SHIPBUILDING. 1-19 of the part below section 21°, amounting to 5489.05, giving for the moment of the entire semi-displace ment, the number 392753.09.
But by a well-known principle of mechanics, if the moment of the semi-displacement be divided by that semi-displacement, the result will be the required depth of the centre of gravity of displacement below 9 3 2753.09 i the water section. This depth therefore 50488.96 = 7.78 feet. The semi-displacement here employed is the mean of the displacement determined by the horizontal and vertical sections.
To determine, in the next place, the position of the centre of gravity of displacement with respect to the length of the vessel, we must have recourse to the lowest horizontal column of the general table beforc referred to, and refer all the calculations to the primi tive vertical plane marked 1.
In the first place, the moment of the rudder will be found by multiplying the semi-solidity abaft the vertical section 5', by the distance of its centre of gravity from the primitive plane 1, and which is 90.04 X 16.4 = 1476.66 . . . (M) Secondly, to find the moment of the part between the vertical sections 5' and we have and applying the column of resulting products to the formula for equidistant ordinates, we shall have and applying the column of resulting products to the formula, we shall have and since = 2, we further have 3 Extreme Products.
00000.00 10787.40 10787.40 = Fourthly, to determine the moment of the part com prised between the sections 1" and 5" 2690.40 = 4 S and since - = 1'1416, the formula will produce 3 + 4 S + 2 s) 3 - = (215.36 + --I- 845'84) X 14416 =4282.83. . (M) Thirdly, to find the moment of the portion of the vessel comprised between the vertical sections 1 and 27, we have the following table: and applying the column of resulting products to the before quoted formula, we have The preceding investigations respecting the dis placement have been conducted on either of the sup positions that the ship and the water are at rest, or of a ship and the water moving in the same direction with the same velocity, in which case the ship is still rela tively at rest. But when the ship and water are rela tively in motion, either by the ship being at rest and the water in motion, or by the ship's moving and the water's being at rest, or by the ship and water moving with un equal velocities, or in directions, the depth to which the ship sinks must be determined in connex ion with other considerations. As a proof or a dif
ference in the two conditions of a vessel alluded to, we may adduce the observations of M. Romme, that a frigate which was lashed to a sheer hulk in the river Charente, sunk two inches more when the velocity of the stream was great than when the motion of the stream was only just sensible.
In an ingenious disquisition on this subject, Mr. Morgan, one of the foremen of Portsmouth Dock yard, adduces another remark of Rommc on the same subject, in which that learned foreigner describes some experiments he made to determine the vertical pressure of water when in motion compared with its pressure when at rest. He had two tin tubes con structed, the one, Fig. 4. Plate straight as a b, and the other curved as e d e, each open at its ends, and capable of receiving a float g f, the lower part of which, f, was of cork, and the up per part a rod marked with inches and lines. These tubes, containing their •floats, were first plunged into still water, and the division of the rods observed, cor responding with the upper orifices of the tubes. The tubes were then placed in running water, the current being in the direction h i, and the bent tube e d e, with its lower end turned in the same direction; the floats in both tubes were then observed to have sunk an inch below the position they had when the tubes were in still water. The bent tube was then turned so as to present its orifice to the current, when the float rot.: an inch above the position which it had in still water. The bent tube was then placed with the lower end per pendicularly to the direction of the current, when the float sunk an inch below its position in still water. He measured the velocity of the current, and found that the water ran 70 feet in 30", or that its velocity was that due to a height of an inch and a line nearly; which corresponded with the distance the floats in the tubes rose or fell in the experiments. Other ex periments in currents of different velocities produced similar results. In some instances the depression and elevation of' the floats were as much as five or six inches, being always the height due to the velocity of the current. He ascertained also that the results were the same, to whatever depth the tubes were plunged into the water.