Encyclopaedia Britannica [20, 8 ed.]

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ENCYCLOPAEDIA BRITANNICA. EIGHTH EDITION.

ENCYCLOPAEDIA BRITANNICA, OR

DICTIONAEY

ARTS. SCIENCES, AND GENERAL LITERATURE.

EIGHTH EDITION.

WITH EXTENSIVE IMPROVEMENTS AND ADDITIONS; AND NUMEROUS ENGRAVINGS.

VOLUME XX.

ADAM AND CHARLES BLACK, EDINBURGH. MDCCCLX. [The Proprietors of this Work give notice that they reserve the right of translating it.]

EDINBURGH : FEINTED BY NEILL AND CO,

ENCYCLOPEDIA

BRITANNICA

SEAMANSHIP. Seaman- THE present article will be found to embrace a threefold ship. 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 bearDefinition. ]ng ancj 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. 1106 e are ust ec n ca n andcTffi m ^ortance j ^ ^ ' s U* g it a noble art, not only by its culty of the * P ’ its immense it i quite needless to amplify embel. lish, but by extent and difficulty, andorthe proart digious 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 inVOL. xx.

stant, otherwise the so-called seaman, whatever be his pre- Seamantensions, cannot be trusted in charge of a watch. ship. 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 difierent 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 A

2

SEAMANSHIP.

