52 



THE POPULAR EDUCATOR. 



HYDROSTATICS. IV. 



CENTRE OF PRESSURE LEVELS SPRINGS AND ARTESIAN 

 WELLS LAWS OF PRESSURE SAFETY VALVE SOLIDS 

 IMMERSED IN LIQUIDS. 



ALTHOUGH the mean pressure is that at the centre of gra- 

 vity, wo must not imagine that this point is the centre of 

 pressure that is, that a support placed behind this would 

 balance the pressure. If we suppose the surface divided into 

 layers, there will, if it be rectangular, bo At^ 

 as many layers above the centre of gravity 

 as below it; but, since the pressure is 

 greater on the lower layers than on those 



higher up, the larger part of the pressure ~~~ ~ w 



will be below the centre of gravity. The 

 centre of pressure is therefore below this point. Its position 

 varies with the shape of the surface, but in a rectangular sur- 

 face is situate at about two-thirds of the depth. This fact 

 should be borne in mind in the construction of lock-gates, for 

 if a hingo be placed near the top, and a pivot and socket at the 

 bottom, an undue pressure is thrown on the lower support, and 

 thus there is a tendency to wring or twist the gates. The sup- 

 ports should be arranged as nearly as possible equi-distant from 

 the centre of pressure, one being near the bottom, and the other 

 about a third of the way .from the top, as then the pressure is 

 equally distributed. 



There is another property of liquids which results from the facta 

 already noticed, and that is, that the surface always maintains 

 its level and forms an horizontal plane. This fact is familiar to 



us by every-day experience, 

 and the reason of it is easily 

 seen. Let A B c D (Fig. 

 7) be a vessel containing 

 liquid, and let the surface bo 

 supposed to have the figure 

 A G H B. Take any layer, 

 E F, in the fluid, and ima- 

 gining it to become solid, 

 let us see what is the pres- 

 sure at each end of it. At 

 E it is equal to that of a 

 column of water having the 

 height G E ; at F it is equal 

 only to the column F H. 

 The former of thcso is ob- 

 viously greater, and there- 

 fore equilibrium cannot 

 exist till this difference is 

 removed. The particles of 

 fluid will therefore move 

 from E towards F until the 

 surface becomes even. 



Exactly the same result will occur if, instead of one vessel, 

 we have any number communicating with each other, no matter 

 what their shape may be. The apparatus usually used for the 

 proof of this is shown in Fig. 8. A number of glass vessels, 

 varying greatly in size and shape, but all having the same 

 height, are arranged so as to communicate freely with each 

 other. If now water be poured into any one of them, all will 

 be filled, and the water will rise in each of them to the same 

 height ; or, if a stopcock be fitted at the bottom of each, and 

 they be filled to different levels, immediately on the taps being 

 trrned, the level will become the same in all. The mass of 

 water in M is many times greater than in N, yet it will stand at 

 exactly the same height in 

 each. --- 



Familiar illustrations are 

 seen in tea-pots, or other ves- 

 sels used to pour liquids from. 

 The spout is always so ar- 

 ranged that the open end of it 

 is at least as high as the sur- 

 face of the liquid within. 



The practical applications of pj 



this principle are numerous 

 and important. The most common is the level, which is such 



Kg. 



an important instrument in surveying operations. In making 

 roads or railways, or still more in canals, it is necessary that all 

 parts should have as nearly as possible the same elevation, so 

 as to avoid inclines. If. is desirable, too, to do this with p,s little 

 labour as possible, and therefore that route is chosen which will 

 require least cutting or embankment. To ascertain this, level- 

 ling is required. The form of level which shows best the 

 principle, though not the one commonly used, is shown in Fig. 9. 

 A glass tube is taken, and each end is bent at right angles. 

 This is supported on a stand, and water poured in so as to rise 

 a little way in each limb. A float rests on the liquid at each 

 end, supporting a framework with cross wires. A graduated 

 pole is then set up at a distance, and the observer notes what 

 part of it is in a straight line with the points where the wires 

 cross, and thus finds the difference in height between the place 

 where the pole is and that where he stands. 



The surface of the earth, however, is not a true level, but a 

 curve which differs from a straight line by about eight inches in 

 a mile ; an allowance to this extent has accordingly to be made, 

 for the surface of water keeps to the curve, or natural level, as 

 it is called. In a small surface this is not noticed at all, but 

 we observe that when a ship is going out to sea the hull is 

 hidden by this curve, while the masts still remain visible. 



The more common form of level consists of an even tube of 

 glass nearly filled with spirit, so that only a small bubble of 

 air remains in it. Both ends are then closed up, and it ia 

 mounted in a case, so that the sides of the tube are exactly 

 parallel to the bottom. If it be placed on an horizontal surface, 

 the bubble will remain exactly in the middle ; but if either end 

 be elevated at all, the bubble will rise to that end. In levelling-, 

 one of thcso levels is fixed to the stand of the telescope so as 

 to be parallel to it. It is then adjusted by means of thumb- 

 screws so as to be perfectly horizontal, and on looking through 

 the telescope the elevation on the pole may be read off with 

 much more accuracy and at a greater distance than when the 

 other form of level is used. 



It is on this principle of water always finding its level that 

 a town is supplied with water. If there bo a convenient eleva- 

 tion outside the town a reservoir is made there, and the water 

 pumped up into it. Pipes are then laid on from this to all 

 parts of the town, and in these the water will rise to an eleva- 

 tion nearly equal to that of the reservoir. The small difference 

 in height arises from the friction of the water in the pipes. 

 Instead of a reservoir the water is sometimes forced into a 

 lofty pipe open at the upper end, and from this it flows to all 

 parts, the principle being exactly the same. In the samo 

 way a fountain acts, and any one with a little mechanical 

 ingenuity can easily fit one up for himself. A reservoir has to 

 be provided at a height exceeding that to which the water is re- 

 quired to rise, and a pipe is brought down from this to the jet. 



Springs and artesian wells depend on this same principle. 

 In mountainous and elevated districts there is always a larger 

 fall of rain, because the hills condense the clouds. This rain 

 soaks in through crevices of the rocks, till it finds its way to 

 some largo cavity. Many different crevices often lead thus to 

 one largo chamber, and the water being unable to find any other 

 escape, rises from this to the surface, forming a spring. 



In some places all the upper strata of the soil are easily 

 permeated by the rain, but at a greater depth there exists one 

 through which it cannot pass. It accordingly accumulates 

 there, and if a hole be bored in the ground down to this level, 

 the water will frequently rise to the surface and form an 

 artesian well. One of these near Paris is bored to a depth of 

 1,800 feet, and the water in it rises with such force that in a 

 vertical tube it would rise over 100 feet. It is said to be capable 

 of supplying over 14,000,000 gallons per day. 



We have seen that the pressure in any liquid depends upon 

 the area of the surface and the depth. It is manifest, how- 

 ever, that this pressure must vary with the density of the 

 liquid, and it is found to be in direct proportion to it. The 

 apparatus represented in Fig. 10 supplies us with a proof 

 of this. A glass tube is bent into the shape of a U, except 

 that one limb is shorter than the other. If now we take two 

 liquids of different densities which will not mix, and pour one 

 into each limb, we shall find that the level will not be the 

 same in each, as it would were both filled with the samo 

 liquid. Suppose, for instance, that mercury is poured into the 

 bend of the tube till it rises a little way in each limb. Now 



