The mountain-barometer, as It is called, is usually provided with an adjusting screw, by which the surface of the mercury in the cistern may be made to coincide with the zero of the scale of inches by which the height of the column is expressed; but those of a more portable kind have net that adjusting screw, and then a correction must be made for the error of the scale. [Benosirrsit.] Water boils when the elastic power Of the vapour formed from it is equal to the incumbent pressure ; and consequently the temperature at which the boiling takes place in the open air will depend upon the weight of the atmospheric column above it. Therefore, since this weight becomes less as the station is more elevated, it is evident that water will boil at a lower temperature on a mountain than on the plain at its foot; and the Rev. Mr. Wollaston constructed an instru ment called a thermometrical barometer, by which, on the principle just mentioned, the relative heights of stations can be found. A tube containing the mercury is provided with a graduated scale, and, when used, the bulb is placed in a vessel of water, which is made to boil by means of a spirit-lamp. An improved form of the apparatus is repre sented under BOILING OF Livros.
In order to determine the heights of stations merely by the know ledge of the temperature at which water boils, the formula F given by Mr. Tredgold, might be employed. Here t is 85 the temperature of the water at the station, expressed in degrees of the centigrade thermometer ; F is the measure of the elastic force of the steam at the temperature t under the pressure of the atmosphere, and is expressed by the corresponding height, in centi metres, of the column of mercury in a barometer.
The velocity with which air flows into a vacuum through an aperture in a vessel follows the same law as water or any other nonelastic fluid [livimoramaxics); for though, in the former case, the quantity of air passing through the orifice in a given time varies with the density of that which successively comes to the orifice, yet the pressure by which the air is forced out varying in the same proportion, the velocity, by dynamics, remains constant.
Now, the velocity acquired by a falling body in vacuo is known to be= Nagx, if g= 32 feet, and x =height fallen through. (Dynamics.) Hence, if v = velocity with which the air rushes through a small hole into a vacuum at the sea-level, v= aF.E.Fx, namely, v = the velocity of a particle of air supposed to have fallen from the height of a homogeneous atmosphere into the aforesaid hole. So that v= s/2 x 32 x 27803, from above.
. v =about 1339 feet per second.
The law is the same, whether we consider the air to act only by its weight, or whether it bo confined in a vessel and the efflux be produced by the elasticity. For, the air in the vessel being in the ordinary stele of the atmosphere, the pressure against every point on the interior surface is equal to the pressure of the atmosphere by which, if not otherwise confined, it would be kept in its actual state ; consequently it begins to flow from the orifice with the same velocity as if it had been impelled by the weight of the whole column of atmosphere above the orifice, that is, with the velocity due to the descent of a body from a height equal to that of a homogeneous atmosphere. After this
moment, the density of the air in the vessel diminishing, its elasticity diminishes with it, and consequently the power of motion is diminished in the same ratio as the density. It may be added also that, since density of air increases with the pressure, an additional pressure on the fluid in a vessel will not increase the velocity of the efflux. But the law just mentioned only holds good when the vacuum is supposed to remain perfect on the exterior of the orifice : for, if the air be received in a vessel, it will expand in that vessel and re-act against the effluent air at the orifice, thus diminishing the velocity till the latter finally becomes equal to zero ; and this will take place when the air has attained the same density in the two vessels.
If the effluent air be of a given density, but not the same as in the ordinary state of the atmosphere, the force by which it would be made to flow into a vacuum must be determined by the above equation me= P'D ; where r is the pressure (or weight of the column) of the ordinary atmosphere, and D its density at the earth's surface ; a' is the given density and r' is the required pressure or force by which that air would be impelled through the orifice. Now if air in the ordinary state be allowed to rush into a vessel containing air less dense than itself, and the velocity of efflux be required, the moving force will be the difference between that with which the ordinary air is driven through the orifice and that with which the rarer air would be so driven ; that is, it may be represented by P — P'; then the velocities of efflux being as the square roots of the forces [HYDRODYNAMICS], if the velocity due to the force r is given, the required velocity at the commencement of the efflux may be found.
The determination of the velocity with which dry steam or any other elastie fluid rushes into a vacuum, or into a fluid of less density than itself, in made in the same manner as for air. Thus, knowing the temperature of steam, and consequently its elasticity, or the equiva lent pressure, we can find the height of a homogeneous atmosphere which would produce the same pressure ; and then the velocity with which the steam flows into a vacuum would be equal to that acquired by a body in falling down the height of such atmosphere. But if the steam is to flow into any elastic fluid of less density than itself, the height of the homogeneous atmosphere must correspond to the difference of the pressures arising from the different elasticities of the two fluids.
Finally, it has been lately found by some very accurate experiments recorded by Professor Potter, that, if we represent by v the theoretic velocity of efflux of air through a small orifice, and by I/ the experi mental velocity, thee v'=.65 v, for orifices in a thin wall, =.93 v, for cylindrical spouts, =.94 v, for conical spouts, and those narrowing from the wall of the gasometer ; so that there is, as for liquids, a true rota contract], which reconciles theory with experiment, as in the case of Torricelirs theorem. [Erresicee ' • HYDRODYNAMICS.)