CD (Fig. 85) is a vessel composed of two cylindrical parts of unequal diameters, and filled with water to _a_. From what has been said before, the bottom of the vessel CD supports the same pressure as if its diameter were everywhere the same as that of its lower part; and it would at first sight seem that the scale MN of the balance, in which the vessel CD is placed, ought to show the same weight as if there had been placed in it a cylindrical vessel having the same weight of water, and having the diameter of the part D. But the pressure exerted on the bottom of the vessel is not all transmitted to the scale MN; for the _upward_ pressure upon the surface _n o_ of the vessel is precisely equal to the weight of the _extra_ quantity of water which a cylindrical vessel would contain, and balances an equal portion of the _downward_ pressure on _m_. Consequently the pressure on the plate MN is simply equal to the weight of the vessel CD and of the water which it contains. [Illustration: FIG. 85.] _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. [Illustration: FIG. 86.] [Illustration: FIG. 87.]