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which are designed after the midship-section and leading waterline. Their position is optional; but in most cases it is convenient to place them (as directed by Fincham in his Outlines of Naval Architecture) at one-third of the length of the fore-body and after-body respectively, from the ends of the line of flotation, AB. They are so placed in the figure, where the forward balancesection is marked E, and the after balance-section, F. In vessels. with very fine and sharp ends, it may sometimes be convenient to place the balance-sections at the middle of the length of the forebody and after-body respectively. One half-breadth in each of those sections is already determined-viz., where they intersect the leading water-line, DD. The sections are completed according to the judgment of the naval architect; and their form is generally such as to give sharpness to the floor for resisting rolling and leeway, to make the water-lines gradually become finer from above downwards, and to flare out above water, for the sake of liveliness in pitching and scending, and of giving sufficient breadth to the decks, especially towards the stern of the vessel.

Additional Water-lines (such as ACB, and GG) can now be designed in any required number above as well as below water, by drawing (either by the eye, or by process described in WaveLine theory,) a series of fair curves through the points where a series of horizontal planes cut the midship and balance-sections.

Vertical Longitudinal Sections.-Additional longitudinal sections, or bow and buttock-lines, can now be laid down, by first drawing straight lines (such as those marked H) on the halfbreadth plan and body-plan to represent the planes of those sections, and then marking on the sheer-plan the points where those planes intersect the midship and balance-sections, and the waterlines, and drawing fair curves through those points. An example of a longitudinal section is represented by the dotted line, marked HH in the sheer-plan, Fig. 32.

The fairness of the buttock lines, or after-parts of the longitudinal sections is so important, that the naval architect may sometimes find it advisable to design a leading buttock-line before any of the water-lines, and then adapt the water-lines of the afterbody to it.

Riband or Diagonal Lines are oblique longitudinal sections, sometimes used in testing the fairness of the body; but it is unnecessary to refer to them further here, as their construction will be described in a subsequent division of this work.

Additional Cross-sections, in any number that may be considered necessary, can now be constructed, so as to complete the body plan, by taking their half-breadths at the several water-lines from the half-breadth plan. None of these are shown in Fig. 32, but numerous examples of them are contained in the other plates. By the Main-breadth-line is meant, a line on the surface of the vessel, cutting each of the cross-sections at the point where its breadth is greatest. Its figure can be constructed on the three plans after the cross-sections have been completed. It is represented in Fig. 32 by the dotted curves marked L. It forms, of course, the outline of the half-breadth plan, in which it very often coincides with the load-water-line in the middle part of its length, and with the gunwale or the plank-sheer, near the head and stern. In former times, one of the first steps taken in designing a ship was to assume a figure for the main-breadth-line; but, as its shape has little direct influence on the qualities of the ship, that method is seldom followed now.

When a ship has a "straight of breadth" vertically; that is, when her cross-sections are partly vertical at the sides, there are two main-breadth-lines at the upper and lower boundary of the straight of breath respectively.

Sheer-lines.-Head and Stern.-The under side of the gunwale, marked K in the figure, is designed so as to form a fair curve on the half breadth plan. Its form near the bow is like that of a water-line; but in most cases somewhat fuller. Near the stern, its figure is fuller still, with a view to giving a convenient breadth to the after-part of the decks. It may sometimes be advisable to design the gunwale before completing the cross-sections.

In almost every vessel the gunwale has an upward curvature longitudinally, called the sheer. The true practical object of this is, to protect the vessel against waves breaking over her, by giving her greater height out of water at the bow and stern, where her vertical motion relatively to the water is greatest.

The bow, as having more vertical motion relatively to the water than the stern, and also as being more exposed to the waves, requires the greater height of sheer. This may be effected by making the curvature of the sheer vanish, or nearly so, at the stern, and increase gradually in sharpness towards the bow.

The less lively a vessel is in pitching and scending, the more sheer does she require; and it is specially needed at the bow of a vessel with fine lines, and little or no flaring out above the water

line. Large vessels have proportionately less sheer than small vessels, and ships-of-war than merchant-ships. The reason in the latter case is, that the decks follow the form of the sheer, and that decks with much sheer are inconvenient for working guns.

