CONTENTS. PRELIMINARY DEFINITIONS AND EXPLANATIONS. Definition of a fluid, 1; explanation of the term fluid pressure and the definition of its measure, 2, 3, 4; a supposed solidification of a por- tion of fluid does not affect its action upon the remainder, 5; hydrostatic action of rigid surfaces upon fluids, 6; transmission of pressure by a fluid, 7; distinction between elastic and inelastic fluids, 8; measures of mass, PAGE Definition of vertical and horizontal; pressure at a point in a heavy fluid, 13; pressure uniform in the same horizontal plane, 14; free surface horizontal, 15; common surface of two fluids which do not mix, 16; heights of the free surfaces above this, 17; total normal pressure on a surface immersed, 18; resultant of the same pressure, 19; conditions which a floating body satisfies, 20; stable, unstable and neutral equilibrium, 21; conditions of a body's sinking, rising, or remaining stationary when immersed totally in a fluid, 22, 23, 24, 25; Hydrostatic Balance, 26; methods for finding the specific gravity of a body or fluid, 27, 28, 29, 30; Common Hydrometer, 31; Nicholson's Hydrometer, 32; specific gravity Pressure in elastic fluids sometimes termed elastic force, 34; assumed to be uniform under certain conditions, 35; Barometer, 36; Boyle's Law, 37; pressure varies as the density, 38; to find k for air, 38*; law of density in the atmosphere, 39; barometer employed to measure heights, 40; Air-Pump, 41; density after the nth stroke, 42; causes limiting the exhaustion, 43; Hawksbee's air-pump, 44; Smeaton's ditto, 45; the Con- denser, 46; Common Pump, 47; tension of its piston-rod, 48; Lifting Pump, 49; Forcing Pump, 50; Bramah's Press, 51; Siphon, 52, 53; Diving-Bell, 54; Atmospheric Steam Engine, 55; Watt's improvements, SECTION IV. GENERAL PROPOSITIONS. Virtual Velocities, 58; resolved parts of normal pressures upon the PAGE 86 Examples, 104 I12 SECTION V. MIXTURE OF GASES.-VAPOUR. Boyle's law holds for a mixture of gases, 74; gas absorbed by a liquid General Examples. Answers to the Examples 113 138 151 HYDROSTATICS. SECTION I. PRELIMINARY DEFINITIONS AND EXPLANATIONS. 1. DEF. A fluid is a collection of material particles so situated in contact with each other as to form a continuous mass, and such that the application of the slightest possible force to any one of them is sufficient to displace it from its position relative to the rest. That part of Statics, where a fluid appears as the principal means of transmission of force, is termed Hydrostatics. The law of that transmission must, like the law of transmission by a rigid body, by a free rod or string, or by contact of surfaces, &c., be established by experiment. The mutual forces called into action by the contact of surfaces are in Statics called pressures: this term is used in the same sense in Hydrostatics, where it is applied to denote the forces of resistance, which adjacent particles of the fluid exert, either upon one another, or upon rigid surfaces in contact with them. The nature of the reaction between a rigid surface and a fluid in contact with it might perhaps be arrived at by the aid of analysis from the above definition. But such an investigation, even if entirely satisfactory in itself, would P. H. 1 be out of place in this treatise. It may here therefore be taken as the result of experiment that: When a fluid rests in contact with a rigid body, a mutual force of resistance is called into action at every point of the common surface of contact, the direction of which force is normal to that surface. 2. If in the side of a vessel, containing fluid upon which forces are acting, a piston be placed, the pressure exerted upon it by the fluid particles with which it is in contact, would thrust it out, unless a force sufficient to counteract this pressure were applied to the back: this counteracting force is of course exactly the measure of the pressure of the fluid upon the piston. It is not difficult to conceive that, generally, the magnitude of this pressure would be different for different positions of the piston in the sides of the vessel; inasmuch as the portions of the fluid which it would touch at those different places, would not necessarily be similarly circumstanced, and would not therefore require for the maintenance of their equilibrium that the piston should exert the same force upon them: when, however, the pressure for every such supposed position of the piston, wherever taken, is the same, the fluid is said to press uniformly; and when not so, its pressure is said to be not uniform. Again, it is clear that the pressure upon the piston in any given position must vary with the magnitude of its surface, and if this were reduced to a mathematical point the pressure upon it would be, strictly speaking, absolutely nothing, because the surface pressed is nothing; but even in this case the conception of the pressure at the point is perfectly definite; it signifies the capability or tendency which the fluid there has to press, and which, if existing over a definite area, would produce a definite pressure; and this |