HYDROSTATICS. 



become changed into a solid, which, though to dittiuguivh it, wo 



not a now substance, but merely the water in a 



.iiil'.-ivnt state. So also an increase of heat will change the 



into mi invisible gas or vapour which wo call steam. In 



tho agent which (mxlm-cx these changes of 



.ml it does so by driving tho ultimate particles of the 



DM fiirth< r upurt from each other. Many of the metals, 



as is well known, assume tho liquid state under tho influence of 



heat, and hence can be molted and cast into moulds of any 



1 Hlmpe. If they be exposed to a much higher degree of 



. be done in the electric lamp, they, too, will become 



: t . (! into vapour. 



'I'll" 'iitr.-runoo between these states depends upon the rela- 

 tions existing between tho ultimate particles of which tho 

 masses are composed. In a solid these particles have a strong 

 attraction for each other, that is, cling closely together, and 

 resist any effort to separate them. Many of the metals can bo 

 drawn out into fine wires, and yet will sustain considerable 

 weight before tho attraction or cohesion, as it is termed, is 

 overcome. If we take two lead bullet*, and scrape a por- 

 tion of tho surface of each so as to rendor them even, and 

 then, by pressing them firmly together, drive out the air, this 

 cohesion will cause them to cling 1 to each other so tightly as 

 to require a considerable degree of force to separate them. 

 Another property of solids which results greatly from this, 

 is the amount of friction with which their ultimate particles 

 move* over one another. In some solids this is so great that 

 no moderate degree of force will suffice to move them or to 

 niter the form of the mass. In this respect there is, however, 

 a great difference between solids, for they merge so gradually 

 into liquids that it is difficult to draw a well-defined line 

 separating them. 



In liquids both these properties are present in a much smaller 

 degree. The cohesion of the particles is so much less that 

 scarcely any force is required to separate a mass of liquid into 

 portions ; in fact, it falls apart from its own weight, unless it 

 be put into some vessel capable of containing it, and it imme- 

 diately assumes the shape of such vessel. The same, however, 

 might bo said of a heap of fine powder : how then does this 

 differ from a liquid ? The difference consists, first, in the fact 

 that there is a large amount of friction between the atoms of 

 powder, so that if placed in a heap they do not spread them- 

 selves out as particles of liquid would ; and next, in tho 

 ultimate atoms of the liquid being so minute as even under tho 

 most powerful microscope to bo invisible, while those of the 

 powder have a definite size. Tho property the particles have 

 of moving over one another with scarcely any friction is one of 

 very great importance, and accounts for several of the pheno- 

 mena wo shall meet with. 



If we now look at the case of a gas, we shall find that not 

 only is there no cohesion between the particles, but they 

 repel one another, and, unless confined, will fly apart as far 

 as possible. If a cubic inch of any gas be placed in a largo 

 box, it will immediately fill it and become equally distri- 

 buted in every part. There is also this further difference 

 between liquids and gases, that whereas a gas may be com- 

 pressed almost indefinitely, regaining its former bulk on the* 

 pressure being removed, a liquid is for all practical purposes 

 incompressible. 



It was for a long time believed to be absolutely so, but it 

 has since been found that a pressure equal to that of the 

 atmosphere, or 15 pounds per square inch, will cause a com- 

 pression in water to the extent of 40 or 50 millionth* of its 

 bulk. The simplest way of ascertaining this is to procure a 

 cylinder closed at one end, and having a piston fitting very 

 tightly into it. This is filled with water, and a spring ring 

 placed just under the piston, so that if it be driven in at 

 all, the ring will remain at the part of the cylinder which it 

 reached, and thus show the extent of the compression. The 

 apparatus thus arranged is fixed to a heavy weight, and by 

 means of a chord lowered to a known depth in the sea. Tho 

 pressure, as will be seen, increases with the depth, and the 

 position of the ring will indicate the extent of the compres- 

 sion. 



