened in one direct transverse line by a series of rivets, placed so close together as to lessen the strength of the plates in an undue degree at that line. The Board of Trade insist upon the bulkheads being attached to two frames, but it is not apparent how the difficulty is got over by this means alone, because on one or other of these frames the rivets must be sufficiently close to make the joint water-tight. This would be advantageous if the bulkhead were made to run home to the side of the ship, and be made water-tight there by an additional angle-iron, while the two frames on either side are united together through the bulkhead, so as to prevent the vessel separating along the line of weakness between them. In this view the inner line of plates uniting the frames to the bulkhead should be kept as close as possible to the ship's side, and therefore as much as possible in the direct line of the strain to be resisted.

The following is a specification of an iron screw-steamship for the Peninsular and Oriental Steam Navigation Company:

**Principal Dimensions.**

Length between the perpendiculars..................................................335 feet. Length of the keel for tonnage..........................................................(To be according to the approved design.) Breadth, extreme..................................................................................39 feet. Depth amidships (from top of keel)......................................................31 feet. Burthen in tons, Nos.............................................................................2520, 11 o.m.

Keel.—To be formed of plates, as shown in figs. 51 and 52, the centre through-piece to be 3 feet 6 inches deep from bottom of keel to top of floors, and 1½ inches thick right fore and aft. The plate on each side to be 10 inches deep by 1½ inches thick. The fore and aft plate shown on top of floors to be ¾ in. thick, and 2 feet 6 inches wide, worked so as to fit on top of floors, and connected to centre through-piece by two angle-irons 4 x 4 x ¼. The after-end of keel to have an angle-iron 6 x 4 on each side, and a plate ¾ in. thick on the bottom, to run for 50 feet from the aftermost stem-post.

Stern.—To be made of plate in exactly the same manner as the keel, the plate on each side the centre through-piece to gradually taper to ¾ inches deep at the top, and all the bow-frames to be riveted to it.

Bread-Angle.—As may be required.

Stern-post.—15 inches broad by 7 inches thick, and a heel left on the after-side to bear the rudder, with eyes for the pintles, and turned so as to form a knee forward on the keel. The screw-port to be forged in one piece to suit the drawing, or as the engineer may require.

Frames.—Of angle-iron, 5½ x 4 x ¼, and 20 inches from centre to centre. In engine and boiler spaces, the frames to be doubled in the bottom, and a reverse angle-iron on every frame, 4 x 3 x ¼, from floor to gunwale, the whole length of the vessel.

Plates.—Garboard-strake, ¾ plates, as broad as can be procured or worked; bottom-plates 1½, next plates up to the wales 1½, from the wales to gunwale 1½, except two plates, 2 feet 6 inches wide, 1½ thick, or one plate equal to this to form the wales; the sheer strake, 1½ thick, to be doubled right fore and aft, and butt-straps inside, as in single plates, all double riveted from keel to gunwale, and all butts to be flush; the upper or sheer-strake to go 12 inches above top of water-way, as per sketch. All spaces formed by the projections of the plates to be fitted with liners, so as to avoid small

Practical places and rings being used, except in the case of the sheer and upper wale-strakes, which will be doubled, and the inner strake will necessarily form the liner. The butts to be perfectly close as well as the seams, as no pieces will be allowed to be put in and caulked over. The counter-sinking to be carefully done, and all rivets to be full and smooth outside plates, and to be chipped down while hot. The greatest care to be taken in the punching, to prevent unfair holes.

Floors.—30 inches deep in engine and boiler spaces of 1½ plates, with angle-irons 4½ x 2½ x 1½ on each side, on top of every floor, to run from 14 to 16 feet up the turn of bilge. The floors in after-hold, 30 inches deep, 1½ thick, with single angle-iron on top, 4½ x 3 x 1½. The floor-plates to run 6 feet up the turn of bilge on each side of frames in one piece.

Keelsons.—As may be required, and to suit the engineer's drawings, to run right fore and aft as far as the form of vessel will allow.

Pillars.—In holds between keelsons and beams, to be 3½ inches in diameter amidships, tapering to 2½ at the ends. One on every beam, or as may be directed. Pillars on main-deck, one on every other beam, arranged so as to suit the cabin plan.

Bulkheads.—Water-tight; one in fore-peak, two before the engine, one abaft the boilers, and one in after-peak; to be in accordance with the Board of Trade regulations in every respect. To have true bulkheads, or floors, every frame from stern-post for 40 feet, and on every frame from stem for 20 feet, the after ones ½ inch thick, the foremost ¼ inch. Those abaft the aftermost water-

tight bulkhead to run up to the lower-deck water-way plate, and an angle-iron on the top of each, with a water-tight deck, riveted to the same. The lower-deck water-way plate will run through these bulkheads, as well as the water-way forming part of the deck. Proper man-holes, cut through each floor above the shaft, and sufficient water-tight man-hole doors, fitted to the holes in the iron-deck. The floors before the water-tight bulkhead to run up as far above the shaft as may be required. Every other bulkhead, the length of screw-shaft, to have a forged iron-ring, 3 inches wide, 1 inch thick, riveted round shaft-space. The holes for shaft to be drilled from after-end through all these by the engineers. All watertight bulkheads to be fitted with approved brass sluice-valves. The space below the screw-shaft, abaft the aftermost water-tight bulkhead, to be filled-in solid with bricks and cement. Iron-tie bulkheads to be placed, as directed, between main and lower decks, about 20 feet apart.

