At 30 ft. 6 in. waterline, C. B. is 10-35 ft. below 27 ft. 6 in. waterline A curve drawn through these points gives the locus of centres of buoyancy. = In a similar manner the distance BM is determined for each of the four conditions of draught. Thus at 30 ft. 6 in. waterline, BM 14.9 ft.; at 27 ft. 6 in. waterline, BM = 17.3 ft.; at 24 ft. 6 in. waterline, BM = 20·5 ft. ; at 21 ft. 6 in. waterline, BM=24.5 ft. These distances, set up from B1, B2, B3, B4 respectively, give the spots M1, M2, M3, M4, and the curve through these is the locus of Fig. 167 shows the curves of C.B. and metacentres of a number of ships all placed together. The sections of these ships are shown in Fig. 168. The battle-ship is very broad, and the metacentre is consequently high. The Devastation has a sudden drop as she lightens, owing to the overhang of the armour. With the first and second class cruisers the finer body causes a lift in the locus of the C.B. The Maine is a typical merchant vessel (she has been taken into the service, and converted into a hospital ship). She is much narrower than the other vessels, and the effect of this is seen in the low locus of metacentres. (Such ships, carrying great weights of cargo, have their C.G. low as compared with war-ships which have to carry heavy weights of guns, armour, etc., high up). The Waterwitch (formerly an auxiliary steam yacht, now a surveying vessel), presents some points of interest. The pegtop section causes a high C.B. As the ship lightens the M curve dips downwards, owing to the small breadth at the waterline. Position of the Centre of Gravity. We have been dealing above with the position of the transverse metacentre, but in order to know anything about the initial stability of a ship we must also know the vertical position of the C.G. It is possible to determine this position by means of direct calculation, and this very laborious calculation has to be done in the case of a new design. Finding the position of the C.G. in the various conditions of the ship, deep, normal, and light, it is possible to arrive at the estimated metacentric height in these conditions. Inclining Experiment. When a ship is completing or finished it is possible, by means of the "inclining experiment," to determine the metacentric height, and thus to find the position of the C.G. This experiment is always carried out on new ships of the Royal Navy, and also after a vessel has undergone extensive alterations likely to affect the stability. The information obtained from this experiment forms the basis of the stability calculations for the completed ship, and the main features of the vessel's stability are furnished to the Ship's Book in the Stability Statement. The information thus obtained also enables us to see how far the estimate of the design has been realized, and gives most valuable data for use in subsequent designs. The main features of an inclining experiment are as follows. Weights are placed on the upper deck, as Fig. 169, and w tons, say, is moved across the deck, a distance of d feet. Then the C.G. of the ship will shift to G', such that The ship cannot remain upright as shown, because the second condition of equilibrium is not fulfilled, viz. that the C.G. and the C.B. must be in the same vertical. The ship must heel over until the new C.B., B', comes into the same vertical as the new C.G., G'. Then the point where B'G' meets the middle line is M, the transverse metacentre. If is the angle of heel, then The only part in this that we do not know is tan 0, and this is easily obtained by suspending two or more plumb-lines down hatchways. Then if a be the deflection along a base AB, 7 feet a from the point of suspension, we have tan 0 = 4. It is desirable で to have more than one pendulum, because of the check obtained on the angle. Also the weights are shifted across in various lots, both to port and starboard, so as to obtain a number of results, the mean of which can be taken. The GM thus obtained will enable us to fix the position of G, because M will be determined from the metacentric diagram. The following is taken from an actual inclining experiment A vessel displacing 5372 tons is inclined by shifting 25 tons of ballast across the deck, the mean deflection observed being 101 in. in 15 ft. The transverse metacentre was measured off the metacentric diagram 3·1 ft. above the L.W.L. at the draught given, so that the C.G. of the ship in the inclined condition was 3.1 - 2·9 = 0·2 ft. above the L.W.L. The ship was incomplete at the time of the experiment, so the weights to complete and remove were determined, amounting to a net total of 600 tons, with the C.G. 35 ft. above the L.W.L., or 33 ft. above the C.G. in the inclined condition. The rise of the C.G. due to this addition was so that the C.G. in the completed condition, 5972 tons, would be 0.5 ft. above the L.W.L. At the draught corresponding to this displacement the transverse metacentre was measured to be 2.9 ft. above L.W.L, so that the GM in the completed condition was 2.9 - 0.5 = 2.4 ft. In this way, using the results of the inclining experiment as a basis, we are enabled to determine the draught and metacentric height in any desired condition. The usual conditions are deep load, normal load, and light, which have been defined in Chapter XV. These are shown on the metacentric diagram, as Fig. 166. In that case we have Deep load; draught 28 ft. 8 in., GM = 3.7 ft. These particulars are given on the stability statement, a specimen one being given at the end of Chapter XIX. In cruisers, in which the coal capacity is relatively very large and a large proportion of it is above the protective deck, a special condition looked into is that, supposing the upper bunkers are full, while the lower bunkers are empty. This would be an extreme condition, and the ship, unless damaged, would hardly get into a worse condition of stability than under such circumstances. If the condition thus found gives too small a GM, a special notation would be made on the stability statement giving definite instructions as to the coal stowage. In most cases, however, sufficient stability is retained even under these extreme conditions, and a note is made on the statement that, so far as stability is concerned, the coal may be worked in any manner desired by the commanding officer. Figs. 170 to 174 show metacentric diagrams of some typical ships. We have already had the case of a battle-ship in Fig. 166. It is usually the case that, although M rises as the ship lightens to the light draught, yet G rises still more because the coal and stores |