Page images
PDF
EPUB

which air is composed, may readily be shown by placing a brass plate upon an open receiver and forcing a plug of dry wood through its centre, so that the end may be immersed beneath a vessel of water. If the receiver be now exhausted, bubbles of air will be seen rapidly rising through the water, having previously passed through the pores of the wood. In proof of this, the ebullition may be immediately and entirely stopped, by closing the aperture; and, if this be effected with the thumb, it may be afterwards withdrawn and the motion renewed. A nearly similar effect may be produced by merely immersing a piece of marble in water, as, on placing it beneath an exhausted receiver, its whole surface will be found studded with bubbles of air, which have passed through a variety of minute pores in its apparently solid surface.

51. The Bacchus apparatus' is usually employed as an amusing mode of illustrating the action of the lungs-glass. The figure is seated on a cask, with a tube proceeding from the mouth of the barrel; this is filled with red wine or colored water, so that being put under a receiver when the air is exhausted, the liquor is thrown up to his mouth by the expansion of the air which is thus imprisoned, and the deity seems to be at his usual employment. While he is drinking his stomach expands, which is effected by a bladder containing a small quantity of air concealed under his external silk covering. See fig. 4, plate I., Pneumatics.

52. There is an exceedingly beautiful philosophical toy, of which the action depends chiefly on the elasticity of the air. It is a small balloon or thin globe of glass, having an opening at the bottom, and a small car or basket hanging to it. If put to float in water, while the globe contains air only, it is so light that half of it remains above the surface; but water may be introduced to adjust the specific gravity so that it may be only a little less than that of water. If such a balloon be placed in a tall jar of water, the mouth of which is closely covered by bladder, or India rubber tied upon it, or pressing such covering with the hand, the balloon will immediately descend in the water, it will rise again when the pressure ceases, and will float about, rising, or falling, or standing still according to the pressure made. The reason of this is, that the pressure on the top of the jar immediately condenses the air between the surface of the water and the cover; this condensation acts upon the water below, and, by influencing it through its whole extent, compresses also the air in the balloon or globe, and forces just as much more water into it as will render the balloon heavier than water, and therefore heavy enough to sink. As soon as the pressure ceases, the elasticity of the air in the balloon repels again the lately entered water; and the machine then becoming lighter than water ascends to the top. If the balloon be adjusted to have a specific gravity nearly that of water, it will not rise of itself after once reaching the bottom, because the pressure of the water then above it will perpetuate the condensation of the air which caused it to descend; it may even then however be made to rise again, by inclining the water jar to one side, so that the per

pendicular height of water over it shall be diminished.

53. This toy proves many things-the materiality of air, by the pressure of the hand being communicated to the water below through the air in the upper part of the jar-the compressibility of air, by what happens in the globe just before it descends-the elastic force of air when, on the pressure ceasing the water is again expelled from the globe-the lightness of air in the buoyancy of the globe-it shows that in a fluid the pressure is in all directions, because the effects happen in whatever position the jar be held--it shows that the pressure is as the depth, because, a less pressure of the hand is required the farther that the globe has descended in the water-and it exemplifies many circumstances of fluid support.

54. A very important pneumatic engine, intended to raise water by the pressure of the atmosphere, must now be noticed. It is represented at fig. 5, plate I. PNEUMATICS. AA is a beam, capable of vibrating upon a centre a B; C and C two chambers, formed of metal, of sufficient strength to resist the pressure of the atmosphere (about fourteen pounds to the square inch upon its external surface, and having the caps C2, C3, suspended, one at each end of the beam, capable of closing each of these chambers in an air-tight manner. The chamber C1 is shown in section.

55. E E and E' E' are two pipes, containing valves opening upwards, leading and affording a communication from the vessels F and F1. These contain floats, F2, F2, attached to the beam AA by rods which receive motion from the floats; to these rods are attached the slides t, t, to close alternately, at each vibration of the beam, the apertures h h. The pins p, p, attached to one of the rods from the floats, give motion to the small vibration tube R, which, by the rods R R1 attached to the cranks in the chamber S, alternately opens and closes the pipes S'S' communicating with the vessel F and F'.

