OF THE SCALE OF SOLIDITY.
By a scale of solidity, we are to understand a method employed by naval- architects, for ascertaining the displacement of a ship, at different depths below the load water line, by means of a curve, whose abscissae d to the respective draughts of water, and ordinates to the displacements at the same points.
To construct a scale of solidity for the vessel whose entire displacement was before calculated, we must have recourse to the last column of the general table of results, named Areas of Semi-Horizontal Sections." If we refer to the table of results here quoted, and to the second figure of Plate CCCCLXXXVIII, we shall, in the first place, perceive that the total dis placement of the vessel, or, in other words, the dis placement below the load water line 1°, amounts to 100977.93 cubic feet, or 2885.08 tons; and that to as certain the displacement below the horizontal section 2°, we must deduct from the total displacement, the solidity of the part comprised between the sections 1° and 2°. In performing the subsequent calculations, the areas of the semi-horizontal sections contained in the column above referred to, must be doubled to ob tain the total areas of the horizontal sections, and also the total displacements.
To obtain the contents of the solid between the ho rizontal sections 1° and 2', it is manifest, since the interval between the sections is one foot, that the 7517.42 + 7438.64 mean of the two, or = 7478.03 cubic feet is the quantity desired; and that by tracting this result from the total displacement, and dividing the result by 35, there will remain 2671.43 tons for the displacement of the vessel below the hori zontal section 2°. Hence it appears, that by decreas ing the draught of water one foot, the displacement will be diminished 213.65 tons.
To determine, in the next place, the displacement below the horizontal section 3°, the solidity between the sections 1° and 3° must he determined, and the result subtracted from the total displacement. This
must be accomplished by means of the formula (1* + 4 S + 2 $) 3, and for which in the present case, we have the following elements: Extreme Areas. Even Area. Odd Area.
7517.42 7438.64 7335.24 414852.66 =X 29754.56 = 4 S Zero.
And since - = Nie shall have (1 4 S + 2 3 3 3 - (14.852.66 + 29754.56 + 1 0.0) X = 14869.07, for the solidity of the part required. Hence, by tak ing this from the total displacement, and reducing the result into tons, we shall have 2460.25 tons for the displacement of the vessel below the section 3°. So that by decreasing the draught of water 2 feet, the displacement is diminished 424.83 tons.
Again, to determine the displacement below the ho rizontal section 4°, the solidity of the part contained between the planes 3° and 4° must be first determined, and to it added the solidity of the part between the sections 1° and 3° before determined, and the sum taken from the total displacement.
The solidity between the sections 3° and 4° is evi 7335.24 ± 7204.54 dently 27269.89 Solidity between the sections 1° and 3° before determined = 14869.07 Solidity between the sections 1° and 4° = 22138.96 109977.93 - 22138.96 Hence = 2252.54 tons, 35 which is the displacement below the horizontal section 4°. Thus, by decreasing the draught of water 3 feet, the displacement is diminished 632.54 tons.
To determine, in the next place, the displacement below the section recourse must be again had to the formulator equidistant ordinates, by which means we have • Extreme Areas. Even Areas. Odd Area.
7517.42 7438.64 7335.24 7046.80 7201.54 214564.22 = 1 14643.18 14670.48=-2: 4 58572.72 = 4 S and since = 1 we shall farther have 3 3+ 4 S 2 s) --,-.- (14564.22 + 58572.72 14670.48) X = 29269.14. Hence, by subtracting this from the total displacement, and reducing the result into tons, we have 2048.82 tons for the dis placement below section 5°. Therefore, by decreasing :he draught of water 4 feet, the displacement is di minished 836.26 tons.