Beams.—Of plate, 10 x 1½, with two angle-irons on top, 3½ x 2½ x 1½. Beams not to be turned at the ends, but to have a vertical and horizontal plate, riveted to under side of beams and side-frames, with an angle-iron in the angle, and to be finished on the lower edge, with half-round iron, as may be required. An angle-iron on each alternate frame, for main and lower decks, with as many in the engine and boiler spaces as the position of the machinery will allow. To have orlop-beams and a deck to allow of such accommodation for stores as may be required (figs. 54). Engine-beams as the engines may direct. Eight of the foremost beams to be made of an elliptical shape, turned down 2 feet 6 inches to strengthen the bow, and likewise for the hawse-pipes to pass through. The plate to be twice the thickness of the other beams.

Stringers.—An angle-iron, 6 x 4, all round the gunwale, with two covering plates, the outside one 18 x 1½, the inside one 24 x 1½, riveted to gunwale stringer, and upper-side of deck-beams, and 6 pieces apiece, to allow for pipe or stingers to pass through the first plank from water-way, which is to be East India teak (figs. 54 and 55). The same for main and lower decks. The lower-deck plates to run right through engine-room and boiler space, and to have in that space an angle-iron top and bottom, and to be from the foremost to the aftermost midship water-tight bulkhead in engine-room 1¾. Two midsip deck-plates, of the same dimensions as the inside gunwale stringer, to run right fore and aft, full length of vessel, on each side of engine-room skylight, and riveted to upper-side of deck-beams. To have at least 6 diagonal spar-deck plates, 12 x 4, riveted on top of all these stringers, to tie the sides of the vessel together, to be placed as may be required (fig. 55). The butts of all these fore and aft stringers, to be placed so that the whole of them come on beams, and to have a butt-strap to each butt 12 inches in width, and a row of rivets on each side of the edge of the beams. A vertical stringer, 2 feet 2 inches wide, 1½ thick, to run round the main-deck at back of spritketting, and to be connected to side deck-plate, or horizontal stringer, by

Practical an angle-iron, 6 x 4 x 1½. All these fore and aft stringers and deck-plates to run fore and aft, and not to be disconnected or cut through anywhere, and all water-tight bulkheads, beams, or any athwartship work to be cut round them, and all to terminate at each end in plate-breaks of ¼ in. thicker plate than the stringers, and to run out as far from either end as may be required. A bilge-stringer, formed of two angle-irons, 6 x 4 x 1½, with a plate at back 18 x ¾, fastened to frames to run right fore and aft the ship. All stringers, vertical and horizontal, water-way plates, &c., to be doubled for 30 feet in way of cargo gangways.

Riveting.—The vessel to be all double riveted with 5 rivets, except in keel and stern-post, which must be 4th inch thicker than the plates they pass through.

Other Iron Work.—Iron casing round boiler space and stoke-hole, between main and upper-decks, likewise all coal-bunker bulk-heads (except what forms part of the engineer's contract). Coal-shoots and deck-plates for them, flat in bunker-bottoms, casing of bunkers, engine-beams, screw-tunnel, iron gratings over stoke-hole on upper deck, ash-bucket pipe from stoke-hole to spar deck, with recesses on top, to be furnished by the contractors. A water-tight slide, at foremost end of screw-tunnel, to be fitted in accordance with the Board of Trade regulations. Preparation to be made for a lifting-screw on the most approved principles. The engineer to furnish all slides and lifting apparatus.

Topgallant Forecastle.—To be in accordance with the drawing given both in length and height, to be plated up from sheer-strake to within 2 feet of plates, and to be fitted up inside as may be directed. A manger, 3 feet deep, to be fitted forward, with 4 hawse-pipes, bucklers, plates, and all complete, as may be required by the company. The deck to be 3 inches thick, with iron-stanchions, and rails running the top-beams, 8 x ¾, bulb-iron, with 2 angle-irons on top, 3 x 3 x ¾. A water-closet on each side, the aftermost and outside, with pumps, and all complete for the crew.

Inside Cement.—The vessel to be filled up solid to the limber-holes with Portland cement.

Quality of Iron.—Garboard-strake, sheer-strake, and longitudinal stringers, of Staffordshire B.B., of an approved maker, all the other plates of Staffordshire B.B., except curves, which are to be the best Lowmoor, or of iron made from best picked scrap equal to this.

Wood Work and General Outfit.

Upper or Spar Deck.—East India teak 3¼ inches thick, secured to beams by two 4-inch galvanized iron bolts and nuts, let in ¾ of an inch below the surface, and doweled with wood. The midship's deck-strakes to be 1 inch thicker, and to run fore and aft, or as may be required.

Main Deck.—Yellow pine 6 x 5, caulked and secured with iron bolts and nuts as upper deck.

Lower Deck.—Yellow pine 9 x 3½, caulked and secured with iron bolts and nuts as above.

Stanchions.—Teak or British oak 6 x 5. Stern timbers of the same 7 x 6, and to run well down, to give strength to the stern. Practical All the other stanchions to run down on top of spar-deck, watery plate through covering-board, and the space between underslides covering-board, and top of water-way to be filled in solid and caulked, and a piece of teak spiralling inside of stanchion, bolted through and through, from outside of hull to inner-strake, except in those stanchions which come in way of boats' davits, which will have an angle iron knee to turn under water-way, inside of bulwarks, well riveted to water-way plate. Oak or teak spirketting 18 x 9, to run right round the main-deck inside, on top of water-ways.