that the persons who shou/a direct the operations on ship- Seamanboard, in conformity to the maxims deducible from M. Bou- ship, a set of practical maxims, as well founded and as logically guer’s propositions, would be baffled in most of his attempts, *~ deduced as the working of a steam-engine or a cotton-mill ? and be in danger of losing the ship. The whole proceeds The stoker or the spinner acts only with his hands, and on the supposed truth of that theory which states the immay “ whistle as he works, for want of thought; hut the pulse of a fluid to be in the proportion of the square of the mechanist, the engineer, thinks for him, improves his ma- sine of the angle of incidence; and that its action on any chine, and directs him to a better practice. May not the small portion, such as a square foot of the sails or hull, is seaman look for the same assistance ; and may not the in- the same as if that portion were detached from the rest, and genious speculist in his closet unravel the intricate thread of were exposed, single and alone, to the wind or water in the mechanism which connects all the manual operations with same angle. But it can be shown, both from theory and the unchangeable laws of nature, and both furnish the sea- experience, that both of these principles are erroneous, and man with a better machine, and direct him to a more dex- this to a very great degree, in cases which occur most frequently in practice, that is, in the small angles of inclinaterous use of it. which has We cannot help thinking that much may be done ; nay, tion. When the wind falls nearly perpendicular on the been zeal- we may say that much has been done. We think highly sails, theory is not very erroneous ; but in these cases, the ously culti- of the progressive labours of Renaud, Pitot, Bouguer, Du circumstances of the ship’s situation are generally such that vated by the practice is easy, occurring almost without thought; and the French Hamel, Groignard, Bernoulli, Euler, Romme, and others ; in this case too, even considerable deviations from the very and are both surprised and sorry that Britain has contriphilosobuted so little in these attempts. Gordon is the only one best practice are of no great moment. The interesting phers. of our countrymen who has given a professedly scientific cases, where the intended movement requires or depends treatise on a small branch of the subject. The government upon very oblique actions of the wind on the sails, and its of France has always been strongly impressed with the no- practicability or impracticability depends on a very small tion of great improvements being attainable by systematic variation of this obliquity ; a mistake of the force, either as study of this art; and we are indebted to the endeavours of to intensity or direction, produces a mighty effect on the that ingenious nation for any thing of practical importance resulting motion. This is the case in sailing to windward, that has been obtained. M. Bouguer was professor of hy- the most important of all the general problems of seamandrology at one of the marine academies of France, and was ship. The trim of the sails, and the course cl the ship, so enjoined, as part of his duty, to compose dissertations both as to gain most on the wind, are very nice things; that is, on the construction and the working of ships. His Traite they are confined within very narrow limits, and a small du Navire and his Manceuvre des Vaisseaux, are undoubt- mistake produces a very considerable effect. The same edly very valuable performances. So are those of Euler and thing obtains in many of the nice problems of tacking, boxBernoulli, considered as mathematical dissertations; and they hauling, wearing after lying-to in a gale of wind, &c. The error in the second assertion of the theory is still are wonderful works of genius, considered as the productions of persons who hardly ever saw a ship, and were totally greater, and the action on one part of the sail or hull is so unacquainted with the profession of a seaman. In this re- greatly modified by its action on another adjoining part, spect Bouguer had great superiority, having always lived that a stay-sail is often seen hanging like a loose rag, alat a sea-port, and having made many very long voyages. His though there is nothing between it and the wind ; and this treatises, therefore, are infinitely better accommodated to the merely because a great sail in its neighbourhood sends off a demands of the seaman, and more directly instructive ; but lateral stream of wind, which completely hinders the wind still the author is more a mathematician than an artist, and from getting at it. Till the theory of the action of fluids his performance is intelligible only to mathematicians. It be established, therefore, we cannot tell what are the forces is true, the academical education of the young gentleman of which are acting on every point of the sail and hull; therethe French navy is such, that a great number of them may fore we cannot tell either the mean intensity or direction of acquire the preparatory knowledge that is necessary ; and the whole force which acts on any particular sail, nor the inwe are well informed that, in this respect, the officers of the tensity and mean direction of the resistance to the hull; Argument British navy are greatly inferior to them. At the same time, circumstances absolutely necessary for enabling us to say against the we may observe, that the French themselves appear so little what will be their energy in producing a rotation round any utility of sensible of the advantage of these publications, that no per- particular axis. In like manner, we cannot, by such a comtheir perputation, find the spontaneous axis of conversion, or the formances ; son among them has attempted to make a familiar abridg- velocity of such conversion. In short, we cannot pronounce ment of them, written in a way fitted to attract attention ; and they still remain neglected in their original abstruse and with tolerable confidence & priori what will be the motions uninteresting form ; in consequence of which, these very in any case, or what dispositions of the sails will produce ingenious and learned dissertations are by no means so use- the movement we wish to perform. The experienced seaful as we should expect. They are large books, and appear man learns by habit the general effects of every disposition to contain much; and as their plan is logical, it seems to of the sails; and though his knowledge is far from being occupy the whole subject, and, therefore, to have done al- accurate, it seldom leads him into any very blundering opemost all that can be done. But, alas! they have oihy ration. Perhaps he seldom makes the best adjustment opened the subject, and the study is yet in its infancy. I he possible, but seldomer still does he deviate very far from it; whole science of the art must proceed on the knowledge of and in the most general and important problems, such as the impulsions of the wind and water. These are the forces working to windward, the result of much experience and which act on the machine; and its motions, which are the many corrections has settled a trim of the sails, which is ultimatum of our research, whether as an end to be ob- certainly not far from the truth, but it must be acknowtained or as a thing to be prevented, must depend on these ledged, deviates widely and uniformly from the theories of which are forces. Now it is with respect to this fundamental point the mathematician’s closet. After this account of the theoretical performances in confessedly that we are as yet almost totally in the dark. And in the erroneous performances of M. Bouguer, as also in those of the other the art of seamanship, and entertaining, as we do, small in their hopes of seeing a perfect theory of the impulse of fundamen- authors we have named, the theory of these forces, by which fluids, it will not be expected that we enter very their quantity and the direction of their action are ascertal princitained, is altogether erroneous; and its results deviate so minutely on the subject in this place; nor is it our ples ; enormously from what is observed in the motions of a ship, intention. But let it be observed that the theory is defectSeaman- know the results of its construction; all these are as fixed ship. as the laws of motion. What hinders this to be reduced to

