The development by a vessel’s engines of the power requisite to drive her at a certain speed is always very considerably more than the power required simply to overcome her total resistance at that speed. This excess of power developed over power usefully employed in overcoming resistance is known as “waste work.” It amounts in many cases to as much as from 50 to 60 per cent. of the gross indicated power, and it is absorbed mainly as follows:—In overcoming frictional and other resistances of the engines and shafting, working air pumps, &c., and in overcoming the frictional and edgeways resistance of the propeller. The residue of power usefully employed is known as the ‘effective’ horse-power. The respective causes of ‘waste’ and their relative amounts are problems constantly demanding solution. Progressive speed trials with actual vessels and experiments with small scale models are daily contributing to their solution, and to some extent to their reduction. STRUCTURAL STRENGTH. Considering a ship as floating in a state of rest in still water, the volume of displacement represents a weight of water equal to the weight of the ship. This equality, however, does not exist evenly throughout the length of the vessel, or for individual portions: thus, amidships the weight of water displaced by a given length—in other words, the buoyancy—is usually considerably in excess of the weight of that portion of the vessel and her contents. Similarly at the extremities the ‘weight’ of a certain length exceeds the ‘buoyancy.’ Between the part or parts of the vessel in which there is excess of buoyancy over weight, and the part or parts in which the weight exceeds the buoyancy, there must obviously be sections of the ship at which the two are equal, and these are termed “water borne” sections. A ship circumstanced as described is in a condition similar to that of a beam supported at the middle and loaded at each end. Such a beam tends to become curved, the ends dropping relatively to the middle, and the ends of the ship tend to drop similarly, the change of form being called “hogging.” On the other hand, if the excess of buoyancy occurred at the extremities and that of weight amidship, the ship would resemble a beam supported at the ends and loaded at the middle. In such a condition the middle would tend to drop relatively to the ends: a change of form called “sagging.”