Assuming Stanchions.—Of iron, all round the vessel.

Water-ways.—Upper or spar deck, and main deck, to be East India teak 18 x 9, and, if required, to be fitted over the angle-iron stanchions.

Ceiling of Hold.—Flat of floor laid with 3-inch American elm, and from that to be ceiled with yellow pine, room and space to the main deck beams. The remainder to be 2-inch close furring, caulked, payed, and beaded over seams, as will be pointed out.

Bulwarks.—Yellow pine 3 x 2½ thick, and to have a panel grooved in the centre.

Main-Rails.—Teak, 12 x 4½; to have copper or yellow metal along the edge outside, fore and aft.

Gangways.—To be where shown on plan—viz. four cargo-gangway ports with all doors, brass scuttles, hanging platform to turn outside or inside as may be required, between main and upper decks, lined in all and edges, with twenty ounces copper or yellow metal. Two passenger gangways on upper deck, fitted with the most approved accommodation-ladders complete, with all necessary fittings. Four coaling gangways on upper deck, fitted with doors complete; also hanging brackets riveted on ship's side, to carry pipe when lowered. The ends of rough-tree-rail and gangway to be topped with a casing of brass.

Cleats.—British or African oak, 18 x 16, mounted with all stoppers, cleats, &c., as may be required.

Bits.—Of British or African oak, 22 x 22, stepped on keelson. Towing bits, topall-sheet bits, belaying pin-racks, cleats, eyebolts, timber-heads, &c., to be fitted as and where required.

Bridge.—To be 5 feet 6 inches wide, to be supported with sufficient iron stanchions, and fitted with ladders, lamp-boxes, handrails, and all complete, as may be required.

Masts.—Lower mast and bowsprit of iron or steel as may be approved, and a provision to be made for cutting them away if required, the other masts and spars to be of black spruce or red pine, to be rigged according to plan.

Rigging.—Standing rigging of wire-rope, the rest of best hemp, with all requisite blocks. All blocks to be brass-bushed, or patent leather bushes, as may be preferred; all dead eyes, both upper and lower, to be made of lignum vitae; if required the vessel to be fitted with Cunningham's patent self-reeling topsails.

Storm House.—To be built at after-end of upper deck, with two two-berth cabins on each side of wheel, with a water-closet in each, and fitted up inside in every respect as first-class cabins. The top of this house, as well as those of all other cabins and offices on the upper deck, to be double; the upper one teak, the lower one pine, covered with canvas.

Companions and Skylights.—To be built according to plan. The tops of all of them on the upper deck to be made of East India teak.

Boats.—To be in accordance with the Board of Trade regulations, and to be fitted complete, with masts, sails, oars, boat-hooks, breeches, seatings, davits for ship's sides, and all necessary fittings as may be required; brass rowlocks to mail-boat; life-boats to be according to Lamb and White's plan.

Foot-Coops.—Twelve; 12 feet by 2 feet 4 inches high.

Sheep Pins.—To hold forty sheep.

Scuppers.—Eight on each side on each deck, to be placed where shown.

Fish-Davits.—For fishing anchors to be fitted, as will be shown.

Anchors and Chain Cables.—In proportion to tonnage of vessel, the anchors to be patent, or as required by the Board of Trade regulations.

Winches.—Two; if steam, the difference in price to be paid by the company.

Sails.—One unit of sails complete.

Tarpaulins.—One for each hatch and scuttle.

Pumps.—A complete set, fore and aft.

Pumps.—One copper chambered pump 8 inches in diameter, with brass bucket and lead pipe, fitted in every compartment, and a 7 inch and a 6-inch Downton, fitted as may be directed.

Wheels.—Two of mahogany, brass-mounted, hide-rope, fitted with patent steering gear complete.

Fenders.—With chains, &c., complete.

Ports.—Of East India teak, 21 inches square, with a 5-inch brass. Specification of an Iron Screw-steamship to be built for the European and Australian Royal Mail Company.

Principal Dimensions.

| Dimension | Ft. In. | |------------------------------------|---------| | Length of keel | 310 | | Breadth of beam | 42 | | Depth of hold to spar-deck | 29 | | To have three decks, with full poop and full topgallant-forecastle | | | Height of poop | 8 | | " topgallant-forecastle | 6 | | " from main to spar-deck | 8 |

Keel and Keelson.—The keel to be formed of three thicknesses of plate; the centre plate to be 1 inch thick, and 45 inches deep; forming, at same time, the main keelson and centre of keel; these plates to be in as long lengths as possible, to be put together, butt-jointed, with angle-irons, riveted through the whole length of the part which forms a portion of the keel; the plates to run the entire length of the vessel, and for 10 feet up the stem. The keel side-plates to be 12 inches x 1½ inches; to be in as long lengths as can possibly be obtained; to be all scarphed on to each other, scarps 6 inches long; these three thicknesses of plate, to be partially riveted together before the garboard-strake is fitted on; the garboard-strakes to be double-riveted to the keel with 1¼ inch rivets; all the holes to be runneled out perfectly true before riveting; the butt of the keel-plates and garboard-strakes to be carefully shifted and caulked, and made water-tight. (Section AB, fig. 59.)

