ON THE ARCHING OF SHIPS.
By the arching of a ship, we mean that alteration of form which every vessel undergoes from the mo ment it is launched. In every point of view in which the general problem of arching can be contemplated, it will be found to involve considerations of the high est importance to naval architecture. Owing its origin to those peculiarities of form, which the complicated conditions of stowage, stability, velocity, and general sailing qualities render necessary, it has been a great and principal object with the naval engineer, to pre serve to the floating vessel unimpaired, those essen tial properties of form, which he endeavoured to im part to her in the process of building. Constructed, as ships in general are, of timbers of the most varied dimensions and forms,—disposed in directions of so many different kinds, and subjected to strains so changeable in direction and quantity, it may be fairly said, that next to the original determination of the best form, the skill and intelligence of the ship builder may be measured, by the degree in which the tendency to arching may he diminished. We shall hereafter have reason to admire the masterly combinations of Sir Robert Seppings, to prevent this derangement of the frames of our ships of war.* We shall proceed to trace, by an inductive pro cess, the operation of those forces that contribute to arching.
If, in the first place, an elastic body of any magni tude, specifically heavier than water, be wholly im mersed in that fluid, no tendency to derange the figure or position of any of its axes will be produced, from the equal and uniform action of the water on its dif ferent surfaces. But if the solid be specifically lighter than water, and have consequently only a portion of its volume immersed,either of its axes,—whether it he longitudinal, lateral, or vertical, will be subjected to peculiar alterations of position and figure,—partly from the pressure of the fluid operating only on por tions of its sides, and partly, if the form of the body be irregular, from the upward pressure of the water on its different vertical sections, not being equivalent to the weights of the sections themselves.
Let us, however, first take the case of a body, whose superior and inferior surfaces are equal, similar and parallel, and any vertical section of which is re presented by ABCD, Fig. 1, Plate CCCCXCV. and
let the line EF represent the surface of the water sec tion, and therefore indicating the depth of the por tion immersed.
Then since the upper and lower surfaces of the body are, by the hypothesis, equal, similar, and parallel, it follows that its sides are, in every part, perpendicular to the fluid surface. Suppose also the body to be composed of vertical laminae of equal thickness, at right angles to the section ABCD, and let GH denote one of them. Then since the gravitating force of this lamina is exerted in the direction GH passing through its centre of gravity, and that this same line likewise passes through the centre of gravity of the column of fluid IH, displaced by the lamina; it follows from the laws of hydrostatics, that there will be an equlibrium. between the gravitating force or the lamina, and the upward pressure of the fluid displaced by it; and that hence no derangement will take place in the particles constituting–the lamina, from the influence of the pressure here alluded td. And since all the lamina constituting the body are, by the hypothesis, similarly acted on by the fluid, it_ follows that no effort will be produced by the upward pressure of the fluid, to de range the form of the solid.
But suppose, in the next place, that some of the vertical lamina:, which make up the solid,should cease to preserve a perfect equality between the gravitating force and the upward pressure of the fluid; a case that would arise if a vertical section of the body were of the form ABCD, Fig. 2, Plate CCCCXCV; some of the lamina?, as KL, receiving no upward support from the fluid, while their own gravitating powers remain undiminished; and others, as MN, deriving from the water only a partial support; it follows, that even if the sections between B and C could preserve their forms unchanged, those beyond the same points would by no means do so; and that, therefore, from the ne cessary adhesion existing among all the lamina con stituting the body, there would be a general tendency in the whole body to alter its form.