Now let us suppose this solid mass of lead to be rendered liquid by being melted. The constituent particles will then be deprived of that cohesion by which they were held together; they will accordingly have a tendency to separate, and fall asunder by their gravity, and will only be prevented from actually doing so by the support afforded to them by the sides, [Pg026] A B, D C, of the vessel. They will therefore produce a pressure against the sides, which was not produced by the lead in its solid state. This pressure will vary at different depths: thus a part of the side of the vessel at P will receive a pressure proportional to the depth of the point P below the surface of the lead. If, for example, we take a square inch of the inner surface of the side of the vessel at P, it will sustain an outward pressure equal to the weight of a column of lead having a square inch for its base, and a height equal to P A. And, in like manner, every square inch of the sides of the vessel will sustain an outward pressure equal to the weight of a column of lead having a square inch for its base, and a height equal to the depth of the point below the surface of the lead. (10.) We have here proceeded upon the supposition that no force acts on the upper surface A D of the lead. If any force presses A D downwards, that force would be transferred to the bottom by the lead, and would produce a pressure on the bottom B C equal to its own amount in addition to the weight of the lead; and if the lead were solid, this would be the only additional mechanical effect which such a force acting on the surface A D of the lead would produce. But if, on the other hand, the lead were liquified, then the force now adverted to, acting on the surface A D, would not only produce a pressure on the bottom B C, equal to its own amount in addition to the weight of the lead, but it would also produce a pressure against every part of the sides of the vessel, equal to that which it would produce upon an equal magnitude of the surface A D. Thus if we suppose any mechanical cause producing a pressure on the surface A D amounting to ten pounds on each square inch, the effect which would be produced, if the lead were solid, would be an additional pressure on the base B C amounting to ten pounds per square inch. But if the lead were liquid, besides this pressure on each square inch of the base B C, there would likewise be a pressure of ten pounds on every square inch of the sides of the vessel. All that has been here stated with respect to a square or a cubical vessel will be equally applicable to a vessel of any other form. [Pg027]