speed. As already stated, the objection to deeprolling-aside from the discomfort it causesis that the roll may go so far that the righting force disappears; for this varies with every change in inclination, usually becoming zero at or about 90° in small craft and 60° to 75° in larger vessels (see Fig. 6). This position is reached when the vertical rising from the centre of buoyancy passes through the centre of gravity; any further roll will cause this vertical to pass between the centre of gravity and the keel and then the ship must capsize.

The position of the centre of gravity and the metacentric height are readily determined. If a weight r (Fig. 5), which is one side when a vessel is vertical, be moved across the ship a total distance of a feet, the centre of gravity will move parallel to the movement of r and be at some point G'. The vessel will therefore heel through the angle 0. We have then, if we is the weight of the ship, w× GG' = x x a; but GG' GM tan

=

a x x; W

cot. The

position of M being readily calculated from the position of B (centre of gravity of immersed body), the position of G is at once known. For large inclinations the righting arm is computed by another and more accurate method. A curve giving the righting arm for any degree of hull is shown in Fig. 6.

The effect upon speed of variations in the form of the hull was but imperfectly understood until within the past fifty years, and there is still much to learn. Until the adoption of the steam engine we were without power susceptible of exact measurement, but soon after this took place information was rapidly gained and results compared. A really scientific investigation of the problem, however, was not reached until Mr. William Froude began his famous experiments in the model tank at Haslar, England. Much that had been previously guessed at he definitely proved, some time-honored beliefs were shattered, and a great deal that was wholly new was discovered.

In

deed, his work is the foundation of a great portion of all we know of the resistance of ships, though his discoveries and conclusions have been greatly extended, and in some minor points modified by the work of later experimenters -a model tank being now regarded as a most necessary means of ascertaining the best forms for speed under given conditions. The models are 10 to 25 feet in

length-usually 12 to 15 feetand are towed by a travelling car containing apparatus which records the speed, resistance, etc. To connect the data thus obtained with similar information for the full-sized ship we must apply Froude's law, which is as follows: If a ship be D times the "dimensions," as it is termed, of the model, and if at the speeds V1, V2, V3, etc., the measured resistances of the model are R1, R2, R3, etc., then for speeds VD, V1, VD, V2, VD, Vз, etc., of the ship. the resistances will be D3 R1, D3 R2, D3 R3, etc. To the speeds of model and ship thus related it is convenient to apply the term corresponding speeds.' Thus, if a ship have length, breadth, and depth each sixteen times those of the model, and if at a speed of 2 knots of the model the ascertained resistance is a, then at a speed of V 16 x 2 = 8 knots of the ship, the resistance will be 16 × 16 × 16 x a 4096a. This law was effectively demonstrated by towing a full-sized ship and her model at various speeds. By means of model tank experiments the form of hull best adapted to each particular size and speed is readily obtained, provided we add to the model results the necessary power to overcome friction and other losses in the machinery, propeller, etc.

The resistances to propulsion are of three kinds-surface friction, wave making, and eddy making. In a vessel of fine or moderately fine line (ie. one fairly sharp at both ends) the friction between the skin of the ship and the water is the cause of nearly all the resistance at low speeds, and this frictional resistance varies directly as the area of wetted surface and as the square of the speed, while for rough surfaces the resistance is vastly greater than for smooth. The wave-making resistance is unimportant at low speeds with vessels of fine lines, but rapidly increases with the speed. Other things being equal, a vessel should have no greater fineness of lines than is necessary to enable her to be economically driven at her designed speed, for fineness of form means loss of carrying power or increase of surface friction per unit of carrying capacity or both. And if a vessel has the fullest lines consistent with a definite speed, no attempt should be made to drive her faster than this. Thus, if a vessel be designed to give the greatest carrying capacity for a speed of 16 knots, the expenditure of power to drive her 17 knots may be almost twice that for 16. The waves which are made by vessels

passing through water are of three types. One consists of divergent waves which form at the bow, rise to a certain height and then break off, when a new wave of similar size and direction is formed and so on. The crests of these waves are sharp and make an angle of considerably less than 90° with the course of the vessel, the end farthest from the vessel's side being farthest to the rear. A second set of waves has its crests at right angles to the course. These waves are highest at the side of the ship, two or more appearing between bow and stern, depending upon the length of the ship. Both crests and hollows are smoothly rounded. Lastly, there are the divergent stern waves, somewhat similar to those which form at the bow; these waves are distorted and reduced in height by the action of the propeller. The height, length, and volume of waves and the speed with which they travel indicate the amount of power expended in producing them. The resistance due to the formation of eddies is comparatively unimportant. Eddies are formed along the sides of vessels when the surface is very rough, but the loss thereby is a small per cent. of that one to surface friction. In the early days of steam vessels many of them were so bluff at the bow and stern as to cause eddies, those at the stern being strongly marked. The result was a dragging of the water after the vessel and a great loss of power and speed.

From the various investigations and experiments that have been made we deduce that if high speed is an object, a vessel must have fine lines (i.e. be very sharp) at bow and stern, but particularly at the stern. That the surface of the hull must be kept as smooth as possible and that the shape and stability should be such as to reduce rolling and pitching to a minimum. The fineness of the after body is not only necessary in order to reduce the stern wave, but also that the water may flow in freely and solidly to the propeller. It may be proper to remark here that the position of the propellers has been the subject of investigation. They have been tried at the bow, at the sides, at the stern, and underneath the bottom, but the position of maximum efficiency was found to be at the stern.