SEAMANSHIP. Seaman- ive in one point only; and although this is a most import- able difficulty. It is sometimes possible to shape the course Seamanship. ant point, and the errors in it destroy the conclusions of precisely along th^ line of the voyage; and yet the intel- ship, the chief propositions, the reasonings remain in full force, hgent seaman knows that he will arrive sooner, or with v^— though use and the modus operandi is precisely such as is stated in the greater safety, at his port, by taking a different course; may be theory. The principles of the art are therefore to be found made of in these treatises; but false inferences have been drawn, because he will gain more by increasing his speed than he loses by increasing the distance. Some principle must them. by computing from erroneous quantities. The rules and direct him in the selection of this course. This we must the practice of the computation, however, are still beyond attempt to lay before the reader. controversy. Nay, since the process of investigation is leHaving chosen such a course as he thinks most advangitimate, we may make use of it in order to discover the tageous, he must set such a quantity of sail as the strength very circumstance in which we are at present mistaken ; of the wind will allow him to carry with safety and effect, for by converting the proposition, instead of finding the and must trim the sails properly, or so adjust their positions motions by means of the supposed forces, combined with to the direction of the wind, that they may have the greatest the known mechanism, we may discover the forces by possible tendency to impel the ship in the line of her course, means of this mechanism and the observed motions. and to keep her steadily in that direction. Design „ of We shall, therefore, in this place, give a very general His other task is to produce any deviations which he this article. v;evv 0f tjie movements of a ship under sail, showing how sees proper from the present course of the ship ; and to prothey are produced and modified by the action of the wind duce these in the most certain, the safest, and the most on her sails, the water on her rudder and on her bows. We expeditious manner. It is chiefly in this movement that shall not attempt a precise determination of any of these the mechanical nature of a ship comes into view, and it is movements ; but we shall say enough to enable the curious here that the superior address and resources of an expert landsman to understand how this mighty machine is man- seaman is to be perceived. aged amidst the fury of the winds and waves; and, what is Under the article SAILING, some notice has been taken more to our wish, we hope to enable the thinking seaman, of the first task of the seaman, and it was there shown how to generalise that knowledge which he possesses ; to class a ship, after having taken up her anchor and fitted her sails, his ideas, and give them a sort of rational system; and even accelerates her motion, by degrees which continually dito improve his practice, by making him sensible of the im- minish, till the increasing resistance of the water becomes mediate operation of everything he does, aud in what man- precisely equal to the diminished impulse of the wind, and ner it contributes to produce the movement which he has then the motion continues uniformly the same, so long as in view. the wind continues to blow with the same force, and in the A ship con- A ship may be considered at present as a mass of inert same direction. sidered as matter in free space, at liberty to move in every direction, It is perfectly consonant to experience, that the impulse in free space, im- according to the forces which impel or resist her; and of fluids is in the duplicate ratio of the relative velocity. pelled and when she is in actual motion, in the direction of her course, Let it be supposed that when water moves one foot per r resisted by we may still consider her as at rest in absolute space, but second, its perpendicular pressure or impulse on a square opposite exposed to the impulse of a current of water moving equally foot is m pounds. '1 hen, if it be moving with the velocity forces. fast in the opposite direction; for in both cases the pres- V estimated in feet per second, its perpendicular impulse sure of the water on her bows is the same ; and we know on a surface S, containing any number of square feet, must that it is possible, and frequently happens in currents, that be m SV2. the impulse of the wind on her sails, and that of the water In like manner, the impulse of air on the same surface on her bows, balance each other so precisely, that she not may be represented by n SV2; and the proportion of the only does not stir from the place, but also remains steadily impulse of these two fluids will be that of m to n. We may in the same position, with her head directed to the same point of the compass. This state of things is easily con- express this by the ratio of q to 1, making^ =ly lineinofthat her course intended voyage, shapin his „ „ as the front of a box 1 foot long.1-42 „ l lns is frequently very different from that line, and the course „ „ as the front of a box 3 feet long. 129 „ choice of the best course is sometimes a matter of considerThe resistance of sea-water is about greater.