Having thus cleared our way, we can enter more directly on 

 the science itself. It is usually divided into two branches 

 Hydrostatics proper and Hydrodynamics ; the former treating 

 of the equilibrium of liquids and the pressures they produce, 



\vhilo tho latter ha* to do with their motions. The term 

 hydraulics, derived from two Greek word* meaning "water" 

 and "a pipe," in sometimes tued instead of hydrodynamics, 

 but it i more ttrictly applied to the raiding of water by 

 means of pipes ; wo shall, however, use it in iU more extended 

 meaning. 



Water is by far the most common of all liquids, and hence 

 will bo taken as a type. In its physical properties, however, 

 it differs little from other liquids, and what is said of it 

 may, with the necessary modifications, be applied to liquids 

 generally. 



We found in Mechanics that though the lever and other 

 mechanical powers possessed weight, we could understand their 

 principles better by neglecting it at first ; just so here it is easier 

 to omit at first all notice of the weight of the liquid. 



The fundamental principle of hydrostatics is that of the 

 quality of pressure, or, as it is sometimes called, after 

 the philosopher who first stated it, Pascal's law. It is a* 

 follows : 



It any pressure be exerted on any part of a liquid, that pres- 

 sure in transmitted equally and with equal force in all directions. 

 A little explanation will make this clear. If we have a solid 

 cylinder made to fit exactly and move without friction in a tube, 

 and we press with any force against one end of it in a direction 

 parallel to its length, the pressure will be transmitted un- 

 diminished to tho other end, and will there act against any 

 obstacle just as if the cylinder were not interposed ; no pres- 

 sure will, however, be exerted against the side of the tube. If 

 now the cylinder be removed and the tube filled with water, 

 a piston being made to fit each end of it, any pressure exerted 

 on one end will, as before, be transmitted to tho other, but a 

 similar pressure will also be exerted against every part of the 

 inner surface of the tube. If the surface of the piston have an 

 area of one square inch, and a pressure of 10 pounds be exerted 

 on it, every square inch of surface in the cylinder will sustain a 

 similar pressure ; and if we insert into any part of it a tube 

 with a piston one square inch in area, this piston will be forced 

 out with a pressure of 10 pounds. If tho tube be bent or twisted 

 in any direction, the pressure is still transmitted exactly as if it 

 were perfectly straight. This property of liquids follows from 

 the fact of their particles moving without friction, and is of 

 great practical importance. In Mechanics, even with the best 

 and more flexible ropes and chains, there is always a great 

 loss from friction and rigidity, but by means of a liquid a 

 pressure can be transmitted in any required direction without 

 sensible loss. 



Similarly, if wo have a closed vessel with several equal open- 

 ings in it, in each of which a piston of one inch diameter works, a 

 pressure of 10 pounds on one will cause a similar pressure on each 

 of the others. If now another piston be fitted to the vessel, 

 10 inches in diameter, a pressure of 10 pounds will be exerted on 

 every portion of its surface equal in area to the smaller piston. 

 Now the areas of circles are proportional to the squares of their 

 diameters ; the area of the larger piston is therefore 100 times 

 that of tho small one, and the total pressure on it is therefore 

 100 x 10, or 1,000 pounds. We have thus what we may consider 

 as another mechanical power, a gain being effected by the use 

 of it as there was by the lever. The principle of virtual velo- 

 cities holds good here as well as in the powers we previously 

 considered ; for if tho small piston be forced in 1 inch, it is clear 

 that the other will only be moved to the extent of i loth of an 

 inch, and thus, though 100 times the pressure is exerted, it is 

 only through T J B th part of the space. A simple experiment can 

 easily be tried to show that this pressure is transmitted upwards 

 as well as in other directions. Procure a tube of large diameter, 

 and grind one end of it flat, so that it can be closed by a disc of 

 glass fitting closely against it. Fasten a piece of string to the 

 middle of this disc, and pass the end up through the tube, so 

 that by holding the string it may be kept in its place. If the 

 whole be now lowered into a vessel of water, the upward pres- 

 sure will keep the disc in its place without the string being 

 held ; but on the tube being gradually raised till the end comes 

 nearly to the surface, the pressure will diminish until it will 

 be unable any longer to sustain tho disc, which will then fall to 

 the bottom. 



This principle of equality of pressure leads to many strange 

 and important results, which we will consider fully in our next 

 lesson. 



