Pneumatics (Gr. Pneumatics 1300609 , wind, air), that branch of general mechanics which treats of the equilibrium and motion of aeriform fluids. Many portions of this subject being embraced and treated under special topics, as Air Pump, Atmosphere, Balloon, Barometer, Blowing Machines, Boiling Point, Chimney, Diving Bell, Expansion, Explosives, Furnace, Gas, Heat, "Wind, etc, a statement of the general theory only, with such applications as are not elsewhere made, will here be in place. Many gases, as the air, are permanent, preserving their gaseous form under all degrees of temperature or. compression to which they have yet been subjected. Other gases, as chlorine and ammonia, by the agency of cold and pressure, change their state, become liquids or solids, and for the time, of course, lose the peculiar properties of the aeriform condition; these are non-permanent gases. As ordinarily understood, pneumatics treats of the action only of bodies in the form of permanent gases of which atmospheric air is the type; but the principles of this science can be so extended as to investigate the elasticity and action of the vapors and non-permanent gases, through all stages of condensation, down to the liquid condition.

Except when otherwise stated, the principles which follow will relate to the permanent gases only. - The distinguishing characters of these bodies grow out of the fact that their molecules do not sensibly cohere, but can move with perfect freedom both about and away from each other; and that between these molecules there are repulsive forces greatly exceeding any forces of attraction which may act, causing them at all times to strive to recede from each other. From these circumstances the following principles are deduced: 1, all gases can be compressed, or if allowed will expand, and so far as yet known, in the case of perfect gases, to an indefinite extent; 2, when compressed, a perfect gas will always exert a pressure in the contrary direction, or against the compressing force, thus manifesting the peculiar form of elasticity possessed by these bodies, or what is called their expansive force, the measure or amount of which for a given case is termed the tension of the gas or vapor; 3, wherever a gas or vapor is found to exist as a body, having appreciable density, this is the result of some confining pressure applied to it from without, and compelling its particles into a certain degree of proximity; 4, when a body of gas does not expand, this is because the pressure from without equals and balances its tension at the time; and 5, when a body of gas is at rest throughout all its parts, this is because at every point the various pressures exerted in different directions are in equilibrium.

From the foregoing laws, and also from the fact that the particles of a gas possess weight as well as those of a liquid, the following laws also result: 1, equal pressures in every direction are exerted upon and by every portion of a gaseous body at rest; 2, a pressure made on a confined body of gas, as in a liquid mass, is perfectly transmitted in every direction, and in the atmosphere to great distances; 3, such pressure is proportional to the area of surface receiving it, and consequently multiplied when the receiving surface is larger than that communicating it; 4, pressure on a given surface at a given depth, due to weight, is calculated in a similar way; 5, the free surface of any such body, as the upper aerial surface, tends to a level at any place; and 6, within any body of gas, at any given depth, there is exerted a supporting or buoyant power, which is as the density or tension of the gas at the place. - The weight of a column of air resting on a horizontal square inch, at the sea level, is, at an average temperature, very nearly 14*6 lbs.; and a pressure of this amount is termed a pressure of one atmosphere.

The first pneumatic law, discovered by Boyle in 1650, and independently by Mariotte in 1676, and known as Boyle's and Mariotte's law, affirms that, at a given temperature, the volume of an aeriform body at rest is inversely as the compressing force. Direct consequences are, that the density and the tension are proportional to the compressing force. As the density of the air is about 1/773 that of water, it follows from this law that if we could subject it to a pressure of 773 atmospheres, or about 11,320 lbs. to the square inch, its density would equal that of water. Whether under such circumstances it would still remain a gas, is not known. The second great law of tension and pressure is that of Dalton and Gay-Lussac (1801), by both of whom it was independently discovered, according to which, when the tension of a gas or vapor is constant, the density diminishes as the increase of temperature; in other words, for equal increments of temperature, a gas or perfect vapor expands by the same fraction of its own bulk; this being 1/490 of its volume at 32° F., and for each degree above that point, or about three eighths of its volume between 32° and 212°. However long any permanent gas may be kept under pressure, its tension remains unimpaired.

