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against the convex surface, as, FD: to CO-FD XCOʻ-FD2

CF2 The whole resistance therefore of the medium will be 082.00-FDo XCO--FD?.

2. Consequently, if we sup

CO2XCO2 pose FD=0, the expression will become

; and if we take CF=CO, we fhall have CO2 for the force of the particles of water striking against the mast or tree when towed with the but-end foremost. Now it is very evident, that when it is towed with the other end foremost, CO-X will express the force acting in that direction; but as CF will always be greater than Co, it follows, that CO2 CEE must be less than unity; whence it is evident, that CO2 will always be greater than CO-xam; and as these expresfions are respectively as the forces of the water acting upon the tree or mast, it must neceíTarily follow, that when the but-end moves foremost, the force of the water to oppose that motion, will be greater than the force of the water to oppose the motion of the moving body when towed in a contrary direction. Q.E.D.

"Since capacity, proceeds our Author, is an essential quality, the immerged part must be of such a form as to be able to sustain the whole weight of the ship compleatly rigged, with guns, stores, &c. The weight of all ships of war, of every rate, is now well known; lo that we may find, by calculation, if the load water line be properly placed: but this is not all that is to be considered ; great regard must be had to the velocity, stability, property of steering well, carrying fail, and many other necessary and seemingly opposite qualities. How to attain all these qualities has been attempted by several eminent mathematicians and builders, who, instead of determining any particular form, have produced as many different, and seemingly directly, contrary rules, as there are different complections and ftatures among the projectors.

« The mathematicians have given certain rules for finding the center of gravity, both of the ship when loaded, and also the center of gravity of the column of water she displaces; M. Bouguer likewise gives directions how to ftow the goods, so that the center of gravity may be properly placed with respect to the metacenter and the center of gravity of the column of displaced water, which last cannot be altered after the ship is built. It is on the proper situation of these that the stability of the ship depends. As to velocity, they have given us rules for calcuJating the resistance of the fluid on the fore part of the thip:

but

towed the ware to opposen the but the

ged part of the thip.comips of war, by calcu

water, wheints lee way then fail w

but unless it can be proved that the velocities are always proportional to the resistances, it seems we shall gain little by this; as there is no account taken of the after body, and in the calculations they suppose the ship to be upright, and failing in the di. rection of the keel; whereas a fhip often lays her scuppers in the water, when close hauled on a wind, and sometimes makes two or three points lee way, seldom less than one ; and yet some ships in smooth water will then sail within two or three knots as fast as when going large. We may venture to assert, there will be no proportion betwixt the velocities and resistances in these two cases; for in the first all the particles that strike the fore part loose their power as soon as they pass the midship frame ; afterwards, according to his principles, they occasion no refiftance ; whereas, in the second, every particle has its full force, acting on the whole length of the fide, and the area of the section, which in this last case would receive the perpendicular shock, would be almost double that of the midship frame; add to all this that there is room to suspect these rules of being de-. duced from wrong principles, as was before observed. But admitting all this, and that the velocities may be calculated, after the ship is built, and found even by experience to be proportionate to the resistances, what will that avail us, if we have no inst uctions how to form the body, so as to be capable of the greatest velocity, in all positions, consistent with the requisite capacity, stability, &c? There are other very material points to be considered, such as the center of rotation, or the axis on which the ship turns when she inclines to one side, when the tacks or pitches; these are continually shifting, as is the point of luftentation or suspension.

In all branches of the mathematical sciences, there are certain theorems demonstrated, from whence the practical rules for the solution of various problems are deduced, in which there are always some necessary data given, by which the unknown things may be discovered.

• It is to be wished we could proceed in the same manner, and with the same certainty, in ship-building; but I do not find that any who have treated that subject have given us any invariable rules for settling these points; and indeed, considering the infinite number of properties, and in some cases so opposite to 'one another, that if any of them be pursued to too great a degree, it will destroy another very essential quality. I say confidering all these things, it will be a very difficult task, if not impoffible, to unite them all in one body; add to this that the different seas, and different services in which they are to be employed, will require as different forms; fo that theory alone, without actual experiment, seems insufficient to reduce this complicated art to a regular system. I thall just mention fome of the necessary data.

ift, The ift. The whole weight of the ship compleatly rigged and

board This is gene fervice, bunss but

- This is generally given, both in fhips of war, and in those for the merchant service, being what is generally understood by tuns; that is, builder's tuns, but the true tunnage of most Thips of war is now pretty well known, as the number and weight of the guns, provisions, &c. of each rate is established. • 2d. The length of the gun deck.

This in thips of war may be nearly determined by the numbor of guns.

o 3d. The breadth.

. If the section of the load-water line were a regular curve, the length would determine this, and its area might be calculated ; and converting the whole length into cubick feet of salt water, and dividing those by the area of the load-water line, we should have the depth or draught of water ; that is, supposing the form of the body to be that of a bathing tub, which perhaps would be very proper for carrying goods in a canal, where it might be dragged by horses; but as ships are to encounter high seas, and sustain the violence of storms of wind, it is plain they will require a quite different form. i ' 4th. The depth of the hold, and draught of the water fore and aft.

o sth. The extreme breadth of three sections at right angles to the keel, and perpendicular to the plain of flotation; and likewise the extreme heights of these breadths, together with the breadths and heights of the top-timbers of these sections ; one of them to be near the middle, another at the after end of the keel, and the third at the beak head. • 6th. The rake of the post and stem.