Stem-post.—To be of best hammered scrap-iron in one piece, the after-post to be 12 x 6 inches, the inner-post to be 12 x 7 inches; the lower portion, uniting the two posts, to be 12 x 8 inches, and to have about 8 feet of keel attached to it, and with corresponding scarf for riveting to keel. The keel portion to be planed out into a groove, 1 inch wide and 6 inches deep, into which the keelson plate is to be worked, and double-riveted through and through. The end of the keelson-plate to be secured to the inner post by two vertical bars of angle-iron secured to it by rivets, and to the post by tapped bolts (fig. 57). The inner post, at the line of the lower deck-stringer, to have a palm welded to it, which is to be firmly riveted to the stringer, so as to give security to the post (fig. 58). To be formed in the same way as the keel, from iron of the same dimensions, and riveted together in the same way; the keelson, floors, stem, and stern-post to be according to sketch to be furnished.

Frames.—To be spaced throughout the vessel 18 inches apart from centre to centre, of angle-iron, 4 x 3½ x 4½ inch, to have a reverse angle-iron on every frame, 4½ x 3½ x ½ inch, riveted along the top of the floor-plates, and up the frames, to the height of the upper deck-beams, by 1¼ inch rivets, 6 inches apart (every alternate frame from main-deck may be left without reverse iron, a piece being put in underneath the clamp-plate). Where desired, in wake of boilers and engines, the frames and reverse bars to be worked double.

Floors.—The floor-plates at keelson or amidships to be 33 inches deep x 4½ inch thick; to be carried up past the turn of bilge, say to the 6 feet water-line, and riveted to the frames and reverse angle-irons at the end of each floor, which butts against the keelson; to have a vertical angle-iron, 5 x 3 x ¾ inch, riveted to the floors and to the future keelson, (section CD, fig. 69). Along each side of the top of keelson-plate there will be angle-iron 6 x 5 x 4½ inches riveted on a level with the top edge of keelson-plate and floors. A

The following is a copy of the specification of an iron screw-steamship, built for the European and Australian Royal Mail Company. The Australasian was built in 1857, by Messrs J. and G. Thompson, of Glasgow, under the inspection of Mr Bowman, of London, who has kindly permitted its publication here. The strength of this vessel, and the soundness of the principles on which she is constructed, were well proved by her grounding in the Clyde, on her first passing down the river after being launched, when she came off, as before stated, quite uninjured.

Practical plate 33 x 1/8th inch in engine-room, and 36 x 1/2ths at ends of vessel, in long lengths, will run the whole length of the vessel, and be riveted to the angle-iron on top of keelson, and to the reverse angle-irons of the floors; these plates to be built jointed, and double riveted, section GG.

Keelson.—To have two side and two bilge keelsons, to be formed of plates 30 inches broad x 1/4th inch, riveted to the reverse frames. On the centre of these plates there will be double angle-irons 6 x 3 x 1/4th, riveted back to back, and to the plates. From between these angle-irons there will be fitted to the skin plate 1/4th inch thick, the breadth regulated by the distance apart of the frames and reverse angle-irons; these plates to be riveted at the foot to show pieces of angle-iron, secured to the skin, and at the top, between the floor angle-irons, section H, H., &c., &c., to have intermediate keelsons for about 150 feet amidships, to be double angle-iron 6 x 3 x 1/4th inch, riveted back to back, and to the reverse angle-irons on the floors, and to be connected to the outer skin, same as the other keelsons, section H, H. The whole of the stringers, main, bilge, and other keelsons, to pass unbroken through the bulkheads, and to be made water-tight by strong brackets, riveted to them, and to the bulkheads.

Bulkheads to be carried to main deck, and to be fitted in every respect in accordance with the Board of Trade regulations. Between the aftermost bulkhead, to which screw-propeller pipe is attached, and the stern-post, to have fitted on every frame, up to the height of lower-deck beams, a series of bulkheads formed of 1-inch plate, and firmly riveted to the frames, and secured on the top with double angle-iron; at this list forward, the specifications onwards, are to be worked forwards to the pipe bulkhead, so as to form an iron deck above these bulkheads specified, and to be riveted to the main angle-iron on them. The hole for passing stern-tubes through to be carefully arranged, so that no more than necessary space is cut.

Reefer.—The stock to be 71 inches diameter, with turned pintles, of best hammered scrap-iron, in one piece with the frames, and plated with 3/8th plate.

Breakboards and Crutches.—To be fitted at each deck, fore and aft the ship, at the junction of the stringer plates; bilge and side keelson formed by riveting triangular plates about 9 feet long to these fore and aft ties, so as to firmly unite the two sides of the ship.

Mast-Partners.—On the various decks to be formed of materials similar to the beam, and to be securely riveted to them.

Gunwale Molding.—To be formed of 6-inch half-round iron in lengths alternately riveted to the upper edge of wale stroke by rivets about 8 inches apart.

Water-way.—On main and lower deck of red pine 41 inches thick, and on the upper deck of East India teak 18 inches broad by 9 inches thick, both securely bolted to the stringer plates by two rows of bolts and nuts.

Decks.—To have three decks. Upper deck throughout where exposed to be of best East India teak 31 inches thick, to be secured to the beams by bolts and nuts at every third beam, and with a wood screw of best form on both sides of the alternate beams, the whole to be planed true on the edges, top, and bottom before being laid, and thoroughly caulked and payed with resin or pitch, as may be directed by the company, and made perfectly water-tight; main-deck to be of best seasoned Quebec yellow pine 31 inches thick, securely secured to the beams by wood screws with bolts in the bolts, thoroughly caulked, painted, and made water-tight; lower-deck of 3 inches yellow pine to be similarly fitted.

