ning and moving on the ground. There are various forces acting, the weight of the top, the resistance and the friction from the ground, and the resistance of the air. Suppose all these forces moved up to the centre of gravity of the body, each force remaining parallel to its original direction, and let their resultant be found; then if this resultant act on a particle of the same mass as the whole top the motion will be the same as the actual motion of the centre of gravity of the top.

345. Another result of the same kind is the following. The motion of a body round its centre of gravity is the same as the body would take if its centre of gravity were fixed and the body were left to turn round under the influence of the forces really acting. But this, like the former proposition, is beyond the range of an elementary work.

XXV. FLUIDS.

346. Two opposing principles are found to operate extensively throughout the material world; one is the principle of cohesion which tends to bind the component particles of bodies together, and the other is the principle of repulsion which tends to separate the particles. The principle of cohesion is perhaps connected with that of attraction between bodies at a distance; the principle of repulsion is perhaps identical with heat, or at least intimately connected with it. Now the three forms under which matter presents itself depend upon the relative influence of these two principles. In solid bodies cohesion prevails over repulsion, so that the particles form one connected mass, not to be separated without the application of force. In air and gases the principle of repulsion predominates, and the particles require the application of force in order to keep them in contact or near each other. The third form of matter, namely that of water and other liquids, is one in which neither of the two principles is predominant; the particles can be separated by the application of forces so slight as to be practically insensible, but they do not require to be confined in every direction, like those of air and gases to prevent them from escaping.

347. The term fluid includes two classes of objects, namely liquids like water, and gaseous bodies like air; the two classes have some properties in common, and each class has also some of a special kind. We shall treat first of liquids and then of gases. The most common liquid is water, and this may be taken as the type of all. Hence the science which we are about to consider has received names derived from the Greek word for water. The term Hydrostatics has been applied to all that concerns the mechanical properties of liquids in equilibrium, and Hydrodynamics to the subject of liquids in motion: the term Hydraulics is sometimes applied to the theory of machines which depend on the action of liquids.

348. The general properties which we are about to consider are those which belong to what are called perfect liquids. By perfect liquids we mean such as offer no resistance whatever to the separation of their parts, and on this account adapt themselves to the shape of the vessels containing them. Strictly speaking no liquids are perfect; but still for water and other liquids there will be no error of practical importance introduced in the statements we shall make. There are however substances which though liquids are far from being perfect in the sense we have explained, and to which therefore our subsequent statements will not apply; for instance tar or melted glue. Water approaches more nearly than oil to the idea of a perfect liquid, and alcohol more nearly than water.

349. It was formerly supposed that liquids were incompressible; that is to say it was held that a liquid could not have its bulk diminished by any pressure however great. An experiment was made at Florence, and thence known as the Florentine experiment, which seemed to confirm this notion. Water was enclosed in a hollow globe of gold; the globe was squeezed in such a manner as to alter its form, and therefore by the conclusions of Geometry to diminish its size, and it was found that the water was forced through the pores of the gold. But it is now well ascertained that water is compressible, though the compressing force must be very great in order to produce a sensible effect. The standard fact may be put in the following form, which will be fully comprehended as the reader proceeds with the subject: water when pressed by a column of water 33 feet high has its density increased by 000046 of its original density. Also the increase of density will be in proportion to the pressure; so that under the pressure of a column of water 3300 feet high the density would be increased by 0046 of the original density, and under the pressure of a column of water 7000 feet the density would be increased by about 01 of the original density. Or we may put the last fact in this form at the depth of 7000 feet in the sea a mass of water will lose of the bulk it would have at the

1

100

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