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Whence we conclude that

The pressure which air exercises on a given surface varies as the density of the air. Q. E. D.

[NOTE. In the experiment here described the longer leg of the tube is placed in a vessel from which the air has been exhausted, so that there is no pressure at all in the surface of the mercury in the longer leg. If A communicated with the open air, the surrounding atmosphere would press on the surface of the mercury in AB and would have to be taken into consideration in estimating the whole amount of pressure sustained by an area A placed at e or g.

The method of making the experiment described in the above Proposition has been selected as being more simple than the other. The same result, however, is arrived at in whichever of these two ways the experiment is conducted.]

22. PROP. XIV. The elastic force of the air is increased by an increase of temperature. This is proved by experiment.

If a bladder be partially filled with air and then brought near the fire, the included air immediately expands and the bladder becomes fully distended. On the included air cooling down, the bladder returns to its original flaccid appearance.

23. DEFS. (1). A VALVE is a kind of door which fits an orifice, such that if a fluid press on one side of it, it opens and allows the fluid to pass through, but which keeps the orifice tightly closed if the fluid press on the other side.

[Valves are of various forms,-a flap of leather (4) fastened at one edge,

a frustum of a cone (B) made A
of metal,-a sphere (C),-
or a plate of metal (D) with c
an axis passing perpendicularly
through it. By any of these


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contrivances the flow of a fluid upwards would be

prevented only by the weight of the valve, but a rush of fluid from above would carry the valve along with it, and keep the orifice which the valve fits completely closed.

When the fluids employed are very rare,-like air or gas,—the valves are generally made of flaps of oiled or varnished silk, which, being attached at two or three points to the surfaces in which the orifices are situated, are raised by a very slight pressure, and so allow a fluid to pass under whose density is exceedingly small.]

(2) A PISTON is a plug, mostly cylindrical, which, by means of a rod attached to it, can be made to play within a tube which it fits accurately.

24. PROP. XV. To describe the construction of the common Air Pump and its operation.


DESCRIPTION. The Air Pump consists of a glass vessel A, called the Receiver, made to fit a table BC so as to be air tight. A tube DE connects the Receiver with a cylinder EF, called the Barrel. At the bottom of the Barrel there is a valve E opening upwards, and a piston F (also furnished with a valve opening upwards) plays within the Barrel.



OPERATION. Let the piston F be at its highest point, and the instrument filled with air the same as that of the surrounding atmosphere.

When the piston is driven down, the air at first in the barrel is condensed and its pressure therefore.

increased. The valve E is kept closed, and the valve in F being pressed on the under surface more strongly than on the upper, opens and allows the air in the barrel to escape through it.

Next, on raising the piston, the external air keeps F closed, and there now being no air in EF, the pressure on the under surface of the valve at E will open that valve and allow air from the receiver and pipe to flow into the barrel. The figure represents the instrument during the ascent of the piston.

When the piston descends again, the air in EF is condensed until it opens the valve in F and escapes; and on the piston reascending, more air rushes from the receiver into the barrel.

The process may be repeated until the air in the receiver becomes so rare, that its pressure is insufficient to overcome the weight of the valve at E.


PROP. XVI. To describe the construction of the Condenser and its operation.

CONSTRUCTION. The Condenser is a Barrel AB furnished with a piston A that has a valve in it opening downwards; at the bottom of the Barrel there is a like valve C. The neck of the Barrel communicates with an A air-tight vessel D, called the Receiver.



OPERATION. Let the instrument be filled with common air, and the piston be at its greatest height. On the piston being forced down, the air in the barrel is condensed, and its pressure being therefore increased,

Prop. XIII, it keeps the valve A closed, opens the valve C, and escapes into the Receiver. The figure represents the instrument during the descent of the piston.

On the piston's ascending, the air in the receiver keeps C closed, and there now being no pressure on the under surface of the valve A, the external air opens the valve, and the barrel is filled with air, which may be driven into the receiver by forcing down the piston a second time. In this manner the condensation of the air in the receiver may be carried on to any required extent.

[The communication between the barrel and the receiver can be cut off at pleasure by means of a stopcock at E, and the barrel is made to screw off and on at its lower end.]

26. PROP. XVII. To explain the construction of the common Barometer, and to shew that the mercury is sustained in it by the pressure of the air on the surface of the mercury in the basin.

The Barometer is an instrument for measuring the pressure of the air. It consists of a glass tube (see fig. Prop. XVIII.) of uniform bore, closed at one end, and not less than 33 or 34 inches long. This tube is filled with mercury, and the open end, being first stopped with the finger, is placed below the surface of some mercury in a basin, when the tube being held in a vertical position and the finger being withdrawn, the mercury in the tube subsides, and stands at a height above the mercury in the basin

that varies on different days from about 28 to 32 inches. A small scale of inches is attached to the upper part of the tube, to shew the height at which the mercury may be standing at any time.

That the column of mercury is supported in the tube by the pressure of the atmosphere appears from this experiment. When the whole is put into the receiver of an air pump, the mercury sinks in the tube more and more for every barrel of air that is pumped out, until at length it is all but on a level with the surface of the mercury in the basin. On readmitting the air into the receiver the mercury in the tube rises again to its first level.

27. PROP. XVIII. The pressure of the atmosphere is accurately measured by the weight of the column of mercury in the [vertical tube of the] Barometer.

Let P be the surface of the mercury in the vertical tube; AB the section of the tube made by the horizontal surface of the mercury in the basin; CD an area equal to AB in that surface.


Then, Weight of mercury contained in

= pressure downwards on the area AB, Prop. iv;

= pressure upwards on AB,

= pressure upwards on CD, since AB and CD

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are equal areas situated in the same horizontal plane of a fluid at rest. Prop. II.

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