Rails.—The rails to be of best East India teak, of suitable breadth, firmly bolted to stanchions, to be covered on the outside and inside edge with 18 oz. yellow metal, firmly nailed; to have a netting all round of best cordage, firmly secured to galvanised iron rods on rail and water-way.

Bulwark Stanchions.—To be of East India teak, and to be fitted into sockets formed of angle-iron, 7 x 3 x 1/2th; these to be riveted to the stringer plates at proper intervals for the stanchions, one bolt through each socket and stanchion.

Hatch Coverings.—On main, upper, and lower decks, of East India teak, of dimensions to suit the size of the hatches, and securely bolted to the trimmings; to be protected by iron plates on sides and top, and to be wired from battens, cleats, and curbstones; on upper decks to have teak of sufficient size on the hatchways.

Ceilings.—In flat of floor in holds of 2-inch elm, thence to hold beams of 2-inch red pine from hold beams to main-deck beams, and cabins and store-rooms of 1-inch yellow pine close scamed; the ceilings to be bolted to reverse angle-irons with galvanised screw-bolts.

Portes.—To have four gun-ports on each side, with flaps properly arranged in netting, and fitted with ring-and-eye bolts as required.

Capstans.—To have one of Brown's patent capstans of suitable size, placed forward, with patent chain-stoppers, and four riding bits complete for working cable; in addition, to have a cast-iron working capstan, with brass top on quarter-deck poop, both complete, with all necessary bars.

Gunwales.—Of British oak, with anchor stoppers, and all usual fittings.

Ditto.—To have at least five cast-iron mooring timber-heads on each side, of suitable strength, properly bolted through water-ways and stringer plates, with heavy chocks of hard wood timber below.

House-pipes.—To have a strong cast-iron house-pipe on each bow,

Practical of size to suit chains, firmly secured to the skin of the ship; also stern-side mooring pipes of cast-iron where required, and firmly secured.

Chains.—To be built of wood where required.

Anchors and Chains.—To have anchors and chains; the chain cables of best beat iron, and to be tested to the government test. Hemp-warps according to Lloyd's rules.

Anchor Davits.—To have two strong anchor-davits, with blocks and falls complete for lifting anchors.

Pumps.—To have a pair of 6-inch Redpath's patent pumps in each compartment, with lead-pipes and roses, and all the necessary iron gearing for working.

Scuppers.—To have sufficient lead scuppers on upper and main deck, well secured to ship's side and waterways.

Tanks.—To have suitable iron tanks made of quarter plates, capable of containing 10,000 gallons of water, with two fixed copper pumps with brass boxes, lead pipes, and iron gearing complete for working, and placed throughout the vessel.

Masts and Spars.—To be rigged as a ship, with one complete set of masts and spars according to plan; lower masts and bowsprit of yellow, red, or pitch pine in one stick, or built and hooped if necessary; topmasts, lower and topsail yards, and jibboom to be of red or pitch pine, the remainder of black spruce; to be all according to plan, and complete with all usual iron work of best quality.

Rigging.—All the standing rigging to be of galvanised wire, the running rigging to be of the best St. Petersburg or Manilla hemp and chain where required, chain of best beat iron.

Blocks.—To have a complete set of iron and rope stroped blocks of suitable sizes, the lower and topsail yards brace blocks, topping peak and throat halyards, catblocks, &c.; to have Dalton's patent rope block in the sheaves, the standing rigging to be set upon lignum vitae dead eyes of proper size; to have all necessary snatch-blocks, catblocks, watch-tackles, and belaying-pins of greenheart.

Sails.—To have one complete suit of sails, the topsails to be fitted with Cunningham's patent reefing apparatus according to plan, of Gonvock extra canvas, with suitable Nos. complete, ready for bending with sail covers as required.

Iron Work.—All the small iron work of the hull to be furnished complete of the best quality.

Boats.—To have at least six boats, according to Act of Parliament, complete with strong iron davits, tackle falls, &c., as usual. The boats to be supplied with ash oars, rudders, tillers, and boat-hooks, and the fores largest to have masts and sails.

All the boats to be fitted with canvass sails and grips as required; to have four midship boats to be carried inboard on beams of proper strength, and properly supported on iron stanchions from the rail, and to be fitted with patent lowering apparatus to a plan to be furnished.

Gangways.—To have properly-fitted gangways opposite to each hatch for receiving cargo; to have on each side a passenger-gangway, with suitable accommodation-ladders, davits for lifting, iron railing, and man-ropes.

Coaling-Ports.—To have fitted along ship's side, between upper and main decks, the number of coaling-ports that may be afterwards found necessary, properly hinged, so as to be perfectly watertight when closed, and fitted with strong iron shoots inside, compassed, by grated openings, with the upper-decks and with coal-boxes.

Painting.—The outside of the ship to receive three coats of the best oil paint, the inside two coats, except the bottom, which is to be coated with patent cement. The woodwork on deck to receive three coats, and to be grained in imitation oak. Masts and spars to receive two coats of paint or varnish. Cabins and internal fittings to be painted in the best manner, as may be afterwards directed.

Winches.—To have three double-power cargo winches, with dericks and chains complete, for working cargo.

Side Lights.—To have two brass side lights in each state-room on main-deck and spar-deck, all securely riveted to ship's side, and made watertight.

Bells.—To have a ship's bell and belfry, with name engraved on it, and binnacle-bell.

Binnacle.—To have two brass and one mahogany binnacle, with lamps.

