PNEUMATICS

, that branch of natural philosophy which treats of the weight, pressure, and elasticity of the air, or elastic fluids, with the effects arising from them. Wolfius, instead of Pneumatics, uses the term Aerometry.

This is a sister science to Hydrostatics; the one considering the air in the same manner as the other does water. And some consider Pneumatics as a branch of mechanics; because it considers the air in motion, with the consequent effects.

For the nature and properties of air, see the article Air, where they are pretty largely treated of. To which may be added the following, which respects more particularly the science of Pneumatics, as contained in a few propositions, and their corollaries.

Prop. I. The Air is a heavy fluid body, which surrounds and gravitates upon all parts of the surface of the earth.

These properties of air are proved by experience. That it is a fluid, is evident from its easily yielding to any the least force impressed upon it, with little or no sensible resistance.

But when it is moved briskly, by any means, as by a fan, or a pair of bellows; or when any body is moved swiftly through it; in these cases we become sensible of it as a body, by the resistance it makes in such motions, and also by its impelling or blowing away any light substances. So that, being capable of resisting, or moving other bodies by its impulse, it must itself be a body, and be heavy, like all other bodies, in proportion to the matter it contains; and therefore it will press upon all bodies that are placed under it.

And being a fluid, it will spread itself all over upon the earth; also like other fluids it will gravitate upon, and press every where upon the earth's surface.

The gravity and pressure of the air is also evident from many experiments. Thus, for instance, if water, or quick-silver, be poured into the tube ACE, and the air be suffered to press upon it, in both ends of the tube; the fluid will rest at the same height in both the legs: but if the air be drawn out of one end as E, by any means; then the air pressing on the other end A, will press down the fluid in this leg at B, and raise it up in the other to D, as much higher than at B, as the pressure of the air is equal to. By which it appears, not only that the air does really press, but also what the quantity of that pressure is equal to. And this is the principle of the Barometer.

Prop. II. The air is also an elastic fluid, being condensible and expansible. And the law it observes in this respect is this, namely, that its density is always proportional to the force by which it is compressed.

This property of the air is proved by many experiments. Thus, if the handle of a syringe be pushed inwards, it will condense the inclosed air into a less space; by which it is shewn to be condensible. But the included air, thus condensed, will be felt to act strongly against the hand, and to resist the force compressing it more and more; and on withdrawing the hand, the handle is pushed back again to where it was at first. Which shews that the air is elastic.

Again, fill a strong bottle half full with water, and then insert a pipe into it, putting its lower end down near to the bottom, and cementing it very close round the mouth of the bottle. Then if air be strongly injected through the pipe, as by blowing with the mouth or otherwise, it will pass through the water from the lower end, and ascend up into the part before occupied| by the air at G, and the whole mass of air become there condensed because the water is not easily compressed into a less space. But on removing the force which injected the air at F, the water will begin to rise from thence in a jet, being pushed up the pipe by the increased elasticity of the air G, by which it presses on the surface of the water, and forces it through the pipe, till as much be expelled as there was air forced in; when the air at G will be reduced to the same density as at first, and, the balance being restored, the jet will cease.

Likewise, if into a jar of water AB, be inverted an empty glass tumbler C, or such like; the water will enter it, and partly fill it, but not near so high as the water in the jar, compressing and condensing the air into a less space in the upper part C, and causing the glass to make a sensible resistance to the hand in pushing it down. But on removing the hand, the elasticity of the internal condensed air throws the glass up again.—All these shewing that the air is condensible and elastic.

Again, to shew the rate or proportion of the elasticity to the condensation; take a long slender glass tube, open at the top A, bent near the bottom or close end B, and equally wide throughout, or at least in the part BD (2d fig. above). Pour in a little quicksilver at A, just to cover the bottom to the bend at CD, and to stop the communication between the external air and the air in BD. Then pour in more quicksilver, and observe to mark the corresponding heights at which it stands in the two legs: so, when it rises to H in the open leg AC, let it rise to E in the close one, reducing its included air from the natural bulk BD to the contracted space BE, by the pressure of the column He; and when the quicksilver stands at I and K, in the open leg, let it rise to F and G in the other, reducing the air to the respective spaces BF, BG, by the weights of the columns If, Kg. Then it is always found, that the condensations and elasticities are as the compressing weights, or columns of the quicksilver and the atmosphere together. So, if the natural bulk of the air BD be compressed into the spaces BE, BF, BG, or reduced by the spaces DE, DF, DG, which are 1/4, 1/2, 3/4 of BD, or as the numbers 1, 2, 3; then the atmosphere, together with the corresponding column He, If, Kg, will also be found to be in the same proportion, or as the numbers 1, 2, 3: and then the weights of the quicksilver are thus, viz, He = (1/3)A, If = A, and Kg = 3A; where A denotes the weight of the atmosphere. Which shews that the condensations are directly as the compressing forces. And the elasticities are also in the same proportion, since the pressures in AC are sustained by the elasticities in BD.