56. DD is a pipe leading from the gasometer, branching off at Di D' into the two chambers C and C', for the purpose of supplying the gas that is to be consumed in effecting the vacuum. This supply can be admitted or shut off by means of the cocks D2, D, which open and close by cranks worked by the movement of the beam.

57. G, G, two other branch pipes, supplied with gas from the gasometer, and ending in a jet at each end. By the slanting directions of the ends, it is evident that the flames from these jets will, when their respective orifices h, h, be open, protrude into the chambers C and C'. K and Ki are two pipes, affording a communication from the outer air to the interior of each of the chambers C and C1; their outer ends are capable of being closed by means of the cranks n, n, which are attached by chains to the floats F2, F2. The mode of operation consists in allowing the gas to pass from the gasometer along one of the branches of the pipe D D, and thence into one of the chambers C or C1 (suppose C1), where, by the jet of ignited gas playing in the orifice h, it becomes ignited, and by its combustion rare

fies and expels a considerable portion of the atmospheric air from that chamber. Suppose now the cap of the chamber be put down, and, by the movement of the rod attached to the float, the orifice h and gas pipe D be closed, the combustion will immediately cease, and leave therein a partial vacuum. The atmosphere, beginning now to press upon the vessel F, will cause so much of the water to pass from it into the chamber C1 as will nearly compensate the vacuum, when the valve through which the water passed being closed, and a communication between the interior of the chamber and the open air effected by the opening of K', the water contained in the chamber flows from thence into the aperture u, and affords power by its fall and weight to the overshot water-wheel W. From thence it passes into the vessel S, and finally is admitted by S'S' into F or F', leaving the engine in a condition to renew the operation. It will be seen that when the cap of one chamber closes, the several openings to the same chamber close with it; and by the rising of the other end of the beam, the similar openings to the other chamber are opened, and prepared for a like operation. It will also be seen that the production of this motion is attained by the rising of the two floats in the chambers F and F1.

58. The advantages to be derived from this engine, as detailed in the descriptive outline of the inventor, are,

59. First, The quantity of gas consumed being very small, the expense of working the engine is moderate. In its application on land the saving will be extremely great, the cost of the coal gas (deducting the value of the coke) being inconsiderable. The expense of working a marine engine will certainly be greater, as the gas used for that purpose must be extracted from oil, resin, tar, or some other substances equally portable; yet, even in this case, it will not equal the cost of the fuel required to propel a steam boat: and, as a few butts of oil will be sufficient for a long voyage, vessels of the largest tonnage may be propelled to the most distant parts of the world. 60. Secondly, The engine is light and portable in its construction, the average weight being less than one-fifth of the weight of a steam-engine (and boiler) of the same power. It also occupies a much smaller space, and does not require the erection of so strong a building, nor of a lofty chimney. In vessels, the saving of tonnage will be highly advantageous, both in the smaller comparative weight and size of engine, and in very reduced space required for fuel. 61. Thirdly, This engine is entirely free from danger: no boiler being used, explosions cannot take place; and as the quantity of gas consumed is so small, and the only pressure that of the atmosphere, it is impossible that the cylinder can burst, or the accidents incident to steam boats occur. The power of the engine (being derived from the atmospheric pressure of ten pounds and upwards upon the square inch) may be increased with the dimensions of the cylinders to any extent, and always ascertained by a mercurial gauge.

the

62. It is scarcely necessary to allude to the well known fact, that, after the deduction, the

friction arising from the use of the air and cold water pumps, &c., the general available power of the condensing steam engine is little more than two-thirds of its estimated amount. The cost of the machine will be less, particularly as constructed for raising water; it is therefore peculiarly adapted for draining fens, &c., or supplying reservoirs. The expense of wear and tear will also be considerably less than that of the steam engine, and, when occasionally out of order, it may be repaired at a trifling cost, and with but little delay.

