ENCYCLOPÆDIA BRITANNICA.

SEAMANSHIP.

THE present article will be found to embrace a threefold division of the subject of seamanship. The reader will find, in the first portion, those general principles which are applicable alike to all cases, and suited to all times of the past and present state of naval affairs. The second portion will be closely connected with this, and will, in fact, consist of a description of some manoeuvres, of which the object is to illustrate and further explain the theory previously laid down. Whilst the third portion will bring up the knowledge of the subject in its improved condition, and deal with all those questions which the invention of chain cables, steam, as applied to marine engines, the new system of signals, and other discoveries have introduced into nautical affairs during the last fifty years; avoiding minute details, when they are given under the separate heads in other parts of this work. We commence, therefore, with the great facts and principles of seamanship, in its most general bearing and aspect. By this word we express that noble art, or, more properly, the qualifications which enable a man to exercise the noble art of rigging and working a ship. A SEAMAN, in the language of the profession, is not merely a mariner or labourer on board a ship, but a man who understands the structure of this wonderful machine, and every subordinate part of its mechanism, so as to enable him to employ it to the best advantage for pushing her forward in a particular direction, and for avoiding the numberless dangers to which she is exposed by the violence of the winds and waves. He also knows what courses can be held by the ship, according to the wind that blows, and what cannot, and which of these is most conducive to her progress in her intended voyage; and he must be able to perform every part of the necessary operation with his own hands.

We are justified in calling it a noble art, not only by its importance, which it is quite needless to amplify or embellish, but by its immense extent and difficulty, and the prodigious number and variety of principles on which it is founded, all of which must be possessed in such a manner that they shall offer themselves without reflection in an in-

stant, otherwise the so-called seaman, whatever be his pretensions, cannot be trusted in charge of a watch.

The art is practised, to a certain extent, by persons without what we call education, and in the humbler walks of life, and therefore it suffers in the estimation of the careless spectator. It is thought little of because little attention is paid to it. But if multiplicity, variety, and intricacy of principles, and a systematic knowledge of these principles, entitle any art to the appellation of scientific and liberal, seamanship claims these epithets in an eminent degree. We are amused with the pedantry of the seaman, which appears in his whole language. Indeed, it is the only pedantry that amuses. A scholar, a soldier, a lawyer, nay, even the elegant courtier, would disgust us, were he to make the thousandth part of the allusions to his profession that is well received from the seaman; and we do the seaman no more than justice. His profession must engross his whole mind, otherwise he can never learn it. A sailor, although uneducated, may possess a prodigious deal of knowledge; but cannot tell what he knows, or rather what he feels, for his science is really at his finger-ends. We can say with confidence, that if a person of education, versed in mechanics, and acquainted with the structure of a ship, were to observe with attention the movements which are made on board a first or second rate ship of war during a shifting storm, under the direction of an intelligent officer, he would be rapt in admiration.

What a pity it is that an art so important, so difficult, and so intimately connected with the invariable laws of mechanical nature, should be so held by many of its possessors, that it cannot improve, but must die with each individual. Having no advantages of previous education, they cannot scientifically arrange their thoughts. They can far less express or communicate to others the intuitive knowledge which they possess; and their art, acquired by habit alone, is little different from an instinct. We are not entitled to expect much improvement here; yet a ship may be considered as a machine. We know the forces which act on it, and we

know the results of its construction; all these are as fixed as the laws of motion. What hinders this to be reduced to a set of practical maxims, as well founded and as logically deduced as the working of a steam-engine or a cotton-mill? The stoker or the spinner acts only with his hands, and may "whistle as he works, for want of thought;" but the mechanist, the engineer, thinks for him, improves his machine, and directs him to a better practice. May not the seaman look for the same assistance; and may not the ingenious speculist in his closet unravel the intricate thread of mechanism which connects all the manual operations with the unchangeable laws of nature, and both furnish the seaman with a better machine, and direct him to a more dexterous use of it.

We cannot help thinking that much may be done; nay, we may say that much has been done. We think highly of the progressive labours of Renaud, Pitot, Bouguer, Du Hamel, Groignard, Bernoulli, Euler, Romme, and others; and are both surprised and sorry that Britain has contributed so little in these attempts. Gordon is the only one of our countrymen who has given a professedly scientific treatise on a small branch of the subject. The government of France has always been strongly impressed with the notion of great improvements being attainable by systematic study of this art; and we are indebted to the endeavours of that ingenious nation for any thing of practical importance that has been obtained. M. Bouguer was professor of hydrology at one of the marine academies of France, and was enjoined, as part of his duty, to compose dissertations both on the construction and the working of ships. His Traité du Navire and his Manœuvre des Vaisseaux, are undoubtedly very valuable performances. So are those of Euler and Bernoulli, considered as mathematical dissertations; and they are wonderful works of genius, considered as the productions of persons who hardly ever saw a ship, and were totally unacquainted with the profession of a seaman. In this respect Bouguer had great superiority, having always lived at a sea-port, and having made many very long voyages. His treatises, therefore, are infinitely better accommodated to the demands of the seaman, and more directly instructive; but still the author is more a mathematician than an artist, and his performance is intelligible only to mathematicians. It is true, the academical education of the young gentleman of the French navy is such, that a great number of them may acquire the preparatory knowledge that is necessary; and we are well informed that, in this respect, the officers of the British navy are greatly inferior to them. At the same time,

we may observe, that the French themselves appear so little sensible of the advantage of these publications, that no person among them has attempted to make a familiar abridgment of them, written in a way fitted to attract attention; and they still remain neglected in their original abstruse and uninteresting form; in consequence of which, these very ingenious and learned dissertations are by no means so useful as we should expect. They are large books, and appear to contain much; and as their plan is logical, it seems to occupy the whole subject, and, therefore, to have done almost all that can be done. But, alas! they have only opened the subject, and the study is yet in its infancy. The whole science of the art must proceed on the knowledge of the impulses of the wind and water. These are the forces which act on the machine; and its motions, which are the ultimatum of our research, whether as an end to be obtained or as a thing to be prevented, must depend on these forces. Now it is with respect to this fundamental point

that we are as yet almost totally in the dark. And in the performances of M. Bouguer, as also in those of the other authors we have named, the theory of these forces, by which their quantity and the direction of their action are ascertained, is altogether erroneous; and its results deviate so enormously from what is observed in the motions of a ship,

that the persons who should direct the operations on ship-board, in conformity to the maxims deducible from M. Bouguer's propositions, would be baffled in most of his attempts, and be in danger of losing the ship. The whole proceeds on the supposed truth of that theory which states the impulse of a fluid to be in the proportion of the square of the sine of the angle of incidence; and that its action on any small portion, such as a square foot of the sails or hull, is the same as if that portion were detached from the rest, and were exposed, single and alone, to the wind or water in the same angle. But it can be shown, both from theory and experience, that both of these principles are erroneous, and this to a very great degree, in cases which occur most frequently in practice, that is, in the small angles of inclination. When the wind falls nearly perpendicular on the sails, theory is not very erroneous; but in these cases, the circumstances of the ship's situation are generally such that the practice is easy, occurring almost without thought; and in this case too, even considerable deviations from the very best practice are of no great moment. The interesting cases, where the intended movement requires or depends upon very oblique actions of the wind on the sails, and its practicability or impracticability depends on a very small variation of this obliquity; a mistake of the force, either as to intensity or direction, produces a mighty effect on the resulting motion. This is the case in sailing to windward, the most important of all the general problems of seamanship. The trim of the sails, and the course of the ship, so as to gain most on the wind, are very nice things; that is, they are confined within very narrow limits, and a small mistake produces a very considerable effect. The same thing obtains in many of the nice problems of tacking, box-hauling, wearing after lying-to in a gale of wind, &c.

The error in the second assertion of the theory is still greater, and the action on one part of the sail or hull is so greatly modified by its action on another adjoining part, that a stay-sail is often seen hanging like a loose rag, although there is nothing between it and the wind; and this merely because a great sail in its neighbourhood sends off a lateral stream of wind, which completely hinders the wind from getting at it. Till the theory of the action of fluids be established, therefore, we cannot tell what are the forces which are acting on every point of the sail and hull; therefore we cannot tell either the mean intensity or direction of the whole force which acts on any particular sail, nor the intensity and mean direction of the resistance to the hull; circumstances absolutely necessary for enabling us to say what will be their energy in producing a rotation round any particular axis. In like manner, we cannot, by such a computation, find the spontaneous axis of conversion, or the velocity of such conversion. In short, we cannot pronounce with tolerable confidence a priori what will be the motions in any case, or what dispositions of the sails will produce the movement we wish to perform. The experienced seaman learns by habit the general effects of every disposition of the sails; and though his knowledge is far from being accurate, it seldom leads him into any very blundering operation. Perhaps he seldom makes the best adjustment possible, but seldom still does he deviate very far from it; and in the most general and important problems, such as working to windward, the result of much experience and many corrections has settled a trim of the sails, which is certainly not far from the truth, but it must be acknowledged, deviates widely and uniformly from the theories of the mathematician's closet.

After this account of the theoretical performances in the art of seamanship, and entertaining, as we do, small hopes of seeing a perfect theory of the impulse of fluids, it will not be expected that we enter very minutely on the subject in this place; nor is it our intention. But let it be observed that the theory is defect-

Seaman-ship. ive in one point only; and although this is a most important point, and the errors in it destroy the conclusions of the chief propositions, the reasonings remain in full force, and the modus operandi is precisely such as is stated in the theory. The principles of the art are therefore to be found in these treatises; but false inferences have been drawn, by computing from erroneous quantities. The rules and the practice of the computation, however, are still beyond controversy. Nay, since the process of investigation is legitimate, we may make use of it in order to discover the very circumstance in which we are at present mistaken; for by converting the proposition, instead of finding the motions by means of the supposed forces, combined with the known mechanism, we may discover the forces by means of this mechanism and the observed motions.

Design of this article. We shall, therefore, in this place, give a very general view of the movements of a ship under sail, showing how they are produced and modified by the action of the wind on her sails, the water on her rudder and on her bows. We shall not attempt a precise determination of any of these movements; but we shall say enough to enable the curious landsman to understand how this mighty machine is managed amidst the fury of the winds and waves; and, what is more to our wish, we hope to enable the thinking seaman, to generalise that knowledge which he possesses; to class his ideas, and give them a sort of rational system; and even to improve his practice, by making him sensible of the immediate operation of everything he does, and in what manner it contributes to produce the movement which he has in view.

A ship considered as in free space, impelled and resisted by opposite forces. A ship may be considered at present as a mass of inert matter in free space, at liberty to move in every direction, according to the forces which impel or resist her; and when she is in actual motion, in the direction of her course, we may still consider her as at rest in absolute space, but exposed to the impulse of a current of water moving equally fast in the opposite direction; for in both cases the pressure of the water on her bows is the same; and we know that it is possible, and frequently happens in currents, that the impulse of the wind on her sails, and that of the water on her bows, balance each other so precisely, that she not only does not stir from the place, but also remains steadily in the same position, with her head directed to the same point of the compass. This state of things is easily conceived by any person accustomed to consider mechanical subjects, and every seaman of experience has observed it. It is of importance to consider it in this point of view, because it gives us the most familiar notion of the manner in which these forces of the wind and water are set in opposition, and made to balance or not to balance each other by the intervention of the ship, in the same manner as the goods and the weights balance each other in the scales by the intervention of a beam or steelyard.

Impulse of the wind on the sails opposite to that of the water on the bows. When a ship proceeds steadily in her course, without changing her rate of sailing, or varying the direction of her head, we must in the first place conceive the accumulated impulses of the wind on all her sails as precisely equal and directly opposite to the impulse of the water on her bows. In the next place, because the ship does not change the direction of her keel, she resembles the balanced steelyard, in which the energies of the two weights, which tend to produce rotations in opposite directions, and thus to change the position of the beam, mutually balance each other round the fulcrum; so the energies of the actions of the wind on the different sails balance the energies of the water on the different parts of the hull.

Skill of the seaman displayed in shaping his course. The seaman has two principal tasks to perform. The first is to keep the ship steadily in that course which will bring her farthest on in the line of her intended voyage. This is frequently very different from that line, and the choice of the best course is sometimes a matter of consider-

able difficulty. It is sometimes possible to shape the course precisely along the line of the voyage; and yet the intelligent seaman knows that he will arrive sooner, or with greater safety, at his port, by taking a different course; because he will gain more by increasing his speed than he loses by increasing the distance. Some principle must direct him in the selection of this course. This we must attempt to lay before the reader.

Having chosen such a course as he thinks most advantageous, he must set such a quantity of sail as the strength of the wind will allow him to carry with safety and effect, and must trim the sails properly, or so adjust their positions to the direction of the wind, that they may have the greatest possible tendency to impel the ship in the line of her course, and to keep her steadily in that direction.

His other task is to produce any deviations which he sees proper from the present course of the ship; and to produce these in the most certain, the safest, and the most expeditious manner. It is chiefly in this movement that the mechanical nature of a ship comes into view, and it is here that the superior address and resources of an expert seaman is to be perceived.

Under the article SAILING, some notice has been taken of the first task of the seaman, and it was there shown how a ship, after having taken up her anchor and fitted her sails, accelerates her motion, by degrees which continually diminish, till the increasing resistance of the water becomes precisely equal to the diminished impulse of the wind, and then the motion continues uniformly the same, so long as the wind continues to blow with the same force, and in the same direction.

It is perfectly consonant to experience, that the impulse of fluids is in the duplicate ratio of the relative velocity. Let it be supposed that when water moves one foot per second, its perpendicular pressure or impulse on a square foot is $m$ pounds. Then, if it be moving with the velocity $V$ estimated in feet per second, its perpendicular impulse on a surface $S$, containing any number of square feet, must be $mSV^2$.

In like manner, the impulse of air on the same surface may be represented by $nSV^2$; and the proportion of the impulse of these two fluids will be that of $m$ to $n$. We may express this by the ratio of $q$ to 1, making $\backslash frac\{m\}\{n\}\; =\; q$.

M. Bouguer's computations and tables are on the supposition that the impulse of sea-water moving 1 foot per second is twenty-three ounces on a square foot, and that the impulse of the wind is the same when it blows at the rate of 24 feet per second. These measures are all French, and by no means agree with the experiments of Buat and others, whose conclusions confirm the results of investigation, namely, that nothing like precise measures can be expected, and that the impulses and resistances at the same surface, with the same obliquity of incidence, and the same velocity of motion, are different according to the form and situation of the adjoining parts. Thus the total resistance of a thin board is greater than that of a long prism, having this board for its front or bow, &c.

We are greatly at a loss what to give as absolute measures of these impulses.

1. With respect to water. The experiments of the French academy on a prism 2 feet broad and deep, and 4 feet long, indicate a resistance of 0.973 pounds avoirdupois to a square foot, moving with the velocity of 1 foot per second at the surface of still water.

Mr Buat's experiments on a square foot wholly immersed in a stream, were as follow:—

2. With respect to air the varieties are as great. The resistance of a square foot to air moving with the velocity of 1 foot per second, appears from Mr Robin's experiments on 16 square inches to be—

Precise measures are not to be expected, nor are they necessary in this inquiry. Here we are chiefly interested in their proportions, as they may be varied by their mode of action in the different circumstances of obliquity and velocity.

We begin by recurring to the fundamental proposition concerning the impulse of fluids,—viz., that the absolute pressure is always in a direction perpendicular to the impelled surface, whatever may be the direction of the stream of fluid. We must therefore illustrate the doctrine, by always supposing a flat surface of sail stretched on a yard, which can be braced about in any direction, and giving this sail such a position and such an extent of surface that the impulse on it may be the same, both as to direction and intensity, with that on the real sails. Thus the consideration is greatly simplified. The direction of the impulse is therefore perpendicular to the yard. Its intensity depends on the velocity with which the wind meets the sail, and the obliquity of its stroke. We shall adopt the constructions founded on the common doctrine, that the impulse is as the square of the sine of the inclination, because they are simple; whereas, if we were to introduce the values of the oblique impulses, such as they have been observed in the excellent experiments of the Academy of Paris, the constructions would be complicated in the extreme, and we could hardly draw any consequences which would be intelligible to any but expert mathematicians. The conclusions will be erroneous, not in kind but in quantity only; and we shall point out the necessary corrections, so that the final results will be found not very different from real observation.

If a ship were a round cylindrical body like a flat tub, floating on its bottom, and fitted with a mast and sail in the centre, she would always sail in a direction perpendicular to the yard. This is evident. But she is an oblong body, and may be compared to a chest, whose length greatly exceeds its breadth. She is so shaped that a moderate force will push her through the water with the head or stern foremost; but it requires a very great force to push her sideways with the same velocity. A fine sailing ship of war will require about twelve times as much force to push her sideways as to push her head foremost. In this respect, therefore, she will very much resemble a chest whose length is twelve times its breadth; and whatever be the proportion of these resistances in different ships, we may always substitute a box, which shall have the same resistances headways and sideways.

Let EFGH (fig. 1) be the horizontal section of such a box, and AB its middle line, and C its centre. In whatever direction this box may chance to move, the direction of the whole resistance on its two sides will pass through C. For as the whole stream has one inclination to the side

EF, the equivalent of the equal impulses on every part will be in a line perpendicular to the middle of EF. For the same reason it will be in a line perpendicular to the middle of FG. These perpendiculars must cross in C. Suppose a mast erected at C, and YC to be a yard hoisted on it carrying a sail. Let the yard be first conceived as braced

right athwart at right angles to the keel, as represented by $Yy$. Then, whatever be the direction of the wind about this sail, it will impel the vessel in the direction CB. But if the sail has the oblique position $Yy$, the impulse will be in the direction CD perpendicular to CY, and will both push the vessel ahead and sideways; for the impulse CD is equivalent to the two impulses CK and CI (the sides of a rectangle of which CD is the diagonal). The force CI pushes the vessel ahead, and CK pushes her sideways. She must therefore take some intermediate direction $ab$, such that the resistance of the water to the plane FG is to its resistance to the plane EF as CI to CK.

The angle $lCB$ between the real course and the direction of the head is called the leeway; and in the course of this dissertation we shall express it by the symbol $x$. It evidently depends on the shape of the vessel and on the position of the yard. An accurate knowledge of the quantity of leeway, corresponding to different circumstances of obliquity of impulse, extent of surface, &c., is of the utmost importance in the practice of navigation; and even an approximation is valuable. The subject is so very difficult that this must content us for the present.

Let $V$ be the velocity of the ship in the direction $Cb$, and let the surfaces FG and FE be called $A\text{'}$ and $B\text{'}$. Then the resistance to the lateral motion is $mV^2\; \backslash times\; B\text{'}\; \backslash times\; \backslash sin^2\; x$, $lCB$, and that to the direct motion is $mV^2\; \backslash times\; A\text{'}\; \backslash times\; \backslash cos^2\; x$, $lCK$, or $mV^2\; \backslash times\; A\text{'}\; \backslash times\; \backslash cos^2\; x$. Therefore these resistances are in the proportion of $B\text{'}\; \backslash times\; \backslash sin^2\; x$ to $A\text{'}\; \backslash times\; \backslash cos^2\; x$ (representing the angle of leeway $lCB$ by the symbol $x$).

Therefore we have $CI\; :\; CK$, or $CI\; :\; ID\; =\; A\text{'}\; \backslash cdot\; \backslash cos^2\; x\; :\; B\text{'}\; \backslash cdot\; \backslash sin^2\; x$.

Let the angle $YCB$, to which the yard is braced up, be called the trim of the sails, and expressed by the symbol $b$. This is the complement of the angle $DCI$. Now $CI\; :\; ID\; =\; \backslash text\{rad.\}\; :\; \backslash tan\; DCI\; =\; 1\; :\; \backslash tan\; DCI\; =\; 1\; :\; \backslash cotan\; b$. Therefore we have finally $1\; :\; \backslash cotan\; b\; =\; A\text{'}\; :\; B\text{'}\; \backslash cdot\; \backslash tan^2\; x$, and $A\text{'}\; \backslash cdot\; \backslash cotan\; b\; =\; B\text{'}\; \backslash cdot\; \backslash tan^2\; x$, and $\backslash tan^2\; x\; =\; \backslash frac\{A\text{'}\}\{B\text{'}\}\; \backslash cdot\; \backslash cot\; b$. This equation evidently ascertains the mutual relation between the trim of the sails and the leeway, in every case where we can tell the proportion between the resistances to the direct and broadside motions of the ship, and where this proportion does not change by the obliquity of the course. Thus, suppose the yard braced up to an angle of $30^\backslash circ$ with the keel. Then $\backslash cotan\; 30^\backslash circ\; =\; 1.732$ very nearly. Suppose also that the resistance sideways is twelve times greater than the resistance headways. This gives $A\; =\; 1$ and $B\; =\; 12$. Therefore $1.732\; =\; 12\; \backslash times\; \backslash tan^2\; x$, and $\backslash tan^2\; x\; =\; \backslash frac\{1.732\}\{12\}\; =\; 0.1434$, and $\backslash tan\; x\; =\; 0.3799$, and $x\; =\; 20^\backslash circ\; 48\text{'}$ very nearly two points of leeway.