The design of the figure-head or cut-water, and that of the stern, are matters to be regulated chiefly by the taste of the naval architect. In many vessels the figure-head is dispensed with, as was the case in many of our naval vessels.

Use of Models in Designing Ships.-A model, to be used by a naval architect in designing a ship, is usually composed of two sorts of soft wood of different colors, such as pine and cedar, in alternate layers, screwed, pinned or glued together. The seams between the layers represent water-lines. The model usually

represents the starboard half of the vessel, and has a plane side, representing the longitudinal midship-plane, on which the sheerplan is drawn. Its curved side is then gradually carved, shaved, and filed to such a form as to satisfy the eye and the judgment of the designer; the touch also is used, by passing the hand over the model, as a test of the fairness of its figure.

The co-efficient of fineness of a model may be determined by filling a trough with water exactly to the level of a suitable outlet, carefully lowering the model into the water until it is immersed exactly to the load-water-line, and finding, by measurement or by weighing, the volume of water which is made to run over. That volume will be equal to the displacement of the model; and being divided by the product of the principal dimensions of the model, the quotient will be the co-efficient of fineness.

Another mode of roughly determining the displacement of a model is to separate the part below the load-water-line from the rest, weigh that part, and compare its weight with that of a rectangular block made up of the same materials in the same way; when the proportion of the volumes may be taken as approximately the same with that of the weights.

To find approximately the centre of buoyancy of a model, hang up the part below the load-water-line by a fine thread to a single pin in an exactly vertical board, so that the plane side of the model shall be in contact with the board. Mark the two points where a plumb-line hanging from the same pin passes the edges. of the model, and draw a straight line on the plane side of the model through those two points. Repeat the experiment with

the model hanging in a position as nearly as may be at right angles to its former position; the intersection of the two lines on its plane side will correspond to the centre of buoyancy of the vessel represented by the model. In models whose layers are screwed together, the accuracy of the result of this process may be interfered with by unequal distribution of the screws; hence, for the purpose of finding the centre of buoyancy, the best fastening is made with wooden pins or glue.

Models are sometimes built up of small prismatic bars of wood, so as to show the figures of vertical and oblique as well as horizontal sections.

A model may be used either to construct drawings from, or directly in laying off the figures of the pieces of the ship on the mould-loft, without the intervention of drawings.

After a ship has been designed, and the sheer, body, and halfbreadth plans all faired, it may sometimes be requisite to alter the form of the ship slightly, so as to obtain an increased or diminished displacement.

This may often be effected by retaining the water-lines in the half-breadth plan, and increasing or diminishing the common intervals between the water-lines; or the transverse sections of the body-plan may remain unaltered, but the interval between them be increased or diminished.

2

CASE I.-Let D represent the displacement according to the prepared plan, A the increase or decrease of the displacement, d the common interval between the horizontal sections, and the quantity by which this common interval is increased or diminished. Then z=d.; also, since the number of intervals will remain unaltered, the increase or decrease in the whole distance between the extreme horizontal sections will be

Original distance between extreme horizontal sections ×

Δ

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Again, the distance of the centre of gravity of the displacement,,bounded by the extreme longitudinal section, will be to the original distance as D+A: D, or as d+z: d.

Also, the moment of inertia of the load-water-section remaining the same, the height of the metacentre above the centre of buoyancy will be to the original height as D to D+a.

CASE II.-When the forms of the vertical sections are retained, but the interval between them is altered, let 7 represent the in

DIMENSIONS, WEIGHTS, &C., FOR AN IRON CORVETTE.

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terval between the vertical sections, and y its increase or decrease, when the displacement is increased or decreased by the quantity, A. Then

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The depth of the centre of buoyancy below the load-water-line remains unaltered, as also the height of the metacentre above the centre of buoyancy.

Statement of Dimensions, Weights, &c., for an Iron Corvette of

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