7th. The situation and exact form of the midship frame and likewise of the two vertical sections ; and if to these three we add the other two which M. Duhamel calls the balance frames we may safely say the whole form of the ship is determined.

- The great difficulty will be to obtain these data. M. Bouguer, and after him M. Duhamel, hath pursued this subject as far as the nature of theory is capable; from whence they have deduced several useful practical inferences, but have still left these points undetermined, and at last refer us to the general practice of the most experienced builders. So that what improvements have been hitherto made seem chiefly owing to experience; and some think it highly probable that the form which comes nearest nature, such as that of the swiftest fishes, will best answer the purposes of shipping. But here we shall find ouro selves very much embarrassed; for fishes are wholly immerged, and the force that moves them is wholly in their own power, and they are in no danger of being drove out of their intended course

by

by an external force, the author of nature having furnished them with every thing that is necessary, either for pursuing their prey in a direct course, or turning themselves as occafion requires ; whereas in a ship, it is quite otherwise, as she is entirely subject to an external force, and governed by the helm; and therefore her form must be such as may be most capable of receiving these imprefsions, and what nature has denied her, must be supplied by art.'

We shall not pretend to dispute the difficulty, or rather the impoffibility, that must attend our obtaining all the above data in a very accurate manner ; but we will venture to affert, that an experienced ship-builder, who is at the same time an able mathematician, will bid much fairer for making improvements in the art he professes, than another of the fame experience, who knows only the rudiments of mathematics. The various positions, &c. of a ship at sea, will doubtless for ever render it impossible to form a vessel perfect in every respect; but it will furely be granted, that mathematical reasoning, founded on accurate experiments, is the only method that can be pursued with advantage, for carrying the art of thip-building to the greatest degree of perfection it is capable of attaining

Nor is this opinion founded on the mere dictates of the warm imagination of a theorist; no: it is founded on experience. What amazing improvements have the French made in this useful art, during the interval of a few years ! But by what methods have they done this? By employing the most able artists and mathematicians their country could boast of, who have united theory with practice, and drawn just confequences from known data. This is the source from whence they have derived that knowlege, by which they have so greatly improved the forms of ships, and carried the necessary art of thip-building to fo confiderable a degree of perfection.

It is surely a very strange method of reasoning to say, that because theory and experience in the art of thip-building often disagree, the former can be of no use : for we should be glad to know in what branch of literature there is a perfect coincidence between theory and practice? When does the navigator, for instance, find his dead-reckoning agree with celestial observation ? Is not he always obliged to correct the former whenever he has an opportunity of making the latter? But is this any reason that the theory of navigation should be laid aside, and the seaman fufter himself to be guided entirely by practice? It is also well · known that the maximum of every machine, or engine, however complicated, or however constructed, can be found by calculation. But was there ever any machine or engine yet known), whose actual performance exactly coincided with the maximum found by theory ? Surely no. But is there any reason for ex

ploding

ploding the latter, because it will always exceed the former? Does it not, on the contrary, direct how, and in what parts, we should alter the engine, in order to carry it to the greatest degree of perfection it can possibly attain ; and at the same time serve as a fure criterion to judge whether the workmanship itself be well or ill executed ?

But Mr. Murray says that Mesf. Bouguer and Duhamel have already pursued this subject as far as the nature of theory is capable. We must, however, beg leave to be of a different opinion; and will venture to fay, that many ufeful deductions may be made from their data, which they have omitted, and several useful

properties investigated from the known laws of motion, which - they have passed over in silence. But this is not a place to dir

cuss a topic of this kind, as Mr. Murray's Abridgment, not the • works of Bouguer and Duhamel, is the subject of this article.

Another remark may not be improper on the above extract. Mr. Murray fays that till it can be proved, that the velocities are proportional to the resistances, we shall gain little by knowing how to calculate the resistance of a fluid on the forepart of the fhip.' He adds, that some fhips, when close hauled uport a 'wind, tho' often laying their scuppers in the water, and making two or three points lee-way, will fail within two or three knots as fast, as when going large;' and hence concludes, that o there is no proportion, in these cases, between the velocities and the resistances.' But the writer thould have remembered, that - the relative force of the wind is very different in these cases. . - A Thip 'when failing large, moves nearly in the same direction

with the wind, and consequently its velocity is lessened by nearly the whole velocity of the ship: whereas in failing close hauled, the 'wind ftrikes the sails with nearly its whole absolute velocity. Now as action and re-action are always equal, or the refistance of the fluid equal to the force of the wind on the fails, it will follow, that thips may fail almost as fast in the former direction, as in the latter. These cases, therefore, are far from be. ing sufficient to prove that there is no proportion betwen the veJocities and refiftances. We may also observe, that this is one of the principal reasons why a horizontal wind-mill can never be made to do the same quantity of work with a vertical wind-mill.

Mr. Murray adds, in the same paragraph, that there is room no suspect, that these (Bouguer's) rules, are deduced from wrong principles. But furely an infinuation of this kind is beneath either a mathematician or a candid writer. He should have de. monstrated that these principles are really false, instead of contenting himlelf with faying, there is room to suspect they are • so.' The importance of the problèm' demanded, at least, an attempt of this kind; and we could wiin he had made it ; because,

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