SEAMANSHIP. Seaman2. With respect to air the varieties are as great. The ship. 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— On a square foot Chevalier Borda’s on 16 inches ,, „ on 81 inches Mr Rouse’s on large surfaces

O'OOloOo pounds. 0’00175i „ 0'002042 ,, 0-002291 „

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 Direct impulse on concerning the impulse of fluids,—viz., that the absolute the sail pressure is always in a direction perpendicular to the imperpendi- pe]iej surface, whatever may be the direction of the stream cular to the of We must therefore illustrate the doctrine, by alyard. ways 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, A ship compared floating on its bottom, and fitted with a mast and sail in to an ob- the centre, she would always sail in a direction perpendilong box. cular 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 Fig 1 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 ofFG. These perpendiculars must cross in C. Suppose a mast erected at C, and YCy 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 SeamanY'y. Then, whatever be the direction of the wind abaft ship, this sail, it will impel the vessel in the direction CB. But if the sail has the oblique position Yy, the impulse will be Makes lee in the direction CD perpendicular to CY, and will both way when push the vessel ahead and sideways ; for the impulse CD is11®1 sailing equivalent to the two impulses CK and Cl (the sides of a^irectj’ybe' rectangle of which CD is the diagonal). The force Cl wind. °re 8 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 Cl to CK. The angle &CB 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 sjmbol 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' and B'.2 Then the resistance to the lateral motion is mV2 x B' x sine , Z>CB, and that to the direct motion is mY~ x A' x sine2, Z>CK, or rnY2 x A' x cos26CB. Therefore these resistances are in the proportion of B' x sine2, x to A' x cos2, x (representing the angle of leeway Z>CB by the symbol x). Therefore we have Cl : CK, or Cl : ID = A'‘cos.2a?: B'1 sine2#, = A' : B''

: A': B' * tangent2#.

Let the angle YCB, to which the yard is braced up, be How to called the trim of the sails, and expressed by the symbol find the b. This is the complement of the angle DCL Now Cl : quantity of ID = rad. : tan. DCI, = 1 : tan. DCI, = 1: cotan. b. There-leeway fore we have finally 1 : cotan. b = A': B'• tan.2#, and A' * A' cotan. 6 = B' • tangent2#, and tan.2#= ^p-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° with the keel. Then cotan. 30° = 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 1-732= 12 x tangent2#, and tangent2# = —yry—, =0-14434, and tan. # = 0-3799, and # = 20°, 48' 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 tbe angle of incidence on the front FG is about 70°, and the experiments just now mentioned show that the real resistances exceed the theoretical ones only But the angle of incidence on EF is only 20° 48'. 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°. The matter ot 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-