63. In examining the effects of this engine, we cannot to a certain extent withhold our approbation; for the patentee has undoubtedly effected and applied a vacuum, produced by ignition, in a manner much more manageable than by the ordinary process. The probability of its entering efficiently into competition with steam power is a question that requires the data of experience, which, in the present state of the invention, can hardly be procured.

64. Having in the preceding pages fully examined the weight and pressure of the atmospheric fluid that surrounds our globe, we may now consider the motions of which air is susceptible when the equilibrium of pressure (whether arising from its weight or its elasticity) is removed.

65. In this consideration we shall avoid the extreme of generality, which renders the discussion too abstract and difficult, and adapt our investigation to the circumstances in which compressible fluids (of which air is taken for the representative) are most commonly found. We shall consider air, therefore, as it is commonly found in accessible situations, as acted on by equal and parallel forces; and we shall consider it in the same order in which water is treated in a system of hydraulics.

66. In that science the leading problem is to determine with what velocity the water will move through a given orifice when impelled by some known pressure; and it has been found that the best form in which the most difficult and intricate proposition can be put is to determine the velocity of water flowing through this orifice when impelled by its weight alone. Having determined this, we can reduce to this case every question which can be proposed; for, in place of the pressure of any piston or other mover, we can always substitute a perpendicular column of water or air whose weight shall be equal to the given pressure.

67. The first problem, therefore, is to determine with what velocity air will rush into a void when impelled by its weight alone. This is evidently analogous to the hydraulic problem of water flowing out of a vessel. And here we must be contented with referring our readers to the solutions which have been given of that problem, and the demonstration that it flows with the velocity which a heavy body would acquire by falling from a height equal to the depth of the hole under the surface of the water in the vessel. In whatever way we attempt to demonstrate that proposition, every step, nay, every word, of the demonstration applies equally to the air, or to any fluid whatever. Or, if our

readers should wish to see the connexion or analogy of the cases, we only desire them to recollect an undoubted maxim in the science of motion, that, when the moving force and the matter to be moved vary in the same proportion, the velocity will be the same. If, therefore, there be similar vessels of air, water, oil, or any other fluid, all of the height of a homogeneous atmosphere, they will all run through equal and similar holes with the same velocity; for, in whatever proportion the quantity of matter moving through the hole is varied by a variation of density, the pressure which forces it out by action in circumstances perfectly similar, varies in the same proportion by the same variation of density. 68. We must, therefore, assume it as the leading proposition, that air rushes from the atmosphere into a void with the velocity which a heavy body would acquire by falling from the top of a homogeneous atmosphere.

69. All the modifications of motion which are observed in water conduits take place also in the passage of air through pipes and holes of all kinds. There is the same diminution of quantity passing through a hole in a thin plate that is observed in water. We know that (abating the small effect of friction) it issues with a velocity similar to that acquired by falling from the surface; and yet if we calculate by this velocity and by the area of the orifice, we shall find the quantity deficient nearly in the proportion of sixtythree to 100. This is owing to the water pressing towards the orifice from all sides, which occasions a contraction of the jet. The same thing happens in the efflux of air. Also the motion of water is greatly impeded by all contractions of its passage.

70. It requires, therefore, an increase of pressure to force it through them, and this in proportion to the squares of their velocities. Thus, if a machine working a pump causes it to give a certain number of strokes in a minute, it will deliver a determinate quantity of water in that time. Should it happen that the passage of the water is contracted to one-half in any part of the machine (a thing which frequently happens at the valves), the water must move through this contraction with twice the velocity that it has in the rest of the passage.

71. This will require four times the force to be exerted on the piston. Nay, if no part of the passage is narrower than the barrel of the pump, but, on the contrary, a part much wider, and if the conduit be again contracted to the width of the barrel, an additional force must be applied to the piston to drive the water through. It will require a force equal to the weight of a column of water of the height necessary for communicating a velocity the square of which is equal to the difference of the squares of the velocities of the water in the wide and narrow parts of the conduit.

