SHIP BUILDING. 31 



of a body to sustain itself wholly on the surface of the water, or to sink par- 

 tially, is determined by the difference between the weight of the body and of 

 the quantity of water which it displaces ; this difference, under all circum- 

 stances, must be kept as great as possible. 



1. Determination of the Weight. We must first ascertain the entire 

 weight of the vessel, as this is the basis of all subsequent calculations ; but 

 a vessel contains such a variety of parts, and they are so irregular, that this 

 calculation is subject to great difficulties. In the calculation of irregular 

 surfaces and solids we have several approximate methods, where strict 

 accuracy is impracticable. For instance, we take a given axis of the body 

 as the line of abscissas, and erect upon it ordinates at equal distances from 

 each other, and the exactness of the calculation will be in proportion to the 

 number of ordinates. From these abscissas and ordinates Atwood determined 

 the cubic contents of an irregular body by the formula (S + 2P -j- 3Q) j = x, 

 S representing the sum of the first and last ordinates, P the sum of the 

 fourth, seventh, and tenth, &c., ordinates, Q the sum of the second, third, fifth, 

 sixth, eighth, and ninth ordinates, and i the magnitude of the equal abscissas. 

 We thus obtain the area of any number of sections taken at pleasure, from 

 which we may easily calculate the cubic contents. 



2. Displacement of the Water. We know from hydrostatics that every 

 floating body, whatever be its figure, displaces a portion of the fluid of a 

 weight precisely equal to its own ; hence, we may determine the weight of 

 a ship 'by ascertaining the weight of the water which it displaces. This is 

 a simple calculation, as we have only to determine the number of cubic feet 

 in the part under water, its figure and dimensions being given ; but the dis- 

 placement of the water by a vessel varies with the height of the water-line; 

 the lowest water-line gives the minimum, that is to say, the weight of the 

 ship when she is launched ; while the highest gives the maximum, or the 

 weight of the ship after she is fully equipped for service, and with her cargo 

 on board. The determination of this displacement is a problem of great im- 

 portance. The form of the ship, after it is finished, may certainly aid the 

 builder in the solution, but there are often cases in which we are obliged to 

 go back to first principles, and then the calculation becomes quite compli- 

 cated. An approximate method has been proposed by Bouguer, who takes 

 the body of the ship as a semi-spheroid, which figure it in fact resembles 

 more than any other ; now, since the contents of a spheroid are equal to || 

 of the contents of the circumscribed parallelopipedon, he assumes that we 

 shall obtain the displacement by taking the parallelopipedon formed by the three 

 dimensions of the ship under the surface of the water. The formula given 

 above applied to the body of a ship renders a result so exact, that in ships 

 of 3,000 to 4,000 tons the discrepancy will amount to scarcely half a ton. We 

 must have the ground plan and elevation of a ship in order to determine the 

 displacement {pL 7, fig- 1). Let ABCD be the elevation of a ship, and WW 

 the water-line, for which the displacement is to be ascertained. Take the 

 points E and F in this line at the distance of several feet from the stem and 

 stern-post, and divide the line EF into several parts at pleasure, using an 

 odd number, however, or a multiple of 3 + 1 ; through the points of division 



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