This computation, or rather the equation which gives room for it, supposes the resistances proportional to the squares of the sines of incidence. The experiments of the Academy of Paris (see article HYDRODYNAMICS) show that this supposition is not far from the truth when the angle of incidence is great. In the present case the angle of incidence on the front FG is about $70^\backslash circ$, and the experiments just now mentioned show that the real resistances exceed the theoretical ones only $\backslash frac\{1\}\{1.5\}$. But the angle of incidence on EF is only $20^\backslash circ\; 48\text{'}$. Experiment shows that in this inclination the resistance is almost quadruple of the theoretical resistances. Therefore the lateral resistance is assumed much too small in the present instance. Therefore a much smaller leeway will suffice for producing a lateral resistance which will balance the lateral impulse CK, arising from the obliquity of the sail, viz., $30^\backslash circ$. The matter of fact is, that a pretty good sailing ship, with her sails braced to this angle at a medium, will not make above five or six de-

greces leeway in smooth water and fine weather; and yet in this situation the hull and rigging present a very great surface to the wind, in the most improper positions, so as to have a very great effect in increasing her leeway. And if we compute the resistances for this leeway of six degrees by the actual experiments of the French Academy on the angle, we shall find the result not far from the truth,—that is, the direct and lateral resistances will be nearly in the proportion of CI to ID.

It results from this view of the matter, that the leeway is in general much smaller than what the usual theory assigns. We also see that, according to whatever law the resistances change by a change of inclination, the leeway remains the same while the trim of the sails is the same. The leeway depends only on the direction of the impulse of the wind; and this depends solely on the position of the sails with respect to the keel, whatever may be the direction of the wind. This is a very important observation, and will be frequently referred to in the progress of the present investigation. Note, however, that we are here considering only the action on the sails, and on the same sails. We are not considering the action of the wind on the hull and rigging. This may be very considerable; and it is always in a lee direction, and augments the leeway; and its influence must be so much the more sensible, as it bears a greater proportion to the impulse on the sails. A ship under close-reefed topsails and courses, must make more leeway than when under all her canvas, trimmed to the same angle. But to introduce this additional cause of deviation here would render the investigation too complicated to be of any use.

This doctrine will be considerably illustrated by attending to the manner in which a lighter is tracked along a stream. The track-
rope is made fast to some staple or bolt E on the deck (fig. 2), and is passed between two

of the timber-heads of the bow D, and laid hold of at F on shore. The men or cattle walk along the path FG, the rope keeps extended in the direction DF, and the lighter arranges itself in an oblique position AB, and is thus dragged along in the direction $ab$, parallel to the side of the canal; or, if the canal has a current in the opposite direction $ba$, the lighter may be kept steady in its place by the rope DF made fast to a post at F. In this case, it is always observed, that the lighter swings in a position AB, which is oblique to the stream $ab$. Now, the force which retains it in this position, and which precisely balances the action of the stream, is certainly exerted in the direction DF; and the lighter would be held in the same manner if the rope were made fast at C amidship, without any dependence on the timberheads at D; and it would be held in the same position, if, instead of the single rope CF, it were riding by two ropes CG and CH, of which CH is in a direction right ahead, but oblique to the stream, and the other CG is perpendicular to CH or AB. And, drawing DI and DK perpendicular to AB and CG, the strain on the rope CH is to that on the rope CG as CI to CK. The action of the rope in these cases is precisely analogous to that of the sail $yY$; and the obliquity of the keel to the direction of the motion, or to the direction of the stream, is analogous to the leeway. All this must be evident to any person accustomed to mechanical disquisitions.

A most important use may be made of this illustration.

If an accurate model be made of a ship, and if it be placed in a stream of water, and ridden in this manner by a rope made fast at any point D of the bow, it will arrange itself in some determined position AB. There will be a certain obliquity to the stream, measured by the angle $Bob$; and there will be a corresponding obliquity of the rope, measured by the angle $FCB$. Let $yCY$ be perpendicular to CF. Then CY will be the position of the yard, or trim of the sails corresponding to the leeway $bCB$. Then, if we shift the rope to a point of the bow distant from D by a small quantity, we shall obtain a new position of the ship, both with respect to the stream and rope; and in this way may be obtained the relation between the position of the sails and the leeway, independent of all theory, and susceptible of great accuracy; and this may be done with a variety of models suited to the most usual forms of ships.

In further thinking on this subject, we are persuaded that these experiments, instead of being made on models, may with equal ease be made on a ship of any size. Let the ship ride in a stream at a mooring D (fig. 3), by means of a short hawser BCD from her bow, having a spring AC on it carried out from her quarter. She will swing to her moor-

ings, till she ranges herself in a certain position AB with respect to the direction $ba$ of the stream; and the direction of the hawser DC will point to some point E of the line of the keel. Now, it is plain to any person acquainted with mechanical disquisitions, that the deviation $BEb$ is precisely the leeway that the ship will make when the average position of the sails is that of the line GEH perpendicular to ED; at least this will give the leeway which is produced by the sails alone. By heaving on the spring, the knot C may be brought into any other position we please; and for every new position of the knot the ship will take a new position with respect to the stream and to the hawser. And we persist in saying, that more information will be got by this train of experiments than from any mathematical theory: for all the theories of the impulses of fluids must proceed on physical postulates with respect to the motions of the filaments, which are exceedingly conjectural.

And it must now be farther observed, that the substitution which we have made of an oblong parallelopiped for a parison of ship, although well suited to give us clear notions of the subject, is of small use in practice; for it is next to impossible (even granting the theory of oblique impulsions) to make this substitution. A ship is of a form which is not reducible to equations; and therefore the action of the clear water on her bow or broadside can only be had by a most laborious and intricate calculation for almost every square foot of its surface.¹ And this must be different for every ship. But, which is more unlucky, when we have got a parallelopiped which will have the same proportion of direct and lateral resistance for a particular angle of leeway, it will not answer for another leeway of the same ship; for when the leeway changes, the figure actually exposed to the action of the water changes also. When the leeway is increased, more of the lee-quarter is acted on by the water, and a part of the weather-bow is now removed from its action. Another parallelopiped must therefore be discovered, whose resistances shall suit this new position of the keel with respect to the real course of the ship.

¹ Bezout's Cours de Mathem., vol. v., p. 72, &c.

We proceed, in the next place, to ascertain the relation between the velocity of the ship and that of the wind, modified as they may be by the trim of the sails and the obliquity of the impulse.

Let AB (figs. 4, 5, and 6) represent the horizontal section of a ship. In place of all the drawing sails—that is, the sails which are really filled—we can always substitute one sail of equal extent, trimmed to the same angle with the keel. This being supposed attached to the yard DCD, let this yard be first of all at right angles to the keel, as represented in fig. 4. Let the wind blow in the direction WC, and let CE (in the direction WC continued) represent the velocity V of the wind. Let CF be the velocity v of the ship. It must also be in the direction of the ship's motion, because when the sail is at right angles to the keel, the absolute impulse on the sail is in the direction of the keel, and there is no lateral impulse, and consequently no leeway. Draw EF, and complete the parallelogram CFEc, producing cE through the centre of the yard to e. Then wC will be the relative or apparent direction of the wind, and Ce or FE will be its apparent or relative velocity. For if the line Ce be carried along CF, keeping always parallel to its first position, and if a particle of air move uniformly along CE (a fixed line in absolute space) in the same time, this particle will always be found in that point of CE, where it is intersected at that instant by the moving line Ce; so that if Ce were a tube, the particle of air, which really moves in the line CE, would always be found in the tube Ce. While CE is the real direction of the wind, Ce will be the position of the vane at the mast-head, which will therefore mark the apparent direction of the wind, or its motion relative to the moving ship.

We may conceive this in another way. Suppose a cannon-shot fired in the direction CE at the passing ship, and that it passes through the mast at C with the velocity of the wind. It will not pass through the off-side of the ship at P, in the line CE; for while the shot moves from C to P, the point P has gone forward, and the point p is now in the place where P was when the shot passed through the mast. The shot will therefore pass through the ship's side in the point p, and a person on board seeing it pass through C and p, will say that its motion was in the line Cp.

Thus it happens, that when a ship is in motion the apparent direction of the wind is always ahead of its real direction. The line wC is always found within the angle WCB. It is easy to see from the construction, that the difference between the real and apparent directions of the wind is so much the more remarkable as the velocity of the ship is greater. For the angle WCw or ECe depends on the magnitude of Ee or CF, in proportion to CE. Persons not much accustomed to attend to these matters are apt to think all attention to this difference to be nothing but affectation of nicety. All seamen are aware that the velocity of a ship has a sensible proportion to that of the wind. "Swift as the wind," is a proverbial expression; but it is one which sometimes indeed falls short of the truth, as it is known, that at times the ship's velocity may exceed that of the wind. The difference between the real direction of the wind and that which in fact impels the ship, namely, its apparent direction, is of great importance when steam propulsion is combined with sails; and will be again noticed when we come to that part of our subject. We may form a pretty exact notion of the velocity of the wind by observing the shadows of the summer clouds flying along the face of a country, and it may be very well mea-

sured by this method. The motion of such clouds cannot be very different from that of the air below; and when the pressure of the wind on a flat surface, while blowing with a velocity measured in this way, is compared with its pressure when its velocity is measured by more unexceptionable methods, they are found to agree with all desirable accuracy. Now, observations of this kind frequently repeated, show that what we call a pleasant brisk gale blows at the rate of about ten miles an hour, or about fifteen feet in a second, and exerts a pressure of half a pound on a square foot. Mr Smeaton has frequently observed the sails of a windmill, driven by such a wind, moving faster, much faster, towards their extremities, so that the sail, instead of being pressed to the frames on the arms, was taken aback, and fluttering on them. Nay, we know that a good ship, with all her sails set, and the wind on the beam, will, in such a situation, sail above ten knots an hour in smooth water. There is an observation made by every experienced seaman, which shows this difference between the real and apparent directions of the wind very distinctly. When a ship that is sailing briskly with the wind on the beam tacks about, and then sails equally well on the other tack, the wind always appears to have shifted and come more ahead. This is familiar to all seamen. The seaman judges of the direction of the wind by the position of the ship's vanes. Suppose the ship sailing due west on the starboard tack, with the wind apparently N.N.W., the vane pointing S.S.E. If the ship put about, and stands due east on the port tack, the vane will be found no longer to point S.S.E., but perhaps S.S.W., the wind appearing N.N.E., and the ship must be nearly close-hauled in order to make an east course. The wind appears to have shifted four points. If the ship tacks again, the wind returns to its old quarter. We have often observed a greater difference than this. The celebrated astronomer Dr Bradley, taking the amusement of sailing in a pinnace on the river Thames, observed this, and was surprised at it, imagining that the change of the wind was this sub-

ject. The boatmen told him that it always happened at sea, and explained it to him in the best manner they were able. The explanation struck him, and set him a-musing on an astronomical phenomenon which he had been puzzled by for some years, and which he called the aberration of the fixed stars. Every star changes its place a small matter for half a year, and returns to it at the completion of the year. He compared the stream of light from the star to the wind, and the telescope of the astronomer to the ship's vane, while the earth was like the ship, moving in opposite directions when in the opposite point of its orbit. The telescope must always be pointed ahead of the real direction of the star, in the same manner as the vane is always in a direction ahead of the wind; and thus he ascertained the progressive motion of light, and discovered the proportion of its velocity to the velocity of the earth in its orbit, by observing the deviation which was necessarily given to the telescope. Observing that the light shifted its direction about 40', he concluded its velocity to be about 11,000 times greater than that of the earth; just as the intelligent seaman would conclude from this apparent shifting of the wind, that the velocity of the wind is about triple that of the ship. This is indeed the best method for discovering the velocity of the wind. Let the direction of the vane at the mast-head be very accurately noticed on both tacks, and let the velocity of the ship be also accurately measured. The angle between the directions of the ship's head on these different tacks being halved, will give the real direction of the wind, which must be compared with the position of the vane in order to determine the angle contained between the real and apparent directions of the wind or the angle ECe; or half of the observed shifting of the wind

seaman-ship. will show the inclination of its true and apparent directions. This being found, the proportion of EC to FC (fig. 6) is easily measured.

We have been very particular on this point, because since the mutual actions of bodies depend on their relative motions only, we should make prodigious mistakes if we estimated the action of the wind by its real direction and velocity, when they differ so much from the relative or apparent.

Velocity of a ship when its sails are at right angles to the keel. We now resume the investigation of the velocity of the ship (fig. 4), having its sails at right angles to the keel, and the wind blowing in the direction and with the velocity CE, while the ship proceeds in the direction of the keel with the velocity CF. Produce Ee, which is parallel to BC, till it meet the yard in g, and draw FG perpendicular to Eg. Let $\backslash alpha$ represent the angle WCD, contained between the sail and the real direction of the wind, and let $b$ be the angle of trim DCB. CE, the velocity of the wind, was expressed by V, and CF, the velocity of the ship, by v.

The absolute impulse on the sail is (by the usual theory) proportional to the square of the relative velocity, and to the square of the sine of the angle of incidence; that is, to $FE^2\; \backslash times\; \backslash sin^2\; \backslash angle\; CDE$. Now the angle GFE = $\backslash angle\; CDE$, and EG is equal to $FE\; \backslash times\; \backslash sin\; \backslash angle\; GFE$; and EG is equal to $Eg\; -\; Gg$. But $Eg\; =\; EC\; \backslash times\; \backslash sin\; \backslash angle\; ECG\; =\; V\; \backslash times\; \backslash sin\; \backslash alpha$; and $Gg\; =\; CF\; =\; v$. Therefore $EG\; =\; V\; \backslash times\; \backslash sin\; \backslash alpha\; -\; v$, and the impulse is proportional to $(V\; \backslash times\; \backslash sin\; \backslash alpha\; -\; v)^2$. If S represent the surface of the sail, the impulse, in pounds, will be $nS(V\; \backslash times\; \backslash sin\; \backslash alpha\; -\; v)^2$.

Let A be the surface which, when it meets the water perpendicularly with the velocity v, will sustain the same pressure or resistance which the bows of the ship actually meet with. This impulse, in pounds, will be $mAv^2$. Therefore, because we are considering the ship's motion as in a state of uniformity, the two pressures balance each other; and therefore $mAv^2\; =\; nS(V\; \backslash times\; \backslash sin\; \backslash alpha\; -\; v)^2$ and $\backslash frac\{m\}\{n\}Av^2\; =\; S(V\; \backslash times\; \backslash sin\; \backslash alpha\; -\; v)^2$;

therefore $\backslash sqrt\{\backslash frac\{m\}\{n\}Av^2\}\; =\; \backslash sqrt\{S\}\; \backslash times\; V\; \backslash times\; \backslash sin\; \backslash alpha\; -\; v\backslash sqrt\{S\}$, and $v\; =$

We see, in the first place, that the velocity of the ship is, ceteris paribus, proportional to the velocity of the wind, and to the sine of its incidence on the sail jointly; for while the surface of the sail S and the equivalent surface for the bow remains the same, v increases or diminishes at the same rate with $V\; \backslash times\; \backslash sin\; \backslash alpha$. When the wind is right astern, the sine of $\backslash alpha$ is unity, and then the ship's velocity is $\backslash frac\{V\}\{\backslash sqrt\{\backslash frac\{mA\}\{nS\}\}\; +\; 1\}$.

Note, that the denominator of this fraction is a common number; for m and n are numbers and A and S being quantities of one kind, $\backslash frac\{A\}\{S\}$ is also a number.

It must also be carefully attended to, that S expresses a quantity of sail actually receiving wind with the inclination $\backslash alpha$. It will not always be true, therefore, that the velocity will increase as the wind is more abaft, because some sails will then be calm others. This observation is not, however, of great importance; for it is very unusual to put a ship in the situation considered hitherto; that is, with the yards square, unless she be right before the wind.

If we should discover the relation between the velocity and the quantity of sail in this simple case of the wind right aft, observe that the equation $v\; =\; \backslash frac\{V\}\{\backslash sqrt\{\backslash frac\{mA\}\{nS\}\}\; +\; 1\}$ gives us

and $\backslash frac\{nS\}\{mA\}\; =\; \backslash frac\{v^2\}\{(V\; -\; v)^2\}$; and because n and m and A are constant quantities, S is proportional to $\backslash frac\{v^2\}\{(V\; -\; v)^2\}$ or the surface of sail is proportional to the square of the ship's velocity directly, and to the square of the relative velocity inversely. Thus, if a ship be sailing with one-eighth of the velocity of the wind, and we would have her sail with one-fourth of it, we must quadruple the sail. This is more easily seen in another way. The velocity of the ship is proportional to the velocity of the wind; and therefore the relative velocity is also proportional to that of the wind, and the impulse of the wind is as the square of the relative velocity. Therefore, in order to increase the relative velocity by an increase of sail only, we must make this increase of sail in the duplicate proportion of the increase of velocity.

Let us, in the next place, consider the motion of a ship whose sails stand oblique to the keel.

The construction for this purpose differs a little from the former, because, when the sails are trimmed to any oblique position DCB (figs. 5 and 6), there must be a deviation from the direction of the keel, or a leeway BCb.

Call this x. Let CF be the velocity of the ship. Draw, as before, Eg perpendicular to the yard, and FG perpendicular to Eg; also, draw FH perpendicular to the yard; then, as before, EG, which is in the subduplicate ratio of the impulse on the sail, is equal to $Eg\; -\; Gg$. Now Eg is, as before, $V\; \backslash times\; \backslash sin\; \backslash alpha$, and Gg is equal to FH, which is $CF\; \backslash times\; \backslash sin\; \backslash angle\; FCH$, or $v\; \backslash times\; \backslash sin\; (b\; +\; x)$. Therefore we have the impulse $=\; nS(V\; \backslash times\; \backslash sin\; \backslash alpha\; -\; v\; \backslash times\; \backslash sin\; (b\; +\; x))^2$.

This expression of the impulse is perfectly similar to that in the former case, its only difference consisting in the subtractive part, which is here $v\; \backslash times\; \backslash sin\; b\; +\; x$ instead of v. But it expresses the same thing as before, viz., the diminution of the impulse. The impulse being reckoned solely in the direction perpendicular to the sail, it is diminished solely by the sail withdrawing itself in that direction from the wind; and as gE may be considered as the real impulsive motion of the wind, GE must be considered as the relative and effective impulsive motion. The impulse would have been the same had the ship been at rest, and had the wind met it perpendicularly with the velocity GE.

We must now show the connection between this impulse and the motion of the ship. The sail, and consequently the ship, is pressed by the wind in the direction CI perpendicular to the sail or yard with the force which we have just now determined. This (in the state of uniform motion) must be equal and opposite to the action of the water. Draw IL at right angles to the keel. The impulse in the direction CI (which we may measure by CI) is equivalent to the impulses CL and LI. By the first the ship is impelled right forward, and by the second she is driven side-

ways. Therefore we must have a leeway, and a lateral as well as a direct resistance. We suppose the form of the ship to be known, and therefore the proportion is known, or discoverable, between the direct and lateral resistances corresponding to every angle $x$ of leeway. Let $A$ be the surface whose perpendicular resistance is equal to the direct resistance of the ship corresponding to the leeway $x$, that is, whose resistance is equal to the resistance really felt by the ship's bows in the direction of the keel when she is sailing with this leeway; and let $B$ in like manner be the surface whose perpendicular resistance is equal to the actual resistance to the ship's motion in the direction $LI$, perpendicular to the keel. (This is not equivalent to $A$ and $B$ adapted to the rectangular box, but to $A\text{'}\; \backslash cos^2\; x$ and $B\text{'}\; \backslash sin^2\; x$.) We have therefore $A\; :\; B\; =\; CL\; :\; LI$, and $LI\; =\; \backslash frac\{CL\; \backslash cdot\; B\}\{A\}$. Also, because $CI\; =\; \backslash sqrt\{CL^2\; +\; LI^2\}$, we have $A\; :$

$\backslash sqrt\{A^2\; +\; B^2\}\; =\; CL\; :\; CI$, and $CI\; =\; \backslash frac\{CL\; \backslash cdot\; \backslash sqrt\{A^2\; +\; B^2\}\}\{A\}$. The resistance in the direction $LC$ is properly measured by $m\; A\; v^2$, as has been already observed. Therefore the resistance in the direction $IC$ must be expressed by $m\; \backslash sqrt\{A^2\; +\; B^2\}\; v^2$; or (making $C$ the surface which is equal to $\backslash sqrt\{A^2\; +\; B^2\}$, and which will therefore have the same perpendicular resistance to the water having the velocity $v$) it may be expressed by $m\; C\; v^2$.

Therefore, because there is an equilibrium between the impulse and resistance, we have $m\; C\; v^2\; =\; n\; S\; (V\; \backslash cdot\; \backslash sin\; a\; -\; v\; \backslash cdot\; \backslash sin\; b\; +\; x)^2$, and $\backslash frac\{m\}\{n\}\; C\; v^2\; =\; S\; (V\; \backslash cdot\; \backslash sin\; a\; -\; v\; \backslash cdot\; \backslash sin\; b\; +\; x)^2$ and $\backslash sqrt\{q\}\; \backslash sqrt\{C\}\; v\; =\; \backslash sqrt\{S\}\; (V\; \backslash cdot\; \backslash sin\; a\; -\; v\; \backslash cdot\; \backslash sin\; b\; +\; x)$.

Observe that the quantity which is the co-efficient of $V$ in this equation is a common number; for $\backslash sin\; a$ is a number, being a decimal fraction of the radius 1, $\backslash sin\; b\; +\; x$ is also a number, for the same reason. And since $m$ and $n$ were numbers of pounds, $\backslash frac\{m\}\{n\}$ or $q$ is a common number. And because $C$ and $S$ are surfaces, or quantities of one kind, $\backslash frac\{C\}\{S\}$ is also a common number.

