certificate is issued to all the ships of the Navy from measurements made by the officers of the Board of Trade. There are two systems, viz. the British system and the Danube system. They differ in the allowances made for deck erections and machinery spaces. The following shows how these compare with one another, and how the gross tonnage compares with the displacement tonnage in several cases. The Danube rule is the one used when passing through the Suez Canal.

It is seen that the gross tonnage in all cases is considerably less than the displacement tonnage.1

The following extract from the King's regulations gives the instructions concerning the question of tonnage.

The register tonnage according to British rule is to be inserted in all pilotage certificates, and is to be the basis of all tonnage payments at foreign ports by H.M. ships, except when entering Port Said or the Suez Canal, in which case the tonnage according to the Danube rule is to be issued.

The Board of Trade tonnage certificate, which shows the registered tonnage according to both rules, is furnished to all ships as they are commissioned at home ports.

The weight in tons shown in the Navy List is in no case to be used for the payment of pilotage, nor to be mentioned in pilotage certificates.

In the Atlantic liner Campania the displacement tonnage is 18,000 tons, the gross tonnage 12,950, and the register tonnage 4973. The new Cunarders are stated to be designed for a displacement of 32,000 to 33,000 tons, or twice that of King Edward VII. The different systems of reckoning tonnage (viz. war-ships by their displacement and merchant ships by their capacity in tons of 100 cubic feet), has obscured the great increase in size of the large liners as compared with the largest war-ships.

CHAPTER XVI.

BUOYANCY, DISPLACEMENT, TONS PER INCH, ETC.

Buoyancy. At every point of the surface of a body immersed in water there is a pressure which acts normally to the surface. The amount of this pressure will depend on the depth of the point below the surface. If d be the depth of the point below the surface in feet, and w the weight of a cubic foot of water, then the pressure per square foot is w x d lbs. Thus if a hole of 1 square ft. is made in a ship's bottom 173 ft. below the surface of the water, a piece of wood would have to be held against the 64 x 17.5 hole with a force of

2240

= 0.5 ton to keep the water out.

It is because of this pressure that diving operations beyond a certain depth are rendered impossible.

In the case of a floating body like a ship, these normal pressures all over the surface act in many different directions. In each case, however, the normal pressure may be resolved into its three components at right angles, viz. (i.) horizontal in a fore-and-aft direction, (ii.) horizontal in a transverse direction, and (iii.) vertical. If the ship is floating at rest, all these horizontal components must balance between themselves, since there is no bodily movement of the ship in any direction. It is the combined effect of all the vertical components which exactly balances the weight of the ship. The single vertical force, which is the resultant of an infinite number of small vertical forces acting on the ship, is termed the buoyancy. In the same way the forces due to the weights composing the ship have a single resultant, which we term the weight of the ship. The vertical forces acting on the ship at rest are therefore

(a) The weight of the body acting vertically down. (b) The buoyancy acting vertically up.

Since the body has no motion up or down, it follows that the buoyancy exactly equals the weight.

If we take a block of wood, say pitch-pine or teak, and suspend by a spring balance, the dial would show the weight of the wood, say 10 lbs. If we place the block into water we should notice, as the wood descends, that the dial registers less and less, showing that the water is taking some of the weight. A point will at last be reached when the dial will register zero, and then the wood is floating, and instead of the 10 lbs. being borne partly by the balance and partly by the water, the whole weight is taken by the water. That is, the buoyancy is equal to the weight.

Displacement. We now come to a most important proposition in connection with floating bodies. A body floating freely and at rest displaces or puts aside a volume of water having a weight exactly equal to the weight of the body. The water displaced is termed the displacement, and can be either reckoned as a volume, when it is expressed in cubic feet, or as a weight,

WATER

SURFACE.

FIG. 156.

when it is expressed in tons. That the above proposition must be true may be seen by the following:

Consider a vessel floating freely and at rest in still water, and imagine if it were possible that the water is solidified, maintaining the same level, and therefore the same density. If now we lift the vessel out we shall have a cavity left behind, which is exactly of the form of the underwater volume of the ship, as Fig. 156. Now suppose the cavity is filled with water. This amount of water is evidently the displacement of the vessel. Suppose now that the solidified water outside again becomes water. The water we have poured in will be supported by the water surrounding it. The support given, first to the vessel and now to the water we have poured in, by the surrounding water must be the same, and consequently it follows that the weight of the vessel exactly equals the weight of the water poured in to fill the cavity, or, in other words, the weight of the vessel is equal to the weight of the water displaced.