72. The same thing takes place in the motion of air, and therefore all contractions and dilatations must be carefully avoided, when we wish to preserve the velocity unimpaired. Air also suffers the same retardation in its motion along pipes. By not knowing, or not attending to this circumstance, many engineers have been disap

pointed in their expectations of the quantity of air which will be delivered by long pipes. Its extreme lightness of air hindered them from suspecting that it would suffer any sensible retardation. Dr. Papin, a most ingenious man, proposed that as the most effectual method of transferring the action of a moving power to a great distance. Suppose, for instance, that it was required to raise water out of a mine by a water machine, and that there was no fall of water nearer than a mile's distance. He employed this water to drive a piston, which should compress the air in a cylinder communicating by a long pipe with another cylinder at the mouth of the mine. This second cylinder had a piston in it whose rod was to give motion to the pumps at the mine. He expected, that as soon as the piston at the watermachine had compressed the air sufficiently, it would cause the air in the cylinder at the mine to force up its piston, and thus work the pumps. Dr. Hooke made many objections to the method, when laid before the Royal Society; and it was much debated there. But dynamics was at that time an infant science and very little understood, and Newton had not then taken any part in the business of the society. Notwithstanding Papin's great reputation as an engineer and mechanic, he could not bring his scheme into use in England; but afterwards in France and in Germany, where he settled, he got some persons of great fortune to employ him in this project; and he erected large machines in Auvergne and Westphalia for draining mines. But, so far from being effective machines, they would not even begin to move. He attributed the failure to the quantity of air in the pipe of communication, which must be condensed before it can condense the air in the remote cylinder. This indeed is true. He therefore diminished the size of this pipe, and made his water machine exhaust instead of condensing, and had no doubt but that the immense velocity with which air rushes into a void would make a rapid and effectual communication of power. But he was equally disappointed here, and the machine at the mine stood still as before.

73. Near a century after this a very intelligent engineer attempted a much more feasible thing of this kind at an iron foundry in Wales. He erected a machine at a powerful fall of water, which worked a set of cylinder bellows, the blow pipe of which was conducted to the distance of a mile and a half, where it was applied to a blast furnace. But, notwithstanding he took every care to make the conducting pipe air-tight, above ten minutes elapsed after the action of the pistons in the bellows, before the least wind could be perceived at the end of the pipe; whereas the engineer expected, an interval of six seconds only.

74. No very distinct theory can be delivered on this subject; but we may derive considerable assistance in understanding the causes of the obstruction to the motion of water in long pipes, by considering what happens to air. The elasticity of the air, and its great compressibility, have given us the most distinct notions of fluidity in general, proving, in a way that can hardly be controverted, that the particles of a fluid are kept

at a distance from each other, and from other bodies, by their corpuscular forces.

75. The writers on hydrodynamics have always considered the obstruction to the motion of fluids along canals of any kind as arising from something like the friction by which the motion of solid bodies on each other is obstructed; but we cannot form to ourselves any distinct notion of resemblance, or even analogy between them. The fact is, however, that a fluid running along a canal has its motion obstructed; and that this obstruction is greatest in the immediate vicinity of the solid canal, and gradually diminishes to the middle of the stream. It appears, therefore, that the parts of fluids can no more move among each other than among solid bodies, without suffering a diminution of their motion. The parts, in physical contact with the sides and bottom, are retarded by these immoveable bodies. The particles of the next stratum of the fluid cannot preserve their initial velocities without passing the particles of the first stratum; and it appears from the result that they are thus retarded. They retard in the same manner the particles of the third stratum, and so on to the middle stratum. This sort of friction is not a consequence of rigidity alone, as in solids, but that it is equally a property of fluids. Nay, since it is a matter of fact in air, and is even more remarkable there than in any other fluid, as we shall see by the experiments which have been made on the subject; and as our experiments on the compression of air show us the particles of air ten times nearer to each other in some cases than in others (viz. when we see air 1000 times denser in these cases), and therefore force us to acknowledge that they are not in contact; it is plain that this obstruction has but little analogy to friction, which supposes roughness or inequality of surface. No such inequality can be supposed in the surface of aerial particle; nor would it be of any service in explaining the obstruction, since the particles do not rub on each other, but pass each other at some small and imperceptible distance. 76. We must therefore have recourse to some other mode of explication. We shall apply this to air only in this place; and, since it is proved by the incontrovertible experiments of Canton, Zimmerman, and others, that water, mercury, oil, &c., are also compressible and perfectly elastic, the argument from this principle, which is conclusive in air, must equally explain similar phenomena in hydraulics.