This is the simplest expression that we can think of for the velocity acquired by the ship, though it must be acknowledged to be too complex to be of very prompt use. Its complication arises from the necessity of introducing the leeway $x$. This affects the whole of the denominator; for the surface $C$ depends on it, because $C\; =\; \backslash sqrt\{A^2\; +\; B^2\}$, and $A$ and $B$ are analogous to $A\text{'}\; \backslash cos^2\; x$ and $B\text{'}\; \backslash sin^2\; x$.

But we can deduce some important consequences from this theorem.

While the surface $S$ of the sail actually filled by the wind remains the same, and the angle $DCB$, which in future we shall call the trim of the sails, also remains the same, both the leeway $x$ and the substituted surface $C$ remains the same. The denominator is therefore constant; and the velocity of the ship is proportional to $\backslash sqrt\{S\}\; \backslash cdot\; V\; \backslash cdot\; \backslash sin\; a$; that is, directly as the velocity of the wind, directly as the absolute inclination of the wind to the yard, and directly as the square root of the surface of the sails.

We also learn from the construction of the figure, that $FG$ parallel to the yard cuts $CE$ in a given ratio. For $CF$ is in a constant ratio to $Eg$, as has been just now demonstrated. And the angle $DCF$ is constant. Therefore $CF\; \backslash cdot\; \backslash sin\; b$, or $FH$ or $Gg$, is proportional to $Eg$, and $OC$ to

$EC$, or $EC$ is cut in one proportion, whatever may be the angle $ECD$, so long as the angle $DCF$ is constant.

We also see that it is very possible for the velocity of the ship on an oblique course to exceed that of the wind. This

Now this may easily be by sufficiently enlarging $S$ and diminishing $b\; +\; x$. It is indeed frequently seen in fine sailers with all their sails set and not hauled too near the wind.

We remarked above that the angle of leeway $x$ affects the whole denominator of the fraction which expresses the velocity. Let it be observed that the angle $ICL$ is the complement of $LCD$, or of $b$. Therefore, $CL\; :\; LI$, or $A\; :\; B\; =\; 1\; :\; \backslash tan\; ICL\; =\; 1\; :\; \backslash cot\; b$, and $B\; =\; A\; \backslash cdot\; \backslash cotan\; b$. Now $A$ is equivalent to $A\text{'}\; \backslash cos^2\; x$, and thus $b$ becomes a function of $x$. $C$ is evidently so, being $\backslash sqrt\{A^2\; +\; B^2\}$. Therefore before the value of this fraction can be obtained, we must be able to compute, by our knowledge of the form of the ship, the value of $A$ for every angle $x$ of leeway. This can be done only by resolving her bows into a great number of elementary planes, and computing the impulses on each and adding them into one sum. The computation is of immense labour, as may be seen by one example given by Bouguer. When the leeway is but small, not exceeding ten degrees, the substitution of the rectangular prism of one determined form is abundantly exact for all leeways contained within this limit; and we shall soon see reason for being contented with this approximation. We may now make use of the formula expressing the velocity for solving the chief problems in this part of the seaman's task.

And first let it be required to determine the best position of the sail for standing on a given course $ab$, when $CE$ the To direction and velocity of the wind, and its angle with the course $WCF$, are given. This problem has exercised the talents of the mathematicians ever since the days of Newton. The best plan of solving this problem will be to place the yard $CD$ in such a position that the tangent of the angle $FCD$ may be one half of the tangent of the angle $DCW$. This will indeed be the best position of the sail for beginning the motion; but as soon as the ship begins to move in the direction $CF$, the effective impulse of the wind is diminished, and also its inclination to the sail. The wind and angle $DCW$ diminishes continually as the ship accelerates; its angle for $CF$ is now accompanied by its equal $eE$, and by an angle $ECe$, or $WCe$. $CF$ increases, and the impulse on the sail diminishes, till an equilibrium obtains between the resistance of the water and the impulse of the wind. The impulse is now measured by $CE^2\; \backslash times\; \backslash sin^2\; CD$ instead of $CE^2\; \backslash times\; \backslash sin^2\; ECD$, that is, by $Eg^2$ instead of $Eg^2$.

This introduction of the relative motion of the wind renders the actual solution of the problem extremely difficult. It is very easily expressed geometrically: Divide the angle $WCF$ in such a manner that the tangent of $DCF$ may be half of the tangent of $DCe$, and the problem may be constructed geometrically as follows:—

Let $WCF$ (fig. 7) be the angle between the sail and course. Round the centre $C$ describe the circle $WDFY$; produce $WC$ to $Q$, so that $CQ\; =\; \backslash frac\{1\}\{2\}\; WC$, and draw $QY$ parallel to $CF$ cutting the circle in $Y$; bisect the arch $WY$ in $D$, and draw $DC$. $DC$ is the proper position of the yard.

Draw the cord $WY$, cutting $CD$ in $V$ and $CF$ in $T$; draw the tangent $PD$, cutting $CF$ in $S$ and $CY$ in $R$.

It is evident that $WY$, $PR$, are both perpendicular to $CD$, and are bisected in $V$ and $D$; therefore (by reason of

Seaman-ship. the parallels QY, CF) $4\; :\; 3\; =\; QW\; :\; CW,\; =\; YW\; :\; TW$, RP : SP. Therefore PD : PS = 2 : 3, and PD : DS = 2 : 1. Q.E.D. But this division cannot be made to the best advantage till the ship has attained its greatest velocity, and the angle $\backslash omega$ CF has been produced.

We must consider all the three angles, $a$, $b$, and $x$, as variable in the equation which expresses the value of $v$, and we must make the fluxion of this equation = 0; then, by means of the equation $B\; =\; A\; \backslash cdot\; \backslash cotan\; b$, we must obtain the value of $b$ and of $b$ in terms of $x$ and $x$. With respect to $a$, observe, that if we make the angle $WCF\; =\; p$, we have $p\; =\; a\; +\; b\; +\; x$; and $p$ being a constant quantity, we have $a\; +\; b\; +\; x\; =\; 0$. Substituting for $a$, $b$, $a$, and $b$, their values in terms of $x$ and $x$, in the fluxionary equation = 0, we readily obtain $x$, and then $a$ and $b$, which solves the problem.

Let it be required, in the next place, to determine the course and the trim of the sails most proper for plying to windward.

Prob. II. To determine the course and trim of the sails most proper for plying to windward.

In fig. 6, draw FP perpendicular to WC. CF is the motion of the ship; but it is only by the motion PC that she gains to windward. Now CP is $=\; CF\; +\; \backslash cosin\; WCF$, or $v\; \backslash cdot\; \backslash cos(a\; +\; b\; +\; x)$. This must be rendered a maximum, as follows.

By means of the equation which expresses the value of $v$ and the equation $B\; =\; A\; \backslash cdot\; \backslash cotan\; b$, we exterminate the quantities $v$ and $b$; we then take the fluxion of the quantity into which the expression $v\; \backslash cdot\; \backslash cos(a\; +\; b\; +\; x)$ is changed by this operation. Making this fluxion = 0, we get the equation which must solve the problem. This equation will contain the two variable quantities $a$ and $x$ with their fluxions; then make the co-efficient of $x$ equal to 0, also the co-efficient of $a$ equal to 0. This will give two equations, which will determine $a$ and $x$, and from this we get $b\; =\; p\; -\; a\; -\; x$.

Prob. III. To determine the best course and trim of the sails for getting away from a given line of coast CM (fig. 6), the process perfectly resembles this last, which is in fact getting away from a line of coast which makes a right angle with the wind. Therefore, in place of the angle WCF, we must substitute the angle WCM $\backslash pm$ WCF. Call this angle $e$. We must make $r\; \backslash cos(e\; \backslash pm\; a\; \backslash pm\; b\; \backslash pm\; x)$ a maximum. The analytical process is the same as the former, only $e$ is here a constant quantity.

These are the three principal problems which can be solved by means of the knowledge that we have obtained of the motion of the ship when impelled by an oblique sail, and therefore making leeway; and they may be considered as an abstract of this part of M. Bouguer's work. We have only pointed out the process for this solution, and have even omitted some things taken notice of by M. Bezout in his very elegant compendium. Our reasons will appear as we go on. The learned reader will readily see the extreme difficulty of the subject, and the immense calculations which are necessary even in the simplest cases, and will grant that it is out of the power of any but an expert analyst to derive any use from them; but the mathematician can calculate tables for the use of the practical seaman. Thus he can calculate the best position of the sails for advancing in a course of $90^\backslash circ$ from the wind, and the velocity in that course; then for $85^\backslash circ$, $80^\backslash circ$, $75^\backslash circ$, &c. M. Bouguer has given a table of this kind; but to avoid the immense difficulty of the process, he has adapted it to the apparent direction of the wind. We have inserted a few of his numbers,

suited to such cases as can be of service, namely, when all the sails draw, or none stand in the way of others. Column 1st is the apparent angle of the wind and course; column 2d is the corresponding angle of the sails and keel; and M. Bouguer's table for finding the best position of the sails for advancing in any course.

In all these numbers we have the tangent of $\backslash omega$ CD. Intuitively of double of the tangent of DCF. The above table will, we think, be found useful. Column 2 carries the calculation up to $25^\backslash circ$, the angle of the yards with the keel; and although some modern ships may go beyond this, and brace their yards up to $23^\backslash circ$, we consider $25^\backslash circ$ a fair average of what can be effected. Certainly the apparent direction of the wind is unknown to the seaman till the ship is sailing with uniform velocity. It is, however, of service to him to know, for instance, that when the angle of the vanes and yards is $56^\backslash circ$, the yards should be braced up to $37^\backslash circ\; 30\text{'}$. In that case the course would be $94^\backslash circ\; 25\text{'}$, from the apparent direction of the wind, that is, with the wind apparently $4^\backslash circ\; 25\text{'}$ abaft the beam; a good sailing ship in this position, with the water very smooth and the wind light, may acquire a velocity even exceeding that of the true wind. But the mathematician may require that the yards should be braced up to a smaller angle than is possible.

Let us see whether this restriction in power of bracing up, arising from necessity, leaves anything in our choice, and makes one course preferable to another. We see that there are a prodigious number of courses, and these the most usual and the most important, which we must hold with one trim of the sails; no doubt, sometimes sailing with the wind, even no further forward than the beam, must be performed with this unfavourable trim of the sails, as it must be in all cases if plying to windward. We are certain that the smaller we make the angle of incidence, real or apparent, the smaller will be the velocity of the ship; but it may happen that we shall gain more to windward, or get sooner away from a lee-coast, or any object of danger, by sailing slowly on one course than by sailing quickly on another.

We have seen that while the trim of the sails remains the same, the leeway and the angle of the yard and course remains the same, and that the velocity of the ship is as the sine of the angle of real incidence, that is, as the sine of the angle of the sail and the real direction of the wind.

Let the ship AB (fig. 8) hold the course CF, with the wind blowing in the direction WC, and having her yards DCD braced up to the smallest angle BCD which the rigging can admit. Let CF be to CE as the velocity of the

ship to the velocity of the wind; join FE and draw $Ce$ parallel to $EF$; it is evident that $FE$ is the relative motion of the wind, and $ce$ is the relative incidence on the sail.

Draw $FO$ parallel to the yard $DC$, and describe a circle through the points $COF$; then we say that if the ship, with the same wind and the same trim of the same drawing sails, be made to sail on any other course $Cf$, her velocity along $CF$ is to the velocity along $Cf$ as $CF$ is to $Cf$; or, in other words, the ship will employ the same time in going from $C$ to any point of the circumference $CFO$.

Join $fO$. Then, because the angles $CFO$, $CfO$ are on the same cord $CO$, they are equal, and $fO$ is parallel to $dCd$, the new position of the yard corresponding to the new position of the keel $ab$, making the angle $dCb\; =\; DCB$. Also, by the nature of the circle, the line $CF$ is to $Cf$ as the sine of the angle $CFO$ to the sine of the angle $COf$, that is (on account of the parallels $CD$, $OF$ and $Cd$, $Of$), as the sine of $WCD$ to the sine of $WCd$. But when the trim of the sails remains the same, the velocity of the ship is as the sine of the angle of the sail with the direction of the wind; therefore $CF$ is to $Cf$ as the velocity on $CF$ to that on $Cf$, and the proposition is demonstrated.

Let it now be required to determine the best course for avoiding a rock $R$ lying in the direction $CR$, or for withdrawing as fast as possible from a line of coast $PQ$. Draw $CM$ through $R$, or parallel to $PQ$, and let $m$ be the middle of the arch $CmM$. It is plain that $m$ is the most remote from $CM$ of any point of the arch $CmM$, and therefore the ship will recede farther from the coast $PQ$ in any given time, by holding the course $Cm$ than by any other course.

This course is easily determined; for the arch $CmM\; =\; 360^\backslash circ\; -\; (\backslash text\{arch\; \}\; CO\; +\; \backslash text\{arch\; \}\; OM)$, and the arch $CO$ is the measure of twice the angle $CFO$, or twice the angle $DCB$, or twice $b+x$, and the arch $OM$ measures twice the angle $ECM$.

Thus, suppose the sharpest possible trim of the sails to be $35^\backslash circ$, and the observed angle $ECM$ to be $70^\backslash circ$; then $CO\; +\; OM\; =\; 70^\backslash circ\; +\; 140^\backslash circ$ or $210^\backslash circ$. This being taken from $360^\backslash circ$, leaves $150^\backslash circ$, of which the half $Mm$ is $75^\backslash circ$, and the angle $MCm$ is $37^\backslash circ\; 30\text{'}$. This added to $ECM$ makes $ECm\; =\; 170^\backslash circ\; 30\text{'}$, leaving $WCm\; =\; 72^\backslash circ\; 30\text{'}$, and the ship must hold a course making an angle of $72^\backslash circ\; 30\text{'}$ with the real direction of the wind, and $WCD$ will be $37^\backslash circ\; 30\text{'}$.

This supposes no leeway. But if we know that under all the sail which the ship can carry with safety and advantage she makes 5 degrees of leeway, the angle $DCm$ of the sail and course, or $b+x$, is $40^\backslash circ$. Then $CO\; +\; OM\; =\; 220^\backslash circ$, which being taken from $360^\backslash circ$, leaves $140^\backslash circ$, of which the half is $70^\backslash circ$, $=\; Mm$, and the angle $MCm\; =\; 35^\backslash circ$, and $ECm\; =\; 105^\backslash circ$, and $WCm\; =\; 75^\backslash circ$, and the ship must lie with her head $70^\backslash circ$ from the wind, making 5 degrees of leeway, and the angle $WCD$ is $35^\backslash circ$.

The general rule for the position of the ship is, that the line on shipboard which bisects the angle $b+x$ may also bisect the angle $WCM$, or make the angle between the course and the line, from which we wish to withdraw, equal to the angle between the sail and the real direction of the wind.

It is plain that this problem includes that of plying to windward. We have only to suppose $ECM$ to be $90^\backslash circ$; then, taking our example in the same ship, with the same trim and the same leeway, we have $b+x\; =\; 40^\backslash circ$. This taken from $90^\backslash circ$ leaves $50^\backslash circ$, and $WCm\; =\; 90^\backslash circ\; -\; 25^\backslash circ\; =\; 65^\backslash circ$, and the ship's head must lie $60^\backslash circ$ from the wind, and the yard must be $25^\backslash circ$ from it.

It must be observed here, that it is not always eligible to select the course which will remove the ship fastest from the given line $CM$; it may be more prudent to remove from it more securely though more slowly. In such cases the procedure is very simple, viz., to shape the course as near the wind as is possible.

The reader will also easily see that the propriety of these practices is confined to those courses only where the practicable trim of the sails is not sufficiently sharp. Whenever the course lies so far from the wind that it is possible to make the tangent of the apparent angle of the wind and sail double the tangent of the sail and course, it should be done.

These are the chief practical consequences which can be deduced from the theory. But we should consider how far the adjustment of the sails and course can be performed. And here occur difficulties so great as to make it almost impracticable. We have always supposed the position of the surface of the sail to be distinctly observable and measurable; but this can be hardly affirmed even with respect to a sail stretched on a yard. Here we supposed the surface of the sail to have the same inclination to the keel that the yard has. This is by no means the case; the sail assumes a concave form, of which it is almost impossible to assign the direction of the mean impulse. We believe that this is always considerably to leeward of a perpendicular to the yard, lying between $CI$ and $CE$ (fig. 6). This is of some advantage, being equivalent to a sharper trim. We cannot affirm this, however, with any confidence, because it renders the impulse on the weather-leech of the sail so exceedingly feeble as hardly to have any effect. In sailing close to the wind, the ship is kept so near that the weather-leech of the sail is almost ready to receive the wind edge-wise, and to flutter or shiver. The most effective or drawing sails with a side-wind, especially when plying to windward, are the trysails. We believe that it is impossible to say, with anything approaching to precision, what is the position of the general surface of a staysail, or to calculate the intensity and direction of the general impulse; and we affirm with confidence that no man can pronounce on these points with any exactness. If we can guess within a third or a fourth part of the truth, it is all we can pretend to; and after all, it is but a guess. Add to this, the sails coming in the way of each other, and either becalming them or sending the wind upon them in a direction widely different from that of its free motion. All these points we think beyond our power of calculation, and therefore that it is in vain to give the seaman mathematical rules, or even tables of adjustment ready calculated; since he can neither produce that medium position of his sails that is required, nor tell what is the position which he employs.

This is one of the principal reasons why so little advantage has been derived from the very ingenious and promising disquisitions of Bouguer and other mathematicians.

We subjoin an abstract of the experiments made by the Royal Academy of Sciences at Paris. Column 1st gives the angle of incidence; column 2d gives the impulses really observed; column 3d the impulses, had they followed the duplicate ratio of the sines; and column 4th the impulses, if they were in the simple ratio of the sines.

Seaman-
ship. Here we see an enormous difference in the great obliquities. When the angle of incidence is only six degrees, the observed impulse is forty times greater than the theoretical impulse; at 12° it is ten times greater; at 18° it is more than four times greater; and at 24° it is almost three times greater.

No wonder then that the deductions from this theory are so useless and so unlike what we familiarly observe. We took notice of this when we were considering the leeway of a rectangular box, and thus saw a reason for admitting an incomparably smaller leeway than what would result from the laborious computations necessary by the theory. This error in theory has as great an influence on the impulses of air when acting obliquely on a sail; and the experiments of Mr Robins and of the Chevalier Borda, on the oblique impulses of air, are perfectly conformable (as far as they go) to those of the academicians on water. The oblique impulses of the wind are therefore much more efficacious for pressing the ship in the direction of her course than the theory allows us to suppose; and the progress of a ship plying to windward is much greater, both because the oblique impulses of the wind are more effective, and because the leeway is much smaller, than we suppose. Were not this the case, it would be impossible for a square-rigged ship to get to windward. The impulse on her sails, when close hauled, would be so trifling, that she would not have a third part of the velocity which we see her acquire; and this trifling velocity would be wasted in leeway; for we have seen that the diminution of the oblique impulses of the water is accompanied by an increase of leeway. But we see that in the great obliquities the impulses continue to be very considerable, and that even an incidence of 6° gives an impulse as great as the theory allows to an incidence of 40°. We may, therefore, on all occasions keep the yards more square; and the loss which we sustain by the diminution of the very oblique impulse will be more than compensated by its more favourable direction with respect to the ship's keel. Let us take an example of this. Suppose the wind about two points before the beam, making an angle of 68° with the keel. The theory assigns 43° for the inclination of the wind to the sail, and 15° for the trim of the sail. The perpendicular impulse being supposed 1000, the theoretical impulse for 45° is 465. This reduced in the proportion of radius to the sine of 25°, gives the impulse in the direction of the course only 197.

But if we ease off the lee-braces till the yard makes an angle of 50° with the keel, and allows the wind an incidence of no more than 18°, we have the experimented impulse 414, which, when reduced in the proportion of radius to the sine of 50°, gives an effective impulse 317. In like manner, the trim 56°, with the incidence 12°, gives an effective impulse 337; and the trim of 62°, with the incidence only 6°, gives 353.

Hence it would at first sight appear that the angle DCB of 62° and WCD of 6° would be better for holding a course within six points of the wind than any more oblique position of the sails; but it will only give a greater initial impulse. As the ship accelerates, the wind apparently comes ahead, and we must continue to brace up as a ship freshens her way. It is not unusual for her to acquire half or two-thirds of the velocity of the wind; in which case the wind comes apparently ahead more than two points, when the yards must be braced up to 35°, and thus allows an impulse no greater than about 7°. Now, this is very frequently observed in good ships, which, in a brisk gale and smooth water, will go five or six knots close-hauled, the ship's head six points from the wind, and the sails no more than just full, but ready to shiver by the smallest luff. All this would be impossible by the usual theory; and in this respect these experiments of the French Academy give a fine illustration of the seaman's practice. They account for

what we should otherwise be much puzzled to explain; and the great progress which is made by a ship close-hauled being perfectly agreeable to what we should expect from the law of oblique impulses, deducible from these so often-mentioned experiments, while it is totally incompatible with the common theory, should make us abandon the theory without hesitation, and strenuously set about the establishment of another, founded entirely on experiments. For this purpose the experiments should be made on the Experimental impulses of air, on as great a scale as possible, and in as great a variety of circumstances, so as to furnish a series of impulses for all angles of obliquity. We have but four or five experiments on this subject, viz., two by Mr Robins, and two or three by the Chevalier Borda. Having thus gotten a series of impulses, it is very practicable to raise on this foundation a practical institute, and to give a table of the velocities of a ship suited to every angle of inclination and of trim; for nothing is more certain than the resolution of the impulse perpendicular to the sail into a force in the direction of the keel, and a lateral force.

