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as compared with breadth ceases to be an advantage, and becomes a cause of increased resistance.

In the proportion of the length of a ship to her breadth, the ratio of 4 1 was seldom exceeded until after the introduction of steam navigation. Then gradually increasing proportions were introduced, with continually improving results, until the ratio of 7:1 was reached; and it was naturally taken generally for granted that an unlimited increase of length and slenderness would cause an unlimited diminution of resistance. This, however, was not found to be the case in practice, which concurs with theory to show that the proportion of 7:1, or thereabouts, is very nearly the utmost that is attended with advantage in vessels whose draught of water is not specially limited; and that greater proportions, such as 8: 1, 9 : 1, or 10 : 1, are advantageous under special conditions only, such as limited draught of water, or limited breadth of channel.

Another principle which is known independently of the precise mode of action of the particles of water is this-that the resistances of vessels of similar figures, but different dimensions, at the same speed, are nearly proportional to their surfaces—that is, to the squares of their linear dimensions, or to the squares of the cube roots of their displacements; so that, for example, if there be two ships of precisely similar figures, one of 1,000 tons displacement, and the other of 1,331 tons, which are to each other as the cube of 10 to the cube of 11; then the resistances of those vessels at the same speed will be to each other nearly as the square of 10 to the square of 11; that is, as 100 to 121. This principle, however, ceases to be exact in extreme cases; so that it is not applicable, for instance, to the comparison of real ships with small models. To make experiments on the resistance of models available for arriving at correct conclusions respecting vessels on the large scale, the velocities of the models must be kept within certain limits, to be afterwards specified.

It is evident that the smoothness or roughness of a vessel's bottom must materially affect her resistance. The bottom of every ship, how smooth soever it may have been originally, tends to become crusted in time with shells and weeds, which increase the adhesion of the water. It is very common to find the resistance increased by about a fourth from this cause; and occasionally it is increased more. The means of preventing or removing such incrustation consists mainly in coating the vessel with some sub

stance which shall from time to time scale off in thin flakes, carrying the incrustation with it, and leaving the bottom clean.

Such is the action of the copper-sheathing of wooden ships, and of various paints and other compositions used for protecting iron ships.

CHAPTER VI.

Fairness-Models-Propulsion by Machinery-Propulsion by Sails.

ALTHOUGH Some knowledge has been gained of the effect of using certain definite curves, such as the curve of versed-sines or harmonic curve, the trochoid or rolling-wave curve, and some others, for the water-lines or horizontal sections of ships; and although the effect of those and various other forms on the motion of the water has been theoretically investigated, it cannot yet be said that any particular form has been conclusively demonstrated to be the form of least resistance for a given displacement. Still, it has always been admitted by all naval architects, that the figure of a ship should be what mathematicians call "continuous" and shipbuilders "fair" A fair line is a line in which there is not only no sudden change of direction, but no sudden change of curvature; and a fair surface is one whose sections are all fair lines. The fairness of the water-lines, or horizontal sections, is of the highest importance in the form of a ship; next in importance is the fairness of the vertical longitudinal sections, called bow and buttock lines; and sometimes, to test the fairness of the intended form of a ship still further, oblique sections, called diagonal or riband lines, are drawn. The naval architect judges of the fairness of lines by the eye; and sometimes, if a model of the vessel is before him, by the sense of touch. To show the form of lines distinctly, models are made of layers of differently colored wood.

Propulsion by machinery, although of more modern invention. (if we except rowing and paddling by hand) than propulsion by sails, is much simpler in its principles, and will therefore be considered first. The fundamental principle of the action of every propeller is the same, whether it is an oar, a paddle, a screw, a jet, or any other contrivance. The propeller drives backwards a certain quantity of water at a certain speed; in so doing, it presses backwards against the water with a force depending on the quantity of water driven back, and the speed impressed upon it. The water presses forward against the propeller with an equal force; and that force (which is called the "reaction" of the

water), being transmitted to the framework of the machinery and thence to the vessel, is what drives her forward. When the ship is starting from a state of rest, or increasing her speed, the driving force must be greater than the resistance; but so long as the speed is uniform, the driving force and the resistance are equal.

Some propellers act directly backwards on the water, or nearly so, like the feathering paddle; some, like the common paddle, act more or less obliquely in a vertical plane; some, like the screw, act obliquely in various directions. Due regard must be given to those circumstances, and also to that of the working of the propeller in water which has already been disturbed by the vessel.

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The engine-power required to drive a given vessel at a given speed depends on a mechanical principle which governs the actions of all machines whatsoever the equality of the energy exerted to the work performed. The useful part of the work performed in driving a vessel during a given time (such as a second), is found by multiplying, the resistance by the distance through which the vessel is driven. To this has to be added the wasteful work, one part of which is performed in the following manner: The propeller exerts backwards a force equal to that with which the vessel is driven forwards; but it exerts that force through a greater distance, viz. :—the sum of the distance through which the vessel is driven forward, and the water backward (the latter distance is called the slip); so that the total work performed by the propeller is greater than the useful work, in the proportion in which the total backward speed of the propeller exceeds the forward speed of the ship—a proportion which ranges from 1: 1 to 2: 1. Some additional work is wasted in giving lateral and vertical motions to the water, and in overcoming the friction of the machinery. The sum of all those quantities of work, useful and wasteful, which are performed in a given time, is equal to the energy which must be exerted in the same time by the engine. The ratio which the useful work bears to the energy. exerted, is called the efficiency of the propeller and its machinery; in some of the best examples of economy of power in steam-vessels it is about 3:5; in less economical examples it is sometimes as low as 2:5, and perhaps even less.

When resistances are expressed in pounds, and are multiplied by the distances through which they are overcome, in feet, the

products, or quantities of work, are said to be expressed in "foot-pounds." If the total number of foot-pounds of energy exerted per second in driving a vessel be divided by 550, the quotient is the real or indicated horse-power of her engine.

Upon the power of the engine, and its system of construction and working, depends its weight (including that of its boilers), for which, as well as for the store of fuel, provision must be made in the displacement of the vessel, and to which regard must be had in considering questions of stability.

Propulsion by Sails depends upon more complex principles than propulsion by machinery; because the direction of the wind, which supplies the propelling force, is seldom the same with that of the vessel's course, and often makes a great angle with it. The pressure of the air on the sails, moreover, does not depend on the real direction and velocity of the wind relatively to the ocean, but on its apparent direction and velocity relatively to the moving ship, and also on the position of the sails themselves.

The pressure of the wind, diffused over the surface of the sails, is capable, like the pressure of water and the force of gravity (see Chap. III.), of having its action on the ship as a whole represented by one resultant, traversing a point called the Centre of Effort, which is at a height above the deck depending on the figure, dimensions, and positions of the sails. When that resultant is oblique to the ship's course, it is resolved, according to wellknown principles, into two component forces—the longitudinal component, acting forwards parallel to the keel, which is the ef fective effort that drives the ship forward against the resistance of the water; and the transverse component, acting at right angles to the keel, which drives the ship to leeward; so that her real course or direction of motion, instead of being parallel to the keel, makes a small angle to leeward of that line, called the angle of leeway.

The angle of leeway depends on the proportion borne by the velocity with which the ship drifts to leeward, to her forward velocity; and the velocity with which she drifts to leeward is such that the resistance to her transverse motion through the water is exactly equal to the transverse component of the pressure of the wind on the sails. Those two forces, though equal and opposite, are not directly opposed; for the resistance acts below water, and the transverse pressure of the wind high above water; they therefore form a couple (Chap. IV.), tending to make the vessel

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