From the foregoing principles may be deduced many useful remarks, as in the following corollaries, viz:

Corol. 1. The space that any quantity of air is confined in, is reciprocally as the force that compresses it. So, the forces which confine a quantity of air in the cylindrical spaces AG, BG, CG, are reciprocally a<*> the same, or reciprocally as the heights AD, BD, CD. And therefore, if to the two perpendicular lines AD, DH, as asymptotes, the hyperbola IKL be described, and the ordinates AI, BK, CL be drawn; then the forces which confine the air in the spaces AG, BG, CG, will be as the corresponding ordinates AI, BK, CL, since these are reciprocally as the abscisses AD, BD, CD, by the nature of the hyperbola.

Corol. 2. All the air near the earth is in a state of compression, by the weight of the incumbent atmosphere.

Corol. 3. The air is denser near the earth, than in high places; or denser at the foot of a mountain, than at the top of it. And the higher above the earth, the rater it is.

Corol. 4. The spring or elasticity of the air, is equal to the weight of the atmosphere above it; and they will produce the same effects; since they are always sustained and balanced by each other.

Corol. 5. If the density of the air be increased, preserving the same heat or temperature; its spring or elasticity will likewise be increased, and in the same proportion.

Corol. 6. By the gravity and pressure of the atmosphere upon the surfaces of fluids, the fluids are made to rise in any pipes or vessels, when the spring or pressure within is diminished or taken off.

Prop. III. Heat increases the elasticity of the air, and cold diminisbes it. Or heat expands, and cold contracts and condenses the air.

This property is also proved by experience.

Thus, tie a bladder very close, with some air in it; and lay it before the fire; then as it warms, it will more and more distend the bladder, and at last burst it, if the heat be continued and increased high enough. But if the bladder be removed from the fire; it will contract again to its former state by cooling.——It was upon this principle that the first air-balloons were made by Montgolfier: for by heating the air within them, by a fire underneath, the hot air distends them to a size which occupies a space in the atmosphere whose weight of common air exceeds that of the balloon.

Also, if a cup or glass, with a little air in it, be inverted into a vessel of water; and the whole be heated| over the fire, or otherwise: the air in the top will expand till it fill the glass, and expel the water out of it; and part of the air itself will follow, by continuing or increasing the heat.

Many other experiments to the same effect might be adduced, all proving the properties mentioned in the proposition.

Schol. Hence, when the force of the elasticity of the air is considered, regard must be had to its heat or temperature; the same quantity of air being more or less elastic, as its heat is more or less. And it has been found by experiment that its elasticity is increased at the following rate, viz, by the 435th part, by each degree of heat expressed by Fahrenheit's thermometer, of which there are 180 between the freezing and boiling heat of water. It has also been found (Philos. Trans. 1777, pa. 560 &c), that water expands the 6666th part, with each degree of heat; and mercury the 9600th part by each degree. Moreover, the relative or specific gravities of these three substances, are as follow<*> viz, when the barom. is at 30, and the thermom. at 55. Air 1.232 Water 1000 Mercury 13600 Also these numbers are the weights of a cubic foot of each, in the same circumstances of the barometer and thermometer.

Prop. IV. The weight or pressure of the atmosphere, upon any base at the surface of the earth, is equal to the weight of a column of quicksilver of the same base, and its height between 28 and 31 inches.

This is proved by the barometer, an instrument which measures the pressure of the air; the description of which see under its proper article. For at some seasons, and in some places, the air sustains and balances a column of mercury of about 28 inches; but at others, it balances a column of 29, or 30, or near 31 inches high; seldom in the extremes 28 or 31, but commonly about the means 29 or 30, and indeed mostly near 30. A variation which depends partly on the different degrees of heat in the air near the surface of the earth, and partly on the commotions and changes in the atmosphere, from winds and other causes, by which it is accumulated in some places, and depressed in others, being thereby rendered denser and heavier, or rarer and lighter; which changes in its state are almost continually happening in any one place. But the medium state is from 29 1/2 to 30 inches.

