consumed are in the aggregate below the C.G. Thus the GM in the light condition is found to be less than in the other conditions. Fig. 170 is the diagram for a first class cruiser, Fig. 171 for a second class cruiser, Fig. 172 for a destroyer. The diagram for the Maine, originally a merchant steamer, is given in Fig. 173. In this ship it has been necessary to provide 1000 tons of permanent ballast to give proper immersion and stability, and this is so stowed so as to provide stability, when the double-bottom tanks are empty and also the lower bunkers. In this extreme condition a GM of 0.7 ft. only is obtained; but when fully equipped with double-bottom tanks full, a GM of 2.2 ft. is obtained. Fig. 174 gives the diagram for the Waterwitch mentioned above. In this ship, carrying considerable sail power, a good GM is required, and 30 ft. is obtained in the deep load condition. To get this it is necessary to stow 65 tons of permanent ballast.

Values of GM, the Metacentric Height.-The amount of GM given to a vessel is determined by the class of vessel and the qualities it is desired to obtain. To take two instances. In sailingships a sufficient GM must be provided to enable the ship to "stand up" under her canvas. In such a ship a small GM would mean a large angle of heel when sailing, which is undesirable. In a vessel like the Inflexible, in which the armour-belt only extended over one-third the length (Fig. 126), a large GM was provided, viz. 8 ft., to enable the vessel to remain upright, even supposing the unprotected ends open to the sea.

For small angles the moment of the couple tending to right a ship, i.e. the stability, is W × GM × sin 0, so that if GM is large this righting moment is large, and if GM is small, this righting moment is small. If GM is large, the ship comes back to the upright very suddenly after being inclined, and the ship will have a quick motion. Such a ship is stiff. If GM is small, the ship is easily inclined, but returns to the upright slowly with an easy motion.1

There are thus two opposing conditions to fulfil in settling the GM for a war-ship, viz.—

1. GM must be large enough to enable the ship to retain stability after a fair amount of damage.

2. GM must not be so large as to make the ship have violent

This is further considered in Chapter XX. A "crank" ship easily inclined is found to be the steadiest in a seaway.

motions at sea, this being specially important in view of the fighting of guns.

The following are average values of the metacentric height given to the modern ships of the British Navy

For battle-ships it is necessary that sufficient GM shall remain after the unprotected ends are riddled and open to the sea. The gradual enlargement of the waterplane area protected during the last thirty years has been the cause of a gradual reduction of metacentric heights in these ships. Thus in the Inflexible, with a belt only one-third the length, a GM of 8 ft. was provided. In the Admiral class, the belt being four-ninths the length, the GM was 5 to 6 ft. For modern ships with belt about two-thirds the length, the GM is 3 to 4 ft. In a recent ship the effect of riddling the ends is to reduce the GM by about 2 ft. In the Inflexible this riddling reduced the GM by 6 ft.

Vessels like destroyers are given a GM which is relatively large. These vessels, as the speed increases, form a wave which, dipping down amidships, causes a considerable reduction of area and moment of inertia of waterplane. In consequence of this it is necessary to make the GM relatively large. Another reason for this is seen in the inward heel caused by putting the rudder over. If the GM were small, this heeling might be excessive.

For merchant steam-ships, the GM varies continually owing to the different nature and disposition of the cargo carried on different voyages. Ships with cargo of light density frequently go long voyages with metacentric heights of less than 1 ft., and their behaviour is reported to be in every way comfortable and safe. Such ships, however, have to be carefully treated when light, and frequently require water-ballast in the double bottoms to enable them to remain upright. Such a metacentric height as is sufficient in this type of ship would not be permissible in war-ships for the reasons already stated.

1 In the Triumph and Swiftsure, recently added to the Royal Navy, the metacentric heights are

Sailing ships are given metacentric heights of 3 to 3 ft. to enable them to "stand up" under their canvas without heeling to an undesirable angle.

Heel caused by Flooding the Wings, etc.-The following figures are interesting as showing the heel caused by opening up one side of a battle-ship to the sea, in way of the engine

room:

1. Wings only open to the sea (no coal in). A heel of 5° would result.

2. Wings and inner bunkers (no coal in) open to the sea. Α heel of 10° would result.

3. Wings, bunkers (no coal in), and one engine-room open to A heel of 18° would result.

the sea.

