The ordinary paddle-wheel, as I have already stated, is a wheel revolving upon a shaft driven by the engine, and carrying upon its circumference a number of flat boards, called paddle boards, which are secured by nuts or braces in a fixed position; and that position is such that the planes of the paddle boards diverge nearly from the centre of the shaft on which the wheel turns. The consequence of this arrangement is that each paddle board can only act in that direction which is most advantageous for the propulsion of the vessel when it arrives near the lowest point of the wheel. In figure 67. let o be the shaft on which the common paddle wheel revolves; the position of the paddle boards are represented at A, B, C, &c.; X, Y represents the water line, the course of the vessel being supposed to be from X to Y; the arrows represent the direction in which the paddle-wheel revolves. The wheel is immersed to the depth of the lowest paddle board, since a less degree of immersion would render a portion of the surface of each paddle board mechanically useless. In the position A the whole force of the paddle board is efficient for propelling the vessel; but, as the paddle enters the water in the position H, its action upon the water, not being horizontal, is only partially effective for propulsion: a part of the force which drives the paddle is expended in depressing the water, and the remainder in driving it contrary to the course of the vessel, and, therefore, by its reaction producing a certain propelling effect. The tendency, however, of the paddle entering the water at H, is to form a hollow or trough, which the water, by its ordinary property, has a continual tendency to fill up. After passing the lowest point A, as the paddle approaches the position B, where it emerges from the water, its action again becomes oblique, a part only having a propelling effect, and the remainder having a tendency to raise the water, and throw up a wave and spray behind the paddle-wheel. It is evident that the more deeply the paddle-wheel becomes immersed the greater will be the proportion of the propelling power thus wasted in elevating and depressing the water; and, if the wheel were immersed to its axis, the whole force of the paddle boards, on entering and leaving the water, would be lost, no part of it having a tendency to propel. If a still deeper immersion takes place, the paddle boards above the axis would have a tendency to retard the course of the vessel. When the vessel is, therefore, in proper trim, the immersion should not exceed nor fall short of the depth of the lowest paddle; but for various reasons it is impossible in practice to maintain this fixed immersion: the agitation of the surface of the sea, causing the vessel to roll, will necessarily produce a great variation in the immersion of the paddle-wheels, one becoming frequently immersed to its axle, while the other is raised altogether out of the water. Also the draught of water of the vessel