We are also disposed to think that experiments might be made on a model very nicely rigged with sails, and trimmed in every different degree, which would point out the mean direction of the impulse on the sails, and the comparative force of these impulses on different directions of the wind. The method would be very similar to that for examining the impulse of the water on the hull. If this can also be ascertained experimentally, the intelligent reader will easily see that the whole motion of a ship under sail may be determined for every case. Tables may then be constructed by calculation, or by graphical operations, which will give the velocities of a ship in every different course, and corresponding to every trim of sail. And let it be here observed, that the trim of the sail is not to be estimated in degrees of inclination of the yards; because, as we have already remarked, we cannot observe nor adjust the fore and aft sails in this way. But, in making the experiments for ascertaining the impulse, the exact position of the tacks and sheets of the sails are to be noted; and this combination of adjustments is to pass by the name of a certain trim. Thus that trim of all the sails may be called 40, whose direction is experimentally found equivalent to a flat surface trimmed to the obliquity 40°.

Having done this, we may construct a figure for each trim similar to fig. 8, where, instead of a circle, we shall have a curve COMF, whose cords CF, ef, &c., are proportional to the velocities in these courses; and by means of this curve we can find the point m, which is most remote from any line CM from which we wish to withdraw; and thus we may solve all the principal problems of the art.

We hope that it will not be accounted presumption in us to expect more improvement from a theory founded on judicious experiments only, than from a theory of the impulse of fluids, which is found so inconsistent with observation, and of whose fallacy all its authors, from Newton to D'Alembert, entertained strong suspicions.

With those observations we conclude our discussion of the first part of the seaman's task, and now proceed to consider the means that are employed to prevent or to produce any deviations from the uniform rectilinear course which has been selected.

Here the ship is to be considered as a body in free space, convertible round her centre of inertia. For whatever may be the point round which she turns, this motion may always be considered as compounded of a rotation round an axis passing through her centre of gravity or inertia. She is impelled by the wind and by the water acting on many surfaces differently inclined to each other, and the impulse on each is perpendicular to the surface. In order, therefore, that she may continue steadily in one course, it is not only necessary that the impelling forces, estimated in their

mean direction, be equal and opposite to the resisting forces estimated in their mean direction; but also that these two directions may pass through one point, otherwise she will be affected as a log of wood is when pushed in opposite directions by two forces, which are equal indeed, but are applied to different parts of the log. A ship must be considered as a lever, acted on in different parts by forces in different directions, and the whole balancing each other round that point or axis where the equivalent of all the resisting forces passes. This may be considered as a point supported by this resisting force and as a sort of fulcrum; therefore, in order that the ship may maintain her position, the energies or momenta of all the impelling forces round this point must balance each other.

When a ship sails right before the wind, with her yards square, it is evident that the impulses on each side of the keel are equal, as also their mechanical momenta round any axis passing perpendicularly through the keel. So are the actions of the water on her bows. But when she sails on an oblique course, with her yards braced on either side, she sustains a pressure in the direction CI (fig. 5) perpendicular to the sail. This, by giving her a lateral pressure LI, as well as a pressure CI, ahead, causes her to make leeway, and to move in a line Cb inclined to CB. By this means the balance of action on the two bows is destroyed, the general impulse on the lee-bow is increased, and that on the weather-bow is diminished. The combined impulse is therefore no longer in the direction BC, but (in the state of uniform motion) in the direction IC.

Suppose that in an instant the whole sails are annihilated and the impelling pressure CI, which precisely balanced the resisting pressure on her bows, removed. The ship tends, by her inertia, to proceed in the direction Cb. This tendency produces a continuation of the resistance in the opposite direction IC, which is not directly opposed to the tendency of the ship in the direction Cb; therefore the ship's head would immediately come up to the wind. The experienced seaman will recollect something like this when the sails are suddenly lowered when coming to anchor. It does not happen solely from the obliquity of the action on the bows. It would happen to the parallelopiped of fig. 2, which was sustaining a lateral impulsion $B\; \backslash cdot\; \backslash sin^2\; x$, and a direct impulsion $A\; \backslash cdot\; \backslash cos^2\; x$. These are continued for a moment after the annihilation of the sail; but being no longer opposed by a force in the direction CD, but by a force in the direction Cb, the force $B\; \backslash cdot\; \backslash sin^2\; x$ must prevail, and the body is not only retarded in its motion, but its head turns towards the wind. But this effect of the leeway is greatly increased by the curved form of the ship's bows. This occasions the centre of effort of all the impulses of the water on the leeward side of the ship to be very far forward, and this so much the more remarkably as she is sharper before. It is in general not much abaft the foremast. Now the centre of the ship's tendency to continue her motion is the same with her centre of gravity, and this is generally but a little before the mainmast. She is therefore in the same condition nearly as if she were pushed at the mainmast in a direction parallel to Cb, and at the foremast by a force parallel to IC. The evident consequence of this is a tendency to come up to the wind. This is independent of all situation of the sails, provided only that they have been trimmed obliquely.

In the generality of ships sailing in smooth water, there is a tendency in their heads to approach the wind, which must be counteracted by keeping the helm a little a-weather. This tendency is greatest in ships that are sharp forward. This circumstance is easily understood. Whatever is the direction of the ship's motion, the absolute impulse on that part of the bow immediately contiguous to B is perpendicular to that very part of the surface. The more acute, therefore, that the angle of the

bow is, the more will the impulse on that part be perpendicular to the keel, and the greater will be its energy to turn the head to windward.

Thus we are enabled to understand or to see the propriety of the disposition of the sails of a ship. We see of the ship crowded with sails forward, and even many sails extended far before her bow, such as the fore-topmast staysail, the jib, and flying jib. The sails abaft are comparatively smaller. The sails on the mizzenmast are much smaller than those on the foremast. All the staysails hoisted on the mainmast may be considered as headsails, because their centres of effort are considerably before the centre of gravity of the ship; and notwithstanding this disposition, it generally requires a small action of the rudder to counteract the windward tendency of the lee-bow. This is considered as a good quality when moderate, because it enables the seaman to throw the sails aback, and stop the ship's way in a moment, if she be in danger from anything ahead; and the ship which does not carry a little of a weather helm is always a dull sailor.

In order to judge somewhat more accurately of the action of the water and sails, suppose the ship AB (fig. 9) to have its sails on the mizzenmast D, the mainmast E, and the foremast F, braced up or trimmed alike, and the three lines Di, Ee, Ff, perpendicular to the sails, are in the proportion of the impulses on the sails. The ship is driven a-head and to leeward, and moves in the path aCb.

This path is so inclined to the line of the keel, that the medium direction of the resistance of the water is parallel to the direction of the impulse. A line CI may be drawn parallel to the lines Di, Ee, Ff, and equal to their sum; and it may be drawn from such a point C, that the actions on all the parts of the hull between C and B may balance the momenta of all the actions on the hull between C and A. This point may justly be called the centre of effort, or the centre of resistance. We cannot determine this point for want of a proper theory of the resistance of fluids. Nay, although experiments like those of the Parisian Academy should give us the most perfect knowledge of the intensity of the oblique impulses on a square foot, we should hardly be benefited by them; for the action of the water on a square foot of the hull at $p$, for instance, is so modified by the intervention of the stream of water which has struck the hull about B, and glided along the bow Bop, that the pressure on $p$ is totally different from what it would have been were it a square foot or surface detached from the rest, and presented in the same position to the water moving in the direction BC. For it is found, that the resistances given to planes joined so as to form a wedge, or to curved surfaces, are widely different from the accumulated resistances calculated for their separate parts, agreeably to the experiments of the academy on single surfaces. We therefore do not attempt to ascertain the point C by theory; but it may be accurately determined by the experiments which we have so strongly recommended, and we offer this as an additional inducement for prosecuting them.

Draw through C a line perpendicular to CI, that is, parallel to the sails; and let the lines of impulse of the three sails cut in the points $i$, $k$, and $m$. This line $im$ may be considered as a lever, moveable round C, and acted on at the points $i$, $k$, and $m$, by three forces. The rotatory momentum of the sails on the mizzenmast is $D\; i\; \backslash times\; i\; C$; that of the sails on the mainmast is $E\; e\; \backslash times\; k\; C$; and the momentum of the sails on the foremast is $F\; f\; \backslash times\; m\; C$. The two first tend to press forward the arm Ci, and then to turn the ship's head towards the wind. The action of the sails on the foremast tends to pull the arm Cm forward, and produce a

Seaman-
ship. contrary rotation. If the ship under these three sails keeps steadily in her course, without the aid of the rudder, we must have $D\; i\; \backslash times\; i\; C\; +\; E\; e\; \backslash times\; k\; C\; =\; F\; f\; \backslash times\; m\; C$. This is very possible, and is often seen in a ship under her mizen-topsail, main-topsail, and fore-topsail, all parallel to one another, and their surfaces duly proportioned by reefing. If more sails are set, we must always have a similar equilibrium. A certain number of them will have their efforts directed from the larboard arm of the lever $i\; m$ lying to leeward of $C\; I$, and a certain number will have their efforts directed from the starboard arm lying to windward of $C\; I$. The sum of the products of each of the first set, by their distances from $C$, must be equal to the sum of the similar products of the other set. As this equilibrium is all that is necessary for preserving the ship's position, and the cessation of it is immediately followed by a conversion; and as these states of the ship may be had by means of the three square sails only, when their surfaces are properly proportioned, it is plain that every movement may be executed and explained by their means. This will greatly simplify our future discussions. We shall therefore suppose in future that there are only the three topsails set, and that their surfaces are so adjusted by reefing, that their actions exactly balance each other round that point $C$ of the middle line $A\; B$, where the actions of the water on the different parts of the ship's bottom in like manner balance each other. This point $C$ may be differently situated in the ship according to the leeway she makes, depending on the trim of the sails; and, therefore, although a certain proportion of the three surfaces may balance each other in one state of leeway, they may happen not to do so in another state. But the equilibrium is evidently attainable in every case, and we therefore shall always suppose it.

Conse-
quence of
destroying
it. It must now be observed, that when this equilibrium is destroyed, as, for example, by turning the edge of the mizen-topsail to the wind, which the seamen call shivering the mizen-topsail, and which may be considered as equivalent to the removing the mizen-topsail entirely, it does not follow that the ship will turn round the point $C$, this point remaining fixed. The ship must be considered as a free body, still acted on by a number of forces, which no longer balance each other; and she must therefore begin to turn round a spontaneous axis of conversion, which must be determined in the way set forth in the article ROTATION. It is of importance to point out in general where this axis is situated. Therefore let $G$

(fig. 10) be the centre of gravity of the ship. Draw the line $q\; G\; v$ parallel to the yards, cutting $D\; d$ in $q$, $E\; e$ in $r$, $C\; I$ in $t$, and $F\; f$ in $v$. While the three sails are set, the line $q\; v$ may be considered as a lever acted on by four forces, viz., $D\; d$, impelling the lever forward perpendicularly in the point $q$; $E\; e$, impelling it forward in the point $r$; $F\; f$, impelling it forward in the point $v$; and $C\; I$, impelling it backward in the point $t$. These forces balance each other both in respect of progressive motion and of rotatory energy; for $C\; I$ was taken equal to the sum of $D\; d$, $E\; e$, and $F\; f$; so that no acceleration or retardation of the ship's progress in her course is supposed.

But by taking away the mizen-topsail, both the equilibriums are destroyed. A part $D\; d$ of the accelerating force is taken away; and yet the ship, by her inertia or inherent force, tends, for a moment, to proceed in the direction $C\; p$ with her former velocity; and by this tendency exerts for a moment the same pressure $C\; I$ on the water, and sustains the same resistance $C\; I$. She must therefore be retarded in her motion by the excess of the resistance $C\; I$ over the re-

maining impelling forces $E\; e$ and $F\; f$; that is, by a force equal and opposite to $D\; d$. She will therefore be retarded in the same manner as if the mizen-topsail were still set, and a force equal and opposite to its action were applied to $G$, the centre of gravity, and she would soon acquire a smaller velocity, which would again bring all things into equilibrium; and she would stand on in the same course, without changing either her leeway or the position of her head.

But the equilibrium of the lever is also destroyed. It is now acted on by three forces only, viz., $E\; e$ and $F\; f$, impelling it forward in the points $r$ and $v$, and $C\; I$ impelling it backward in the point $t$. Make $r\; v\; :\; r\; o\; =\; E\; e\; +\; F\; f\; :\; F\; f$, and make $o\; p$ parallel to $C\; I$ and equal to $E\; e\; +\; F\; f$. Then we know, from the common principles of mechanics, that the force $o\; p$ acting at $o$ will have the same momentum or energy to turn the lever round any point whatever as the two forces $E\; e$ and $F\; f$ applied at $r$ and $v$; and now the lever is acted on by two forces, viz., $C\; I$, urging it backwards in the point $t$, and $o\; p$ urging it forwards in the point $o$. It must therefore turn round like a floating log, which gets two blows in opposite directions. If we now make $C\; I\; :\; o\; p\; =\; t\; o\; :\; t\; x$, or $C\; I\; :\; o\; p\; =\; t\; o\; :\; o\; x$, and apply to the point $x$ a force equal to $C\; I\; -\; o\; p$ in the direction $C\; I$; we know by the common principles of mechanics, that this force $C\; I\; -\; o\; p$ will produce the same rotation round any point as the two forces $C\; I$ and $o\; p$ applied in their proper directions at $t$ and $o$. Let us examine the situation of the point $x$.

The force $C\; I\; -\; o\; p$ is evidently $=\; D\; d$, and $o\; p\; =\; E\; e\; +\; F\; f$. Therefore $o\; t\; :\; t\; x\; =\; D\; d\; :\; o\; p$. But because, when all the sails were filled, there was an equilibrium round $C$, and therefore round $t$, and because the force $o\; p$ acting at $o$ is equivalent to $E\; e$ and $F\; f$ acting at $r$ and $v$, we must still have the equilibrium; and therefore we have the momentum $D\; d\; \backslash times\; q\; t\; =\; o\; p\; \backslash times\; o\; t$. Therefore $o\; t\; :\; t\; q\; =\; D\; d\; :\; o\; p$, and $t\; q\; =\; t\; x$. Therefore the point $x$ is the same with the point $q$.

Therefore, when we shiver the mizen-topsail, the rotation By shiver-
of the ship is the same as if the ship were at rest, and if a ing the
force equal and opposite to the action of the mizen-topsail
were applied at $q$ or at $D$, or any point on the line $D\; q$. sail.

This might have been shown in another and shorter way. Suppose all sails filled, the ship is in equilibrio. This will be disturbed by applying to $D$ a force opposite to $D\; d$; and if the force be also equal to $D\; d$, it is evident that these two forces destroy each other, and that this application of the force $D\; d$ is equivalent to the taking away of the mizen-topsail. But we chose to give the whole mechanical investigation; because it gave us an opportunity of pointing out to the reader, in a case of very easy comprehension, the precise manner in which the ship is acted on by the different sails and by the water, and what share each of them has in the motion ultimately produced. We shall not repeat this manner of procedure in other cases, because a little reflection on the part of the reader will now enable him to trace the modus operandi through all its steps.

We now see that, in respect both of progressive motion and of conversion, the ship is affected by shivering the sail $D$, in the same manner as if a force equal and opposite to $D\; d$ were applied at $D$, or at any point in the line $D\; d$.

Let $p$ represent a particle of matter, $r$ its radius vector, or its distance $p\; G$ from an axis passing through the centre of gravity $G$, and let $M$ represent the whole quantity of matter of the ship. Then its momentum of inertia is $\backslash int\; p\; r^2$. The ship, impelled in the point $D$ by a force in the direction $d\; D$, will begin to turn round a spontaneous vertical axis, passing through a point $S$ of the line $q\; G$, which is drawn through the centre of gravity $G$, perpendicular to the direction $d\; D$ of the external force, and the distance $G\; S$ of this axis from the centre of gravity is $\backslash frac\{\backslash int\; p\; r^2\}\{M\; \backslash cdot\; G\; q\}$, and it is taken on the opposite side of $G$ from $q$, that is, $S$ and $q$ are on opposite sides of $G$.

Seaman-ship. Let us express the external force by the symbol $F$. It is equivalent to a certain number of pounds, being the pressure of the wind moving with the velocity $V$ and inclination $\backslash alpha$ on the surface of the sail $D$; and may therefore be computed either by the theoretical or experimental law of oblique impulses. Having obtained this, we can ascertain the angular velocity of the rotation and the absolute velocity of any given point of the ship by means of the theorems established in the article ROTATION.

Action of the rudder. But before we proceed to this investigation, we shall consider the action of the rudder, which operates precisely in the same manner. Let the ship $AB$ (fig. 11) have her rudder in the position $AD$, the helm being hard a-starboard, while the ship sailing on the starboard tack, and making leeway, keeps on the course $ab$. The lee surface of the rudder meets the water obliquely. The very foot of the rudder meets it in the direction $DE$ parallel to $ab$. The parts farther up meet it with various obliquities, and with various velocities, as it glides round the bottom of the ship and falls into the wake. It is absolutely impossible to calculate the accumulated impulse. We shall not be far mistaken in the deflection of each contiguous filament, as it quits the bottom and glides along the rudder; but we neither know the velocity of these filaments, nor the deflection and velocity of the filaments gliding without them. We therefore imagine that all computations on the subject are in vain. But it is enough for our purpose that we know the direction of the absolute pressure which they exert on its surface. It is in the direction $Dd$, perpendicular to that surface. We also may be confident that this pressure is very considerable, in proportion to the action of the water on the ship's bows, or of the wind on the sails; and we may suppose it to be nearly in the proportion of the square of the velocity of the ship in her course; but we cannot affirm it to be accurately in that proportion, for reasons that will readily occur to one who considers the way in which the water falls in behind the ship.

Greatest in a fine sailer. It is observed, however, that a fine sailer always steers well, and that all movements by means of the rudder are performed with great rapidity when the velocity of the ship is great. We shall see by and by, that the speed with which the ship performs the angular movements is in the proportion of her progressive velocity: for we shall see that the squares of the times of performing the revolution are as the impulses inversely, which are as the squares of the velocities. There is perhaps no force which acts on a ship that can be more accurately determined by experiment than this. Let the ship ride in a stream or tideway whose velocity is accurately measured; and let her ride from two moorings, so that her bow may be a fixed point. Let a small tow line be laid out from her stern or quarter at right angles to the keel, and connected with some apparatus fitted up on shore or on board another ship, by which the strain on it may be accurately measured; a person conversant with mechanics will see many ways in which this can be done. Perhaps the following may be as good as any: let the end of the tow-line be fixed to some point as high out of the water as the point of the ship from which it is given out, and let this be very high. Let a block with a hook be on the rope, and a considerable weight hung on this hook. Things being thus prepared, put down the helm to a certain angle, so as to cause the ship to shear off from the point to which the far end of the tow-line is attached. This will stretch the rope, and raise the weight out of the water. Now heave upon the rope, to bring the ship back again to her former position, with her keel in the direction of the stream. When this position is attained, note carefully the form of the rope,

How to determine it.

that is, the angle which its two parts make with the horizon. Call this angle $\backslash alpha$. Every person acquainted with these subjects knows that the horizontal strain is equal to half the weight multiplied by the cotangent of $\backslash alpha$, or that 2 is to the cotangent of $\backslash alpha$ as the weight to the horizontal strain. Now it is this strain which balances, and therefore measures the action of the rudder, or $De$ in fig. 11. Therefore, to have the absolute impulse $Dd$, we must increase $De$ in the proportion of radius to the secant of the angle $b$, which the rudder makes with the keel. In a great ship sailing six miles in an hour, the impulse on the rudder inclined $30^\backslash circ$ to the keel is not less than 3000 pounds. The surface of the rudder of such a ship contains nearly 80 square feet. It is not, however, very necessary to know this absolute impulse $Dd$, because it is its parts $De$ alone which measure the energy of the rudder in producing a conversion. Such experiments, made with various positions of the rudder, will give its energies corresponding to these positions, and will settle that long disputed point, which is the best position for turning a ship. On the hypothesis that the impulses of fluids are in the duplicate ratio of the sines of incidence, there can be no doubt that it should make an angle of $54^\backslash circ\; 44\text{'}$ with the keel, being about the angle with the keel that the rudder can be put over in modern ships; the angle of maximum effect assigned by theory.

A ship misses stays in rough weather for want of a sufficient progressive velocity, and because her bows are beat off by the waves; and there is seldom any difficulty in wearing the ship, if she has any progressive motion. It is, however, always desirable to give the rudder as much influence as possible. Its surface should be enlarged (especially below) as much as can be done consistently with its strength, and with the power of the steersman to manage it; and it should be put in the most favourable situation for the water to get at it with great velocity; and it should be placed as far from the axis of the ship's motion as possible. In order to ascertain the motion produced by the action of the rudder, draw from the centre of gravity a line $Gq$ perpendicular to $Dd$ ($Dd$ being drawn through the centre of effort of the rudder). Then, as in the consideration of the action of the sails, we may conceive the line $Gq$ as a lever connected with the ship, and impelled by a force $Dd$ acting perpendicularly at $q$. The consequence of this will be, an incipient conversion of the ship about a vertical axis passing through some point $S$ in the line $Gq$, lying on the other side of $G$ from $q$;

and we have, as in the former case, $GS\; =\; \backslash frac\{\backslash int\; p\; \backslash cdot\; r^2\}\{M\; \backslash cdot\; Gq\}$.