77. The most highly polished body which we know may be considered as possessing an uneven surface when we compare it with the small spaces in which the corpuscular forces are exerted; and a quantity of air moving in a polished pipe may be compared to a quantity of small shot sliding down a channel with undulated sides and bottom. The row of particles immediately contiguous to the sides will therefore have an undulated motion: but this undulation of the contiguous particles of air will not be so great as that of the surface along which they glide; for not only does every motion require force to produce it, but also every change of motion. The particles of air resist this change from a rectilineal to an undulative motion; and, being elastic, that is,

repelling each other and other bodies, they keep a little nearer to the surface as they are passing over the eminence, and their path is less incurvated than on the surface. The difference between the motion of the particles of air and the particles of a fluid quite inelastic is, in this respect, somewhat like the difference between the motion of a spring carriage and that of a common carriage.

78. When the common carriage passes along a road not perfectly smooth, the line described by the centre of gravity of the carriage keeps perfectly parallel to that described by the axis of the wheels, rising and falling along with it. Now let a spring body be put on the same wheels and pass along the same road. When the axis rises over an eminence of perhaps half an inch, and sinks down again into the next hollow, and then rises a second time, and so on, the centre of gravity of the body describes a much straighter line; for, upon the rising of the wheels, the body resists the motion and compresses the springs, and thus remains lower than it would have been had the springs not been interposed. In like manner it does not sink so low as the axle does when the wheels go into a hollow. And thus the motion of a spring-carriage becomes less violently undulated than the road along which they pass. This illustration will, we hope, enable the reader to conceive how the deviation of the particles next to the sides and bottom of the canal from a rectilineal motion is less than that of the canal itself.

79. It is evident that the same reasoning will prove that the undulation of the next row of particles will be less than that of the first that the undulation of the third row will be less than that of the second, and so on. And thus it appears, that, while the mass has a progressive motion along the pipe or canal, each particle is describing a waving line, of which a line parallel to the direction of the canal is the axis, cutting all these undulations. This axis, of each undulated path, will be straight or curved as the canal is; and the excursions of the path on each side of its axis will be less and less as the axis of the path is nearer to the axis of the canal.

80. Let us now see what sensible effect this will have; for all the motion which we here speak of is imperceptible. It is demonstrated in machines that if a body, moving with any velocity, be deflected from its rectilineal path by a curved and perfectly smooth channel, to which the rectilineal path is a tangent, it will proceed along this channel with undiminished velocity. Now the path, in the present case, may be considered as perfectly smooth, since the particles do not touch it.

81. It is one of the undulations only which we are considering, and we may at present conceive this as without any subordinate inequalities. There should not, therefore, be any diminution of the velocity. Let us grant this of the absolute velocity of the particle; but what we observe in the velocity of the mass is different, and we may judge of it by the motion of a feather carried along with the air. Let us suppose a single atom to be a sensible object, and let us attend to two such particles, one at the side and the other in the

middle: although we cannot perceive the undulations of these particles during their progressive motions, we see the progressive motions themselves. Let us suppose that the middle particle has moved without any undulation whatever, and that it has advanced. The lateral particle will also have moved ten feet; but this has not been in a straight line. It will not be so far advanced, therefore, in the direction of the canal ; it will be less behind, and will appear to us to have been retarded in its motion: and, in like manner, each series of particles will be more and more retarded (apparently only) as it recedes farther from the axis of the canal, and what is usually called the thread of the stream.

82. And, as has been already stated, this change of place is shown to be a necessary consequence of what we know to be the nature of a compressible or elastic fluid; and that without supposing any diminution in the real velocity of each particle, there will be a diminution of the velocity of the sensible threads of the general stream, and a diminution of the whole quantity of air which passes along it during a given time. !

