166 



THE POPULAR EDUCATOR. 



Pig. 18. 



HYDROSTATICS. VII 



EQUILIBRIUM OF FLOATING BODIES METACENTRE CAPIL- 

 LARY ATTRACTION HYDRAULIC MACHINES. 



WE have now examined at some length the effects produced on 

 bodies by immersion in liquids, and have seen that one of the 

 conditions of equilibrium is that the weight of the displaced 

 fluid shall be equal to that of the body immersed. This, how- 

 ever, is not the only condition that must be complied with in 

 order to ensure equilibrium. Suppose, for instance, that we 

 have a solid of the shape of A B in the annexed figure, and 

 that the end B has a piece of lead affixed 

 to it, so as to render it heavier than the 

 other. Let us now see what are the 

 forces acting on this body. One force 

 is its own weight, which acts through its 

 centre of gravity G, and as the end B is 

 heavier than the other, this point is 

 nearer that end ; the other force acting 

 upon it is the buoyancy of the liquid 

 which acts through the centre of gravity 



of the displaced liquid, that is, upwards through G'. Now these 

 two forces are equal to one another, and act in opposite direc- 

 tions, but their lines of action do not pass through the same 

 point ; and hence, as we saw in our Lessons on Mechanics, 

 they constitute " a couple," and produce a tendency in the body 

 to twist round. In order, then, that there should be equili- 

 brium, the points G and G' must be in the same vertical line. 



Now either o or G' may be the higher, and, according to this, 

 A B is in a state of stable or unstable equilibrium. If the 

 centre of gravity of A B be above that of the displaced liquid, 

 the body will remain at rest until some disturbing force acts 

 on it ; but as soon as it is moved at all from its position the 

 tendency to rotate will come into action, and the body will 

 move further and further from its original position. If, on the 

 other hand, G' be above G, and the body be then deflected 

 slightly from its position, the forces acting on it will draw it 

 back. Hence it is said to be in a condition of stable equili- 

 brium. In the case of floating bodies, or of vessels going to 

 sea, it is clearly of the utmost importance 

 to be sure that they are in this condition, 

 as otherwise a little wind will cause them 

 to incline, and they must then turn over. 

 We will see, then, what are the conditions 

 requisite to ensure safety. 



The body A B, in Fig. 18, would be 

 found to turn till B was downwards, and 

 it would, then remain at rest. Now let it 

 be turned a little from its vertical posi- 

 tion, as in Fig. 19. The dotted line represents its axis, in 

 which both G and G' were situate, but in the new position G' will 

 be at one side of this axis. Draw from this point a line ver- 

 tically upwards to represent the buoyancy of the water, this 

 line will cut the axis in some point, M. If this point be above 

 G, the body is in a state of stable equilibrium ; if it be below, 

 the .body is unstable. This point M is called the metacentre. 

 Hence, if the metacentre be above the centre of gravity, the 

 vessel will float in safety. Now from this we learn several 

 important things. The first is, that in a vessel the centre of 

 gravity should be as low down as possible. A captain accord- 

 ingly arranges to stow the heaviest part of his cargo in the 

 lowest part of the hold ; and for the same reason, in a ship 

 almost empty, or in a pleasure-boat, a large amount of heavy 

 material, such as clay or pig-iron, is stowed away as ballast. 

 If the lower part were left empty, or filled with light cargo, 

 and heavy goods placed on the deck, the centre of gravity 

 would be raised dangerously high, and the vessel, in all pro- 

 bability, would capsize. Forgetfulness of this fact is a fruitful 

 source of danger to passengers in rowing or sailing boats. If 

 a squall comes on, or any accident seems imminent, the pas- 

 sengers frequently spring to their feet, a,nd by so doing greatly 

 Taise the centre of gravity and increase the danger ; the wisest 

 and safest plan is for all to sit down or, better still, to lie 

 down at the bottom of the boat ; the centre of gravity being 

 thus lowered, the danger will be much diminished. Another 

 thing that should be carefully seen to in sailing vessels is to 

 have the cargo so stowed that the centre of gravity is vertically 

 over the keel, and also to prevent its shifting its position when 



Fig 19. 



the vessel lurches, as, if it does so, she cannot right herself so 

 well. In paddle-wheel steamers, where it is important for the 

 vessel to be upright, small carriages, filled with chain or other 

 heavy material, are often placed upon the deck, so that when 

 the wind inclines the vessel, these may be moved to the higher 

 side, and thus bring it even again. 



We now pass on to notice another property of liquids, known 

 as capillary attraction. If we procure several glass tubes 

 (Fig. 20) of small but different dia- 

 meters, and dip them into water, we 

 shall find an apparent exception to the 

 rule that liquids maintain their level, 

 for the water will rise in them to a 

 height which varies with the size of the 

 tube. This height increases inversely 

 as the diameter. The name, "capillary 

 attraction," or capillarity, is derived 

 from the Latin word capilla, which 

 means " a hair," and was so used be- 

 cause this effect was first observed in 

 tubes almost as fine as a hair. We see 

 a great many common things which 

 afford illustrations of this fact. A 

 lump of sugar consists of a large number of small crystals held 

 together so as almost to touch, and they leave small tubes or 

 passages between them. Hence, if we just dip a corner into a 

 cup of tea, we see that the tea rises at once and wets the whole 

 lump. A better illustration is to procure a tall lump of salt, 

 and set it in a plate filled with some coloured fluid, as water 

 and red ink ; the line produced by the rise of the liquid is then 

 very clearly seen. If a towel or piece of linen be placed in a 

 vessel of water, a portion being allowed to hang over one side, 

 it will in the same way draw up the water in its interstices and 

 allow it to drip from the lower corner, thus emptying the 



Fig. 20. 



A practical application is made of this principle in quarries 

 where millstones are obtained. 



A block of stone is roughly trimmed to a cylindrical form. 

 Grooves are then cut round it at distances regulated by the 

 thickness of the stones. Into these grooves wedges of dry 

 hard wood are firmly driven, and the damp of the air is so 

 powerfully attracted into their pores that they swell and split 

 off the stones from the block. 



On the same principle a candle burns. The heat of the 

 flame melts the tallow or composition, and forms a cup filled 

 with the melted portion ; this rises in the wick by capillary 

 attraction, and there it is converted into a gas, and consumed, 

 while it gives light. 



In all these cases we have supposed the solid has been of 

 such a nature as to be wetted by the liquid. If, however, this 

 be not the case, the liquid in the tube will stand at a lower 

 level ftian that without. This may be tried with a glass tube 

 dipped into mercury, when the 

 mercury within the tube will be 

 seen to be at a lower level than 

 that without. 



These effects are accounted for 

 by the attraction or repulsion of 

 the surface of the tube for the 

 liquid, and may be seen well by 

 immersing a sheet of glass in the 

 liquid, or, better still, by taking 

 two glass plates and moving them 

 different distances apart. If we 

 arrange them, as shown at Fig. 

 21, so that the edges at one side 

 meet, while at the other they are 

 a small distance apart, the liquid 

 will rise between them and form 

 a curve, and thus we can ascertain how high it rises for each 

 different distance between the plates. The elevation hero is 

 found to be just one-half of what it is in tubes having a diameter 

 equal to this distance. 



These experiments you can try for yourselves, and by doing 

 so will be far better able to understand them. Never be satis- 

 fied with reading an account of an experiment, or looking at an 

 illustration of it, if you can try it. 



We have now noticed the main points in the first branch of 



Fig. 21. 