SEAMANSHIP. Seaman- grees leeway in smooth water and fine weather; and yet

If an accurate model be made of a ship, and if it be placed Seamanin this situation the hull and rigging present a very great in a stream of water, and ridden in this manner by a rope shipsurface to the wind, in the most improper positions, so as to made fast at any point D of the bow, it will arrange itself have a very great effect in increasing her leeway. And if in some determined position AB. There will be a certain we compute the resistances for this leeway of six degrees obliquity to the stream, measured by the angle B06 ; and by the actual experiments of the French Academy on the there will be a corresponding obliquity of the rope, meaangle, we shall find the result not far from the truth,—that sured by the angle FCB. Let yCY "be perpendicular to is, the direct and lateral resistances will be nearly in the CF. Then CY will be the position of the yard, or trim of proportion of Cl to ID. the sails corresponding to the leeway 6CB. Then, if we It results from this view of the matter, that the leeway is shift the rope to a point of the bow distant from D by a in general much smaller than what the usual theory assigns. small quantity, we shall obtain a new position of the ship, which de- We also see that, according to whatever law the resist- both with respect to the stream and rope ; and in this way pends on ances change by a change of inclination, the leeway re- may be obtained the relation between the position of the trim of the mains the same while the trim of the sails is the same. sails and the leeway, independent of all theory, and sussails. The leeway depends only on the direction of the impulse ceptible of great accuracy ; and this may be done with of the wind; and this depends solely on the position of the a variety of models suited to the most usual forms of sails with respect to the keel, whatever may be the direc- ships. tion of the wind. This is a very important observation, In further thinking on this subject, we are persuaded and will be frequently referred to in the progress of the that these experiments, instead of being made on models, present investigation. Note, however, that we are here may with equal ease be considering only the action on the sails, and on the same made on a ship of any sails. We are not considering the action of the wind on size. Let the ship the hull and rigging. This may be very considerable; and ride in a stream at a it is always in a lee direction, and augments the leeway; mooring D (fig. 3), by and its influence must be so much the more sensible, as it means of a short hawbears a greater proportion to the impulse on the sails. A ser BCD from her ship under close-reefed topsails and courses, must make bow, having a spring more leeway than when under all her canvas, trimmed AC on it carried out to the same angle. But to introduce this additional cause from her quarter. She fi 3 of deviation here would render the investigation too com- will swing to her moors- plicated to be of any use. ings, till she ranges herself in a certain position AB with IllustraThis doctrine will be considerably illustrated by attend- respect to the direction ba of the stream ; and the direction tion of this mg to the manner in which a lighter is tracked along a 01 the hawser DC will point to some point E of the line of doctrine by canal, or swings to the keel. Now, it is plain to any person acquainted with experimechanical disquisitions, that the deviation BE6 is precisely ments on its anchor in a models and stream. The trackthe leeway that the ship will make when the average posirope is made fast tion of the sails is that of the line GEH perpendicular to to some staple or ED; at least this will give the leeway which is produced bolt E on the deck by the sails alone. By heaving on the spring, the knot C (fig. 2), and is may be brought into any other position we please; and for passed between two every new position of the knot the ship will take a new of the timber-heads of the bow D, and laid hold of at F position with respect to the stream and to the hawser. And on shore. The men or cattle walk along the path FG, we persist in saying, that more information will be got by the rope keeps extended in the direction DF, and the this train of experiments than from any mathematical theory: lighter arranges itself in an oblique position AB, and is for all the theories of the impulses of fluids must proceed thus dragged along in the direction ab, parallel to the on physical postulates with respect to the motions of the side of the canal; or, if the canal has a current in the filaments, which are exceedingly conjectural. opposite direction the lighter may be kept steady in And it must now be farther observed, that the substitu- The comits place by the rope DF made fast to a post at F. In tion which we have made of an oblong parallelepiped for aparison of this case, it is always observed, that, the lighter swings ship, although well suited to give us clear notions of the a shiP t0 in a position AB, which is oblique to the stream ab. Now, subject, is of small use in practice; for it is next to impos- anobl°ng the force which retains it in this position, and which pre- sible (even granting the theory of oblique impulsions) to^y^e cisely balances the action of the stream, is certainly exerted make this substitution. A ship is of a form which is not fui^give in the direction DF; and the lighter would be held in the reducible to equations; and therefore the action of the clear nosame manner if the rope were made fast at C amidship, water on her bow or broadside can only be had by a mosttions on without any dependence on the timberheads at D; and it laborious and intricate calculation for almost every squarethe subjectwould be held in the same position, if, instead of the single foot of its surface.1 And this must be different for every rope CF, it were riding by two ropes CG and CH, of which ship. But, which is more unlucky, when we have got a CH is in a direction right ahead, but oblique to the stream, parallelepiped which will have the same proportion of direct and the other CG is perpendicular to CH or AB. And, and lateral resistance for a particular angle of leeway, it drawing DI and DK perpendicular to AB and CG, the will not answer for another leeway of the same ship; for strain on the rope CH is to that on the rope CG as Cl to when the leeway changes, the figure actually exposed to CK. T. he action of the rope in these cases is precisely the action of the water changes also. When the leeway analogous to that of the sail yY ; and the obliquity of the is increased, more of the lee-quarter is acted on by the keel to the direction of the motion, or to the direction of water, and a part of the weather-bow is now removed the stream, is analogous to the leeway. All this must be from its action. Another parallelepiped must therefore evident to any person accustomed to mechanical disqui- bej discovered, whose resistances shall suit this new posisitions. tion of the keel with respect to the real course of the A most important use may be made of this illustration. ship. ship-

1

Bezout’s

Cours de Mathcm.,

vol. v., p. 72, &c.

S E A M A N S H I P.

