valve 4, the pressure of the external air opens that valve, and the Barrel becomes filled again with air, which may be driven into the Receiver by forcing down the piston, as before. And in this manner the condensation of the air in the Receiver may be carried on to any extent required, as far as the strength of the Barrel and Receiver will permit.

The communication between the Barrel and the Receiver can be cut off at pleasure by means of a stop-cock at E; and the Barrel is made to screw off and on at a point above E.

86. 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 Atmosphere. It consists of a glass tube (see 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below the surface of some mercury in a basin, when the tube being fixed in a vertical position and the finger being withdrawn, the mercury in the tube subsides, and stands at a height, above the mercury in the basin, which varies on different days from about 28 to 32 inches. A graduated scale is attached to the upper part of the tube, to mark 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 the experiment, that, when the whole is. put into the Receiver of an Air-Pump, the mercury in the tube sinks more and more 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*. But on readmitting the air into the Receiver, the mercury in the tube rises to its original level.

for

It has been shewn, in Prop. XV., that it is not possible to pump all the air out of the Receiver. If it were so, the surface of the mercury in the tube would then be on precisely the same level as the surface in the cistern.

87. PROP. XVIII. The pressure of the atmosphere is accurately measured by the weight of the column of mercury in the Barometer.

Let the surface of the mercury in the vertical tube stand at P; and let the area of the section of the tube made by the horizontal surface of the mercury in the basin be represented by AB; CD any portion of area in that surface equal to AB; then

=

=

Weight of mercury contained in PB

pressure downwards on the area AB, by Prop. IV.

pressure upwards on AB, by Prop. I.

= pressure upwards on CD; since AB and CD are equal areas situated in the same horizontal plane of a fluid at rest, by Prop. II.

P

But the fluid being at rest, the pressure downwards on CD, (which arises solely from the pressure of the air in contact with it), is equal to the pressure upwards on it.

Wherefore the pressure of the atmosphere on the area CD is equal to the weight of the column of mercury supported in the [vertical] tube of the Barometer, of a base AB equal to that area; or "the pressure of the atmosphere is accurately measured by the weight of the column of Mercury in the Barometer".

88. COR. 1. By Art. 64, the pressure of a fluid on a horizontal plane immersed in it was shewn to be the weight of a column of the fluid, whose base is equal to the area of the plane, and whose height is the depth of the plane below the surface of the fluid. Wherefore, the pressure exerted by the atmosphere on such an area,-being measured by the weight of the vertical column of mercury (of equal section) which is supported in the Barometer,-is equal to the weight of a column of mercury whose base is equal to the plane acted upon, and whose height is the same as that of the column of mercury supported in the vertical tube of the Barometer.

89. COR. 2. The pressure of the air being measured by the weight of the column of fluid which it supports, the Barometer might be filled with any fluid whatever. But mercury being by far the heaviest fluid known, the column of mercury required to produce a given pressure is very much shorter than if any other fluid were employed.

For example, if it took 30 inches of Mercury to balance the pressure of the air, then since Mercury is 13'6 times as heavy as Water (see Art. 69), it would take a column of Water 136 × 30 inches, or 34 feet high, nearly, to produce the same effect.

90. COR. 3. The mercury in the Barometer standing at 30 inches, the pressure of the air on a horizontal square inch of surface is equal to the weight of a column of mercury 30 inches long, and whose base is a square inch; i.e. to the weight of 30×1, or 30 cubic inches of mercury.

To find how much this pressure amounts to.

The weight of a cubic foot of Water is 1000 ounces avoirdupois, very nearly,

.. the weight of a cubic foot of Mercury = 1000 × 13'6 oz. (Art. 69.)

And the pressure of the air on a square inch will be greater or less than 14 lbs. according as the mercury in the Barometer stands at a greater or less height than 30 inches.

It appears, then, that every square inch with which the air at the Earth's surface is in contact is subjected to a pressure of about 14 lbs.; so that a page of a book 6 inches long by 5 inches wide sustains a pressure of about 6x5x14 lbs., or 420 lbs. The reason why the leaf is not torn by this enormous pressure is, that the pressure of the air on one side of it is counterbalanced by that on the other side.

91. COR. 4. In Chapters 1. and II. the pressure of the Air on the surface of the fluid contained in an open vessel has been left out of consideration; in other words, the experiments there described

were supposed to be made in the exhausted Receiver of an Air

Pump.

From Art. 89 it appears, that when water is the fluid employed, the pressure of the air on its surface is equivalent (when the mercurial Barometer stands at 30 inches), to that which would be produced by a head of water 34 feet deep. In estimating, therefore, the pressure on any surface placed at a given depth below the surface of water, this large additional pressure, amounting to more than 14 lbs. on a square inch of surface (Art. 90), must be taken into account.

92. PROP. XIX. To describe the construction of the COMMON PUMP and its operation.

EF

CONSTRUCTION. In the Common Pump two hollow cylinders AB and BH, whose axes are in the same vertical line, are connected together, and at their junction is fixed a valve B opening upwards. The upper cylinder D AB is called the "Body of the Pump"; and in it a piston C, containing a valve opening upwards, plays by means of a rod attached to the end E of a lever EFG, whose fulcrum is F. A spout D is placed just above the highest point to which this piston ascends. The lower cylinder BH, which is called the "Suction-Pipe", reaches below the surface H of a well of water.

B

OPERATION. Suppose the piston to be at B, and the Suction-Pipe full of common air. As C is raised, the pressure of the external air keeps the valve at C closed, and a vacuum between B and C being consequently made, the air in HB, pressing against the under surface of the valve at B, opens it, and a portion of the air escapes into BC.

The air, therefore, which, before the ascent of the piston occupied the space BH, now occupies the greater space CBH, and so, becoming less dense than before, has less elastic force, and exercises a less pressure on the surface of the water at H, by Prop. XIII. Wherefore, since

the external air continues to exercise the same pressure as before on the surface of the water in the well, it will force up water into the Suction-Pipe to a certain height K, such that the pressure of the air in CK, together with the weight of the column of water KH, produces the same effect on the section of the water in the Suction-Pipe at H, as the external air does on an equal area situated in the surface of the water in the well.

When C has reached the highest point of its ascent, and equilibrium exists between the pressure of the external air on the surface of the water in the well on the one hand, and the pressure of the air in CK together with the weight of the fluid column KH on the other, the valve B, being equally pressed on its upper and its under surfaces, will shut by its own weight. The piston C is then pushed down; the air in CB is condensed, until its elastic force becomes greater than that of the external air, when it opens the valve in C and escapes.

When C is raised again, the same circumstances recur. The water rises a little higher in the Suction-Pipe at every stroke of the piston, and at last flows through B; and on C descending again, it raises the valve C, passes through it, and on the next ascent of the piston, is brought up to the spout at D.

As the average pressure of the atmosphere will not support a vertical column of water more than 34 feet high, if the valve B be more than 34 feet above the surface of the water in the well, the average pressure of the external air not being sufficient in that case to force the water up so high as B, the pump will not work.

N.B. The figure represents the pump during an ascent of the piston; when (air, or water, flowing through it) the valve at B is open, and that at C'is shut.

93.

PROP. XX. To describe the construction of the Forcing-Pump, and its operation.

6

CONSTRUCTION. The FORCING-PUMP consists of a cylindrical Barrel' AB in which a solid piston C works by means of a rod GC; BD is a Suction-Pipe' reaching below the surface D of a well of water; BE a pipe con