There appear to be limits, beyond which the mag nitude of the three great divisions of the navy into ships having one, two, or three decks, cannot be car ried, without injuring their properties, and increasing the expense of construction, equipment, and wear and tear, to an extent incompatible with their respective force and general service. If a nation does not pos sess ships of each of these three divisions, of the greatest magnitude of the respective limits, which although not yet correctly defined, experience has ad vanced far towards approximating to, it may he sur prised in wars with other nations, by having to op pose, with great inconvenience and additional expense, and perhaps ineffectually, the smaller ships with two decks to the largest ships of one deck, and ships with three decks to the largest ships with two decks. The large ships with two decks, of 84 guns, and the large frigates of 60 guns, may probably have arrived near the greatest limits of magnitude of these divisions, and therefore would prevent surprise by new classes of ships of other nations.
To illustrate the loci of certain remarkable points connected with the formation of a vessel, Chapman constructed an ingenious figure, and which we have given in Fig. 1, Plate CCCCXCIV, for the informa tion of our readers. Its description is as follows:— On the load water line AB, a series of intervals 20, 40, 60, 80, 100, &cc. are assumed as representatives of different lengths from the stem to the stern post of a vessel. Chapman then found, that in the case of a bark, the locus of the centre of gravity of displace ment would be denoted by the line CGB, the locus of the metacentre by DDB, and that of the centre of gravity of the ship and lading by EEB. In the case of a frigate, he found 'TB to be the locus of the cen tre of gravity of displacement, GGB that of the me tacentre, and IIHB that of the ship with its lading. So that for a vessel of the form of a bark 80 feet long, the distance from the load water line to the centre of gravity of displacement, would be denoted by LC; the height of the metacentre above the load water line by LD, and the depression of the centre of gravity of the vessel with its lading, below the load water line, by the quantity LE. But For a frigate, the distance of the centre of gravity of displacement below the load water line would be LF, the height of the meta cent•e above the same line LG, and the distance of the centre of' gravity of the ship and lading below the water, LH. The length of the mainmast, moreover, is determined by the distance of the line IIB front the same plane BA, so as to be of a magnitude corres ponding to the stability.
If there be given to large and small ships, a form similar to that which is 110 feet in length, the straight line MB in the figure will represent the locus of the metacentre, and the line K K B the curve which will determine the length of the mainmast, so as to be in its proper relation to the stability.
In the formation of these curves, Chapman has in troduced one supposition not strictly proper, and that is a uniformity in the density of the lading, a condition which, it is manifest, cannot in all cases be fulfilled. The graphic representations, however, he has given will be found of very essential service in the practice of shipbuilding. It would be possible to construct a
series of curves for ships of the same class, which should embrace the important condition of a variable density in the lading.
Experience has taught its that the place of the mid ship bend exercises a very sensible influence on the properties of a ship; its situation depending more or less on the form of the extremities.
This will be apparent, if we compare a body com posed of two wedges joined at their bases, and the place of whose centre of gravity is given, with another body of the same length, but composed of two hemi spheroids; then it will be found, that the lengths of these spheroids will not bear the same proportion to the whole length as those of the wedges; or, in other words, the greatest breadths of the two bodies will be at different distances from their extremities.
To approximate in some degree to the situation of the mid ship bend, let ADM, Fig.2, Plate CCCCXCIV, represent the body of a ship, in which DI is supposed to denote the position of the section desired, and ADF, AIF similar parabolas, and BDF, BD: other like curves of that kind. Let C moreover be the middle point of the length from the stem to the stern post; E the centre of gravity of the entire vessel;* G the centre of gravity of DAI before the greatest section, and 11 the centre of gravity of the other portion of the vessel, abaft the same plane.
Assume All, the entire length of the vessel = FA the distance of the midship section from the ex tremity A = a•, and CE the interval between the mid dle point of the length, and the centre of gravity of the vessel = M. Now, by the property of the para bola, the distance of its centre of gravity G front the point A = a AF, and Fil = FB. Moreover, the areas of the parabolic spaces ADI,BDI vary as x and and referring every thing to the point A, we obtain the equation (x a (2 which furnishes, by the ordinary processes of algebraic reduction, the value of x m; and from which it follows, that the distance between the middle of the length of the ship, and its greatest section, ought to he four times the distance between this middle point and the centre of gravity of the ship. In a ship fuller at its extremities, so that AG = AF, the distance of the greatest section from the mid dle - 6 m. Should it be still fuller, so that AG = AF, the distance of the greatest section before the middle point will be 8 m.
Hence it is seen, says Chapman, that the greatest section should be before the middle of the length for sharp ships, as frigates, four times the distance of the middle point of the length from the centre of gravity of the ship; and for merchant ships, which are very full, eight times the same distance.
This is the place of the midship bend, when the distances are estimated on the load \yawr line; but if they are taken on the upper part of the keel, to which the frames are commonly placed perpendicular,t the midship bend ought to be a little before the greatest section, by a quantity depending on the difference of the draught of water forward and aft, and on the cur vature of the ship at the middle.
This distance may be considered, in general, as equal to the difference of the draught of water.