surface of the sea. When the force which compresses a liquid is removed the liquid regains its original bulk and density.

350. We may if we please imagine that a liquid is composed of very small smooth spherical particles, and thus connect the properties of a liquid with those of an assemblage of particles; but such a supposition is not necessary for our purpose.

XXVI. PRESSURE TRANSMITTED IN ALL

DIRECTIONS.

351. THE foundation of all we have to teach about liquids is a principle which seems to have been first enunciated by Pascal; it is called the transmissibility of pressure in every direction.

Let ABCD be a vertical section of a closed vessel full

of liquid. At two places in the upper surface, E and F, let there be equal holes in which are placed tubes of equal bore; the holes and the tubes may for simplicity be supposed circular. In these tubes let there be pistons which can work easily up and down, remaining water tight, like the moveable part of a boy's squirt. Push one of these pistons down with a certain force; say that the piston at E is pushed down with a force of one pound. Then it will be found on trial that the piston at F is thrust up, and if we wish it to stop in its place we must push it down also with a force of one pound. In other words, if we apply any force on a part of the upper surface of the liquid in the closed vessel, that force is as it were transmitted in equal amount to any other equal part of the same upper surface.

352. Next let the tubes at E and F be of unequal bore; suppose the area of F to be double the area of E. Then it will be found on trial that if the piston at E is pushed down with a force of one pound, and we wish to keep the piston at F in its place, we must push it down with a force of two pounds. This is an immediate result from the principle of Art. 351; for according to the principle a pressure equal to that exerted on the piston at E is transmitted to each of the portions of the same area of the piston at F. In like manner if the area of

the tube at F is ten times the area of the tube at E, then when the piston at E is pushed down with a force of one pound the piston at F must be pushed down with a force of ten pounds if we wish to keep it in its place.

353. The preceding two Articles supply rather an illustration of the meaning of the principle of the transmissibility of pressure than a mode of establishing it very strictly. For in practice there would be friction which would impede the motion of the pistons, and prevent the accurate accordance of the facts with the theory. But the truth of the principle may be readily admitted, as it will be confirmed by numerous results which can be deduced from it and verified by trial.

354. We have hitherto supposed the two pistons to be placed in the upper surface of the vessel. But suppose we have a piston at G, a place in the side of the vessel; let this be of equal area with the pistons at E and F. It will

be found on trial that even if we exert no force at E and F the piston at G will be thrust out; this arises from the weight of the liquid, as we shall see in the next Chapter.

T. P.

10

Suppose that a force is applied to the piston at G, just sufficient to keep it in its place, so that the liquid remains in equilibrium. Let now the piston at E be pushed down with any force, say a force of one pound; it will be found, as we said before, that to preserve equilibrium the piston at Fmust be pushed down with a force of one pound: and moreover we must push in the piston at G with a force of one pound in addition to the force already exerted on it. Thus the force applied at E is transmitted to the equal area at G. Also if the area of the piston at G is ten times the area of the piston at E, then when a force of one pound is applied to the piston at E we must in order to preserve equilibrium apply a force of ten pounds to the piston at G, in addition to the force which it was necessary to exert to keep this piston from being thrust out before any force was applied to the piston at E.

355. In our illustration we have supposed the tubes at E and F to be vertical, and that at G to be horizontal; but the principle is not to be restricted to these cases. The side of the vessel in which the tube is supposed to be inserted need not be necessarily either horizontal or vertical, but may be inclined at any angle to the horizon. Still the result will hold, namely, that when equilibrium has been obtained by applying proper forces to the pistons, then if any additional force be applied to one piston we must apply an equal additional force to every portion of the same area in all the other pistons, in order to maintain equilibrium.

356. The principle of the transmissibility of pressure through a fluid explains the action of a little contrivance which is called the hydrostatic paradox; the name is given because at first sight the effects seem out of proportion to the causes in action.

CD and EF are flat boards, which are connected by flexible leather, or cloth, so as to form a water-tight vessel. AB is a vertical tube which communicates with the vessel. Let the vessel and a part of the tube be filled with water, and suppose a piston to work in the tube and to be retained in its place by a suitable force. Suppose, for an example, that the area of the bore of the tube is one square inch, and that the area of the upper board of EF is

a thousand square inches. Then if the piston is pushed down with an additional force of one pound the board EF

will be thrust upwards with a force of a thousand pounds; so that in fact the board would support the weight of a thousand pounds placed on it without sinking down. It will be seen after reading the next Chapter that instead of using a piston in the tube AB the required force may be obtained by making the column of water in the tube of sufficient height. We shall see hereafter that the principle of the hydrostatic paradox is the essential part of a valuable machine called Bramah's Press.

The important principle of Art. 208 applies here, namely that what is gained in power is lost in speed: for if we were to force the piston in the tube down through one inch the board EF would ascend through only one thousandth of an inch.

XXVII. PRESSURE FROM THE WEIGHT OF LIQUIDS.

357. We have hitherto considered liquids as contained in closed vessels and transmitting to all points any pressure which may be applied at their surfaces; but we have now to treat of the pressure produced by the weight of liquids.

358. Suppose liquid put into a vessel open at the top; then the upper surface will be a horizontal plane. That it is a plane surface is obvious from common observation. To

say that it is a horizontal plane means that it is at right angles to the direction of gravity, and this may be established by an easy experiment. If a plumb line be hung over the surface of a liquid at rest the eye can discern that the direction of the plumb-line and the direction of its image reflected in the liquid seem to fall in the same straight line; and when the student is acquainted with the elements of Optics he will know that this shews the surface of the liquid to be at right angles to the direction of the plumb line. The result may also be established by reasoning. Suppose the surface of a liquid to be curved, as denoted by ABCDE. Consider a portion of the fluid BCD such as would be cut off by a plane BD inclined to the horizon. Then this portion would be like a body placed on a smooth Inclined Plane, acted on only by its own weight; and so it would not be in equilibrium but would run down the Plane.

B

D

359. Let there be an open vessel with vertical sides containing liquid. Consider any portion of the area of the

base, as for instance, one square inch near the point P; then the liquid itself produces on this square inch a pressure equal to the weight of a column of the liquid, of which the area of the base is one square inch, and the height is the vertical depth of P below the surface of the liquid. Thus if the depth PQ is 28 inches, and the liquid is water, the pressure on a square inch of the base at P would be