Corol. 1. Hence the pressure of the atmosphere upon every square inch at the earth's surface, at a medium, is very near 15 pounds avoirdupois. For, a cubic foot of mercury weighing nearly 13600 ounces, a cubic inch of it will weigh the 1728th part of it, or almost 8 ounces, or half a pound, which is the weight of the atmosphere for every inch of the barometer upon a base of a square inch; and therefore 29 3/4 inches, the medium height of the barometer, weighs almost 15 pounds, or rather 14 (3/4)lb very nearly.

Corol. 2. Hence also the weight or pressure of the atmosphere, is equal to that of a column of water from 32 to 35 feet high, or on a medium 33 or 34 feet high. For water and quicksilver are in weight nearly as 1 to 13.6; so that the atmosphere will balance a column of water 13.6 times higher than one of quicksilver; consequently inches or 34 feet, is near the medium height of water, or it is more nearly 33 3/4 feet. And hence it appears that a common sucking pump will not raise water higher than about 34 feet. And that a syphon will not run if the perpendicular height of the top of it be more than 33 or 34 feet.

Corol. 3. If the air were of the same uniform density, at every height, up to the top of the atmosphere, as at the surface of the earth; its height would be about 5 1/4 miles at a medium. For the weights of the same volume of air and water, are nearly as 1.232 to 1000; therefore as feet, or 5 1/4 miles very nearly. And so high the atmosphere would be, if it were all of uniform density, like water. But, instead of that, from its expansive and elastic quality, it becomes continually more and more rare the farther above the earth, in a certain proportion which will be treated of below.

Corol. 4. From this prop. and the last, it follows that the height is always the same, of an uniform atmosphere above any place, which shall be all of the uniform density with the air there, and of equal weight or pressure with the real height of the atmosphere above that place, whether it be at the same place at different times, or at any different places or heights above the earth; and that height is always about 27600 feet, or 5 1/4 miles, as found above in the 3d corollary. For, as the density varies in exact proportion to the weight of the column, it therefore requires a column of the same height in all cases, to make the respective weights or pressures. Thus, if W and w be the weights of atmosphere above any places, D and d their densities, and H and h the heights of the uniform columns, of the same densities and weights: Then , and ; therefore W/D or H is equal to w/d or h; the temperature being the same.

Prop. V. The density of the atmosphere, a<*> different heights above the earth, decreases in such sort, that when the heights increase in arithmetical progression, the densities decrease in geometrical progression.

Let the perpendicular line AP, erected on the earth, be conceived to be divided into a great number of very small parts A, B, C, D, &c, forming so many thin strata of air in the atmosphere, all of different density, gradually decreasing from the greatest at A: then the density of the several strata A, B, C, D, &c, will be in geometrical progression decreasing.

For, as the strata A, B, C, &c, are all of equal thickness, the quantity of matter in each of them, is as the density there; but the density in any one, being as the compressing force, is as the weight or quantity of matter from that place upward to the top of the atmosphere; therefore the quantity of matter in each stratum, is also as the whole quantity from that place upwards. Now if from the whole weight at any| place as B, the weight or quantity in the stratum B be subtracted, the remainder will be the weight at the next higher stratum C; that is, from each weight subtracting a part which is proportional to itself, leaves the next weight; or, which is the same thing, from each density subtracting a part which is always proportional to itself, leaves the next density. But when any quantities are continually diminished by parts which are proportional to themselves, the remainders then form a series of continued proportionals; and consequently these densities are in geometrical progression.

Thus, if the first density be D, and from each there be taken its nth part; then there remains its (n - 1)/n part, or the m/n part, putting m for n - 1; and therefore the series of densities will be D, m/n D, m2/n2 D, m3/n3 D, &c, m/n being the common ratio of the series.

Schol. Because the terms of an arithmetical series, are proportional to the logarithms of the terms of a geometrical series; therefore different altitudes above the earth's surface, are as the logarithms of the densities, or weights of air, at those altitudes. So that, if D denote the density at the altitude A, and d the density at the altitude a; then A being as the logarithm of D, and a as the logarithm of d, the dif. of altitude A - a will be as the log. of D - log. of d, or as log. of D/d.

And if A = 0, or D the density at the surface of the earth, then any altitude above the surface a, is as the log. of D/d. Or, in general, the log. of D/d is as the altitude of the one place above the other, whether the lower place be at the surface of the earth, or any where else.

And from this property is derived the method of determining the heights of mountains, and other eminences, by the barometer, which is an instrument that measures the weight or density of the air at any place. For by taking with this instrument, the pressure or density at the foot of a hill for instance, and again at the top of it, the difference of the logarithms of these two presfures, or the logarithms of their quotient, will be as the difference of altitude, or as the height of the hill; supposing the temperatures of the air to be the same at both places, and the gravity of air not altered by the different distances from the earth's centre.