Thus the action and effects of the sails and of the rudder are perfectly similar, and are to be considered in the same manner. We see that the action of the rudder, though of a small surface in comparison of the sails, must be very great: for the impulse of water is many hundred times and very greater than that of the wind; and the arm $Gq$ of the lever, by which it acts, is incomparably greater than that by which any of the impulses on the sails produces its effect; accordingly, the ship yields much more rapidly to its action than she does to the lateral impulse of a sail.

Observe here, that if $G$ were a fixed or supported axis, it would be the same thing whether the absolute force $Dd$ of the rudder acts in the direction $Dd$, or its transverse parts $De$ act in the direction $De$, both would produce the same rotation; but it is not so in a free body. The force $Dd$ both tends to retard the ship's motion and to produce a rotation: it retards it as much as if the same force $Dd$ had been immediately applied to the centre. And thus the real motion of the ship is compounded of a motion of the centre in a direction parallel to $Dd$, and of a motion round the centre. These two constitute the motion round $S$.

As the effects of the action of the rudder are both more

remarkable and somewhat more simple than those of the sails, we shall employ them as an example of the mechanism of the motions of conversion in general; and as we must content ourselves, in a work like this, with what is very general, we shall simplify the investigation by attending only to the motion of conversion. We can get an accurate notion of the whole motion, if wanted for any purpose, by combining the progressive or retrograde motion parallel to $Dd$ with the motion of rotation which we are about to determine.

In this case, then, we observe, in the first place, that the angular velocity is $\backslash frac\{Dh\; \backslash cdot\; qG\}\{\backslash int\; pr^2\}$; and, as was shown in ROTATION,

this velocity of rotation increases in the proportion of the time of the forces' uniform action, and the rotation would be uniformly accelerated if the forces did really act uniformly. This, however, cannot be the case, because, by the ship's change of position and change of progressive velocity, the direction and intensity of the impelling force is continually changing. But if two ships are performing similar evolutions, it is obvious that the changes of force are similar in similar parts of the evolution. Therefore the consideration of the momentary evolution is sufficient for enabling us to compare the motions of ships actuated by similar forces, which is all we have in view at present. The velocity $v$, generated in any time $t$ by the continuance of an invariable momentary acceleration (which is all that we mean by saying that it is produced by the action of a constant accelerating force), is as the acceleration and the time jointly. Now, what we call the angular velocity is nothing but this momentary acceleration. Therefore the

velocity $v$, generated in the time $t$, is $\backslash frac\{F\; \backslash cdot\; qG\}\{\backslash int\; pr^2\}\; t$.

The expression of the angular velocity is also the expression of the velocity $v$ of a point situated at the distance $l$ from the axis $G$.

Let $z$ be the space or arch of revolution described in the time $t$ by this point, whose distance from $G$ is $l$.

Then $z\; =\; \backslash dot\{z\}t\; =\; \backslash frac\{F\; \backslash cdot\; qG\}\{\backslash int\; pr^2\}\; t^2$, and taking the fluent $z\; =\; \backslash frac\{F\; \backslash cdot\; qG\}\{\backslash int\; pr^2\}\; t^2$.

This arch measures the whole angle of rotation accomplished in the time $t$. These are, therefore, as the squares of the times from the beginning of the rotation.

Those evolutions are equal which are measured by equal arches. Thus two motions of 45 degrees each are equal. Therefore because $z$ is the same in both, the quantity

$\backslash frac\{F\; \backslash cdot\; qG\}\{\backslash int\; pr^2\}\; t^2$ is a constant quantity, and $t^2$ is reciprocally pro-

portional to $\backslash frac\{F\; \backslash cdot\; qG\}\{\backslash int\; pr^2\}$, or is proportional to $\backslash frac\{\backslash int\; pr^2\}\{F\; \backslash cdot\; qG\}$, and $t$ is

proportional to $\backslash frac\{\backslash sqrt\{\backslash int\; pr^2\}\}\{\backslash sqrt\{F\; \backslash cdot\; qG\}\}$. That is to say, the times of the

similar evolutions of two ships are as the square root of the momentum of inertia directly, and as the square root of the momentum of the rudder or sail inversely. This will enable us to make the comparison easily. Let us suppose the ships perfectly similar in form and rigging, and to differ only in length $L$ and $l$; $\backslash int\; P\; \backslash cdot\; R^2$ is to $\backslash int\; p\; \backslash cdot\; r^2$ as $L^2$ to $l^2$. For the similar particles $P$ and $p$ contain quantities of matter which are as the cubes of their lineal dimensions; that is, as $L^3$ to $l^3$. And because the particles are similarly situated, $R^2$ is to $r^2$ as $L^2$ to $l^2$. Therefore $P\; \backslash cdot\; R^2\; :\; p\; \backslash cdot\; r^2\; =\; L^2\; :\; l^2$. Now $F$ is to $f$ as $L^2$ to $l^2$. For the surfaces of the similar rudders or sails are as the squares of their lineal dimensions; that is, as $L^2$ to $l^2$. And lastly, $Gq$ is to $gq$ as $L$ to $l$, and therefore $F\; \backslash cdot\; Gq\; :\; f\; \backslash cdot\; gq\; =\; L^2\; :\; l^2$. Therefore we have $T^2\; :\; t^2\; =$

Therefore the times of performing similar evolutions with similar ships are proportional to the lengths of the ships when both are sailing equally fast; and since the evolutions are similar, and the forces vary similarly in their different parts, what is here demonstrated of the smallest incipient evolutions is true of the whole. They therefore not only describe equal angles of revolution, but also similar curves.

A small ship, therefore, works in less time and in less room than a great ship, and this in the proportion of its length. This is a great advantage in all cases, particularly in wearing, in order to sail on the other tack close-hauled. In this case she will always be to windward and ahead of the large ship, when both are got on the other tack. It would appear at first sight that the large ship will have the advantage in tacking. Indeed the large ship is farther to windward when again trimmed on the other tack than the small ship when she is just trimmed on the other tack. But this happened before the large ship had completed her evolution, and the small ship, in the meantime, has been going forward on the other tack, and going to windward. She will therefore be before the large ship's beam, and perhaps as far to windward.

We have seen that the velocity of rotation is proportional, ceteris paribus, to $F\; \backslash times\; Gq$. $F$ means the absolute impulse on the rudder or sail, and is always perpendicular to its surface. This absolute impulse on a sail depends on the obliquity of the wind to its surface. The usual theory says, that it is as the square of the sine of incidence; but we find this not true. We must content ourselves with expressing it by some as yet unknown function $\backslash phi$ of the angle of incidence $a$, and call it $\backslash phi\; a$; and if $S$ be the surface of the sail, and $V$ the velocity of the wind, the absolute impulse is $nV^2S\; \backslash times\; \backslash phi\; a$. This acts (in the case of the mizen-topsail, fig. 10) by the lever $qG$, which is equal to $DG\; \backslash times\; \backslash cos\; DGq$, and $DGq$ is equal to the angle of the yard and keel; which angle we formerly called $b$. Therefore its energy in producing a rotation is $nV^2S\; \backslash times\; \backslash phi\; a\; \backslash times\; DG\; \backslash times\; \backslash cos\; b$. Leaving out the constant quantities $n$, $V^2$, $S$, and $DG$, its energy is proportional to $\backslash phi\; a\; \backslash times\; \backslash cos\; b$. In order, therefore, that any sail may have the greatest power to produce a rotation round $G$, it must be so trimmed that $\backslash phi\; a\; \backslash times\; \backslash cos\; b$ may be a maximum. Thus, if we would trim the sails on the foremast, so as to pay the ship off from the wind right ahead with the greatest effect, and if we take the experiments of the French academicians as proper measures of the oblique impulses of the wind on the sail, we will brace up the yard to angle of $45^\backslash circ$ with the keel. The impulse corresponding to $45^\backslash circ$ is 615, and the cosine of $45^\backslash circ$ is 669. These give a product of 411.435. If we brace the sail to $54.44$, the angle assigned by the theory, the effective impulse is 405.274. If we make the angle $45^\backslash circ$, the impulse is 408.774. It appears then that $45^\backslash circ$ is preferable to either of the others. But the difference is inconsiderable, as in all cases of maximum a small deviation from the best position is not very detrimental. But the difference between the theory and this experimental measure will be very great when the impulses of the wind are of necessity very oblique. Thus, in tacking ship, as soon as the headsails are taken aback, they serve to aid the evolution, as is evident. But if we were now to adopt the maxim inculcated by the theory, we should immediately round in the foreweather braces, so as to increase the impulse on the sail, because it is then very small; and although we by this means make the yard more square, and therefore diminish the rotatory momentum of this impulse, yet the impulse is more increased (by the theory) than its vertical lever is diminished. Let us examine this a little

more particularly, because it is reckoned one of the nicest points of seamanship to aid the ship's coming round by means of the headsails; and experienced seamen differ in their practice in this manœuvre. Suppose the fore-yard braced up to $40^\backslash circ$, the sail shivers, and from letting go the head bow-lines the sail immediately takes aback, and in a moment we may suppose an incidence of $6^\backslash circ$ degrees. The impulse corresponding to this is 400 (by experiment), and the cosine of $40^\backslash circ$ is 766. This gives 306.400 for the effective impulse. To proceed according to the theory, we should brace the yard to $70^\backslash circ$, which would give the wind (now $34^\backslash circ$ on the weather-bow) an incidence of nearly $36^\backslash circ$, and the sail an inclination of $20^\backslash circ$ to the intended motion, which is perpendicular to the keel. For the tangent of $20^\backslash circ$ is about $\backslash frac\{1\}\{2\}$ of the tangent of $36^\backslash circ$. Let us now see what effective impulse the experimental law of oblique impulses will give for this adjustment of the sails. The experimental impulse for $36^\backslash circ$ is 480; the cosine of $70^\backslash circ$ is 342; the product is 164.160, not much exceeding the half of the former. Nay, the impulse for $36^\backslash circ$, calculated by the theory, would have been only 346, and the effective impulse only 118.332. And it must be farther observed, that this theoretical adjustment would tend greatly to check the evolution, and in most cases would entirely mar it, by checking the ship's motion ahead, and consequently the action of the rudder, which is the most powerful agent in the evolution; for here would be a great impulse directed almost astern.

We were justifiable, therefore, in saying, in the beginning of this article, that a seaman would frequently find himself baffled if he were to work a ship according to the rules deduced from M. Bouguer's work; and we see by this instance of what importance it is to have the oblique impulses of fluids ascertained experimentally. The practice of the most experienced seamen is directly the opposite to this theoretical maxim, and its success greatly confirms the usefulness of these experiments of the academicians so often praised by us.

We return again to the general consideration of the rotatory motion. We found the velocity $v\; =\; \backslash frac\{F\; \backslash cdot\; qG\}\{\backslash int\; pr^2\}$. It is

therefore proportional, ceteris paribus, to $qG$. We have seen in what manner $qG$ depends on the position and situation of the sail or rudder when the point $G$ is fixed. But it also depends on the position of $G$. With respect to the action of the rudder, it is evident that it is so much the more powerful, as it is more remote from $G$. The distance from $G$ may be increased either by moving the rudder farther aft or $G$ farther forward. And as it is of the utmost importance that a ship answer her helm with the greatest promptitude, those circumstances have been attended to which distinguished fine steering ships from such as had not this quality; and it is in a great measure to be ascribed to this, that, in the gradual improvement of naval architecture, the centre of gravity has been placed far forward. Perhaps the notion of a centre of gravity did not come into the thoughts of the rude builders in early times; but they observed that those boats and ships steered best which had their extreme breadth before the middle point, and consequently the bows not so acute as the stern. This is so contrary to what one would expect, that it attracted attention more forcibly; and, being somewhat mysterious, it might prompt to attempts of improvement, by exceeding in this singular maxim. We believe that it has been carried as far as is compatible with other essential requisites in a ship.

We believe that this is the chief circumstance in what is called the trim of a ship; and it were greatly to be wished that the best place for the centre of gravity could be accurately ascertained. A practice prevails, which is the opposite of what we are now advancing. It is usual to load a ship so that her keel is not horizontal, but lower abaft. This is

found to improve her steerage. The reason of this is obvious. It increases the acting surface of the rudder, and allows the water to come at it with much greater freedom and regularity; and it generally diminishes the griping of the ship forward, by removing a part of the bows out of the water. It has not always this effect; for the form of the ship's bow is sometimes such, that the tendency to gripe is diminished by immersing more of the bow in the water.

But waiving these circumstances, and attending only to the rotatory energy of the rudder, we see that it is of advantage to carry the centre of gravity forward. The same advantage is gained to the action of the after-sails. But, on the other hand, the action of the headsails is diminished by it; and we may call every sail a headsail whose centre of gravity is before the centre of gravity of the ship; that is, all the sails hoisted on the bowsprit and foremast, and the staysails hoisted on the mainmast; for the centre of gravity is seldom far before the mainmast.

Suppose that when the rudder is put into the position AD (fig. 11), the centre of gravity could be shifted to $g$, so as to increase $qG$, and that this is done without increasing the sum of the products $pr^2$. It is obvious that the velocity of conversion will be increased in the proportion of $qG$ to $qg$. This is very possible, by bringing to that side of the ship parts of her loading which were situated at a distance from $G$ on the other side. Nay, we can make this change in such a manner that $\backslash int\; pr^2$ shall even be less than it was before, by taking care that everything which we shift shall be nearer to $g$ than it was formerly to $G$. Suppose it all placed in one spot $m$, and that $m$ is the quantity of matter so shifted, while $M$ is the quantity of matter in the whole ship. It is only necessary that $m\; \backslash cdot\; gG^2$ shall be less than the sum of the products $pr^2$, corresponding to the matter which has been shifted. Now, although the matter which is easily moveable is generally very small in comparison to the whole matter of the ship, and therefore can make but a small change in the place of the centre of gravity, it may frequently be brought from places so remote that it may occasion a very sensible diminution of the quantity $\backslash int\; pr^2$, which expresses the whole momentum of inertia.

This explains a practice of the seamen in small wherries or skiffs, who, in putting about, are accustomed to place themselves to leeward of the mast. They even find that they can aid the quick motions of these light boats by the way in which they rest on their two feet, sometimes leaning on one foot, and sometimes on the other. And we have often seen this evolution very sensibly accelerated in a ship of war, by the crew running suddenly, as the helm is put down, to the lee-bow. And we have heard it asserted by very expert seamen, that after all attempts to wear ship (after lying-to in a storm) have failed, they have succeeded by the crew collecting themselves near the weather foreshrouds the moment the helm was put down. It must be agreeable to the reflecting seaman to see this practice supported by undoubted mechanical principles.

It will appear paradoxical to say that the evolution may be accelerated even by an addition of matter to the ship; and though it is only a piece of curiosity, our readers may wish to be made sensible of it. Let $m$ be the addition, placed in some point $m$ lying beyond $G$ from $q$. Let $S$ be the spontaneous centre of conversion before the addition. Let $v$ be the velocity of rotation round $q$, that is, the velocity of a point whose distance from $q$ is 1, and let $\backslash rho$ be the radius vector, or distance of a particle from $q$. We have

Therefore $v\; =\; \backslash frac\{F\; \backslash cdot\; qg\}\{\backslash int\; pr^2\; +\; M\; \backslash cdot\; Gg^2\; +\; m\; \backslash cdot\; mg^2\}$. Let us determine $Gg$ and $mg$ and $qg$.

Let $mG$ be called $z$. Then, by the nature of the centre

Seaman-ship. of gravity, $M+m:M\; =\; Gm:gm\; =\; z:gm$, and $gm\; =\; \backslash frac\{M\}\{M+m\}$

and $m\; \backslash cdot\; gm^2\; =\; \backslash frac\{mM^2\}\{(M+m)^2\}\; z^2$. In like manner, $M\; \backslash cdot\; Gg^2\; =\; \backslash frac\{Mm^2\}\{(M+m)^2\}\; z^2$. Now $mM^2\; +\; m^3M\; =\; Mm\; \backslash times\; M+m$. Therefore

$M\; \backslash cdot\; Gg^2\; +\; m\; \backslash cdot\; gm^2\; =\; \backslash frac\{Mm\; \backslash times\; (M+m)\}\{(M+m)^2\}\; z^2\; =\; \backslash frac\{Mm\}\{M+m\}\; z^2$. Let $u$

be $\backslash frac\{m\}\{M+m\}$, then $M\; \backslash cdot\; Gg^2\; +\; m\; \backslash cdot\; gm^2\; =\; Mnz^2$. Also $Gg\; =\; nz$, being $\backslash frac\{m\}\{M+m\}z$. Let $qG$ be called $e$: then $gg\; =\; c+nz$.

Also let $SG$ be called $e$.

We have now for the expression of the velocity $v\; =\; \backslash frac\{F(c+nz)\}\{\backslash int\; pr^2\; +\; Mnz^2\}$ or $v\; =\; \backslash frac\{F\}\{M\}\; \backslash times\; \backslash frac\{c+nz\}\{\backslash int\; pr^2\; +\; nz^2\}$. But $\backslash frac\{\backslash int\; pr^2\}\{M\}\; =\; ce$.

Therefore, finally, $v\; =\; \backslash frac\{F\}\{M\}\; \backslash times\; \backslash frac\{c+nz\}\{ce+nz^2\}$. Had there been no addition of matter made, we should have had $v\; =\; \backslash frac\{F\}\{M\}\; \backslash times\; \backslash frac\{c\}\{ce\}$.

It remains to show, that $z$ may be so taken that $\backslash frac\{c\}\{ce\}$ may be less than $\backslash frac\{c+nz\}\{ce+nz^2\}$. Now, if $c$ be to $z$ as $ce$ to $z^2$,

that is, if $z$ be taken equal to $e$, the two fractions will be equal. But if $z$ be less than $e$, that is, if the additional matter is placed anywhere between $S$ and $G$, the

complex fraction will be greater than the fraction $\backslash frac\{c\}\{ce\}$, and the velocity of rotation will be increased. There is a particular distance which will make it the greatest possible,

namely, when $z$ is made $=\; \backslash frac\{1\}\{n\}(\backslash sqrt\{c^2\; +\; nce\}\; -\; e)$, as will easily be found by treating the fraction $\backslash frac\{c+nz\}\{ce+nz^2\}$ with $z$, considered as the variable quantity, for a maximum. In what we have been saying on this subject, we have considered the rotation only inasmuch as it is performed round the centre of gravity, although in every moment it is really performed round a spontaneous axis lying beyond that centre. This was done because it afforded an easy investigation, and any angular motion round the centre of gravity is equal to the angular motion round any other point. Therefore the extent and the time of the evolution are accurately defined. From observing that the energy of the force $F$ is proportional to $qG$, an inattentive reader will be apt to conceive the centre of gravity as the centre of motion, and the rotation as taking place, because the momenta of the sails and rudder, on the opposite sides of the centre of gravity, do not balance each other. But we must always keep in mind that this is not the cause of the rotation. The cause is the want of equilibrium round the point $C$ (fig. 10), where the actions of the water balance each other. During the evolution, which consists of a rotation combined with a progressive motion, this point $C$ is continually shifting, and the unbalanced momenta which continue the rotation always respect the momentary situation of the point $C$. It is, nevertheless, always true, that the energy of a force $F$ is proportional, ceteris paribus, to $qG$, and the rotation is always made in the same direction as if the point $G$ were really the centre of conversion. Therefore the mainsail acts always (when oblique) by pushing the stern away from the wind, although it should sometimes act on a point of the vertical lever through $C$, which is ahead of $C$.

These observations on the effects of the sails and rudder in producing a conversion, are sufficient for enabling us to explain any case of their action which may occur. We have not considered the effects which they tend to produce

by inclining the ship round a horizontal axis, viz., the motions of rolling and pitching. To treat this subject properly would lead us into the whole doctrine of the equilibrium of floating bodies, and it would rather lead to maxims of construction than to maxims of manœuvre. M. Bouguer's Traité du Navire and Euler's Scientia Navalis are excellent performances on this subject, and we are not here obliged to have recourse to any erroneous theory.

It is easy to see that the lateral pressure both of the wind on the sails and of the water on the rudder tends to incline the ship to one side. The sails also tend to press the ship's bows into the water, and if she were kept from advancing, would press them down considerably. But by the ship's wind on motion, and the prominent form of her bows, the resistance of the water to the fore part of the ship produces a force which is directed upwards. The sails also have a small tendency to raise the ship, for they constitute a surface which in general separates from the plumb-line below. This is remarkably the case in the staysails, particularly the jib and fore-topmast staysail. And this helps greatly to soften the ship's bows into the head seas. The upward pressure also of the water on her bows, which we just now mentioned, has a great effect in opposing the immersion of the bows which the sails produce, by acting on the long levers furnished by the masts. M. Bouguer gives the name of point velique to the point

$V$ (fig. 12) of the mast, where it is cut by the line $CV$, which marks the mean place and direction of the whole impulse of the water on the bows. And he observes, that if the mean direction of all the actions of the wind on the sails be made to pass also through this point, there will be a perfect equilibrium, and the ship will have no tendency to plunge into the water or to rise out of it; for the whole of the water on the bows, in the direction $CV$, is equivalent to, and may be resolved into the action $CE$, by which the progressive motion is resisted, and the vertical action $CD$, by which the ship is raised above the water. The force $CE$ must be opposed by an equal force $VD$, exerted by the wind on the sails, and the force $CD$ is opposed by the weight of the ship. If the mean effort of the sails passes above the point $V$, the ship's bow will be pressed into the water; and if it pass below $V$, her stern will be pressed down. But, by the union of these forces, she will rise and fall with the sea, keeping always in a parallel position. We apprehend that it is of very little moment to attend to the situation of this point. Except when the ship is right before the wind, it is a thousand chances to one that the line $CV$ of mean resistance does not pass through any mast; and the fact is, that the ship cannot be in a state of uniform motion on any other condition but the perfect union of the line of mean action of the sails, and the line of mean action of the resistance. But its place shifts by every change of leeway or of trim; and it is impossible to keep these lines in one constant point of intersection for a moment, on account of the incessant changes of the surface of the water on which she floats. M. Bouguer's observations on this point are, however, very ingenious and original.

