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matter, fluidity may be caused by a certain degree of fire, which, when employed for this purpose, seldom manifests itself by any other perceptible effect: not dilating the volume, but resisting the particular attachment of the parts. Some strive to give me chanical ideas of a fluid body, by comparing it to a heap of sand: but the impossibility of giving fluidity by any kind of mechanical comminution will appear by considering two of the circumstances necessary to constitute a fluid body: 1. That the parts, notwithstanding any compression, may be moved in relation to each other, with the smallest conceivable force, or will give no sensible resistance to motion within the mass in any direction. 2. That the parts shall gravitate to each other, whereby there is a constant tendency to arrange themselves about a common centre, and form a spherical body; which, as the parts do not resist motion, is easily executed in small bodies. Hence the appearance of drops always takes place when a fluid is in proper circumstances. It is obvious that a body of sand can by no means conform to these circumstances.
Different fluids have different degrees of fluidity, according to the facility with which the particles may be moved amongst each other. Water and mercury are classed among the most perfect fluids. Many fluids have a very sensible degree of tenacity, and are therefore called viscous or imperfect fluids.
DEF. Fluids may be divided into compres sible and incompressible, or elastic and nonelastic fluids. A compressible or elastic fluid is one whose apparent magnitude is diminished as the pressure upon it is increased, and increased by a diminution of pressure. Such is air, and the different vapours. An incompressible or non-elastic fluid is one whose dimensions are not, at least as to sense, affected by any augmentation of pressure. Water, mercury, wine, &c. are generally ranged under this class. By many modern writers the term fluid is confined to those which are compressible, and liquid to such as are incompressible,
Although the use of that well-known instrument the thermometer is founded upon the circumstance of different degrees of heat and cold causing a corresponding dilatation or condensation in spirits of wine, mercury, and some other fluids; a fact which it might be supposed would have led to the opinion that such fluids were compressible by other means; yet has it been universally believed and asserted till within the last half century, that after the fluid was freed from all air, no art or violence could press it into less space. This opinion has been grounded chiefly, if not altogether, on a gross and inadequate experiment made by the Academi del Cimento, at Florence; in which water when violently squeezed made its way through the fine pores of a globe of gold, rather than yield to the compression. Even so lately as VOL. VI.
1790, so skilful a mathematician and philosopher as M. Prony speaks of the incompressibility of water with an obvious allusion to the Florentine experiment, as though he was not at all conscious of its insufficiency, and seeming quite ignorant of any contrary experiments. For, says he, "Si une quantité d'eau est renfermée dans un vase de capacité et de forme quelconque, et qu'on l'y comprime avec toute la force qu'on voudra, jamais on ne pourra la reduire à occuper un espace moindre que celui qu'elle occupoit d'abord. Tout le monde connoit les experiences qu'on a faites pour constater cette propriété; on sait que l'eau etant renfermée dans des globes de métal, quelque percussion ou quelque pression qu'on emploie pour le faire diminuer de volume, on n'y parvient jamais, et que lorsque la résistance qu'elle oppose à de pareils efforts ne lui fait pas briser son enveloppe, elle se fait jour à travers les pores du métal, d'où elle sort en forme de rosée."
But our ingenious countryman, Mr. Canton, attentively considering this experiment, found that it was not sufficiently accurate to justify the conclusion which had always been drawn from it; since the Florentine philosophers had no method of determining that the alteration of figure in their globe of gold occasioned such a diminution of its internal capacity as was exactly equal to the quantity of water forced into its pores. To bring this matter therefore to a more accurate and decisive trial, he procured a small glass tube of about two feet long, with a ball at one end, of an inch and a quarter in diameter. Having filled the ball and part of the tube with mercury, and brought it exactly to the heat of 50° of Fahrenheit's thermometer, he marked the place where the mercury stood in the tube, which was about six inches and a half above the ball; he then raised the mercury by heat to the top of the tube, and there sealed the tube hermetically; then upon reducing the mercury to the same de gree of heat as before, it stood in the tube
of an inch higher than the mark. The same experiment was repeated with water exhausted of air instead of mercury, and the water stood in the tube of an inch above the mark. Since the weight of the atmosphere on the outside of the ball, without any counterbalance from within, will compress the ball, and equally raise both the mercury and water, it appears that the water expands of an inch more than the mercury by removing the weight of the atmosphere. Having thus determined that water is really compressible, he proceeded to esti mate the degree of compression corresponding to any given weight. For this purpose he prepared another ball, with a tube joined to it; and finding that the mercury in an inch of the tube was the hundred thousandth part of that contained in the ball, he divided the tube accordingly. He then filled the ball, and part of the tube with water ex
hausted of air; and leaving the tube open, placed this apparatus under the receiver of an air-pump, and observed the degree of expansion of the water answering to any degree of rarefaction of the air and again by put ting it into the glass receiver of a condensing engine, he noted the degree of compression of the water corresponding to any degree of condensation of the air. He thus found, by repeated trials, that, in a temperature of 50°, and when the mercury has been at its mean height in the barometer, the water expands one part in 21740; and is as much compressed by the weight of an additional atmosphere; or the compression of water by twice the weight of the atmosphere, is one part in 10870 of its whole bulk. Should it be objected that the compressibility of the water was owing to any air which it might be supposed to contain, he answers, that more air would make it more compressible; he therefore let into the ball a bubble of air, and found that the water was not more compressed by the same weight than before.
