war-ship can only have a small effect on the period. We should expect, therefore, to find that an armoured ship would roll more slowly than an unarmoured ship of about the same displacement and metacentric height, and this is confirmed by experience of ships in the Royal Navy.

A very considerable effect in lengthening the period is obtained by reducing the metacentric height. Thus in the Royal Sovereign, in which ship the period is 8 seconds and the GM about 3 ft., suppose the GM is reduced to 3 ft., without altering the radius of gyration. Then we should get a period of 8.64 seconds, or an increase of 8 per cent.

An interesting application of the above principles is found in the current practice of many merchant vessels. In many trades, voyages have to be undertaken with little or no cargo, because of the absence of return freights. It is necessary, for seaworthiness and proper immersion of the propellers, to sink the vessels by means of water-ballast. This has usually been placed in the doublebottom compartments. This, however, frequently pulls down the C.G. of the ship so far as to give the ship a large GM. This causes a very quick period, and in some cases this has not merely rendered the ship uncomfortable, but actually unsafe. In many ships, therefore, it is the practice to provide tanks in the 'tween decks and hold at the sides, and even on the upper deck. These tanks below are frequently large enough to hold ordinary cargo when necessary, but for "light" voyages they can be filled with water. The weight thus added, while giving sufficient immersion, does not produce excessive GM, and being at the sides tends to lengthen the period by increasing the radius of gyration.

lever varies directly as the angle or GZ = GM × 0, i.e. it assumes that the curve of stability is a straight line up to the angle considered. Under this condition large and small inclinations will be performed in the same time. A ship rolling in this manner is said to be isochronous.

Although the various assumptions made in obtaining the above formula are not strictly true, yet it is found by actual experiment that, within angles of 10° to 15° of the vertical, ships are very nearly isochronous in their rolling. This is the case although the ship experiences resistances which eventually bring her to rest.

The following are the approximate periods of some typical ships, i.e. the time from port to starboard, or vice versâ.

Resisted Rolling in Still Water.-Under the actual conditions under which a ship will roll in still water, resistances to the rolling are set up which drain the ship of energy and which sooner or later will bring her to rest. These resistances may be classified as follows::

1. Friction of water on the ship's surface.

2. Effect of sharpness of form of ship's section.

3. Effect of bilge keels or keel projections (if any), including the flat portions of the ship.

4. Creation of waves on the surface.

5 Air resistance.

6. Use of water chambers.

1. Friction. This cannot be of great amount in ordinary ships, because the surface is kept smoothly painted to reduce the resistance when steaming to the smallest possible amount.

2. Form of Section. In a ship of circular section the relative velocity of the water and the surface of the ship is the same at all points of the section. In a ship of sharp form at the bilge, however, the water at the corner gets a motion opposite to the ship, and having to slip past the bilge, the effect both as regards friction and on bilge keels is greater in a sharp bilge than in a rounder form of section.

3. Bilge Keels.-The reason of the great extinctive effect of bilge keels in reducing rolling has been imperfectly understood until recently. The explanation is of considerable difficulty, and the following remarks do not pretend to completely deal with the subject:

(a) A bilge keel is like a flat surface passing through water broadside on. The laws governing the resistance of such flat surfaces have been investigated, but in applying them to the case

Q

of a ship it has been found that the extinctive effect observed could not thus be fully accounted for.

(b) A further influence has been suggested by Prof. Bryan, F.R.S. Consider the flow of water round a right angle as Fig. 192.

FIG. 192.

The water next the surface has to suddenly change its direction at B. This causes a diminution of speed up to the point B, where it must be zero. The other streams of water are deflected, and along AB we get a diminution of velocity of the stream lines. This falling off of speed is accompanied by an increase of pressure, both along AB and BC.1 If, for instance, a boat's rudder is suddenly put over to right angles, the leverage of the water pressure on the rudder about the axis of rotation of the boat is small, but the turning effect on the boat is considerable. This is caused by the pressure on the deadwood of the boat, which has a considerable leverage about the C.G. of the ship.

