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It is obvious that each horizontal row of numbers forms an arithmetical series of which the common difference is equal to the first term; the sums of these series, will therefore form another arithmetical series, the common difference of which is equal to the first sum or term, or the sum of the numbers in the upper row, the last term being equal to the sum of the numbers in the lower row. Now, by the rule for summing an arithmetical series, the first term or the sum of the numbers in the upper row, is (n + 1) x which is also the

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YACHT BUILDING.

Sir,-Having seen a letter in one of your late Numbers on the subject of

yacht building, and as it is one in which I feel great interest, and have availed

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YACHT BUILDING.

myself of every opportunity, both of observing different models, and practically testing the results as to their sailing qualities an amusement to which I did always most seriously incline"-and having on two occasions reduced my ideas on it into practice in two small vessels-I think, too,, with rather a successful result-I send you a few observations on the subject, for insertion in your Magazine, should they seem likely to be of service. It is not my intention at present to make any observations on the wave line, nor on the remarks made on that subject in the letter of your correspondent "Forrester;" not that I underrate the importance of that point, or the assistance which a scientific investigation would afford in laying down the most eligible lines for the construction of vessels, but because I wish to confine my remarks to some other points, which seem to me of considerable importance, and yet not to be sufficiently considered, or to occupy so prominent a position in the scientific treatment of this question, as their practical importance would seem to entitle them to.

Persons in general seem to me to consider it too much as if vessels were impelled forward by some inherent principle of motion, acting horizontally, and not, as is the case in sailing vessels, by a force acting in a peculiar manner, and modified in its effects by a great variety of causes. Their different states, when in motion under sail, I will class under two heads. The first is, when the wind is more or less astern. In this case, the boat is propelled by the pressure of the wind acting altogether, or nearly, in the direction of her course; but as the resistance offered by the sails acts on a considerable lever, the mast, the tendency of the moving power is to bury the bows until they are sufficiently sunk to offer the necessary resistance. Now in this case the effect of a long fine bow, from whose facility in heading the water so much is expected, differs materially from those that were calculated on, because, from the sinking forward and rising aft, the theoretical lines have ceased to be the practical ones, and her horizontal section at the water line would now probably be an oval with large end foremost, instead of the reverse, as it was before. Again, an equal mistake would be made if the run should be made too

fine; for vessels built thus, in scudding, are apt to settle by the stern, and are counted very dangerous. The second state is, where a vessel is said to be, on a wind; that is, when the direction of the wind is at either a right, or less than a right angle, with that of her course. In this case, her progress results from a less resistance being offered by the water to her moving ahead than laterally; in fact, its rapidity is proportionate to the comparative difference between the amount of both. I am aware that the difference of the angle at which the wind strikes the sails, and other matters of detail, cause irregularities of various degrees in the practical application of these general principles; but as these modifications are incidental to all forms, and do not particularly affect the principles themselves, I shall not dwell on them.

Vessels intended to go near the wind, or fast on it, are therefore generally constructed sharp in the bottom, with a deep draught of water, and a sharp entrance and run; this form being regarded as the one calculated to offer the greatest resistance to any motion in a direction at right angles to the vessel's length, and the least to one in the direction of it. Experience shows that it is a form which does not produce the full effect anticipated, besides being attended with some drawbacks. No boat sails upright (even the mere spars, lying to one side or other, tilts her, and the more so the sharper she is,) but in proportion as she is pressed with canvass throws up her side; the draught of water is thereby reduced, and the line of her side, from being tolerably perpendicular, is brought nearly horizontal. Thus the resistance her side offered to the water is greatly diminished, while the flat of her bow being sunk in it, her way is greatly retarded; and these tendencies, it must be recollected, increase in proportion as the wind does,just the reverse of what would be desirable. The following sections will explain this better (See next page). No. 1 shows the vessel as she is intended to be; No. 2, as she really becomes. A B, elevations; D E, depth of bearing when upright; B C, as reduced; DFE shows the angle at which the resistance acted on the side, and BIC, the less favourable one to which it changes; causing manifestly a much greater lia

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bility to drift sideways, the water from the direction in which it is acted on, yielding with great facility. The very sharp entrance and run, when the draught of water is very deep, must greatly interfere with any length of floor, and therefore injure her seaworthy qualities, diminishing the ability of carrying sail, her steadiness and tightness in a seaway. The resistance, too, of a deep keel, acting at the extremity of the lever, must of course increase the disposition of a vessel to heel under sail, besides losing its effects in proportion as she does. Of late, I know, yachts have been built of great length to meet many of these difficulties; but, inasmuch as this renders it necessary greatly to reduce the beam, they are seldom able sea-boats. They are, no doubt, often very fast, and may answer very well for racing or river practice, under favourable circumstances; but beyond that I would not trust them much.

