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the elongation is proportioned to the length of the rod: a wire I metre in length will be stretched twice as far by a weight of I kilogramme as a piece of the same wire only half a metre long.
Liquids possess a very perfect elasticity, which varies in amount in different liquids; the densest liquids, in general, being those which least admit of compression, i.e., possess the greatest coefficient of elasticity. The following table exhibits some experimental results obtained on this subject by Colladon and Storm (Ann. Chim. Phys. 1827 , xxxvi. 113, 225).
Compressibility of Liquids.
One million parts of mercury, for example, were found, by each additional pressure of i"033 kilogrammes per square centimetre, or of about 15 pounds upon the square inch, to diminish in volume $'03 parts One million parts of water "jeered a compression ten times as great, being reduced more than 51 parts; the pressure of the atmosphere being estimated on an average at 1.033 kilo, per square centimetre, or about 15 pounds weight upon every square inch of the earth's surface.
Regnault has more recently determined the compressibility both of water and of mercury with very great care. He considers the results of Colladon and Storm to be a little too high: and estimates the diminution in the volume of mercury for each atmosphere at 3-5 millionths of its volume; whilst he found that of water to be equal to 47 millionths of its volume.
The compressibility of water is greater at low than at high temperatures; but according to the experiments of Grassi (Ann. Chim. Phys. 1851 , iiii. 477) the compressibility of ether, alcohol, and chloroform is increased by elevation of temperature; and in the case of these liquids, and notably in that of wood spirit, the compressibility increased with the pressure within the range of bis trials, which, however, did not exceed 9 atmospheres.
Andrews has lately shown that liquid carbonic anhydride is much more compressible than ordinary liquids.
(27) Boyle's or Mariotte's Law of Elasticity in Gases.—It is, however, in gases that the most extensive and perfect display of elasticity is to be seen; their great elasticity constitutes indeed their most important physical peculiarity. It may be stated, without sensible error, that within the limits of ordinary experiment, 'the volume of an aeriform body is inversely as the pressure to which it is exposed;' consequently by doubling the pressure *e halve the volume, by trebling it we reduce it to one-third;
Fig. 7. 17
'but the elasticity is increased directly as the pressure;' by doubling the pressure we double the elasticity. These facts are strikingly exhibited in the following experiment devised by Boyle, and more accurately performed by Mariotte; and the law has hence been termed Boyle's or Mariotte's law :—
Take a bent tube (fig. 7) of uniform bore, one limb of which is about 12 inches or 30 centimetres long, and furnished with a stop-cock; the other limb being 6 feet, or about 2 metres, in length, and open at the top. Pour a little mercury into the bend of the tube, and close the stop-cock. The air in the short limb now has the same elasticity as the atmosphere at the spot; and the air at the surface of the earth, as will presently be more fully explained, is under the pressure due to the weight of its own superincumbent mass; the amount of this pressure is ascertained by observing the height of the mercurial column in the barometer at the time. Next pour mercury into the open limb of the bent tube; the air in the shorter limb will slowly diminish in volume: wheu the mercury in the longer limb stands above the level of that in the shorter, at a height exactly equal to the height of the barometer at the time, say 29/92 inches (76omm), the compressed air will occupy a length of the shorter tube exactly equal to one-half of that which it did at the beginning of the experiment; the air is subject to a pressure exactly double. On adding more mercury, till the length of the column in the long tube, above the level of that in the shorter, is equal to twice the height of the barometric column, the pressure will be increased threefold, and the air will now occupy only one-third of its original volume.''
* The researches of Despretz, and the more recent and elaborate experiments of Regnault have, however, shown that this law is not rigidly accurate, but it is what is termed a limited law, as it fails in extreme cases. For atmospheric air, for hydrogen, oxygen, and nitrogen, and generally for gases which have either never been liquefied, or only liquefied under enormous pressures, the law is very nearly correct, even under a pressure of several atmospheres: but for gases which may be liquefied more readily H is not so; the nearer they are made to approach to the point of liquefaction the greater is the difference between the volume actually observed, and the
(28) Mutual Repulsion of the Particles of Gases.—Gases and vapours, or elastic fluids, as they are frequently termed, differ from liquids in the entire absence of cohesion among their particles. A vessel may be filled either partially or completely with a liquid, and this liquid will have a definite level surface or limit. With gases it is otherwise; they always perfectly fill the vessel that contains them, however irregular its form. Instead of cohesion there is a mutual repulsion among their particles. These particles have a continual tendency to recede further from each other, and they therefore exert a pressure in an outward IG-' direction upon the sides of the vessel which contains them. This outward pressure is greater or less according as the pressure of the gas is increased or diminished. Indeed, the volume of a gas depends entirely upon the pressure. These facts admit of experimental proof in the following
Procure a stout cylindrical glass tube open at one extremity, and capable of being closed at the other by a stop-cock; fit it with a solid plunger that slides airtight up and down within it; open the stop-cock, place the plunger half-way down, and fill the vessel with some coloured gas, such as chlorine, for example, as shown in fig. 8; now close the stop-cock, and drawthe piston upwards, the gas will be seen to dilate, and the green vapour will still entirely fill the tube; but a considerable resistance to
result calculated. The contraction is nearly always found to be more considerable by experiment, than it should be by the law usually assumed (197)
Some of the results obtained by Regnault are embodied in the following table; they show considerable deviations from the law in four important gases under high pressures.