In the case of bilge keels projecting from the surface of a ship, suppose the ship is rotating clockwise, as in Fig. 193. The relative

A2

FIG. 193.

velocity of the ship and the

water along AA, has to be brought to zero at A1, and there is caused an increase of pressure along AA1. This results in a resultant force P acting as shown, a similar force Q being found on the other side of the ship. These forces both

act in such lines that they give a moment tending to stop the rotation. This effect will be more pronounced as the section of the ship is sharper, because of the greater relative velocity of the water past the bilge as compared with a round section.

4. Wave Formation.-At each roll of the ship a wave is

The relation between speed and pressure in flowing water, by which if speed diminishes the pressure increases, and vice versâ, is noticed in water-pipes. If a tap is turned off suddenly, as in the old-fashioned taps, a knock is heard in the pipes, caused by the sudden rise of pressure consequent on the motion being stopped. If, as in taps now in domestic use, the water is turned off gradually, the rise of pressure is not so sudden and the pipes are not so severely strained.

created on the surface of the water at each side; this wave passes away from the ship, and requires energy spent to create it. A wave of very small height represents a large amount of energy, and the drain on the ship's energy is a distinct resistance reducing the rolling.

5. Air Resistance.-The resistance of the air must be quite small under ordinary circumstances, but it may be made considerable by the use of steadying sails. It is well known that sails have a great steadying effect on a ship's rolling.

6. Water Chambers.-In the Inflexible and following ships a large metacentric height was an essential feature of the design, because it was necessary to provide such stability that the vessels should be able to stand upright, even supposing the unarmoured ends were completely riddled. It was known that this would cause a short period and quick rolling motion. This is an undesirable quality in any ship, and especially in a war-ship. The bilge keels could only have been of limited size because of the great beam of the ship causing difficulties in docking. On this account it was proposed and approved to fit athwartship chambers containing loose water. This water passes from side to side as the ship rolls, and causes waste of energy. This must be taken out of the ship, and so lessens the rolling. These water chambers were found to fulfil their purpose in diminishing the rolling, but the system was ultimately abandoned on account of the noise of the water rushing from side to side, and because the spaces were required for other purposes. As we have seen, there has been a gradual increase of waterplane area protected by armour in battleships since the Inflexible, so that the riddling of the ends has a less proportionate effect. On this account metacentric heights have been diminished from 8 ft. in that ship to 3 to 4 ft. in more recent ships. This has resulted in longer periods, so that the conditions of rolling are quite different, and the steadying effect of water chambers has not been required.

Bilge Keels.-Fig. 194 shows several forms of bilge keel as fitted to ships of the Navy. The standard form for steel ships is made of two 17-lb. (7 in.) plates connected to the ship's bottom as shown, the space between being filled in with light wood. The projection in battle-ships is inconvenient in connection with docking, and the breadth of the bilge keel is made somewhat less amidships than forward and aft where the ship gets

narrower.

For smaller steel ships the bilge keel can be formed as shown; the figure gives the construction in a torpedo gunboat.

For sheathed ships the keel is formed of a single steel plate connected to the bottom by double angles, and supported at intervals by brackets. This is cased in with teak as shown. Navy, including the latest destroyers, are The keels usually extend over rather less

All vessels in the fitted with bilge keels. than half length.

Rolling among Waves.-In dealing with this subject it is important to note that a wave is not the passage of water but the passage of motion. The motion of the particles of water composing a wave is quite small, as may be noticed by watching a piece of wood among waves. The wave profile is seen to move along with considerable speed, but the wood sways backwards and for

wards about a mean position. As a matter of fact the particles of water are moving in circular orbits, the radius of these orbits decreasing with the depth, so that at a moderate depth the water has a very slight motion. In waves, therefore, we find that the force of gravity is modified because of the centrifugal force set up by the orbital motion of the water.

It is well known that a can of water can be swung right round without any water spilling. When at the highest point the weight of the water acts down, but the circular motion gives rise to a centrifugal force acting outwards, and so long as this latter force is greater than the weight no water will be spilled. If the motion is slowed up a point would be reached when the weight would be greater than the centrifugal force, and the water would be spilled. It is the centrifugal force being greater than the force of gravity which keeps the car on the rails in "looping the loop."