And

as people are apt to mast vessels more according to their length than their beam, they are in general quite oversparred for going to sea. Now it is not because I regard the defects to which I have alluded as capable of being completely remedied, that I have made these observations, but because I look upon them as inevitable, or at least to a certain extent more or less incidental to every form of vessel; and ought, therefore, to be more kept in mind in their construction than is done, and greater provision should be made for meeting the consequences of such disturbing causes, and moderating their effects. With this view, another gentleman and I constructed for our amusement a small boat of the form we thought most calculated to diminish or correct

generally the objectionable tendencies. She was a small open boat, of about 21 feet on the keel, something about 7 on the beam, not drawing over 3 feet of water with two or three persons on board. The particulars of her mould are shown by the sketches figs. 1, 2, and 3. (See next page.)

She was what is commonly called a yawl, and therefore, of course, flatter on the floor than a cutter-built boat. The greatest breadth, as will be seen by fig. 1, was at, or just immediately below, the water line A B, from which she tumbled into the gunwale; the difference being about 2 inches of a side. Her floor, E, was straight, and she was turned up sharp at F. CD represents her water line when heeled under sail. The form of this section was adopted as the most likely, under general circumstances, to be the most affected by the lateral resistance of the water, as it secured the sides, being, when submerged by the listing of the boat from the pressure of the wind, in the position most sure of rendering that resistance effective; that is, nearly perpendicular. The stronger, too, the pressure was, the greater would become the surface of the side acted upon, the spread and straightness of the floor giving her great steadiness and power for carrying sail.

Fig. 2 represents a side view, in which A B is the water line, and CDE an imaginary one, pointing out the particular line throughout her length when the side is what is technically called turned up, and equally showing the position of her greatest bearing. The lines marked with the small letters, a, b, c, d, e, f, g, h, are to give some idea of the form of the

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timbers at a few different places. It will be seen by fig. 2 that her floor was both long and straight; an object, in my opinion, of great importance, whether we consider her power of carrying sail, or ability in a seaway; it also keeps tolerably horizontal, so that, though her entrance and run are both sharp, there are no sudden transitions in that direction. By this mould, too, great bearings are placed close to the water, which is also very desirable-ready for service when required in light winds-interfering but little with the facility of motion,

but coming into operation in proportion as the pressure of the wind, and the demand for and utility of supports, increase. In fig. 3 the deck line is given for the purpose of showing that, to carry out the same principles, her beam was made not excessive, but generally diffused, carried well forward and aft; not differing, in several feet amidship, more than sufficient to prevent her being straight-sided (any perfectly straight lines I have always observed make a boat dull and sticky): thus her real bearing was more than if the beam had been greater; but in one

YACHT BUILDING.

place her quarter was full and able (which is absolutely essential for cutterrigged boats), and gently rounded, so as to prevent, as much as possible, any drag in her wake, while the long side bearing against the water checked lee

way.

On trial these lines proved most satisfactory, and we had every reason to be pleased with her general qualities. As a sailing boat in light winds, she was as fast as any boat of her size, even when bearing to windward against a short head-sea-a severe trial, as any person will allow, to most boats; while when it was blowing hard I never saw her equal, carrying her sail and turning to windward like a large vessel; and though only boat built, with a light draught of water, drifting as little as those of twice her size. This was owing, I am sure, to the disposition of the different bearings alluded to above. She headed but little, too; not turning upon her side much, but settling steadily into the water, by which her powers were augmented as they were wanted. This was owing greatly to the form of her bottom, and the principal lateral resistance being high up. The ballast thus acted at one end of the lever, the pressure of the sail at the other, while the top side, resisting the side motion, acted as a fulcrum; whereas, had the principal resistance been made by the keel, the ballast and sails would, to

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a certain extent, have co-operated, in causing a contrary effect, while the equality of her bearings prevented much alteration in her trim fore and aft. Thus they were in action not much different from what they were when she was at rest; at all events, not more than there was a provision for meeting. Before the wind, from her shallow draught, and very steady floor, nothing could catch her. I do not mean that she excelled every boat in every good quality, for that would not be possible-for some, to be perfect, require peculiarities incompatible with excellence in others; but she certainly did surpass most boats of her size that she tried; indeed, I may say all, in the extent to which she combines a variety. In vessels of this mould it is much easier to stow the ballast, and in an effective manner; and their trim is less liable, of course, to error than those whose position varies constantly and greatly. Indeed, we were so well satisfied with this experiment, that we built another (with our own hands too), of about 15 tons, a cutter 27 feet 6 inches on the keel, and about 11 feet 5 inches on the beam; draught of water, 6 feet. Her lines did not differ more from the other than resulted from the one having been a yawl, the last a cutter, and therefore, of course, deeper in the hold, drawing more water, and having a sharper floor. The section was more of this form:

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