In either of these cases it would be advisable to admit water to the wings on the opposite side of the ship, to restore the vessel to the upright. Not only because the guns on the opposite side to the damage would be unable to get horizontal fire, but because the lower edge of armour comes out of water between 8 and 10°, leaving the vitals of the ship completely unprotected (see Fig. 130). In such ships provision is made for flooding the wings, if necessary, to correct heel or trim. We have already seen that the middle line bulkhead of the engine-room is made strong enough to stand the pressure, supposing one engine-room to be flooded.

A similar state of things obtains in vessels with a middle line bulkhead through the boiler-rooms, like the Majestic. In more recent vessels, however, this bulkhead is not fitted, because of the new arrangement of watertube boilers. The flooding of a boilerroom, therefore, causes a bodily sinkage; the flooding of wings, etc., will cause heeling, as seen above.

Influence of Coal stowed in Upper Bunkers.-1. The question of coal in the upper bunkers at the side of war-ships is important because of the resistance such coal offers to direct penetration. It has been found that 2 ft. of coal is equivalent in resisting power to 1 in. of iron. This is specially important in deck-protected cruisers (Figs. 21, 22, 24, 26), which depend so largely on the coal above the protective deck for their protection, and on this account the coal in the upper bunkers at the side should be the last to be used. All ships of this type in the Royal Navy have sufficient stability even supposing all the coal in the lower bunkers burnt out and the upper bunkers completely full. In the sloops, which are quite unprotected save

by the coal, a division is placed in the bunkers, so that some coal may remain above the flat as long as possible, in order to retain its protection (Figs. 29, 30).

2. In addition to this direct protection there is the fact that the bodily sinkage on riddling the side and admitting water would be less with coal than without it. Every cubic foot of bunker space, with coal in, contains five-eighths solid space occupied by the coal, and three-eighths vacant space, into which water could penetrate. The influence of this in limiting bodily sinkage has already been seen in Chapter XVI.

3. Of greater importance, however, than (1) or (2) is the influence of the coal in preserving the initial stability, supposing the side of the ship

is riddled in way of the upper bunkers.

(a) With the side of the ship intact,

the shaded parts in

Fig. 175 will con

UPPER -BANKERS.

FIG. 175.

tribute their full value to the moment of inertia of the waterplane.

(b) With the side riddled and no coal, the shaded parts will contribute nothing to the moment of inertia of the waterplane.

(c) With the side riddled and coal in, the shaded parts will contribute five-eighths their area to the moment of inertia of the waterplane.

We have seen that the position of the transverse metacentre, on which the initial stability so largely depends, is directly influenced by the trans

to be gradually riddled. The vessel starts with a GM of 34 ft. If coal is in the upper bunkers the riddling of both sides for the

length of 230 ft. leaves the ship with a GM of 9 in., so that the ship although tender would be stable. If the bunkers are empty the reduction of GM as the sides are riddled is much more rapid, and the vessel would become unstable when about half the length of bunkers was riddled.

Fig. 177 gives the result of calculations made on a cruiser 370 ft. x 57 ft. x 20 ft. x 6160 tons, having one side only

leaves the ship with a GM of 2 ft., supposing that water is admitted to the wings to keep her upright. BB is the curve, supposing the coal out of the upper bunkers and the heel corrected by admitting water to the wings. The ship still retains a GM of 1 ft., supposing the length of 165 ft. is riddled. A rather smaller GM is found to result if the heel is corrected by admitting water to the double bottoms only, curve CC. In these cases the lowering of M due to the loss of moment of inertia of the waterplane is partially compensated for by the lowering of G due to the admission of water to the wings or double bottoms.

The following example is introduced to show that a given quantity of coal on board a vessel is more usefully disposed, as regards stability, when the side is riddled, when in the upper bunkers at the side than in the lower bunkers, in spite of the lowering of the C.G. of the ship that takes place when the coal is trimmed down.

EXAMPLE.-A box-shaped vessel is 350 ft. x 60 ft. with bunkers at the side amidships 10 ft. wide, 160 ft. long, extending from 14 ft. to 26 ft. above the keel. When these bunkers are full the draught is 20 ft., and the metacentric height 3 ft. Determine the effect on the initial stability—

(i.) With sides riddled in way of upper bunkers, coal in.

(ii.) With sides riddled in way of upper bunkers, the coal having been trimmed to the lower bunkers 8 ft. above keel.

Taking 43 cubic ft. of coal to the ton, the side bunkers will hold about 900 tons. The displacement of vessel is 12,000 tons.