_Pressure exerted anywhere upon a mass of liquid is transmitted undiminished in all directions, and acts with the same force on all equal surfaces, and in a direction at right angles to those surfaces._
To get a clearer idea of the truth of this principle, let us conceive a vessel of any given form in the sides of which are placed various cylindrical apertures, all of equal size, and closed by movable pistons. Let us, further, imagine this vessel to be filled with liquid and unaffected by the action of gravity; the pistons will, obviously, have no tendency to move. If now a weight of P pounds be placed upon the piston A (Fig. 86), which has a surface A, it will be pressed inwards, and the pressure will be transmitted to the internal faces of each of the pistons B, C, D, and E, which will each be forced outwards by a pressure P, their surfaces being equal to that of the first piston. Since each of the pistons undergoes a pressure, P, equal to that on A, let us suppose two of the pistons united so as to constitute a surface 2_a_; it will have to support a pressure 2P. Similarly, if the piston were equal to 3_a_, it would experience a pressure of 3P; and if its area were 100 or 1,000 times that of _a_, it would sustain a pressure of 100 or 1,000 times P. In other words, the pressure on any part of the internal walls of the vessel would be proportional to the surface.
The principle of the equality of pressure is assumed as a consequence of the constitution of fluids.
By the following experiment it can be shown that pressure is transmitted in all directions; a cylinder provided with a piston is fitted into a hollow sphere (Fig. 87). in which small cylindrical jets are placed perpendicular to the sides. The sphere and the cylinder being both filled with water, when the piston is moved the liquid spouts forth from all the orifices, and not merely from that which is opposite to the piston.
The reason why a satisfactory quantitative experimental demonstration of the principle of the equality of pressure cannot be given is that the influence of the weight of the liquid and of the friction of the pistons cannot be altogether eliminated.
NOTE.—_The influence of the weight (or gravity) of water and its fractional resistance in practical use_ is so great upon all the processes of numbers and of the application of the natural laws governing the operation of fluids, as stated under the heading of Hydraulic Data, that separate pages will hereafter be found devoted to a more extended explanation of this subject of gravity and friction of water.
