In consequence of the principle of the equality of pressure, the downward pressure exerted by the small piston, a, is transmitted upwards upon the piston C. The pressure which can be obtained depends on the relation of the piston C to that of the piston a. If the former has a transverse section fifty or a hundred times as large as the latter, the upward pressure on the large piston will be fifty

or a hundred times that exerted upon the small one. By means of the lever, O, an additional advantage is obtained. If the distance from the fulcrum to the point where the power is applied is five times the distance from the fulcrum to the piston, a, the pressure on a will be five times the power. Thus, if a man acts on O with a force of sixty pounds, the force transmitted by the piston a will be 300 pounds, and the force which tends to raise the piston C will be 30,000 pounds, supposing the section of C is a hundred times that of a.

The hydraulic press is used in all cases in which great pressures are required. It is used in pressing cloth, in extracting the juice of beet root, in expressing oil from seeds, and in pressing apples in making cider; it also serves to test the strength of cannon, of steam boilers, and of chain cables. The parts composing the tubular bridge which spans the Menai Straits were raised by means of an hydraulic press. The cylinder of this machine, the largest which has ever been constructed, was nine feet long and twenty-two inches in internal diameter; it was capable of raising a weight of two thousand tons.

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Equilibrium of Liquids.

73

CHAPTER II.

EQUILIBRIUM OF LIQUIDS.

83. Conditions of the equilibrium of liquids.-We have seen that the conditions of the equilibrium of a solid are that its centre of gravity be supported by a fixed point; all the other parts of the body then retain the same state of equilibrium in consequence of cohesion, which unites the particles together and to the centre of gravity. This is by no means the case with liquids: owing to the greater mobility of their molecules, and the facility with which they obey the force of gravity, they would flow away and spread out in a horizontal position, if they were not retained by some obstacle. Hence a liquid cannot be at rest in any vessel, unless it satisfies the following conditions:

I. The free surface of the liquid must be horizontal, that is, perpendicular every where to the direction of gravity.

II. Every molecule of the mass of the liquid must be subject in every direction to equal and contrary pressures.

The second condition is self-evident; for if, in two opposite directions, the pressures exerted on any given molecule were not equal and contrary, the molecule would be moved in the direction of the greater pressure, and there would be no equilibrium. Thus the second condition follows from the principle of the equality of pressures, and from the reaction which

all pressure causes on the mass of liquids.

a

Fig. 65.

To account for the first condition relative to the free surface of the liquid, let us observe that in a liquid whose surface is horizontal, all the molecules supporting each other, the action of gravity is destroyed, and the liquid is at rest. But if the surface is not horizontal, if some parts are higher than others (fig. 65), the higher part, ab, exerts upon any horizontal layer, bd, a greater pressure than the part cd, and therefore as a given molecule, o, of the horizontal layer is exposed to a greater pressure in the direction bo than in the direction do, equilibrium is impossible.

In saying that in order that a liquid be at rest its surface must be horizontal, we must remark that that presumes the liquid only to be acted upon by gravity, which is usually the case; if it is under the action of other forces, as is the case with the capillary phenomena, where it is attracted by the sides of the vessel, its surface is then inclined so as to be perpendicular to the resultant of the forces which act upon it.

84. Level of liquids.-A liquid is said to be level when all the points of its surface are in the same horizontal plane. This, however, only applies to surfaces of small extent. For as the direction of the vertical constantly changes from one place to another on the surface of the globe, the direction of the horizontal surfaces changes too; that is to say, that a plane which is horizontal at one part of

the earth's surface, is not parallel to a horizontal plane at a small distance; they form an angle with each other. Hence a liquid surface of some extent in a state of equilibrium, being necessarily horizontal in each of its parts, does not form one single perfectly plane surface, but a series of plane surfaces inclined to each other; which of course produces a curved surface. This curvature cannot, however, be perceived on surfaces of small extent, as in water contained in a vessel; for the surface of such a liquid is so perfectly levelled, that it reflects the rays of light like the most per

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True and Apparent Level.

75

fectly polished plane mirror. The curvature is, however, easily observed on large surfaces like those of the sea. For if this surface were perfectly level, a ship in sailing away from the shore would only cease to be visible in consequence of increasing distance, and the less apparent parts, the masts and the cordage, would disappear first. This, however, is not the case; the hull first sinks below the horizon, then the lower part of the masts, and ultimately the top, as seen in fig. 66, thus proving the curvature of the surface of the sea. 85. True and apparent level. When we consider a great surface of water-the Mediterranean sea, for instance-its surface is said to be level when all points of the surface are equidistant from the centre of the earth. This is the true level; while that level which is defined as having all the points of its surface in the same horizontal plane, is the apparent level, the level for the eye. The true only coincides with the apparent level when the liquid surfaces are very small. If the earth did not rotate about its own axis, the surface of all seas would form a true level; but owing to the centrifugal force which results from its diurnal motion, the surface is heaped up at the equator, and the level is higher than at the poles. 86. Equilibrium of the same liquid in several communicating vessels.-Not merely do liquids tend to become level

when they are placed in the same vessel, but also when they are placed in vessels which communicate with each other. Whatever

the shape and the dimensions of these vessels, equilibrium will exist, when the surfaces of the liquids in all the vessels are in the same horizontal plane.

This principle may be demonstrated by means of the apparatus represented in fig. 67. It consists of a series of vessels of different shapes and capacities connected together by a common horizontal tubulure. When water or any other liquid is poured into the vessel, the level is seen to rise at the same time, and stop at exactly the same height in each. Equilibrium is then established. For as we have seen that the pressures exerted by a liquid do not depend upon its quantity but upon its height (80), when this is the same for all the vessels above the tube of communication abc, the pressure is necessarily everywhere equal, and therefore, as the liquid has no more tendency to flow from b towards a than from b to c, equilibrium continues.

87. Equilibrium of different liquids in communicating vessels. In what has been said the communicating vessels all

contained the same liquid.

Fig. 68.

It may, however, happen that the

vessels contain liquids of different densities, which do not mix.