6

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. The relaLet AB (figs. 4, 5, and 6) represent the horizontal section hetion of a ship. In place of tween the a][ ^jie drawing sails—that is, Seaman-

ship,

the°sChiy

of the sails which are real, filled

y

—we can always substitute one ascertain- sail of equal extent, trimmed ed. to the same angle with the keel. This being supposed attached to the yard DCD, Fig. 4. 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 CFEe, producing eC through the centre of the yard to zv. 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. When a Thus it happens, that when a ship is in motion the apehip is in parent direction of the wind is always ahead of its real dimotion, the rection. The line wC is always found within the angle apparent WCB. It is easy to see from the construction, that the and Vind

ih^wind Is difference between the real and apparent directions of the alway^dif- wind is so much the more remarkable as the velocity of the ferent from ship is greater. For the angle WCw or ECe depends on the real the magnitude of Ee or CF, in proportion to CE. Persons direction. 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 Seamanbe very different from that of the air below ; and when the ship, 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 nay, 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 closehauled 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. 1 he celebrated as- observatronomer Dr Bradley, taking the amusement of sailing in a tion 0f Dr pinnace on the river Thames, observed this, and was sur- Bradley on prised at it, imagining that the change of the wind was this subowing to the approaching to or retiring from the shoreJect* The boatmen told him that it always happened at sea, and explained it to him ig 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

SEAMANSHIP. 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 We now resume the investigation of the velocity of the a ship ship (fig. 4), having its sails at right angles to the keel, and when its the wind blowing in the direction and with the velocity sails are CE, while the ship proceeds in the direction of the keel at right angles to with the velocity CF. Produce Ee, which is parallel to and draw FG perpendicular the keel. BC, till it meet the yard in to E?. Let a represent the angle WCD, contained between the sail and the real direction of the wind, and let 6 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 FE2 x sin 2/47CD. NOW the angle GFE = wCD, and EG is equal to FE x sin GFE ; and EG is equal to E# - G^. But E^ = ECxsin EQy, = V x sin a ; and ffG = CF, = v. 1 herefore EG = V x sin a — v, and the impulse is proportional to (V x sin a — v)2. If S represent the surface of the sail, the impulse, in pounds, will be «S (V x sin a — 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 w ith. This impulse, in pounds, will be mA.v2. Therefore, because we are considering the ship’s motion as in a state of uniformity, the two pressures balance each other; and thereSeaman ship.

fore m Air =raS(V x sin a — u)2and — A.v2 = S(V xsina-t?)2; therefore x

nW

A x i; =

V x sin a __ V x sin a r

mA \/~ +l T

x V x sin a - fly's, and

v=

V x sin a

\/ < ^

A + \/ 6 7S + 1* n ' / ~ W e see, in the first place, that the velocity of the ship is, cater is paribus, proportional to the velocity of the wind, and to the sine of its incidents on the sail jointly ; for while the smface of the sail S and the equivalent surface for the bow remains the same, v increases or diminishes at the same rate with ¥• sin. a. When the wind is right astern, the sine of

a

T

7

is unity, and then the ship’s velocity is-

V raS +

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,-^-is also a number. It must also be carefully attended to, that S expresses a quantity of sail actually receiving wind with the inclination a. it will not always be true, therefore, that the velocity wi increase as the wind is more abaft, because some sails will then becalm others. This observation is not, however ot great importance ; for it is very unusual to put a ship m 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^-j-A gives us no

+ L

__ . //«A K/m\. V ^ + «=V, andV

n

and^gn2 =

-2 Seamany ? ship.

, nS

and because n and m and A are Con(V—li)2 a slant quantities, S is proportional to^ v or the surand —- =

«*A

face 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 onefourth of it, we must quadruple the sail. This is more easily seen in another wray. 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. I herefore, 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 Its velocity former, because, when the sails are trimmed to any oblique sa when the position DCB (figs. 5 and 6), there must be a deviation ^.s stan(l from the direction of the ,, oblique to keel, or a leeway BC6. ^ the keel. 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 x sin a, and Fis 5 G