83. Let us now suppose a parcel of air impelled along a pipe, which is perfectly smooth, out of a larger vessel, and issuing from this pipe with a certain velocity, it requires a certain force to change its velocity in the vessel to the greater velocity which it has in the pipe. This is abundantly demonstrated. How long soever we suppose this pipe, there will be no change in the velocity, or in the force to keep it up. But let us suppose that about the middle of this pipe there is a part of it which has suddenly got an undulated surface, however imperceptible. Let us further suppose that the final velocity of the middle thread is the same as before. In this case it is evident that the sum total of the motions of all the particles is greater than before, because the absolute motions of the lateral particles is greater than that of the central particle, which we suppose the same as before. This absolute increase of motion cannot be without any increase of propelling force: the force acting now, therefore, must be greater than the force acting formerly. Therefore, if only the former force had continued to act, the same motion of the central particle could not have been preserved, or the progressive motion of the whole stream must be diminished.

84. And thus we see that the insensible undulations become a real obstruction to the sensible motion which we observe, and occasions an expense of power.

85. Let us see what will be the consequence of extending this obstructing surface further along the canal. It must evidently be accompanied by an augmentation of the motion produced, if the central velocity be still kept up; for the particles which are now in contact with the sides do not continue to occupy that situation: the middle particles moving faster forward get over them, and in their turn come next the side; and as they are really moving equally fast, but not in the direction into which they are now to be forced, force is necessary for changing the direction also; and this is in addition to the force necessary for producing the undulations already so VOL. XVII.

minutely treated of. The consequence of this must be, that additional force will be necessary for preserving a given progressive motion in a larger pipe, and that the motion produced in a pipe of greater length, by a given force, will be less than in a shorter one, and the efflux will be diminished.

86. There is another consideration which must have an influence here. Nothing is more certainly demonstrable than the necessity of an additional force for producing an efflux through any contraction, even though it should be succeeded by a dilatation of the passage. Now both the inequalities of the sides and undulations of the motions of each particle are equivalent to a succesion of contractions and dilatations; although each of these is next to infinitely small, their number is also next to infinitely great, and therefore the total effect may be sen

sible.

87. We have hitherto supposed that the absolute velocity of the particles was not diminished: This we did, having assumed that the interval of each undulation of the sides was without inequalities. But this was gratuitous; it was also gratuitous that the sides were only undulated. We have no reason for excluding angular asperities. These will produce, and most certainly often do produce, real diminutions in the velocity of the contiguous particles; and this must extend to the very axis of the canal, and produce a diminution of the sum total of motion and, in order to preserve the same sensible progressive motion, a greater force must be employed. This is all that can be meant by saying that there is a resistance to the motion of air through long pipes.

88. There remains another cause of diminution, that is, the want of perfect fluidity, whether arising from the dissemination of solid particles in a real fluid, or from the viscidity of the fluid. We shall not insist on this at present, because it cannot be shown to obtain in air, at least in any case which deserves consideration.

89. What has been said on this subject is sufficient for the purpose of illustrating the retardation of air when passing through long and narrow pipes. We are able to collect an important maxim from it, viz. that all pipes of communications should be made as wide as circumstances will permit; for it is plain that the force to overcome it must be in proportion to the mass of matter which is in motion. The first increases as the diameter of the pipe, and the last as the square. The obstruction must therefore bear a greater proportion to the whole motion in a small pipe than in a large one.

90. Mr. Hachette has just published a very important paper illustrative of the flowing of aeriform fluids into the atmosphere, and on the combined action of the striking of the air and of the atmospherical pressure. Mr. H. commences by observing that the flowing of aeriform fluids into atmospheric air has recently offered several phenomena deserving the attention of philosophers. I shall adduce in the first place a very curious observation of Messrs. Gay Lussac and Welter, communicated to the Institute the 29th of April 1822, and published in the Annales, tome xix. p. 436. They have confirmed this very

2 M

« PreviousContinue »