To prevent unnecessary complication in this treatise, it has been supposed, what is no doubt correct in theory, that the helm acts upon the ship in the same proportion, only upon the producing exactly contrary effects, whether the vessel is going ahead or astern. But in practice this is not the case, and the reason is as follows:—In general a ship is so constructed, unless brought down extremely by the stern, that with headway, sailing with a side-wind, the natural tendency of the bow of the vessel is to approach the wind. That is prevented, partly by the sails before the centre of

VOL. XX.

gravity being larger than those abaft, and partly by keeping the helm a little a-weather. As soon, however, as the ship gets stern-way, she acquires a tendency to fall off from the wind, in the same proportion as her tendency was to approach the wind, as long as the vessel went ahead. But on account of the larger size of the sails forward to those abaft, this tendency to put before the wind is so increased, that with a very moderate breeze, a ship, when making a stern-board, soon pays off against her helm, until the wind is on the quarter. No doubt the helm will counteract this motion to some extent, but in practice the effect is hardly perceptible.

The substance of this article, up to this point, has been taken from one written by the celebrated Professor John Robison, for a former edition of this work. The course of adopting Professor Robison's treatise as a groundwork has been taken, not only out of deference to the high authority of that author, but it is also believed that the interests of the readers of the Encyclopædia have been considered in this matter. We have indeed the means of knowing that the original article has been of extensive utility.

We shall now, instead of repeating the evolutions, which are described by the Professor, give a few examples of the manner in which a ship is manoeuvred, in order to elucidate the theory which has been already explained.

To tack ship, in smooth water, with a fine breeze, and under all sail.—Everything being ready, the ship is gradually luffed up, putting the helm down slowly, at the same time hauling over, until nearly amidships, the spanker-boom. As soon as the helm is down, the word is given, the "helm is a-lee," immediately the fore and head sails are let go. As soon as the wind is fairly out of the after-sails, or when the ship is about three points from the wind, the order is given to raise tacks and sheets. As the ship approaches to about half-a-point of being head to wind, the after-yards are braced round, and their sails trimmed. As soon as she commences fairly to fall off on the new tack, the order is given of "all haul;" then the head-yards are braced round, and all the sails are trimmed. During this evolution the way of the ship must be watched, and if lost, the helm must be righted; if the ship gets stern-way, the helm must be shifted.

The above is the ordinary process of tacking ship under favourable circumstances; a process in which all the different modes of action of the rudder and sails may be employed. To execute this evolution in the most expeditious manner, and so get the ship as much as possible to windward, is considered as the test of an expert seaman.

A fast-sailing ship, just able to carry three reefs out of the topsails and top-gallant sails, working to windward under the above-mentioned circumstances, ought to make about 9 knots per hour, and sail within five and a-half points of the wind. Such being the case, and supposing half-a-point leeway to be made, if nothing was lost in stays, the ship would go to windward at the rate of 3-4 miles per hour. Perhaps 0-3 of the whole distance run may be considered good for a square-rigged vessel.

We have here supposed that, during this operation, the ship has preserved, or nearly so, her progressive motion. She must therefore have described a curved line, advancing all the time to windward; and the ship has been tacked without much assistance from the sails, but principally by the action of the rudder. But this evolution has often to be performed when, either from a swell, want of wind, or, on the other hand, too much wind, sluggishness of the vessel, or from too little sail being set and the ship having little velocity, there arises a considerable probability that, unless great care is used, the ship may not stay, or as it is technically called, may miss stays. Under these circumstances the skilful sailor will adopt many devices, which are neither necessary nor useful, when he is placed in a more

favourable situation. For instance, before putting the helm down, the jib-sheet ought to be eased off, or perhaps the jib hauled down. As soon as the word "helm-is-a-lee" is given, besides the fore-sheet, the foretop-bowline is also let go, and the weather-foretop-sail-brace is hauled in, the yard to be braced up again as soon as the ship approaches within two points of being head to wind. When the word "raise tacks and sheets" is given, the fore-tack is to be kept fast until the ship is head to wind. The after-yards ought not to be hauled until the ship is quite head to wind. The shaking of the spanker under these circumstances affords a good guide to show when the after-yards ought to be braced round. During the time occupied by this evolution, the way of the ship ought to be watched; and as soon as the ship begins to go astern, the helm ought to be shifted. Sometimes it is necessary that the ship should have well paid off on her new tack, before the head-yards are braced round, otherwise the vessel may be placed in what is called irons; that is to say, for some considerable time her head will not pay off either way, and the ship during this time is going astern.

If the ship loses all her headway after the headsails have taken aback, but before the wind has been brought right ahead, the evolution becomes uncertain, but by no means hopeless. Under these circumstances, the ship will soon have stern-way, and the helm must then be shifted hard over. It is evident that the resistance of the water to the stern-way of the rudder will act in a favourable direction, pushing the stern outwards. In the meantime, the action of the wind on the headsails pushes the head in the opposite direction. These actions conspire, therefore, in promoting the evolution; and if the wind can be brought right ahead, it cannot fail, but may even be completed speedily. As soon as the wind comes on the former lee-bow, the action of the water on the now lee-quarter will greatly accelerate the conversion. Therefore, when the wind has once been brought right ahead, there is no risk of failure.

To get under Weigh.—When a ship's anchor is to be weighed, the head-yards are braced round to the opposite tack to which it is intended to cast the ship, the after-yards being braced upon the other tack. Supposing it is intended to cast upon the port tack, the helm will be ported, but shifted when the anchor is out of the ground, and the ship commences to get stern-way. As soon as the head sails will take on the port tack, they are hoisted, and after that, the head-yards braced round, and the sails properly trimmed.

To wear Ship.—Put the helm up, and brail up the after-sails, round in the weather after-braces, keeping the mizzen-topsail shivering, and the main-topsail just touching. When the wind is about one point abaft the beam, let go the head bowlines, and get a pull of the weather head-braces. This is preferable to the usual plan of not touching the head-yards, until the wind is well on the quarter. When the wind is nearly aft, square the head-yards; and when it comes on the other quarter, haul out the spanker, shift over the head-sheets, righting the helm in time, and brace sharp up. We cannot help losing much ground in this movement. Therefore, though it be simple, it requires attention and rapid execution to do it with as little loss as possible. At first one is apt to think, that it would be better to keep the head-sails braced up on the former tack, until the ship is nearly before the wind; as we might expect assistance from the obliquity of the head-sails. But the rudder being the principal agent in the evolution, it is found that more time is gained by increasing the ship's velocity than by an impulse upon the head-sails more favourably directed. It has been considered by many seamen, that a ship, when she cannot be stayed, loses the least ground by what is termed box-hauling. This is effected by bracing the head-yards flat aback as soon as the

Seaman-ship. helm is put up, and keeping the after-sails shivering; when the ship gets stern-way, the helm is shifted, to be righted when she gathers headway; when before the wind, square the yards, and proceed as in wearing. This evolution, if well done, may be useful if some danger be suddenly seen right ahead.

In a strong gale with a contrary wind, or even with a fair wind with too heavy a sea to run with safety, the ship is obliged to lie to. Some sail is absolutely necessary to keep the ship steady, otherwise she might strain and work herself to pieces. Different ships behave best under different sails. In a very violent gale, the main-topsail close reefed, storm-trysails and fore-staysail are in general well adapted for keeping a ship steady, and distributing the strain. Under this sail, unless a very heavy sea is running, the ship will have sufficient way to be steered. This is far preferable to the plan adopted before storm-trysails had superseded storm-staysails; the helm used then to be kept a-lee, and the ship's head came up and fell off, the same as a ship hove to in fine weather, with a main-topsail aback.

To take in a topsail during a gale of wind.—Let go the top-bowline, lower the yard, and slack about 4 feet of the lee-sheet. Clew the yard down by the weather clewline, and haul in the weather topsail brace. As soon as the yard is down, ease away the weather-sheet, and haul up the clewline and buntline; when up, ease off the lee-sheet, and haul up the lee clewline and buntline.

To set a topsail blowing hard, the lee-sheet must first be hauled home.

Omitting the details, which we do not pretend to give, the above shows the principle upon which square sails are set and taken in during gales of wind.

Dangerous position of the Magnificent, and her preservation from it described. In closing this head, we would refer to one of the finest manoeuvres of seamanship, and one which has been fully recorded, we mean the saving from a most perilous position Her Majesty's ship Magnificent, of 74 guns, commanded by Captain John Hayes. The following are some of the particulars:—

On the evening of December 16, 1812, the Magnificent anchored with the best bower in 16 fathoms, between Chasseron and Isle of Rhe, in the neighbourhood of the Basque Roads, at 9 h. 40 m. P.M. The ship drove, when the small bower anchor was let go, and brought the ship up in 10 fathoms, the Isle of Rhe reef being distant about the length of two cables. The lower yards and topmasts were immediately struck. By the lead it was soon discovered that they were anchored amongst rocks; and as they were without chain-cables, it was quite obvious the hempen cables would soon be chafed through. The gale continued, with squalls from the S.W., with rain, and a heavy cross sea running. At daylight the ship again drove, and the spare anchor was let go, which brought her up. At noon the gale had increased, without any indication of a favourable change in the weather, joined to which one of the cables having parted, Captain Hayes resolved to make an attempt to save the ship. The courses having been previously reefed, and the topsails close-reefed, the lower yards were swayed up to three-fourths of their usual height; the topmasts were secured close down, leaving the topsail-yards to work on the caps; the largest hawser was passed through the starboard quarter-port, and bent to the cable of the small bower, for the purpose of acting as a spring in casting the ship to port previously to cutting the cable.

The courses and topsails were secured on their respective yards with stops of spun yarn, the gaskets having been removed. The head and main yards were braced up on the starboard tack, the yards on the mizen-mast being kept square. It is quite evident that, in the event of the spring canting the ship, the head-yards would require no alteration. On the other hand, if the spring broke, the yards could not be better placed for producing the stern-board,

which would in that case be necessary to clear the reef. The spring was now hove in to a tolerable strain, and all being ready, the cables were cut. The heavy sea on the port-bow acting against the spring, caused it to snap; it was immediately cut adrift to prevent retarding the ship's way, the helm was put hard to starboard, the fore-staysail hoisted, the fore-topsail let fall and sheeted home, the foresail let fall, the tack hauled on board, and the sheet roused aft. All this sail was flat aback, and set in less than half-a-minute. The ship's head paid round quickly towards the reef. When the wind was abaft the beam, the mizen-topsail was set, and the helm shifted. When the wind came right aft, the main-topsail was set, and immediately afterwards the mainsail. As soon as the wind came on the starboard quarter, the sails were trimmed, and the yards braced up on the starboard tack. Thus the ship was saved.

This manoeuvre, from the cutting of the spring until the sails were set, did not exceed two minutes. At the moment when the ship's head was in the direction of the rocks, and then only in five fathoms water, the vessel made a desperate plunge; and in hauling to the wind, the end of the sea did not leave, by the soundings, more than a single foot of water under the keel.

We now propose to direct attention to the most important improvements in the art of seamanship which have taken place within the last fifty years. This science, as it may now fairly be called, has greatly advanced within that period. With the improvements which have been made in most other departments of industry and knowledge, the public are more or less familiar, and great pains have been taken throughout this work to extend that familiarity by such popular explanations as shall not only be intelligible to general readers, but be useful to those whom pleasure or business inclines to go deeper. But before explaining the more recent changes that have taken place in this art or science, we would direct some attention to its general progress.

Most other sciences may be studied with effect in the closet. An amateur astronomer, for example, or a chemist, furnished with good instruments, and having confidence in the skill and good faith of the leaders in the particular walk of knowledge to which his taste inclines him, may, by adopting their results, pursue the same paths with almost equal profit, and perhaps with more pleasure than those who take all the labour and incur all the responsibility. But there is no royal road of this sort by which an amateur sailor can investigate the results of seamanship, the mysteries of which, to be fully understood, must be studied afloat, at sea, in all weathers, and in every climate.

All the world, however, knows that the results of nautical skill and exertion are not the same as they used to be. A voyage to India and back, in former times, occupied a couple of years, or more; it is now currently done in eight months, even by ordinary merchant-vessels, including the time taken to unload and reload their cargoes. In consequence of the increase of passengers between England and Australia, great emulation has been excited amongst the merchant-ships running between the two countries, and many improvements have taken place. That voyage is now often performed (without the aid of steam) in eighty days, and has been done in seventy. It is recorded that one of these clipper ships, as they are designated, has run the enormous distance of nearly 3000 miles in ten days. In former days, the scurvy struck down half the crew of every ship which made a long voyage, and was even fearfully prevalent in the navy; now the disease is almost unknown. The numbers of all kinds of ships afloat have enormously increased, and the war of the elements by which they were formerly assailed is no less violent than it was; but assuredly a far smaller proportion of vessels are now driven on shore than

were formerly wrecked. The comforts, too, of travelling by sea, in the articles of provisions and water, are all essentially improved; and, finally, the security, as well as the happiness of all persons on board, whether passengers or crew, has been marvellously augmented by the general establishment of a better system of discipline than was known in bygone days; whilst many old manipulations of seamanship are so modified by new contrivances, that if old Benbow, or even Kempenfelt, were to arise from the dead, he would scarcely know how to handle his ship.

It may not be without use, and it certainly must be interesting to those who have not studied such things personally, to see by an example how scientific seamanship is made to triumph over that groping and blundering method of navigating ships which is technically known by the name of the "rule of thumb." If we take a globe, and trace on it the shortest route, by sea, to India, and then fancy that such must be the best course to follow, we shall be very much mistaken. And yet this is very much what our ancestors actually did, till time, and repeated trials, and multitudinous failures, gradually taught them where to seek for winds, and how to profit by them when found. According to the "rule of thumb" sailing, a ship had only to steer from England to Madeira, pass the Canaries and Cape de Verds, and then to make a direct course to the Cape, and thence to India. On trial, however, this experiment always failed; for on getting near the equator, a series of calms and squalls put a stop to this straight-line scheme, and the mariners of old were then forced to toil along the coast of Africa, or were driven towards that of the Brazils, and very often they came back in utter hopelessness. Now-a-days, the exact spot where the north-east trade wind, which prevails in the northern Atlantic, ought to be parted with; in what district the calms and variables are most easily managed; over what degree of longitude on the equator the ship should pass; and, finally, in what place the south-east trade wind of the southern Atlantic is to be found, and how it is to be made most use of when found,— are all matters of such familiarity to the really qualified navigator, that they scarcely occupy his thoughts, but are acted upon as matters of course, and, unless some unforeseen accident occurs, absolutely ensure the success of his voyage. The line he follows, however, is by no means the straight one which an ill-informed person would naturally have chalked out for him to follow, ignorant of the impossibility of pursuing it.

The modern navigator, by not seeking to husband the south-east trade wind too much, but by freely "flanking" through it, sweeps past the coast of Brazil, and by boldly dashing down into pretty high south latitudes, is certain, or almost certain, of finding there such a vein of westerly wind, as amply compensates for the apparent roundabout he has made in his course. In like manner, after passing the Cape, which to the old navigators was truly a "Cabo de tormentos," instead of vainly trying to reach India by steering straight through the Mozambique Channel, the scientific navigator, disregarding the increase of distance, maintains his position in a high latitude, and sails resolutely along a parallel of latitude, with the wind in his poop, till he has obtained such a degree of easting, that, on hauling up to the northward, and making for the south-east trade wind, he enters that mysterious aerial current on such terms as ensure his making it serve his purpose. If, however, he be timid or impatient by nature, and not duly instructed by experience, he will be very apt to haul up too soon to the northward, from not liking to run, as it appears, so far past his port. The consequence will be, that when he encounters the south-east trade wind, he will find, that instead of its being fair, it is blowing in his teeth, and he will have to run back again to the southward to borrow a little more easting from the westerly breezes which prevail there.

Be it observed, however, that the above instructions would lead a seaman into great error, were he to make the rule absolute; for, at certain seasons of the year, that is, when the sun is far to the north of the line, and the south-west monsoon blowing in the Indian Ocean, his course from the Cape to India would lead him between Madagascar and the main land of Africa; and so he would sail across the equator, and enter the Bay of Bengal with a flowing sheet. At other seasons, so far from having a flowing sheet on reaching India, he may have to beat up the bay, "hank for hank," unless he has knowledge enough to know at which side to enter it, and skill enough—for it requires a good deal—to know how to profit by the land and sea breezes of the coasts respectively of Coromandel and of Pegu.

In short, not to swell this example too far, the truly scientific navigator, possessed of the requisite nautical instruments (the most important of which we propose to speak of by and by), by which means he may at all times be certain of his place, may almost command a fair wind at every stage of his voyage, and thus secure his passage within a certain number of days; though, in his way, he will have had to vary his course a hundred times from that which, at first sight, might have been thought the best, merely because, on the map, it seemed the shortest. The old proverb, indeed, which warns us that the longest way about is often the shortest way home, has perhaps its amplest illustration in the practice of modern seamanship; but, let it be always borne in mind, that this is true only when all the varying circumstances of time and place are duly taken into account, and so appropriated as to give to the ship those advantages of fair wind and moderate weather without which no voyage can be securely or speedily made. This branch of seamanship, therefore, more than any other, requires for its successful exercise a singular combination of the widest generalizations in theory, with the most minute and specific disintegrations of scientific research in practice. In the Indian seas especially, the whole history of the winds, examined without some theoretical clue, is a mass of confusion; and yet the profoundest meteorological science would inevitably prove not only useless, but absolutely dangerous to the navigator who should trust to it alone, without the aid of local information, and of the improvements of modern art.

The first great improvement of recent times to which we shall allude, is the mighty revolution in nautical affairs the introduction of steam, that the first instance we have of the application of steam-power to propel vessels in this country took place in 1815, and Glasgow led the way. No doubt, steam-engines had been tried on board ships before that time, but in 1815 commenced the first commercial employment of steam-vessels. In the beginning of 1816, a small steam-vessel, of about ten horse-power, began running as a passage-vessel between Sheerness and Chatham. Immediately after that steam-vessels were used upon the Thames. The first time that they made coasting sea-voyages was in 1821, when they commenced running between London and Edinburgh. The first of what may be called an ocean-voyage took place in 1826, when two steam-vessels commenced running between London and Lisbon. Our present object, however, is not to give a history of steam as applied to navigation, but to notice that change, so far as seamanship proper is concerned. For fuller explanations of the subject, and its progress, we would refer to the article STEAM-ENGINE.

Now, to a considerable extent, steam does not essentially interfere with seamanship proper, the manipulations of which remain nearly as before; whilst steam navigation, in spite of its boasted contempt of wind and tide, is still obliged to borrow so much from seamanship to complete its success, that without its aid it would often be useless, and even dangerous in the highest degree. It is quite evident,

Seaman-ship. that nearly all that branch of our subject which relates to navigation; that is, to the method by which a ship's place is determined at sea, the proper course shaped, and the different ports of the world recognised and made use of, remains the same. Latitudes and longitudes, and the variation of the compass, are evidently just as important to a steam-vessel as to a sailing one; and though winds and currents are not quite so essential, every one who has made a steam voyage of any length is aware how materially its celerity depends upon a knowledge of and due attention to these particulars. It is one of the chief points of a seaman's duty to know where to find a fair wind, and where to fall in with a favourable current; but the obligation, if not equally binding on a steam navigator, is so, to a certain extent, when his voyage is a long one. The most remarkable occasions on which steam has the advantage over sails are in a calm, and when the wind is directly ahead. In a calm, a sailing ship is utterly helpless, and must stand stock-still; with a wind in her teeth, if it blow hard, she can do nothing, or does worse than nothing, drifts away from her point. Although the above statements, as far as they go, are true to the letter, still there are other points of seamanship connected with steam that now can only be acquired on board steam-vessels; one of such points, of most importance, is the best and most efficient mode of combining steam with the use of sails, and to which we would first draw attention.

