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work, the close and particular examination it contains of all the circumstances connected with the art of which he treats, the beautiful simplicity of his geometrical solutions, adapted to the study of the least informed in mathematics, are such as to have acquired for him at once a high reputation throughout all Europe. Bouguer was a teacher of hydrography in the French seaport of Havre-de-Grace, and his own country was the first to derive: fruit from his investigations. And in truth it may be said, that, had he joined more of practical acquaintance with maritime affairs, to his mathematical skill, he might, with his marked zeal and perseverance, have produced a work, that would probably have left little to be performed by his successors. Indeed, the greater part of the practical writers on ship-building, seem to have been satisfied with the investigations of Bouguer.

In the year 1749, the celebrated Euler gave to the world his great work" Scientia Navalis." This treatise is remarkable, not only for its value in the advancement of the theory of vessels, but as a model of well ordered and correct mathematical investigation. And if, from the same want of experimental basis that has been remarked in the instances of Bernouilli and Bouguer, it be not perfect, it still serves, and will probably always serve, as an example of the best manner in which such inquiries should be conducted. Finally, in 1771, appeared the Examen Maritimo of Don George Juan. This author is better known to most readers, as the companion of the French academicians. who measured a degree of the meridian in Peru, and has been recently brought anew to the notice of the world, by the publication, in Madrid, of his private official reports to the Spanish government, upon the condition and prospects of their South American colonies. He alone, of all writers upon the subject, appears to have possessed, in an equal degree, scientific knowledge and practical skill. He may be ranked in point of learning, with the ablest mathematicians and philosophers of Europe; and being by profession a seaman, holding a high rank in the navy of Spain, he had every opportunity of testing the accuracy of the theories of former writers, by the sure criterion of actual experiment, and of making observations that should serve as the basis of one more accurate. His work is therefore a much more perfect theory of the construction and manœuvre of vessels, than can be found in any previous author; his mathematical investigations furnish results much more conformable to the facts that occur in practice; while he deduces from them many practical rules of the greatest value and importance.

The Examen Maritimo was translated into the French language by Leveque, and published in 1783, and still continues to attract the attention of all who take an interest in the important subjects of which it treats.

In addition to the above continental writers, we have to mention, as having aided in extending and improving the theory, at different times, the English names of M'Laurin and Atwood.

The work before us is principally composed of a new transla tion of the Examen Maritimo, corrected however, and improved in many important points; and M. Poterat has also given many valuable additions that are entirely original. The most important of these has reference to the action of the wind upon the sails of vessels, whence he has deduced rules for trimming them in oblique courses, entirely contrary both to the received theories and ordinary practice. An important difference is also found in the concluding part of the work, which contains a collection of the theoretic principles, with their application to practical points. In the Examen Maritimo, Juan devotes this portion of his treatise more especially to the instruction of the builders of ships; our author has, on the other hand, restricted himself almost exclusively to rules for their management and manœuvres. M. Poterat has shown himself, in this work, to possess, in an equal degree with his predecessor Don George Juan, all the requisites necessary for treating successfully a subject of such difficulty and importance; he exhibits at every step his intimate acquaintance with mathematical and physical science, while he draws largely from his experience as a seaman, in order to illustrate and confirm his theory by practical instances. His work, therefore, may be perused with pleasure by those whose taste confines their studies to the pure mathematics, will aid those who cultivate experimental philosophy, and cannot fail to be of the greatest service, as a preparatory study, to those who mean to devote themselves to naval affairs as a profession. We are, in truth, of opinion, that the acquisition of nautical skill, although it can never be effected by mere study of theory, may be much accelerated by a previous acquaintance with sciences having with it an im

mediate or remote connexion.

Fully impressed with this truth, we shall endeavour to draw the attention of our readers to this work, and those of similar character, by a brief exposition of the theory it contains, and a synopsis of a few of its practical applications.

Most of the valuable properties of vessels are derived from the peculiar position in which they are placed in respect to the waters in which they float, by whose pressure they are supported, and to the air, to whose action the greater part of their surface is exposed. Were they entirely confined to one of these fluids, wholly supported in the air, or wholly immersed in the water, their motion and guidance would be attended with far greater difficulties. A submarine vessel, that shall, at the will of its navigator, rise to the surface, or sink to the bottom, is no difficult achievement; this much has been successfully effected by

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. Eronauts 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 VOL. II.-No. 3.

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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 seve-ral cases been lost by the entrance of the water, in such an event, through their cabin windows. Upon this fact, rests the chief valueof 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

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