_The pressure upon any particle of a fluid of uniform density is proportioned to its depth below the surface._
_Example 1._ Let the column of fluid ABCD Fig. (1) be perpendicular to the horizon. Take any points, _x_ and _y_, at different depths, and conceive the column to be divided into a number of equal spaces by horizontal planes. Then, since the density of the fluid is uniform throughout, the pressure upon _x_ and _y_, respectively, must be in proportion to the number of equal spaces above them, and consequently in proportion to their depths.
_Example 2._ Let the column be of the same perpendicular height as before, but inclined as is Fig. (2); then its quantity, and of course its weight, is _increased_ in the same ratio as its length exceeds its height; but since the column is partly supported by the plane, like any other heavy body, the force of gravity acting upon it is _diminished_ on this account in the same ratio as its length exceeds its height; therefore as much as the pressure on the base would be augmented by the increased length of the column, just so much it is lessened by the action of the inclined plane; and the pressure on any part of C_c_ will be, as before, proportioned to its perpendicular depth; and the pressure of the inclined column AC_ac_ will be the same as that of the perpendicular column ABCD.
_Fluids rise to the same level in the opposite arms of a recurved tube._
Let ABC, (Fig. 90) be a recurved tube: if water be poured into one arm of the tube, it will rise to the same height in the other arm. For, the pressure acting upon the lowest part at B, in opposite directions, is proportioned to its depth below the surface of the fluid. Therefore, these depths must be equal, that is, the height of the two columns must be equal, in order that the fluid at B may be at rest; and unless this part is at rest, the other parts of the column cannot be at rest. Moreover, since the equilibrium depends on nothing else than the _heights of_ the respective columns, therefore, the opposite columns may differ to any degree in quantity, shape, or inclination to the horizon. Thus, if vessels and tubes very diverse in shape and capacity, as in Fig. p. 84 be connected with a reservoir, and water be poured into any one of them, it will rise to the same level in them all.