When first the steam-engine was applied to the propulsion of vessels, the propeller universally adopted was the paddle-wheel; and a general idea existed, that sails under these circumstances were of very little use; acting upon this notion, these vessels were fitted with very small masts and yards. But as soon as we commenced to have steam men-of-war, it was apparent, that if they were not provided with the power of moving under sail alone, so as to save burning their coals, their utility for distant stations, and cruising with a fleet, would be much curtailed. For the above reasons, steam men-of-war, even before the introduction of the screw, were being gradually fitted with loftier masts and squarer yards; so that, by the year 1846, our steam frigates had in general about three-fourths the same extent of canvas that they would have had as sailing ships of the same dimensions. To render these vessels at all effective under sail alone, the wheels had either to be disconnected, or the floats taken off. But even after either of these plans had been adopted, the vessel, owing to its cumbrous paddle-boxes, remained an indifferent sailing vessel. Under these disadvantages, the introduction of the screw as a propeller made here a most important change. A screw-vessel, with its screw hoisted up, becomes as well fitted for sailing as any other vessel; and as the engines can be placed under the water-line, therefore protected from shot. This mode of propulsion was quickly adopted for the navy, and the ships so fitted are now rigged the same as if they had no steam, but were simply sailing-vessels. We need hardly add, that in future no men-of-war will proceed to sea without steam-engines being placed on board. The mercantile world were not slow in adopting screw-vessels; and at present they are not only employed in the coasting trade, but largely in the foreign commerce of the country. Although many of these vessels have great steam-power placed on board, still in a considerable number the power is small in proportion to their tonnage. In all cases large fore and aft sails are fitted for shorter voyages, and they are fully rigged for the longer ones. Although the screw has to a great extent taken the place of the paddle-wheel, and entirely so in the navy, yet, for the mercantile marine and post-office packets, under certain circumstances, the paddle-wheel is still used; for instance, in rivers, and for distant voyages, where strong head winds may be expected, and where a few hours even of delay may be of conse-

quence. Thus we see, that a further advance in the science of steam navigation has had the effect of restoring the use of sails where engine-power is used. It would, indeed, be a disgrace to modern science if such a cheap and powerful agent as the wind could not be applied for our benefit, and that our discoveries only forced us to have recourse to expensive methods to gain our object. The action of the winds as a moving power is now brought under subjection, to be used when it is favourable; but at times when such is not the case, we then, and not till then, ought to have recourse to that power which we have in reserve. It is certainly comparatively easy to have a mere sailing-vessel, or a mere steamer. It is the combination of the two qualities which forms the desideratum, and to which we would now draw attention.

Often with men-of-war the length of a passage is of little moment, in these cases the sails alone ought to be used. But, on the other hand, in post-office packets and mercantile vessels with passengers, time is of so much importance, that if the supply of fuel be sufficient, it is their policy to push on; but there are a great variety of cases, where, although no extreme haste is necessary, yet it is of importance that the voyage should not be protracted beyond a certain time; in those cases a judicious employment of steam and sail is of consequence.

To aid a further elucidation of this subject, we propose now to give a table of the velocity and pressure of the wind:—

From this table it appears that the pressure of the wind increases as the square of its velocity; and as the power necessary to overcome the resistance to the speed of the ship is in all cases as the cube of her velocity, the following circumstance is therefore deducible. With a ship propelled by steam, if twice the velocity is to be attained, eight times the power must be used; but under sail (all things remaining the same, and a similar number of square yards of canvas spread), then wind, with three times its former velocity, would give rather more than twice the speed. But take the action of the wind in another point of view, and suppose a ship, with her steam up, going before the wind; if the velocity of the ship be greater than the wind, it is quite evident that the sails would only be a hindrance; but supposing that there is some difference, and that the ship is going slower than the wind, then all the assistance that the ship can receive is the difference between her velocity and the velocity of the wind. From this it is evident, that in a steam-vessel, when the wind is aft, or nearly so, the economical policy is to put the ship under sail alone, and not to use the steam at all, for by so doing, the whole power of the wind is made available. On the other hand, a light breeze on or abaft the beam, otherwise of little importance, may be taken advantage of in the propelling of the ship, by combining with it the power of steam. The reason is this. The ship passing rapidly along creates a considerable breeze; this unites with the wind, no doubt causing it to act more forward upon the ship in the same proportion as it increases its strength. From this we learn, that with light breezes on or about the beam, policy directs to make sail, but also to retain the steam, as it is by the velocity imparted by the engines to the vessel that these light winds become available.

It is not necessary to enlarge further upon this subject,

as in a former part of this treatise (and the principle is the same) we demonstrated, that a fast ship, under sail alone, with the wind abast the beam, might go faster than the ordinary current of the wind; although, no doubt, such cases seldom occur. With regard, however, to a vessel propelled by steam it is very different. In this case it will often happen, under the circumstances stated above, that the way of the ship will be increased by the power of the apparent wind, whilst the real wind has not the velocity of the vessel.

In connection with this subject, we would now draw attention to a mistake which sailors in charge of steam-vessels sometimes have committed. The mistake made is this. In order, as they consider, to save coals, they keep the steam so low, with sail set, as not to turn the screw or paddle-wheel so fast as the vessel would go under sail alone. We have read an account of a voyage intended to show the advantage of using the sails and steam combined; and although attention is drawn to the small quantity of coal thereby consumed, yet, upon examination, there can be no doubt that the vessel would often have gone faster if the steam had not been used at all, and in such cases there would have been a saving of the whole of the coal.

The principles involved are as follows. With a fair wind, the number of miles obtained from a ton of coals is the number of miles that the engines increased the speed of the vessel above that which she would have gone with sails alone; that is to say, suppose a steam-ship goes nine knots with a fair wind, under sail alone, steam is applied, and the ship goes ten knots; the consumption of coal is, say two tons per hour, then 0.5 knot is obtained from each ton of coal. But now, under the same circumstances, suppose that a comparatively small amount of steam is applied, then it will follow that, unless a sufficiency of coal is used to keep up the revolutions of the screw or paddle-wheel equal to what would be the rate of the ship under sail alone, the way of the ship is less under sail, and this small supply of coal, than it would have been under sail alone; in short, the coal used in such a case would only retard the ship; and from this it may be deduced, that although fore and aft sails, and square sails also, when the wind is not too far forward, with the steam, may, under certain circumstances, often be useful, and save coal; so that, when the object is to make quick and economical passages, steam and sail ought certainly to be combined. Still it is advisable that steam and sail be generally used separately.

With strong head winds, the seaman often finds in his steam-vessel he is burning a large quantity of coal, more particularly if propelled by a screw, and making little way. In such cases the best plan is to keep the ship away and make sail, and if time is an important object, still keeping the screw in motion. So situated, even a dull sailing-vessel with small steam-power, if judiciously handled, will work to windward with considerable celerity.

We have already given an outline of the courses usually followed by a sailing-ship in passing through the tropics. In similar voyages, however, a vessel with steam-power has great advantages; and the skillful seaman would take a much shorter route, regulated of course, first, by his supply of coals and the time of their probable duration, and, secondly, by calculating the importance of time in opposition to expenditure of fuel.

We now propose to give a short account of two voyages made by Her Majesty's steam-frigate Terrible, where sail and steam were combined, and which will therefore show the results of this combination; and as they were made through the tropics, these voyages will also prove that a much more direct and shorter route in such cases can be advantageously taken by steam-vessels than by mere sailing ships. It is necessary, first, to premise, that the Terrible was a steam-frigate carrying heavy armaments of guns,

both on the main and upper decks. The Terrible's size was 1847 tons, with 800 horse-power of engines, stowing about 500 tons of coal, barque-rigged, and spreading about the same quantity of canvas as the old 44-gun frigates. It is also proper to state, that during both these voyages, when the steam was employed, it was used as expansively as possible, and with only two boilers, there being four on board for full power. The length of the stroke was 8 feet; the steam was cut off at 22 inches.

The first voyage was performed in August 1847, and was from Madeira, in Lat. 32. 58. N., Long. 16. 55. W., to St Paul de Loando, Lat. 8. 48. S., Long. 13. 13. E. The following is a short summary of the particulars of this voyage, and which requires no explanation:—

The equator was crossed in Long. 6. 0. E. It is quite obvious from the above table, that the Terrible, in this voyage, took almost the nearest possible route; now, every one at all acquainted with the winds and currents on the African coast to the southward of the line, is well aware that such a plan in a sailing-vessel is totally out of the question, and if attempted might even have prolonged the voyage for months.

The second voyage, concluding October 7, 1847, was from St Paul de Loando to Lisbon; and the following is a table similar to the one given for the previous voyage:—

The equator was crossed in Long. 13. 0. W. It will be observed that the same principle was adopted in the second voyage, namely, to make as nearly as possible a direct course. After the Terrible crossed the line, a nearly straight course was made up to 30. N. Lat., steaming through the N.E. trades, passing between Africa and the Canary Islands.

We have now shown that even in long voyages the steam-ship has an immense superiority over the sailing-vessel. We may, however, observe further, that she still retains that superiority under circumstances where both description of vessels are forced to anchor upon a dangerous lee-shore. From the anchors not holding, or the insufficient strength of the cables, there is then risk of their being forced on shore. But in this predicament, a steam-vessel, by the mere agency of her steam, although not exerted to any great extent, will either keep the cable slack, or at all events very materially relieve it from the strain produced by the wind.

There are many other details constantly arising on board steam-vessels, such as taking ships in tow, &c. These are operations which, to do well, require good seamanship; but, as we believe, that they can only be fully and practically learned on board a steam-vessel, it is hardly necessary to enter further upon these arrangements than we have done already.

There is, however, a very natural consideration that arises from the fact, that the royal navy is now entirely steam, and

Seaman-ship. that the mercantile marine is gradually becoming so. The consideration we allude to is this, Has this change deteriorated our skill and knowledge of seamanship? In our own opinion, to a certain extent, it has, not that our ships are worse rigged or worse handled in any way, in the open sea, but officers and pilots are gradually shrinking from performing those manoeuvres that were formerly often executed by mere sailing-vessels, close to the shore or in narrow passages. Suppose, for example, a ship placed, in the present day, in the same position as the Magnificent, which we have already described, most probably she would have steam-power, by which aid the ship could be easily extricated; but if not, it appears to us very doubtful whether the daring manoeuvre which saved that ship would now be attempted under sail alone. Formerly it was quite common for ships of the line, with their lower deck guns out, to beat up (not back and fill) from Sheerness to Chatham, and vice versa; and we much fear that no pilot would undertake now the responsibility of such a proceeding.

Introduction of chain-cables; The next improvement to which we shall refer, are the remarkable advantages which have been gained by the extensive use of iron on board ship.

As far back as 1808, Captain Brown, of the navy, proposed the use of iron cables and rigging. There was, however, some difficulty in applying the peculiar welding that was found necessary for the links, so that it was not until 1811 that the cables were fairly tried. Since that time they have gradually been more and more adopted, so much so, that their use may now be considered universal, and certainly no greater boon was ever conferred upon the sea service. The original cost of a chain-cable is about the same as a hempen one, whilst its duration is so much greater that there can be no comparison. The security afforded by it is vastly superior, for it is exposed to none of the deteriorating causes which soon render a hempen cable comparatively so little trustworthy. The alternate wetting and drying which saps the strength of a hempen cable, has little effect on one of iron. The friction against rocks, especially against coral, may fatally damage a cable of hemp in a few minutes; but the same friction, after days of hard use, only polishes a few links of the chain. The introduction of chain-cables has, therefore, whenever the bottom anchored upon is rocky, increased the safety of ships tenfold. Nor does this advantage consist solely in their strength and durability, for they are managed with more facility, occupy much less space, and are coiled away with little trouble; for as they are hoisted in, they fall in and adjust themselves into a case near the hatchway, from which they are drawn up when wanted. Those who remember the toil and trouble of stowing away a hempen cable into its tier, the wet and dirt, and the number of men required, will not consider these advantages as small ones.

Several adaptations have been found necessary in consequence of the use of chain-cables. The hawse-holes require to be lined with iron, and the bitts cased with the same metal; a new kind of stopper was also required, by which the cable could at any time be prevented from running out, whatever might be the strain upon it. The stopper first adopted, and which answers extremely well, was invented by Captain Brown himself, and is of the nature of a compressor. This stopper is delineated in a figure, and explained in the article CAPSTAN, to which the reader is referred. But the stopper generally used on board men-of-war was invented by Sir Thomas Hardy, and consists of a large swan-necked bar of wrought iron, which embraces the cable as it comes up the hatchway, having one of the ends of the curve fixed to the beams of the lower deck by a powerful bolt, whilst to the other end is attached a tackle, worked on the lower deck, by which the curved stopper can be drawn tight, and the chain pressed so firmly in its embrace against the angle of the hatchway that, however quickly it may be

running out, or whatever strain may be brought on it, the cable is at once arrested. For some years after the introduction of chain-cables, hempen messengers were used to leave them in; now chains are adopted, with a considerable saving of expense. The messenger is the endless rope which is taken round the capstan, and being attached to the cable, by what are called nippers, draws in the cable along with it as the capstan is hove round. Nippers are made of rope; iron has been tried, but not, as yet, with much success. But the best arrangement, and that which, we think, will soon be universally adopted, is to dispense with the messenger altogether, and to bring the chain-cable direct to the capstan. (See article CAPSTAN.) No doubt, on board those ships which were first fitted in this way, the chain slipped occasionally, indeed often, when a shackle or swivel came to the capstan; but that defect has now been obviated. When this plan is used, it is necessary to have an addition, called a controller, and which is placed before the bitts, and secures each link of the chain as it is hove in.

One advantage of chain-cables is, that a ship may often lie at single anchor without risk of fouling the anchor. In this case, a good scope of cable ought to be veered out, and the ship backed from her anchor, either by the sails or the power of steam, and if the tides are not very rapid, and if the ground consist of mud, there is no probability of this accident occurring. But if the scope of chain be too short, the tides very strong, and the ground hard, there will be almost the same risk of fouling the anchor as with a hempen cable.

With all these numerous advantages that chain-cables have over hempen ones, there are situations where they cannot be used without modification. For example, anchoring near the land in upwards of forty fathoms water. From such a depth, the great weight of the chain-cable renders the labour of heaving up the anchor very severe; added to which, from the vicinity to the shore, it may be indispensable to get the anchor speedily up, and stowed, so that the ship may be under command. To remedy this evil, which arises from the greater weight of an iron-cable in comparison of one made with hemp, and yet to profit by the security which belongs to rendering invulnerable that part of the cable most exposed to friction by rocks, it has been proposed to bend a length of chain (by seamen called a ganger) to the anchor, and upon the chain to splice a hempen-cable. The outer end of a length of chain being thus shackled to the anchor, the cable may be used in any depth of water, with nearly as much security as if it were made of iron from end to end, with only the inconvenience arising from the additional weight of one length of chain.

Chain-slings for the lower yards have been long in use; and, about thirty years ago, chain-topsail-sheets, and chain-ties were introduced, as well as chain-gammoning for the bowsprit, and chain-bobstays, and all have been found, more or less, improvements upon the old plans.

The great objection to chain-rigging for the lower masts has been its great weight; and, for that reason, it has only been used for those masts of steam-vessels where the hempen rigging would have received injury from the heat coming from the funnel. There is, however, no such objection to rigging made from wire-rope, which, along with all the advantages possessed by chain, is about the same weight and has much of the elasticity of hempen rigging. This wire-rigging is now widely used, and with the most perfect of success, for the standing rigging of lower masts. It also, in some respects, answers extremely well for topmast and topgallant-rigging, the only objection being a difficulty of handling it, in the event of its being necessary to shift a mast, or in the event of one being carried away. Her Majesty's ship Terrible, in 1845, was rigged throughout with wire-rope, the lower topmast, topgallant, and royal rigging being all made of it, and there was no complaint of its being

found inefficient. Besides the great advantage that wire-rigging possesses, of not being affected by the heat and sparks from the funnel, its durability is, at least, three or four times that of common rope, and, when once completely stretched, does not require any further setting up. We may add, that wire-rope can also be used for strapping blocks, and will be found both neat and serviceable.

In men-of-war, the use of iron-ballast, instead of dirty shingle, is also comparatively a recent, but valuable, improvement.

Soon after the introduction of chain-cables, attention was directed to the defects of the anchor then in common use; but, for a full description of anchors, we must refer our readers to the article under that head; here we shall only briefly allude to the improvement that has taken place. One great defect in the old anchor was the extreme length of the shank, which no doubt was the cause that it so often broke in that part. This accident, after chain-cables were introduced, became more frequent, and was caused by the weight of the chain, which often fell upon the shank and snapped it. Many proposals for a new formation of anchors were made and tried; but, where the old form of anchor was retained, the great principle appears to have been to shorten the shank, but keeping the same weight of iron, thereby increasing the strength of that part. Rodgers, in his anchor, which is now so generally used, adopted that principle, and at the same time made the palm as small as possible. Another species, known by the name of Porter's anchor, improved by Trotman, is now much used in merchant-ships, but has not found much favour with naval officers. This anchor differs from all others, by the flukes being moveable upon a strong pin in the crown of the anchor. Its defect is said to be this: if once it starts from the ground, the facility of biting again is less than it is with those constructed upon the old plan. In 1852, a committee of naval officers and ship-owners was appointed by the Admiralty to investigate and report upon the properties of different anchors. This committee reported that Trotman's anchor bore the greatest strain without coming home or breaking; but they recommended Lieutenant Rodger's small palmed anchor as the best for all practical purposes.

But anchors are not only now better planned, but by the aid of the powerful steam-hammer, invented by Nasmyth, better made. Formerly, when manual labour only was employed, it often happened, with large anchors, that the iron was not completely welded; that defect is at present unknown. Thus has been added a further security to our ships. The last most important use of iron, to which we shall draw attention, is in a department of seamanship that is of great importance. We allude to the watering of ships. About 1812, iron-tanks were introduced into the navy and mercantile marine, and has very greatly increased the quantity of water which can be carried to sea; whilst the quality has been improved in a manner, of the extent of which no one can form an idea unless he has actually drunk some of the filthy stuff which had been taken out of the wooden casks of bygone days.

An iron-tank of the largest kind at present made for ships of war is called a four-foot cube, though it measures about an inch more in its external dimensions, and occupies sixty-eight cubic feet of space. This area, if entirely filled with water, would contain 424 gallons; but it actually holds 400, which is only twenty-four gallons less than the space would possibly contain.

An increase in the stowage of water is also gained by having tanks made in a form to suit the curve of the ship's hold, or to enter spaces too low to receive cubical tanks.

But the supply of fine wholesome water for steam-ships has been still further increased, by the plan of distilling water on board, as arranged by Sir Thomas Grant, late comptroller of victualling to the navy. By this arrange-

ment, a large ship of the line can distil about two tons an hour by the use of the full power of the apparatus; and, at any time when under steam, can always obtain a sufficient quantity of water from the waste steam without burning extra coals to supply the ship's company's daily use, without trenching upon the stock on board. The plan by which the distilled water is obtained is very simple. The steam is conveyed from a boiler in the engine-room to a condenser placed in the fore-hold. This condenser is placed in water, which is supplied from outside the ship, and conveyed off as it becomes hot. As the steam is condensed into water, it is carried by means of a gutta percha hose into the tanks, where, after it has remained two or three days to be impregnated with atmospheric air, it is ready for use. And we can bear our testimony to all who have not experience of this process, that the water which it produces is of the finest quality, and is fully appreciated by seamen, who justly consider Grant as one of their greatest benefactors—as one of those useful inventors who have added to the comfort, and promoted the health, of their fellow-creatures.

Connected with the food of seamen is the discovery of Preserved preserving meats, soups, and vegetables, without salt, in cylindrical tin-cases, first devised by M. Appert, a Frenchman, and now in general use at sea. In all her Majesty's ships, these preserved meats have long been supplied to the sick with great advantage. To which has been added for all, rations of chocolate, tea, and sugar, with an increased allowance of the other kinds of provisions, and a decrease of the spirits. This new plan of victualling our seamen has added to their health and sobriety, and leaves little to be desired.

In stating these different naval improvements which Snow Harris have characterized the present day, the lightning-conductors of Snow Harris must not be omitted. All who are acquainted with the frequency of disasters at sea are perfectly aware how many are produced by ships being struck by lightning. Impressed with that idea, Snow Harris, as far back as 1822, devised his present plan of conductors, which was fairly tested on board our men-of-war in 1830. They were found to answer their purpose so completely, that all the ships of the navy have long been fitted with these conductors, and gradually they are being adopted in large merchant-ships. And we can state, that there is no instance of a ship being damaged where these conductors were used. Snow Harris's plan differs from all others formerly used in placing his conductor along the different masts, of which it forms, in fact, a component part, and is, therefore, always in its place. In the event of the lightning being about to strike the ship, it comes upon the conductor, and by that means is conveyed through the bottom of the ship without causing the slightest injury. For full details see article ELECTRICITY.

There can be no doubt that, at quite an early period, ships of war had some means of communicating by signals with each other; but it is only within the last few years that this great benefit has been extended to merchant-ships; and at the present time the vessels belonging to the mercantile marine of every nation can, by means of signals, make known their wants, or give intelligence to each other—a boon to the seaman and to the ship-owner that may be easily appreciated.

The codes of signals that are best known in this country, Various and are of the greatest importance, are comprised in the codes of following list:—

Plan of signalizing explained. There is, however, one general principle adopted in all these codes, whatever be the details, and that is as follows:—A certain number of flags and pendants of different patterns are chosen, and to each is assigned its own name. Some of these flags are called by the different numerals: for instance, one flag is called 1; another 2; and so on. In other systems, the letters of the alphabet are used to denominate the flags. Besides which, other flags or pendants are used for specific purposes: for instance, one pendant is called the interrogative, that is to say, when it is hoisted, it shows that a question is asked, another flag signifies affirmation, another negation, and so on for a variety of other expressions. In the Admiralty signals, this system is carried to a considerable extent; but, in the mercantile codes, the same comprehensiveness is neither attempted nor required, and the number of flags and pendants used is much less. To correspond with the flags, signal-books are formed with sentences or words, which these flags represent. For instance, in using Wilmot's signals, if it were wished to make known the following:—"Boats are in want of ammunition." That sentence would be found in this signal-book opposite to 32; and, therefore, the two flags which express those two numbers must be hoisted. If it were wished to ask the question—"Are the boats in want of ammunition?" then the interrogative pendant would be hoisted over 32.