Figurehead.—To have a handsome full-length figurehead, with trail-boards, stern and quarter carving, as may be required to suit name, all handsomely relieved with gilding.

Flags.—To have one ensign, one burgee, one union-jack, one blue-peter, one private signal, and one set of Maryat's signals with chest and book.

Signal Lanterns.—To have complete set of Admiralty signal lanterns (brass, of large size).

Gun.—To have two brass 4-pounder, and four iron 9-pounder guns, with breechings, rammers, and sponge complete, with all the usual complement of smoke-tubes, and curtains.

Steering Apparatus.—To have a handsome double-steering gear of E. L. tank, fitted with right and left handed screw-steering gear, brass nuts, malleable iron crosshead, connecting-rods, and screw.

To have two portable tillers fitted to rudder-stock; wheel to be covered by a substantial house, with glass front.

Cook-House.—To have a spacious galley of iron fitted on main or spar-deck, near funnel, with the most improved form of cooking apparatus and baking ovens for crew and passengers; the woodwork of the galley to be lined with 5lb. lead and felt, and the floor to be covered with fire-tiles, and to have proper ventilators on sides and top.

Poop.—To have a poop to extend from after-part of vessel to after-part of fore-hatch, about 90 feet long; in forming the poop, every alternate frame of the vessel to be doubled up, to which are to be joined the beams of the poop, of size of main-deck frames. The sides and after-end of the poop to be rounded over and plated with 3" plates, the poop-deck to have teak waterways, 12" x 5"; teak decks, 3" x 5". The whole fastened to the beams with bolts and screws, every butt to have a screw-bolt. Stanchions of galvanised iron to be carried round the poop, with a teak rail on top. The poop to be fitted with suitable skylights, made of teak, fitted in the best style for light and ventilation; also to have round or square side lights in state-rooms, as may be required; to have side stairs, with brass rails, from the upper deck. The inside of poop to be fitted up in first style for passenger accommodation, and in accordance with a plan to be approved; to have two bath-rooms; also a water-closet for every eight passengers, side-state-rooms, ladies' dressing cabin, captain's cabin and steward's pantry, with all the necessary furniture and fittings; the whole of the very best description of workmanship and material, as usual in large passenger steamers of the first-class.

Main-Deck.—On the main-deck a dining-room, to be entered by a spacious stair, either from inside of poop or from upper-deck, to be fitted with all the necessary furniture; a full set of dining-tables, sofas, settees, and chairs covered with morocco; to have mirrors, carpets, sideboards, stoves, lamps, swinging trays, &c., &c., and to have side-state-rooms for first-class passengers, with carpets, curtains, sofas, wash-stands, &c., the whole arranged to a plan to be approved of.

Second-Class Accommodation.—To be fitted on main-deck forward for 100 passengers, with a water-closet for every 12 passengers, bar-room, &c. Saloon under spar-deck, of polished E. I. teak, with tables, settees, &c. The steward's bar and other conveniences all in the best manner.

Deck-House.—To have a strongly-fitted deck-house, as large as possible, consistent with other deck arrangements; to be constructed with iron frames and beams, made fast to strong teak comings, bolted to the deck-beams. The deck of the house to be of 2½ inches yellow pine, with a side covering board to form moulding, of E. I. teak; the sides and ends to be of 1½ inch yellow pine, half checked or feathered, and grooved; the house to be fitted according to a plan to be arranged and approved.

Officers' Accommodation.—To have accommodation for the officers, engineers, stokers, and stewards, with a sufficient number of water-closets and other conveniences, fitted on main-deck, between the first and second-class cabins, with separate ladder-ways, all as may be afterwards arranged.

Topgallant Forecastle.—To extend from the back of the figurehead rearward to the fore side of the fore-hatch, being about 68 feet in length, and in height about 6 feet to 6 feet 6 inches; every alternate frame of the vessel at forecastle to be carried up to deck of forecastle, with reverse angle-irons, 4 x 3 x ½ inches, by piecing the present frames; to have an angle-iron stringer, 4 x 4 x ½ inches, with plates 18 x ½ inches. The beams to be of bull-iron, 7 x ¾, placed on every frame; these beams to be turned down at ends, to form knees, same as the other beams of the vessel; the beams to have an angle-iron, 2½ x 2½ x ½ inches, riveted on each side, for fastening down decks; to have two beam-ties riveted on top of plates, 12 x ½; and that part of the forecastle deck where captain comes through, to be all plated between the beam-ties; same to extend a sufficient length for strengthening that part of captain's cabin; riveting to be ½th the thick, and to extend from gunwale to deck at top of forecastle, and the whole length of forecastle, with double riveted butt-joints.

The decks to be of teak, 6½ x 3 inches, with teak waterways, 12 x 4½; well fastened down, caulked, and made watertight; the part of deck at capstans to be well fastened and strengthened with teak planks, of increased thickness to those on deck; the top of forecastle to be fitted with all the necessary chocks, &c., required for a vessel of this class. The capstan for anchors to be double, and wrought on substantial forecastle; but the stopper and riding-bits to remain on spar-deck, as originally intended. The front of fore- Practical castle to be neatly closed in and panelled, equal to bulwarks of vessel. The interior to be fitted up for crew, as may be directed by owners, with suitable brass side lights for ventilation.

Forecastle.—The crew to be accommodated in forecastle, under spar-deck, with berths, mess tables, &c., as may be required.