Relative Volume* of Oases at Sigh Pressure.
The elasticity of hydrogen therefore increases even more rapidly than the pressure; with the other gases the elasticity does not quite keep pace with it. It would seem from these experiments as if there were more probability of liquefying oxygen than nitrogen, and both these than hydrogen.
the upward motion of the piston is experienced, the dilated gas has its pressure reduced below that of the external air, and on releasing the handle, the piston is forced back to the middle of the tube; the pressure of the gas within, and that of the air without, are now equal. Now attempt to thrust the piston to the bottom of the tube; great resistance will be experienced, but the gas will yield and will be condensed into a smaller space, while its pressure will be proportionately increased; but the instant that the pressure on the piston is removed, the piston will rise up again, and occupy its first position midway between the two ends of the cylinder. (29) Air-Pump.—Advantage is taken of this elasticity 9- and expansibility of gases in the construction of the airpump, an instrument designed for the removal of air Ifrom closed vessels. The principle of its construction may be explained in the following manner:—
Suppose that a metallic cylinder, accurately bored, be fitted with a piston similar to that shown in fig. 8, but provided in addition with a small opening, covered by a flap or valve of oiled silk, which opens upwards or outwards (fig. 9): on forcing the piston downwards the compressed air will escape through the valve, but on attempting to withdraw the piston no air will be able to re-enter the cylinder, and a resistance will be experienced, owing to the pressure on the upper surface of K the piston occasioned by the pressure of the external \|JP air. If the cylinder be provided with a second valve at the bottom, opening in the same direction as that in the piston, this valve will, on thrusting down the piston, be closed by the pressure of the included air, while the upper valve will be
opened; on withdrawing the piston the effect is reversed, the lower valve rises, and the air enters, while the valve in the piston is firmly closed. Such an arrangement constitutes the exhausting syringe or airpump in its simplest form. In the usual and more convenient form of the airpump (fig. 10), a brass tube passes from the bottom of the syringe and terminates
in the centre of a disk of brass or of glass, ground accurately flat; the vessel from which the air is to he exhausted also has its edge ground truly, and it is inverted upon the plate. On elevating the piston, the pressure of the air within the vessel or receiver raises the lower valve, and the dilated air enters the vacuum produced in the lower part of the cylinder by the withdrawal of the piston; the air thus admitted, again raises the valve of the piston, when the latter is so far depressed as to render the pressure of the air beneath it greater than that of the atmosphere: the same action goes on with every successive motion of the piston, until the pressure of the air within becomes so much diminished as to be insufficient to raise the lower valve. For convenience, two of these exhausting syringes are often combined in the air-pump, and are made to work alternately by a rack and pinion.
(30) Air-Pump with Single Barrel.—A more complete vacuum may be obtained with a pump of simpler construction, but the labour of using it is considerably greater. The difference between this form of the instrument and the one just described will be readily understood with the assistance of fig. T 1. This pump consists of a single barrel, within which a solid plunger, A, moves air-tight. The plunger is connected with a smooth solid rod, B, which also works air-tight through a stuffing-box, s, at the top of the barrel. In the head of the cylinder is a conical metallic plug, or valve, v, opening upwards and projecting a little way below the under surface of the head, which is ground flat. The communication, p, between the plate of the pump and the barrel, is made at a sufficient distance from the bottom to allow the plunger to pass completely beyond it. In order to use the instrument, the plunger is carried down to the bottom of the barrel, the receiver is then attached to the plate, and the piston raised. In rising, the air contained in the barrel is expelled through the valve in the cylinder head, and bubbles up through the oil placed there to keep the joints airtight. When the piston now descends, a complete vacuum is formed above it, until it passes below the aperture which leads to the receiver; the air then rushes in above the piston; this portion is in turn expelled by raising the piston again; and the exhaustion may in this way be carried on till it becomes almost complete, because the valve is now raised not simply by the elastic force of the air confined between it and the piston, but it is pushed up by the upper surface of the piston itself, and the last bubble of air is displaced by a drop of oil which flows past the valve and thus effects its expulsion.
(30 a.) Sprengel's Mercurial Air-Pump.—A very ingenious and valuable instrument has been described by Dr. Sprengel (Journ. Chem. Soc. 1865 , iii. 9), by which a very high degree of rarefaction may be obtained. The pump is based on the same principle as that of the blowing apparatus of the Catalan for««—viz., the carrying of a stream of gas down a tube by the fall of a liquid. The simplest form of the Sprengel that was first described is shown in fig. 44 (70); in this apparatus, the mercury from the funnel in falling past the branch tube incloses bubbles of air, which are carried down the tube and delivered at