The Admiralty signals, for the use of men-of-war, are very comprehensive, and require about fifty flags or pendants, and include the following codes:—

First. There is the general signal-book, by which orders for all evolutions are given to the fleet. This also comprises a great deal of routine communication; for instance, one signifies, "Send for fresh beef;" another, "Send for bread;" and so on. The flags that belong to this book are called after the numerals.

Second. The telegraph book includes nearly all the most common words in the English language, and a variety of sentences likely to be useful, a geographical table, and a list of all the ships belonging to her Majesty's navy, with the names of the flags by which each ship is distinguished. The flags and pendants used in this book are called after the letters of the alphabet.

Third. Night-signals: The principle of conveying messages here is the same as in the general signal-book, only the position of lanterns, with or without blue-lights or guns, makes known to the fleet the evolution which the admiral wishes to be performed.

Fourth. Fog-signals: These are, of course, very limited, and can be made only by firing guns; the variation in the signals must be marked by the time elapsed between each report. These signals are confined to a few evolutions, such as giving orders to alter the course, to heave to, anchor, &c. As none of the Admiralty codes are published, we refrain from giving examples.

Each commander of a man-of-war is also furnished with private and secret signals. These are only used to determine whether a ship of war that may be in sight, is a foreigner or not, according as they answer the secret signal; because these signals can only be known to the service.

To the late Captain Marryatt is due the credit of having introduced a code of signals that was practically useful to merchant-vessels, and down to the beginning of 1857 it was the one generally adopted. At that time the Board of Trade gave to the world their work, entitled, The Commer-

cial Code of Signals for all Nations. This leaves little to be desired, and is now to be found on board almost all merchant-ships of any size.

This code requires eighteen flags or pendants, which are named from the consonants of the alphabet; and it is so planned that it can show the distinguishing flags of every British merchant-ship. Those at present amount to 35,000 registered vessels, and are increasing at about the rate of 1500 per annum; yet, as this system is so arranged as to be able to express the names of 70,000, it will be some years before any enlargement will be required.

The other advantages of this code are as follows:—

1. 1. It is capable of providing for not less than 20,000 distinct signals.
2. 2. Each signal requires at most four flags to be hoisted at the same time.
3. 3. It is so arranged in classes as to admit of the subject being referred to with great facility.

For the further elucidation of these signals, it is necessary to explain, that the Board of Trade publishes annually a list of all British ships registered, with an official number assigned to each. The name and the number never altering, although the port to which the vessel belongs may be changed.

We shall give, as an example, how three vessels of the Examples same name would make themselves known by this code:— in signalizing.

As it may have some interest with our readers, we give, as a specimen of telegraphing, how Nelson's last signal would have been made by Wilmot's code, and also by the code of the board of Trade.

By Wilmot's Code.

By the Code of the Board of Trade.

The next most material change for the better, to which improvements we have already shortly alluded, and to which it is our duty now to advert, in speaking of seamanship in the most extensive sense of that word, relates to the manner in which ships are now navigated from port to port, and to and from the most distant parts of the globe, not only with greater celerity, but with greater safety than formerly. No doubt the greater celerity with which voyages are performed is partly due to the better formation of ships (see article SHIP-BUILDING), but the improvements whose tendency have been to add to the security of voyages are mainly due—first, to the superior knowledge of those persons who have charge of ships; secondly, to the improved quality, lower cost, and greatly increased number of scientific instruments and astronomical tables now in the hands of every seamanlike officer; thirdly, to the numbers, accuracy, and cheapness of all the charts of almost all the navigable regions of the world; and lastly, to the more extensive and correct knowledge of the phenomena of the winds, weather, and currents of the ocean. And here we would direct the attention of seamen to the wind and current

charts of Lieutenant Maury, United States navy, and also to his work, entitled Explanations and Directions to accompany the above Charts (eighth edition). Such a magazine of information has never before been opened out to the mariner. In place of giving our own description of the above work, we shall borrow largely from the pages of a popular periodical.

"We may expect, as one of the consequences of this publication, that navigation will be divested of some of its delays and dangers. For instance, a sailor, looking at the fog-charts, observes that in one hundred crossings between New York and Liverpool, he may expect to encounter a fog twenty-eight times; that fogs are most frequent in the months of most daylight, and fewest in the darkest months; that certain latitudes are more subject to fogs than others, and hence he can shape his course accordingly. He finds a similar explanation with respect to gales of wind, the seasons when the gales will be favourable, and the reverse; the latitudes where the changes may be looked for, and the course to be taken to make the quickest passages during each month of the year. The scope of the work may be inferred from the fact, that it describes the courses from New York to California, India, Australia, to England and the North of Europe as far as the White Sea, to Africa and the Mediterranean. Mariners know, to their loss and vexation, that crossing the line involves delay. Lieutenant Maury shows how the delay may be avoided, and indicates the best place of crossing the equatorial region for each month of the year.

"Considering the increase of commerce between this country and the United States, and the multiplication of screw-steamers, which make less noise than paddles, we cannot forbear to notice Lieutenant Maury's recommendation for the establishment of what he calls 'steam-lanes' across the Atlantic. Let this recommendation be faithfully followed, and we shall hear but little of collision and loss of life on the sea. Broad as the ocean is, the route taken by steam-ships between this country and the States comprehends a belt of but 300 miles wide. In 1857 there were always fourteen steamers, seven each way, plying within that belt, exclusive of man-of-war steamers; the number is doubtless greater now, whereby the chances of collision are multiplied; and seeing that the number of passengers conveyed in 1857 was 54,700, any practicable measure for diminution of the risk would be worthy of attention. Lieutenant Maury proposes a practicable measure; namely, to set off a lane 20 or 25 miles wide on the northern edge of the belt for steam-ships going west, and a similar lane on the southern edge for those going east, leaving all the middle space, 150 miles in width, for sailing-ships. Were this proposal followed, it is clear that steamers could never meet, though they might overtake each other; and this latter contingency would be an advantage, because, in case of accident, a disabled vessel might be assisted. When once such lanes are properly laid down on the charts, a sailing-ship, if compelled to cross them, would do so as quickly as possible, and would know on what side to look for danger."

Along with this question of currents we must not lose sight of the question of the depths of the ocean. Beyond the depths of three or four hundred fathoms, the usual methods of sounding are very uncertain, and cannot be depended on. When the common lead is used, no shock is communicated at these great depths to those above, and therefore they are not aware when the lead reaches the bottom. Nor when Massey's sounding machine is used does it avail, as that instrument cannot be so constructed as to bear the enormous pressure of so many hundred atmospheres exerted by the vast column of water, which it is necessary to penetrate.

Now, until the Atlantic Ocean between England and America was sounded, and the great problem of the depths

of water ascertained, it was quite obvious that no attempt could reasonably be made to sink a telegraph cable to the bottom of the ocean, and so join the two countries. To gain the proper soundings, many contrivances were proposed and tried without much success; at length a very simple and ingenious plan was suggested by Lieutenant Brooke, of the United States navy. By his contrivance the sounding line, with an apparatus attached to it, was taken down by a heavy weight, which acted as a sinker; when the bottom was reached, the weight immediately detached itself by a mechanical contrivance, and the apparatus being relieved of its load, was lifted again through the water, bringing up with it, if sufficiently soft, a specimen of the bottom as a proof of its having actually reached solid matter. The contrivance in question consists of a rod, at whose lower end is an inverted cup, provided with a valve, and from the upper end of which is slung a cannon-ball, hollowed to receive the rod. The mode of slinging the ball and suspending the rod is such, that as soon as the bottom of the rod rests upon the bottom of the sea, and the weight is thus removed from the line, the ball is released from its sling, and drops off. The rod, which is of no great weight, can be lifted with the line, and the cup carries up indications of the bottom, and when soft, a portion of the bottom itself.

This apparatus, with some modifications by Massey, has been adopted by British navigators. The weights to be detached vary from 32 lb. to 96 lb. In the year 1857 her Majesty's steam-vessel Cyclops, Lieutenant Dayman, furnished with these machines, sounded the Atlantic Ocean between Ireland and Newfoundland, and verified the soundings previously ascertained by Lieutenant Berrysman, of the United States steam-vessel Arctic.

It may not be uninteresting to the reader to state, that the greatest depth of water obtained by the Cyclops was nearly 2500 fathoms; at that depth the pressure would be nearly three tons to the square inch. In hauling in the line the friction in lifting it through the water was so great, that before overcoming the inertia and moving the line, it required the whole power of a 12-horse steam-engine, with which the Cyclops had been fitted expressly for the purpose.

We are indebted to the Americans for the first successful attempt to bring to the light of day the secrets of the deep, dark dwelling places, till now, without any relation to human interests, but through which hereafter many of the important events of the world will be communicated. And we have no doubt, that our naval officers will follow up these investigations, and if so, we may hope that in a few years we shall have obtained such accurate knowledge of the bottom of the whole ocean, that the placing of telegraph cables will become a comparatively easy task. For further information upon this subject, the reader is referred to a work entitled, Deep-Sea Soundings in the North Atlantic Ocean, by Lieutenant-Commander Joseph Dayman, 1858; also to the fifth article in the Westminster Review for October 1859.

In the first rank of instruments used at sea, we would place the sextant, not the old wooden quadrant, but the brass sextant, as improved by Troughton and Cary, divided to ten seconds, and capable of taking observations with a precision formerly considered inconsistent with the use of a reflecting instrument. The seaman, with such an instrument in his hands, aided by the present nautical almanac, accompanied with either of the excellent treatises on navigation, by Raper or Inman, may determine with exactness the ship's place, in the midst of a boundless ocean, a thousand miles from land. This exactness, within certain appreciable limits, distinguishes the sextant from all other nautical instruments. Its operations are connected with those of the sun, moon, and stars; and by its very construction, its

Seaman- principal error may often be ascertained at the very time ship. of making the observation, and allowed for accordingly. The chronometer, which stands next in utility, is essentially a fallible instrument, and although eminently useful in the navigation branch of seamanship, can never be depended upon as the sextant. These two instruments are excellent allies, but neither is sufficient without the other to meet the requirements of modern navigation. A chronometer may, and often does, change its rate, and thus it may deceive; and though the chances of its doing so without detection is much lessened by taking two or three more chronometers in conjunction, still there never can be positive certainty in the result. On the other hand, for all practical purposes, the errors of a sextant lie within the reach of detection and appreciation.

We consider a seaman, who is provided with a modern sextant, with a stand to which it can be fixed, an artificial horizon, and a watch with a compensation balance, or hack chronometer, has a portable observatory, by which he can ascertain the rates of his chronometers with the utmost precision, and that without moving them from their places on board. (For full description and use of the sextant, chronometer, and other nautical instruments, see article NAVIGATION, and also CLOCK and WATCH-WORK.)

Chronometer, im- The next in order of importance in the list of nautical portance of. instruments, after the sextant, is the chronometer, an instrument to which modern seamanship is indebted for very great service. We are old enough to remember when chronometers were only supplied in the navy to ships about to proceed on voyages expressly scientific, and to those ships which bore an admiral's flag. In the merchant service, the East India Company were the only shipowners who supplied chronometers. Certainly at that time a good chronometer cost from £100 to £150, the price is now about £40, with all the modern improvements; but still, when we consider the number of valuable vessels and lives lost by the want of this instrument, all must agree it was a miserable saving. A great change has now taken place; all men-of-war, and we believe all merchant-vessels employed in the foreign trade, are now furnished with chronometers.

Patent sounding machine and patent log. There are two important instruments used in navigation, not in the department of nautical astronomy, which have been introduced within the last fifty years, and to which we shall merely allude. We mean the patent sounding machine and the patent log. By the patent sounding machine the seaman is enabled to determine the depth of water up to 60 fathoms, whilst the ship may be still going about 6 knots through the water. By the patent log, if sufficient care be taken, the exact distance that a ship has gone through the water in a given time may be ascertained with accuracy. No doubt, the common log, supposing it carefully hove, and the officer of the watch attentive to any change of the ship's way during the intervals of heaving the log, will give the distance gone with tolerable accuracy, as long as the ship is under sail alone; but when the steam is used, the common log is not to be depended upon; the seaman must then look to his patent log.

Mariner's compass. Not many years ago, the compasses, on which depended the safety of the ship, on board our men-of-war, were consigned to the charge of the boatswain, and were kept in his store-room, with little more attention given to them than to such articles as twine, canvas, &c.; and in merchant-vessels they even fared worse. At present great pains are taken in the construction of the mariner's compass, and a proper closet is fitted up for their reception. The importance of such care is manifest, when it is recollected that when magnets are placed in proximity to each other, and like poles are laid together, the effect is seriously to impair the magnetic power.

What is called the local deviation of the compass, caused by the iron on board of the ship, is now well under-

stood. Professor Barlow invented a plan of counteracting the effect of the iron of the ship upon the needle, by fixing a circular iron-plate in a vertical position abaft the compass. Professor Airy suggested, to answer the same purpose, placing two large and powerful magnets in the deck, near the compass. But these plans have only partially succeeded, and all men-of-war, and most large merchant-ships, have now their local deviation for each point of the compass, before proceeding to sea, ascertained by actual experiment. A table of these deviations is thus formed, which the seaman uses to correct his courses. The manner of doing this is by taking advantage of a calm day, when the ship is at anchor, and, by means of hawsers, swinging her head round to each point of the compass, noting at the same time the bearings shown by a compass on shore, where there is no local deviation, and by one on board the ship. The differences between the two compasses will show the local deviation, which must be tabulated. (See Mariner's Compass in article NAVIGATION; also Johnson On the Deviation of the Compass, second edition, 1852.)

Amongst the scientific instruments which have within Marine this century been introduced into the art of seamanship, the barometer marine barometer occupies a high and important place. Formerly the only kind of barometer used at sea was the and aneroid. mercurial one. This barometer has the advantage, if properly constructed, of being, from its very nature, always correct; but has this disadvantage, when the ship has much motion, its reading off becomes extremely difficult, from the pumping of the mercury up and down the tube. To remedy this defect, about ten years ago, the aneroid, a French invention, was introduced. This instrument is not the least affected by the motion of the ship, and can be read off at all times with the greatest accuracy. It has, however, a defect, which is this. Although it marks with the utmost precision the relative rising and falling, according to the state of the atmosphere, there may be an error in its positive height, which requires correction from time to time. (See article BAROMETER, in which the principle both of the mercurial marine barometer and the aneroid is fully explained.)

The use of the barometer at sea consists in giving the Use of barometer at sea. seaman information, beforehand, of the changes likely to take place in the direction as well as force of the wind; or, which is sometimes as useful, to let him know, in spite of appearances to the contrary, that there will be no change. But the seaman must recollect that this instrument, as a prognosticator of weather, varies in its degree of utility in different parts of the world. For instance, it is only serviceable in those parts of the tropics which are subject to hurricanes, as it is not affected at all in those regions, except when those great tempests are coming on, and then it suddenly falls about an inch. In this country it often rises, if the wind be easterly, although bad weather may be approaching. On the contrary, off the Cape of Good Hope implicit reliance may be placed upon the rising or falling of the barometer, and the seaman must act accordingly.

We must not forget, amongst the modern improvements Charts. in seamanship, the great advantage of correct charts. Any one aware of the dangers which really exist, but which are omitted in the old charts, wonders how ships in those times ever escaped destruction; and, on the other hand, he finds the sea so covered with rocks, shoals, and those vague "vigias," as they are called, now known to have no existence, that his admiration is great at the boldness of navigators who could sail on at all during the night.

The government of most civilized countries—and here we are pleased that we are enabled to say that the English government has led the way—have taken up this matter in earnest, and sent their surveyors abroad; the result has been that the world has been put in possession of charts of all those harbours, coasts, and seas which are most fre-

quented. At the same time much remains to be done; but if the present progress in marine surveying be continued for a few more years, so accurate will be the construction of charts, that ships duly provided with nautical instruments will seldom incur the danger of running on shore, except by stress of weather, or experience any difficulty in finding safe passages amongst sand-banks, coral reefs, or any other description of submarine dangers, the terror of old navigators.

It would lead us beyond our limits were we to go into further detail, in order to point out the various minor improvements which have been introduced into the practice of navigation. For the same reason, we must omit all mention of the improvements that have taken place in the rope, canvas, rigging, and fitting out of ships.

But with all this that is so favourable, there is still a dark side to the question. By official returns it appears that, in spite of all these improvements, there are annually lost upon our own coasts, upon an average of seven years, about 1200 British merchant-vessels. The number of British seamen drowned, excluding fishermen, and those wrecked in foreign voyages, taking the same average, amount to 750. It also appears that a large proportion of these wrecks arises from causes that might have been easily avoided. The causes are, chiefly going to sea with rotten masts and sails, either bad or no charts on board, not heaving the lead, or not taking an observation, and the ignorance or drunkenness of those in charge of the navigation of the vessel. Surely such a reckless destruction of life and property conveys a very urgent lesson upon all persons in authority, that they should not only foster every improvement connected with our mercantile naval service, but that they should also enforce upon all who are concerned the responsibility they incur to make these experiments effectual.

There are still two topics remaining on which we must be allowed to touch before bringing this article to a close. One is the importance of discipline on board ships, and the amelioration in the moral character of all the seamen of the country. The other is the change which has taken place in the armaments of ships of war, and the alterations and improvements in the training of our seamen, which are now required in consequence of this change. As both of these points have become part and parcel of the seamanship upon which our prosperity as a nation mainly depends, we cannot on this occasion pass them over in silence.

There can be no good seamanship without discipline, for it is as essential to the correct working of a ship that there should be a clearly understood subordination established on board, as it is to the correct going of a chronometer that all the wheels and pinions be made to fit, and be so placed as to work properly into one another.

This well-defined system of discipline and organization is doubly necessary in the navy. In that service large bodies of men are thrown together, and must be governed by the strict application of martial law, which is essentially peremptory in its action, and requires immediate obedience. We are happy to be able to state, that within the last few years the practical and working system has been, that whilst a rigid law must always be kept up, yet the main dependence for bettering the habits and improving our seamen has been based more decidedly on religious and moral training. To this training has been added the plan of giving extra pay for good conduct, and providing pleasant reading for our ships' companies. We are old enough to remember the time when coercion was considered the only means of having an evolution quickly performed. Now, another element is introduced, namely, emulation; and the consequences are these, that in performing evolutions in the fleet, the officers oftentimes are not only spared the necessity of urging their seamen and marines to exertion, but actually have to restrain their ardour to prevent accidents.

All ships commanded by a captain have now chaplains

appointed, joined to which are also the seaman's school-master, to teach the boys, and those of the ship's company who wish to avail themselves of his instructions; and we can also add, as we have already stated, a small library of Religious books is now always supplied, including a sufficiency of instruction. Religious Books, Testaments, prayer-books, and religious tracts.

Something has been done also for our merchant-sailor, but much yet remains to be done for him. Cut off as so many of these seamen are from all religious instruction for a great portion of their lives, it is much to be desired that more active exertions were made at our large seaports to bring a knowledge of Christianity to meet their wants. All that is done to raise the seaman's character, and to give him habits of sobriety, is so much added to the prosperity of the country.

It is now, we are sorry to say, almost the universal practice, for a merchant-ship to be fitted out and rigged by those hired for the express purpose; the crew not going on board until the vessel is on the very point of sailing on her voyage. Following that plan, as soon as the ship returns, the crew are landed. The effect has been, that a large proportion of merchant-sailors at the present time are unable to rig a ship. Now, as no seaman who is not a competent rigger can expect to rise above an able seaman in the navy, that is one reason why it has become very rare for any person arrived at full manhood, and who has been brought up in a merchant-ship, to enter the royal navy. He sees his inferiority to the regular man-of-war sailor, and the two professions are in consequence now almost completely disjoined.

About the year 1827, the maritime nations of the world commenced gradually increasing the size of their ships of war, and adding to the weight of metal of the great guns. Soon after this period the use of shells, fired horizontally, was introduced. The shells are not, as formerly, fired from mortars only, but are thrown from the long guns used in ordinary warfare, and treated the same as round-shot. Within the last few years the quantity of shells supplied to each ship has so much increased that a large proportion is now allowed to each gun on board our men-of-war, and no doubt will now become the principal weapon that will decide the fate of naval warfare. This change in the armaments of our ships required a superior training to be given to both our officers and seamen. An express gunnery department was established for the purpose of instruction, and the manner in which it has been carried out in our ships of war has produced a marked effect in the knowledge of gunnery in the seamen throughout the fleet. We have no hesitation in saying, that a large proportion of the regular men-of-war sailors of the present day are the most perfect artillerymen that the world has ever seen. Such being the case, without a long previous training, it is quite evident, that in the event of a battle, the uninstructed merchant-sailor hastily joining a man-of-war would be of little more service than a landsman, indeed not so much as a landsman who had received any former training at the great guns. It must also be recollected, that the next naval engagement will be fought by ships propelled by the screw, and that the sails will be furled. It will then be found, that the great battle which has to decide the fate of empires will not be so dependent on seamanship as heretofore. It will hang upon the conjoined action of men well trained and well disciplined, but the necessity still remaining of fighting under the direction of able officers, and stimulated by the influence of national sentiment.

Notwithstanding the changes which have taken place within the recollection of many now alive, we cannot foresee all that modern science, skill, and enterprise may effect. A recent invention in the construction of a new species of war-vessel, with sides plated with metal, and carrying the maximum of steam-power with the minimum size of sails,