tion of the vessel. The more acute the angle of the prow, the less would the former, and the more the latter of these maxima be lessened; hence, in vessels of the usual form, the resistance to lateral motion is much greater than to that in the plane of the keel; and instead of considering the path to be in a direction perpendicular to the sails, we assume it to be in that of the length of the vessel. But, as the lateral resistance is not so great, as the amount of the pressure of the wind in that direction, this assumed course requires a correction, which is called the Leeway. This is less or greater, according to the ratio of the length to the breadth, and varies inversely, according to the laws we have stated, with the greater or less sharpness of the vessel, the draught of water and the length of keel; but in a well-constructed vessel is never very large. Hence it follows, that, as the sails of nearly every description of vessels may be trimmed to make an acute angle with the plane of the keel, the course may also make an acute angle with the same plane, and the vessel actually ply to windward. By a series of diagonal movements, exposing the opposite sides of the vessel alternately to the action of the wind, a point directly to windward of the place of departure may be reached.

This manœuvre, or the operation of beating to windward, appears to have been unknown to the ancients, who therefore could only use sails in favourable winds, and were, at other times, compelled to run for a harbour, and anchor, or to force themselves painfully forward, by means of oars. Hence their navigators were confined to timidly following the coasts, and they could only venture in settled weather, and with the prospect of a fair wind, out of sight of the land. That change in the rigging and structure of ships, which fitted them for performing this manœuvre, seems to have had its origin among the Italian republics; but the person or state to whom we are indebted for it, is lost in the darkness of the middle ages. Few greater benefits have ever been conferred upon mankind, than by this discovery, made in practice, at least seven centuries before the state of mathematical learning would have enabled us to have derived it from scientific investigations.

Yet, although thus lately introduced among nations comparatively civilized, and unknown to those of more high antiquity, although even more refined, the principle has been developed by a barbarous people, and applied with even more skill, than it has been by the nations of Europe and America, up to the present day. The earlier circumnavigators found a vessel in use among the inhabitants of the Ladrone Islands, which, from its very remarkable properties, they called the flying Proa. The body of this vessel, was in shape like that of the half of one of ours; it had therefore one side an absolutely plane surface, the other curved, and

was similar at both ends. As such a figure could not float upright, a long outrigger was attached, which bore at its extremity a vessel similar in shape, but much smaller than the first, and carefully closed, so as to be impervious to water. The weight of this acting on the extremity of so long a lever, kept the larger body upright, while its buoyancy insured stability, and prevented rolling. The plane surface being kept to leeward, was more resisted than the curved could have been, and the leeway therefore less than in any of our vessels. The sail was prevented from bellying in a horizontal direction by transverse strips of cane, and hence would be filled by a wind, making a less angle with it, than if it had been made of canvass, stretched as ours is. The whole furnished an instance of ingenuity and talent, the more remarkable from its contrast with the unseamanlike junks of the neighbouring cognate nations, the Chinese and Japanese.

When a vessel is sailing before the wind, the utmost velocity that can be attained, is less than that of the wind itself, by the whole amount of the resistance of the water to the direct course of the vessel. But in sailing upon a wind, its effective action depends, not upon the absolute velocity of the current, but upon the sum of the velocities of the wind itself, and of such part of the speed of the vessel, as is estimated in a direction contrary to the wind. Hence, were there no resistance from the water to the direct course, the velocity of a vessel lying near to the wind, would be in theory limited only by the resistance of the air. Various other circumstances, however, besides the resistance of the liquid medium, act, and combining with that cause, prevent the velocity on such courses, from exceeding that which has already been assigned. Thus, as the force of the wind increases, the stability of the vessel diminishes, the strain on the canvass, the masts, and the rigging, becomes excessive, the sails must in part be taken in, and others reefed. Still however, in light winds, and upon oblique courses, a vessel when close hauled, will acquire a speed greater than that of the wind itself. This fact, which is deduced from his theory, was observed by Juan to hold good in the lateen-rigged ferry-boats in the bay of Cadiz, and has been found by our author to be true even of ships of the line, since the introduction of copper-sheathing, an invention that has not only prolonged the duration, but added to the speed of ships.

Vessels of different kinds possess the property of plying to windward, and having their speed increased upon this principle, in different degrees. In this respect, they may be arranged in two classes, vessels with square sails, and those rigged fore and aft. The primitive position of the sails of the former is at right angles to the plane of the keel; in the latter they hang in that plane. In the first case, the sails must be braced round by their sheets and bow-lines to receive an oblique wind; in the second,

VOL. II.-No. 3.

3

Bushnell and Fulton; but to give it a motion and direction different from that of the fluid, is yet a desideratum in mechanics. Fish, endowed with great muscular power, with an admirably contrived apparatus, which acts powerfully upon the water in one direction, while its influence in the other is hardly perceptible, may indeed be rapidly propelled through the water; but we neither know of any adequate artificial substitute for the energy of their muscles, nor any modification of mechanic powers, that will produce a similar motion in an inert and lifeless mass. In the case of birds, the imitation is still less practicable; they are supported wholly by their own muscular strength, applied to their wings, instead of deriving buoyancy, like fish, from the fluid in which they move. Aronauts then have been compelled to resort to the less difficult imitation of aquatic animals, by rendering their apparatus capable of rising or sinking in the air by a difference in its specific gravity. The usual modes of propelling vessels, are ineffectual in both these cases; oars, paddle wheels, and sails, are alike inapplicable. Oars have a reciprocating motion, and act, while moving in one direction, upon the water, while they return through the air to their primitive position, in respect to the vessel. Wheels, although revolving continuously, perform the greater part of their rotation in the lighter fluid. In both cases then, the vessel is propelled by a power equivalent to the difference of the resistances that the air and water oppose to the motions of the apparatus. But the application of sails is still more scientific; in consequence of the greater density of water, the vessel has a tendency rather to remain at rest in respect to it than to the air, and hence, as the latter is almost constantly in motion, with a velocity different from that of the water, it will act powerfully upon sails spread so as to intercept its currents; so powerfully indeed, that cases occur in practice, where the velocity of the vessel may exceed that of the wind itself.

