A fluid is usually defined to be : "A bodj whose particles move easily among themselves and to yield the least force impressed.' —(Webster ; but from the true nature of i definition, which should include the sense o: the thing defined and exclude everything else the above does not, strictly speaking, define i fluid. The "particles" of fine sand, superfine flour or of any body in a finely pulverized condi tion, "move easily among themselves and yielc to the least force impressed" upon them and t( some extent, "when that force is remored, recover the previous condition;" but the substances mentioned are not fluids, and we musi look a little deeper into the constitution o fluids, and from an understanding of them thus obtained, frame their definition. Without regard to the constituents of th atoms or particles of which a fluid is com- posed when viewed chemically, it is sufficient here to consider each and every one of itself incompressible and surrounded by an atmosphere, so to speak, of heat—that each particle attracts every other, and is itself attracted by a force which we call cohesion, and that the atmospheres of heat strive continually to separate the particles from one another. The modified action of these forces—the attraction of cohesion and the repulsion o heat— determine the three forms in which all matter is known to exist—solid, fluid and gaseous. When a certain portion of heat is driven from a mass of matter, cohesion draws the particles together, and a solid body is formed ; on the other hand, when we add heat to a solid body, it becomes fluid, and a further addition of heat expands it into the gaseous form. It will appear that the less heat a body contains the more permanent is its character. Solid bodies retain their form for years; fluids, though easily placed in vessels, readily evaporate ; gaseous are difficult to retain—very evanescent, and when not closely confined, almost immediately expand into space. But regarding fluids, of which water may be called the type, they may be said to be bodies in which the attractive force of cohesion exactly balances the repulsive force of heat, and thus the particles of which they are composed, still retaining their atmospheres of heat, (all bodies having some heat, and it can never all be expelled,) move among each other, and are separated and brought together with the greatest facility. Here, then, is the definition of a fluid :—A body in which the force that would draw its particles together exactly balances the opposing force that would drive them asunder. It is plain that in solid bodies cohesion preponderates over the repulsive force of heat, as in gaseous bodies the atoms are entirely beyond the sphere of its influence. When investigating the mechanics of a fluid, it is as necessary to omit certain considerations which would be likely to complicate and confuse the process; as when we study the properties of a lever, we pay no attention to the weight of the same, nor of the material of which it may be made. It is true that fluids are affected by gravitation, and have weight in common with matter of all kinds; but we can imagine a fluid— water for instance—ceasing to possess weight without ceasing to lose its peculiar properties as a fluid. Such a body would act very strangely—it would neither fall nor flow from a vessel; being perfectly passive in its nature, it could be moulded into any form, separated into parts and put together again ; but the most remarkable property it would display next to its incompressibility, would be that of equally transmittingpressure in all directions. Suppose it was contained in a vertical cylinder of say one hundred inches area, and on it was resting a closely fitting piston. If the piston have no weigbt, it is clear the fluid experiences no pressure, and if the bottom or the sides of the cylinder or if the piston were pierced with an orifice, no portion of the fluid would escape ; but, if we load the piston with say 100 pounds, it will tend towards the bottom of the cylinder, and, of course, will press upon the fluid, the particles of which having perfect mobility, the mass would at once conform itself to the shape and size of the cylinder, and would sustain the piston ; not, however, unless it, in turn, is snstained by the bottom of the cylinder. Being incompressible it may be regarded as a solid body, and then the transmission of the 100 pounds to the bottom of the cylinder is easily understood. Now, as the whole pressure of the piston is borne by the whole area of the cylinder's base, it is evident that one-half of the base sustains fifty pounds, and that any square inch of surface on the base sustains one pound. So far, this imaginary fluid does not differ from a solid in the transmission of pressure, but the peculiar characteristic of a fluid is that the same effects are produced upon the sides of the cylinder, and against the under side of the piston. The fluid being under pressure as before, and its particles free to move in any direction which is consistent with the nature of all fluids, if an opening be made in the side of the cylinder, it will spout out, and if the piston be perforated, the fluid will spout upwards. If these openings are one inch square each, it will require one pound pressure to prevent the fluid from escaping; if fifty inches, fifty pounds, and so on proportionally. Admitting these facts to be true, it must be evident that fluids transmit equally and in all directions the pressures exerted upon them. Again, let us suppose we establish a direct communication at the bottom of this cylinder with a small cylinder of one inch area, also fitted with a piston, from what has been shown, it is plain the small piston must receive an outside pressure of one pound to keep it in place against the outward thrust of the fluid. If we force the small piston in its cylinder against the fluid, say a distance of one inch, the large piston must be raised, but it need not move only one hundredth part of that distance to make room for one cubic inch of fluid, because that cubic inch must spread over 100 square inches of surface ; we have really raised 100 pounds by the movement of one pound, but we have only raised it a hundredth part of the distance—what we have gained in power we have lost in distance. Thus we have a simple machine, which, like all others, depends upon the principle of virtual velocities, and is to all intents and purposes the hydrostatic press, known in mechanic arts and appliances to possess extraordinary advantages over the wedge, lever or screw, especially where immense pressures are required. If we now confer weight—the attraction of gravitation—upon the fluid in question, it must be evident that it can in no wise alter the property of equality of pressure, except so far as the additional pressure arising from the gravitating tendency of the fluid is concerned. The fluid by no means exists as such by virtue of gravitation, but is only modified in its mere mechanical performances by it, and under the influence of this force finds the lowest position possible for its parts, and seeks a level for its surface. Considerations of this character seem to clear up the apparent anomaly which is inseparable from the ordinary method of statement regarding the equality of pressure. We say the pressure is equal in every part of a vessel containing fluid, and in all directions, and every one knows that in a vessel containing water, the heaviest pressure is on the bottom ; that the pressure on the sides is greatest at the bottom, and least at the top, and if the vessel be full and have a lid, the lid would experience no pressure at all. We must understand that equality of pressure is due to fluidity only, and that the inequality of pressure which every vessel containing fluid experiences is due to gravity ; the one is determined by estimating density and altitude, the other is the active principle of fluidity.
This article was originally published with the title "Fluid Pressure" in Scientific American 13, 14, 110 (December 1857)