To know what this expansive force is, let the part O N of the vessel be removed, and the perpendiculars L O and M N be prolonged; then by means of some pipe fixed over N O let water be filled between these perpendiculars up to P Q an equal height with E F. Here the water between the perpendiculars L P and M Q is of an equal height with the highest part of the water in the vessel; therefore the water in the vessel cannot by its pressure force it up higher, nor can the water in this column subside; because, if it should, it would raise the water in the vessel to a greater height than itself. But it follows from hence, that the weight of water contained between P O and Q N is a just balance to the force, wherewith the column between L O and M N endeavours to extend. So the part L M of the bottom, which sustains both this force and the weight of the water between L O and M N, is pressed upon by a force equal to the united weight of the water between L O and M N, and the weight of the water between P O and Q N; that is, it is pressed on by a force equal to the weight of all the water contained between L P and M Q. And this weight is equal to that of the water contained between G I and H K, which is the weight sustained by the part G H of the bottom. Now this being true of every part of the bottom B C, it is evident, that if another vessel R S T V be formed with a bottom R V equal to the bottom B C, and be throughout its whole height of one and the same breadth; when this vessel is filled with water to the same height, as the vessel A B C D is filled, the bottoms of these two vessels shall be pressed upon with equal force. If the vessel be broader at the top than at the bottom, it is evident, that the bottom will bear the pressure of so much of the fluid, as is perpendicularly over it, and the sides of the vessel will support the rest. This property of fluids is a corollary from a proposition of our author[263]; from whence also he deduces the effects of the pressure of fluids on bodies resting in them. These are, that any body heavier than a fluid will sink to the bottom of the vessel, wherein the fluid is contained, and in the fluid will weigh as much as its own weight exceeds the weight of an equal quantity of the fluid; any body uncompressible of the same density with the fluid, will rest any where in the fluid without suffering the least change either in its place or figure from the pressure of such a fluid, but will remain as undisturbed as the parts of the fluid themselves; but every body of less density than the fluid will swim on its surface, a part only being received within the fluid. Which part will be equal in bulk to a quantity of the fluid, whose weight is equal to the weight of the whole body; for by this means the parts of the fluid under the body will suffer as great a pressure as any other parts of the fluid as much below the surface as these.