Lower-Deck Fittings.—The lower-deck, forward and aft, to be fitted with butchery-room, saloon-room, wine-cellar, store-rooms, &c., as may be directed, all in the most approved manner.

On the upper-deck, forward of second-class cabin, the remaining space to be fitted with butcher's shop, cabin for petty officers, and other necessary fittings, as may be directed.

Skylights.—The second-class cabin to be lighted and ventilated by skylights, fitted on cargo hatches, with suitable gratings, and other particulars as required.

Sundries.—All the locks, hinges, hat-hooks, &c., to be of brass, and fitted as required, and of the best description; to have complete sets of lamps for all the cabins, locks and bars for all the hatches and store-rooms; hen-coops, sheepfold, pigsty, sets of capstan bars for both capstans; four 60-gallon water-casks, four harness-casks, twenty-four buckets, twenty-four mess kids; four water-funnels, six breakers, four deck-tubs, and four tar buckets; awnings for quarter-deck, with iron stanchions, binnacles, and bellcovers; skylight-covers and tarpaulins as required; iron bell-mouthed ventilators, and windalls for engine-rooms where required.

Messrs Taylerson and Company, of Port-Glasgow, have patented a diagonal arrangement of the frames of iron vessels. They substitute diagonal framing in the place of the ordinary vertical framing, or intersperse diagonal with vertical frames. The annexed figure shows the latter system of arrangement. No addition of strength, however, to the side of a ship will obviate the necessity for strength in the bottom and in the deck. If rupture were to take place at the top edge of the side, it may be doubted whether the diagonal frame would do more than divert the line of rupture into the sloping between itself and the next frame. The same builders use a remarkably strong form of keel and keelson (fig. 61); and a representation of this is annexed, showing at the same time their mode of attaching the water-tight bulkheads; they introduce a piece of timber at each bulkhead, where it is attached to the ship's side, and fasten this by screws from the outside, with a view of lessening the number of rivet-holes. This most desirable object is no doubt attained, but great care must be taken that corrosion of the fastenings does not take place.

Mr L. Arman, of Bourdeaux, has constructed ships with diagonal iron framing inside a framing of wood of very light scantling, the sheathing of the ship being of wood. Inside the vessel, and attached to the iron frames, he introduced a series of horizontal stringers of plate-iron at intervals from the deck to the keelson, which is also of iron. This system imparts great strength to the framework of the vessel, and it is believed that it has, upon the whole, been very successful. Altogether the combination of wood with iron has been carried much further in France than in this country. Iron beams are being much used in Practical building, vessels, and iron rudder-pieces, the latter being very Building, advantageous in men-of-war, from their smaller size.

Before closing these remarks, the influence or effects of exercised upon the practical construction of ships by the Lloyd's rules of Lloyd's register require to be noticed, as they register is rules of Lloyd's register require to be noticed, as they register is form a code of instructions to which all merchant-builders ship-builders of this country are compelled to adhere. These rules are stated to be compulsory, because if a builder deviates from them, or ventures to differ in any point from the opinions of the surveyor, his vessel loses caste, either by being excluded altogether from the first class, or by being put on it for a less term of years. This does not suit the purchaser, and as there is no appeal from the decision of the surveyor, the builders must submit. In the first place, it may be remarked, that there is but one table of scantlings, &c., for ships of the same tonnage, while it is evident that the same rules as to scantling, &c., cannot be correct for the sharp long ship intended for carrying light cargoes, such as tea, wool, &c., and also for those which are intended for heavy dead-weights. Nor is any difference permitted in the scantlings of the timbers at the bow and at the stern of full or sharp ships. The rules do not directly interfere with the forms of ships, but in some respects they have undoubtedly militated against the production of fast-sailing vessels.

The supporters of Lloyd's register claim to themselves the credit of having improved the British mercantile marine; but, in the opinion of many experienced persons, its effect has been to produce a dead and spiritless mediocrity. That the construction of many very bad ships is greatly prevented is true, but there is no actually compulsory law to force every ship to be inspected and classed at Lloyd's, and many ships are sailed independent of any such inspection: its action in this respect, therefore, is not complete. On the other hand, it is equally true, that men of skill and talent are restrained from introducing improvements in the combination of materials. That this is the effect produced is well known; and as an instance, it may be mentioned, that on the first proposal being made to introduce iron beams into a wooden vessel, leave was refused unless the vessel was put into a lower class; and this improvement,

which is now fully admitted by Lloyd's, was kept back for many years. It is natural that the general feeling of servants of the government, or of large public or joint-stock companies, should be against taking responsibility upon themselves by introducing or permitting changes; but it is much to be deplored if this spirit is brought into such a position as to be a drag upon the talent and energies of the whole nation. Shipowners who are not themselves practically acquainted with ship-building, take the natural course of adopting Lloyd's register as their standard. They contract for a ship to be built in such a manner that she may be put into the first class at Lloyd's, and thus declare themselves ready to pay the cost of the builder's adherence to Lloyd's rules.

The ship-builder knows, perhaps, that he could introduce improvements, but he is unwilling to subject himself to the risk of a refusal by Lloyd's surveyors, and as the purchaser for whom he is working is satisfied, he builds accordingly. The want of encouragement by Lloyd's rules to increase the durability of ships has been before noticed. Under the existing rules, then, there seems to be reason to fear that the tendency of Lloyd's register has been to some extent to cause increased expenditure, to restrain improvement, and to uphold a dead and stagnant mediocrity. It is to be hoped that care will be taken to guard against the possible existence of such evils for the future.

