It shall now be our object to enter into some of the theoretic and practical details of this important sub ject; and as we would on the one hand endeavour to avoid every thing which bears the aspect of merely speculative inquiry, with no practical object in view, so we would on the other avoid any description of those merely practical details of the art, which can only be acquired at the dock side, or which have been already minutely and clearly detailed by the practical writers on the subject. We shall therefore begin with the consideration of the displacement, an element which meets us on the very threshold of the inquiry.
We refer to the article Hydrostatics for the consi deration of the principle, that a body specifically lighter than water will sink in the fluid, until it has displaced a portion of it, equal in weight to the entire body itself. On this simple elementary law of Hydro statics is primarily founded the process commonly employed by naval architects for determining the dis placement of a vessel.
By the displacement of a ship we are to understand the cubical contents of that part of it which is below the water's surface, and which, it is obvious, must be more or less, according to the degree in which the ship is immersed, by the variable conditions of its lading.
In making a design for a ship, the first object of the constructer must be, to form as accurate an estimate as possible of its weight; and if this is to be done without any assistance derived from former construc tions, exact calculations must be made of the dimen sions and specific gravity of all the materials to be employed in her formation; the number of guns she is destined to carry; her complement of men; and the quantity of provisions and stores necessary for her complete equipment. When her total weight is thus determined, the constructer must endeavour to obtain for her a corresponding displacement, and at the same time secure to her such dimensions, as shall impart to her every property he may desire, and. if a ship of war, to ensure her lower deck guns a sufficient eleva tion above the water's surface. The displacement
therefore is a fundamental element in shipbuilding, and on its right determination depends many import ant considerations.
If the form of the body immersed in the fluid were generated according to any known and determined law,—if, for example, it partook of the figure of any solid of revolution, the application of the particular rule of mensuration belonging to that figure, would readily furnish the solidity of the part immersed. But there is no certain form yet determined for a ship's bottom: and, accordingly, no approximate formula has yet been devised, which can furnish, by a short and convenient operation, the displacement. Bouguer it is true, attempted an approximation of the kind, by assimilating a ship's body to a spheroid; and then es timating the contents of its displacement at 11 of the rectangular solid formed by the three principal di mensions of the length at the water's sur face, and its breadth and depth estimated at and from the same plane. This method, however, although it might afford tolerably correct results for ships whose fulness of figure approached nearly to a spheroidal form, yet in vessels of a sharper class, the errors aris ing from its application would be too considerable to admit of its employment in any other way than as an approximation of the roughest kind.
Accordingly, constructers have had recourse to the well-known method of ordinates; a process contrived by mathematicians to obtain the areas and cubical contents of bodies, whose forms are destitute of symmetry and proportion. It consists essentially, in the case of a solid, in dividing it into an unequal number of lamina or sections of uniform thickness, and determining their aggregate solidity by means of the formula + 4 S 2 3) 4, in which Y. denotes the sum of the first and last ordi nates, S the sum of the even ordinates, s that of the odd ordinates, and i the common interval or distance between the ordinates; and we shall now proceed to exhibit its application, by calculating the displacement of a seventy-four gun ship. This may be enunciated as a