In some further experiments of the same kind, Mr. Canton found that water is more compressible in winter than in summer; but he observed the contrary in spirit of wine,
See PHIL. TRANSAC. for 1762 and 1764. Indeed it seems reasonable to conclude, independent of all experiments, that no fluids are absolutely incompressible: for all bodies being porous, their parts may be brought nearer to each other; and a liquid being an assemblage of solid bodies, should, therefore, be compressible. Hence, then, the usual distinction of fluids into compressible and incompressible is, strictly speaking, inaccurate. Nevertheless, as the compression of the liquids in the preceding table is very small compared with their mass, it may safely be neglected in most practical cases, so that the fluids usually considered as incompressible may still be reckoned so in the investigations we are about to enter upon; and the consideration of air, and other easily compressible and elastic fluids, may be properly referred to the separate head of Aereostatics or Pneumatics.
We know so little of the essential nature and constitution of fluids, that it would be by no means advisable to apply to them the principles of equilibrium and of motion, as they have been stated in the articles DyNa MICS, &c., without first inquiring whether there is not some other general law which appertains to fluids only, and from which, in conjunction with the principles just ad
verted to, the doctrines of hydrostatics may readily be deduced. For the action of fluids upon each other, differs so essentially in some particulars from the mutual actions of solid bodies, that some distinct principle must be sought, to account for such varying effects. The parts of a solid are so connected together as to form but one and the same whole; their effort is, according to its nature, concentrated into one point (as the centre of gra vity, centre of gyration, &c.); which is by no means the case with fluids, their particles being extremely moveable, and entirely independent of each other. Again: no statical equilibrium can take place between two bodies of different weights, unless the lighter body acts at some mechanical advantage; whereas a very small weight of fluid may, without acting in so advantageous a posi tion, be made to balance any weight however large. Solid bodies, again, when left to themselves, press only in the direction of gravity; while fluids press equally in all di rections. This property indeed is one of the most extraordinary which we meet with in fluids, and from it most of the other proper ties may be readily inferred; on which account the continental philosophers assume it as a kind of definition. The Newtonian definition is more simple, and naturally leads to this property, which can only be conceived to arise from the extreme freedom with which the particles move amongst each other. But the most satisfactory proof results from experiment, to which it is proper to have recourse in the establishment of the first principles of hydrostatics, and which will at once furnish the general law necessary to be combined with the received principles of proper mechanics.
DEF. The specific gravity of any solid or fluid body is the absolute weight of a known volume of that substance, namely, of that which we take for unity in measuring the capacities of bodies.
density, it will appear that the two terms Comparing this definition with that of density and specific gravity express the same thing under different aspects; the former being more accurately restrained greater or less vicinity of particles, the latter to a greater or less weight in a given volume; hence as weight depends upon the closeness of particles, the density varies as the specific gravity, and the terms may in most cases be indiscriminately used. The specific gravi ties of fluids are usually considered without any regard to the empty spaces between the particles; though, if the particles of fluids are spherical, the vacuities make at least 4 of the whole bulk. But it is sufficient that we know precisely in what sense the specific gravity of fluids is understood. See GRAVITY, Specific.
On the Pressure of non-elastic Fluids. Prop. The upper surface of a homogene ous heavy fluid in any vesel, or any system of communicating vessels, is horizontal."
This is a matter of universal experience; and, as it is easily observed, may be taken for the distinguishing property of fluids. Thus, if ABCDEF (fig. 9. pl. 87.) be a vessel in which the branches CDH, EFG, have a free communication with the part AB; then, if water, or mercury, or wine, or any other fluid commonly reckoned non-elastic, be poured in, either at A, C, or E, and when the whole is at rest, the surface of the fluid stands at IK in the larger trunk; if the line LIKM be drawn parallel to the horizon, the surface of the fluid will stand at L in the branch EF, and at M in the branch CD; and this whatever are the inclinations of those branches, or the angles at F and D, G and H.