The internal structure of a ship consists of frames, beams, knees, bulkheads, decks, etc. Wooden vessels have a keel, and upon it are laid the floor timbers, which are curved at the 'turn of the bilge' and carried up to form the framing of the sides. Over the floor timbers, parallel to the

keel and through-bolted to it, is the keelson. Deck-beams extend from side to side under each deck, the ends joined to the frames by deep knees. Additional strength is obtained by filling timbers' between the floor timbers of the frames, by outside planking and inside ceiling,' and by transverse and longitudinal bulkheads. Steel sailing ships have an external bar keel, but steel steamers have no projecting external keel. The keel-plate is flat, broad, and thick. The vertical keel is inside the keel-plate, is usually two feet or more in depth, and extends to the bow and stern to meet the castings or forgings which form the stem and stern-post. The frames are of I, T, channel (U-shape), or Zsection. The beams are usually of T-bulb steel riveted directly to the frames, the end being split and the lower half bent down to form a brace or knee. In most large ships the inner sides of the frames up to the turn of the bilge or beyond are covered with a plating which forms the inner bottom. At intervals of several feet vertical (or nearly vertical) fore-and-aft plating is worked between the frames to form longitudinal stringers; and these, with the frames, divide the space (called the double bottom) between the inner and outer bottoms into numerous water-tight compartments. To reduce unnecessary weight lightening holes are cut through the frames and longitudinals and these reduce the number of water-tight compartments while affording access to all parts of each compartment without requiring too many manholes through the inner bottom. This cellular double bottom adds considerably to the strength of the hull and greatly to the safety of the ship in case of grounding, many large ships having safely reached port with their outer bottoms badly torn. The doublebottom system is chiefly due to Brunel, the designer of the Great Eastern (1852), in which vessel it was first fully developed. Above the inner bottom most ships are divided into many large water-tight compartments by the deck-plating and by longitudinal and transverse bulkheads, and these divisions add to the stiffness and rigidity of the hull. The smaller bulkheads in the living spaces are not usually watertight; and if not they are of such light material as to add but little to the structural strength in any direction. All water-tight compartments are connected by drain pipes to the pumps in order that they may be pumped out if the water should enter in quantities not too great for the pumps to handle.

The strength of vessels to resist transverse stress is usually greatly in excess of the requirements, but in a longitudinal direction the case is different. To secure adequate longitudinal rigidity considerable care is exercised in the design. The sides, decks, and fore-and-aft bulkheads give most of the fore-andaft strength. When a vessel, supported at the end, sinks in the middle she is said to 'sag,' and when supported in the midIdle and the ends sink down she is said to hog.' When a vessel is floating in rough water, sagging strains may be produced in all parts not water-borne, and ' hogging strains in all parts which are water-borne, though these strains (particularly the sagging) are reduced by the tendency of the hull to act as a cantilever.

PLANS. The general characteristics of a vessel having been decided upon, a preliminary set of drawings is made to determine the general arrangement and the principal features. Based upon these, calculations are made of the weights, stability, trim, strength, speed, etc. If the shape of the hull has been determined by model experiments the drawings are made in accordance with the ascertained results. The general drawings embrace three plans called the sheer plan, the half-breadth plan, and the body plan, and represent the lines of the ship as developed upon three plans at right angles to each other. The sheer plan shows the lines cut out of the hull by plans parallel to the fore-and-aft vertical plane through the keel; the half-breadth plan shows the lines cut by horizontal plans; and the body plan shows the lines cut by vertical transverse planes. From these principal drawings the detail drawings are prepared, the plans of every part being drawn to scale and its dimensions marked. The drawings having been completed the ship is laid down on the mould loft floor in its full size as a whole or in parts. The laying down' consists in cutting lines representing those which appear on the plans. From the mould loft plans, or directly by measurement from the drawings, the scrive board, moulds, and templates are prepared. The scrive board is in effect a full-sized drawing showing the shape of every frame in the vessel, but it is not always used, templates being sometimes built up from the smaller drawings and carried directly to the bending slab where the frames are shaped. Detail drawings are made of all parts showing, on a convenient scale, their exact shape and size.

After the keel plates and a number of midship frames are shaped or built up (according to the character of the framing), the keel may be laid and the first frames erected. The keel-plates are laid on the keel blocks, lined up and riveted together. The frames are then erected and held in place by braces, cross-spawls, ribands, or similar falsework. After the transverse frames are erected and riveted to the keel, they are connected by the intercostal sections of the longitudinals and the inner and outer plating. The stern-post and stem (in a steel ship) are heavy castings or forgings and are not usually put in place until the framing has so far proceeded that they may be quickly supported. After the frames are up the work on the interior is pushed at the same time as that on the exterior. After the outside plating or planking is completed and calked the vessel may be launched at any time. Large vessels are usually put in the water before the machinery is installed and while much of the interior work is unfinished. This admits of a lighter cradle being used, brings less pressure on the ways, and makes an easier launching. Small vessels are occasionally completed on the ways and launched with steam up ready for preliminary trials. To effect the launch a wooden framework called the cradle, resting upon the launching ways, is built under the ship and fitted to her bottom. By means of wedges the upper part of the cradle is forced upward, lifting the vessel off the keel blocks and building ways or shores. The upper side of the launching ways being well lubricated, the cradle, carrying the vessel, slides down the ways into the water as soon as the tie plate is cut or dog-shore knocked out.

The cradle then breaks up and is hauled clear.

Shipbuilding in the United States is chiefly confined to vessels for the Lake and coast trades and to men-of-war, though many large vessels have been built for the foreign trade. The principal shipbuilding works are located at or near Bath (Me.), Boston, New York, Philadelphia, Newport News, San Francisco, Seattle, and the ports on the Great Lakes, especially Lake Erie (Lorain, Cleveland). The total shipbuilding in the United States during the years 1902-5 was as follows: