CO-FD XCO-FD against the convex furface, as, FD2 to CF2 The whole refiftance therefore of the medium will be CO-FD XCO-FD2 DF2+ Confequently, if we fup CF2 and if we take CF CO, we fhall have CO2 for the force of the particles of water ftriking against the maft or tree when towed with the but-end foremost. Now it is very evident, that when it is towed with the other end fore CF CO moft, COXCF will exprefs the force acting in that direction; but as CF will always be greater than CO, it follows, that CO2 must be lefs than unity; whence it is evident, that CO2 CO2 will always be greater than COX-CF2 and as these expresfions are refpectively as the forces of the water acting upon the tree or maft, it must neceffarily follow, that when the but-end moves foremoft, 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 effential quality, the immerged part must be of fuch a form as to be able to fuftain the whole weight of the hip compleatly rigged, with guns, ftores, &c. The weight of all fhips of war, of every rate, is now well known; fo that we may find, by calculation, if the load water line be properly placed: but this is not all that is to be confidered; great regard must be had to the velocity, ftability, property of fteering well, carrying fail, and many other neceffary and feemingly oppofite qualities. How to attain all these qualities has been attempted by feveral eminent mathematicians and builders, who, inftead of determining any particular form, have produced as many different, and feemingly 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 fhip when loaded, and alfo the center of gravity of the column of water fhe difplaces; M. Bouguer likewife gives directions how to flow the goods, fo that the center of gravity may be properly placed with refpect to the metacenter and the center of gravity of the column of difplaced water; which last cannot be altered after the fhip is built. It is on the proper fituation of thefe that the stability of the ship depends. As to velocity, they have given us rules for calculating the refiftance of the fluid on the fore part of the fhip: but but unless it can be proved that the velocities are always proportional to the refiftances, it seems we fhall gain little by this; as there is no account taken of the after body, and in the calculations they fuppofe the fhip to be upright, and failing in the direction of the keel; whereas a fhip often lays her fcuppers in the water, when close hauled on a wind, and fometimes makes two or three points lee way, feldom lefs than one; and yet some fhips in fmooth water will then fail within two or three knots as faft as when going large. We may venture to affert, there will be no proportion betwixt the velocities and refiftances in these two cases; for in the firft all the particles that ftrike the fore part loofe their power as foon as they pafs the midship frame; afterwards, according to his principles, they occafion no refiftance; whereas, in the fecond, every particle has its full force, acting on the whole length of the fide, and the area of the fection, which in this laft cafe would receive the perpendicular fhock, would be almost double that of the midship frame; add to all this that there is room to fufpect these rules of being deduced from wrong principles, as was before obferved. But admitting all this, and that the velocities may be calculated, after the fhip is built, and found even by experience to be proportionate to the refiftances, what will that avail us, if we have no inft uctions how to form the body, fo as to be capable of the greatest velocity, in all pofitions, confiftent with the requifite capacity, ftability, &c? There are other very material points to be confidered, fuch as the center of rotation, or the axis on which the ship turns when fhe inclines to one fide, when fhe tacks or pitches; thefe are continually fhifting, as is the point of fuftentation or fufpenfion. In all branches of the mathematical sciences, there are certain theorems demonftrated, from whence the practical rules for the folution of various problems are deduced, in which there are always fome neceffary data given, by which the unknown things may be discovered. It is to be wifhed we could proceed in the fame manner, and with the fame certainty, in fhip-building; but I do not find that any who have treated that fubject have given us any invariable rules for fettling thefe points; and indeed, confidering the infinite number of properties, and in fome cafes fo oppofite to one another, that if any of them be purfued to too great a degree, it will deftroy another very effential quality. I fay confidering all thefe things, it will be a very difficult task, if not impoffible, to unite them all in one body; add to this that the different feas, and different fervices in which they are to be em-s ployed, will require as different forms; fo that theory alone, without actual experiment, feems infufficient to reduce this complicated art to a regular fyftem. I fhall juft mention fome of the neceffary data. ift, The ift. The whole weight of the fhip compleatly rigged and boarded. This is generally given, both in ships 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 moft ships of war is now pretty well known, as the number and weight of the guns, provifions, &c. of each rate is established. 2d. The length of the gun deck. This in fhips of war may be nearly determined by the number of guns. 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 falt water, and dividing those by the area of the load-water line, we fhould have the depth or draught of water; that is, fuppofing 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 fhips are to encounter high feas, and fuftain the violence of storms of wind, it is plain they will require a quite different form. 4th. The depth of the hold, and draught of the water fore and aft. 5th. The extreme breadth of three fections 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 fections; 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 fituation and exact form of the midship frame and likewife 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 fay the whole form of the fhip is determined. The great difficulty will be to obtain thefe data. M. Boùguer, and after him M. Duhamel, hath purfued this fubject as far as the nature of theory is capable; from whence they have deduced several useful practical inferences, but have ftill left these points undetermined, and at laft refer us to the general practice of the most experienced builders. So that what improvements have been hitherto made feem chiefly owing to experience; and fome think it highly probable that the form which comes nearest nature, fuch as that of the fwifteft fishes, will beft anfwer the purposes of shipping. But here we fhall find ourfelves very much embarralled; for fifhes 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 courfe by 1 by an external force, the author of nature having furnished them with every thing that is neceffary, either for pursuing their prey in a direct course, or turning themselves as occafion requires; whereas in a fhip, it is quite otherwife, as fhe is entirely fubject to an external force, and governed by the helm; and therefore her form must be fuch as may be most capable of receiving these impreffions, and what nature has denied her, must be fupplied by art.' We fhall 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 fhip-builder, who is at the fame time an able mathematician, will bid much fairer for making improvements in the art he profeffes, than another of the fame experience, who knows only the rudiments of mathematics. The various pofitions, &c. of a fhip at fea, will doubtless for ever render it impoffible to form a veffel perfect in every refpect; but it will furely be granted, that mathematical reafoning, founded on accurate experiments, is the only method that can be pursued with advantage, for carrying the art of hip-building to the greateft degree of perfection it is capable of attaining. Nor is this opinion founded on the mere dictates of the warm imagination of a theorift; 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 artifts and mathematicians their country could boaft of, who have united theory with practice, and drawn juft confequences from known data. This is the fource from whence they have derived that knowlege, by which they have fo greatly improved the forms of fhips, and carried the neceffary art of fhip-building to fo confiderable a degree of perfection. It is furely a very ftrange method of reafoning to say, that because theory and experience in the art of fhip-building often difagree, the former can be of no ufe: for we fhould be glad to know in what branch of literature there is a perfect coincidence between theory and practice? When does the navigator, for inftance, find his dead-reckoning agree with celeftial obfervation? 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 fhould be laid afide, and the feaman 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 conftructed, can be found by calculation. But was there ever any machine or engine yet known, whofe actual performance exactly coincided with the maximum found by theory? Surely no. But is there any reafon for ex 6 ploding ploding the latter, because it will always exceed the former? Does it not, on the contrary, direct how, and in what parts, we fhould alter the engine, in order to carry it to the greatest degree of perfection it can poffibly attain; and at the fame time ferve as a fure criterion to judge whether the workmanship itself be well or ill executed? But Mr. Murray fays that Meff. Bouguer and Duhamel have already pursued this fubject as far as the nature of theory is capable. We muft, however, beg leave to be of a different opinion; and will venture to fay, that many useful deductions may be made from their data, which they have omitted, and feveral useful properties inveftigated from the known laws of motion, which -they have paffed over in filence. But this is not a place to difcufs a topic of this kind, as Mr. Murray's Abridgment, not the works of Bouguer and Duhamel, is the fubject of this article. 6 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 refiftances, we fhall gain little by knowing how to calculate the resistance of a fluid on the forepart of the fhip.' He adds, that fome fhips, when close hauled upon 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 faft, as when going large;' and hence concludes, that there is no proportion, in thefe cafes, between the velocities and the refiftances.' But the writer fhould have remembered, that -the relative force of the wind is very different in these cases. -A fhip when failing large, moves nearly in the fame direction with the wind, and confequently its velocity is leffened by nearly the whole velocity of the fhip: whereas in failing clofe hauled, the wind ftrikes the fails with nearly its whole abfolute velocity. Now as action and re-action are always equal, or the refiftance of the fluid equal to the force of the wind on the fails, it will follow, that ships may fail almoft as faft in the former direction, as in the latter. Thefe cafes, therefore, are far from being fufficient to prove that there is no proportion betwen the velocities and refiftances. We may alfo obferve, that this is one of the principal reasons why a horizontal wind-mill can never be made to do the fame quantity of work with a vertical wind-mill. -Mr. Murray adds, in the fame paragraph, that there is room to fufpect, that thefe (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 fhould have demonftrated that these principles fare really falfe, instead of contenting himfelf with faying, there is room to fufpect they are fo. The importance of the problem demanded, at leaft, an attempt of this kind; and we could with he had made it; becaufe, |