HYDROSTATICS. 



poor water into B until it stand* 13J incho* above the surface of 

 the mercury, we shall find that then the level of the mercury in A 

 will be only 1 inch IM^HT than in B. The 13| inches of water are, 

 then, balanced by the 1 inch of mercury. If a layer, t o (Fig. 10), 

 of the mercury be supposed to become solid, 

 the proMuro on each tide of it must bo equal, 

 sinoo the fluid is at rest. Now the pressure 

 on the aide towards B is equal to the weight of 

 the moroury on that side, and of 13J inches of 

 water, while that on the other aide in equal 

 t<> t!i" naino amount of mercury, and a column 

 1 in.-li high in addition. 



If tho column of mercury, instead of being 

 1 inch high, wore made as long aa that of 

 the water, or 13J inches, the pressure would 

 be 13J times as great. 



We see, then, that the pressure on any 

 body immersed in mercury is 13| times as great 

 aa on tho same body immersed to tho same depth in water. 

 But tho density of mercury is 13J ; the pressure, then, varies as 

 the density. Hence, when two different liquids are placed in 

 vessels communicating with each other, the heights at which 

 they stand will be in inverse proportion to their densities. 



Wo have now seen tho most important facts concerning the 

 pressure of liquids ; but before passing on, wo may just notice the 

 construction of the safety-valve, which involves some of these 

 principles. In an hydraulic press, tho boiler of an engine, and 

 other similar machines, there is a danger of tho pressure be- 

 coming greater than tho strength of tho materials can over- 

 come, in which case tho cylinder will burst. To guard as much 

 as possible against this, a safety-valve is introduced, tho object 

 of which is to relieve or remove tho pressure when it is becoming 

 dangerous. 



In a convenient part of tho surface which is exposed to the 

 pressure, a conical hole (A, Fig. 11) is drilled, and a valve or 

 plug is made to fit accurately into it. This plug is fixed to a 

 lever, c D, which turns on a hinge at c, and at the other extre- 

 mity carries a weight, w. This weight can be fixed at any part 

 of the lover, and thus tho pressure exerted by it can be altered; 

 it is usually so adjusted that, before tho pressure inside tho 

 boiler begins to bo dangerous, it overcomes the weight, and, 

 opening the valve, relieves tho pressure by allowing the steam 

 to escape. Suppose, for instance, that a safety-valve has to bo 

 fitted to a boiler so as to limit the pressure to 40 Ib. per 

 square inch. Let the plug, A, have an area of half a square 

 inch, and be attached to the lever at a distance of 2 inches 

 from the fulcrum, also let the weight 

 be 2J Ib. Since the plug has an 

 area of half a square inch, it must 

 yield when a force of 20 Ib. is ap- 

 plied to it, and must therefore be 

 Fig. 11. pressed down with this force. The 



weight is one-eighth of this, and hence 



it must act at a leverage 8 times as great that is, it must be 

 fixed 16 inches from c. If, then, the weight be adjusted thus, 

 the boiler is perfectly safe, for when the pressure exceeds 

 40 Ib. to the inch, the valve will open and allow some of tho 

 steam to escape. These valves are sometimes made with a 

 spiral spring instead of a lever, but they act in the same way. 

 In practice it is common to have two ; one is so placed that it 

 cannot be touched or altered, and this is adjusted to the greatest 

 pressure that can with safety be applied ; the other is under the 

 control of the engineer, who adjusts it according to the pressure 

 he requires. The sides of the valve are always made to slope 

 considerably, as otherwise it might become rusted in, and thus 

 cause an explosion. 



We now pass on to notice the effects produced on solids by 

 their immersion in liquid. Of course, we only deal now with 

 the mechanical or physical effects, and therefore speak only of 

 substances that are insoluble in water. Some bodies are dis- 

 solved, and others are chemically altered by immersion in liquid ; 

 but it is the province of chemistry to examine theso changes. 



The main effects produced by the immersion of a solid in a 

 liquid are tho following: 



1. It displaces a volume of fluid equal in bulk to itself. 



2. It is buoyed up with a force exactly equal to the weight of 

 an equal bulk of the fluid, and therefore loses a portion of its 

 weight equal to this. 