For, if the pressure which acts upon the surface were not exerted perpendicularly, it is easy to see that it could not be entirely annihilated by the reaction of that surface; the surplus of force would, therefore, occasion fresh action upon the particles of the fluid, which must of consequence be transmitted in all directions, and thus necessarily occasion a motion in the fluid: that is, the fluid could not be at rest in the vessel, which is contrary to experience.
Cor. 2. Hence, also, if the parts of a fluid contained in any vessel ABCD (fig. 8. pl. 87.) open towards the part AB, are solicited by any forces whatever, and remain notwithstanding in equilibrio, these forces must be perpendicular to the surface AB. For the Remark. This is usually explained by equilibrium would obtain in like manner if saying, that, since the parts of a fluid area cover or a piston of the same figure as the easily moveable in any direction, the higher surface AB were applied to it; and it is maparticles will descend by reason of their su- nifest that, in this latter case, the forces which perior gravity, and raise the lower parts till act at the surface, or their resultant, must be the whole comes to rest in a horizontal plane. perpendicular to that surface. Now what is called the horizontal plane is, in fact, a portion of a spherical surface, whose centre is the centre of the earth: hence it will follow, that if a fluid gravitate towards any centre, it will dispose itself into a spherical figure, the centre of which is the centre of force.
Prop. If a fluid, considered without weight, is contained in any vessel whatever, and an orifice being made in the vessel, any pressure whatever be applied thereto, that pressure will be distributed equally in all directions.
Through any point N (fig. 9.) taken at pleasure below the surface of the fluid LIKM, imagine the horizontal plane PNOQ to pass. It is obvious the weight of the fluid contained in the vessel below PNOQ contributes nothing to the support of the columus LP, 10, MQ; so that the equilibrium would obtain in like manner if the fluid contained in that part of the vessel below PNOQ had lost its weight entirely. We may, therefore, regard this fluid as being solely a mean of communication between the columns LP, IO, and MQ; in such manner that it will transmit the pressure resulting from the columns LP, MQ, to the column IO, and reciprocally. If now, instead of the column LP, IO, MQ, of the finid, pistons were applied to the surfaces, P, NO, and Q, and were separately urged by pressures respectively equal to the pressures of the columns LP, IO, MQ, the equilibrium would manifestly obtain in like manner. Or, if a pressure equal to that of the column MQ be applied at Q, while the columns LP, 10, remain, the equilibrium will still obtain; and this whatever are the directions of the several branches, and their sinuosities at D, F, &c. whence the proposition is evident.
Cor. 1. Not only is the pressure transmitted equally in all directions, but it acts perpendicularly upon every point of the surface of the vessel which contains the fluid.
Cor. 3. If, therefore, the forces which act upon the particles of the fluid are those of gravity, we shall see that the direction of gravity is necessarily perpendicular to the surface of a tranquil fluid: consequently, the surface of a heavy fluid must be horizontal to be in equilibrio, whatever may be the figure of the vessel in which it is contained.
Cor. 3. If a vessel, as ABCD (fig. 8.) closed throughout, except at a small orifice O, is full of a fluid without weight; then if any pressure be applied at O, the resulting pressure on the plane surface or bottom CD, will neither depend upon the quantity of fluid in the vessel nor on its shape; but, since the pressure applied at O is transmitted equally in all directions, the actual pressure upon CD will be to the pressure at O as the area of CD is to that of the orifice.
Cor. 4. In the same manner will the pressure applied at O be exerted in raising the top AB of the vessel; so that if the top be a plane, of which O forms a part, the vertical pressure tending to force AB upwards will be to the force applied at O as the surface AB to the area O.
Prop. The pressure of a fluid on the horizontal base of a vessel in which it is contained is as the base and perpendicular altitude, whatever be the figure of the vessel that contains it: the upper surface of the fluid being supposed horizontal.
Let any horizontal plane GH (fig. 12, 13, pl. 87.) be supposed drawn, and conceive the fluid contained in the part GCDH of the vessel to be void of weight; then is it evident from cor. 3. of the foregoing proposition, that any vertical filament whatever, El of the heavy fluid ABHG, exerts at the point I a pressure which is distributed equally through the fluid GCDH; and that this pressure acts equally upwards, to op pose the action of each of the other filaments which stand vertically above GH;