On Launching.

Ships are generally built on blocks which are laid at a declivity of about \( \frac{4}{5} \)ths of an inch to a foot. This is for the facility of launching them. The inclined plane or sliding plank on which they are launched has rather more inclination, or about \( \frac{3}{5} \)ths of an inch to the foot for large ships, and a slight increase on this for smaller vessels. This inclination will, however, in some measure, depend upon the depth of water into which the ship is to be launched.

While a ship is in progress of being built, her weight is partly supported by her keel on the blocks, and partly by shores. In order to launch her, the weight must be taken off these supports, and transferred to a movable base; and a platform must be erected for the movable base to slide on. This platform must not only be laid at the necessary inclination, but must be of sufficient height to enable the ship to be water-borne, and to preserve her from striking the ground when she arrives at the end of the ways.

For this purpose, an inclined plane, \( q, a \) (figs. 62 and 63), purposely left unplanned to diminish the adhesion, is laid on each side the keel, and at about one-sixth the breadth of the vessel distant from it, and firmly secured on blocks fastened in the slipway. This inclined plane is called the sliding-plank. A long timber, called a bilgeway, \( b, b \), with a smooth under surface, is laid upon this plane; and upon this timber, as a base, a temporary frame-work of shores, \( c, c \), called "poppets," is erected to reach from the bilgeway to the ship. The upper part of this frame-work abuts against a plank, \( d \), temporarily fastened to the bottom of the ship, and firmly cleated by cleats, \( e, e \), also temporarily secured to the bottom. When it is all in place, and the sliding-plank and under side of the bilgeway finally greased with tallow, soft soap, and oil, the whole framing is set close up to the bottom, and down on the sliding-plank, by wedges, \( f, f \), technically called slivers or slices, by which means the ship's weight is brought upon the "launch" or cradle.

When the launch is thus fitted, the ship may be said to have three keels, two of which are temporary, and are secured under her bilge. In consequence of this width of support, all the shores may be safely taken away. This being done, the blocks on which the ship was built, excepting a few, according to the size of the ship, under the foremost end of the keel, are gradually taken from under her as the tide rises, and her weight is then transferred to the two temporary keels, or the launch; the bottom of which launch is formed by the bilgeways, resting on the well greased inclined planes. The only preventive now to the launching of the ship is a short shore, called a dog-shore (\( g \)), on each side, with its heel firmly cleated on the immovable platform or sliding-plank, and its head abutting against a cleat (\( h \)), secured to the bilgeway, or base of the movable part of the launch. Consequently, when this shore is removed, the ship is free to move, and her weight forces her down the inclined plane to the water. To prevent her running out of her straight course, two ribands are secured on the sliding-plank, and strongly shored. Should the ship not move when the dog-shore is knocked down, the blocks remaining under the fore part of her keel must be consecutively removed, until her weight overcomes the adhesion, or until the action of a screw against her forefoot forces her off.

A much less expensive mode of launching is now much practised in the merchant-yards of this country, and has been long in use in the French dockyards, allowing the keel to take the entire weight of the vessel. The annexed figure represents this method (fig. 64). The two pieces (\( a, a \)), which are shown in the figure as being secured to the ship's bottom, are the only pieces which need be pre- pared according to this system for each ship, the whole of the remainder being available for every launch. A space of about half an inch is left between them and the bulk timber placed beneath them, as it is not intended that the ship should bear on these bulk timbers in launching, but merely be supported by them in the event of her heeling over. The ship, therefore, is launched wholly on the sliding-plank (c), fitted under the keel. Messrs Hall of Aberdeen launched a vessel of 2600 tons in this manner without a single cleat upon her bottom or riband of any kind, and avoided all the making-up of the side-ways, except for about 60 feet in midships for keeping the ship upright. The centre-way was hollowed, and a round sliding-way fitted in it, and the keel was thus supported from end to end. This may, therefore, be considered to be the safest, cheapest, and easiest mode of launching long sharp ships.

If a ship is coppered before launching, so that putting her into a dry-dock for that purpose becomes unnecessary, it is then desirable that she should be launched without any cleats attached to her bottom. This method of fitting the launch, as represented in figure 65, is then adopted for this purpose. The two sides of the cradle are prevented being forced apart when the weight of the ship is brought upon them by chains passing under the keel. Each portion of frame-work composing the launch has two of these chains attached to it, and brought under the keel, to a bolt a, which passes slackly through one of the poppets, and is secured by a long forelock b, with an iron handle (c), reaching above the water-line, so that when the ship is afloat it may be drawn out of the bolt. The chain then draws the bolt a, and in falling trips the cradle from under the bottom. There should be at least two chains on each side secured to the fore-poppets, two on each side secured to the after-poppets, and two on each side to the stopping up, and this only for the launch of a small ship: in larger ships the number will necessarily be increased according to the weight of the vessel and the tendency that she may have, according to her form, to separate the bilgeways. This tendency on the part of a sharp ship by a rising floor, or by her wedge-shaped form in the fore and after bodies, is great, but there is not much probability of a ship heeling over to one side or the other.

It is recorded that upon one occasion of our sailors having taken possession of an enemy's arsenal, and finding a vessel on the stocks nearly completed, they removed the shores from one side, and tried to upset her by wedging up the shores on the other side, but were unable to do so. There appears, therefore, to be no valid objection to the cheaper and more ready method of launching on the keel.

(A.M.—Y.)