ELASTICITY OP OASES AND VAPOURS.] APPLIED MECHANICS. 



843 



of the substances most widely diffused in nature, and 

 therefore most cheaply obtained, holds a middle course 

 in this respect between these extremes, and attains, by 

 no great accessions of temperature, properties which 

 render it especially serviceable for human use. It is, 

 indeed, among the most obvious of the beneficent 

 arrangements of Providence, that this fluid almost every- 

 where accessible, possessed of no corroding power like 

 acids or alkalies, of no intoxicating qualities like spirits, 

 not of inconvenient gravity like metals should be at 

 the same time capable of absorbing vast quantities of 

 heat, and of giving it out in the shape of active motive 

 power. It has been proposed to employ the vapours of 

 ether, alcohol, sulphide of carbon, and mercury, for 

 moving engines ; but no advantages from their use in 

 this way have presented themselves, such as could bring 

 them into competition with water. We will, therefore, 

 confine ourselves to it, as the only substance turned prac- 

 tically to account. 



The atmosphere which envelops the earth, though in- 

 visible, is nevertheless possessed of weight, and presses 

 on the surface of all bodies in it exactly as the water 

 contained in a cistern presses on bodies immersed in it. 

 The pressure of the atmosphere at the surface of the 

 earth is about 15 Ibs. on every square inch. This pres- 

 sure varies with changes in the density of the atmosphere, 

 but not to a great extent. The average is generally 

 stated at somewhat less than 15 Ibs. per square inch ; 

 but, for all practical calculations, 15 Ibs. may be assumed 

 will, ut involving material error. Water contained in 

 any vessel exposed to the air is thus pressed upon, and 

 retains its liquid form at ordinary temperatures. But 

 if the temperature of the water be raised to 212, as 

 measured by Fahrenheit's thermometer, its vapour at 

 that temperature has an elastic force which exactly 

 balances the atmospheric pressure, and part of the water 

 consequently rises in the form of vapour, and mingles 

 with the air, displacing as much of the latter as is equi- 

 valent to its own bulk. Were the pressure of the air 

 removed, vapour would rise from the water at much 

 lower temperatures than 212, and occupy the vacant 

 space in the vessel containing it. Thus, when a saucer 

 containing water is placed under the receiver of an air- 

 pump, as the air is extracted from the receiver, vapour 

 rises from the water ; and however low may be the tem- 

 perature of the water, vapour continues to rise from it as 

 the pressure of air on its surface is diminished. Even 

 under the full atmospheric pressure, water is constantly 

 evaporating at ordinary temperatures, for the air seems 

 to have a power of dissolving water or taking it up in a 

 vaporous form, just as water dissolves salt and retains it 

 ditl'used through it in a liquid form. 



ELASTICITY OF FLUIDS. At every different tem- 

 perature at which vapour may exist, its elastic force is 

 different, being greater the greater the temperature, but 

 not proportionally so. When we inquire what is meant 

 by the elastic force of a vapour, we can only say that it 

 is a property common to all aeriform bodies, by which 

 they react on any surface compressing them, or tend to 

 expand into a larger volume than that in which they 

 are confined. There seems, indeed, to exist, a repulsive 

 force among the particles which constitute a gaseous 

 body, pushing them asunder with equal power in every 

 direction, and requiring some contrary compressing force 

 to retain them in their places. We have no example of 

 a gaseous body existing without being contained in an 

 envelope of some kind, or being pressed upon by some 

 surrounding medium. The air at the surface of the 

 earth is pressed upon by the weight of air above it, and 

 exerts an elastic force exactly balancing the pressure of 

 the superincumbent fluid.* If its elastic force were 

 greater than the force compressing it, it would expand 

 and lift the air above it ; or if less, it would collapse 

 under a pressure greater than it could resist. As we 

 ascend higher, the weight pressing on the air is dimi- 

 nished, because there being a certain amount of the 

 atmosphere left below, there remains a less amount above. 

 We find accordingly, that at any height above the earth's 



See ante, p. 770, Pneumalia. 



surface, the elastic force of the air is diminished in pro- 

 portion as the pressure upon it is lessened. At the top 

 of a high mountain, like Mout Blanc, the elastic force 

 of the air is not more than half that of the air at the sur- 

 face. If we were to introduce a drop of oil into a small 

 glass tube closed at one end (Fig. 141), so that the oil 

 should form a film, or diaphragm, across the tube at 

 Fig. Hi, 



JL 



some point A, we should enclose between A and B a por- 

 tion of air in the same condition as that surrounding us. 

 If, now, we ascended a mountain, we should find the 

 air-film at points C, D, E, successively, as we attained 

 greater height. Before our ascent commenced, the 

 elastic force of the air in A B pressed the oil-film out- 

 wards with exactly the same force as that of the weight 

 of superincumbent air pressing it inwards, and accord- 

 ingly the film remained at rest. As we ascended, we 

 subjected the film to less external pressure, because we 

 had less weight of air above us ; and accordingly the 

 elasticity of the air in A B overbalanced the pressure, 

 and pushed the film to some such point as E ; not by fits 

 and starts, but gradually as we ascended. 



We have now to inquire why there should be any point 

 such as C, where the film could rest ; in other words, 

 why the elastic force of air in the tube, having once 

 overbalanced the pressure of the external air, should 

 again become equal to it, and no longer force the film 

 outwards. The reply to this question involves the con- 

 sideration of a most important law to which all elastic 

 fluids are equally subjected. It is called Marriotte's law, 

 after the name of the person who gave it to the world, 

 and is to this effect : The elasticity of a gas is propor- 

 tional to its density that is to say, the greater the num- 

 ber of particles of a gas we force into a certain space, or 

 the smaller we make the space containing a certain 

 weight of gas, the greater we make its elastic force, and 

 conversely.f Referring now to the air in the tube, we 

 find that when the film has arrived at C, the space con- 

 taining the air is extended from A B to C B, and the 

 elastic force is diminished in like proportion. In fact, 

 the density and elasticity of the air within the film is 

 exactly the same as that of the air without, and the film 

 remains motionless at C as long as this equality subsists. 

 Again, as we ascend, the external pressure diminishes ; 

 the elasticity of the air within pushes the film outwards, 

 and thus extends its space until its elasticity is reduced 

 to an equality with the pressure of the external air ; and 

 so on without limit. In descending, we should find the 

 film moving inwards, according as it became subjected to 

 a greater external pressure, to positions, such that the air 

 confined within it became of a density sufficient to balance 

 the pressure. Notwithstanding the extreme simplicity 

 of Marriotte's law, it is one of the greatest importance, 

 and should be thoroughly understood by any one desirous 

 of an acquaintance with the steam-engine, for it applies 

 Fig. 142. to steam as closely as to any gas. 



From this law, it follows, that if 

 we forced air or steam occupying a 

 volume of 2 cubic feet into a vessel 

 of the capacity of 1 cubic foot, we 

 should find the elasticity doubled, 

 because the density would be 

 doubled, or the volume reduced to 

 half. Conversely, if we permitted 

 1 cubic foot of air or steam to 

 occupy a volume of 2 cubic feet, 

 we should reduce its elastic force 

 to half of what it was before ex- 

 pansion, because we should have 

 doubled its volume, or reduced its 

 density to half of what it was. In 

 order to illustrate these facts, let 

 us suppose that a cylindrical vessel 

 is fitted with a piston that can 



+ Sec ante, p. 770, Pncumatia. 



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