The laws of Mariotte and Dalton have been modified by the discovery that vapors and non-permanent gases undergo compression in a ratio greater than that of the increase of pressure upon them, and that near the point of liquefaction this deviation becomes very great. More recently, Mariotte's law has been found to need still further qualifications. Despretz (1829) announced that carbonic acid, ammonia, cyanogen, and some other gases, undergo at ordinary temperatures a compression more rapid than that of the increase of pressure, and in a ratio uniformly increasing; while above 14 atmospheres the result with hydrogen was the opposite. Kegnault has confirmed these results, and has even shown a deviation from the law in the case of a confined body of pure air. He obtained, for instance, a 10 and 20 fold density of air by applying respectively 9.9 and 19.7 atmospheres of pressure; of carbonic acid, by 9.2 and 16.7 atmospheres; of hydrogen, by 10.05 and 20.26. It follows that Mariotte's law is to be accepted as but approximately true, the variations being different for different gases; but the deviation in the case of non-permanent gases, such for example as carbonic acid gas, decreases as the temperature is raised, and at the boiling point of water it is much less than at ordinary temperatures.

The conclusion of modern physicists is, that there is for each gas a certain normal temperature at which it exactly conforms to Mariotte's law, while above and below this temperature it varies in opposite directions. This deviation, however, especially in air, is so slight, that for ordinary determinations of the volume of gases, and in the use of air in manometers, or pressure gauges, it may be overlooked. (See Manometer.) The earth's atmosphere being subject to compression by its own weight, it results that at heights in it increasing in an arithmetical ratio the density and tension diminish in a geometrical ratio. All the relations expressed in Mariotte's law and its consequences are conveniently exhibited in a table like the following; and by including the last column, that of heights, the 0 of height being the sea level, and the height 1 denoting that experimentally found as 2'705 miles, all the relations in the first four columns become represented as they exist theoretically, and very nearly actually, in our atmosphere:

Pressures.

Densities.

Tensions.

Volumes.

Heights in the air,

1

1

1

1

0

X1/2

1/2

1/2

2

1

1/4

1/4

1/4

4

2

1/8

1/8

1/8

8

3

1/16.

1/16

1/16

16

4

....

....

....

....

....

1/1024

1 /1024

1 /1 024

1024

10

&C.

etc.

etc.

etc.

etc.

In the atmosphere, however, other causes of slight deviation from the relation of density to height exist. Among these are: 1, that the earth's attraction diminishes somewhat, about 1/2000 part for each mile near the earth, at points taken in ascending through the atmosphere; 2, that the attractions of the sun and moon at some times and places conspire with, at others oppose, the action of the earth; 3, variations due to changing temperatures; 4, admixture of vapors, etc, in the lower atmosphere. The general effect is a slightly more rapid diminution of density than that above given, with increase of altitude. - Aero-dynamic problems, or those investigating the flow and delivery of gases through orifices, in tubes, and in currents, and the consequences of the impact and momentum of moving air, are too intricate to be presented fully except in special treatises on the subject. Torricelli's principle for liquids, that the velocity of discharge from an orifice is that which the body of liquid would acquire in falling freely from the height of its surface to the centre of the orifice, applies quite as strictly to gases as to liquids.

A heavy body, in falling through one foot, acquires a velocity of 8 ft. a second; and the velocities of discharge being as the square roots of the depths, and the height of the surface of a homogeneous atmosphere above the sea level being 27,720 ft., it follows that, at the latter level, the velocity with which air should jet into a vacuum through an opening not too small will equal nearly the product 8 4/27,720=1,332 ft. Experiments show that the actual velocity, as in the case of water,- is somewhat less; that for orifices in a thin wall it is about 65 per cent, of that named; for short cylindrical spouts, •93; and for conical, narrowing outward, '94. These facts correspond in a degree with the results in spouting liquids, and show that, as well as in these, the " contracted vein " exists in the efflux of gases. The movement of gases through pipes is also subject to retardation similar to that affecting the delivery of liquids; and roughness of the inside of tubes, sharp angles, inequalities of size, etc, here also increase the amount of retardation.

This retarded flow has proved, unexpectedly, a chief difficulty in the way of using the pneumatic power transmitter proposed by Papin - in substance a hydrostatic press containing air, with a long pipe connecting the two pistons, so as to allow of action at distant points. So, in the case of a blowing tube constructed in Wales to catch the air impelled by a waterfall, and convey it to a distance, in order to feed the blast of a foundery, the time estimated for the delivery of the air being six seconds, it was found that the jet of air did not arrive until after the lapse of ten minutes, and it was then but feeble. The remarkable retardation of gases in tubes must be due in a considerable degree to adhesion of the gases to the solid surfaces, a principle well known; and Robison has also supposed much of it due to an undulation arising from this and other causes in the transmitted air. It is well ascertained that, besides varying in the force of horizontal movement, producing gusts, winds also undulate vertically, as do water waves. "Moreover, winds are retarded by obvious causes near the surface of the earth, just' as a stream of water flows slowly at its bottom; and thus they are always less violent in cities than in the country.

Similar influences must modify their flow at the sides and above, and especially where winds flow in unlike directions along an aerial plane dividing them.