3. The upward pressure of the surrounding liquid act* ver- 

 tically through the centre of gravity of the displaced liquid. 



If wo dip our hand* into heavy liquid we feel thu 

 buoyancy; or if, when bathing, we lift a Urge atone, we shall 

 find that it u earner to carry it when it is under water than 

 when above. A more ooncloaivo proof U to suspend a heavy 

 body from a spring balance, and having observed the weight, 

 dip the body into water and observe again how much it weigh*. 

 Wo Mliall find that iU weight U apparently less than it was. 



When a solid is thai immersed, it is clew that it moat dis- 

 place a quantity of water equal in bulk to itself . Two sub- 

 stances cannot occupy the same space at the same time the 

 solid, therefore, takes the place of an equal volume of the 

 liquid ; and if before immersion we completely fill the vessel 

 with water, and carefully catch all that runs over when the 

 solid is dipped into it, we shall have an experimental proof of 

 the fact. In this way the bulk of a solid of irregular shape 

 may easily be ascertained. We have only to plunge it into 

 vessel brim-full of water and measure tho amount that runs over, 

 and this will give us the bulk of the solid. 



Now tho loss of weight in tho solid is exactly equal to that of 

 this bulk of water. Let it have the shape of A (Fig. 12), and 

 let a portion of the water in the vessel having the tame bulk and 

 shape bo supposed to become solid ; it will 

 remain in equilibrium, the forces acting 

 upon it being its own weight acting down- 

 wards through its centre of gravity, and 

 tho upward pressure of the surrounding 

 water which is exactly equal and opposite 

 to this. Now let tho solid take the 

 place of this, and it will bo buoyed up to 

 exactly the same extent, since no change is made in the water 

 around. The strain on the cord will be equal to the weight of 

 A, less the weight of the equal bulk of liquid. A, therefore, 

 loses this portion of its weight. Just the same reasoning will 

 apply if tho solid, instead of being wholly immersed, floats on 

 the surface. The weight of the water it displaces will be exactly 

 equal to its own. If, then, it weighs only half as much as an equal 

 bulk of water, it will only be immersed to half its depth. We 

 thus see that a body will float, remain suspended, or sink, 

 according as its weight is less, equal to, or greater than that 

 of an equal bulk of water. Thus any solid, however heavy, 

 may be made to float, provided it be flattened out and shaped 

 so as to displace a bulk of water weighing more than itself. In 

 this way, though iron is seven times heavier than water, ships 

 are made of it, which, even when loaded with a heavy cargo, 

 are perfectly safe. 



The human body, in its ordinary condition, is lighter than 

 water, and hence will float with a small portion above the sur- 

 face. The art of swimming, therefore, is to keep the body in 

 such a position that tho nose and mouth may bo above, so that 

 breathing may not bo interrupted. Fear, however, causes the 

 chest to be contracted, and thus a less bulk of water is dis- 

 placed, and tho body sinks deeper. Tho same principle account* 

 for the fact which every swimmer must have noticed, that it is 

 easier to swim in salt water than in fresh. A volume of sea 

 water weighs more than an equal volume of fresh; hence a 

 smaller bulk is displaced by his body, and accordingly he is 

 lifted higher out of it, and has a smaller quantity to displace 

 as he moves through it. In the same way a ship is always 

 found to draw less water in the sea than in a river; hence, 

 a vessel in a river may be loaded till she is immersed too far 

 below the water-line to be able to stand rough weather, but on 

 reaching the sea she rises sometimes three or four inches. 



We may state, then, generally that a body in any liquid loses 

 as much of its weight as is equal to that of the liquid it dis- 

 places. There is one simple experiment which furnishes an 

 elegant proof of this. Let a cylinder of brass be procured, and 

 also a case which it fits into and exactly fills. Place the cylinder 

 and case in one pan of a pair of scales and carefully balance it. 

 Now take the cylinder from the case, and by a fine thread or 

 hair suspend it under tho pan, and so arrange the apparatus that 

 it may dip into a jar of water. The scale will at onoo rise, 

 showing that the cylinder has lost weight by immersion ; but if 

 we pour water into the case till it is filled, we shall find that the 

 scales balance as at first. We have thus a conclusive proof of 

 the proposition, the water in the case being clearly exactly 

 equal in bulk to the cylinder, 