This fact is of immense assistance in dealing with the weights of ships. We do not need to estimate the weights, which would be an almost impossible task, but, knowing the line at which the ship is floating, and having the drawings giving the shape of the ship, we can calculate the volume of displacement up to that line. Then, knowing the density of the water, we at once have the weight of the ship with everything she has on board.

When a man is floating in water, it is manifestly desirable to keep the arms below the surface because of the buoyancy due to their displacement. It will be noticed that, when thus floating, if the arms are held up out of the water, a certain amount of sinkage occurs. The weight of the body remains the same, but the buoyancy is reduced and must be made up by the sinkage before the balance is obtained, viz. that the weight equals the buoyancy.

The same principle has to be borne in mind when constructing a raft. All the human beings have to be placed on it, but a great quantity of provisions, etc., may be safely carried under it. For instance, a cask of beef weighs 300 lbs., and its volume displaces 184 lbs, of water, so that if carried beneath the raft we get 184 lbs. of buoyancy from it, the net weight of the cask is therefore only 116 lbs.

The density of water varies at different places, and often at the same place at different states of the tide. Thus in places on the coast and at sea it is practically constant, viz. 64 lbs. per cubic foot, giving 35 cubic ft. to the ton. At Glasgow, well up the Clyde, the water weighs 62 lbs. per cubic foot. giving 35 84 cubic ft. to the ton. At Gravesend the water is 63.7 lbs. per cubic foot at high tide, and 634 lbs. per cubic foot at low tide. It is because of the difference of density that a vessel decreases her draught in going from fresh to salt water. This is of importance in merchant vessels, which are allowed to be loaded below the load line disc, when floating in water less dense than salt. Thus a vessel of 20 ft. depth, if in fresh water (1000 ozs. to the cubic foot), is allowed by the Board of Trade officers to be loaded 4 in. deeper than the load line disc, because it is known that when she has got to sea she will rise this amount. If the same ship were being loaded in Aberdeen Harbour, for instance, where the water weighs 1015 ozs. to the cubic foot, 13 in. only would be allowed.

The vessel whose displacement has been calculated in the previous chapter as 4052 cubic ft., will weigh if floating at the top waterplane in salt water

4052
35

115 8 tons. If floating at the

same waterplane in river water, of which 35:6 cubic ft. go to the

Curve of Displacement.-We have seen how to determine the volume of displacement of a ship when floating at a given waterplane. The draught of a ship, however, continually varies owing to having different weights of coal, stores, etc., on board, and so it is desirable to have the means of determining quickly the displacement of a ship at any other given draught. The body having been cut by a series of equidistant planes, we calculate the displacement to each of these planes in succession. Thus in a battle-ship the following figures were obtained at planes 4 ft. 3 in. apart, the top one being at a draught of 31 ft., viz. 18,300, 15,016, 12,121, 9,293, 6,510, 3,923, 1,901, 268 tons respectively. We can then set up a scale of draughts, as in Fig. 157, and at each line set out the corresponding displacement. Through the spots thus given we then draw a curve, which is termed the curve of displacement. In this case, suppose the ship is floating at a draught of 19 ft. 6 in. forward and 20 ft. 10 in. aft, i.e. 20 ft. 2 in. mean. We set up this draught at AB and measure to the curve, and find the displacement to be 10,550 tons. It is usual to continue the curve right down to zero draught, although the ship could never float at a less draught than would be due to her structure alone. The smallest displacement obtained in the history of any ship would be when she was launched.

Tons-per-inch Immersion. It is frequently necessary to know how much a vessel, when floating at a given draught (a) will sink, if certain known weights are put on board, or (b) will rise if certain known weights are removed. Since the displacement of a vessel equals the weight, any extra displacement caused by adding a weight must equal the added weight. If A is the area in square feet of the waterplane at which a ship is floating, then the volume of a layer 1 in. thick is cubic ft., and the displacement of this

A

12

tons. This must be the weight neces

A 420

sary to add to sink the ship 1 in., or to take out to lighten the ship 1 in. This is termed the tons-per-inch immersion.

EXAMPLE. The area of the waterplane at which a vessel is floating is 7854 square ft. Find the rise due to burning 56 tons of coal.

Rise

=

= 3 in.