The two important points to be considered in the theory of ships, are their conditions of equilibrium, or stability, and their motion. Any floating body whatever, will remain in equilibrio at the surface of a fluid, when the part immersed displaces a mass of the fluid equal in weight to that of the whole vessel with its cargo and equipment, and when in addition the centre of magnitude of the part immersed, and the centre of gravity of the whole vessel with its load, are in the same vertical line. Until the former condition is attained, the vessel will oscillate on each side of the horizontal surface of the water, while to fulfil the latter, she will turn around a horizontal axis. A vessel then will, in a few moments after she is launched, assume the position of equilibrium; and, as the cargo and equipment are laden, will be gradually immersed, so as to maintain and preserve that state. In the case of a solid body, supported by a prop of the same na

ture, there exist three different states or conditions of equilibrium; the centre of gravity may be vertically above the point of support, in which case the smallest possible force will change the position of the body, and it can never again return, except by the action of extrinsic forces, to its primitive position; the centre of gravity may coincide with the point of support, when it will readily be moved around the latter, and remain indifferently in any position in which it may be placed; or the centre of gravity may be vertically beneath the point of support, in which case the equilibrium is stable; for however far the body may be caused to diverge from this primitive position, it will, if abandoned to itself, again return to it after a series of oscillations. But when the support, instead of being a solid prop, is the upward pressure of a fluid, the case is widely altered; for the centre of gravity may be above, or coincide with the point to which the supporting forces may be considered as applied, (the centre of magnitude of the part immersed,) and the equilibrium shall still be stable. This arises from the circumstance, that while the centre of gravity of the whole mass remains fixed, the centre of magnitude of the part immersed will change its position, with every variation of inclination, whether in the direction of the length, or the breadth of the vessel. If this point change its place so rapidly as to move in the direction of the inclination faster than the vertical line passing through the centre of gravity, the equilibrium is stable. If one vertical still continues to pass through both points, the vessel will remain indifferently in any position. But when the vertical line, passing through the centre of gravity, falls nearer to the side of the vessel than the centre of magnitude of the part immersed, the very weight of the vessel, independently of all other circumstances, will now act to overthrow her. In these motions, the centre of gravity of the part immersed, describes a circular arc whose centre is in the vertical axis of the vessel, considered as fixed in respect to the vessel, but moveable in respect to the water. This point of intersection is called the Metacentæ, and on its position the stability of the vessel will depend; the higher it is placed, the greater the stability; and it is indispensable that it should be above the centre of gravity. Were all the sections of vessels portions of equal circles, they would have each but one metacentre, but as their sections, although symmetrical on each side of the plane of the keel, are in other respects irregular, it is usual to resolve all the forces that act to cause the inclination of vessels into two, one acting in the direction of the plane of the keel, the other at right angles; and each of these component forces has its appropriate metacentre. The metacentre that has respect to the force acting in the longitudinal direction, is always sufficiently high, and therefore the examination of its position

has little to do with mere stability; but that which refers to the lateral force, may easily, by bad construction, or an improper distribution of cargo, be brought too low; and hence the mode of finding it, when the figure of the vessel, and the distribution of the weight with which it is loaded are given, is of extreme importance both to naval architects and seamen. Our author points out the mode of doing this, in the fourth chapter of the first book of his second volume.

However high the metacentre may lie, it will be possible that a vessel may be so far inclined in a lateral direction, as to throw the vertical line, passing through its centre of gravity, without the vertical passing through the centre of the hollow. In this case, the equilibrium ceases to be stable, and the joint action of the weight and buoyancy of the vessel will tend to increase the inclination. This occurs, when a vessel, by a sudden effort of the wind, is thrown upon the beam ends. The greater the draught of water, the greater the liability to this accident, and investigations have pointed out this practical rule: viz. that the draught of water should in no case exceed half the main breadth.

But it is not sufficient that a vessel shall be merely stable. When the wind acts to incline a ship, the joint effort of the buoyancy of the water and the weight, tends, in a proper position of the metacentre, to restore the vertical position; this is not done at once, but by a series of oscillations. These oscillations, however varied, may be resolved into such as have their direction either in the plane of the keel, or at right angles thereto. The first of these, goes by the name of pitching, the last, of rolling. The violence of both of these, is increased by the motion of the waves, which would of themselves give similar motions to the vessel. The action of pitching tends to strain a vessel, and to lessen its duration, but it is rarely attended with immediate danger, except in the case of the extremities being too sharp, or the close wood-work of the vessel of too small an elevation above the water's edge. Hence it is proper to make the bow of a vessel, which is especially exposed to this action, full, particularly above the load water-line; and the determination of the prow of least resistance, is of no value in practice. The stern is also occasionally exposed to a similar danger, as in the case of the sails being suddenly taken aback by a change of wind; vessels in truth have in several cases been lost by the entrance of the water, in such an event, through their cabin windows. Upon this fact, rests the chief value of circular sterns, that are now about to be restored in naval architecture. As to that value which is attributed to them in naval actions, we conceive it to be overrated. A vessel is equally exposed, when raked from the bow and from the stern; the danger arises from the greater number of persons that are exposed to a flanking fire, from the greater injury done to the wood-work, and from the