But as this formula expresses only the relations between different altitudes, with respect to their densities, recourse must be had to some experiment, to obtain the real altitude which corresponds to any given density, or the density which corresponds to a given altitude. Now there are various experiments by which this may be done. The first, and most natural, is that which results from the known specific gravity of air, with respect to the whole pressure of the atmosphere on the surface of the earth. Now, as the altitude a is always as log. D/d, assume h so that a may be , where h will be of one constant value for all altitudes; and to determine that value, let a case be taken in which we know the altitude a corresponding to a known density d: as for instance take a = 1 foot, or 1 inch, or some such small altitude; and because the density D may be measured by the pressure of the atmosphere, or the uniform column of 27600 feet, when the temperature is 55°; therefore 27600 feet will denote the density D at the lower place, and 27599 the less density d at one foot above it; consequently this equation arises, viz, of 27600/27599, which, by the nature of logarithms, is nearly nearly; and hence h = 63451 feet; which gives for any altitude whatever, this general theorem, viz, , or feet, or fathoms; where M is the column of mercury which is equal to the pressure or weight of the atmosphere at the bottom, and m that at the top of the altitude a; and where M and m may be taken in any measure, either feet, or inches, &c.

Note, that this formula is adapted to the mean temperature of the air 55°. But for every degree of temperature different from this, in the medium between the temperatures at the top and bottom of the altitude a, that altitude will vary by its 435th part; which must be added when the medium exceeds 55°, otherwise subtracted.

Note also, that a column of 30 inches of mercury varies its length by about the 320th part of an inch for every degree of heat, or rather the 9600th part of the whole volume.

But the same formula may be rendered much more convenient for use, by reducing the factor 10592 to 10000, by changing the temperature proportionably from 55°: thus, as the difference 592 is the 18th part of the whole factor 10592; and as 18 is the 24th part of 435; therefore the corresponding change of temperature is 24°, which reduces the 55° to 31°. So that the formula becomes of M/m fathoms when the temperature is 31 degrees; and for every degree above that, the result must be increased by so many times its 435th part.

See more on this head under the article BAROMETER, at the end.

By the weight and pressure of the atmosphere, the effect and operations of Pneumatic engines may be accounted for, and explained; such as syphons, pumps, barometers, &c. See each of these articles, also Air.

Pneumatic Engine, the same as the Air-Pump.

POCKET Electrical Apparatus.—This is a contrivance of Mr. William Jones, in Holborn, the form of which is represented in plate xxiii, fig. 4.|

This small machine is capable of a tolerably strong charge, or accumulation of electricity, and will give a small shock to one, two, three, or a greater number of persons.

A is the Leyden phial or jar that holds the charge. B is the discharger to discharge the jar when required without electrifying the person that holds it. C is a ribbon prepared in a peculiar manner so as to be excited, and communicate its electricity to the jar. D are two hair, &c, skin rubbers, which are to be placed on the first and middle fingers of the left hand.

To charge the Far.

Place the two finger-caps D on the first and middle finger of the left hand; hold the jar A at the same time, at the joining of the red and black on the outside between the thumb and first singer of the same hand; then take the ribbon in your right hand, and steadily and gently draw it upwards between the two rubbers D, on the two fingers; taking care at the same time, the brass ball of the jar is kept nearly close to the ribbon, while it is passing through the fingers. By repeating this operation twelve or fourteen times, the electrical fire will pass into the jar which will become charged, and by placing the discharger C against it, as in the plate, you will see a sensible spark pass from the ball of the jar to that of the discharger. If the apparatus is dry and in good order, you will hear the crackling of the fire when the ribbon is passing through the fingers, and the jar will discharge at the distance represented in the figure.

To electrify a Person.

You must desire him to take the jar in one hand, and with the other touch the nob of it: or, if diversion is intended, desire the person to smell at the nob of it, in expectation of smelling the scent of a rose or a pink; this last mode has occasioned it to be sometimes called the Magic Smelling Bottle.

POETICAL Numbers. See Numbers.

Poetical Rising and Setting. See Rising and Setting.

The ancient poets, referring the rising and setting of the stars to that of the sun, make three kinds of rising and setting, viz, Cosmical, Acronical, and Heliacal. See each of these words in its place.

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Entry taken from A Mathematical and Philosophical Dictionary, by Charles Hutton, 1796.

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PLOUGH
PLUMMET
PLUNGER
PLUS
PLUVIAMETER
* PNEUMATICS
POINT
POINTING
POLAR
POLARITY
POLES