HYDROSTATICS-HYDRODYNAMICS- 

 PNEUMATICS. 



' I ^HE properties of matter treated of under 

 J. MECHANICS are such as arise chiefly from 

 the solid state of bodies. But consequences 

 scarcely less important arise from the other two 

 states in which matter presents itself from the 

 liquid condition, as in the case of water, and the 

 gaseous or aeriform condition, as in the case of 

 air ; and these form the subjects of the present 

 treatise. The nature of the difference between 

 these three states of matter is considered in the 

 number on NATURAL PHILOSOPHY. 



Liquids and gases agree in this, that their par- 

 ticles seem at liberty to glide about among one 

 another, seemingly without resistance ; they flow, 

 and hence both classes of bodies are called fluids. 

 There are very different degrees of fluidity. Some 

 fluids are thick and viscid ; such as tar, honey, 

 and some metals in a state of fusion. Viscid 

 fluids are, in general, not homogeneous ; they 

 consist of solid granules floating in a real fluid. 

 Alcohol and ether are more fluid than even water. 

 The most perfect fluidity belongs to the gases. 



But what chiefly distinguishes gases from liquids 

 is elasticity. A cubic foot of any gas may readily 

 be compressed into half a foot ; double the pres- 

 sure will reduce it to a quarter of a foot ; and 

 when the pressure is removed, the gas returns to its 

 original bulk. But no ordinary pressure produces 

 any sensible compression on water or any other 

 liquid. Hence gases have been denominated 

 elastic fluids, and liquids, non-elastic. It is on 

 account of this difference that the mechanical 

 properties of the two classes of fluids are treated 

 of apart. 



We have said that liquids cannot be sensibly 

 compressed by any ordinary force ; and this is so 

 far true, that both in the theory of hydrostatics 

 and in practice they are assumed to be perfectly 

 incompressible. But the assumption is not ab- 

 solutely correct. They are slightly compressible 

 under great pressure. By sinking a vessel in the 

 ocean to the depth of 6000 feet, where every 

 square inch supports a weight of 2648 pounds, it 

 is found that twenty cubic inches of water con- 

 tained in the vessel are reduced to nineteen cubic 

 inches, or the volume of water is diminished by 

 one-twentieth. A pressure equal to that of the 

 atmosphere, or fifteen pounds on the square inch, 

 reduces a million cubic inches of water to forty- 

 five or fifty inches less. 



The phenomena of liquids are considered under 

 two heads, according as the pressures to which 

 the liquids are subjected produce rest or motion. 

 The laws of liquids at rest or in equilibrium form 

 the subject of Hydrostatics (from two Greek words 

 signifying water and to stand} ; those of liquids 

 in motion form the subject of Hydrodynamics 

 (from the Greek words for water and power). 

 Hydraulics is sometimes used in the same sense 

 as Hydrodynamics, but has more especial refer- 

 ence to the flow of water in pipes (Gr. aulos). 

 15 



HYDROSTATICS. 



In treating of the mechanical properties of 

 liquids, water, as the most common and import- 

 ant, is taken to represent the whole class. 



It is the perfect mobility of the particles of 

 liquids that gives them the mechanical properties 

 considered in Hydrostatics. The fundamental 

 property may be thus stated : WHEN A PRESSURE 



IS EXERTED ON ANY PART OF THE SURFACE OF 

 A LIQUID, THAT PRESSURE IS TRANSMITTED 

 UNDIMINISHED TO ALL PARTS OF THE MASS, 

 AND IN ALL DIRECTIONS. Most of the Other 



propositions of Hydrostatics are only different 

 forms or direct consequences of this truth. 



The proposition may be experimentally proved 

 in a variety of ways. If, for instance, a bladder is 

 filled with water, and tied, and then pressed down 

 with one hand ; the other hand, if applied to the 

 bladder, will be pushed out with corresponding 

 force, and that whether resting on the top, the 

 sides, or under. Suppose, again, a close box, B, 

 filled with water, and having a tube, a, inserted 

 into the upper cover, of an inch in area, and 

 with a plug or piston fitting into it If the pis- 

 ton a is now pressed 

 down upon the water 

 with a force equal to a 

 poundweight, the water, 

 being unable to escape, 

 will react upon the 

 piston with the same 

 force ; but it obviously 

 will not press more 



Fig. i. 



against a than against any other part of the box, 

 therefore every square inch of the interior surface 

 of the box is pressed outward with the force of a 

 pound. If, then, there is another tube inserted in 

 any part of the box with a plug of the same area, 

 as at b, it will require a force of a pound to keep 

 this plug in its place. (We leave out of account 

 at present the pressure upon b arising from the 

 weight of the water in the box above it, and con- 

 sider only the pressure propagated by the forcing 

 down of the plug a.) However many plugs of the 

 same size there were, each would be pressed out 

 with the same force of a pound ; and if there 

 were a large plug of four times the area, as at c, it 

 would be pressed out with a force of four pounds. 

 We have only, then, to enlarge the area of the 

 piston c to obtain any multiplication of the 

 force exerted at a. If the area of c is 1000 

 inches, that of a being one inch, a pressure of 

 one pound on a becomes a pressure of 1000 

 pounds on c ; and if we make the pressure on a 

 one ton, that on c will be icoo tons. This 

 seemingly wonderful multiplication of power has 

 received the name of the hydrostatic paradox. It 

 is, however, nothing more than what takes place 

 in the lever, when one pound on the long arm is 



